Part 8! What is real in quantum mechanics, and what are mere mathematical tricks? Can the probability waves be real, and what would that mean? What is Pilot-Wave theory? I discuss these questions and more in today’s Ask a Spaceman!

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EPISODE TRANSCRIPTION (AUTO-GENERATED)

What is real and what is merely a mathematical trick. That seems to me to be the central question, the real heart of these explorations into the meaning of quantum mechanics. I first asked this question. I don't know how many episodes ago it's It's been a long time. We've been on this journey for quite a while and and as we explored this question that once we get quantum mechanics, we start debating What does quantum mechanics teach us about reality? What is actually going on? Can we describe the physical processes happening in the subatomic world, or is this all just a series of mathematical tricks? And we actually don't know and we can still get results, but we can't actually derive meaning from it. We saw how this central question led to the major split between the very founders of quantum mechanics, with people like Heisenberg on one side saying, it's all mathematical trickery, don't worry about the details.

It's impossible to visualize or explain. What's actually happening in subatomic process is it's impossible to explain how entanglement actually works. It's impossible to explain how quantum quantum jumps actually work. It's impossible to explain how collapse of the wave function actually works, so don't sweat it because it's so far outside of our everyday experience. Just do the math because you get results right. And on the other side, you have people like Schroedinger saying that we need to focus on the real. Otherwise, we're not understanding subatomic physics. We're just developing a set of tools that allow us to make predictions. But that doesn't lead to any revelation. It doesn't lead to any deeper insight. We just have. Well, we just have mechanics. We just have tools for getting the job done without knowing what the job is and that we need to focus on the real. Ladies and gentlemen, we are now eight episodes deep into this discussion of quantum mechanics. I want you to know that this is by no means a complete or exhaustive analysis of quantum mechanics that would take its own.

Ask a Quantum Mechanic podcast show in several decades of episodes. But I hope that I've provided at least a high level overview of why quantum mechanics see so challenging and also fun and also mysterious and also spooky and also complex and also beautiful. There. There really is a lot of beauty in quantum mechanics. The fundamental postulates that well breaking everything we know about classical physics in the microscopic world are relatively straightforward. Remember that episode months ago we were so young? Then, if we're carefree, we hadn't worried about all these interpretations yet. And we just got to learn about the postulates of quantum mechanics and the actual mathematical underpinnings of the theory that make it so successful that make it agree with experiment. The math there that those postulates lead into the math and the actual mathematics of quantum mechanics is actually pretty simple. It it's college level mathematics and and the mathematics can even be taught in high school if we wanted to.

I know back in the day, Heisenberg's Matrix mechanics approach, uh, seemed really crazy and out there and unfamiliar. Nowadays it's it's standard. Every physicist is trained in linear algebra in matrix methods, and and when you do that, the mechanics of quantum mechanics become second nature. The math, certainly in quantum mechanics, is far easier than the math behind general relativity or quantum field theory. From firsthand experience, I can tell you that the math of quantum mechanics quickly becomes natural and intuitive and dang it, you can solve a whole lot of problems with it. But when you stare at those equations in those quiet moments and you get away from the current problem, you're trying to solve the current experiment you're trying to verify, and you just sit there quietly and you stare at the equations. The equations stare back at you, and you can't help but wonder what is real and what is merely a mathematical trick.

What does nature actually do when I write down the measurement operation in quantum mechanics? What's actually happening when I describe a a quantum jump from one energy state to another what's actually happening when I write down the equation that describes the entanglement of two particles in their subsequent evolution? What's actually happening? Do we have a grasp on subatomic reality, or do we just have a series of equations that allow us to solve problems and make predictions? Now you might be tempted to throw your hands up and say, I don't know. It's not my problem. Paul Dura, one of the founders of quantum mechanics, did not feature much in this story. He wrote a foundational textbook on quantum mechanics to help teach the next generation. Uh, he was definitely part of the Copenhagen school, although he had some pretty cool ideas of his own that we'll explore later but definitely was a fan of just doing the math, he said.

Quote The interpretation of quantum mechanics has been dealt with by many authors, and I do not want to discuss it here. I want to deal with more fundamental things now. That's a pretty sassy approach. If you ask me saying, Oh, the actual interpretation of what is real is somehow less fundamental than the mathematics. And I suppose from a purely mathematical point of view, that's correct. Like who cares what nature does? We are trying to discover deep truths of logic and reason, and Paul Dra was a master of mathematical physics. So it's not surprising, he said, that any mathematicians out there in the audience probably agree with the same sentiment. But I'm not a mathematician, OK, I'm a physicist. I do care about what the universe is actually doing, and I don't want just a simple set of rules. I wanna know what's going on. I'm curious. How how does a quantum jump work. I want to envision it. I wanna think about it.

I wanna I wanna feel it. You know, in my soul what a quantum jump is. And when I stare at those equations, they stare back at me. Maybe we have an escape hatch out of all this, maybe quantum mechanics isn't correct. Maybe it's simply wrong, but we can't take that escape hatch our understanding of quantum mechanics that's behind so much technology in the modern world. Take away experiments and laboratories. The semiconductors in your cell phone that are letting you listen to this episode right now are powered by our knowledge of quantum mechanics. If we did not understand quantum mechanics, then the semiconductor wouldn't work. Lasers wouldn't work. Nuclear power wouldn't work literally. All of chemistry wouldn't work. If you wanna say quantum mechanics is wrong, then you're challenging nuclear power, semiconductors, lasers and all of chemistry and more.

Something like 25% of the gross domestic product of Europe and North America is driven by our knowledge of quantum mechanics. You can't escape the reality even though we don't know what the reality is. Despite our best attempts to prove quantum mechanics wrong for over a century. It just keeps showing up, like those slow moving killers in scary movies. You think you've found a way out in a in a way to to hide and then it just like they just show up. They just don't stop. Run as fast as you want. Quantum mechanics is always going to get you OK, so maybe it's not incorrect. Incorrect. Maybe it's just incomplete. Maybe quantum mechanics is missing something. This was Einstein's main point, he said. All of quantum mechanics is mathematical trickery. We have the signs of this mathematical trickery with these weird things, like uncertainty and probabilities and non locality in the form of entanglement. These are signs telling us that we do not yet have a fundamental theory of the subatomic world and that we're just not thinking hard enough.

And if we do some more digging, ask the right questions in the right way. At the right time, the real truth of quantum mechanics of the subatomic world will reveal itself to us. We'll have quantum mechanics 2.0 and we can put away uncertainty, put away probabilities, put away the measurement problem. Heck, even put away entanglement we'll have a deeper, more fundamental theory that will appear sensible and real, and we can talk about it over coffee without sweating. We can rest easy and put this nasty century of quantum mechanics based thinking behind us. That was Einstein's argument. From the very beginning, he said. We're missing something. And so from the very beginning, people tried to find a deeper version of quantum mechanics. Is there something in there some subatomic process, Some thought, some idea. Some equation that will take away all the nasty bits of quantum mechanics and replace it with something that we can wrap our minds around.

We can describe with words and little diagrams in kindergarten books of what's happening in the subatomic world, because that is one big thing that quantum mechanics continues to fail at again and again, which is actually describing what's happening. Quantum mechanics is great at saying what happens, but it doesn't say how it happens in there. It stands alone from every other theory of physics, every other theory of physics. I can say this is how it works, not just Here's the result. Here's the result you'll get in your experiment. Here's my prediction But also here's how this process unfolds. Not so with quantum mechanics. So from the very beginning, people tried to find loopholes, shortcuts, new ideas to try to go deeper than quantum mechanics. One of these branches of lines of thinking relied on hidden variables, which we've met before that what appears to us in our experiments as probabilistic and non deterministic and nonlocal.

And all this could be explained if the subatomic particles of our world actually carried around with them secret information that told them what to do. And if we had access to that secret information, if we could read that secret code, we would reveal a normal universe. But just at a tiny scale that every particle has a little notes, a list of instructions from headquarters of what to do. And it's because we don't have access to that hidden knowledge that things appear to us to be random and nonlocal and and measurement issues and all the rest. So the quest was on instigated by Einstein, who felt like this was a promising direction, saying, Maybe we should focus on finding more information about the subatomic world. Maybe we need to broaden our thinking beyond Heisenberg and even Schroedinger. Maybe there's more to the story. Maybe this book that we're carrying around called Quantum Mechanics doesn't make sense because we're missing a few chapters.

One of the first attempts to go beyond regular quantum mechanics actually started with Louis Deroy or de broccoli. If you're feeling like it, you know the guy that proposed the whole maybe matter, has waves to idea and really kick started the modern quantum movement. He developed the first of what we call these hidden variable theories of quantum mechanics that underneath all the probabilities and the messiness and uncertainty and non locality and everything else that gives you a headache about quantum manics. Deep down there's a very clean, very classical description of nature where everything is deterministic, where you know exactly what the future will bring. You know exactly what happens during the process of measurement. You know exactly what happens when you separate two particles where we can recover some classical music. If we dig deep enough into our death metal tunes, we can find something familiar. Debrox looked at the wave particle duality of nature and took a different approach than the standard Copenhagen interpretation remember, The Copenhagen interpretation said the wave in wave particle duality when it comes to matter, is merely a mathematical trick for calculating probabilities that the particles were real particles existed.

We just couldn't tell where they were gonna go, what they were gonna do until we actually made a measurement. We could give a range of probabilities like, OK, there's a blob over here of where the particle might be with high degrees of certainty and and less certain over here and like, almost definitely not over there. And that was the wave function. The Schrodinger wave function. The wave component of matter just tells us where we're gonna find matter the next time we look for it. But the wave itself wasn't real. It wasn't a physical object that you could hold in your hand and whisper to at night, you know, and cuddle on a rainy day. The wave is just a mathematical trick, Deroy said. Something else, He said, that particles exist in our real and the waves associated with them also exist and are also real. That the waves were a separate entity that evolved in their own rights. Did their own thing followed completely totally deterministic paths.

Normal classical physical waves propagating throughout the universe. And doing so according to the Schroedinger equation. The Schroen equation says what matter? Waves do, how they change in time. And so these waves exist. They are real, they evolve, and the waves tell the particles where to go. So you have this idea that there's a particle traveling in the Copenhagen interpretation. You don't get to know what the particle is doing and until you play peekaboo and look for it. Then its wave function collapses, and it appears somewhere in this idea by Deroy, that electron that is, moving that subatomic particle that is moving it has a wave associated with it. One particle, one wave. They go together like twins. The wave propagates outward. It has a physical, real existence, and the information in that wave tells the particle where to eventually go. So if we could somehow dig in deeper and understand the evolution of the wave, we would be able to predict where the particle could go.

Like if there's a ship adrift in the ocean and a wave passes by, the wave carries the particle along with it. In this model, everything is deterministic. The waves move as waves are want to do. They are propagating there, moving there, doing their thing. And then the particles just do what they're told. The waves interact with each other, they propagate the move forward. And then they're like, All right, particle, um, you're gonna go here and then go over here like Google Maps is gonna say, you're gonna take a left here. Uh, and then when you reach the second stoplight, uh, you're gonna take a right. It it the waves tell the particles what to do. But but the true locations of the particles are hidden from us. We don't get to follow the exact path of the particle until the end of our experiment. This way, the probabilities of quantum mechanics are still maintained because the probabilities are an experimental fact of nature.

You can't get around the probabilities. So how do you fold in a purely deterministic way of particles moving like we see with this idea of de broy and end up with probabilities. The only way to reconcile those two because those two don't go together because the waves know what they're doing, and the waves are telling the particles what to do. But then somehow we don't know what the particles are doing. There has to be a conspiracy, deRoy said, that the waves hide the particle motions from us. The waves move around, do their thing, and they tell the particles what to do. But they tell it in secret. It's hidden from our view. It's hidden information. It's a hidden variable where the variable itself is the location of the particle. It's only when the experiment is over and the particle has finally landed somewhere and registered on a detector. Do we get to reveal that information?

That's the only way to make this work to have both a deterministic set of equations that govern reality but then also acknowledge the fact that we get probabilities and randomness in our actual experiments, this interpretation of quantum mechanics And in even though I want to say, even though it sounds like a completely new theory, it truly is an interpretation because it's designed to give all the exact same experimental results as any other. Interpretation of quantum mechanics was eventually dropped by Deroy, and it's hard to tell from the experimental record either. He changed his mind and picked up the Copenhagen interpretation because he just thought this was, you know, an idea that sounded good on paper. But once he started flushing out, couldn't make any sense or because Neil's Moore bullied him into it. We'll never quite know decades later in the next generation of quantum mechanics, when they came around was picked up by another physicist, David Boum.

And so this idea has various names pilot wave theory, bom mechanics, Debrox bom theory and, truly, truly, this idea of Pilot Wave theory, or bom and mechanics has some nice benefits. For one, it includes patreon patreon dot com slash PM. Sutter is your way to not hide how much you like and support the show. You can make it known to the entire world, and I thank you for your support. That's patreon dot com slash PM Sutter. One of the biggest benefits of Pilot Wave theory is that there are no actual uncertainties in the universe. Remember, these interpretations of quantum mechanics are deciding about what's real and what's merely a mathematical trick. In the Copenhagen interpretation, it says that the uncertainties are real. This is a fact. This is a feature of our universe. We don't know how it works. Don't ask us that, but it just uncertainties are real. All right. You can't measure anything. Precisely. You never know where a particle exactly is gonna go you but it But it happens because it's real.

In pilot wave theory, it says, Yeah, yeah, yeah, yeah, There are uncertainties in our measurements, but that's very different from reality itself being uncertain. Instead, the uncertainty flows from the fact that the particle's true position is hidden from us, even though it really has a true position. If you had some godlike superpower, you would see a little particle down there doing its little particle thing, zigzagging all around doing whatever the wave is telling it to do. But we don't have those godlike superpowers. And so we're left to do the best we can, which is the appearance of uncertainty, but not the reality of it. That's the big advantage of pilot wave theory. It moves the uncertainties and probabilities that are inherent in quantum mechanics and moves them away from reality into mere mathematical trickery because reality is hidden obscured from us. We're missing those pages in the Book of Subatomic physics.

And if we had access to those pages, we would be able to see a purely deterministic, purely non probabilistic world, and everything would be sane again. If you listen carefully to the death metal, you can hear a little bit of Buck playing in the background. Another big benefit of pilot wave theory is that there's no measurement problem anymore. Remember, the measurement problem happened when quantum systems evolve one way, when we're not looking the Schrodinger equation and another when we are the collapse of the wave function In pilot wave theory, there's always a wave and always a particle. Both are real objects. The wave doesn't collapse because it's just like a sound wave or a water wave that just goes from place to place. And the particle is always there, just going from place to place. Every particle has a wave associated with it. There's no collapse of the wave function because the wave is just there. Everywhere where you have a particle, there's also a wave associated with it, and the wave is always telling the particle what to do. And when you start broadening this perspective, it gets really, really fun because you realize that every particle has its own wave associated with it, even the particles inside your body.

So the act of measurement is really just all these waves interacting with each other and telling their little particles what to do. And so if we look at that measurement process, what does measurement actually entail? Let's say an electron hits a screen. Well, the wave associated the pilot wave associated with the electron interacts with the pilot wave associated with the detector, which interacts with the pilot wave associated with the electrons flowing down the back of the wire, uh, up to the screen, which is associated with the waves associated with the photons leaping into my eyeballs and all the waves of all the particles inside my brain. And what happens when quantum mechanical ways meet each other? Well, everybody's favorite word entanglement. This show is sponsored by better help. One of the most awesome things about physics is that it's like a user manual for the universe. You can literally use it to predict the future Now. Now humans are a little bit more complicated. Believe it or not, people are more complicated than quantum physics.

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When you take pilot wave theory and work it out, you address the measurement problem. Sure. Do you address the non determinative and probabilities you solve it, But you have to pay a price, and the price you pay is more entanglement. What you end up with isn't just one pilot wave one wave function for every particle you end up with a single wave function that gets shared between all particles in the universe. You scale it all the way out, and I mean all the way you end up with a single wave function that encompasses the entire universe. And that single wave function is just evolving Deterministically constantly interacting with itself, telling all the particles in the universe where to go. There is some master wave that encompasses all of physical reality. And you, if you could find that wave, feel that wave, see that wave. You would see it evolving according to deterministic equations and telling all the little particles what to do. But it appears hidden to us because the waves obscure the locations of the particles.

How exactly do the waves obscure the positions of the particles? Well, let's not get too far ahead of ourselves because we don't have an answer for that. If this sounds familiar, you are not the only one. Some people have criticized pilot wave theory as merely many worlds theory with extra steps. Because you end up with entanglement at the end, you end up with universal wave functions at the end. But if you remember, the many worlds interpretation had only waves. And now pilot waves. It's like it's making things even more complicated because now you're taking the waves that you except to exist the same ones that you do in the many worlds interpretation. But now you're adding particles. Now you're adding guiding equations. Now you're adding all these hidden information like, Why are you doing so much work? If every if, if waves are so critical, why don't you just have waves? But perhaps the biggest headache with pilot wave theory is non locality. Once you start adding up all these interacting waves together, you get automatic entanglement across the entire universe, which means every particle receives information from every other particle, no matter where it is in the cosmos, which kind of destroys all of physics, because what happens in my experiment should stay in my experiment.

And what I do here on Earth shouldn't be affected by some random hydrogen atom in the Andromeda galaxy. We, we we we we we wait. Hold up. Isn't non locality like AAA thing? Didn't we already decide that quantum mechanics is non local? Didn't we talk about that in a previous episode? Or am I losing my mind? I have here in my notes to slowly exhale, and so that's exactly what I'm gonna do. Life is kind of funny, isn't it? Not necessarily. Ha, ha. Funny, but usually more like ha. Funny funny. Einstein thought that quantum mechanics was incomplete and that the answer to uncertainties and probabilities and entanglement was some sort of hidden physics that we have yet to uncover. As he expanded his arguments against quantum mechanics over the decades, he realized that the ultimate expression of quantum mechanics dysfunction was the idea of entanglement that one quantum system could affect another one, regardless of distance. That was his big issue. He's like, Look, quantum mechanics is non local.

We got a problem here. This is a symptom of a deeper disease that you have a broken theory, a toxic theory working off of Einstein's line of thinking that quantum mechanics is incomplete, that there's more to the story that maybe there is hidden information. Deroy and Eventually, David Boum would develop a version of quantum mechanics that relies on hidden information, namely, the precise location of the particles is hidden from us. They developed this as a way to support Einstein's thing. He's like, Yeah, yeah, you're right, you're right, Einstein. Quantum mechanics is incomplete. We think there's more to the story where we think there's deeper hidden information and they developed pilot wave theory or bone in mechanics. However, you want to refer to it along those lines. But as the theory developed, it was realized that the only way to make this idea work was if everything was entangled all the time. And so the one theory that had a promising start of realizing Einstein's dream turned into his nightmare.

Einstein didn't like the probabilities and then over time, realized that the bigger issue was entanglement and non locality. People developed a solution to quantum mechanics that avoided probabilities, gave us back a deterministic universe, but had to pay a price which was even more non locality. Like I said, Huh? Funny, you've heard me correctly. One of the main criticisms of Pilot wave theory is that it leads to non locality, but non locality appears to be baked into quantum mechanics. Trust me, we've tried really, really, really, really hard to get around non locality, and we just can't. So what's the beef? Why does regular Copenhagen interpretation Quantum mechanics get to have non locality and everyone shrugs and say, I guess non locality is a thing, even though we can't explain how it works. But it's here. But then pilot wave theory gives us non locality, and all of a sudden it's like Whoa, whoa, whoa, whoa, whoa. Slow down there, tiger.

You got a whole lot of non locality going on there. Why is this a criticism? The criticism here is that pilot wave theory is a little too nonlocal. Sure, we can start to get comfortable or at least used to the idea of entangled spin states or other abstract quantum ideas. But with pilot wave theory, we're now entangling positions of particles, which seems, oh, as in a hydrogen atom in the Andromeda Galaxy Isn't just quantum mechanically vaguely entangled with me, but it's literally entangled with me in a very real way, as in the motion of that hydrogen atom in the Andromeda Galaxy literally changes the positions of the atoms inside of my body. Not just spin states, Not just polarization, Not just some other you know, random quantum, mechanical, weird abstract state that actually no one really cares about.

Except quantum physicist. We're talking about entanglement, of position, of movement, of location. Where when I move furniture around my room and I'm shoving on that couch, I am somehow directly influencing the behavior of Adams throughout the cosmos instantaneously, with no communication, no force applied. That's a lot to swallow. It's OK for physicists. I think over the past 100 years, we've gotten used to the idea of entangling spin states and polarization, but entangling position, movement, location that seems to break like fundamental concepts of, like, conservation of momentum. How can I be sure? Like if I if I say I'm going to target practice and I shoot and misses and they're like, Oh, you miss? I said, No, no, no, no. You don't understand. The movement of the bullet that I shot was entangled with a supernova that went off 4 billion years ago.

And because the in pilot wave theory the positions of these particles are entangled, there was actually a nonlocal influence that happened instantaneously. Nobody's gonna buy that. Why? Because it goes back to Einstein's main criticism. How are we supposed to have a sensible theory of physics? How how are we supposed to have a consciousness where the movement and choices I make somehow depend on calculating all the entangled properties of the entire universe? Like, how can anything be local? There are other criticisms. Pilot Wave theory says that position is a hidden variable, but not momentum, not velocity. Uh, but we know from special relativity that position and momentum are on equal footing. You know, space and time are connected. Why should position be singled out? But not not momentum? Why is position the hidden variable and not the momentum of the particle? So there isn't really a reconciliation between pilot wave theory and special relativity. That means there isn't a relativistic version of pilot wave theory.

Copenhagen interpretation, normal vanilla quantum mechanics. We have a version of that that is compatible with special relativity. We call it quantum field Theory. We do not have a version of that in the language of pilot wave theory, and, you know, good old Newton equal and opposite forces for every action. There's an equal and opposite reaction. You know that. That seems pretty familiar. Uh, that has stood the test of time for, like, 400 years. We have never found a single violation of this principle. In fact, it's encoded now in our conservation of momentum. But here we have in pilot wave theory, the waves tell the particles what to do. But the particles don't tell the waves what to do. How does that influence only flow in one direction? So you come up with things in pilot wave theory that don't make sense. Like how do these pilot waves actually do the job of hiding the particle positions from us? Why do they single out the position and not the momentum of the particles?

Why do the waves act on the particles, but the particles not act on the waves? Yes. If you want to say these waves are real and actual physical objects in our universe. Um, well, where are they? Can I isolate them? Can I manipulate them? Can I study them in isolation without their attendant particles? How does this link actually work? If you want to say they're real, how are they real it seems like you just end up in the same kinds of questions that you end up with in the Copenhagen interpretation. In the many worlds theory, these ideas sound great, but then they run into problems. When you try to describe how it's all supposed to work now, none of these are necessarily deal breakers. There could be a relativistic version of pilot wave mechanics out there that we just haven't figured out yet with a little bit more thought and thinking, we could figure out how the waves act on the particles, but not the reverse. Uh, we could figure out a how the waves single out the position of the particles to be special, not their Momenta.

Like we could do this, we could end up saying, Yeah, positions of particles throughout the universe are entangled with each other and operate on each other instantaneously. We could figure out how that works, but we haven't. And so we're left with a bad taste in our mouths. But we're also left with a bad taste in our mouth from the Copenhagen interpretation and the many worlds interpretation and honestly, every interpretation, like any of the criticisms of any of the interpretations. That's about the long and short of it. There's some aspect of the interpretation that just seems funky, and you're left pointing to one or more statements, and you just say, How is this supposed to work? When I look at the Copenhagen interpretation, I say, Well, how is measurement actually operating? When I look at many worlds, I say, How does the splitting of the universe actually happen? When I look at pilot waves, I say, How do the waves actually hide the information about the location of the particles?

How if you want to say this is real and not just a mere mathematical trick, you need to explain how it works and all the interpretations come up short and all of the interpretations every single one that we visited so far. Copenhagen Many worlds pilot wave, all end up falling into Einstein's trap. All of them end up involving entanglement. All of them end up involving non locality. Every single one, if there's anything we've learned from quantum mechanics, is that non locality appears to be a thing because every interpretation that we have met involves some form of non locality, and that's what Einstein despised the most about quantum mechanics. So again I ask what is real and what's just a mere mathematical trick. What does quantum mechanics actually teach us about reality?

We have all these interpretations. We've met three of them. We're going to meet some more. But in the spirit of quantum mechanics, perhaps we shouldn't be thinking either. Or maybe the answer isn't Copenhagen or many worlds or pilot wave or anything else? Maybe instead of either or we should think both. And maybe we have to take a completely different and radical perspective, but that we'll have to wait until next time, thanks to everyone who have asked questions about quantum mechanics. Mihail E on email at Sharman on Twitter. Massimiliano S on Facebook. Isaac P on email at on Twitter. Chris F on Facebook, aka B on email at SMTR on Twitter. Albert R on email Julius M on email. Martin EON email John T on Facebook RC on email. Nick S on email at Jordie R on Twitter at Pizza Larger on Twitter Ara An email HP Ariana and email Scott M on email.

Graeme Deon email Martin An on email sample SAPIENs on Twitter. Peter WE on email. Mark Reap on Twitter Shanel on email. Susan on email. Daniel Jan email. Campbell Dion email Timothy Be on YouTube, Fernando G on email and James W on email. Thank you, of course, to my top patreon contributors. That's patreon dot com slash PM Sutter Top ones this month. Justin G, Chris L Barbeque Duncan MD, Justin Zed, Andrew F, NAIA Scott M Rob Justin Lewis M John W, Alexis Aaron J, Jennifer M, Gilbert M, Joshua Bob H, John S, Thomas D, Michael R and Simon G. You can join their illustrious ranks by going to patreon dot com slash PM Sutter. Thank you so much, everyone, please keep sending those questions to ask us spaceman at gmail dot com Hashtag ask us spaceman on social and I'm at Paul Met on all social channels. Ask us spaceman dot com for all your well ask us spaceman needs and I will see you next time for more complete knowledge of time and space

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