Question about Quantum mechanics

[Perpetual Student]

s. i.:
I believe the above summary of the three interpretations of QM is a bit biased.
It is also true that the Copenhagen interpretation requires accepting the concept of "superposition of states" a very non-intuitive, magical kind of reality.
Many worlds infinitely complicates reality if every collapse of the wave function results in an additional universe, which is magically undetectable and cannot be unambiguously demonstrated.
Bohm's approach is simply that the wave function "guides" the particle in a very intuitive and non-mysterious way. (i. e.: the wave goes though both slits but the particle goes through only one.) All the descriptions I have read (as a layman) seem to have no problem with SR, so I'm not convinced by that objection.
Non-locality (which seems to me to be preferable among these convoluted choices) is the price one pays for accepting a non-magical interpretation.

 

[Vorpal]

I'm not sure what "slice of constant t" means. But certainly you can write down laws of physics that depend on derivatives of your "clock scalar". If your clock scalar has the kind of profile I think you have in mind (it depends on t only in some specific Lorentz frame), ...

It's some real scalar field with sets of the form {x^μ: t(x^μ) = const} giving a spacelike foliation with increasing t in the future direction. It could be the time coordinate in some Lorentz frame, but that's not necessary.

... then the solutions to those laws will not be Lorentz invariant, in the sense that experiments at rest in different Lorentz frames will give physically different results.

Yeah, that's why I thought it breaks (1). But such a law gives an acceleration four-vector that's the same geometrical quantity in every frame, so I thought it would satisfy (2).

Generally one requires neither of those, although it's closer to (1). Lorentz invariance of laws really means that the laws are derivable from a Lorentz invariant action principle. It usually also means that experiments done carefully enough, at short enough distance or at high energy energy, will satisfy (1).

Ah! That directly answers my original question about the implicit assumption about the laws of physics. Thanks.

So you certainly cannot require (2) - for example, rather than the acceleration consider the trajectory. Any trajectory at all breaks Lorentz invariance.

But can't I blame that on the initial conditions rather than the law itself, and still say that the above acceleration satisfies (2)?

 

[Perpetual Student]

Originally Posted by sol invictus
Because in SR, space and time are mixed. A non-locality in space is a non-locality in time, from both past to future and future to past. Therefore non-locality implies acausality, which destroys not just every known law of physics, but the entire conceptual framework they are based in.

One could also say, superposition of states destroys every known law of physics and the entire conceptual framework. OK, which is less appealing -- "non-locality in space as well as time" or "superposition of states"? Many decades of familiarity with superposition of states has made it more familiar as a concept, but it is no more sensible than non-locality, in my view.

 

[Vorpal]

Many worlds infinitely complicates reality if every collapse of the wave function results in an additional universe, which is magically undetectable and cannot be unambiguously demonstrated.

I disagree with both the conclusion and the reason given (to a point). MWI is like Copenhagen without the state collapse due to measurement. Copenhagen already says that the state of isolated systems evolves through the Schrödinger equation; MWI simply applies this to the universe. MWI simply doesn't collapse the wavefunction of the universe, which continues to evolve by the Schrödinger equation at all times. Therefore, it is is theoretically simpler, as it has fewer postulates.

MWI's worlds are components along some particular axes in the Hilbert space, so their "creation" is nothing at all magical: it's just the state evolving to have a component along that axis.

I think calling them "universes", although strictly speaking an unproblematic issue of vocabulary, introduces a kind of anti-MWI bias (of the "that's ridiculous" knee-jerk type) and invites possible confusion.

 

[randman]

Ok, just want to get this clear what MWI says in terms of the physical world. If you fire a photon through 2 slits and it appears to go through both at the same time, there is another identical world doing the exact same thing. Both worlds appear to be the same, but that's not the case actually.

If you fire the photon through and determine the which-way path, another world ran the experiment firing it through without doing that and likely one did it where it went through the other slit. Every possibility is happening.

So there's a lot of us doing similar things in other universes, people exactly like us except in respect to finding out the which-way path of a particle.

The photon interacts with more than one universe, or are there multiple photons? In other words, and this is what I am trying to get an answer on, does the photon travel though both slits or is it one world fires the photon at the same time and it goes through one slit and another going through the other? We just experience both photons because our universe is so close together, but once we determine more information, we've moved further apart and so only see "our" photon.

I am assuming since the idea is the photon collapses, that there is just the single photon initially existing in a wave-like pattern. Is that assumption correct?

So why wouldn't other informational changes result in a split as well. For example, say I think something different than my counterpart in the identical universe, wouldn't that also cause a divergence?

So thoughts too should be able to and do all the time create a divergence from other universes. Maybe each thought and feeling means there is a different universe because the counterpart that was the same thought something else while at the same time, there could be more duplicates of me, would have to be billions even, that are still experiencing the exact same universe but each time one of us chooses something different in thought (in the brain) or action, one of those counterparts is off experiencing a different reality.

This brings up another question then. Since we are experiencing the exact same thing, are we interacting with each other in the same way as the photon? We'd have to be, right? We just don't know it.

So our consciousness would then occupy maybe billions of universes which all at that time are identical but with some that will be splitting off shortly.

So can we then choose by our thoughts and actions where our consciousness will go?

Anyway, back to the photon, if there are so many universes and we in our experience split off from them by obtaining which-way path of the photon, then why do we need to think of the photon as wave-like at all?

Wouldn't we just be seeing the other universe's photons because we are so close together. Our photon never collapses, it just separates itself from the other photons by the other universes splitting off at that point.

 

[Perpetual Student]

I disagree with both the conclusion and the reason given (to a point). MWI is like Copenhagen without the state collapse due to measurement. Copenhagen already says that the state of isolated systems evolves through the Schrödinger equation; MWI simply applies this to the universe. MWI simply doesn't collapse the wavefunction of the universe, which continues to evolve by the Schrödinger equation at all times. Therefore, it is is theoretically simpler, as it has fewer postulates.

MWI's worlds are components along some particular axes in the Hilbert space, so their "creation" is nothing at all magical: it's just the state evolving to have a component along that axis.

I think calling them "universes", although strictly speaking an unproblematic issue of vocabulary, introduces a kind of anti-MWI bias (of the "that's ridiculous" knee-jerk type) and invites possible confusion.

Perhaps I don't understand MWI well enough. From Wikipedia:

Many-worlds is a postulate of quantum mechanics that asserts the objective reality of the universal wave-function, but denies the reality of wave-function collapse, which implies that all possible alternative histories and futures are real —each representing an actual "world" (or "universe").

That certainly seems to imply a multiplicity of universes, whatever that means. Are these universes ghosts? phantoms? ethereal realities? It all seems to be quite spooky (borrowing Einstein's word).

 

[W.D.Clinger]

Usual disclaimer: I am not a physicist.

s. i.:
I believe the above summary of the three interpretations of QM is a bit biased.
It is also true that the Copenhagen interpretation requires accepting the concept of "superposition of states" a very non-intuitive, magical kind of reality.
Many worlds infinitely complicates reality if every collapse of the wave function results in an additional universe, which is magically undetectable and cannot be unambiguously demonstrated.
Bohm's approach is simply that the wave function "guides" the particle in a very intuitive and non-mysterious way. (i. e.: the wave goes though both slits but the particle goes through only one.) All the descriptions I have read (as a layman) seem to have no problem with SR, so I'm not convinced by that objection.
Non-locality (which seems to me to be preferable among these convoluted choices) is the price one pays for accepting a non-magical interpretation.

With my background, I'm inclined to think about these interpretations by employing an abstraction motivated by quantum computation. I think of quantum mechanics as a composition of two parts:

1. Evolution of wave functions.
2. Interactions/measurements/observations.

That first part involves differential equations and related math I've never been very good at. That second part involves Hilbert spaces, probabilities, partial orders, modal logics, nondeterminism, and other stuff with which I'm more comfortable because (apart from Hilbert spaces) it's the kind of math we use to describe the semantics of nondeterministic computer programs.

In particular, I'd like to point out that a guy I know won a Turing Award in 2007 for using temporal logic to reason about nondeterministic programs. The class of models he used were invented by philosopher Saul Kripke circa 1960.

The central idea of Kripke's semantics is that of a modal frame, which consists of a set of worlds W and a binary relation on worlds that tells which worlds are accessible from a given world. I don't know whether physicists use modal logic, but it seems to me that Kripke-style semantics provides a natural logical foundation for Everett's many-worlds interpretation of quantum mechanics.

 

[sol invictus]

s. i.:
I believe the above summary of the three interpretations of QM is a bit biased.
It is also true that the Copenhagen interpretation requires accepting the concept of "superposition of states" a very non-intuitive, magical kind of reality.

Why would you expect reality to conform to your intuition? If there's one thing the history of physics should teach you, it's how rarely intuition is correct when applied to anything other than human scale phenomena in environments similar to that of the earth's surface.

Many worlds infinitely complicates reality if every collapse of the wave function results in an additional universe, which is magically undetectable

There's nothing "magical" about any of this - that's just nonsense. We're talking about a precisely formulated mathematical theory that either behaves as advertised or doesn't.

 

[sol invictus]

But can't I blame that on the initial conditions rather than the law itself, and still say that the above acceleration satisfies (2)?

It might be that the acceleration satisfies (2) (although I don't actually see why, since the time slice does not), but if so that's a minor miracle. There's no reason or need for it to. After all, the laws of physics that govern this world are Lorentz invariant as far as we can tell, but very few if any of the trajectories of objects around us have accelerations that are Lorentz invariant.

 

[Vorpal]

Ok, just want to get this clear what MWI says in terms of the physical world. If you fire a photon through 2 slits and it appears to go through both at the same time, there is another identical world doing the exact same thing. Both worlds appear to be the same, but that's not the case actually.

Not quite.

If you fire the photon through and determine the which-way path, another world ran the experiment firing it through without doing that and likely one did it where it went through the other slit. Every possibility is happening.

There is no another world prior to the which-way measurement. Call the paths 1 and 2, which the measurement apparatus will report, and the state of the apparatus prior to measurement 0.

Then you the combined (particle,appartus) initial state is
[latex]|\psi\rangle = \frac{1}{\sqrt{2}}\left[|1\rangle+|2\rangle}\right]\otimes|0\rangle[/latex]
But after measurement, it is
[latex]|\psi\rangle \approx \frac{1}{\sqrt{2}}\left[|1\rangle\otimes|1\rangle + |2\rangle\otimes|2\rangle\right][/latex]
(btw, what's with the malformed |ψ> in LaTeX on this board?)

So really all that happens is that your universe's wavefunction evolved to have components along the |1>⊗|1> and |2>⊗|2> axes (subspaces), whereas it did not before. One could interpret this as a world that "splits" into two other worlds, and one could say a lot of things about why the final state becomes like that (and I'll leave decoherence to those with better understanding than mine), but at the end of the day, the state is still in the same Hilbert space, and the "worlds" are still given by the components of the state along some particular axes.

That certainly seems to imply a multiplicity of universes, whatever that means. Are these universes ghosts? phantoms? ethereal realities? It all seems to be quite spooky (borrowing Einstein's word).

I think it becomes a lot less spooky if one thinks of them in the above manner. There's nothing mystical about a vector that, being rotated in some manner, comes to have components along some axes that it didn't before.

 

[sol invictus]

All the descriptions I have read (as a layman) seem to have no problem with SR, so I'm not convinced by that objection.

Have you ever seen a relativistic version of Bohm?

One could also say, superposition of states destroys every known law of physics and the entire conceptual framework.

One could say that, but one would be completely wrong.

 

[sol invictus]

If you fire the photon through and determine the which-way path, another world ran the experiment firing it through without doing that and likely one did it where it went through the other slit. Every possibility is happening.

That might be true, but it doesn't need to be. We can instead imagine an initial state wavefunction that describes a single experimental setup.

what I am trying to get an answer on, does the photon travel though both slits or is it one world fires the photon at the same time and it goes through one slit and another going through the other?

That just doesn't have a simple answer, sorry. You can think of it either way, so long as you bear in mind that the two "worlds" in the latter view are not classically distinct and can interfere with each other in the future.

So why wouldn't other informational changes result in a split as well. For example, say I think something different than my counterpart in the identical universe, wouldn't that also cause a divergence?

Every interaction will cause a divergence - but let's focus on one at a time.

 

[Vorpal]

It might be that the acceleration satisfies (2) (although I don't actually see why, since the time slice does not), but if so that's a minor miracle.

It does because the time slice is not according to the time of any Lorentz frame (except possibly by accident), but rather a scalar field on spacetime, so that any two observers will agree on its value provided they have some way of measuring it.

There's no reason or need for it to. After all, the laws of physics that govern this world are Lorentz invariant as far as we can tell, but very few if any of the trajectories of objects around us have accelerations that are Lorentz invariant.

That's fair, but the question of whether the actual laws of physics have anything like that particular acceleration is different from deriving the non-locality = acausality equivalence from STR's spacetime alone, which is what we started with. (Or, at least, how I interpreted your initial statement, though you've clarified it to include a particular interpretation of Lorentz invariance of laws.) That acceleration is consistent with STR.

 

[sol invictus]

It does because the time slice is not according to the time of any Lorentz frame (except possibly by accident), but rather a scalar field on spacetime, so that any two observers will agree on its value provided they have some way of measuring it.

Sure - but that doesn't imply that the resulting acceleration is Lorentz invariant, and in fact I don't see how it could be. If you disagree, please give me an example of a trajectory with an acceleration that's Lorentz invariant (you might succeed in finding an example that's Lorentz invariant about some special point, but you will not succeed in finding one that's LI about any point).

In other words your rule for determining the acceleration (integrate that integrand along a surface of constant \phi) might be Lorentz covariant, but that does not mean that the result will be Lorentz invariant.

That's fair, but the question of whether the actual laws of physics have anything like that particular acceleration is different from deriving the non-locality = acausality equivalence from STR's spacetime alone, which is what we started with. (Or, at least, how I interpreted your initial statement, though you've clarified it to include a particular interpretation of Lorentz invariance of laws.) That acceleration is consistent with STR.

If the laws are Lorentz invariant, they allow us to perform a boost on any given configuration, and then know that the same laws apply to the boosted configuration. So suppose you have non-locality, in the sense that event A can influence distant event B instantaneously (or at any time before light could propagate from A to B). Consider a configuration where A influences B. Now boost, and you'll find that A influenced B even though B occurred before A. But since the same laws of physics apply in the boosted frame, the laws must therefore be acausal.

 

[Vorpal]

You're right in that having a rule for quantity that's invariant (which is what I was thinking of) is different from the result being invariant (which is what I actually said in #58). Hence the follow-up

But can't I blame that on the initial conditions rather than the law itself, and still say that the above acceleration satisfies (2)?

Regarding Lorentz invariance of physical laws, I've already conceded that your clarification side-steps my criticism entirely, and renders it arguably moot.

My only contention was the original context of your claim referred to SR's mixing of space and time only, so that the above acceleration is both (a) non-local, and (b) not acausal, and hence a counterexample your original statement.

If the laws are Lorentz invariant, they allow us to perform a boost on any given configuration, and then know that the same laws apply to the boosted configuration. So suppose you have non-locality, in the sense that event A can influence distant event B instantaneously (or at any time before light could propagate from A to B).

OK. I can jiggle some masses and send a superluminal signal assuming gravity behaves like the postulated acceleration.

Consider a configuration where A influences B. Now boost, and you'll find that A influenced B even though B occurred before A. But since the same laws of physics apply in the boosted frame, the laws must therefore be acausal.

I don't think the acceleration is Lorentz-invariant by the definition you gave in #60, but if having an invariant rule qualifies, then I don't see why causality is broken. Yes, the coordinate time in the boosted frame is as you say, but this fact alone seems of little relevance, because I still can't see any experimental setup that sends a signal to one's own past: the scalar field makes the order of events unambiguous.

That's unlike the situation with hypothetical 'ansibles' that send an instantaneous signal in their own rest frame. One can use them as relays to send information to the past by boosting them.

 

[sol invictus]

I don't think the acceleration is Lorentz-invariant by the definition you gave in #60, but if having an invariant rule qualifies, then I don't see why causality is broken. Yes, the coordinate time in the boosted frame is as you say, but this fact alone seems of little relevance, because I still can't see any experimental setup that sends a signal to one's own past: the scalar field makes the order of events unambiguous.

Try considering a different configuration of the scalar - one where the constant surfaces aren't spacelike, for example, or one where in one part of the space they are boosted relative to another part.

If such configurations aren't allowed by whatever fundamental laws of physics govern your scalar, then the fundamental laws cannot be Lorentz invariant. But if they are allowed, you can build time machines (actually I'm not sure you can in your example, but I think you could in any example that's non-local in the sense I described above).

 

[randman]

Seems like a lot of trouble to preserve some basic assumptions of physics that may not really be laws in the first place but just probabilities that work on a macro-level.

This site suggests you cannot under MWI have preexisting universes but that a split definitely takes place.

Can we regard the separate worlds that result from a measurement-like interaction (See "What is a measurement?") as having previous existed distinctly and merely differentiated, rather than the interaction as having split one world into many? This is definitely not permissible in many-worlds or any theory of quantum theory consistent with experiment. Worlds do not exist in a quantum superposition independently of each other before they decohere or split. The splitting is a physical process, grounded in the dynamical evolution of the wave vector, not a matter of philosophical, linguistic or mental convenience (see "Why do worlds split?" and "When do worlds split?") If you try to treat the worlds as pre-existing and separate then the maths and probabilistic behaviour all comes out wrong.

http://www.hedweb.com/everett/everett.htm#relative
http://www.hedweb.com/everett/everett.htm#relative

 

[randman]

The series of delayed-choice experiments and quantum eraser experiments seem to disagree with the MWI.

Our realization of Wheeler’s delayed- choice GedankenExperiment demon- strates beyond any doubt that the behavior of the photon in the interferometer depends on the choice of the observable which is measured, even when that choice is made at a position and a time such that it is separated from the entrance of the photon in the interferometer by a space-like interval. In Wheeler’s words, since no signal traveling at a velocity less than that of light can connect these two events, “we have a strange inversion of the normal order of time. We, now, by moving the mirror in or out have an un- avoidable effect on what we have a right to say about the already past history of that photon” (7).

http://fr.arxiv.org/PS_cache/quant-ph/pdf/0610/0610241v1.pdf

This is just one of the latest but the experiments suggest that measuring for the which-way path determines not just the path from that point forward but also the path in the past, and that contrary to earlier thoughts (quantum eraser experiment), that past which-way path is not set in stone.

The quantum eraser delayed-choice experiment suggests that the collapse of the wave function into a discrete state is actually reversible.

In a quantum eraser experiment, one arranges to detect which one of the slits the photon passes through, but also to construct the experiment in such a way that this information can be "erased" after the fact.

http://en.wikipedia.org/wiki/Delayed_choice_quantum_eraser

If these experimenters are correct in saying their work shows that measurement causes the path of the photon prior to the measurement to have taken a which-way path, then MWI does not solve the issue of causality and locality.

 

[sol invictus]

Seems like a lot of trouble to preserve some basic assumptions of physics that may not really be laws in the first place but just probabilities that work on a macro-level.

I'm not sure what you're referring to.

This site suggests you cannot under MWI have preexisting universes but that a split definitely takes place.

The way that site defines "world" isn't quite the way I have been in this thread.

Obviously nothing can stop me from writing |psi> = |psi>/2+|psi>/2, or |psi>=(|chi>+|phi>)/root(2), or any one of an infinite number of other possible combinations of states that add up to |psi>. It's obviously not the case that "something goes wrong with the math" if I do so.

But as I've said several times, different terms in a superposition don't necessarily correspond to distinct "worlds" in the sense that they cannot interfere with each other. It's only when those terms correspond to states that will have extremely small interference with each other (to be a little more precise, when the Hamitonian has very small off-diagonal matrix elements in that basis) that we can say they are distinct worlds.

So when I say you should consider the initial state to be collection of worlds that later split off, that's a fine way to think about it, but you have to understand that prior to the split those worlds are really not distinct - they are just identical copies of each other and therefore can interfere (constructively in that case).

 

[sol invictus]

The series of delayed-choice experiments and quantum eraser experiments seem to disagree with the MWI.



http://fr.arxiv.org/PS_cache/quant-ph/pdf/0610/0610241v1.pdf

This is just one of the latest but the experiments suggest that measuring for the which-way path determines not just the path from that point forward but also the path in the past, and that contrary to earlier thoughts (quantum eraser experiment), that past which-way path is not set in stone.

The quantum eraser delayed-choice experiment suggests that the collapse of the wave function into a discrete state is actually reversible.



http://en.wikipedia.org/wiki/Delayed_choice_quantum_eraser

Those experiments work like this. You set up a quantum Mach-Zender interferometer. Single photons entering the interferometer will interfere with themselves at the outputs if no measurement is made along the arms, and will not if a measurement is made along the arms. You set up a random number generator to decide whether to make such a measurement, and the decision is taken after the photon has entered the interferometer. What you find is that, even though the decision was made after the photon entered the interferometer, you still observe or don't observe the interference as above.

Does this conflict with the MWI? Nope, not at all. Let's see how it works. First, the photon enters the interferometer and goes both ways. Second, the random number generator fires and determines whether or not to make a measurement. So the state is now something like (|A>+|B>)*(|M>+|NM>), where A and B refer to arms of the interferometer and M and NM refer to measurement and no measurement.

Next, the measurement occurs in the "world" where it was selected. After that, the state is

|A>|MA>+|B>|MB>+(|A>+|B>)|NM>,

where MA means "measured photon in arm A", etc.

Finally, in the "no measurement" world the photon arrives at the final beam splitter in the interferometer, interferes with itself, and we have

|A>|MA>+|B>|MB>+|I>|NM>

where I means the result of the photon interfering with itself. Note that all of those interactions are local and causal.

The MWI predicts three possible outcomes, and that's exactly what is observed.

If these experimenters are correct in saying their work shows that measurement causes the path of the photon prior to the measurement to have taken a which-way path, then MWI does not solve the issue of causality and locality.

They would be correct if there was a unique outcome to the experiment. But there isn't, at least not according to the MWI.