# Electron indeterminism Problem

1. Oct 4, 2006

### 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.

2. Oct 4, 2006

### 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 eachother 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 eachother through some faster than light method to tell eachother which spin they each were gonna be. this is know as non-locality.

2. there is something about the electrons that quantum mechanics doesnt 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

3. Oct 5, 2006

### 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

4. Oct 5, 2006

### DrChinese

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.

5. Oct 5, 2006

### 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?

6. Oct 5, 2006

### 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 wont try to confuse you with a kabillion interpretations. The most straightforward one (i think) is that it is a probability current and doesnt have a solid physical interpretation. however what i have given you is the vanilla, standard university explanation, there are many other interpretations.

gabe

7. Oct 5, 2006

### 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?

8. Oct 5, 2006

### Staff: Mentor

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.

Last edited: Oct 6, 2006
9. Oct 6, 2006

### kvantti

Understanding QM becomes even harder if you look at the http://www.einstein-online.info/en/spotlights/path_integrals/index.html [Broken] 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.

Last edited by a moderator: May 2, 2017
10. Oct 7, 2006

### ueit

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.

11. Oct 8, 2006

### kvantti

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

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.

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

12. Oct 8, 2006

### pibomb

13. Oct 9, 2006

### kvantti

Take a look at http://superstruny.aspweb.cz/images/fyzika/simulace/schrodinger.htm [Broken], for example. The applet simulates time dependant statefunction of position of a particle in two dimensions. Lets 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].

Last edited by a moderator: May 2, 2017
14. Oct 9, 2006

### ueit

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.

15. Oct 9, 2006

### kvantti

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. :surprised

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:

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:

Also, the MWI allows time traveling without paradoxes.

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.

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].

Last edited: Oct 9, 2006
16. Oct 9, 2006

### cesiumfrog

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/" [Broken], 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

Last edited by a moderator: May 2, 2017
17. Oct 10, 2006

### ueit

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.

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.

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

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

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

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.

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.

18. Oct 10, 2006

### pibomb

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

19. Oct 11, 2006

### 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 gonna 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.

Last edited by a moderator: Oct 11, 2006
20. Oct 11, 2006

### kvantti

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. :uhh:

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.

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...

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.

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.

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

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.

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21. Oct 13, 2006

### ueit

kvantti,

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

22. Oct 13, 2006

### ueit

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.

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.

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.

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

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.

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.

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"?

23. Oct 13, 2006

### ueit

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

24. Oct 13, 2006

### ueit

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

25. Oct 14, 2006

### ttn

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 [Broken]

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