Part 6! What were Einstein’s objections to quantum mechanics? Why was he so bothered by non-locality? What is the EPR paradox? I discuss these questions and more in today’s Ask a Spaceman!

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EPISODE TRANSCRIPTION (AUTO-GENERATED)

What is reality? No, really, What is reality? What do we mean when we say that something is real rather than you know, not real. What's the difference? I suppose when you tuned into this episode, you were not expecting a deep, profound real huh? Question. I bet you weren't expecting Ask a philosopher in today's episode. But when we start digging into the meaning of quantum mechanics, of which we are now an astounding six episodes deep, I gotta warn you, it's basically all philosophy from here on out. In the last episode, we highlighted the debates between Heisenberg and Boer on one side and and Schroedinger in the other about the reality of the wave function. Schroedinger thought it was a real thing that subatomic particles were literally smeared out over space and others believed that it didn't have physical existence but was merely a mathematical convenience for expressing a fundamental randomness and uncertainty of the physics of the subatomic level.

That view would eventually become to dominate and be called the Copenhagen interpretation. Folks, these questions like the very first question we ask about quantum mechanics, which is Is the wave function real? Is matter, actually wavy shaped or or does the wave function merely represent a mathematical trick for calculating probabilities? These are straight up, no holds barred philosophical questions. We've moved beyond the pure physics. If if there can ever be such a thing that quantum mechanics had already established, it was a mathematical theory that could predict the outcomes of experiments done shares that with literally every other physical theory in existence. Uh, but that was it. Now we're past that, and it's important to get past that even a little because we need to learn what quantum mechanics is teaching us about the universe. Is it teaching us about reality or just our views of reality? What I left out intentionally in the last episode was a major player in these philosophical debates.

Einstein. Einstein was one of the founders of quantum mechanics. Some people call him the first modern physicist. And yet, after his initial work in 19 05, the spotlight of the quantum mechanical stage shifts to other actors. Schroedinger, Heisenberg, bore and and so on. Einstein appears here and there in the record, following 19 05 as more of a commentator and communicator and eventually a critic of the emerging theory rather than one of its leading lights. This is especially true in the 19 thirties, when Einstein moves from Nazi Germany to Princeton, New Jersey Quantum mechanics is very much a German theory of physics. Almost all the principal players were German people and thinking German thoughts. And I have to wonder if some other group of scientists at some other time and place and culture in the world other than Germany in the 19 tens and 19 twenties had first encountered subatomic physics.

If we would have a different theory, a different default interpretation, I honestly don't know. But it is what it is. Quantum mechanics was largely developed by Germans in the 19 tens and 19 twenties. Einstein was one of them and the development of quantum mechanics, especially after the foundations were laid in the mid 19 twenties as it started to get fleshed out. And as people started to debate the meaning and whether it was ultimately correct, or if there's something deeper going on as that continued into the 19 thirties, Einstein left the scene, and actually so did a lot of people because it was kind of hard to do fundamental physics and really much of anything as Nazism was growing in Germany at the time. But the end result that was that Einstein was physically thousands of miles away from where the quantum mechanics action was taking place, which was Europe and threading through all of this the 19 twenties and the 19 thirties, beginning with letters and then moving on into in person.

Discussions at conferences were the famous Einstein Boer debates, these debates that took place between Albert Einstein and Neil Spore, a series of debates, and I'm not going to get into the nuts and bolts of the debates. I've I've discussed them before. Uh, but here, the important part isn't the debate itself and what Einstein was thinking. The important part is the essence of the debates. What Einstein was doing through the 19 twenties and 19 thirties was developing thought, experiment after thought experiment. And he was the unequivocal master at this at thought experiments. Uh, he was developing these thought experiments to show that quantum mechanics was incomplete. He had a gut feeling going way back decades back that something was missing from Heisenberg's Matrix mechanics from Schrodinger's Wave mechanics and basically everybody's mechanics of everything.

He honestly thought there were all these weird things that that every time we developed something in quantum mechanics that flew in the face of classical physics, that every time we developed a new death metal song and we were able to describe what defines death metal and how it's different than classical physics, he thought that this wasn't a sign that we should extend our thinking and broaden our horizons and abandon classical thought processes. He thought it was a sign that we were missing something. Now there's a standard a story here, and and it's a story that that I'm even guilty of of telling about these Einstein Bo debates these series of debates between Einstein and Neels. Spor. Uh uh, The standard story is that Einstein is insanely bugged by the Heisenberg uncertainty principle. This apparent fact that we can't measure the position and momentum of a particle simultaneously to as high precision as we want.

We can easily do that in classical physics. We can't do that in quantum physics. Uh, the standard story is that Einstein was deeply upset by this thought. It was a sign that we were missing something more fundamental and came up with thought, experiment after thought experiment to find ways around the Heisenberg uncertainty principle to show violations of it. Because if he could show violations of it, it would prove that quantum mechanics is incomplete. In the standard telling of these debates, Einstein's arguments get almost more and more desperate as they go on and at every turn, Neil's Boer is able to come up with a rebuttal. Einstein proposes a thought experiment and say, Hey, look, look, look, I told you Heisenberg's uncertainty principle is violated. Quantum mechanics is incomplete, and then bore comes in a a few months later or a night later after, you know, not getting being able to sleep, he said. 00, actually, you didn't think of this angle This particular, uh, affect this particular part of the physics. You didn't look at the complete picture. And then Heisenberg's uncertainty principle is saved.

The standard story is that these debates go back and forth. It ends up with a triumphant Neils bore standing on the mountain, defending quantum mechanics and then a senile old Einstein twiddling his thumbs. In Princeton, Abraham Pace, one of the great biographers of Einstein, said quote Einstein is the only scientist to be justly held equal to Newton. That comparison is based exclusively on what he did before 1925 in the remaining 30 years of his life. He remained active in research, but his fame would be undiminished, if not enhanced had he gone fishing instead. Parts of this standard story are true. Einstein did spend decades believing that quantum mechanics was incomplete. Boer is considered to have won the debates. Einstein would come up with thought experiments showing violations of the Heisenberg uncertainty principle, and Neil's boor would show him to be wrong.

Einstein spent decades trying to find a path out of quantum mechanics and failed. But take this story with a grain of salt because the perspectives we have on the debates and the success of board and the defense of quantum mechanics against uh uh, increasingly crazy, senile old Einstein, who's, you know, was was cool back in the day but then sold out. Those perspectives are written by Boer. It's It's Neil's, Boer's letters and autobiography that we get to this story. We don't have Einstein's thoughts on the subject. He didn't write a lot about his thoughts on the debates with Boer. So if the story looks like Neil's, Boer is defending successfully quantum mechanics against an Einstein that just doesn't get it. Maybe there's more to the story, the standard story, which, like I said, I've been guilty of perpetuating misses a couple things. One. Einstein was a genius with a capital G, a capital E, and then a capital ni.

The whole word capitalized. I mean, come on. We're talking about the guy who established the existence of atoms, the guy who revolutionized our understanding of space and time and matter and energy, who gave us a new theory of gravity, unlike anything seen before he proposed. That light itself is quantized. He kickstarted modern cosmology. I mean, come on, this is no senile old school thinker. This is the front man of the death metal Quantum revolution. He's in it. He's doing it. He led it. So if Einstein objects to your theory, you should probably pay attention to this standard history that focuses on the debates between Einstein and Boer and focuses on the Heisenberg uncertainty principle ignores Einstein's real objections to quantum physics. Those real objections were deeply philosophical and truly cut right into the middle of the nature of quantum mechanics and what it proposed to teach us about the subatomic world.

His objections were about the reality of quantum mechanics. Yes, he didn't like the Heisenberg uncertainty principle. Yes, he didn't like the the randomness and probabilities and in determinism in Quantum Mechanics. And and he has that famous 1926 quote that quote. God does not play dice. But to him, those were all symptoms of a larger disease. It wasn't necessarily the uncertainty principle. It wasn't necessarily the nondeterminism. It wasn't necessarily the probabilities to him. Those were all just signs. All those were symptoms of a deeper disease, which was that he believed that quantum mechanics was missing, something that we were not yet at a true theory of subatomic physics. So, for example, the randomness in quantum mechanics when he says God does not play dice, he's not saying like, I don't like quantum mechanics. I don't like randomness. He's saying that that randomness that we see in our results in our theories is an illusion.

It's not real. It's a reflection of our ignorance of physics, not an expression of a true underlying randomness to the universe. It's not a feature of the natural world. It's not real. Einstein didn't know what was missing in quantum mechanics, and he spent decades trying to figure it out and never could. In addition to the probabilities which he ultimately came to accept, there was one thing about quantum mechanics that he could never get over this one aspect of quantum mechanics. To him, he would point to again and again, because to him, it stood out like a giant, glowing billboard standing off the dark highway that we were all driving down on our way to Quantum bill. The objection that Einstein had to quantum mechanics, this feature of quantum mechanics that he simply couldn't accept he could. He ended up as decades went by, accepting the rest. But there was one he just couldn't get over. And his objections to this aspect don't get talked about much because he was right, the aspect of quantum mechanics that troubled him the most.

When Einstein first started making noises about this aspect, it didn't have a name, but eventually Schroedinger would coin the term entanglement. That's when Einstein didn't like entanglement. What a simple word. An innocent word even even a nice word. It sounds kind of fun, but entanglement is perhaps the greatest source of angst and anxiety and hand wringing to ever come out of quantum mechanics. And there are a lot of contenders, and we will get to the other aspects of quantum mechanics that aren't pretty. To Einstein, this was worse than the Heisenberg uncertainty principle. It was worse than the probabilities in non deter nondeterminism. It was worse than anything. As the decades went by after the mid 19 twenties and the first formulations of quantum mechanics, people were slowly getting cool with going beyond no physics, you know, like, OK, even Einstein said, You know what? OK, I guess we we have to push past past classical physics to get a handle of what's going on, and there's no way around it.

Experiment after experiment after experiment was just validating quantum mechanics, but entanglement was too far. What is entanglement? Well, it's entanglement. I don't know. It's this uniquely quantum thing that simply doesn't happen in the classical universe. Um, let me give you an example of what happens in the classical normal universe, so we can contrast it with what entanglement is, let's say you have two particles, all right, A and B. And they interact. Yeah, one at one time, they were far apart. And then they get close to each other. Maybe they bounce off of each other. Maybe they, uh, magnetically or electrically interact or whatever. It doesn't matter. They just interact. And then they go flying off after they've gone flying off. They they're they're independent. They have their separate and local existences. There's this particle over here on one side of the galaxy and that particle over there on the other side of the galaxy. Sure, 5 billion years ago, they interacted with each other, but now they're on their own.

And particle A on this side of the universe or this side of the galaxy only cares about what's near that particle, and the other particle only cares about what's near that one. They don't talk to each other anymore. It's like it's like when you when you break up with someone and you move to opposite opposite coasts and you live separate lives. What your ex does has absolutely no bearing on what you do and vice versa. You have your own friend groups you've got your job, your hobbies, your activities, your new relationships. You couldn't care less about what your ex is doing. Sure, you had something going there for a while. But now you don't. And you don't let your ex influence you. This is how physicists viewed the world where physics was separate and local that after an interaction once particles once anything was far away from anything else. It just cared about its environment. It didn't carry a memory of that interaction. Einstein was a firm believer in these ideas of separateness and locality in physics, where what matters to you as a physical object is what's near you.

Stuff far away simply doesn't influence you. He really cared about this for a few reasons. One through his development of general relativity, he had gotten rid of Newtonian action at a distance. Your own Newtonian gravity. Just as one massive object instantaneously affects another massive object like that, the gravity of Jupiter when it moves immediately affects the Earth. It doesn't take time to propagate from one place to another. It's instant Physicists have been bugged by that forever. In fact, these kinds of debates about reality versus mathematical tricks go back forever. Where Newton said, Yeah, this this works universal gravity. I got it. How it works. I don't know. I'll leave it to future generations. That future generation was Einstein who figured out how gravity actually operates at a more fundamental level. So he had just done that. He had taken a problem where it seemed like objects on distant ends of the universe would instantaneously affect each other and turn it into a local area of theory of physics that if you want to affect something gravitationally, uh, gravitational waves have to emanate off of you and propagate at the speed of light like there's a transmission mechanism.

Another reason he he really liked this idea of locality in physics was that he had developed special relativity, which demanded locality in all of physics via the speed of light. If I wanna affect you, if I want to interact with my ex man, I gotta pick up the phone and talk. I don't just get magically interacted or affected by my ex unless I actually communicate. And lastly, Einstein argued that without locality, if physics wasn't local, you can't have a theory of physics. Let's say you're running an experiment in a laboratory and you get a result. Now, if physics wasn't local, if the results of your experiment depended on what else is happening throughout the universe in some very nonlocal, fuzzy way Well, then, when you got that result, did you get that result from the interaction you were studying inside of your experiment? Or was it from some random alien fart in the Andromeda galaxy? How do you know?

Without locality, you can never know exactly what is influencing the outcome of your experiments. And so physics is useless if I can't tell what is happening in my experiment, Uh, how can I get physics done? Einstein argued that in order for something to be real, it had to be local. And Einstein realized very early on that quantum mechanics was leading to some very non local interactions. 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 I am not joking. And and life and dealing with people does not come with a user manual, and the next best thing is therapy. I have been using therapy for years. It's such a powerful tool for me to to answer life's questions when those questions don't come in the form of of of physics problems.

And I think you will benefit a lot from it, too. And that's why I'm proud to have better help as a sponsor. Better help is the world's largest therapy service. Better Help has matched 3 million people with professionally licensed and vetted therapists available 100% online. Plus it's affordable. Just fill out a brief questionnaire to match with the therapist. If things aren't clicking, you can easily switch to a new therapist any time. It couldn't be simpler. No waiting rooms, no traffic, no endless searching for the right therapist to learn more and save 10% off your first month at better help dot com slash spaceman. That's better. Help HE LP dot com slash spaceman. You take two particles. They're initially separate. They each have their own individual wave functions associated with them. The the cloud of probabilities however you want to interpret it, they have their own wave function associated. Then you bring the particles together, they interact.

Then they get a shared wave function, their wave function, which is spread out over space. Uh uh, mingles overlaps and you end up with a single wave function, a single cloud of probabilities that describes both particles instantaneously. The very active interaction mixes their quantum states in such a way that you can't separate them ever again. It's like if you broke up with your ex and you moved to opposite sides of the country, but you still follow each other on social media. You still text each other, even though you're very far away in space, you still affect each other. Your ex gets gets a new romantic partner, and and and you feel weird about that's affecting you. You're entangled. You get trapped in all the same arguments all the same, toxic cycles, all the same emotional ups and downs. You're not really broken up. You're just not living together anymore. You're entangled for relationship advice. Please subscribe to patreon dot com slash PM. Sutter. Feel free to ask your relationship questions there, and I will cast them in terms of physics, which is all I know.

I can't guarantee it will be helpful, but it's patreon dot com slash PM. Sutter Quantum mechanics allows for entanglement where I can bring two particles together. The classic example is is quantum spin. I can bring two particles together. They become entangled. Their wave functions overlap. Now I have a single wave function that describes both particles simultaneously. Then I pull these particles very far apart. They're still entangled. And then if I flip one upside down or I measure one and I see it's, uh, it pointing up, I immediately know that the other particle is pointing down, even though I don't have to go visit that particle to find out. I know immediately I don't have to communicate with that particle. I don't have to call. I don't have to text. I just immediately know that that particle, the state of that particle this drove Einstein nuts. How could you know the state of something on the other side of the galaxy without receiving any signals from it? How could measurement influence things across these distances and apparently instantaneously?

How could the quantum world be nonlocal but the classical world local. How could quantum theory be a sensible version of physics if, like everything, we're connected? Man ultimately appeared to Einstein that quantum mechanics was nonlocal, and to Einstein, this meant it was a bad theory of physics. Physics should be local. If I have a particle right in front of me, it shouldn't care what's happening to particles on the other side of the universe. It should care about what's happening right in front of its nose. That's a local theory of physics. How is non locality supposed to work? If these questions the focus on how quantum mechanics is supposed to, you know, work seem similar to Schrodinger's objections to Matrix and mechanics, where he said, OK, there's this quantum jump. How is a quantum jump supposed to work? Here's Einstein saying, How is entanglement supposed to work? How is this nonlocal effect supposed to work? You won't be surprised to know that Einstein and Schrodinger exchange a lot of letters complaining about the kids these days.

To Einstein, this giant, glowing billboard of entanglement signaled that we were missing something in our formulations of quantum mechanics. He believed in something that we call local hidden variables where our version of quantum mechanics was really an expression of our ignorance of a true, real underlying physics. It didn't represent a fundamental ignorance in reality itself. Einstein believed that when two particles come closer together, they exchange some information that is hidden from us. Then when we separate them and it appears that they are affecting each other instantaneously over great distances, they're really not really. They just came with information that's hidden from us. And so, in our current formulation of quantum mechanics, we're missing that hidden information. And so it looks like these particles are entangled with each other and influencing each other.

But that's only because of an incompleteness in our theories. It's like when two particles interact, they like, exchange secret notes with each other to tell each other what to do, and then they carry these secret notes folded up in their back pocket as they travel these great distances. And then when we look at the particles and we figure out their state, the the result that we get isn't because there's this fundamental randomness in the universe and this particle is influenced by the state of its entangled pair partner, uh, across the galaxy. No, it's because it just opened up its secret envelope with its hidden variable information. And then once it read it, it had the instructions and it knew what to do. That's what Einstein believed, that what we see as entanglement is really a sign telling us that quantum mechanics is incomplete. This line of thinking culminated in a famous 1935 paper co-authored, with Boris Podolski and Nathan Rosen entitled Can quantum mechanical descriptions of physical reality be considered complete?

But it's called the E PR paper for Einstein, Podolski Rosen. It's called the E PR paper. Ironic, this criticism of quantum mechanics would turn out to be one of the most highly cited papers of all time. In fact, it might be the most highly cited paper of all time, including in the field of quantum mechanics itself. Now I'm not going to get into the guts or details of the paper, just like I didn't get into the guts or details of the arguments between Einstein and Boer, and I'm not gonna do it because the paper itself was actually really poorly written. Uh, Einstein himself admitted this to Schroer in a letter, and and the argument in the paper isn't very strong. In short, the E PR paper used a thought. Experiment again said, OK, let's take two particles A and B. Let's entangle them. So what does entanglement mean? It means once you separate them, if you measure the properties of one of them, you automatically know the properties of the other because they share a single quantum state. Knowledge of one entails knowledge of the other automatically, so OK, entangle them, then let them let them go flying, measure the position of particle A and then a little while later, measure the momentum of particle A two separate measurements.

Now Einstein knew from Heisenberg uncertainty principle that you couldn't make these measurements at the same time. But you could measure the position to as high precision as you want and then a little while later, measure the momentum to as high precision as you want and then boom from entanglement. You know the position and momentum of particle B without ever touching it. The paper essentially said, Either you have to let go of the Heisenberg uncertainty principle, or you have to give up locality and physics or you need to introduce extra hidden variables to rescue everything. And and that just shows that quantum mechanics is incomplete if that argument in that paper like, doesn't sound the greatest, and you're like wait a minute, like it. Like I said, it's not the greatest argument. It's not very well put together. Our man, our quantum man, Neels Boer, who was seemed always ready to fight with Einstein, wrote a rebuttal paper A few months later. He submitted it to the exact same journal and took the very sassy move of using the exact same title, the title being.

Can quantum mechanical description of physical reality be considered complete? Boer's response was to show that the Heisenberg uncertainty principle was never violated in the example given in the paper, arguing that if you measure the position of particle A, you change what particle A is, and so you can't just follow it up with a momentum measurement and then automatically learn something about particle B and so non locality stands. Uh, Heisenberg's uncertainty principle is preserved, and so therefore, quantum mechanics is nonlocal. Uh, Boer's rebuttal is considered successful, but that's only in the very limited context that the E PR paper itself was pretty lame and poorly written. Bore's response itself wasn't very strong, uh, in contrast to his earlier rebuttals against Einstein during those famous debates, where his rebuttals about the nature of the Heisenberg uncertainty principle were very, very strong, very coherent, very well put together. Essentially, Bore's rebuttal is like, Yeah, Einstein, you have this scenario, but it's more complicated than that. And and the Heisenberg uncertainty principle isn't violated.

And so I'll repeat non locality stance. But Einstein's main point remained unchallenged. His main beef was that quantum mechanics was nonlocal. That was supposed to be the point of the E PR paper was to demonstrate that quantum mechanics is nonlocal, and that's a problem. And then Bore responded by saying, Yeah, it's nonlocal. What's your deal? Particle A. Does influence particle B Across the universe, knowledge of particle a automatically gives you knowledge of particle B regardless of how far away it is. What came out of this was that non locality was became an un ague feature of quantum mechanics. But ultimately you had to decide if you were OK with non locality or not, and Einstein most definitely was not years later. Years later, decades later, other physicists would pick up this problem of non locality and devise ways to test the non locality of quantum physics and devise ways to test the non locality of quantum mechanics.

I am happy to do an entire episode expanding on that. Just ask me about Bell's theorem and Bell's inequalities. The details of the test aren't important for this story. The result is that quantum mechanics is nonlocal, no theory that includes local hidden variables, these secret sea old envelopes that particles carry along with them to instruct them what to do and that they have that knowledge. But we don't. In quantum mechanics, the probabilities, the uncertainty, the non locality is an expression of our ignorance of the true underlying physics. Those theories don't survive our current tests. It seems that it's perfectly possible to know the state of an entangled quantum system regardless of distance. If I entangle two particles, send them on their merry way, I measure one. I automatically know what the other one is up to. This should make you uncomfortable. This should make you question reality. All of Einstein's objections to non locality hold. How can you trust an experiment?

Your experiment is supposed to be local. You perform your experiment, you get a result. How can you guarantee that the results of that experiment aren't influenced by entangled particles all across the universe? You can't. How does the influence of entanglement this non locality actually take place? What is the mechanism? Come on, Bor, Explain it to me. How does it work? How do two particles know what the heck they're doing after they're entangled and they can't share messages? There's no speed of light construction. There's no signal. There's no emission. There's no hidden information. So how does it work? How does consciousness even work? How can it be possible? How can I I have a pen sitting next to me? I'm going to decide to pick up that pen. How can how can that decision somehow appear? Local, where it's just me. Just the pen, just the two of us. I don't need to take into account the motions of Galaxies across the universe and quantum entangled interactions throughout all of space and time in order to make that decision of whether to pick up the pencil or not.

This feels local. If I didn't know that the Andromeda Galaxy existed or not. It wouldn't influence my decision or my ability to pick up the pencil. Seriously, if if you if Andromeda Galaxy blinked out of existence right now, I could still pick up that dang pencil. Was it depend earlier? I don't remember. It's quantum mechanics, all right? The universe appears local at classical levels. Local physics is obeyed. I can guarantee the result of an experiment, and I can verify it. And it doesn't depend on the rest of the universe consciousness itself. How can I possibly have a thought and be able to make predictions and go about my daily life? If I had to perform the calculations necessary to consider the entire universe? How would it be possible to take a single step forward if I needed to understand and account for the entire physics of the universe? No, I just need to care about the sidewalk in front of me. A molecule drifting through the atmosphere of Jupiter doesn't seem to affect me.

And yet a naked reader in quantum mechanics says that everything is entangled. What gives Einstein's objections stand? It doesn't make sense. You just get used to it. The majority of physicists just got used to the weirdness of quantum mechanics. Somehow, classical physics remains unaffected. Somehow, classical physics is local, and yet quantum mechanics is not local. We don't know how to connect those two dots. We don't know how to translate from the quantum world to the classical world. How does it work? Nobody knows. This is weird and we don't have any answers. Does this mean that our knowledge of quantum mechanics is incomplete? Is what quantum mechanics teaches us about the universe real or just a mathematical convenience for expressing our ignorance? Because we don't have a better idea. Einstein's objections remain. Yeah, Bore won the debate, but he lost the war. Quantum mechanics appears to be non local. Einstein went to his grave believing that quantum mechanics was incomplete. Because of this non locality, no one could come up with an answer to Einstein.

Like they say, physics advances one funeral at a time. So stay tuned for more, thanks to everyone who have asked questions about quantum mechanics. Mail E on email at Sharman on Twitter, Massimiliano S on Facebook. Isaac P on email at on Twitter. Chris F on Facebook A Be on email at SMTR on Twitter. Albert R on email. Julius M on email. Martin EON email JOHN ON FACEBOOK RC on email. Nick S on email at Jordie R ON TWITTER AT PIZZA LARGER on TWITTER ARAS 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 Sean 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 stutter top ones this month.

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