Theories of Everything with Curt Jaimungal - Aephraim Steinberg: The Physicist Who Measured Negative Time

Episode Date: April 13, 2026

SPONSORS: - Go to https://expressvpn.com/theoriesofeverythingyt to find out how you can get up to 4 extra months thanks to our sponsor, ExpressVPN - Accelerate your efficiency. Sign up for your one-dollar-per-month trial today at http://shopify.com/theories - I subscribe to The Economist for their science and tech coverage. As a TOE listener, get 35% off! No other podcast has this: https://economist.com/TOE This conversation belongs in a category I wish were larger on this channel: the experimentalist who also thinks (deeply) about foundations. Professor Aephraim Steinberg, winner of Physics World’s Breakthrough of the Year in 2011, is that species! For basically 30 years, he’s been measuring aspects of physics that others wouldn’t touch: Bohmian trajectories, Heisenberg’s disturbance bound (he showed it was wrong), even where the photon is inside the double slit (which most textbooks will tell you is impossible). His lab measured negative time — and it keeps reappearing across completely different experiments, stubbornly suggesting it means something. FOLLOW: - Spotify: https://open.spotify.com/show/4gL14b92xAErofYQA7bU4e - Substack: https://curtjaimungal.substack.com/subscribe - Twitter: https://twitter.com/TOEwithCurt - Discord Invite: https://discord.com/invite/kBcnfNVwqs - Crypto: https://commerce.coinbase.com/checkout/de803625-87d3-4300-ab6d-85d4258834a9 - PayPal: https://www.paypal.com/donate?hosted_button_id=XUBHNMFXUX5S4 TIMESTAMPS: - 00:00:00 - Defining Negative Time - 00:06:50 - Quantum Trajectory Theory - 00:12:44 - The Holland Tunnel Analogy - 00:18:40 - Resonant Atomic Interactions - 00:26:05 - Superluminal Energy Propagation - 00:32:00 - Eight Velocities of Light - 00:38:00 - Causality and Retrocausality - 00:44:00 - Dwell Time vs. Delay - 00:50:24 - Time: Operator or Parameter? - 00:58:21 - Bell’s Theorem and Realism - 01:04:55 - Heisenberg’s Measurement Disturbance - 01:11:26 - Weak Measurement Formalism - 01:17:37 - Time Symmetry and Entropy - 01:27:07 - Bohmian Trajectories Observed - 01:35:56 - Spin-Statistics and Indistinguishability - 01:42:14 - Quantum Computational Advantage - 01:48:15 - Many Worlds vs. Complexity - 01:54:51 - Psi-Ontic vs. Psi-Epistemic - 02:01:37 - Collapsing Tunneling Particles - 02:08:48 - Larmor vs. Atto Clocks - 02:15:24 - Locality and Information LINKS MENTIONED: - Aephraim's Website: https://www.physics.utoronto.ca/~aephraim/ - Aephraim's Papers: https://scholar.google.com/citations?user=PzUyb6IAAAAJ - Photon Negative Time in Atom Cloud [Paper]: https://arxiv.org/pdf/2409.03680 - How Much Time Does a Photon Spend as Atomic Excitation? [Paper]: https://arxiv.org/abs/2310.00432 - Measuring Time Atoms Spend in Excited State [Paper]: https://journals.aps.org/prxquantum/abstract/10.1103/PRXQuantum.3.010314 - Tunneling Atom Time in Barrier [Paper]: https://arxiv.org/abs/1907.13523 - Single-Photon Tunneling Time [Paper]: https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.71.708 - Traversal Time for Tunneling [Paper]: https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.49.1739 - Propagation of a Gaussian Light Pulse [Paper]: https://journals.aps.org/pra/abstract/10.1103/PhysRevA.1.305 - Linear Pulse Propagation in Absorbing Medium [Paper]: https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.48.738 - Eighth Velocity of Light [Paper]: https://pubs.aip.org/aapt/ajp/article-abstract/45/6/538/1045817/Eighth-velocity-of-light - Attosecond Ionization [Paper]: https://www.science.org/doi/10.1126/science.1163439 - Tunneling Optical Pulses Photonic Band Gaps [Paper]: https://attoworld.de/fileadmin/user_upload/tx_attoworld/publications/paper_PhysRevLett_Y1994_M10_D24_V73_P2308.pdf - Evidence of Negative Time [Article]: https://www.scientificamerican.com/article/evidence-of-negative-time-found-in-quantum-physics-experiment/ - Light Speed Reduction [Article]: https://www.nature.com/articles/17561 - On the Theory of Light and Colors [Paper]: https://www.jstor.org/stable/pdf/107113.pdf - Wave Propagation and Group Velocity [Book]: https://amazon.com/dp/1483253937?tag=toe08-20 - EPR Paper [Paper]: https://journals.aps.org/pr/abstract/10.1103/PhysRev.47.777 - Uncertainty Principle: https://en.wikipedia.org/wiki/Uncertainty_principle - QBism [Paper]: https://arxiv.org/abs/1003.5209 More links at https://curtjaimungal.substack.com Guests do not pay to appear. #science Learn more about your ad choices. Visit megaphone.fm/adchoices

We just realized we were wrong. And that makes no classical sense. This physicist has been asking questions we're told not to ask. What is a particle doing between measurements? Where does it go? How long does it spend there? I travel to my alma mater of the University of Toronto to speak to Professor Steinberg, the winner of the physics world's breakthrough of the year,

whose lab investigates photons traveling through a barrier that apparently causes atoms to spend negative time in an initial. excited state. And it took us a while to appreciate. It wasn't just any old negative number. My name's Kurtzimungle, and on this channel, I interview researchers regarding their theories of reality with rigor and technical depth. Today, we discuss negative time beyond the pop science headlines, because if you just go by them, you'll be misled. Many other YouTubers or magazines will tell you that his results are about faster than light travel, but today we go into the recondite details exploring the truth behind these negative time results. We also, we also

We also talk about what weak measurements are and how they recover Bohemian trajectories in the double-slid experiment and why Heisenberg's original disturbance argument about his uncertainty principle was experimentally incorrect. Again, we're all taught that Heisenberg's uncertainty comes from literally disturbing the atoms with other measuring devices, but that's false. We close with consciousness, quantum computing, and whether Bell's inequalities mean what we think they mean. Negative time, what does that mean? You're really going to jump right in. That means many different things in different contexts. And we got interested in it because there's an old context in which negative times were already known,

but people tended to dismiss them. They recognize that there are certain things you can define operationally. If you define it that way, you see what number comes out, it turns out to be negative. this surprised us. I can go into more detail afterwards, but little by little we understood sort of a way to patch things up and sweep it under the rug. And more recently, what we realized is it wasn't so easy to sweep it under the rug

and that we might have been missing something and there might be a sense in which negative times have more physical reality than we were ascribing to them. So I begin with that preamble because it's kind of a long story the way we stitch these different things together. But I think the simplest question to ask yourself is the following.

Suppose I fire a particle at a certain medium, some kind of a tunnel, and the particle gets through the other side, and it is time. When does it arrive on the other side? That's an old question. It's an easy question to ask about particles. It's more complicated with waves.

And of course, now we know that, according to quantum mechanics, everything is both a particle and a wave in some sense. By the late 19th century, though, we already knew that light was a wave. So people were asking this question, how does a light wave travel through a piece of glass or a cloud of atoms? And as they began to address it,

they realized that there were funny situations where if you just looked at the peak of the wave and said, well, that's a reasonable place to talk about the average position of the energy or, you know, the most likely time for a detector to fire or something like that, the time at which we predicted a detector was most likely to fire on the far side of this medium could be earlier than the time at which the detector placed before the medium would have fired. In other words, it seemed that the particles could arrive sooner than they departed, and that's what we meant by a negative time. Now, that plays all sorts of havoc with ideas of causality,

how can it effect precede a cause? So Zammerfeld and Brin famously dealt with this problem and explained how, even though mathematically that's what came out, you shouldn't worry about it. No information was traveling even faster than light, let alone back to negative times,

and everything was okay. And this sort of came up in several different contexts. I mean, it was very theoretical in the early part of the century. In the 1960s, after the invention of the laser, people started being able to address this experimentally,

And in fact, there was a little bit of a surprise. The old treatment, the Zamoraud-Briand treatment, basically said, in places where this formula comes up negative, it's the wrong formula to use. It's never going to describe what actually occurs. And it wasn't until the late-1960s, early 70s, I forget, the two theorists, I think at Bell Labs, showed that, in fact, there are regimes where, if you just ask that simple question,

what's the most likely time for this detector to fire or this detector to fire, the time could really be negative. And the trick here is it only happened when you had absorbing media. In other words, you've got something that's mostly opaque, only a little bit of light gets through. And the classic way to think about it

is to say, oh, I see, I had a wave that's spread out in time. It's not really all localized here. It's extended. And only some of that energy gets through, and the energy that gets through is earlier in time than I expected, it must just be that only the first part of the wave was transmitted and all the rest was reflected.

And there are reasonable ways to explain why you might even expect that classically. And that's a perfectly safe way of kind of stitching these facts together. And if you think more carefully about information, you know, I press a telegraph key over here, how long does it take before you receive the message, we can rigorously show that that's okay. None of that information goes extra fast. So that seemed to be one sort of explanation of what was going on, that only in cases where very little gets transmitted, do you see these funny effects?

And then it's not because anything is actually traveling faster than light or taking negative time to go through the medium. It's just because you're biasing your sample towards the stuff that was already out front. Okay? So the example I use sometimes with people, as I say, imagine I have 500 passengers spread out on 100 train cars. I guess it's not many passengers per car, but that's all right. And as the train is on its way from Chicago to New York,

someone decouples the first car from all the others, and only the first car makes it to New York. If the folks in New York now ask, when did the average passenger arrive? He seems surprisingly early, but that's just because they got rid of 99% of the passengers who were further back in the train. And somehow that seems to be what's happening.

with light. So for years, this is the story we all told ourselves, that there is this negative quantity that comes out of a calculation. It does describe the average arrival time of the energy that arrives, but it's not because anything really took negative time. It's just this weird reshaping and cutting off part of a wave packet. For us, the new surprise occurred around five years ago, when my student at the time Josiah Sinclair was doing a series of experiments, and actually predicted that a certain time was going to be zero. We decided to show that this time was zero. And long story short, we didn't find it was zero. We found that it was some positive number, and we realized there was no existing theory to even predict what that number should be.

and we worked with a friend of ours in Australia, guy named Howard Wiseman, to build up the theory behind this quantum theory of open systems, post-selection, kind of state of the art for how people are doing these quantum trajectory calculations. And Howard's theory kind of confirmed the experiment that we had already done.

And we said, well, what does it say about a simpler regime? We sort of expected that if we went to a thinner sample, and made our light, our photons, much, much better energy resolved, really tuned them exactly to resonance. These complications should go away,

and there should be a clearer intuition. And instead, when we took Howard's equations and applied them in that regime, we got this negative number again. And it took us a while to appreciate it. It wasn't just any old negative number. It was the same negative number that we'd known about in the 1990s,

this one that we had discarded saying, that's not really a description of what's happening physically. It's just this funny illusion. And that led us to say, maybe we were too hasty. Maybe these negative times that come out of these formulas are describing more about the actual physics of the situation than we'd appreciated. So I don't think the story is complete yet.

I can't give you a simple answer, what does a negative time mean? It is a negative number that appears in some formulas. Those formulas are designed to express, to pretext, predict the outcomes of particular experiments. But for us, the surprise is that the same negative number, the same formula, seems to describe a bunch of different effects, which to me suggests that it's telling us something deeper about the physical reality and not just about, you know, the happenstance of one particular measurement design. To the viewer or listener, it still may seem

like you have a basketball, let's just say that, and that's a photon. Okay, then you throw it to me and you say there must be some barrier. So let's imagine there's a curtain here, like you're a first class and I'm in the economy, and they just put that through. Okay, so that's the barrier, and then I catch it. It sounds like what you're saying is I'm going to catch it prior to you throwing it,

but then also it sounds like you're saying wave packet and is a photon a wave packet, is a wave packet a collection of photons? So please help spell out this analogy. Yeah. So I think, first of all, you're hitting at the questions that really motivate, a lot of our work in this lab,

which is that we don't have complete answers to these questions. As you know well, we have a mathematical formalism that lets us predict the outcomes of particular experiments. It's incredibly powerful, incredibly well tested, incredibly accurate, and people still argue about what it really

means about the reality that's truly behind. And we don't have, you know, absolute proof of the right or the wrong way to think about it. We don't even know if there is only one right way to think about it. So when you ask, is a photon, a wave packet, is a wave packet, a collection of photons and so forth, this is language that we, you know, paste on top of the mathematical formalism, and different people will use different language.

So I'll use a picture that makes sense to me, but I want to be clear that some people will object to the way I describe it. And on a more careful day, I might even not describe it this way. I think of a wave, a wave packet as a probabilistic description of where particles are. So the point is, we cannot say the photon is exactly here or exactly there. And I think even this description of, I throw one basketball and you catch it. When did I throw it? When did you catch it? Well, that's classical thinking.

We do need to move a little bit beyond that. So at the very least, it's still a classical analogy. but I imagine many different basketball players here all trying to throw you a basketball around noon, but some throw it a few seconds before noon, some throw it a few seconds after noon. On average, the basketballs have been released at noon. You catch the basketball, and we discover that on average,

when you catch the basketball, you're catching it at 1159 and 59 seconds. And we, you know, look confused, and we say, wait a second, the basketball arrived, a second before it was thrown, and then we say, oh, wait, no, you didn't catch most of the basketballs. Most of the basketballs are rolling around on the ground because you missed them. For some reason, you were better at catching the early basketballs. I don't know what it is about the way those guys threw it or, you know, when you had lunch or whatever, but for whatever reason, you caught the early basketballs, and that seems like a way out. Nothing had to travel

faster than light. But we measured something else. And here, I might have to switch analogies one more time. We had a lot of trouble coming up with ways to try to make this a little accessible. And the one that we settled on for a while was to actually think about a tunnel. We were thinking about the Holland Tunnel, thousands of cars that are driving through the tunnel, trying to get to Manhattan. and at some point there's an accident and the cops say,

no, everyone turn around, go back to which one is which, New Jersey. There were just a few cars that managed to make it into Manhattan. So just as in the basketball case, this is an example where we'd see, well, the average car making it into Manhattan arrived earlier than the average car leaving New Jersey,

but that's because 99% of the cars were just turned back by the cops. Okay? So perfect analogy with the basketball thing, it doesn't say anything about where the cars spent their time. So now we imagine something else. We imagine that some of those cars have a problem with the engine, and they're giving off a lot of carbon monoxide. So the longer a car like that spent in the tunnel, the more carbon monoxide we would sense in the tunnel afterwards. So what we do is we wait and see, is this car that's giving off all the extra CO, in the end, does it show up in Manhattan or does it end up back in New Jersey?

And depending on where it ends up, we send a guy in with a CO meter to measure how much was released in the tunnel. And what we'd expect, you know, from this classical picture, is, well, it still takes 10 minutes or whatever to drive through the tunnel. It doesn't matter whether the car got through or not. there's going to be this extra CO when the car spends that time in the tunnel. Our measurement tried to really look at that. So on the physics side, not look at when does the photon reach the detector.

That was well understood. Look instead at how long is the photon inside the atom cloud, meaning look not at the state of the photon, look at the state of the atom, look at what information it's leaving behind in the atoms. And that's like looking for the carbon monoxygen, side in the Holland Tunnel, what we found is that whenever that photon was transmitted and got to the far side,

it was as though the atoms were spending less time in their excited states than if there hadn't been a photon at all instead of more time. It's as though when you measured the CO level in the tunnel, you found every time the car get through, there was actually a negative change in the carbon monoxide level in the tunnel. And that makes no classical sense. I don't understand how that could be. quantum mechanically, we can think it through. I could give you a physical picture of exactly what we're measuring and why it turns out this way. But that's not really our goal. I mean, it's nice to be able to do that, make sure everything hangs together.

But our goal is to try to universalize, right? And to say there's something interesting about this formula, it doesn't only describe the most likely time of arrival. It also describes the behavior of the atoms. It also describes all these other features of the process. And in that sense, it starts to seem like even for something like time, negative quantities can have a real physical meaning. And I think that puts us in a position of struggling to understand exactly what is that meaning. When I'm deep in research reading papers on, say, the philosophy of mind or quantum gravity,

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Why is the tunnel so important to this? Why is this curtain that's in front of us needed? So, it doesn't need to be a tunnel, like in the sense of a quantum mechanical tunnel barrier. That's, in fact, not what I'm talking about right now. But we're asking about the time spent in a given region. And if there's nothing in that region, if it's vacuum, the time spent in that region is the thickness divided by the speed of light. There's no complication there. and if it's air, well, then it's the velocity of light in air.

It's still pretty close to see. But as soon as you put something there that the light can interact with, then there's the possibility of the light slowing down. So there are a few different examples of this we found interesting. But the one we're looking at now is really the more than a hundred-year-old example of just if you have the simplest model for an atom that can interact with light, what happens as light goes through this cloud of atoms? and that's easier than thinking of a piece of glass or something like that,

but it really is supposed to capture the same kind of physics. So the idea is we have a cell that has a bunch of rubidium floating in it, and our lasers are tuned so that they're on resonance with the rubidium atoms. When a photon hits a rubidium atom, there are sort of two things that can happen. It can be absorbed and excite the rubidium to its upper state, or it can just miss the atom, so to speak, and keep drowning. After an atom ends up in the excited state,

it doesn't stay there forever. That state has a finite lifetime. It will spontaneously fall to the ground state and spit the photon back out as fluorescence, generally in a random direction. So normally we think of that as absorption or scattering, that photon is lost to our laser beam. But if the sample isn't too thick,

some fraction, maybe 10% of our photons, get through to the far side. Now, we know that while the light, is inside the atom cloud, it's moving atoms up and down into the excited state, or in a classical sense, that's an electric field,

it's polarizing the atoms, it's giving them an electric dipole moment. And that's something that we know how to probe with a second laser beam. So we can send another laser beam through there and study what are the atoms doing while this light is being transmitted. And this is like the starting point

for all quantum optics. It's, you know, again, really well studied since the 1916, a little less before the invention of the laser because it wasn't that physically relevant. But now it's the first chapter of the textbooks on quantum optics. However, nowadays we can study it at the level of one photon at a time, which wasn't possible earlier. And we can in, in principle, send in one photon at a time and check was that photon transmitted or was that photon reflected? And ask ourselves, do the atoms do something different

when they're transmitting a photon or reflecting the photon. So for other reasons, actually, this was meant to be a kind of practical experiment. We started it looking for certain applications. Josiah came to me and he said, you know, if we make these photons interact on resonance, the way we're doing right now,

we can see some interesting effects, but I don't think any of them will happen for the transmitted photons. And he explained the following picture, which is that whenever this single photon gets absorbed by an atom, it's lost to the beam. So whenever we see a transmitted photon,

we know that in some sense it's just the photon that got lucky. It's the one that missed all the atoms, never excited any atoms, and therefore the probe beam won't know about it either. And we went back and forth on this a while, but I came to believe the same thing, and the two of us set out to demonstrate that experimentally. Josiah set out to demonstrate it in the laboratory.

And it was one of the few cases in like basic quantum optics, basic atomic physics, where we didn't experiment and found the opposite of what we expected. Normally, we're confirming our intuitions and testing them and seeing how well we can implement them when they break down. But in this case, we just realized we were wrong. And we came to understand why many other people I know in the end when I told them the story guessed the right answer faster than we had. But as I said, most of the modeling of these sorts of experiments that we do doesn't actually go down to the level of one photon at a time and asking where that photon ends up. That's a more complicated and modern perspective. And none of the existing theories were actually able to make this prediction. That's why we didn't know for sure what the right answer was when we started.

There was a really good hint, though, that the right answer was what Josiah and I had landed on, and it's the following. If you don't do any post-selection, you're just saying, I'm going to send one photon to time here, and I'll send through a probe beam to see how much time atoms are spending in the excited state. It's pretty easy to show that you get a very, very simple expression. You get the probability of this photon being absorbed, multiplied by the, excited state lifetime of the atom. So the simple way to put that into words is to say, oh, I see, every absorbed photon caused the atom to spend on average one lifetime in the excited state. Every transmitted photon caused it to spend zero, and that's why I get that weighted average. So in fact, when our experiment contradicted that, it led to another puzzle, because now it said, wait a second, on average, each absorbed photon causes the

atom to spend one lifetime in the excited state, but we just learned experimentally that some of that time came not from the absorbed photons, but from the transmitted photons. That implies that each absorbed photon must have caused an atom to spend less than one excited state in the, sorry, less than one lifetime in the excited state. How is it that the atom fell out of the excited state in less than its average lifetime? So that was another puzzle that we had to solve. And we went through, and as I said in this theory that Howard helped us develop, we were able to put the whole thing together. That theory was published last year, finally.

But it made this really weird prediction that if we studied it in a different regime, we'd get this negative time. Now, if you have a sample where 100% of the light is transmitted, you never get into these puzzles because, as I said, information can't be transmitted faster than light, and energy can't move faster than light. So in most situations, I should be a little careful here,

unless you have some selection event where only a subset of the particles get through to the other side, you don't get these confusing situations. So that's why we've tended to focus on either resonant atoms where they absorb a lot of the light or tunnel barriers where they reflect a lot of the incident wave. There's one very strange counter-example that my PhD supervisor came up with

around 92 or 93, and it still leads to some controversy, but there's an extra loophole built into that one. Is that the subtlety that you just referred to? Sorry? Where you said there's some subtlety. Yeah, the subtlety is this loophole due to my supervisor.

So this was a funny one. And quite a lesson for me, actually, because the loophole was the following. We knew what happened if you have a two-level atom, the simplest quantum mechanical model of an atom, and it's a ground state, has an excited state. send light close to resonance and normally it slows down

but it turns out that if you're right on resonance or very, very close to resonance, you get instead these anomalous group velocities that can be faster than light or even negative, which means even faster than faster than light. And this again is the stuff that was known mathematically from the early 1900s and had been sort of swept under the rug for good reason

and then reinvigorated a bit in the 1970s and 80s. The trick is, on resonance, you have a lot of distortion. That's why Zabert and Brian, later Jackson, argued you'll never see this in practice. Garrett and McCumber and then Steve Chu and Stephen Wong showed that, in fact, you could see it if you were really, really careful. There are sort of narrow regimes where even though most of the light is absorbed, you could see this superluminal transmission. And what Ray Chow, my PhD supervisor, wanted to do,

is move beyond that very delicate regime. And he had this brilliant insight. He said, that's what happens if the atom is in the ground state. If it's in the excited state, everything is going to flip. So instead of having really slow propagation outside of the absorption band and fast propagation inside, the absorption turns into amplification or gain, and I end up with really slow propagation in that gain line, and faster than light propagation outside

where I just have 100% transparency. And again, that seemed really weird because we'd always said the loophole is most of the stuff isn't getting transmitted. If just the subset that gets transmitted shows up early, I can explain that away. But if everything gets through and it shows up early, now it seems like we're communicating faster than a light.

We know that's not going to be the full answer. So the way I always like to explain it, again, sort of semi-classical hand-waving, is to say, what is the velocity of the energy? How fast is the energy moving? That's only one of many questions you could ask, but just think about that one. That's complicated because an amplifier, by definition, is something that has energy in it. You know, it's plugged into the wall so it can add energy to your system. So I have my amplifier, I fire a laser at it, some light comes out.

Which energy is that? Is that from my laser? Or is it from the amplifier? There's no way to tell. Energy is fungible. Energy is energy. So the natural explanation, if you believe that energy fundamentally can't go faster than light, is to say, no, the energy that was already stored in the amplifier in these inverted two-level atoms

leaks out and then gets repaid later by the laser beam. Why that happens? I don't know, mathematics, quantum interference, but that must be the explanation. The thing is, how do you rigorously prove that that's the right way to think about it? How do you show where the energy came from? Don't really know how to do that,

and there are a number of people who've tried to define better ways of talking about the energy velocity. The motivation for this, if I go back a step, is I keep referring to this century-old work by Zammerfaird-in-Briand. It's because they really were the pioneers

in getting rid of these paradoxes. And they said, look, we talk about waves. People learn probably in first year physics that it's hard to talk about the propagation velocity of the wave. There are ripples, they move at one velocity, but the whole wave packet may have a kind of envelope that can move at another velocity.

And the first thing we learn is don't worry about the ripples. The meaningful thing is the envelope. Not the phase velocity, but the group velocity. Why? because it tells you where the energy is on average. I think that's the simplest way to put it. So, we already knew about phase velocity and group velocity, and funny situations where the phase velocity could be faster than light,

and people said, don't worry about it, it's not energy, it's not information. But the group seemed like it was telling us, where's the energy, where's the information? Then when the group velocity turned out to be faster than light, these guys said, oh, wait, we must be missing something. So they came up with better ways to say, well, where's the information? And they showed how the information velocity is still slower than light, we're okay. And then they said, what about the energy? And they came up with a way to calculate the energy velocity.

And typically that was also slower than light. It turns out that by their definition, in the case of a tunnel barrier or an absorbing medium where very little is transmitted, the group velocity may be faster than C. The information velocity is never faster than C. It can be arbitrarily close to C, but it can't go any faster. But the energy velocity was much slower because most of the energy is actually getting absorbed or sent back. And Ray really wanted to push on that and say, are there interesting cases where we can make the energy velocity high? And that's why he looked for this transparent case.

if you use the textbook formula to calculate the energy velocity in that case, it also turns out to be faster than light. And that's why we said, oh boy, even that definition isn't enough. We need to come up with a better definition for where's the actual propagating energy. And I would say the jury is still out there. I mean, we know it can't be faster than light. But there are different ways people are proposed defining it. And I don't know, you know, a complete satisfactory definition yet. So are you saying there are at least four different kinds of velocity? One is phase, another is group, and that's something everyone learns, but then there's energy velocity and then informational velocity?

Yes. There was a paper, I think, in the 90s that I think was called the eighth velocity of light, because it argued that people had already defined seven, and they were still missing something. And I don't remember what all eight are. You know, these are definitions, right? So it's not that they're all completely different very often. Many of them coincide. And their physical meaning is a little up for debate.

So already what you define is information velocity. The approach that was frequently taken and some of my colleagues who do like microwave signal engineering and things like that ascribe to it, because it's a good model for what we do in practice and communication systems is they say, well, I'm going to hit a button and send out a nice sharp pulse. It might get distorted going under the trans-specific fiber by the time it gets to you, but you'll receive some sort of pulse, and you'll set up an electronic system to determine when do I know there's a pulse. And very often you use a technique called constant fraction discrimination.

You maybe try to see when do I reach one half of the maximum amplitude. And they define information velocity by how long does it take to reach that half maximum. that's just a working definition. There's nothing deep and physical about it, but it gives a sense of what's going on. And I think that that's the definition that Zammerfeld and Brin used for their information velocity.

They did something more fundamental as well. They defined what they called the front velocity. And there they said, I can't believe information is going faster than light. If I was sending nothing out until T equals zero, I don't believe that you could receive that information in time less than D over C. So they imagined a wave that was strictly zero up until T-equal zero,

and then began oscillating sinusoidally at T-equal zero. One model for flipping a switch, not a very realistic model. And they showed that the moment of first disturbance arriving at the receiver was exactly D-over-C. So that's the fundamental limit on the fastest you can send information. So that's what I would tend to call the ultimate information. velocity. They actually called it the front velocity. When I'm wrestling with a guest's argument about, say, the hard problem of consciousness or

quantum foundations, I refuse to let even a scintilla of confusion remain unexamined. Claude is my thinking partner here. Actually, they just released something major, which is Claude Opus 4.6, a state-of-the-art model. Claude is the AI for minds that don't stop at good enough. It's the collaborator that actually understands your entire workflow thinks with you, not for you, whether you're debugging code at midnight or strategizing your next business move, Claude extends your thinking to tackle problems that matter to you. I use Claude actually live right here during this interview with Eva Miranda. That's actually a feature called artifacts, and none of the other LLM providers have something

that even comes close to rivaling it. Claude handles, Interalia, technical philosophy, mathematical rigor, and deep research synthesis, all without producing slovenly reasoning. The responses are decorous, precise, well-structured, never sycophantic, unlike some other models. And it doesn't just hand me the answers. The way that I've prompted it is that it helps me think through problems. Ready to tackle bigger problems?

Get started with Claude today at clod.a.i slash theories of everything. That's clod.a.i slash theories of everything and check out Claude Pro, which includes access to all of the features mentioned in today's episode. You said something interesting, that this was just a working definition. Right, Zumberfell and Breon? Yep. Okay. So in math, there's no such thing as a working definition.

You just put, here's the definition of a group, and then here's three. It looks like an equal sign with three. I'd sooner say everything is a working definition. No, what's interesting is that if we're going to say that so-and-so is a working definition, then it implies that there's some other concept that we're trying to capture. This may or may not. So then what is it that is this cloudy substance

or what have you over here that you're saying that informational velocity is trying to capture? And how do we know once we've got it? Again, I think you're touching on a much deeper issue, and it is at the heart of the difference between physics and math and at the heart of asking

interpretational questions about physics, right? In physics, we have this rigorous side where we imagine precise experiments or physical situations and how to calculate or predict exactly what will happen. And we also imagine a story behind it. Why is that happening? What should I think about really existing? And the second part isn't rigorous,

but it's always what we're kind of aiming at. So I think here we have this intuition that nothing travels faster than light. Don't know exactly what that means. We have to say, what is a thing, what is no thing? part of it, I think, is that energy should not travel faster than light, although there are questions about why we should believe that. Part of it is definitely that information shouldn't travel faster than light, but why do we believe that? Goes back to Einstein, of course. It goes back to saying, if something could go backwards in time in my reference frame,

then I can imagine some other observer in whose reference frame that, That actually, wait, did I, I don't know if I already said this wrong. If in my reference frame it's going faster than light, I don't know if I said that wrong. There will be some other reference frame in which it's actually going backwards in time. And that other reference frame is as valid as mine, obeys the same laws of physics according to relativity. If something I do now can affect the past, then all of our ideas about cause and effect get thrown into disarray. We don't have any physics proof that that can't happen. and it just contradicts our whole idea of science and of causality.

So by and large, we just take that as a given. It would be interesting if you tried philosophically to just deny that. There are people who work a little bit on retrocausality or things like that. It's a very fraught philosophical domain. But if we leave that aside, then we say there must be something that prevents me from having effects on distant systems faster than light, because that could lead to, say, the famous grandfather paradox or something like that. But then I've got a model, well, what would it mean for me to try to have an effect on another system?

So we start making up models for how I could imagine doing it. I could imagine, you know, sending you a telegraph message. And I stick to the telegraph because it has this nice, you know, discrete on-off key, right? So we try to model that and say, right, at least if you did it this way, I can show you that there's no way that Kurt could react faster, than D over C, sigh of relief, everything's okay. But was our model good? Could you imagine a different way I could get to the information faster? So the idea is to cook up schemes that should show what the ultimate bounds are. We really believe there's no way you could know anything. And that, to my

mind, is the purpose of the front velocity. What it really shows is that at a given time, nothing you can measure depends in any way on what I do at times too late for me to send you a signal at the velocity of light. So the only thing you have information about is in your past light cone, times where I could have communicated with you at the speed of light. And I really think that's what the front velocity argument does. Whereas the signal velocity, well, it was one experiment a little closer to what you might imagine really doing in a lab. it is a little closer to what we really do for communications, and it's always slower than that fundamental limit.

So I think in a sense what it shows is that real world systems are even worse than the fundamental limit. They have extra latency, they have extra time delays. That's okay. I remember the doubt before launching this podcast. What if no one listens? What if I'm wasting my time? If you've ever felt that way about starting a business,

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$1 per month trial at Shopify.com slash tow. That's Shopify.com T-O-E. Hi, everyone. Hope you're enjoying today's episode. If you're hungry for deeper dives into physics, AI, consciousness, philosophy, along with my personal reflections, you'll find it all on my substack. Subscribers get first access to new episodes, new posts as well, behind-the-scenes insights, and the chance to be a part of a thriving community of like-minded pilgrimers.

By joining, you'll directly be supporting my work and helping keep these conversations at the cutting edge. the link on screen here. Hit subscribe and let's keep pushing the boundaries of knowledge together. Thank you and enjoy the show. Just so you know, if you're listening, it's c-U-R-T-J-A-I-M-U-N-G-A-L.org. Kurtjymungle.org. Can you give a flavor to those who think that quantum mechanics is just quantum mechanics? How is it for something that sounds as simple as a photon being emitted and then there's some rubidium atom and then there's a detector here?

why is there no calculation that shows so-and-so? It seems like there's the theory, quantum mechanics. It doesn't even sound to me like you're using QFT. So quantum mechanics is settled, in a sense. Yes, no, of course you're right. I'm sorry, we are using, in some sense, QFT, because the photon is a relativistic particle or relativistic field. So this is a relatively simple branch of quantum field theory,

quantum electrodynamics. the full quantum mechanical theory is perfectly known. That's sort of like saying, in principle, if we know all the fundamental laws of nature, we can predict what you're going to say five minutes from now. Well, yes, if we had all the information and could calculate everything. This is a simpler situation,

but it turns out that already, if you have a cloud of atoms and a mode that might or might not have a photon in it and many, many different modes into which the atoms can spontaneously emit, that's not a trivial system. to completely treat quantum mechanically. But yes, we know how to do it.

Then we have to post-select on what happens on those particular occasions when I see this photon on the far side. And sorry, in the actual experiment we're modeling, I left out one thing. There's an additional light beam that's interacting with the same atoms and through the medium of those atoms

becoming entangled with the initial signal light beam. So it is a complicated multi-mode problem, but the underlying theory is indeed perfectly well known. No one, as far as we know, happened to work out that precise set of equations and then look at what it means about this post-selection. And again, I always think what's interesting is the unifying, not saying, all right, since we've got the complete theory,

if you tell me you care about this one particular setup, this is the measurement you're going to do, this is how you're going to do it, and I turn the crank long enough, I can calculate exactly what you're going to see. The question is, how should we think about the photon while it's going through the atom cloud?

Does this teach us something bigger picture? So what we try to do in this formalism is actually do a more general treatment, show both that it described the experiment we had done, but also that it describes a broader class of experiments, and that in that sense, it's telling us how the photon behaves as it traverses the atom cloud.

So let me back up again. This isn't historically our motivation for doing the experiment, but to me it's the conceptual motivation that I use to try to get people interested in it now. We talked about how fast light goes, travels at sea and vacuum. If I put it through an atom cloud,

it might slow down. The photon might take a nanosecond to go through this millimeter-sized cloud. For scale, that's dramatic. In free space, it takes light a nanosecond to go 30 centimeters. So this one millimeter of tiny little atomic gas can slow it down, so it takes hundreds of times longer than it should. Famously, Lena Howe in the 1990s did experiments

where she made light travel slower than she could ride her bicycle. It was her claim to fame in the New York Times or whatever. So people ask, what's the light doing? Doesn't light travel at 300,000 kilometers per second, or was I taught wrong? And a common way that people hand waved it and say, here's how you can think about it. Just think about it.

Is that while the light is going through the atoms, sometimes there's a photon just propagating in free space between atoms, so to speak. And sometimes the photon gets absorbed, and there's no photon anymore. there's just an excited atom. But the excited atom doesn't move, or doesn't move very fast.

It's more or less sitting still or floating around. So why does the light take longer to get out the far side? It's because it wasted a lot of time in the station sitting there as an excited atom. And if we just calculate how much time do the atom spend in the excited state, that might give us the time delay. I was never sure how seriously to take that. There are regimes in which it seems to work very well,

close to resonance, it seemed a little bit nonsensical, and right on resonance, I told you before, we actually know that the peak comes out before the peak even arrives, that negative time seems like it's completely unrelated. I couldn't explain that by saying the photon, you know, wasted time sitting in the excited state. So what was our big surprise?

We measured directly how long did the atom spend in the excited state. And when the traversal time was known to be negative, we found that dwell time is also negative. So it does sound like the two are equal, even when it's really hard to put into words what that means. Sorry, the dwell time is what? Sorry, I'm throwing around different words. We sometimes just call it the excitation time,

the amount of time atoms spend in the excited state. And it wasn't obvious that that time should be the same thing as the delay time for the peak of the pulse. That's why I give them different names. Our discovery was that mathematically equal. They're defined in very different ways, but we can show if you measure this one, you're going to get the same answer as if you measure that one. Completely different measurements

looking at different things. But, you know, this is what we're used to classically. If I, you know, again, go back to my silly Holland Tunnel example, if I sent one car through a tunnel and I measured, when did it enter the tunnel, when did it leave the tunnel, okay, it spent 10 minutes there, and then I measure how much carbon monoxide is in the tunnel, I should expect to see about 10 minutes worth of CO emissions, and that's what I would see. Quantum mechanically, that's not always true. It turns out that things that we're used to assuming

are identical classically can give different results quantum mechanically. So for 30 years, we, and for 100 years, some others, have been arguing about some of these funny traversal times. Again, I can tell you more about them later, and discovering that there are different ways of defining them that you would have thought meant the same thing classically, but in fact you're described by different functions quantum mechanically. So, you know, when you say,

why is there a working definition, are you groping towards something else? Well, yeah, we have this idea that there's a time, and there are cases where I think we just learned that that's wrong. There are several times. We should learn what the different times are and think about what they mean. but we began by saying

there's this thing that has an obvious meaning classically, let's figure out how to define it quantum mechanically and how to measure it. And historically, that's how quantum mechanics has worked. You know, it said there are things we're used to measuring classically. Where is the moon?

Where is the basketball? And for an electron, Heisenberg would have just said, well, you can't talk about that. You don't measure those things. But in more modern quantum mechanics, we define operators, that correspond to these observables.

And how do we define them? We define them according to this correspondence principle, that there should be a limit where they give the answers we already understand classically. And if we can find the measurement that gives us the thing that we're used to calling position classically, then we'll say, oh, okay, that's what we mean by position quantum mechanically.

Let's see what it would yield in quantum mechanics. But in most cases, we're used to that being a well-defined procedure where there's one answer. there are stranger cases like measuring time where, turns out there are still different definitions that might coincide at the classical level, but not at the quantum mechanical. When I'm wrestling with a guest's argument

about, say, the hard problem with consciousness or quantum foundations, I refuse to let even a scintilla of confusion remain unexamined. Claude is my thinking partner here. Actually, they just released something major, which is Claude Opus 4.6, a state-of-the-art model. Claude is the AI for minds that don't stop at good enough.

It's the collaborator that actually understands your entire workflow thinks with you, not for you. Whether you're debugging code at midnight or strategizing your next business move, Claude extends your thinking to tackle problems that matter to you. I use Claude, actually live right here, during this interview with Eva Miranda. That's actually a feature called Artifacts,

and none of the other LLM providers have something that even comes close to rivaling it. Claude handles, interalia, technical philosophy, mathematical rigor, and deep research synthesis, all without producing slovenly reasoning. The responses are decorous, precise, well-structured, never sycophantic, unlike some other models,

and it doesn't just hand me the answers. The way that I prompted it is that it helps me think through problems. Ready to tackle larger problems? Sign up for Claude today and get 50% off Claude Pro when you use my link, clod.a.ai slash theories of everything, all one word. So when the headlines say Steinberg showed negative time, what they should say is Steinberg showed negative time sub three. It's a specific time. And also, of course, ate all. I mean, you and your collaborators. Yes, of course. We showed that you can measure

something that has the dimensions of time and that it turns out to be negative. Not that time is negative, that there is a timescale that turns out to be negative. And as I want to tell you, there are already other timescales that were known to be negative. We found that another one, which honestly we expected should be restricted to positive numbers or non-negative numbers, is also negative. And we found that these different time scales that you might have thought to be unrelated can all be equal even when they're negative.

Is time an operator or a parameter? Yeah. This is a big controversy in quantum mechanics. Sometimes I think it goes beyond that, though. People are fond of saying that time measurement in quantum mechanics is really tricky because we talk about measuring

things that are mathematically described as operators, as you said, and time does not have that status. Fundamentally, you cannot write a time operator that has all the characteristics you would want of time. Do you mind briefly giving a flavor as to what the heck the difference between an operator and a parameter would be? It doesn't have to do with time, just so people who don't know the difference can understand. Let me begin instead by backing up to classical physics, because I think there's already something funny about saying that we measure time classically. And I think even classically, it behoos us to worry about what it means to measure something and how we define these things. So I can ask you, hey, what's the position of this basketball now? There's a clear, well-defined

answer to that. What's the position of Artemis five seconds ago? There's an answer to that. Now let me ask you, what is the time of the earth? that doesn't even mean anything right anything that you might measure time color sleep state you know whatever these are functions of time they have a different answer at every time that's what it means for it to be a parameter the things we measure are functions of time i can ask you what your location is now i can ask you what your location was yesterday i can ask you what your location will be in one week for any time I name, I can ask you a question about any observable property. The reverse doesn't hold.

So when we talk about measuring time, that's not really what we need. We could mean we're going to measure the first time at which some other statement becomes true. But how do we do that? I'm going to measure whether or not you're in this room. I'm going to keep looking at my watch, looking at the room, you're not here yet. And the first time I see you in the room, I'm going to look at my watch, and I'm going to say that was the first time

at which you were in the room. And we say, I measured Kurt's arrival time. But you see, it's an indirect measurement. And in fact, physically, what have I measured? I've measured the position

of a needle on the hand of my watch. I'm still doing a position measurement in the end. We're looking at correlations of different measurements. So, I'd say quantum mechanically,

we just run into the same problem. It becomes mathematically a little more pronounced. but it comes back to that same issue. Particles are supposed to have observable properties at every time, and time itself is not an observable property, the position of the hands of a clock, maybe. Let me ask you a funny question.

Yeah. How is it that we know that some experiment is correct? So, for instance, let's imagine I give you a ruler, then you could always question, well, I don't know if this ruler is actually ticking forward equally. I don't know if it's measuring. 30 centimeters. So then how do you measure that ruler?

How do you measure the success of that ruler? Maybe with another canonical ruler? Right. The practical answer is you need to have multiple rulers. And at some point you have one, you know, platinum meridium bar in Paris in the old days. And you say, well, that's just our definition. That is one meter.

You compare your ruler to that. And if you say, yeah, it agrees to a part in a million, then I'm going to trust your ruler to a part in a million. and that's as good as I can do. And there's no meaning to the question of whether it's right or wrong. It's just the definition. We do want to define things so that they make sense in terms of physical constants. So we do want to ask, does a clock tick at a constant rate?

Well, how do you compare a clock tick now to a clock tick next year? How do you verify that that's constant? So the best you can do again is compare two different things. Build two different clocks and confirm that at every time all the clocks I build by the same recipe using the physical definition now of what a second is. Agree at every time.

You still raise the question, well, maybe all of the clocks are changing as a function of time. Is that a conspiracy theory? Why would they change the same way? Well, unless the laws of physics, themselves are changing the same way, of course they couldn't. Are the laws of physics themselves changing? That's again a tough question. People ask themselves that. They look for drifts in

fundamental constants. But I think even there, you've got a matter of definition. You have to say, what are the two things I would compare and call a change? You'd be free to define either one of those to be constant. You know, I could say this clock made out of cesium is my definition of a second, so I know that its click rate is not changing because that's what I mean by click rate.

What I will do is see whether the orbital period of a hydrogen atom is changing with respect to that, or whether some binary pulsar system is changing with respect to that. But no, in the end, you can only compare. And I think, you know, that's been a big part of the 20th century evolution in physics and in philosophy and culture more broadly,

to think in terms of what it means to measure something, to say time is what a clock measures, distance is what a ruler measures, let's think of an idealized way you might define the construction of a clock or a ruler, and then see whether there are cases where different clocks or different rulers disagree. And if so, we draw a conclusion about the fundamental nature of the universe. and quantum mechanics does something very similar, saying, I mean, if you really want to be a formalist and a purist, you'd say quantum mechanics says nothing about what's actually out there. All it does is predict probabilistically the results of different measurements.

And I mean, I'm a realist. I think most experimentalists tend to be realist. We feel like there's something out there. I don't claim to have some epiphany in no more than you do about what it is, but I think our goal is to try to understand that. and, you know, we make educated guesses based on our formalism, Occam's Razor and things like that. But I've gotten in trouble where I've written papers describing what we did,

and I literally once had a referee report that said, I'm not sure what the author means when he uses the word is. He wanted me to take out, you know, the electron is here, whatever I had written, and say, had one conducted a measurement of the position of the electron, one would have found and be very, very, very conscientious. Yeah. Okay, so you said that most experimentalists have an idea that there is something there's real. I believe that's true.

Okay. And many theorists, but I think it's a little hard to be an experimentalist without imagining some actual external reality. But to my mind, you know, this is part of the big question, right? The reason I'm in this field is not originally to study photons and atoms. I mean, photons and atoms are cool. So are quarks, so are black holes, or LLM, so is consciousness. Many different things out there are interesting.

I think what really struck me as a kid is reading some science fiction book that alluded to Bell's inequalities in Aspe's experiments, kind of remarkably because I later understood the book was written only a few years after Asper's experiments, but this guy was pretty knowledgeable. And it wrote about Bell's theorem, saying that Bell proved a theorem

that says that once two particles interact, you can never describe them as independent isolate. And I just thought, well, certainly a deep philosophical question. I guess I'd heard enough about Einstein and the Bohr-Einstein debates that I knew that Einstein seemed to believe that God does not play dice with the universe. And how people like Boer had come to believe that Einstein was wrong about that, I couldn't understand. Where do you get this sort of religious conviction?

That not only is my theory accurate, it, but it's the whole story. You can't know any more than that. You couldn't actually know where every electron is. It seemed impossible to test the possibility of an omniscient being that knew the exact position of all the electrons. And the formalism of quantum mechanics doesn't really answer that. It just says, if I write down a quantum mechanical state, it does not give particles definite positions and definite momentum. Einstein's view of the quantum mechanics, if you kind of read behind the lines of the EPR paper, seem to be, sure,

that state cannot completely describe the position and momentum of a given particle, but couldn't it be that every particle has some position and some momentum, and the state is just a statistical description, like thermodynamics for the air in this room, but that some future theory that we might or might not ever learn would have the total information.

So the title of their famous paper, was can quantum mechanics be considered a complete description of reality or something to that effect? Not that quantum mechanics would have been wrong, just that there had to be something beyond it. Somehow people like Bohr had the hubris to say, no, there's nothing beyond it,

and Bill's theorem made that testable. It showed that if there's something beyond it that behaves locally in the way that Einstein seemed to want, it would make testably different predictions from orthodox quantum theory. So basically the idea that such a fundamental fact about the universe was now subject to experimental test, that's what gets me excited about quantum mechanics.

And I think we're still asking that question now. What does it mean to test these things? Did you ever test and find that Heisenberg's bound is lower than it should be, or higher than it should be? You're leading the witness, I think. So, no, what we frequently call Heisenberg's bound is a rigorous theorem about quantum mechanics,

again, not about reality, but about quantum mechanics. Not originally proved by Heisenberg, but by others, notably Robertson and Walker and Schrodinger as well. And it's completely accurate. The story we tell when we talk about Heisenberg's Bound is kind of funny. We Heisenberger originally wrote about it as well. He had this brilliant Godunken experiment of measuring the position of a particle by using a microscope. How else do you measure the position of a

particle? But again, coming back to this 20th century evolution of the observer effect in self-referentiality and recursion, he imagined that to measure it, you would have to bounce light off it and have that hit your screen or your eye or whatever, and that that light could disturb the system. system. Now, of course, we know that when you measure a system, when I ask you a question, I might affect you. But we always imagine pre-quantome mechanics that in principle you could be as gentle as you liked. And what Heisenberg argued is that that wasn't true, and that to measure the position of the electron to a given precision, you needed to disturb its momentum by more than a certain amount, H-bar over twice the uncertainty in that position. And that's usually the first way

we introduce the uncertainty principle. Then we get up to the math, and we show, actually, you can show, it's not just the measurement disturbing the system. It's a property of the quantum states themselves. They have this intrinsic uncertainty. And I would always have told students, so Heisenberg was right, but this goes even further beyond that. It's even deeper.

And about 20 years ago, a little more, I think, a guy named Masenawah in Japan, proved that the original statement wasn't even correct. that you could, under certain occasions, measure a system and disturb it by less than H-bar over twice the position uncertainty you wanted. There was still a finite disturbance. He just calculated a new bound, and he found sometimes his bound was smaller

than Heisenberg's original. And I should be careful. Again, we have to define what we mean by these quantities, what do we mean by measurement uncertainty? I think his definition is eminently reasonable and very operational, it connects to an experiment we were able to do. So we did confirm that by that definition, the disturbance could be less than what you would think from Heisenberg's bound.

But again, the rigorously proven Heisenberg uncertainty principle in all of our quantum textbooks is not about the disturbance due to a measurement. So it remains correct. It's just taking that same formula and applying it carelessly to a different situation, which we all thought made sense that I now realized was just too rash. Many people, as you said,

when they're being told about Heisenberg's uncertainty, they're given this mental image of suppose you want to measure a bear, some object, let's just imagine it's a bear, I think, because that was the original textbook that I read.

They say you throw basketballs, again, it was basketballs or volleyball or what have you. And if you make the objects more refined, like tennis balls, and all of a sudden, smaller or smaller, then you're able to resolve

smaller and smaller. Actually, it turns out of... Oh, I see, if you make them physically smaller. Yes, but the picture is a classical picture that you're hitting it and disturbing it. So what is the picture that you have? How about, let's not say what is the actual picture, because who knows,

what is the picture that Professor Steinberg has of Heisenberg's uncertainty? How would you teach it in order to not give misleading ideas? Yeah, it's a great question. the first time I had to teach it after doing this experiment, I realized I was still saying it wrong. You know, I think the historical story remains a good one. I think it captures most of the truth.

I think it's just this particular mathematical equality that's tricky. I think the Heisenberg microscope case that Feynman also talks about is a very idealized and somewhat realistic case. where the disturbance really does come from momentum transfer between the probe, these basketballs or tennis balls, and the object being probed. The question, again, is how uncertain does it need to be? One thing you can imagine,

I throw tennis balls at you, they bounce off at some angle. Depending on the angle at which they bounce off, you recoil a little bit. Since they bounce off at all different angles, you're buffeted around. but if I throw one tennis ball at you and they say all right Kurt's probably moving somewhere now

I don't know in what direction but then I catch the tennis ball over here as I catch that I say oh now I know exactly how much momentum was transferred there's no more uncertainty I know exactly what happened to Kurt and that's true of quantum mechanical measurement interactions if I look at the tennis ball and I measure its final momentum

I've learned exactly what momentum disturbance I did to you turns out, and you can understand this from the optics of it, if I do that, I can't use that tennis ball to image where you are. I have no position resolution. And in order to get good position resolution, I have to open up my aperture, basically. And as I open up my aperture,

I lose information about the momentum. So there's the trade-off. The more I open the aperture, the more information I get about your position, but the more I need to disturb your momentum. I think that remains a really good picture. We can write it more mathematically about a much more general interaction,

but you get the same idea that in order for me to have resolution in position, there needs to be uncertainty in how much momentum I can transfer to. And I still have the choice later on to re-measure that momentum and get rid of the uncertainty, but to do that, I have to give up the information.

It still seems like a problem is that tale can be told about purely classically. That is, there's nothing that Heisenberg need to, or anyone needs to know about quantum mechanics in order to come up with that, about momentum transfer, for instance, or opening up an aperture, no? Except for the fact that there's a fundamental limit. Classically, there's no reason that I couldn't throw tiny marbles at you that had almost no momentum and very good position resolution. And I'd get very good resolution and you wouldn't really feel the marbles. I mean, you know, right now that's what I'm doing, right? We're shining 10 to the 18 photons per second off of you in this room, and a few of them are hitting my eye, and I'm getting pretty good information about your position,

and they're really not disturbing your momentum measurably at all. But there's a limit to how far you can go, and that limit does not depend on which projectiles I use. It doesn't matter whether I use visible photons, gamma rays, electrons, nitrogen molecules, the limit just has to do with the relationship between your position uncertainty

and your momentum uncertainty. I guess what I'm getting at is that it's still in quantum mechanics that the energy of a photon is a continuous spectrum from zero upward. So you could go as close to zero as you want. The Heisenberg uncertainty doesn't seem to be

because you can't get as weak as you like and we're going to talk about weak measurement, but it doesn't seem to be about that. So it seems to be about that. something else, if we're going to tell this sort of tale with words. Well, it's not just about the energy. And again, it's more about the momentum transfer.

If the particle has so little momentum, that no matter what direction you scatter it in, the momentum transfer is really, really small, then it turns out that guarantees quantum mechanically that it can't measure your position to very good resolution. And fundamentally,

that's why we use high energy particles to build accelerators, they make good microscopes. You want to learn about the structure of matter on a scale smaller than a Fermi. You need particles that have at least a GEV of momentum or energy. Classically, there'd be no such restriction, right?

You'd think, let me go to smaller and smaller marbles and then grains of sand and then particles of dust, and they're smaller and they're lighter and they have less momentum. I win on all fronts. And quantum mechanically, there's this limit where the lighter they become, the worse my position resolution becomes. That's what doesn't

exist classically. Weak measurements. Okay. So, so far I was talking about a kind of discrete measurement. You know, I fire one particle at you and looking at where it bounces off. I can either learn what the momentum exchange was or the position. If I don't want to disturb you very much, I use a particle that's not going to have a very big momentum change. And what we discover is, I can't have very good resolution. I'm not going to get a lot of information about where you are. Then again, whenever real-world experimentalists do measurements, they know it's hard to get a lot of information from any one measurement.

That's why we take measurement for hours or years, if we're sarin or something like that. And we average and average and build up statistics. It's not that we learned about the existence of the Higgs boson from one muon that landed in one detector somewhere. We needed to do the statistics. So in the 1980s, Yakira Aronov and his collaborators started thinking about this and realized,

I can do a measurement that doesn't disturb the system very much. And if I do it millions of times and I look at the average, I still learn on average what the system was doing. I don't learn on one particular trial exactly where it was. But maybe that's not what I'm interested in. So the reason this gets people like me excited is because there's a strange issue in quantum mechanics where we're often told not to think too much about the past, not to think about the history of a system or how to get where it is.

In fact, we're told unless you actually built your experiment to measure X at the end of the day, you shouldn't even talk about X, only talk about the things that you've built your apparatus to measure. and those of us who are realists want to say, well, I'd like to say something about what X was before I measured it or what P was before I measured it. I mean, to me, the simplest case is the following. Fire a particle from this position

detected over here at this position and ask how fast was it moving, or what angle was it moving at? Classically, I'd say, well, obviously, it must have been moving along that line, right? Quantum mechanically, that's not so clear. And yet, we ask ourselves, is there some way I could talk about

what the average momentum of the particle had been after I emitted it but before I detected it? And the problem is, you need to condition on this detection event. You have to say, I don't just want to look at the whole wave function, and the whole wave function is spreading out all over the place, and its average momentum is zero.

I want to know just about the part of the wave function that reach this detector. How do you even begin to calculate that? And the reason that, let's say, from the 1960s to the 1980s, this seemed like an intractable problem, was that if I did measure the momentum along the way, I would disturb the particle. We've just been talking about how measurements disturbed particles. And then if I happened to find the particle at my detector, I'd say, well, it's not that that was the path the particle was taking to the detector. it's just that you kicked the particle when you made this measurement,

and that's what sent it to the detector. So this is why starting in 1988, when a lot of Albert and Weidman realized that you could make the measurements weekly, they were able to say, wait a second, if we kept measuring this average momentum or whatever we wanted to know, but without disturbing the particle, then sometimes the particle would reach this final detector, and on those occasions, I could go back and look at my measurement,

result and say, on average, whenever the particle made it there, this is what my meter read. So this was the average momentum, not of all the particles, but of the particles that made it from point A to point B. So I wish they hadn't named these things weak measurements. To me, what's interesting about it is they're conditional measurements. It made it possible quantum mechanically to say, what is the average momentum of the particles that later on are guaranteed to get to this point. If I find the particle here, what was it doing before it got there? And that's something that a lot of traditional textbook quantum mechanics had denied being even possible. So in this quest to understand what is quantum mechanics really telling us about the

nature of the world, about external reality, it seemed really important to me to be able to correlate final events with these measurements, and that's what weak measurement allows. Is there something more to weak measurements than simply measuring the systems weekly over and over in order to get some picture, but just many hazy pictures, but then you average out these pictures? Because it seems like that wouldn't take until the 80s then. It seems like five years after Heisenberg already put that idea in our minds, we would have thought, well, why don't we just disturb it less and less, but take many snapshots. Yeah, it's a great question.

I don't know of earlier work on it, but of course, everything these kinds of things, did is building on the 1926 theory of quantum mechanics, and there's no good reason that someone in 1930s could not have done this, except it's not what they were looking for, you know, it's not what they were motivated to do. We've all been trained with the idea of a measurement as this kind of mathematical operation where you get a precise result. And of course, everyone knew early on, no measurement is absolutely precise. But the normal approach of physicists is to say, well, that's just experimental reality.

We'll deal with that later. We'll add the uncertainties later and say, okay, we can't do the perfect job, but this is, you know, the gold standard that we're aiming at. And it was really new to say, no, we actually want the uncertainty. I think there was also a conceptual shift. Another of Honov's big interests has been in the time symmetry of quantum mechanics.

So like classical physics, all of quantum mechanics, leaving aside weak interactions, which isn't really fundamental to quantum mechanics, is time reversal invariant, meaning it is just as easy or difficult to predict the future from my present observations as to retradict the past. There's no mathematical difference between the two. except we're also taught in quantum mechanics that there's measurement, and that measurement is this mystical event that we never define really clearly, but that breaks the time symmetry,

because after a measurement, the state is completely reset. There's no experimental evidence whatsoever that we need to think of that as breaking time reversal symmetry. There's no reason when I find a particle at some position that I have to use that new state to calculate the future wave function, but something different to calculate the past. And yet that's what we were all taught. And Yarkir has been struggling for decades

with the question of how to make sense of the symmetry of quantum mechanics. So he really wanted to say, if I know what a system was doing at T equals zero and I know what a system is doing at T equals one, both of those pieces of information should be equally useful to tell me what was going on at T equals 0.5.

And it's weak measurement that allowed him to mathematics, dramatically showed that that was true. So to Yakir, I spoke to him on the podcast. I think I have the first podcast with him ever. Really? Maybe the only one. I don't know why he said yes to me, maybe.

I got him on a good day. And so he told me that that implies to him that the future informs the past. Ontologically, metaphysically, whatever that means. Yeah, I find that difficult. Yakir is much smarter than I am, so I don't want to say he's wrong.

But I will say that that to my mind is the religious side of his belief. You know, as I said, we separate out the formalism that we can prove from what we argue about what it teaches us about reality. And the second is kind of a little more subjective at first and, you know, harder to make rigorous. So I find it really interesting that that's the conclusion he leaps to from his equations. As far as you know, am I mischaracterizing him, or have you also heard this from them?

No, I think that's reasonable. And there are, as I said, many people who are very, very seriously thinking about this idea of retro causality that the past affects the present. I don't know what the arrow of time is. That's one of the deepest mysteries in physics. It in some sense predates quantum mechanics.

It becomes maybe more dramatic with quantum mechanics. I think it's something fascinating to think about. So... Oh, sorry. I was like a professor. It was like a student in the classroom. Sir, I was going to say... Much more polite than the students, but aren't sure.

I was going to say then, just connecting back to our earlier part, do you then imagine that there are several arrows of time, that time sub one, time sub two, and that some could go forward, some can go backward? I certainly think that's possible in a laboratory scale setting. I think for the universe, as far as we can tell, there's one arrow of time, but there are different ways to define it.

as you say, we have working definitions to grope towards something. So, you know, there's the second law of thermodynamics. Which direction does entropy increase? And, okay, it increases in the same direction as you and I know time evolves. Is that a coincidence, or can you prove that once you have the second law, the psychological hour of time must follow from it? I'm tempted to say the latter, but I've had trouble actually showing rigorously how that would occur. We don't currently believe that the universe is supposed to stop expanding and collapse on itself.

we can imagine universes that were going to do that. And there were speculations that when the universe turned around, that cosmological arrow of time reversing would also reverse the entropy and psychological arrows. So you could imagine saying, oh, it'll look really weird when the universe turns around and people all realize they're heading towards the big crunch. And someone else saying, they're never going to realize that. Because for them, time will be running backwards too. So we all think the universe is expanding,

and there's a law of physics that shows that what feels future to you is always the expanding universe. We don't know that that's true, and we don't think it's the real universe anyway. What I do think is interesting is that even classically, to understand the origin of the thermodynamic arrow of time, seems to require putting it in by hand.

And people gloss over that when they teach thermodynamic, but it's the best of our current understanding, I would say, that all we can do is say the reason time is moving in one direction now is because we live in a universe that happened to start in this particular way. And if it hadn't started that particular way, maybe we wouldn't have that arrow of time, but we can go back and simplify the explanation. And that's what physics usually does, right?

You know, we show you can explain this effect by postulating one axiom, but I can't tell you where the axiom came from. I can't tell you why the Big Bang happened. But if we just assume that one thing, the rest follows. There are people who argue quite reasonably, maybe the universe isn't set just by one particular past boundary condition 15 billion years ago or whatever it is,

but by some other boundary condition in the future. Why is that any less likely? And if our universe is conditioned, both by how it has to start by some law of physics I don't know yet, and how it has to end by some other law I don't know, then that does guarantee

a lot of things about the middle, and in that sense, that future condition would be constraining what we're doing right now. That's really not crazy, but I don't know where it would come from. With Heisenberg's uncertainty,

we talked about momentum and position, but there's obviously the conjugate side of other variables, and you've talked about negative time, So is there anything about one of those four other times or eight other times or what have you that could potentially be negative that would allow you to borrow energy? I mean, sorry, not borrow energy, but violate the Heisenberg uncertainty in some other manner? I'm not sure what it means to borrow something to violate the uncertainty principle there.

I mean, honestly, you know, I was giving you this picture of how you can think of photons traveling through atoms by temporarily giving their energy to the atom and taking it back. When you're very far off resonance, like light going through a piece of glass that's essentially completely transparent, people do often describe that through the uncertainty principle, saying that, well, you can't violate energy conservation permanently, but you can temporarily borrow a little energy for time less than H bar over Delta E. And that actually gives you a pretty good understanding of the timescale for propagation far from resonance, not on resonance. I don't see how any of these uncertainty principles can help you, though, with the, the, negative time. What's a misconception that many graduate students have when they come to you,

or physics students I'm talking about, about physics, that you have to dispel constantly? I'm not talking about undergrads. Undergrads have various ideas and high school students, of course. I mean, what's something that is taught that you say, that's not taught correctly, and when it comes to me, I have to re-teach it? I mean, there are a lot of, there are a lot of technical things. that one wants to go over more carefully, depending on what field one's in, I'd say the bigger issue just has to do with the role of experiment,

how to think about the interplay between theory and experiment. I don't like the way that we teach students about experimental physics. They come out with a very strange, mechanistic view of what it means to write a lab report and report what you are supposed to have seen.

It's probably not specific to experiments. True in theory as well, because we teach people the stuff that we already understand really well. And it's natural to come out thinking my whole job is to just reproduce the right answer. And of course, once you're doing research, you don't know the right answer. And the important thing is to be skeptical of yourself and limit what your conclusions are and talk about the range of uncertainty. I'd say that's the harder thing. But these issues about measurement are probably

a good one as well. This idea that the ideal measurement is collapse. And whenever we have an uncertain measurement, it's just because our experiment isn't good enough.

I think these days we try to pull people beyond that and teach them instead that what the theory should do is model what measurements actually are in the real world, and every real measurement has some finite uncertainty. and there's a better formalism

that isn't taught in undergraduate quantum mechanics that's much more general and deals with that properly. You made headlines 10 years ago or so about showing where the photon went in the double-slid experiment, which is supposed to not be done, as you mentioned, you can't say what the photon,

what the particle is doing prior to a measurement, only when you've measured. That's right. But what did you actually show? Yeah, so I'm always a little worried about the wording of that experiment well, we did and why we did it, but I think it demonstrates a few interesting things. First of all, we can come back to this distinction between strong and weak measurement.

Send a photon through a double slit. It's going to hit this screen eventually. But along the way, what stops me from measuring exactly where the photon is? In principle, I can do that. The problem is usually when we measure where a photon is, we do that by absorbing the photon. Now it's never going to reach that screen. I just created a new screen a little earlier. You can instead imagine other non-destructive ways of measuring. it, but again, we know the uncertainty principle. We know that anything I can do to get good enough position resolution here is likely to disturb the momentum so much that it will change the pattern I see on the screen. So, experimentally, this was yet another application of these weak measurement ideas,

that we can measure on average where is the photon in this plane without disturbing it, let it continue along its way, and then ask, where is it later? If I found it here, where was it on average before? If I found it here, where was it on average before? And the motivation for this was actually a bit convoluted. One of the other things my students need to learn is that we cannot rule out hidden variable theories of quantum mechanics. Many people, when they're taught about EPR, are taught, we learned that there are no hidden variables. and that's not correct. We learned that there aren't local hidden variables, but in fact, since 1950, we've had a very good hidden variable theory that is predictionally indistinguishable from quantum mechanics due to David Bohm,

building on De Breuroy's ideas. And it's a dualistic theory of nature. It has particle wave duality explicitly and literally, meaning that there exists a wave and there also exists a particle and the particle rides along the wave. So every particle has a definite position and yet when you look at where the statistics

of where the particles end, they end up being described by the wave theory. So there's an interesting question. Can you actually measure those Bohmian trajectories where a given particle went? And with Howard Wiseman, our common collaborator,

realized, again, about 15, 20 years ago now, was that if you weakly measure the position of particles in this plane and then post-selected on where do they land in this plane. So you asked on average, where did a particle here come from? And you find here, and you connect those dots. And then you do it again in the next plane. On average, where does the particle here come from?

You connect those dots. you'd get many different trajectories depending on where you put that final selection and they would agree exactly with the trajectories in the bone model. Now, that's not a proof that the bone model is correct. It's just an interesting connection between measurable reality

once you understand weak measurements and these things in the bone model that people used to think were beyond the realm of direct observation. So it made it exciting to us that that was directly accepted, and that's what we actually did. A way that you can think about it without the metaphysical language

in terms of things that straight textbook quantum mechanical people know is that there's an operator in quantum mechanics that gives the flux, the number of particles per unit time traveling through a given region or even what direction they're traveling in. And if I have a double-slit wave function, maybe I can't ask exactly where is the particle, But I can ask, at each position, what is the net flux? Where is the probability density moving as a function of time?

And what we discovered is that we could directly measure that observable and that that observable is equal by construction to the momenta of the trajectories in BOMES model. So many people would say that BOMS model is already it's supposed to be consistent with quantum mechanics. It's experimentally indistinguishable. Some people say, so why would it be surprising that what you find is consistent with BOMian mechanics?

Wouldn't it also be correct to say it's just consistent with... Oh, I see. Pick your flavor. Right, sorry. So, of course, you're 100% right. At the end of the day, if we just measure where do the particles land on the screen, that's describable by straight quantum mechanics,

or honestly by Maxwell's equations in our optical experiment, or by Bomeon mechanics because it was built to give the same. same answers. That's guaranteed. But Bohmian mechanics adds something else to the story. It talks about where each individual particle was along the way, building up these trajectories that we always used to think could not be directly observed. Only the statistics were observable. So to most people, us included, it was surprising that there was a direct measurement with a sort of clear operational motivation that revealed those so-called hidden trajectories.

of the bone model, not just the prediction for the final state. Now, if that's true, do you think you, Professor Steinberg, can find a preferred reference frame? I don't think it's directly connected to the question of a preferred reference frame. The question in relativity of preferred reference frames is a really interesting one. First of all, the universe has a preferred reference frame. There is a rest frame of the cosmic microwave background. So there is a clear sense in which it's preferred. The laws of physics happen to behave in such a way

that they are the same in any other reference frame. The state of the universe happens not to be. There's a really interesting article again by John Bell, but on relativity, not on locality and his theory, arguing that our usual university treatment of relativity emphasizes the relativity aspect too much and the equivalence of different reference frames too much. And he would point out that it's entirely consistent

to think of there being a preferred reference frame and that in some ways maybe that's a cleaner way to think about it. That said, you could pick whichever reference frame you want it and call it preferred, so is it really preferred? I guess where I was going is that Tim Modlin, who is a reformed boean or a boean with an... Is that what he is? I know Tim a little bit, but not well enough.

Okay. He may say maybe I misread, or maybe I'm conflating someone else, that your experiment demonstrates is evidence for boeumian mechanics, and in his view, there's a preferred reference frame. So that's where I was going about. Okay.

So standard boeumian mechanics, first of all, is non-relativistic. So it has a preferred reference frame because we didn't move beyond that. Other people since then have tried to relativize it and we didn't use any of those more modern approaches. So in our case, there's a Newtonian preferred reference friend.

Also, I'd be really surprised if Tim thought our experiment could give any evidence for BOMian mechanics. I think he'd pretty adamantly say no experiment can give evidence for or against BOMian mechanics without giving evidence for or against quantum mechanics because they're operationally indistinguishable. You can imagine extensions of Bomeon mechanics that then deviate from, from textbook Copenhagen quantum mechanics. That would be different.

I feel like experiments do more than just test a theory. Experiments tell you which elements of the theory turn out to be important for describing the situations we can really get into. And that gives you intuition for which aspects of a theory you want to ascribe reality to. It's not a proof, but I think it guides us until we can get something more like a proof, or at least an Occam's razor. So I do think experiments like ours give more ammunition to the camp

that says, no, you should think of these trajectories as being real. It doesn't prove that. You don't have to. I'm still not at all convinced that I do. I liked Bomi and mechanics a lot when I first learned of it. I learned about some of its predictions

that were so strained. When I say predictions, again, I mean for these intermediate steps, what the trajectories are doing, that I said, I can't see that as a helpful view of reality, I'd be really surprised if that turned out to be the quote-unquote right description. And then later on, I saw more that made me think, all right, maybe I was too quick to jump to

conclusions, and it's still okay. But I'm certainly not adherent to BOMian mechanics. So I apologize, Tim. I didn't meet to put words in your mouth. I probably put words in your mouth. So those words are mine that I miss remember. I hope I'm remembering this part correctly. Okay. Did you go in physics in part because your dad asked you what an electron was and you couldn't answer? Yeah, I did tell someone this story. There's some truth to it. My dad was an electrical engineer, and unlike me, he was very focused on practical issues that I only grew to appreciate decades later. And the story I told is of him teaching me about electric circuits when I was quite little. And I don't know, at some point he must have needed to explain to me why. electrons flowed the way they did, and I remember him somehow alluding to the Pauley exclusion principle. The two electrons couldn't be in the same state at the same time.

And all I cared about is knowing why that was true and where that principle came from. And I think I disappointed him and that he didn't, I didn't let him explain the rest about his transistor to me because I just wanted to know that. And he couldn't answer that question. And what I didn't know at the time is that neither could physicists. And we can answer it mathematically, but why fundamentally? That remains the deep question. Well, decades later, what have you learned? What would you tell your dad now?

What a great question? What would I tell my dad now? So there's a mystery in quantum mechanics about the treatment of indistinguishable particles, and that's where the Pali Exclusion principle comes from. And it's also where superconductors, Bose-Einstein condensates, that we also work with in my lab come from.

and I don't think we have a very deep understanding of why it's the way it is. In three dimensions, we can show that particles have to either behave like photons and, quote, unquote, like falling into the same state and condensing and making things like laser beams or superconductors, or they have to forbid any two particles falling into the same state and make sure that one excludes the other from that state. There's a theorem known as the spin statistics theorem that shows that this is fundamentally related to the angular momentum of the particle. I kind of think that the formulations I've heard of that theorem are almost a little bit circular. You have to assume something about the structure

of field theory that I kind of think is as big an assumption as the conclusion of the theorem itself. That's often true. Theorums are often bidirectional, and it's a matter of taste. What do you consider the hypothesis and what do you consider the conclusion. But fundamentally, if you buy the theorem, what it says is that particles with half integral spin can't show up at the same place. They have to exclude themselves. Why are all electrons identical? Couldn't you imagine a universe that was just created with 18 billion electrons and each one had its own serial number? That's not how it works. the way we understand that mathematically now is to say particles are really just

excitations of a field. And there are many fields out there, and when I say there are a million electrons, what I mean is the energy stored in that field is 1 million units above absolute zero. And it's in that sense that the particles are truly indistinguishable. This thing about half-integral spin, though,

when we learn quantum mechanics, one of the first things we learn is that angular momentum is quantized in units of Planck's constant. It can be 10 to the minus 34 joules seconds, or it can be any multiple of that. And then it turns out that the first particle we were worrying about the electron violates that so-called rule, and it has half a unit of angular momentum intrinsically,

and you just need to accept that. And there's a real mystery about particles that behave that way. I think the way to sum it up is that, normal objects, if you rotate them 360 degrees, look exactly the same as before you rotated them. There's a sense in which particles like electrons look like they've undergone a funny flip after you rotate them 360 degrees,

and you need to rotate them 720 degrees to make them actually look the same as how they started. And it's that rotation that mathematically we call half integer spin. it's that rotation that means if you have two electrons and you exchange them, you're doing something that's a little bit different from exchanging two photons or other particles.

But like much of physics, it's something where we have the mathematical law and we don't really know to this day what underlies it. What's the largest open problem in quantum information? The largest open problem in quantum information I mean, quantum information means different things to different people these days. To me, what's most exciting about quantum information is not that we may one day get better computers. You know, that'll be really cool if it happens.

But to come back to my story about my father, I'm a physicist because I care about understanding what we've learned about the universe. And if we can make that useful along the way, that's really great. And if we can point the way and then hand it over to our friends in engineering or our friends in industry so much the better. right now you ask most people what's the biggest problem in quantum information they'll tell you about the biggest problems towards building quantum computers and I want to say that's

not quite the same thing so the field still has this foundational side by discovering the power of quantum information I think we've discovered new things about how to think about the universe and we've also discovered paths towards making better sensors

and better computers and so forth the practical problems are twofold. Actually building a large scale, reliable, fault-tolerant quantum computer. There are a lot of paths that have made amazing progress towards this goal, but actually achieving that fault tolerance while you scale it up remains a huge challenge. And there are promising ways to do it. We don't know how hard each of them will be, which ones will work. And there's a fundamental question, is there a law of physics we don't know about yet that will make it impossible. We'll come back to that in a second. The other practical question, I would say,

is if we had a large-scale good quantum computer, which problems would it be useful for? We don't know the answer to that yet either. We have a handful of problems, and people are working hard to answer, to come up with others, and people are making a lot of money claiming to have the answers to others where honestly, they have no evidence whatsoever that there's any quantum advantage. So in the practical scale, those are the two big issues. Make the thing work and figure out if it's good for anything, and if so, what? We know it's good for some things. In particular, we know that it's good for simulating other quantum systems. And I should stress to people outside physics world,

that sounds a bit like a cheap way out, saying, I've developed a device, and you're not going to be able to use it for anything interesting, but I can use it to study other devices like it. It feels like cheating, isn't it? Except the whole world is devices like it. You and I are devices like it. All of the antigens in our body are quantum machines.

And when we design things we care about, whether those are novel materials that have useful, properties, whether those are drugs, whether those are materials for carbon capture, whether they're classical computers, whether they're the kinds of measurement devices that allow us to test, you know, the state of concrete in a bridge, or what our brains are doing when we have some disorder or anything else, all of that comes down to calculating how some quantum system is going to behave. And we've gotten really good at doing that with classical computers, but there's a limit where it's just way, way beyond us.

If we can devise quantum computers that let us solve quantum mechanics problems, that is the fundamental problem we need to solve to do physics, chemistry, engineering, and so forth. So that will be of huge societal impact, even if that's the only useful thing that quantum computer ever does. But even some of those problems,

it's unclear. You know, people like to say the first application is going to be quantum chemistry allowing us to come up with new anode materials for batteries and new drugs. To my knowledge, we have no definitive evidence that that's even possible. We're still trying to figure that out.

So there's a lot to be done on that side. On the fundamental side, quantum mechanics, like any other physical theory, is a theory that has worked so far. It seems a little early to have the hubris to think that we're done. Every other time we thought we were done, we discovered.

That was a pretty good approximation, but actually it was an approximation to this more complete theory. So I think we should expect, we should hope, that there's more to discover out there. Maybe there isn't, maybe this is as close as we get

to the final theory, right? I don't know. But quantum mechanics is so good at predicting all of the things that it's predicted. You can't just go and do some other random quantum experiment and say,

oh look, he got it right again. Let me publish. more evidence that quantum mechanics is right. You have to be judicious in your choice of where might we expect it to break down when and if it does. And Bell's inequalities, to me, were the big example of that. Quantum mechanics made a prediction so strange that sane people who cared about the interpretation were saying in the 1960s, I need to check whether quantum mechanics is true as far as it takes to reach this outlandish conclusion. or whether that's where we'll see the breakdown.

People like John Clausor were surprised. He expected to show quantum mechanics was wrong, but he's a good scientist. He gave in to his experimental data and said, no, I was wrong. Quantum mechanics still seems to be correct. There are people out there now who say the new frontier is complexity. A lot of people might have said the size of a system.

We learn incorrectly that quantum mechanics is the theory of the microscopic world. Well, no, there's no way to draw that boundary cleanly. Even the founders of quantum mechanics didn't know how to draw it, but they didn't need to. They had dozens of orders of magnitude between the atomic scale and their world, and they just assumed that the right description

of the macroscopic world was kind of classical, and you had to just understand that there was some transition. But we keep pushing it, and trying to look for quantum effects with larger and larger systems, since the world seems classical to us, the standard common intuition is that the real world is classical

and somewhere along the line quantum mechanics is going to break down. It doesn't describe big, massive systems. That's the view that, for instance, Roger Penrose likes to take, and it's very well motivated because we know that quantum mechanics and our best theory of gravity,

general relativity, are not consistent the way we're used to writing them down. Something has, has to give. So many general relativists over the decades believed quantum mechanics would be shown to be wrong. That was the popular view among relativists when I was a grad student in the 1990s. By now, I'd say it's really flipped. Most of them come from a quantum mechanics background and tend to think that we have to approach the world quantum mechanically and modify gravity to accept that.

We don't know what the right answer is, but the kind of Penrose vision is that, is that that once subjects get large enough that gravity is important, we know the current theory is incomplete, and therefore something else will happen that maybe gives us our classical-seeming world. There's a contrary viewpoint that people like David Deutsch, equally brilliant, I would say, follow,

and people like LeVidemann, who we mentioned before, which is the many-worlds viewpoint or relative state interpretation, as its founder Hugh Everett described it, At its paired down, most simple level, what this really says is nothing about multiple universes. It says the Schrodinger equation is good enough. That's the law of physics that we've tested. This idea that there are a specific instance at which the Schrodinger equation breaks down and a coin flip occurs when we get one thing or another, we don't need that hypothesis.

The Schrodinger equation could describe everything. everything except the fact that you and I think we're having one discrete, well-defined experience now and that's where I usually take the cheap shot and say, the mystery then is not about the physics, the mystery is about consciousness. The thing we don't understand

is not the outcome of any experiment we've ever done in a lab or any observation we make about the universe. But the fact that our experience doesn't seem consistent with uncertainty. It seems to involve a definite state. In fact, if you think carefully enough about this so-called many-worlds theory,

you can understand that as well. You can resolve those paradoxes. So it could be that we're somehow experiencing one version of this big quantum superposition, and we don't need that breakdown at all. That's a possibility. But nowadays, thanks to quantum information, many people have taken a different tack.

And they've said maybe the large-scale world does become classical, not because things are so heavy that gravity is important, but because they become complex. And the argument I first heard made by Charlie Rakoff,

who's a computer scientist here, came down to asking how much information can it take to describe a system or to describe the universe? Quantum Mechanic says that as you make systems, larger and larger. I go from one electron to 10 electrons to 20, 30, 100 electrons. The amount of

information it would take to completely describe that system grows exponentially. And to Charlie, that was just unpalatable at a metaphysical level. He spent his life thinking about discrete information as a computer scientist, and he says, I can't believe that there exists an exponentially large amount of information. Therefore, I think this theory must be wrong. That's not evidence. That's, again, a quasi-religious feeling. But it's reasonable to say that's the frontier in which quantum mechanics has not been probed. Can we build a million-cubit quantum computer and actually have it last in superposition and produce some useful output? It's experimentally really, really challenging, but fundamentally there's no experimental law

that says you couldn't imagine doing a good enough job to get there. Wouldn't it be interesting if no matter how hard we tried, it turns out you can't do it. Once you build a system beyond a certain complexity, quantum mechanics breaks down. Maybe that's connected to gravity, maybe it's connected to consciousness, maybe it's its own fact.

We have no idea. Wildly speculative, right? There's no evidence to say this should happen, but it's one of the few frontiers that have not yet been probed. And one that even though it's incredibly expensive to get there, we now have good motivation, good practical, social, economic motivation to pursue. So that's one of the side effects of the race to a quantum computer.

We'll start seeing whether quantum mechanics really can be the appropriate description of a large-scale complex system. Are you in the minority among your colleagues about consciousness? and its role in reality or its relevance to physics? I have no idea whether consciousness is relevant to physics or not. I don't know what consciousness is. As I said, I'm a realist. I tend to believe that there's some stuff out there that should explain consciousness.

Whether we need quantum mechanics to explain that or not, I have no idea. There are folks like Henry Stapp and Roger Penrose who seem to think that's a reasonable leap to make. It's a leap of faith. I would say I'm in the minority of physicists in that I even entertain the question. Very few physicists even think about these interpretational questions of what should I think quantum mechanics tells us about the nature of the universe. They're happy to accept the rules given in the textbook. some point they're surprised, spooky action at a distance, this, that, and the other, they get over it, they do something practical. A small group of us spend some of our time, at least, you know, on the way to bed or in the shower, and thinking about motivations for new experiments, really wondering what it tells us. That became more popular with the advent of quantum information. It became more widely accepted, but it's still a small subset. And I'll say to me, this is something that's disappointing. I mean, I'm really excited by the developments that quantum information

has led to and by the prospect that quantum mechanics may give us new useful tools that, you know, everyone around the world can get excited about. But I'm even more excited about what it's taught us about the nature of reality and the fact that for a while it made quantum foundations a field with a newly recognized importance. And now that there's so much money and excitement, and rapid progress on the practical and industrial front. I go to conferences where I feel like I could have more and more colleagues asking these deep questions, and they've been co-opted. They've all had their heads turned to the God Mammon

and to saying the important issue right now is to build the computer. Obviously, we need people doing that, and I'm excited about what it'll mean for quantum simulators, maybe for other real world applications and for addressing this fundamental question. But less and less are they actually talking about it? And I'd like to see more people in physics departments talking about what are we still learning about the universe?

Yes, that's a great point. So many physicists that I speak to, especially mathematical physicists, will say that they went into this, or I ask them, well, what makes you interested in mathematical physics? They may say, most of the time, I'm interested in reality.

Then I say, okay, after probing and probing, does the math or the physics tell you about reality? They'll say, reality, I don't even know what that is. I don't know what that means. People like to say that, I don't know what so-and-so means. They say, all I know is that when I follow the formulas or I do this experiment, I get a click here, and it's correlated in the manner that the formulas say.

Yeah. Well, I do know a lot of people who do spend their time thinking about reality, and they come down on different sides. So I feel like to the extent that people thought about this in, let's say, the 80s and 90s, going back to the 60s to the 30s, whatever, they tended to say quantum mechanics gives me a mathematical object that describes as much as I know about a system or maybe as much as I can know about the system,

not what the system is actually doing, but as much as I can know about it. and from that I make probabilistic descriptions. And most of them, if you ask them, well, is it as much as you can know about it because that's all that's out there or because your measurements disturb it or because your knowledge is incomplete, most of them wouldn't have even known how to address that.

Many of them, like, you know, the people who were, you know, my senior idols when I was a grad student did seem to say, it's just a limitation on our knowledge. The wave function is not describing the state of reality, but it's describing what we know. I thought of myself as being very modern in that I said,

there is a reality out there, but we have to let go of classical notions. The reality is not balls and sticks and objects in particular positions. Apparently, the reality is just this wave function psi. I can't picture that very easily. It's a very strange reality, but that is the thing that exists. And my particular view of, you know, you sitting here and shadow is there and whatever, that's a product of how our bodies and our brains work. But the reality is Psi. And we have rules for how it changes. And I'll leave open the question of collapse.

You know, maybe at some point Psi changes and becomes a definite state. Maybe that never needs to happen. By the early 2000s, I discovered that the people who thought about this question much more deeply than I did, and for whom I have great respect, people like Rob Speckins and Terry Rudolph and the leaders, I would say, of modern foundations of quantum mechanics, almost uniformly disagreed with me. And they had swung back to the idea that the wave function is a description of the state of knowledge, and that our knowledge about the universe can only ever be incomplete. So Speckins in particular has a fascinating view of all this,

where he would like that to become the physical axiom, say, somehow what seems to define quantum mechanics is the fact that we never get complete information and if you could begin from the right quantification of how much information is it possible to have maybe that would give rise to the other aspects of the theory and then some of these people would like to say we can think about what the deeper

more complete description of reality would look like even though we're never capable of having that complete description we could describe it. Rob has a kind of toy model for a version you could imagine that reproduces some but not all of quantum mechanics. Other people seem to shy away and say,

no, that's all the information we can have because that's all the information that exists. The universe is just in a state of incomplete information, whatever that means. There are people who describe themselves as cubists, which is a pun that comes from the idea of quantum basianism

and Chris Fuchs at UMass is one of the leaders of this field, and again, a very deep thinker, but whenever I talk to him, he insists that he believes in some external reality, but when I ask him to explain to me what his picture of that reality is, I don't get a response that feels to me coherent, whether the problem is in the ear of the beholder or not, I can't tell you. But there is more and more this view that maybe the wave function is a description

of information and a state of knowledge and not a complete description of the universe and maybe there is more complete description and maybe there isn't. I don't know the answer to that. Where can people find out more about you and what are you working on? What excites you?

Where can people find out more about me? From my webpage, which links to a lot of the articles that we've written at a few semi-popular descriptions of those articles, What excites me these days? As always, the question of how can we think about the external world, which I think we've made a little sharper by focusing on how can we think about the history of a quantum system, what's the most you can say about the past of a quantum system,

and how does measurement influence these things? So those are the big questions. The particular experimental system that I've spent most of my, my career trying to move towards is atoms that we prepare in a Bose condensate a kind of atom laser and fire at a barrier that's just a sheet of light and asking what happens as the atoms traverse this tunnel barrier? We've not asked that just because it's a hundred-year-old question people argue about, but because we think it's an exciting way to approach this broader issue of how do you think about what the atom was doing

after I prepared it but before I found it. And most recently we've been working on a theory paper there. It's been delayed by a year or two, but I think it's about

to see the light of day and about to turn into experiment as well in our lab, I hope, which addresses the question of if measurement disturbs the system, can the mere act

of looking for a particle in a region where it's not supposed to be found give it an extra possibility to traverse that region. Can it enhance the probability of the particle making it all the way across? And we know in some sense the answer is yes, but asking what would that look like in the lab and how you do it raised a whole bunch of exciting questions. So for me, this went back to my idea of weakly measuring a particle while it traverses this tunnel barrier.

So without disturbing the tunneling, tweak it, let it interact with some clock hands, so that if I see the particle on the far side, I can say that was a particle that was crossing the barrier, what did it do to the clock end? And average that to see how long did it spend in the barrier? I have been talking about doing that experiment for almost 30 years now. About 25 years ago, I was at a conference in Korea, where I explained the basic idea and how we planned

to build an apparatus to address these things. And Bill Phillips was also at that conference, and he was in the audience. and Bill is an amazing scientist in that he generates questions more rapidly and more pointedly than anyone else I know. And he said, why measure it gently? Why not just strongly measure? Is the particle in the barrier or not? And I said, yes, of course, I've thought about that. But if you measure, are you in the barrier or not, you can only get two answers, yes or no. and if you get yes, then you discover, that's a particle in a barrier.

If you prepare a particle in a given region, it's guaranteed to have enough energy to be there. That turns out to be very clear from quantum mechanics. So it's weird. Quantum mechanically, I can send a particle in towards this hill with insufficient energy to surmount the hill, and yet, at any given time, there is some probability for the particle to be inside.

However, if I ever find the particle inside, I'm guaranteed to have given it enough energy to exist there legally. So I explained a bill, that's not what we want to do. And he said, yeah, obviously I know all that. He always asks questions where he knows at least the first half of the answer. But what's interesting, he said, where did the energy come from? How is it that your measurement is guaranteed to give it the energy? And where does that come down?

And I vaguely answered the question for one model of how you might do a measurement. It seemed kind of straightforward. Terry Rudolph pointed us towards a more complicated example where I hand waved a little more vehemently, and I'm no longer sure I really like the answer that I gave back at the time. And just about five years ago,

we started thinking about this much more carefully with my then student, David Spearing, which is now a post-talk at MIT. And we found something interesting. We found that there was a way to get this perfect information, not all of the time, to get it probabilistically.

And it turns out, this builds on what we were already doing in the lab, where we use these weak magnetic fields to gently probe the atom. There's a funny feature quantum mechanically, which is that there are things called orthogonal states, states that you can distinguish perfectly. So we're able to prepare our atoms

in a particular state, basically an angular momentum state, actually the kind of state that's used to help define the second when I was talking about atomic clocks earlier. And although there's uncertainty in most quantum measurements, one thing we can do is look for the particle in the sort of diametrically opposed state and say, I know it's not there. The one thing I know with certainty, I'll never find the particle there. And if anything happens to this particle, tilt it a little bit. Suddenly there's a finite probability to find it in that opposite state.

But if you flip that around, you think about the contrapositive, or the converse or something, what it means is that if I ever find the particle in that distinct state, I know something must have disturbed it with certainty. So that was our trick to do a measurement that tells me with certainty, hey, that particle must have been in the barrier back whenever. And I asked David to do some simulations to show, would this actually have the effect of collapsing, the particle, giving it enough energy to show up on the far side. And if so, let's go into the lab and do it and show that the mere act of looking at the particle really did enhance the transmission. And what he found is that only under certain conditions did this work. And we grew to understand this pretty quickly. You have to do the measurement quickly. This magnetic field can't just be on

all the time as it is in our current experiments. Because if it were, then, finding the particle in that diametrically opposed state would only tell me, oh, that Adam must have seen the magnetic field at some point in its history. It doesn't show me the particle was in the barrier now or was in the barrier at this time 10 nanoseconds ago. It shows me at some point it felt the barrier. That, we realized, is not sufficient to collapse the particle. You need to know

there's some time at which the particle was definitely in the barrier. So you need to turn this field on and off quickly enough that the particle doesn't have the chance to leak back out before the measurement is done. So by probing that time scale, so far theoretically, soon I hope experimentally, we're able to look at how quickly does a measurement need to occur to collapse a particle, which I think is really pretty deep and striking. And from the point of view of tunneling, it actually reveals a new timescale there. It tells us, while a is tunneling through a barrier, if I look for it somewhere inside, how long would it take on average for it to get back out of the barrier from that point? And we found a timescale that

does not seem to be equal to any of the other timescales we knew other folks had defined to describe tunneling. So we feel that we've discovered a new timescale that describes something in the interplay between tunneling and quantum measurement. That's my current big excitement. I want to do that experiment. Wasn't there an experiment where you measured something with the Larmer clock, if I'm pronouncing that correctly? You are. And then some other team measured it with an ato clock or an atoll clock, and then they had

something that was instantaneous, whereas you had something that was finite but positive. Yep. So again, tunneling times are this controversy that go back to 1932. So tunneling is one of these phenomena that was basically predicted more or less the same year as Schrodinger's equation came out. and within at most six years people were calculating how fast should it be. And those answers lay dormant for decades because people didn't understand how to talk about them. Because again, they predicted things faster than light.

And when in the 1990s I alluded to the fact that we came to understand faster than light effects better, that's really what I meant, is through the lens of tunneling, more and more groups started asking, how should you think of how long a particle is in the forbidden region? Is it ever in the forbidden region? The answer is yes, it is in this classically forbidden region. But we wanted to know, do transmitted and reflected particles, spend the same amount of time, or is there a difference in those trajectories? And that's the thing that we really couldn't put our fingers on

without the tool of weak measurement that lets us really do that. So, finally, in 2019 or so, we successfully did this weak measurement experiment to ask how long are just the transmitted atoms inside this tunnel barrier. And we found a result that agrees with what we expect from weak measurement theory, which is also known as the Larmer Clock due to Marcus Burekir's pioneering work there. The Atto Clock is work that have been going on in parallel pioneered by Urs Le Keller, in Switzerland. Also looking at tunneling

in a very different time scale, a very different physical situation, and a very different measurement technique. And as I've been hinting, when we try to understand times, it leads people to ask, well, let's be careful how do you define time. We'd better define it by

imagining how you measure it. And since you could imagine different measurements, we end up with different definitions. By now, I think we mostly understand that those definitions break into a few subgroups, that there are a few certain kinds of timescale that describe tunneling, certain clocks are good for measuring one, certain clocks are good for measuring another. The fact that Ursula's experiments come out in the outer second regime and ours in the millisecond regime is not a disagreement. It's that she's studying

things that are moving at, you know, 100 to the speed of light, and we're measuring things that move at three millimeters per second, or just in different regimes. So we could have the same formula and still differ by 15 orders of magnitude. That would be fine. However, she tended to find results consistent with zero. I find that surprising. I think they're consistent with zero because of error bars and other people have since analyzed complicated issues in those experiments that can switch things around.

But I also think that the time they're measuring is fundamentally related to the arrival time of a wave packet, where does the peak show up? And honestly, we did an experiment to demonstrate that in 1993. We already know the answer to that. It's given by the group delay, even if the group delay is faster than light, and that's well established.

It was news to the ultra-fast laser community, well, to some of them. Actually, Ference Krause, shared one of the Nobel Prizes in that community, did a follow-up to our experiment, in 94 or 95. So some of them should have known. But if that's all they reproduce,

I think that was known. Whereas our experiment is measuring not when does the peak show up, but how long was it actually spending inside that forbidden region? And that's a different quantity, and they're not even mathematically exactly equal. So it's all right if those two disagree. Now the final question. Yeah.

People have been watching now for probably over two hours, I assume. I don't know if everyone's been watching for two hours. We'll see. So they've absorbed the majority of this, and I know that this has been a through line throughout, what is time? I'm going to ask you again, even though they've listened,

and you can just give an essay summary. What is time? Was it St. Augustine who said, I can tell you what time is if you don't ask, but once you ask me, I can't answer. Mathematically, time in both classical physics and quantum physics is a, a parameter. Things exist at all times, and I can ask what the value of any quantity, observable,

whatever is, at any given time. It's like complexity due to space time and relativity, but it doesn't change the fundamental issue there. Time, of course, is different from space for us in that we inexorably travel in one direction in time, and we don't know why. We might look at a lot. We might look for a new law of physics that explains why that is. We might look for boundary conditions that say it could have been different, but we happen to live in a universe where time is moving in this direction. We can also look quantum mechanically for something even stranger, a situation where the universe is not evolving in time. Nothing is changing in time. And there are good reasons to think that that would be a good quantum mechanical description of the universe, leaving out for the time being the

Big Bang, which we know breaks this symmetry. And there are approaches that can yield the sort of illusion of time in the sense that everything is uncertain, but everything is correlated. That part of my wave function is sitting here now talking to you, and part of my wave function is still back in bed this morning. And that's all right, because if the part of my wave function that's back in bed, in bed this morning, suddenly woke up and decided to check where you were and called you on your cell phone, it would discover that you were also back in bed, and the part of me now reaches out to you, and any one part of me that's conscious sees things that are consistent with that particular time. There are different formalisms to describe how this might arise, but I'd say it remains one of the

deep mysteries of physics. So you mentioned Bill, Bill that asked questions great. Yes. What is a question someone asked you that you thought you knew the answer, then as you started explaining it, you realized only then that I actually don't know the answer. Well, this happens all the time

and all sorts of little technical issues, things that I've taught to graduate courses for decades, and no one asked me a hard enough question to make me stop. The experiment I was telling you about, about how long atoms spend in photons, that would have been one.

Atoms spent in photons, photon spent in atoms, I probably would have answered that one incorrectly. And there are many. I mean, I think to be doing interesting science, you should always be at the level of asking yourself questions about things you thought you knew, but questions that go beyond what you've asked before that lead you to have to think a little bit harder.

But I'd say the most exciting one is about what we really learned from Bell's inequalities. And as I said, you know, that's fundamentally the kind of experimentally testable foundations question that drove me to stay in physics. the way we talk about Bell's inequalities has changed over time and I would usually tell students

what we learn from Bell's inequalities is that, or from the violation, the experimental violation of Bell's inequalities, is that the world we live in is not local, that you cannot describe what happens to you and what happens to me independently and still have a complete description of reality.

And that's pretty shocking. And as I say, you know, seems to be experimentally borne out. I was reminded recently that a lot of brilliant people disagree with this. And Gilles Brasser, who was the recent winner of the Turing Medal, along with Charlie Bennett, was recently giving us a talk in which he explained that he thinks the rest of us are all wrong and that in fact he can prove that the world is local. And while Bell's inequalities have been wrong, violated, they do not disprove what he would describe as Einstein's notion of locality. They only

disprove this much more stringent notion of locality that Bell introduced. And this goes back to a brilliant paper by David Deutsch, whom I mentioned before, and Patrick Hayden, who I don't think I've mentioned before, that makes this argument that you can understand EPR, Einstein-Pedal-Padolski-Rosin correlations and violations of Bell inequalities without needing to resort to thinking about information ever traveling faster than light. And mathematically, it's a very beautiful paper. Interpretationally, every few years, I have to go back and try again to see what are they really saying about the nature of reality. And I don't know. I don't know if when I teach students about Bell's inequalities, I'm giving them the right picture or not. So there's one thing that I think many of us

need to go back and keep thinking about more deeply. Has your work shown that quantum mechanical objects have definite values of position prior to be measured? No. It seems like it because of the weak measurement and the which way measurement reveals an average. So we've shown that there is a sense in which you can track average positions look at their correlations, that gives a picture that agrees with the definite positions, Bohm would say, are real. But Bohm was designed mathematically to agree with quantum mechanics. Our measurement is fundamentally measuring this flux operator that exists in quantum mechanics. The fact that those quantities are equal does not prove that you should think of this one is real

or that one is real. And in particular, since we know that we're averaging over a distribution, you can imagine many different theories that have different trajectories that are certain or uncertain, but agree with that average. So, no, I certainly don't think we have an experiment that proves that anything is real. I think what we're trying to do is keep reminding people that the jury is out, and there are seemingly conflicting views of reality that are all consistent right now with the formalism that we have.

but also that there are measurable quantities that come out of some of these formalisms or out of weak measurement theory that seem to be so universal that we're tempted to say they're at least pointing us towards the deeper theory of what's really out there. If there is some deeper theory,

maybe it's something that reflects some of these quantities and that's what we should be looking for. But those are hints. Those aren't rigorous proofs of anything. Professor, thank you. Thank you. It's always fun to talk about these questions. I'm sure I'm going to regret something or other. I didn't think to tell you, but you asked a lot of great questions.

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