There are many spooky things about QM, but I want to share with you what I think is the spookiest. You might want to read the QM for dummies post to get a slightly deeper feel for the math, but this post should stand on its own.
Okay, suppose we have a particle that's in a superposition of spin-up and spin-down (I'm leaving out the normalization term $\frac{\sqrt{2}}{2}$ for simplicity):
$$|\phi\rangle = |p_{up}\rangle + |p_{down}\rangle$$
Don't be scared by the bra-ket notation. $|x\rangle$ is just another way of writing the vector $\vec{x}$.
But of course we never see a particle in a superposition state. Whenever we check, the particle is either spin-up ($|p_{up}\rangle$) or spin-down. The other term disappears:
$$|\phi\rangle = |p_{up}\rangle$$
The question is, when does it disappear? When has it been measured?
Suppose we try to "measure" it by bouncing a second particle (q) off of it. (To measure spin we don't actually "bounce" anything, but the idea is the same.) But instead of that "collapsing" the first particle's state, we discover that the two are now entangled in a joint superposition, written:
$$|\phi\rangle = (|p_{up}\rangle \otimes |q_{up}\rangle) + (|p_{down}\rangle \otimes |q_{down}\rangle)$$
In one of the sum terms, p is spin-up and q "agrees," and in the other term, p is spin-down and q agrees. This doesn't look at all like the earlier "collapsed" state, and indeed we can tell it apart by some clever interference experiment. On the other hand, if we check whether particle p by itself is still exhibiting interference, the answer will be no. So in a sense, p behaving classically, but the p-q system as a whole is "still quantum."
What if we introduce a third particle r? Will it collapse the first two? No, it will just join in on the fun (I'll drop the $\otimes$ symbol for cleanliness):
$$|\phi\rangle = (|p_{up}\rangle |q_{up}\rangle |r_{up}\rangle) + (|p_{down}\rangle |q_{down}\rangle |r_{down}\rangle)$$
So then what does collapse it? As the system encounters more particles -- a few more in a controlled lab setting, or trillions more as it contacts the messy environment -- they should all just join in. If we lump q and r into the environment (env):
$$|\phi\rangle = (|p_{up}\rangle |env_{up}\rangle) + (|p_{down}\rangle |env_{down}\rangle)$$
In the first term, p is spin-down and the environment reflects this (and vice versa for the other term). So we still haven't answered the question: why do I only see one of those two outcomes?
There are two broadly popular answers to that question:
1) The orthodox ("Copenhagen") interpretation. It says, essentially, that somewhere on the way from one particle to trillions, it suddenly "collapses" into one state or the other. This was by far the favored interpretation in the early days, and roughly 39% of physicists still prefer it even though it's ill-defined[3].
2) The Many Worlds Interpretation (MWI), which says that no collapse ever happens. Instead, the universes keep splitting, ad infinitum. Every time you encounter the result of some indeterminate experiment (which is nonstop, since your environment is filled with tiny particles), your universe splits and you do, too.
The problem with Copenhagen (other than the fact that nobody seems to agree on what it is) is that it doesn't really tell us when or why this special "collapse" (which, by the way, disobeys what is known as unitary evolution which applies in all other cases) happens. We should just quietly assume it does. And for any practical experiment, that's good enough.
But as technology improves and we are able to isolate larger and larger quantum systems, we haven't run into this magic wall where the unitary laws of physics suddenly break down. We keep getting bigger entanglements rather than a sudden collapse. We're starting to question why we needed such an odd assumption to begin with. As a result, more and more physicists are switching to MWI.
But the problem with MWI is in how it answers the fundamental question "why do I only see one outcome?" The answer is that you don't -- you "actually" see all of them. You see, when you encounter the system, you become entangled with it. Each branch of the superposition becomes a parallel universe, and each universe has one copy of you. One copy of you sees "up" and the other copy sees "down." Asking why you you see "up" is nonsense, because in a parallel universe, the "other you" is asking why she sees "down." There isn't one you. In fact, as the universes keep splitting and splitting, there become infinitely many of you.
Yeah.
Now consider what happens after we run 100 iterations of the up/down experiments above. According to Copenhagen, since each time there is a 50%-50% chance of each outcome, you should expect that roughly half of the experiments come out heads. If you get a "lucky streak" of all ups, then as that lucky streak gets longer, you should increasingly suspect that something is wrong with either your setup or QM itself.
What about in MWI?
Well, in MWI there will be $2^{100}$ (~$10^{30}$) universes, each with its own string of outcomes ("UUDDUDD..."). On average, across all of them, there will be as many ups as downs. But since the question of where "you" end up is meaningless, there's no reason "you" shouldn't find yourself in a universe with all up, for example. If there were just one of you, and on each split you followed a path randomly, then we could make a statement like "the expected number of ups is 50, and it's very unlikely that you'll end up with all ups," but that doesn't apply here. You didn't end up with all ups; only "one copy of you" did.
On average, the $2^{100}$ copies of you are fulfilling their quantum (Born rule) obligation to see only half ups, but one of those gals had to be the one who saw all ups... so why shouldn't that be this you? What prevents you you from being the lucky one? Nothing. It doesn't contradict the theory or interpretation in any way. The quantum police won't come knocking just because you keep ending up astronomically lucky.
But the weirdness has just begun.
In MWI, you do indeed model the world as:
$$|\phi\rangle = (|p_{up}\rangle |env_{up}\rangle) + (|p_{down}\rangle |env_{down}\rangle)$$
Right up until the moment you see the result yourself (that is, encounter p or env in any way that would reveal the outcome). But env here includes the bodies and brains of any experimenters that encountered the system before you.
On the other hand, once you encounter the system, you can no longer treat it as a superposition. You cannot do any interference experiment, even in principle, that would suggest that it's still in a superposed state. You are definitively in either one or the other branch. Not only that, but everybody else in that universe will see the same thing you do. If you see 100 ups, they do as well -- even if they saw the outcome long before you.
This should give you a bit of pause. There's nobody else in "your universe" that is capable of collapsing the superposition like that. Each one of them just gets swept up into the entanglement, permitting you (in principle, but certainly not in practice -- probably ever) to do an interference experiment that would demonstrate this. But once you encounter it, all bets are off.
You're the only one who can do this.
Of course, the situation is symmetric for all other conscious observers (assuming there are any). From their perspective, in their universe they are the only one able to do this. And there's no contradiction, because you never inhabit the same universe. All the other people you see in your universe are your copies of them. And from your perspective, they are simply globs of matter obeying mindless physical laws.
Somehow, in your universe (this one!) the buck stops with you. Don't take my word for it. This is well-accepted.
Why isn't this mystical interpretation off-putting to believers of MWI? Well, if you could take the "inside perspective" of any object, you indeed would be the sole observer. But since consciousness is just an illusion, you can't take such a perspective, so there's no problem!
Which is all well and good, but I'm one of those weirdos who does believe he's conscious and inhabiting just one universe. And so maybe I have to suck it up and grudgingly accept my fate as the only conscious observer here. On the other hand, nothing seems to stop me (in principle) from "choosing" which of those universes I want to be "birthed into" -- although nothing explicitly permits me to do this either. In fact, there seems to be nothing in physical reality that can have control over which universe I "end up in," period, given that all of physical reality is (by definition) embedded in the universe. So maybe instead of begrudging acceptance, I should be filled with awe and gratitude.
This is your universe, and your playground. Not "you" as in your body or brain (which, being physical objects, are just part of the environment, just like other experimenters), but that which is looking out your eyes, so to speak.
Is there something looking out your eyes? Something non-physical? Obviously physics says "no." But instead of taking anyone's word for it, I invite you to check for yourself. If the answer is "yes," you have a whole lot of responsibility.
As we saw, we should indeed treat things this way... with respect to other experimenters. It does not address the question of why I only see one outcome. Indeed, it doesn't even try to address that question, because strictly speaking, it belongs to metaphysics.
2. Many times physicists will explain that the consciousness thing is a red herring. There's nothing interesting to consider about it, and it has nothing to do with QM. If you don't agree, you have good company. Here's the greatest physicist of modern times agreeing with you.
3. Sean Carroll again: "I think Copenhagen is completely ill-defined, and shouldn’t be the favorite anything of any thoughtful person"
Okay, suppose we have a particle that's in a superposition of spin-up and spin-down (I'm leaving out the normalization term $\frac{\sqrt{2}}{2}$ for simplicity):
$$|\phi\rangle = |p_{up}\rangle + |p_{down}\rangle$$
Don't be scared by the bra-ket notation. $|x\rangle$ is just another way of writing the vector $\vec{x}$.
But of course we never see a particle in a superposition state. Whenever we check, the particle is either spin-up ($|p_{up}\rangle$) or spin-down. The other term disappears:
$$|\phi\rangle = |p_{up}\rangle$$
The question is, when does it disappear? When has it been measured?
Suppose we try to "measure" it by bouncing a second particle (q) off of it. (To measure spin we don't actually "bounce" anything, but the idea is the same.) But instead of that "collapsing" the first particle's state, we discover that the two are now entangled in a joint superposition, written:
$$|\phi\rangle = (|p_{up}\rangle \otimes |q_{up}\rangle) + (|p_{down}\rangle \otimes |q_{down}\rangle)$$
In one of the sum terms, p is spin-up and q "agrees," and in the other term, p is spin-down and q agrees. This doesn't look at all like the earlier "collapsed" state, and indeed we can tell it apart by some clever interference experiment. On the other hand, if we check whether particle p by itself is still exhibiting interference, the answer will be no. So in a sense, p behaving classically, but the p-q system as a whole is "still quantum."
What if we introduce a third particle r? Will it collapse the first two? No, it will just join in on the fun (I'll drop the $\otimes$ symbol for cleanliness):
$$|\phi\rangle = (|p_{up}\rangle |q_{up}\rangle |r_{up}\rangle) + (|p_{down}\rangle |q_{down}\rangle |r_{down}\rangle)$$
So then what does collapse it? As the system encounters more particles -- a few more in a controlled lab setting, or trillions more as it contacts the messy environment -- they should all just join in. If we lump q and r into the environment (env):
$$|\phi\rangle = (|p_{up}\rangle |env_{up}\rangle) + (|p_{down}\rangle |env_{down}\rangle)$$
In the first term, p is spin-down and the environment reflects this (and vice versa for the other term). So we still haven't answered the question: why do I only see one of those two outcomes?
There are two broadly popular answers to that question:
1) The orthodox ("Copenhagen") interpretation. It says, essentially, that somewhere on the way from one particle to trillions, it suddenly "collapses" into one state or the other. This was by far the favored interpretation in the early days, and roughly 39% of physicists still prefer it even though it's ill-defined[3].
2) The Many Worlds Interpretation (MWI), which says that no collapse ever happens. Instead, the universes keep splitting, ad infinitum. Every time you encounter the result of some indeterminate experiment (which is nonstop, since your environment is filled with tiny particles), your universe splits and you do, too.
The problem with Copenhagen (other than the fact that nobody seems to agree on what it is) is that it doesn't really tell us when or why this special "collapse" (which, by the way, disobeys what is known as unitary evolution which applies in all other cases) happens. We should just quietly assume it does. And for any practical experiment, that's good enough.
But as technology improves and we are able to isolate larger and larger quantum systems, we haven't run into this magic wall where the unitary laws of physics suddenly break down. We keep getting bigger entanglements rather than a sudden collapse. We're starting to question why we needed such an odd assumption to begin with. As a result, more and more physicists are switching to MWI.
But the problem with MWI is in how it answers the fundamental question "why do I only see one outcome?" The answer is that you don't -- you "actually" see all of them. You see, when you encounter the system, you become entangled with it. Each branch of the superposition becomes a parallel universe, and each universe has one copy of you. One copy of you sees "up" and the other copy sees "down." Asking why you you see "up" is nonsense, because in a parallel universe, the "other you" is asking why she sees "down." There isn't one you. In fact, as the universes keep splitting and splitting, there become infinitely many of you.
Yeah.
Now consider what happens after we run 100 iterations of the up/down experiments above. According to Copenhagen, since each time there is a 50%-50% chance of each outcome, you should expect that roughly half of the experiments come out heads. If you get a "lucky streak" of all ups, then as that lucky streak gets longer, you should increasingly suspect that something is wrong with either your setup or QM itself.
What about in MWI?
Well, in MWI there will be $2^{100}$ (~$10^{30}$) universes, each with its own string of outcomes ("UUDDUDD..."). On average, across all of them, there will be as many ups as downs. But since the question of where "you" end up is meaningless, there's no reason "you" shouldn't find yourself in a universe with all up, for example. If there were just one of you, and on each split you followed a path randomly, then we could make a statement like "the expected number of ups is 50, and it's very unlikely that you'll end up with all ups," but that doesn't apply here. You didn't end up with all ups; only "one copy of you" did.
On average, the $2^{100}$ copies of you are fulfilling their quantum (Born rule) obligation to see only half ups, but one of those gals had to be the one who saw all ups... so why shouldn't that be this you? What prevents you you from being the lucky one? Nothing. It doesn't contradict the theory or interpretation in any way. The quantum police won't come knocking just because you keep ending up astronomically lucky.
But the weirdness has just begun.
In MWI, you do indeed model the world as:
$$|\phi\rangle = (|p_{up}\rangle |env_{up}\rangle) + (|p_{down}\rangle |env_{down}\rangle)$$
Right up until the moment you see the result yourself (that is, encounter p or env in any way that would reveal the outcome). But env here includes the bodies and brains of any experimenters that encountered the system before you.
On the other hand, once you encounter the system, you can no longer treat it as a superposition. You cannot do any interference experiment, even in principle, that would suggest that it's still in a superposed state. You are definitively in either one or the other branch. Not only that, but everybody else in that universe will see the same thing you do. If you see 100 ups, they do as well -- even if they saw the outcome long before you.
This should give you a bit of pause. There's nobody else in "your universe" that is capable of collapsing the superposition like that. Each one of them just gets swept up into the entanglement, permitting you (in principle, but certainly not in practice -- probably ever) to do an interference experiment that would demonstrate this. But once you encounter it, all bets are off.
You're the only one who can do this.
Of course, the situation is symmetric for all other conscious observers (assuming there are any). From their perspective, in their universe they are the only one able to do this. And there's no contradiction, because you never inhabit the same universe. All the other people you see in your universe are your copies of them. And from your perspective, they are simply globs of matter obeying mindless physical laws.
Somehow, in your universe (this one!) the buck stops with you. Don't take my word for it. This is well-accepted.
Why isn't this mystical interpretation off-putting to believers of MWI? Well, if you could take the "inside perspective" of any object, you indeed would be the sole observer. But since consciousness is just an illusion, you can't take such a perspective, so there's no problem!
Which is all well and good, but I'm one of those weirdos who does believe he's conscious and inhabiting just one universe. And so maybe I have to suck it up and grudgingly accept my fate as the only conscious observer here. On the other hand, nothing seems to stop me (in principle) from "choosing" which of those universes I want to be "birthed into" -- although nothing explicitly permits me to do this either. In fact, there seems to be nothing in physical reality that can have control over which universe I "end up in," period, given that all of physical reality is (by definition) embedded in the universe. So maybe instead of begrudging acceptance, I should be filled with awe and gratitude.
This is your universe, and your playground. Not "you" as in your body or brain (which, being physical objects, are just part of the environment, just like other experimenters), but that which is looking out your eyes, so to speak.
Is there something looking out your eyes? Something non-physical? Obviously physics says "no." But instead of taking anyone's word for it, I invite you to check for yourself. If the answer is "yes," you have a whole lot of responsibility.
Footnotes
1. You will often hear it said that there's nothing special about conscious observers in QM. For example, famed physicist Sean Carroll:“Observation” in quantum mechanics is just a suggestive word meaning “interaction between a quantum system and another quantum system, especially in the case where the second system includes many environmental degrees of freedom that are not explicitly accounted for.”In other words, when q interacted with p, it was an "observation" of sorts. But because it's easy to still see quantum effects with two particles (because we can "explicitly account for" them), we should maybe hold off on calling it an observation until we have so many other particles in on it that we can no longer do so. And since what we call "conscious observers" are themselves made of lots of particles, they qualify as "many environmental degrees of freedom" instead of consciousness being something special.
As we saw, we should indeed treat things this way... with respect to other experimenters. It does not address the question of why I only see one outcome. Indeed, it doesn't even try to address that question, because strictly speaking, it belongs to metaphysics.
2. Many times physicists will explain that the consciousness thing is a red herring. There's nothing interesting to consider about it, and it has nothing to do with QM. If you don't agree, you have good company. Here's the greatest physicist of modern times agreeing with you.
3. Sean Carroll again: "I think Copenhagen is completely ill-defined, and shouldn’t be the favorite anything of any thoughtful person"
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