On the meaning of indeterminism of Quantum Theory

[askhetan]

On the meaning of "indeterminism" of Quantum Theory

I was reading more into the details about the successes and failures(apparently none) of quantum theory. I have some very basic questions that do not require a mathematical answers. When quantum theory describes the indeterministic nature of things, does it mean that properties cannot be determined accurately or does it mean that properties are themselves random and take arbitrary (but quantized) values.

Coming down to a specific example, let's consider the example of the measurement problem where by trying to look at the path of the electron in the double slit experiment, we change its course, the wavefunction collapses, and we say that we have already changed the system to a degree that we cannot say what it was like before we changed it. (I just saw this explanation in a youtube video by a Stanford physics prof giving lectures on basics of quantum mechanics).

Now, I have a problem here. Let's me say there was a billiard ball, 'A', coming from some direction (electron) and i threw another one, 'B', at it (the photon). So if I knew the exact velocity and direction of 'B' and the coefficient of restitution, then by looking at the deflection in 'A' and its subsequent velocity, I could use Newton's laws to find the original conditions of 'A'. Likewise, if I had equipment sophisticated enough to exactly produce photons of known properties and I invoke appropriate quantum mechanical laws, then can I not find what the electron was like before I disturbed it ..?

So from this point it looks to me that if I know what I am throwing at the object then I can also look at the object. Of course, I am wrong. But I need to know where. Has it got to do with the fact that we do not know how much the electron will absorb and emit? The problem still seems to me as the problem of not having the best possible technique to produce well predefined photons and subsequently measure the path of electron.

A recent article,

http://www.nature.com/ncomms/journal/v2/n8/full/ncomms1416.html

which vindicates QT, says that more information from any extension of QT cannot be obtained and that QT is essentially complete. I am not doubting what they say, just wanting to understand it better.

To be very literal, my question is - is it the fact that physical systems cannot be examined, even mathematically, beyond a certain limit? or is it that they don't really have well defined values and definitions but only once we observe they take up values, which will be different every time we try to observe?

On a light note: I have this intuitive feeling that the wave-particle duality in some way corresponds to this indeterminism/uncertainty which we do not know in terms of equations yet.

 

[DrChinese]

...

To be very literal, my question is - is it the fact that physical systems cannot be examined, even mathematically, beyond a certain limit? or is it that they don't really have well defined values and definitions but only once we observe they take up values, which will be different every time we try to observe?

...

Actual experiments demonstrate that there are no simultaneous underlying values for position and momentum. It has nothing whatsoever to do with some kind of observational limitations. What you described is essentially the 1935 EPR paradox, which purported to show that it WOULD be possible to obtain such information (in violation of the HUP*). But Bell (1964) later showed this was not possible. Aspect et al (1981) demonstrated experimentally.

To understand the point better, consider these 2 truths:

a) You CAN know *commuting* values simultaneous, such as spin and momentum. If the problem was due to observational limits, this should not be possible.
b) If you take 2 identical (entangled) particles, you can measure non-commuting values on each. That would lead you to believe you have, by inference, discovered the value of 2 non-commuting observables. However, the particle will simply not have the inferred value, and subsequent tests bear this out. So you can pretend you know the value, however, you don't and there is no experiment that will ever back you up.

It is true that there seems to be some connection between indeterminism and duality, keeping in mind that duality is essentially a consequence of the HUP.

*Heisenberg Uncertainty Principle.

 

[Demystifier]

A recent article,

http://www.nature.com/ncomms/journal/v2/n8/full/ncomms1416.html

which vindicates QT, says that more information from any extension of QT cannot be obtained and that QT is essentially complete.

Impossibility theorems of that kind always involve some additional assumptions. In the paper above, this is their FR assumption. As they discuss in the paper, there are theories, such as deBroglie-Bohm theory, which do NOT obey their FR assumption. Thus, theories with more information than QT are possible, provided that you give up some assumptions such as their FR assumption.

 

[Maui]

A recent article,

http://www.nature.com/ncomms/journal/v2/n8/full/ncomms1416.html

which vindicates QT, says that more information from any extension of QT cannot be obtained and that QT is essentially complete. I am not doubting what they say, just wanting to understand it better.

This reminds of:

"That the automobile has reached the limit of its development is suggested
by the fact that during the last year no improvements of a radical nature
have been introduced."
-- Scientific American, 1909They have a starting premise, an argumentation and evidence for their conclusion.

 

[Many_S_Theory]

Impossibility theorems of that kind always involve some additional assumptions. In the paper above, this is their FR assumption. As they discuss in the paper, there are theories, such as deBroglie-Bohm theory, which do NOT obey their FR assumption. Thus, theories with more information than QT are possible, provided that you give up some assumptions such as their FR assumption.

I'm sure this debate has been played out to excruciating detail on this forum, but even non-local quantum theories like deBroglie-Bohm have no "solution" to the measurement problem and thus are still fundamentally non-deterministic, "non-local hidden variables" or otherwise. It all comes back to the double slit experiment with electrons. There is no quantum interpretation which admits a notion of the electron having a simultaneous position and momentum and allows for a deterministic propagation of those quantities that can be reconciled with such an experiment... (did that make sense, I think that made sense).

 

[Demystifier]

(did that make sense, I think that made sense).

I think it did not.

 

[San K]

Great post DrChinese, great proof/truth/fact.

b) If you take 2 identical (entangled) particles, you can measure non-commuting values on each. That would lead you to believe you have, by inference, discovered the value of 2 non-commuting observables. However, the particle will simply not have the inferred value, and subsequent tests bear this out. So you can pretend you know the value, however, you don't and there is no experiment that will ever back you up.

Trying to understand how this would be done experimentally. To understand this better let's say we have two entangled photons A&B.

Case 1: Non-commuting variables

We measure the position of photon A and momentum of photon B.

We could infer the momentum of A however how do we infer the position of B? is this the position within the small "probability cloud"? of B

So, are you saying that - the inferred values won't match the measured values?

i.e. Would the actual/experimentally-measured momentum of A in this case differ from that calculated via inference (from measured momentum of B)?

Case 2: Commuting variables

We measure the spin of photon A and momentum of photon B. And now we can infer the momentum of A and spin of B.

Would the inferred values (in case of commuting variables) match with the actual/measured values?

 

[DrChinese]

Case 1: Non-commuting variables

We measure the position of photon A and momentum of photon B.

We could infer the momentum of A however how do we infer the position of B? is this the position within the small "probability cloud"? of B

So, are you saying that - the inferred values won't match the measured values?

i.e. Would the actual/experimentally-measured momentum of A in this case differ from that calculated via inference (from measured momentum of B)?

Case 2: Commuting variables

We measure the spin of photon A and momentum of photon B. And now we can infer the momentum of A and spin of B.

Would the inferred values (in case of commuting variables) match with the actual/measured values?

Yes and yes. For non-commuting pairs, the results would match randomly. For commuting pairs, the results match all of the time (ideal case of course). I do not have a reference for such experiments, however.

 

[askhetan]

Thanks but I'm still confused about a few things - is it

1) That our act of measurement disturbs the entanglement in particles

2) That if measurement does not disturb entanglement, but still the inferred value of A did not match with its measured value, then there is really nothing such as entanglement

I mean there is something inconsistent here

I read yesterday that the EPR paradox was resolved by Bell by testing the theories of local hidden variables against his inequalities. Fine. Let's go to non-local hidden variables. But these violate causality because the information to B that something was measured about A cannot travel at infinite speed.

So if I am understanding the whole picture in the correct way, there is still a problem, right? Either we violate special relativity (speed of light) or we must accept that we still can't explain entanglement within the framework of QM and its finite non-hidden local variables alone.

 

[DrChinese]

So if I am understanding the whole picture in the correct way, there is still a problem, right? Either we violate special relativity (speed of light) or we must accept that we still can't explain entanglement within the framework of QM and its finite non-hidden local variables alone.

"Problem" is a relative term. And all of these labels have an issue one place or another. Entanglement is real and definitely has distinct attributes as compared to non-entangled pairs.

There is no mass or energy being transferred at superluminal speeds. So it is not actually clear that there is a violation of SR per se.

 

[zonde]

I read yesterday that the EPR paradox was resolved by Bell by testing the theories of local hidden variables against his inequalities.

Bell did not resolve EPR paradox. He confirmed that this paradox is rather real.
Basically there is no generally accepted resolution to that paradox.

Fine. Let's go to non-local hidden variables. But these violate causality because the information to B that something was measured about A cannot travel at infinite speed.

These do not violate causality. These violate principle of relativity.

So if I am understanding the whole picture in the correct way, there is still a problem, right? Either we violate special relativity (speed of light) or we must accept that we still can't explain entanglement within the framework of QM and its finite non-hidden local variables alone.

Right, the problem is still there.

 

[Demystifier]

1) That our act of measurement disturbs the entanglement in particles

I read yesterday that the EPR paradox was resolved by Bell by testing the theories of local hidden variables against his inequalities. Fine. Let's go to non-local hidden variables. But these violate causality because the information to B that something was measured about A cannot travel at infinite speed.

So if I am understanding the whole picture in the correct way, there is still a problem, right? Either we violate special relativity (speed of light)

I don't think that velocity faster than light violates special relativity or causality. See
http://xxx.lanl.gov/abs/1002.3226

 

[askhetan]

@ demystifyer - thanks thanks thanks thanks! that paper is so well written, i don't know if its completely all correct, but its so well explained about so many recurring concepts like causality and relativity and determinism.

the only assumption is that there is no free will. haha!

amazing!

 

[Meselwulf]

Actual experiments demonstrate that there are no simultaneous underlying values for position and momentum. It has nothing whatsoever to do with some kind of observational limitations. What you described is essentially the 1935 EPR paradox, which purported to show that it WOULD be possible to obtain such information (in violation of the HUP*). But Bell (1964) later showed this was not possible. Aspect et al (1981) demonstrated experimentally.

To understand the point better, consider these 2 truths:

a) You CAN know *commuting* values simultaneous, such as spin and momentum. If the problem was due to observational limits, this should not be possible.
b) If you take 2 identical (entangled) particles, you can measure non-commuting values on each. That would lead you to believe you have, by inference, discovered the value of 2 non-commuting observables. However, the particle will simply not have the inferred value, and subsequent tests bear this out. So you can pretend you know the value, however, you don't and there is no experiment that will ever back you up.

It is true that there seems to be some connection between indeterminism and duality, keeping in mind that duality is essentially a consequence of the HUP.

*Heisenberg Uncertainty Principle.

''Actual experiments demonstrate that there are no simultaneous underlying values for position and momentum. It has nothing whatsoever to do with some kind of observational limitations. What you described is essentially the 1935 EPR paradox, which purported to show that it WOULD be possible to obtain such information (in violation of the HUP*). But Bell (1964) later showed this was not possible.''

I counter this prediction of Bell strongly.

A Curious Statistical analysis of quantum mechanics by three physicists http://prl.aps.org/abstract/PRL/v54/i1/p5_1 suggests it is possible for time symmetric cases to involve violations of the uncertainty principle.

In short, you can make a measurement in the past of a particles position for example, make a measurement in the future of it's trajectory and know with absolute precision the product of both position and trajectory simultaneously.

 

[Meselwulf]

"Problem" is a relative term. And all of these labels have an issue one place or another. Entanglement is real and definitely has distinct attributes as compared to non-entangled pairs.

There is no mass or energy being transferred at superluminal speeds. So it is not actually clear that there is a violation of SR per se.

I find it interesting that we often associate information with the transfer of energy, or other tangible manifestations.

Why has no one ever considered there could be a field which is fundamental yet without particles? Ethereal information written into spacetime, which could answer for the whole dichotomy of the problem of the entanglement problem.

Actually, one had considered this possibility which comes to mind, his name is Cramer, and his Transactional Interpretation. Waves of probability, not made of energy or matter which move time symmetrically from the future to past.

 

[Ken G]

In short, you can make a measurement in the past of a particles position for example, make a measurement in the future of it's trajectory and know with absolute precision the product of both position and trajectory simultaneously.

That's why we shouldn't talk about knowledge of a system (which is essentially a philosophical or even rhetorical claim), we should talk about preparation of a system (which is the concept that is actually used to do physics). What the HUP says is that it is not possible to prepare[\i] a system in a state of certain position and momentum. If we know it had some position and momentum at some past time, we could not have known it at that past time, nor could it still have those values now. Remember, the purpose of a "state" of a system is to be able to connect that knowledge to the ability to make inferences about that system's future or past, but the state to which you refer, a past state where you can infer a position and momentum, does not connect to that kind of useful or testable information. So it's just not the useful version of the "state" concept, it's more like a DeBroglie-Bohm state where you can imagine that particle had those properties if you are so philosophically inclined, but it makes no difference to the physics if you imagine it or not, as it is not predictive of anything.

 

[askhetan]

I find it interesting that we often associate information with the transfer of energy, or other tangible manifestations.

Why has no one ever considered there could be a field which is fundamental yet without particles? Ethereal information written into spacetime, which could answer for the whole dichotomy of the problem of the entanglement problem.

I feel very similar - why do we have to restrain our perspective to locality of variables? and that too to only those which are characteristics of either waves or particles.

I have a different troubling question these days though. As I am studying DFT and ab-initio electrochemistry - i am further more drawn to the conclusion that something very big, even within the wave-particle picture, is missing. Let me explain:

Hartree fock assumes a single slater determinant (and configuration interaction takes a big combination of slater determinants ) in solving a many body (N) problem. The slater form of N wave functions in it are only an approximation to THE ONE wave function which is actually dependent on the spins and coordinates of N bodies in some "complicated" manner. This, in my peanut sized brain creates a massive problem.

Suppose - If we have the coordinates of all bodies (after they have interacted with each other and are is their ground state) and also the correct "ONE" many body wave function (which is known as a function of space coordinates but not in the form of an explicit/implicit dependence on the spins and coordinates of the N bodies). now my question is - aren't we missing the "particle" equation of bodies ?? what is the way in a N body system to distinguish the physical realm of one particle from the other? we always say there is a total wavefunction and there are wavefunctions of individual particles when they are hypothetically isolated from the rest of the universe. but when they interact, the total wf is not more a linear combination of the one body wave function, because now we do not know what are the individual wavefunctions, even if we know their coordinates. What is the explicit/implicit dependence of the "one" wavefunction on individual wavefunctoins? shouldn't there be a fundamental way that they combine to result in the ONE wave function. Alternately - is this a part of the "indeterminism" that results into us not knowing all about the system??

This, to me, is a big wide gap in my knowledge. AND this also means that i am fundamentally wrong somewhere - please tell me where am i going wrong

 

[audioloop]

I was reading more into the details about the successes and failures(apparently none) of theory. I have some very basic questions that do not require a mathematical answers. When quantum theory describes the indeterministic nature of things, does it that properties cannot be determined accurately or does it mean that properties are themselves random and take arbitrary (but quantized) values.

Coming down to a specific example, let's consider the example of the problem where by trying to look at the path of the electron in the double slit experiment, we change its course, the wavefunction collapses, and we say that we have already changed the system to a degree that we cannot say what it was like before we changed it. (I just saw this explanation in a video by a Stanford physics prof giving lectures on basics of quantum mechanics).

Now, I have a problem here. Let's me say there was a billiard ball, 'A', coming from some direction (electron) and i threw another one, 'B', at it (the photon). So if I knew the exact velocity and direction of 'B' and the coefficient of restitution, then by looking at the deflection in 'A' and its subsequent velocity, I could use Newton's laws to find the original conditions of 'A'. Likewise, if I had equipment sophisticated enough to exactly produce photons of known properties and I invoke appropriate quantum mechanical laws, then can I not find what the electron was like before I disturbed it ..?

So from this point it looks to me that if I know what I am throwing at the object then I can also look at the object. Of course, I am wrong. But I need to know where. Has it got with the fact that we do not know how much the electron will absorb and emit? The problem still seems to me as the problem of not having the best possible technique to produce well predefined photons and subsequently measure the path of electron.

A recent article,

http://www.nature.com/ncomms/journal/v2/n8/full/ncomms1416.html

which vindicates QT, says that more information from any extension of QT cannot be obtained and that QT is essentially complete. I am not doubting what they say, just wanting to understand it better.

To be very literal, my question is - is it the fact that physical systems cannot be examined, even mathematically, beyond a certain limit? or is it that they don't really have well defined values and definitions but only once we observe they take up values, which will be different every time we try to observe?

On a light note: I have this intuitive feeling that the wave-particle duality in some way corresponds to this indeterminism/uncertainty which we do not know in terms of equations yet.

imo determinism is the result of some(s) previous event(s), without previous events there is not posteriori events,

it is not possible, is determined.

and

and what is possible, is likewise determined (by the former, and by itself -previous events-)

i.e. no elephant after a electron fired.

 

[Meselwulf]

That's why we shouldn't talk about knowledge of a system (which is essentially a philosophical or even rhetorical claim), we should talk about preparation of a system (which is the concept that is actually used to do physics). What the HUP says is that it is not possible to prepare[\i] a system in a state of certain position and momentum. If we know it had some position and momentum at some past time, we could not have known it at that past time, nor could it still have those values now. Remember, the purpose of a "state" of a system is to be able to connect that knowledge to the ability to make inferences about that system's future or past, but the state to which you refer, a past state where you can infer a position and momentum, does not connect to that kind of useful or testable information. So it's just not the useful version of the "state" concept, it's more like a DeBroglie-Bohm state where you can imagine that particle had those properties if you are so philosophically inclined, but it makes no difference to the physics if you imagine it or not, as it is not predictive of anything.

It's not about knowing the position and momentum at some past time, the work indicates you can know with absolute precision the position and momentum in the present moment if you make measurement in the past and future on either the position on momentum respectively. But I have no objections to your words in the ''preperation'' of the state.

 

[Meselwulf]

I feel very similar - why do we have to restrain our perspective to locality of variables? and that too to only those which are characteristics of either waves or particles.

I have a different troubling question these days though. As I am studying DFT and ab-initio electrochemistry - i am further more drawn to the conclusion that something very big, even within the wave-particle picture, is missing. Let me explain:

Hartree fock assumes a single slater determinant (and configuration interaction takes a big combination of slater determinants ) in solving a many body (N) problem. The slater form of N wave functions in it are only an approximation to THE ONE wave function which is actually dependent on the spins and coordinates of N bodies in some "complicated" manner. This, in my peanut sized brain creates a massive problem.

Suppose - If we have the coordinates of all bodies (after they have interacted with each other and are is their ground state) and also the correct "ONE" many body wave function (which is known as a function of space coordinates but not in the form of an explicit/implicit dependence on the spins and coordinates of the N bodies). now my question is - aren't we missing the "particle" equation of bodies ?? what is the way in a N body system to distinguish the physical realm of one particle from the other? we always say there is a total wavefunction and there are wavefunctions of individual particles when they are hypothetically isolated from the rest of the universe. but when they interact, the total wf is not more a linear combination of the one body wave function, because now we do not know what are the individual wavefunctions, even if we know their coordinates. What is the explicit/implicit dependence of the "one" wavefunction on individual wavefunctoins? shouldn't there be a fundamental way that they combine to result in the ONE wave function. Alternately - is this a part of the "indeterminism" that results into us not knowing all about the system??

This, to me, is a big wide gap in my knowledge. AND this also means that i am fundamentally wrong somewhere - please tell me where am i going wrong

Well, N-bodies as you will know, can include any particle, but there is a principle in quantum mechanics known as ''the indistinguishability of particles'' http://en.wikipedia.org/wiki/Identical_particles so I hope this answers some of your questions. And, sure, you can combine wave functions, here is an example

[tex]\Psi(x) = \psi(x) + \psi(x)[/tex]