Electron indeterminism Problem

[pibomb]

Hi,

I wanted to know the answer to this riddle:

You have two electrons with unknown spin both inside two different boxes. You and friend take these boxes to the ends of the universe and one of you opens the box. Because the electrons are indeterminate before this, you open your box, find the electron's spin. Let's say, theoretically, that your friend opened the box one second after you. How does the "information" of the first electron's spin reach the other box before your other friend opens it?

I know Einstein tried to use this to disprove quantum theory, but I don't know what the solution physicists came for this problem was. Please answer this somewhat confusing question.

 

[Allday]

Einstein, Podolsky, and Rosen

Hi Pibomb, welcome to physics forums. Let me take a first crack at your question. The situation I think you have in mind concerns the EPR paradox. If you google that you will get a more complete answer. Also try googling the Aspect experiment, but for now here's a little more background.

One key word we need here is entanglement. If you just take 2 random electrons (they need not be in boxes) that have never been in contact before and measure their spins, the two results are uncorrelated. That means the result of one measurement has no effect on the other measurement. BUT if the 2 electrons (or photons or any other quantum particles) have been entangled then the situation you describe below does happen and the results of the measurements are correlated.

Very roughly speaking you can entangle 2 particles by allowing them to come close enough to each other that their wavefunctions overlap, but ill leave the explanation of that to the experimentalists on the site.

Anywho the correlation of the measurements over large distances has been demonstrated and is a very real thing. We are left with 2 possibilities.

1. The electrons communicated with each other through some faster than light method to tell each other which spin they each were going to be. this is know as non-locality.

2. there is something about the electrons that quantum mechanics doesn't currently address that imprinted the spin they would choose when later measured allowing them to have opposite spins. This something was decided between the electrons when they were close and being entangled. this is known as the hidden variable theory.

People have been puzzling over this for a long time and there is still not a overwelming majority view imho. The experiment done by Alain Aspect prooved (some may debate this) that there can be no hidden variable in quantum mechanics and therefore there is non-locality in the theory. The exact way the non-locality enters the theory is a topic that is not settled yet as far as i know.

I typed this out pretty quickly so there may be some gross errors/simplifications here, but i hope it was helpful

Gabe

 

[kvantti]

There is a third solution:

The electrons are deterministic and localized particles which are in the opposite states because of conservation laws.
http://arxiv.org/abs/quant-ph/9906007

 

[DrChinese]

I know Einstein tried to use this to disprove quantum theory, but I don't know what the solution physicists came for this problem was. Please answer this somewhat confusing question.

Einstein thought that quantum theory made an incorrect prediction in this case. After his death, a version of this experiment was performed with entangled particles. The results were as predicted by QM.

It does "appear as if" the wave function of the entangled pair collapses at a velocity greater than the speed of light. The confusing thing about this is that no one *really* knows what "wave function collapse" is. Is it physical? Because there appears to be nothing about this collapse that allows information to itself be transmitted faster than light. The appearance of the correlation is only noticed once the separate results are brought together.

 

[pibomb]

That somewhat clears up my question...but that leads me to question the true definition of a wavefunction. What Allday says is that a wavefunction is more than a number of probability...if this is true...then what is the official definition of a wavefunction?

 

[Allday]

the wavefunction

the wavefunction is easy to desscribe mathematically.

It is a complex function that describes the state of the particle. Think of every point in space having a complex number associated with it. If you take the magnitude squared of that number then you have the probability that a measurement of the particles position will return that point.

What the wavefunction is physically is a very different story and i won't try to confuse you with a kabillion interpretations. The most straightforward one (i think) is that it is a probability current and doesn't have a solid physical interpretation. however what i have given you is the vanilla, standard university explanation, there are many other interpretations.

gabe

 

[pibomb]

I see...I assume when you say complex number you mean a number system incorperating "imaginary numbers" or just a more complicated number. Futhermore, when an electron's wavefunctions "overlap," what does it give to the electron itself?

Also, I did google "quantum entanglement" and I did learn that it associates when a photon splits into two smaller ones and some weird, extraordinary characteristic that tells them when to decide on a spin up or down. But what is the quantum mechanical view of this?

 

[jtbell]

then what is the official definition of a wavefunction?

There is no general agreement about this. There are various interpretations of what the mathematics of quantum mechanics "really means," which all use the same mathematical machinery (or at least reduce to the same mathematical machinery). They make the same predictions for the results of physical experiments, so there is no way to distinguish among them experimentally. People argue passionately about them nevertheless.

 

[kvantti]

Understanding QM becomes even harder if you look at the http://www.einstein-online.info/en/spotlights/path_integrals/index.html of it. Although mathematically equivalent with all the other formulations, it becomes obvious that the particle interferes with itself. Or atleast its statefunction does... which I like to interpret as a description of state of the particle.

 

[ueit]

Understanding QM becomes even harder if you look at the path integral formulation of it. Although mathematically equivalent with all the other formulations, it becomes obvious that the particle interferes with itself. Or atleast its statefunction does... which I like to interpret as a description of state of the particle.

The wave function cannot exist in our 4D spacetime therefore it cannot do anything ("interfering with itself" or whatever). It's only a mathematical abstraction usefull for calculating probabilities.

The "path integral " is another way to make calculations, it doesn't describe reality. Relativity denies the possibility of faster than light travel and it applies to quantum particles too.

 

[kvantti]

The wave function cannot exist in our 4D spacetime therefore it cannot do anything ("interfering with itself" or whatever). It's only a mathematical abstraction usefull for calculating probabilities.

That is the viewpoint of the Copenhagen interpretation. There are others.

The "path integral " is another way to make calculations, it doesn't describe reality.

Again, that is the viewpoint of the Copenhagen interpretation. You can also interpret that the mathematical formulation of quantum mechanics does in fact describe reality, but then you end up with the concept of multiverse.

Relativity denies the possibility of faster than light travel and it applies to quantum particles too.

there's no apparent faster than light communication between entangled particles in the multiverse. Everything is local.

 

[pibomb]

You can also interpret that the mathematical formulation of quantum mechanics does in fact describe reality, but then you end up with the concept of multiverse.

How so?

 

[kvantti]

You can also interpret that the mathematical formulation of quantum mechanics does in fact describe reality, but then you end up with the concept of multiverse.

How so?

Take a look at http://superstruny.aspweb.cz/images/fyzika/simulace/Schrödinger.htm , for example. The applet simulates time dependent statefunction of position of a particle in two dimensions. Let's say its the statefunction of an electron. If we now interpret that what you see does infact describe the position of the electron, not just possibilities of positions, you have to make a huge assumption: there exists a multiverse (= a set of multiple universes) in which the electron is at every location described by the statefunction. The "probability" tells us in how many universes the electron is at a given time, eg. if the probability of finding the electron in location [X] at time [T] is 0.01, the electron is located at [X] in 1% of the universes at the time [T].

 

[ueit]

You can also interpret that the mathematical formulation of quantum mechanics does in fact describe reality, but then you end up with the concept of multiverse.

Yeah, and this is a good reason to conclude that the math of QM does not describe reality as it is, but only a statistical approximation of it. All particles and forces used to calculate the wavefunction exist in 4D spacetime. The conservation laws work on 4D spacetime and they are always obeyed. There is no reason to assume that other universes, interacting with our own do exist.

Just like the other QM interpretations, MWI is a dead end. A big, unfalsifiable assumption on top of a mathematical formalism.

P.S.

I've never found a reasonable explanation of Schrödinger’s cat experiment in MWI. May be you could lighten me.

 

[kvantti]

Yeah, and this is a good reason to conclude that the math of QM does not describe reality as it is, but only a statistical approximation of it. All particles and forces used to calculate the wavefunction exist in 4D spacetime.

The wavefunction is an approximation of the path integral formulation, which is used to formulate quantum field theories. So in a way the path integral is more fundamental than the wavefunction. The simplest way to interpret the path integral formulation is that the particle actually does travel along all the possible paths from A to B. This approach says that the path integral describes all the paths the particle takes from A to B in the multiverse. Although counter intuitive, this is the simplest way to understand QM.

There is no reason to assume that other universes, interacting with our own do exist.

There are two reasons most people don't aknowledge:

The first is the fact that MWI is the only consistent interpretation with the block time interpretation of spacetime described by relativity:

Block time makes two assumptions, which are separable. One is that time is a full-fledged real dimension. The other is immutability. The latter is not a necessary consequence of the first. A universe in which random changes are possible may be indistinguishable from the many-worlds interpretation of quantum mechanics in which there are multiple 'block times'.

The equations of relativity say that the future/past state of a system is predetermined while the equations of quantum physics say that the future/past state is indetermined, so there is a contradiction. MWI erases this contradictions by saying that all the possible future/past states described by the equations of QM actually exist in different parts of the multiverse. This approach restores determinism to reality and is fully consistent with relativity. But don't get it wrong: although reality described by the MWI is deterministic, it is still completely indeterministic from the subjective point of view of an observer who experiences only one universe. But then again, the observer ends up in all the possible universes.

The other reason is the fact that general relativity predicts that our universe is "connected" with another universes through spinning black holes:

Because of its two event horizons, it might be possible to avoid hitting the singularity of a spinning black hole, if the black hole had a Kerr metric. At the outer event horizon, the properties of spacetime allow objects to move only towards the singularity. However, when an object passes the inner event horizon, the object is able to move in directions away from the singularity, pass through another set of inner and outer event horizons, and emerge out of the black hole into another universe or another part of this universe without traveling faster than the speed of light (following a time-like path).

Also, the MWI allows time traveling without paradoxes.

Just like the other QM interpretations, MWI is a dead end. A big, unfalsifiable assumption on top of a mathematical formalism.

The MWI has many implications for the quantum nature of spacetime which might have to be considered when formulating a quantum theory of gravity. For example, it implies that different frames of references are actually just special cases of different universes. In a sense the MWI is a whole theory of its own: the theory of multiverse.

I've never found a reasonable explanation of Schrödinger’s cat experiment in MWI. May be you could lighten me.

My pleasure.
Lets say the half-life of the radioactive substance in the 'machine of death' is [t]. So after t=[t] there is a 50% probability that the radioactive nucleus has decayed, which means that there is a 50% probability that the cat is either alive or dead. In context of the multiverse: after t=[t] the cat is alive in 50% and dead in 50% of the universes where the experiment is performed. After t=2[t] the cat is alive in 25% and dead in 75% of the universes, after t=3[t] alive in 12.5% and dead in 87.5% and so on. That percentage is also the probability of finding yourself in a universe where the cat is either alive or dead after t=x[t].

 

[cesiumfrog]

You can also interpret that the mathematical formulation of quantum mechanics does in fact describe reality, but then you end up with the concept of multiverse.
[...]
MWI is the only consistent interpretation with the block time interpretation of spacetime described by relativity

I think this is untrue. In particular, the various transactional interpretations are an example consistent with the block universe (and have recently been advocated by http://www.usyd.edu.au/time/price/" , who claims to show logical inconsistencies in MWI).

The main interpretations currently seem to be:
- mathematical tool only
- multiple worlds variants
- transactional variants
- wavefunction collapses as an irreversible random process

 

[ueit]

The simplest way to interpret the path integral formulation is that the particle actually does travel along all the possible paths from A to B. This approach says that the path integral describes all the paths the particle takes from A to B in the multiverse. Although counter intuitive, this is the simplest way to understand QM.

The simplest way to interpret QM is to acknowledge that it is only a statistical description of reality.
An electron's trajectory in a double slit experiment certainly depends on the geometry of the wall, but this is to be expected given the fact that the wall is built of particles which interact with electrons via EM force (electrons, quarks). To say that this experiment proves that the electron actually goes all paths is like saying that the Moon must travel with infinite speed to Earth, Sun, Jupiter and every other object in the universe and back so that it can find which trajectory to folow.

There are two reasons most people don't acknowledge:

The equations of relativity say that the future/past state of a system is predetermined while the equations of quantum physics say that the future/past state is indetermined, so there is a contradiction.

What QM equation says that "future/past state is indetermined"? AFAIK Schrödinger’s equation describes a deterministic universe. The indeterminacy comes from the measurement but there is no proof of that. It is a postulate. The fact that we only know to calculate probabilities doesn't mean that these probabilities are fundamental.

The other reason is the fact that general relativity predicts that our universe is "connected" with another universes through spinning black holes

If you carefully read the article (and the arxiv article linked there) you will find a lot of "if's":

it might be possible to avoid hitting the singularity of a spinning black hole, if the black hole had a Kerr metric

Unfortunately, it is unlikely that interior metric of a black hole is the Kerr metric.

I think that "general relativity predicts that our universe is "connected" with another universes" is too strong of a statement.

Also, the MWI allows time traveling without paradoxes.

This certainly explains the great number of time travelers captured by now!

The MWI has many implications for the quantum nature of spacetime which might have to be considered when formulating a quantum theory of gravity. For example, it implies that different frames of references are actually just special cases of different universes. In a sense the MWI is a whole theory of its own: the theory of multiverse.

If MWI is true, it has to be taken into account when formulating a QG theory. The problem is we don't know that, and we will never know because it's unfalsifiable.

Lets say the half-life of the radioactive substance in the 'machine of death' is [t]. So after t=[t] there is a 50% probability that the radioactive nucleus has decayed, which means that there is a 50% probability that the cat is either alive or dead. In context of the multiverse: after t=[t] the cat is alive in 50% and dead in 50% of the universes where the experiment is performed.

How did you get the 50%?

A universe in which the decay happens at time t1 is different from one in which the event takes place at t2. But a universe in which the decay does not happen at time t1 is similar with the one in which the decay does not happen at time t2. So, it seems to me, that MWI predicts a lot of dead-cat universes and only one alive-cat universe.

 

[pibomb]

Uh...excuse my my silly question...but what exactly is the "MWI" thing you guys are talking about?

 

[SF]

There is no information being transmitted between those two electrons.
There needn't be any.

From a purely quantum-mechanical perspective, the two particles were never really in individual states. We like to think of them as separate particles, but that's a mistake from our part, trying to imagine the quantum world in terms of the classical world. Ain't going to happen!
They are not separate entities; they are part of a quantum whole, and up until you measured their state (let's say you measured the spin), neither of them had spin-up or spin-down; their joint configuration was described by a single wavefunction.

 

[kvantti]

I think this is untrue. In particular, the various transactional interpretations are an example consistent with the block universe (and have recently been advocated by http://www.usyd.edu.au/time/price/" , who claims to show logical inconsistencies in MWI).

Wasn't aware that the transactional intepretation was consistent with it also. Thanks. Although I find it odd that a non-local interpretation is consistent with a block universe.

To say that this experiment proves that the electron actually goes all paths is like saying that the Moon must travel with infinite speed to Earth, Sun, Jupiter and every other object in the universe and back so that it can find which trajectory to folow.

I didn't say it proves, I said it was the simplest way to interpret the calculation. Which it is. If the probability of a given path is eg. 0.00000001, then the particle moves along this path in 1/100000000 of the universes. But if the probability of a given path is eg. 1/10^1000 and the number of universes participating in the experiment is only 10^500, then the particle doesn't move along this path in any of the universes. So in the end, the particle doesn't visit Anfromeda or even Jupiter when traveling from A to B.
The instrumentalist point of view you suggest says that QM has nothing to say about the physics behind the phenomenon, and here I disagree.

What QM equation says that "future/past state is indetermined"? AFAIK Schrödinger’s equation describes a deterministic universe. The indeterminacy comes from the measurement but there is no proof of that. It is a postulate. The fact that we only know to calculate probabilities doesn't mean that these probabilities are fundamental.

Huh? Do you think that QM is only a statistical tool or not? What do you think |ψ|^2 stands for? If it doesn't describe a probability of observation, then what? Sure the time evolution of statefunction is deterministic but the predicted observations that count are completely indetermined. The mathematical formulation of QM isn't deterministic in the sense that you can calculate exactly what will the outcome of a measurement be, and this should be the case in a completely deterministic block universe! So again, there is a contradiction between the two if QM is interpreted as a statistical tool. You can interpret that the statefunction describes the whole and deterministic time-evolution of a quantum system, but then you end up with the multiverse...

I think that "general relativity predicts that our universe is "connected" with another universes" is too strong of a statement.

Maybe, but the fact is that GR allows traveling into another universe through areas of spacetime with a certain geometry. Maybe a working theory of QG kills this option, but atm we don't know.

This certainly explains the great number of time travelers captured by now!

Who knows, maybe some of the observed UFOs are time travelers. GR allows time traveling, but it is classically thought to result in many paradoxes, hence it has been thought as a unphysical prediction. The MWI allows time traveling without paradoxes, hence making it possible - in theory.

How did you get the 50%?

The probability of a single radioactive nucleus having been decayed after Δt=[half-life of the nucleus] is 50%.

A universe in which the decay happens at time t1 is different from one in which the event takes place at t2. But a universe in which the decay does not happen at time t1 is similar with the one in which the decay does not happen at time t2. So, it seems to me, that MWI predicts a lot of dead-cat universes and only one alive-cat universe.

Nope. You should remember that every second billions of quantum worlds emerge from one another, so there exists always many universes where the cat is still alive. The probability of finding yourself in one of those universes just gets smaller and smaller when time goes on, because there always exists more of those universes where the cat is dead.

 

[ueit]

kvantti,

Sorry for the delay, I couldn't connect to the server from home. I hope I'll answer you this evening.

 

[ueit]

I didn't say it proves, I said it was the simplest way to interpret the calculation. Which it is. If the probability of a given path is eg. 0.00000001, then the particle moves along this path in 1/100000000 of the universes. But if the probability of a given path is eg. 1/10^1000 and the number of universes participating in the experiment is only 10^500, then the particle doesn't move along this path in any of the universes. So in the end, the particle doesn't visit Anfromeda or even upiter when traveling from A to B.

The "paths" you are speaking of are unphysical because they violate momentum conservation. If no force is acting on the particle, it goes in straight line, its momentum being conserved.

The instrumentalist point of view you suggest says that QM has nothing to say about the physics behind the phenomenon, and here I disagree.

I think we don't know how to interpret QM. Making unfalsifiable assumptions, some of them going against well established physics (like locality or conservation laws) does no good.

Huh? Do you think that QM is only a statistical tool or not? What do you think |ψ|^2 stands for? If it doesn't describe a probability of observation, then what? Sure the time evolution of statefunction is deterministic but the predicted observations that count are completely indetermined.

Yeah, just like in thermodynamics. If you measure the temperature of a gas, you get a probability distribution for the kinetic energy of the molecules. This is very different from saying that the kinetic energy of a molecule is "completely indetermined". QM just doesn't say anything about the stochastic/deterministic nature of the events it describes. So, you have no reason to say that QM contradicts relativity. QM could very well be a statistical description of a purely deterministic universe.

The mathematical formulation of QM isn't deterministic in the sense that you can calculate exactly what will the outcome of a measurement be, and this should be the case in a completely deterministic block universe! So again, there is a contradiction between the two if QM is interpreted as a statistical tool.

Does thermodynamics contradict relativity? According to your line of reasoning it should.

You can interpret that the statefunction describes the whole and deterministic time-evolution of a quantum system, but then you end up with the multiverse.

This is called "reductio ad absurdum". In order to calculate the wave function, you start with the assumption of point particles interacting in a 4D flat spacetime. A multiverse contradicts your original assumptions.

GR allows time traveling, but it is classically thought to result in many paradoxes, hence it has been thought as a unphysical prediction. The MWI allows time traveling without paradoxes, hence making it possible - in theory.

Just like any other QM interpretation, MWI fails to describe black holes or worm holes (if they exist), so bringing GR into discussion doesn't help you. Time travel is pure speculation and requires negative energy to produce the necessary curvature. Needless to say, no negative mass/energy particle was found to exist.

You should remember that every second billions of quantum worlds emerge from one another, so there exists always many universes where the cat is still alive. The probability of finding yourself in one of those universes just gets smaller and smaller when time goes on, because there always exists more of those universes where the cat is dead.

Can you just present this in a more detailed way? How many universes are created when a "splitting" event takes place, how do you calculate probabilities from that? In what way two universes in which the cat is still alive count as "different"?

 

[ueit]

Uh...excuse my my silly question...but what exactly is the "MWI" thing you guys are talking about?

MWI stands for Everett's "Many Worlds Interpretation" of QM.

 

[ueit]

There is no information being transmitted between those two electrons.
There needn't be any.

From a purely quantum-mechanical perspective, the two particles were never really in individual states. We like to think of them as separate particles, but that's a mistake from our part, trying to imagine the quantum world in terms of the classical world. Ain't going to happen!
They are not separate entities; they are part of a quantum whole, and up until you measured their state (let's say you measured the spin), neither of them had spin-up or spin-down; their joint configuration was described by a single wavefunction.

Are you saying that the electron doesn't have a magnetic moment until measured or that it just oscillates randomly?

 

[ttn]

It does "appear as if" the wave function of the entangled pair collapses at a velocity greater than the speed of light. The confusing thing about this is that no one *really* knows what "wave function collapse" is. Is it physical? Because there appears to be nothing about this collapse that allows information to itself be transmitted faster than light. The appearance of the correlation is only noticed once the separate results are brought together.

Well, let's try it both ways:

If collapse *is* physical, than QM is a nonlocal theory (just like some other nonlocal theories that have no trouble explaining the results of the Bell experiments).

If collapse *isn't* physical, then we have several distinct wave functions all describing the same one unchanged physical state -- i.e., QM then fails to provide a complete description of states, thus refuting Bohr and validating Einstein.

That dilemma was precisely Einstein's fundamental objection to the orthodox quantum theory. See

http://puhep1.princeton.edu/~mcdonald/examples/QM/norsen_ajp_73_164_05.pdf

 

[kvantti]

The "paths" you are speaking of are unphysical because they violate momentum conservation. If no force is acting on the particle, it goes in straight line, its momentum being conserved.

Actually the paths satisfy the Heisenberg uncertainty relation between momentum and position. Also, all the possible paths affect the observed position of a particle in the double slit experiment, for example. If the paths are unphysical, how can they affect the observed positions of the particles?

I think we don't know how to interpret QM. Making unfalsifiable assumptions, some of them going against well established physics (like locality or conservation laws) does no good.

The multiverse isn't an assumption; it is a consequence of a postulate. The MWI is completely local and deterministic, so it doesn't violate any "well established physics."

QM just doesn't say anything about the stochastic/deterministic nature of the events it describes.

Again, you can interpret it does. The wavefunction doesn't actually tell the whole story; path integral formulation gives a more fundamental insight about the behaviour of particles. You should read Feynmans QED: strange theory of light and matter if you haven't. I got shocked many times when reading it because you get so confused about how the nature works. Don't worry, there's no mention about the MWI.

So, you have no reason to say that QM contradicts relativity.

Every stochastic/non-local/indeterministic interpretation does contradict relativity. This has more to do with metaphysics than actual physics but you can't fit a model which is interpreted as being indeterministic with a model that is interpreted as being deterministic.

QM could very well be a statistical description of a purely deterministic universe.

That is the case in the MWI.

Does thermodynamics contradict relativity? According to your line of reasoning it should.

Nope, it is a classical theory. Only stochastic particles (that exist in the indeterministic interpretations of QM) contradict relativity.

This is called "reductio ad absurdum". In order to calculate the wave function, you start with the assumption of point particles interacting in a 4D flat spacetime. A multiverse contradicts your original assumptions.

How does it contradict my original assumption? According to MWI, the statefunction/wavefunction is a statistical tool that describes the relative states of a single particle in different parts of the multiverse, ie. it describes the distribution of the particles position in different universes.

Just like any other QM interpretation, MWI fails to describe black holes or worm holes (if they exist), so bringing GR into discussion doesn't help you. Time travel is pure speculation and requires negative energy to produce the necessary curvature. Needless to say, no negative mass/energy particle was found to exist.

It is true that you can't describe GR effects using QM, but a future theory of QG should be consistent with both theories (even if GR is just a classical approximation of it). It might be that the theory forbids time traveling, but as of yet it isn't a closed option. Anyway, I just wanted to point out the fact that MWI allows time traveling without paradoxes. :shy:

How many universes are created when a "splitting" event takes place, how do you calculate probabilities from that?

Number of universes:
http://www.hedweb.com/manworld.htm#how

You can calculate the probability of the cat being alive at a time [t] by remembering that the probability of finding the cat alive after Δt=[half-life of the nucleus] is 50%, so after Δt=n*[half-life of the nucleus] the probability of finding the cat alive is (0.5)^n.

In what way two universes in which the cat is still alive count as "different"?

If a particle is in a superposition of states, say |x1> + |x2>, and you observe the particles state, then the universe is split in two: in one universe you observe the particles state being as |x1> and in the other |x2>. This is sufficient enough to distinguish two universes as being "different".

 

[DrChinese]

Well, let's try it both ways:

1. If collapse *is* physical, than QM is a nonlocal theory (just like some other nonlocal theories that have no trouble explaining the results of the Bell experiments).

2. If collapse *isn't* physical, then we have several distinct wave functions all describing the same one unchanged physical state -- i.e., QM then fails to provide a complete description of states, thus refuting Bohr and validating Einstein.

That dilemma was precisely Einstein's fundamental objection to the orthodox quantum theory. See

http://puhep1.princeton.edu/~mcdonald/examples/QM/norsen_ajp_73_164_05.pdf

I agree with your 1 case, more or less. It could represent a traditional view of non-locality, or a kind of non-locality that is specific to this type of action (perhaps a dimension which is non-local). I personally think that "non-local" action could occur in a variety of ways that we might not fully be able to describe at this time. Example: backwards causation.

The 2 case is tricky, because there may be some subtle assumptions involved. I don't agree with the logic that says: if not collapse is not physical, there must be must be simultaneous reality to non-commuting operators (and therefore QM is incomplete).

From the reference : "Evidently Einstein believed that the claim that wave function collapse represents a physically real change of state, and the claim that it represents a mere change in knowledge, do not 'differ only as to their mode of expression.' "

I'd probably be tempted to agree with Einstein on this one, but I am not sure how you could test these claims anyway. Consequently, you might say that Bohr went too far in that particular regard (i.e. that they are equivalent), not that it much matters.

 

[ttn]

I agree with your 1 case, more or less. It could represent a traditional view of non-locality, or a kind of non-locality that is specific to this type of action (perhaps a dimension which is non-local). I personally think that "non-local" action could occur in a variety of ways that we might not fully be able to describe at this time. Example: backwards causation.

The 2 case is tricky, because there may be some subtle assumptions involved. I don't agree with the logic that says: if not collapse is not physical, there must be must be simultaneous reality to non-commuting operators (and therefore QM is incomplete).

I don't agree either. Or at least, if there *is* some "logic" from "collapse is not physical" to "there must be ...", it certainly isn't clear what the argument is supposed to be (and one is plainly required).

But perhaps you just misunderstand what the claim at issue is. Einstein defines "completeness" as a one-to-one correspondence between physical states and theoretical state descriptions. I think that's completely reasonable. In a complete theory, each distinct description (or "state function" or whatever) maps onto a distinct actual physical state. That's just what it means to say that the theory is complete -- it doesn't leave out of the descriptions, anything that is in fact present in the real physical states.

So then the argument goes like this: if collapse in OQM does *not* involve any physical change in the actual states (but is just some kind of updating of our knowledge or whatever) then there are at least two distinct state descriptions (the before and after collapse ones) which map onto the same identical physical state. That's it. So the one-to-one correspondence fails, and the theory isn't complete. Think about it: if there are two different state descriptions that both describe the same one unchanged physical state, then at least one of those two descriptions leaves something out, and so the theory is not complete.

From the reference : "Evidently Einstein believed that the claim that wave function collapse represents a physically real change of state, and the claim that it represents a mere change in knowledge, do not 'differ only as to their mode of expression.' "

I'd probably be tempted to agree with Einstein on this one, but I am not sure how you could test these claims anyway. Consequently, you might say that Bohr went too far in that particular regard (i.e. that they are equivalent), not that it much matters.

It matters a great deal. But I don't know what you mean by "how you could test these claims anyway." The claim here is just a claim about how a particular theory (OQM) works. It's not the kind of claim you need to do an experiment to test. Given the way the theory works, either OQM is a manifestly nonlocal theory (that is, if we interpret collapse as a real physical process) or it's an incomplete theory (if we interpret collapse as merely epistemic). There's no experiment needed here. Except maybe some kind of sociological experiment to determine how so many physicists can have twisted their minds into pretzels for so long trying to waffle back and forth in order to evade this trivial and obvious dilemma.

 

[ueit]

Actually the paths satisfy the Heisenberg uncertainty relation between momentum and position.

The uncertainty principle does not allow momentum conservation violations, it only limits predictability. If MWI is a realistic interpretation you cannot have multiple paths for the same particle unless its momentum can change at random.

Also, all the possible paths affect the observed position of a particle in the double slit experiment, for example. If the paths are unphysical, how can they affect the observed positions of the particles?

A particle can only change momentum if a force is acting on it (because momentum conservation). In a double slit experiment for example the path of the particle is determined by the interactions between the particle and the charged particles in the wall (electrons and quarks), therefore it depends on the geometry of the wall. But it is possible to describe the same geometry by referring not to the places where there are charges but to the places where there is no charge (the paths you are referring). But this is only a method to make the calculations. The true reason for particle's trajectory stands in its EM interaction with other particles.

QM just doesn't say anything about the stochastic/deterministic nature of the events it describes.

Again, you can interpret it does.

Sure you can, but the burden of proof is on you to show that such an interpretation is inevitable unless MWI is employed.

Every stochastic/non-local/indeterministic interpretation does contradict relativity. This has more to do with metaphysics than actual physics but you can't fit a model which is interpreted as being indeterministic with a model that is interpreted as being deterministic.

This is a good reason to reject such interpretations. However, this doesn't mean MWI wins by default. There is another possibility, that QM is incomplete and, just like thermodynamics, it is only a statistical description of a classical world.

The wavefunction doesn't actually tell the whole story; path integral formulation gives a more fundamental insight about the behavior of particles. You should read Feynmans QED: strange theory of light and matter if you haven't. I got shocked many times when reading it because you get so confused about how the nature works. Don't worry, there's no mention about the MWI.

I see no good reason to believe that "path integral formulation gives a more fundamental insight about the behaviour of particles". It is just another way to do calculations.

I've read Feynman's book about a year ago, so it's not that fresh into my memory but I don't remember him claiming that the path integral is a realistic description of how nature works.

I have nothing against MWI, it's just as good as the other QM interpretations. It may even be true but we'll never know it, because it's unfalsifiable. The assumption that QM is a complete description has to be challenged first.

Nope, it is a classical theory. Only stochastic particles (that exist in the indeterministic interpretations of QM) contradict relativity.

One could produce a fundamentally stochastic interpretation of thermodynamics as well. So what? I agree with you that any stochastic theory contradicts relativity but I disagree that QM is inherently stochastic or that MWI is the only way QM could be deterministic.

How does it contradict my original assumption? According to MWI, the statefunction/wavefunction is a statistical tool that describes the relative states of a single particle in different parts of the multiverse, ie. it describes the distribution of the particles position in different universes.

QM is defined on a Newtonian (or Minkowsky for QFT) background. One universe, three spatial dimensions, one time dimension. Where are these other universes coming from? They do not appear in the initial description of the system.

In the MWI FAQ you linked I read:

Loosely speaking a "world" is a complex, causally connected, partially or completely closed set of interacting sub-systems which don't significantly interfere with other, more remote, elements in the superposition. Any complex system and its coupled environment, with a large number of internal degrees of freedom, qualifies as a world.

I admit I don't understand anything from this definition. There is no such thing as an isolated system (except the universe as a whole) and what is "significant" is a matter of opinion. Just because a force is weak doesn't mean it's not significant.

You can calculate the probability of the cat being alive at a time [t] by remembering that the probability of finding the cat alive after Δt=[half-life of the nucleus] is 50%, so after Δt=n*[half-life of the nucleus] the probability of finding the cat alive is (0.5)^n.

I know that, done in chemistry classes. I don't see where MWI is used here though.

How many worlds are there?

The thermodynamic Planck-Boltzmann relationship, S = k*log(W), counts the branches of the wavefunction at each splitting, at the lowest, maximally refined level of Gell-Mann's many-histories tree. (See "What is many-histories?") The bottom or maximally divided level consists of microstates which can be counted by the formula W = exp (S/k), where S = entropy, k = Boltzmann's constant (approx 10^-23 Joules/Kelvin) and W = number of worlds or macrostates. The number of coarser grained worlds is lower, but still increasing with entropy by the same ratio, i.e. the number of worlds a single world splits into at the site of an irreversible event, entropy dS, is exp(dS/k). Because k is very small a great many worlds split off at each macroscopic event.

So, how do you apply this convoluted explanation to Schrödinger’s cat?

If a particle is in a superposition of states, say |x1> + |x2>, and you observe the particles state, then the universe is split in two: in one universe you observe the particles state being as |x1> and in the other |x2>. This is sufficient enough to distinguish two universes as being "different".

Is world splitting related to observation, like the "collapse" in Copenhagen interpretation or a real, physical event?

 

[selfAdjoint]

So then the argument goes like this: if collapse in OQM does *not* involve any physical change in the actual states (but is just some kind of updating of our knowledge or whatever) then there are at least two distinct state descriptions (the before and after collapse ones) which map onto the same identical physical state. That's it. So the one-to-one correspondence fails, and the theory isn't complete. Think about it: if there are two different state descriptions that both describe the same one unchanged physical state, then at least one of those two descriptions leaves something out, and so the theory is not complete.

This encapsulates my own disquiet with the "knowledge" interpretation of collapse. If observation does not confer some kind of change of state on the observable, then there must be one continuous state from before observing to after. Is there any way of avoiding MWI within the standard QM formalism in this case?

Can appeal to QED or more advanced QFT help at all?