I Quantum mechanics is random in nature?

[entropy1]

I heard from many sources that quantummechanics is purely random in nature. Has this been demonstrated?

If so, what is the proof?

 

[micromass]

1) What sources?
2) What do you mean with purely random? Or what do the sources mean with it?

An answer to your question depends very heavily on this.

 

[entropy1]

1) What sources?
2) What do you mean with purely random? Or what do the sources mean with it?

An answer to your question depends very heavily on this.

1) Scientists (mostly on the internet).
2) Phenomena like the wavefunction collapse are considered 'purely random'. I must add however, that the measurement can be set up in such a way, that there are (strong) statistical correlations established, for instance in the case of commuting observables. However, we can't predict what will be measured in case of collapse. Now, I wonder whether the fact that the measured value cannot be predicted is reason enough to call it "random", or if there are other prerequisites to do so. That we can't predict something only says something about its predictability, not about its properties, right? If we can establish that collapse is random, we have to base that on the propery of being statistical in its nature, right?

 

[micromass]

1) Scientists (mostly on the internet).

You'll need to be more specific. This forum finds statements of right sources very important.

You might find this interesting https://en.wikipedia.org/wiki/Hidden_variable_theory

 

[entropy1]

You'll need to be more specific. This forum finds statements of right sources very important.

I understand that. Unluckily, I can't recall my sources. Is it possible to consider my question as-is?

(I will try to retrace my sources)

 

[micromass]

I understand that. Unluckily, I can't recall my sources. Is it possible to consider my question as-is?

(I will try to retrace my sources)

It'll have to do, I guess. But I thought it was important since it all depends on your definition of "at random". So while I don't doubt that you try your best to stay faithful to the scientists their account, it might still happen that what you said in your OP is not the same as what the scientists really said or meant!

I'll give you one scientist which might have said what you implied in your OP:



At the end he makes some philosophical statements about randomness and determinism in quantum mechanics, I do need to add that I don't think it is completely proven the way he presents it. I consider it very likely that things really do behave the way he said it though.
More specifically, he states that a hidden variable theory is wrong. I think Feynman was incorrect there as this cannot be proven. I consider it very likely to be the case that nature doesn't have hidden variables though.

 

[vanhees71]

Feynman would be very upset if he's know that you say his remarks are "philsophical" ;-). SCNR.

 

[micromass]

Feynman would be very upset if he's know that you say his remarks are "philsophical" ;-). SCNR.

Yes, I know. But he makes fun of a "pompous philosopher" at the end. I was referring to that segment.

 

[entropy1]

I think by "purely random", I mean: "Uncaused". Feyman mentioned in the video that having in principle knowledge of which slit a particle will pass in a double-slit experiment (so, even without actually measuring it), would destroy the interference pattern. So, the theory dictates that it is not possible (it seems so). What I would like to know is if the math is also dictating that for collapse! That is, do we know there is absolutely no physical cause determining the outcome of a collapse?

And even if there is no physical cause for collapse, there still is a correlation between outcomes of collapse. Could this correlation be described in terms of hidden variables? It seems odd that there even is a correlation if there doesn't exist a mechanism to produce it.

 

[DrChinese]

What would it take to convince you something is "really random" - past it appearing random and there being no currently known causes?

 

[entropy1]

What would it take to convince you something is "really random" - past it appearing random and there being no currently known causes?

Good question! That is what I don't know! I thought other people were proposing it! If so, I'd like to know how they come to that!

Perhaps I could add: How can we demonstrate that (for instance) collapse is not 'induced' by 'other causes'?

 

[DrChinese]

Good question! That is what I don't know! I thought other people were proposing it! If so, I'd like to know how they come to that!

Perhaps I could add: How can we demonstrate that (for instance) collapse is not 'induced' by 'other causes'?

I would say past attempting to discover such a cause (and failing to do so) - none. Obviously there are interpretations/theories (Bohmian Mechanics) which posit a cause. However, those cannot be demonstrated - that is part and parcel of the theory.

So we are back to the original question. The most common viewpoint "QM appearing to be random" means we live in a world of random quantum events without a cause.

But this common view would be updated were there to be evidence to the contrary in the future. Presumably that would mean that Bohmian non-locality was specifically demonstrated.

 

[Nugatory]

What I would like to know is if the math is also dictating that for collapse! That is, do we know there is absolutely no physical cause determining the outcome of a collapse?

The randomness follows directly from the axioms of quantum mechanics, and in that sense it is dictated by the math. However, it is possible that there is more to it; it might be that the axioms could be derived from some deeper underlying theory that we don't yet know. That hypothetical deeper theory need not involve randomness. (An analogy: I get excellent agreement with experiment using the axiom "When tossed, my coin will randomly come up heads or tails with 50% probability each way" but the behavior of the coin is governed by deterministic Newtonian mechanics).

However, this discussion is altogether sterile unless and until we have a specific candidate theory in mind.

And even if there is no physical cause for collapse, there still is a correlation between outcomes of collapse. Could this correlation be described in terms of hidden variables? It seems odd that there even is a correlation if there doesn't exist a mechanism to produce it.

It does seem odd, or at least at odds with our classical intuition. That's the motivation for looking for a deeper underlying theory in the first place. However, we have to find one before we can sensibly talk about it.

 

[entropy1]

But this common view would be updated were there to be evidence to the contrary in the future. Presumably that would mean that Bohmian non-locality was specifically demonstrated.

However, it is possible that there is more to it; it might be that the axioms could be derived from some deeper underlying theory that we don't yet know. [..] It does seem odd, or at least at odds with our classical intuition. That's the motivation for looking for a deeper underlying theory in the first place. However, we have to find one before we can sensibly talk about it.

So non-randomness is not yet ruled out, I understand? Then there would be no evidence for randomness yet, as I take it.

 

[DrChinese]

1. So non-randomness is not yet ruled out, I understand?

2. Then there would be no evidence for randomness yet, as I take it.

There is no end of evidence for randomness in the quantum world, and no evidence for any hypothetical underlying cause to explain such events. So I disagree with your 2.

Or to put it on another level: there is equal evidence for an underlying cause for apparent quantum randomness as for the existence of unicorns and mermaids. As far as I know, nothing could rule out the future discovery of non-local hidden variables (your 1).

 

[entropy1]

There is no end of evidence for randomness in the quantum world, and no evidence for any hypothetical underlying cause to explain such events. So I disagree with your 2.

Or to put it on another level: there is equal evidence for an underlying cause for apparent quantum randomness as for the existence of unicorns and mermaids. As far as I know, nothing could rule out the future discovery of non-local hidden variables (your 1).

But can you assert that just because something (ie. collapse) is behaving randomly, it is in its nature random? (I hope I am not getting too philosophical here)

 

[fresh_42]

So non-randomness is not yet ruled out, I understand? Then there would be no evidence for randomness yet, as I take it.

This is a highly philosophical question on what randomness is, rather than the mathematical concept. It reads a little bit like you were looking for evidence to support an ideological point of view, rather than evidence for insights.

An analogy: I get excellent agreement with experiment using the axiom "When tossed, my coin will randomly come up heads or tails with 50% probability each way" but the behavior of the coin is governed by deterministic Newtonian mechanics

Or to put it on another level: there is equal evidence for an underlying cause for apparent quantum randomness as for the existence of unicorns and mermaids.

Even the seemingly resolution of randomness in Nugatory's example isn't one. It simply transforms the randomness to the point where initial conditions on coin tosses are made. Whatever the future might show, it looks hard to get rid of randomness as mathematical concept. And if you visit a casino, you better won't rely on an underlying deterministic process.

 

[entropy1]

This is a highly philosophical question on what randomness is, rather than the mathematical concept. It reads a little bit like you were looking for evidence to support an ideological point of view, rather than evidence for insights.

I was expecting a remark of this kind (with all due respect). I conclude one is free to take either side, given good arguments. There are many good arguments to defend randomness, and none to defend non-randomness (HV).

It occurred to me that randomness maybe can't be proven except for its (random) behaviour. So (many) indications for random behaviour would make a strong case.

However, wouldn't it be a circumstantial one?

 

[fresh_42]

I don't think anything in physics is a "real truth". Newtons gravity pretty well describes the fall of the famous apple. Considering GR, it is wrong. But nobody bothers GR when talking about the apple. At last, it isn't even clear that the apple will always have to land on earth. However, a theory that predicts it won't in $1$ of say $10^{50}$ cases will have it difficult to get established. And it won't even matter, since you cannot test it. It is all about satisfactory models that a) describe what has been found, b) describe what will be found and most important c) can be tested. We observe plenty of phenomena that are perfectly described by the mathematical model of randomness. Whether you call it true or not simply isn't relevant. Nobody cares.

 

[entropy1]

Whether you call it true or not simply isn't relevant. Nobody cares.

I will confess right here my reason for wondering about the answer to my question: I, personally, have a hunch that the apparent randomness is in fact apparent, and can be described by non-random factors. However, I know very little of the matter, so I wanted to have my hunch ruled out to get rid of it. I can't help having the hunch. I deliberately am trying to be very careful with my words here, but that is the reason. I'm sure pretty much of the work has been done already by brilliant minds, of which I am not one, for all that matters.

 

[DrChinese]

But can you assert that just because something (ie. collapse) is behaving randomly, it is in its nature random? (I hope I am not getting too philosophical here)

Sure I can assert it. That is what evidence is for.

What is the evidence of the constancy of c? Could something be seen tomorrow that would change our opinion on that? Sure. But it would have to happen first.

So yes, I would say this discussion is about philosophy - and little about physics.

 

[DrChinese]

I will confess right here my reason for wondering about the answer to my question: I, personally, have a hunch ...

That comes as a bolt out of nowhere.

Seriously, if you prefer an interpretation that takes the randomness out of the equation: go ahead, you will be joining many other fine Bohmians out there. This is a matter of personal taste at this point.

 

[bhobba]

Sure I can assert it. That is what evidence is for.

Of course.

Systems that look random can be the result of deterministic deeper levels, and we have interpretations like BM that postulate exactly that.

But we have this thing called Occam's razor - what is the most likely thing - obviously that is its simply random - nothing more to it. Until we get further evidence anyway. It proves nothing of course, but its hardly controversial doing that.

Thanks
Bill

 

[atyy]

Quantum mechanics is not random in "nature". If nature exists, then it is nonlocal.

However, quantum mechanics is "operationally" random, since it does not allow information to be sent faster than light.

Both are important consequences of the fact that quantum mechanics predicts that experiments can violate Bell's inequality. The consequence of nonlocality in nature is that new physics probably exists. The consequence of operational randomness is that we can use quantum mechanics to guarantee randomness for cryptography, provided we believe that our adversary cannot send information faster than light.

 

[entropy1]

Quantum mechanics is not random in "nature". If nature exists, then it is nonlocal.

However, quantum mechanics is "operationally" random, since it does not allow information to be sent faster than light.

Both are important consequences of the fact that quantum mechanics predicts that experiments can violate Bell's inequality. The consequence of nonlocality in nature is that new physics probably exists. The consequence of operational randomness is that we can use quantum mechanics to guarantee randomness for cryptography, provided we believe that our adversary cannot send information faster than light.

That was really helpful!

 

[The Bill]

It occurred to me that randomness maybe can't be proven except for its (random) behaviour. So (many) indications for random behaviour would make a strong case.

However, wouldn't it be a circumstantial one?

It's only as circumstantial as any opinion based on statistical evidence is. In fact, all evidence we have of the workings of the universe are statistical in nature.

For example, you probably think it's close to certain that if you set a light wooden cube gently on the center of an IKEA tabletop that the cube won't fall through the table. However, that impression is just based on your statistical evidence that every time you've set a small stable object gently on a table, it has stayed on top of the table. You might think you have a lot of evidence for this, but the number of times you've set things on tables is certainly fewer than the number of quantum mechanical events which have been precisely measured by human scientists.

 

[entropy1]

It's only as circumstantial as any opinion based on statistical evidence is. In fact, all evidence we have of the workings of the universe are statistical in nature.

For example, you probably think it's close to certain that if you set a light wooden cube gently on the center of an IKEA tabletop that the cube won't fall through the table. However, that impression is just based on your statistical evidence that every time you've set a small stable object gently on a table, it has stayed on top of the table. You might think you have a lot of evidence for this, but the number of times you've set things on tables is certainly fewer than the number of quantum mechanical events which have been precisely measured by human scientists.

I think I get that. However, suppose that, in an entanglement experiment with polarizers and photons, we could align the polarizers perfectly. The correlation of photons both passing their polarizers would be 100%, right? Of course we can't predict if the photons are going to pass, but we know that if one has done so, the other will do too! (in this setup) This would almost be a law! So I can imagine that the statistical construct of QM could have deterministic properties!

 

[DrChinese]

I think I get that. However, suppose that, in an entanglement experiment with polarizers and photons, we could align the polarizers perfectly. The correlation of photons both passing their polarizers would be 100%, right? Of course we can't predict if the photons are going to pass, but we know that if one has done so, the other will do too! (in this setup) This would almost be a law! So I can imagine that the statistical construct of QM could have deterministic properties!

This logic is a rollback to EPR in 1935. That part is very reasonable. It is the Bell part that tears this view apart. As I have said several times in this thread: if you want determinism, you get nonlocal action at a distance as part of the bargain.

Keep in mind that the "law" is the cos^2(theta) relationship, which can be 100% at appropriate angles. There is nothing about that which requires anything to be predetermined because of that particular value.

 

[entropy1]

This logic is a rollback to EPR in 1935. That part is very reasonable. It is the Bell part that tears this view apart. As I have said several times in this thread: if you want determinism, you get nonlocal action at a distance as part of the bargain.

I think I get that.

Keep in mind that the "law" is the cos^2(theta) relationship, which can be 100% at appropriate angles. There is nothing about that which requires anything to be predetermined because of that particular value.

That is of course true. However, I see it differently: suppose the angle is not 0°, but, for instance 10°. I can interpret that as the "gun pointed 10° off axis". The "balls" could hit target randomly, or they could do so deterministicly as part of the setup. The variables have to be non-local.

I take it you disagree. Is it a matter of preference? Or am I just too unqualified to have a view on this already?

 

[The Bill]

I think I get that.

That is of course true. However, I see it differently: suppose the angle is not 0°, but, for instance 10°. I can interpret that as the "gun pointed 10° off axis". The "balls" could hit target randomly, or they could do so deterministicly as part of the setup. The variables have to be non-local.

I take it you disagree. Is it a matter of preference?

That only holds up as an opinion if you build the experimental apparatus, take exactly one measurement, and then tear down the apparatus(or at least never take seriously any more experiments beyond that first recorded one.)

If you repeat the experiment a statistically significant number of times(and if the polarizer angle is adjustable,) you'll be able to map an underlying probability distribution of possible polarizations for the entangled photon pairs generated by your apparatus.

 

[entropy1]

I'm not sure I get it. In what way, in the entanglement setup, is there nonlocality?

For instance: if the photons get in a (weighted) superposition of passing and not passing their polarizer, can this superposition of states (or its information) persist and propagate all the way to the top where the information is joined and the outcome is produced by that? Is there any nonlocality that way?

 

[The Bill]

You're making things difficult for yourself. With entanglement experiments, we're just measuring a property that the two entangled particles have been forced to share in common. It's not much more mysterious than cutting two slivers off a block of metal, transporting them to different locations, and discovering that they're made of the same type of metal as each other.

I suggest you watch some of Leonard Susskind's lectures on entanglement on Youtube, study the problem for a while in your textbooks, then come back and see if you understand it a bit better.

 

[entropy1]

I suggest you watch some of Leonard Susskind's lectures on entanglement on Youtube, study the problem for a while in your textbooks, then come back and see if you understand it a bit better.

Ok. You're in good company saying a thing like that to me. Apparently I was not as clear as I hoped to be. Maybe I do not understand this matter. Thanks for the insight.

 

[StevieTNZ]

The correlation of photons both passing their polarizers would be 100%, right? Of course we can't predict if the photons are going to pass, but we know that if one has done so, the other will do too! (in this setup)

I, and most, would hope so. But this is inductive reasoning. [see pgs 189 - 191, "Quantum Enigma" by Bruce Rosenblum and Fred Kuttner (2nd edition)]

 

[entropy1]

Why does nobody in the physics world care about the random/non-random question?

 

[vanhees71]

Because, it's pretty obvious that this is not a physics question. To the overwhelming high-accuracy evidence the behavior of matter is described by quantum theory, and the physical part of its interpretation, i.e., the minimal interpretation, linking the elements of the mathematical formalism ($C^*$ algebra on Hilbert space, to say it in an quite abstract way) to the real-world observables (cross sections of scattering processes, atomic, molecular and nuclear spectra, condensed-matter phenomena,...) is probabilistic. Further, thanks to Bell's work it is also a physical question, whether you can mimic this probabilistic behavior with a local deterministic hidden-variable theory, and the answer is a clear no. Again the overwhelmling high-accuracy evidence shows that the corresponding Bell inequality is violated precisely in the way as predicted by quantum theory, and since there is no consistent non-local hidden variable theory compatible with Einstein causality from a physicist's (who is not spoiled by thinkgin about socalled "deep philosophical problems" ;-)) point of view it's a clear case that according to present overwhelming evidence the world is intrinsically and irreducibly probabilistic.

 

[entropy1]

@vanhees71 Is QM random in different, unrelated ways? Then I would see it is a fundamental property of the quantumworld.

I still got no answer to this, of which I would very much like some respons from someone if possible.

I'd like to understand! It is not so obvious to me why I should just shut up and calculate. That just doesn't seem to be so much fun to me, though I would probably get to it if I knew why I should!

 

[vanhees71]

What do you mean by "random in different, unrelated ways"? It's random in the usual sense of random. According to quantum theory an observable of a quantum system have either determined values due to a preparation in a corresponding quantum state or this observable has no determined value, and the state tells you the probability for measuring a certain value of this observable and nothing else.

Entanglement means that you have a quantum system with parts that can be far appart with each other showing very strong correlations, stronger correlations than possible than in any local deterministic theory. This is the content of the fact that Bell's inequality is violated with high precision, and it is precisely violated in the way as predicted by quantum theory.

In physics (or the natural sciences) "to understand" means to be able to explain a phenomenon from what has been determined to be fundamental laws of nature. These laws can not be further "understood" in the sense that you can derive them from even more fundamental laws. Of course, what you call a fundamental law may change when one finds new evidence, like in the early 1900s, where it became very clear that classical electrodynamics cannot describe the spectrum of thermal radiation ("black-body spectrum"), and Planck discovered quantum theory (in a very rough preliminary form, which was developed further to modern quantum theory in 1925/26). In this sense you can only take the fundamental laws as formulated in modern quantum theory as a condensed form of our knowledge about how nature behaves. There's no "deeper understanding" to it. We can just learn the formalism and how to apply it to new experiments and observations to test its validity in more and more detail. Perhaps one day one finds a discrepancy, and then one has to find some new even more fundamental theory adapted to this new evidence. That's how science works, and Nature is not there to give you fun. It just is as it is (in my opinion there's still a lot of fun in learning about it using mathematics and the natural sciences).

 

[DrChinese]

I'd like to understand! It is not so obvious to me why I should just shut up and calculate.

What other choice is there on this point? You are welcome to look for the underlying cause*. Look anywhere you like, and let us know when you find one.*As if no one thought of that previously, and already came up short - and you were already told this.

 

[entropy1]

Ok. I think I get it now. However, I remain that it is extremely unsatifying to me that QM has no philosophical interpretation*. However, I am not the one to find it if it would exist. So I think I just have to throw the towel in.

* Having equally qualified candidates that will never be resolved is the same thing to me.

 

[vanhees71]

There are tons of philosophical interpretations of QT. Theyr are only not of any relevance from a natural-science point of view.

 

[Nugatory]

What does one understand if anything after studying QM? Is there some answer to that?

No, but there's nothing special about QM in that regard.

Consider what happens with classical gravitation. We start by investigating such diverse phenomena as falling objects, thrown stones, the atmospheric pressure, the motion of the planets. We don't understand any of them, we follow many false paths, and eventually Isaac Newton discovers the law of gravity. One equation, $F=Gm_1m_2/r^2$, explains everything and we understand gravity in all of its varied manifestations...
Except that then some clever high school kid who should be doing her exercises and calculating the speed of a dropped object interrupts her teacher to ask "What makes the objects want to move together? What's going on that makes $F=Gm_1m_2/r^2$ work so well? What's the reason the math works?". The answer is going to be some variant of of "It works. Experiments prove it. Shut up and calculate, you still haven't finished your exercises".

What's different here is that classical gravitation fits in well enough with our common sense that once we see how well it works we tend to accept it without digging deeper. QM, on the other hand, is counterintuitive enough to provoke that "yes, but why?" question, and a feeling of deep dissatisfaction when no answer is forthcoming.

 

[Zafa Pi]

Whatever the future might show, it looks hard to get rid of randomness as mathematical concept.

Randomness is not a mathematical concept. There are random variables (functions) and probabilities, but no definition of random. Sometimes people use the word random to refer to a finite valued r.v. with equal probabilities, e.g. a random coin flip, meaning heads and tails each have probability 1/2.

 

[fresh_42]

Randomness is not a mathematical concept. There are random variables (functions) and probabilities, but no definition of random. Sometimes people use the word random to refer to a finite valued r.v. with equal probabilities, e.g. a random coin flip, meaning heads and tails each have probability 1/2.

Replace it by stochastic.

 

[Zafa Pi]

Replace it by stochastic.

If you look up stochastic in an English dictionary it will say (essentially) random. There are stochastic processes like random variables, but stochastic is no more defined in math than random.
I'm not trying to be picky. Terms like random or unpredictable are intuitive, but are too nebulous to pin down mathematically. There are some that say random means there is no algorithm that gives its value. But there is no algorithm that generates the busy beaver function, but few would call it random. That physicists often use the term random I don't find problematic, anymore than when they refer to reality. But reality isn't a math term either.

 

[David Lewis]

...can this superposition of states (or its information) persist and propagate all the way to the top where the information is joined and the outcome is produced by that?

It could be that in quantum processes, some information is lost along the way. Otherwise, by running time backwards you'd be able to figure out what the initial conditions were.

 

[vanhees71]

Randomness is not a mathematical concept.

To the contrary, randomness is a very mathematical concept, called probability theory and the theory of stochastic processes. The latter are, of course, very much motivated by physics (starting with kinetic theory in the 19th century by Maxwell and Boltzmann with some preliminary work by Bernoulli).

 

[entropy1]

I thought probability was well-defined (like $P(i) = \lim_{N \rightarrow \infty} \frac{N(i)}{N}$). In this form the equation seems to suggest that one has to possesses all information conceivable to be able to determine the probability with certainty (for at any point it could start to deviate, due to whatever factors). However, if a lengthy sample is cut into smaller samples that exhibit the same probability, is this probability then more precise? You could continue to extend with small samples and measure a different probability at some instance. How large a sample should be or how small can you make it?

 

[bhobba]

However, I remain that it is extremely unsatifying to me that QM has no philosophical interpretation*.

Where have you been dude. There are tons of them, and many are simply philosophical arguments about the meaning of probability:
http://math.ucr.edu/home/baez/bayes.html

For what its worth I hold to the formal view its just the elaboration of the Kolmogorov axioms as espoused by Feller in his classic:
https://www.amazon.com/dp/0471257087/?tag=pfamazon01-20

He explains it very well in the early chapters.

Thanks
Bill

 

[bhobba]

I thought probability was well-defined (like $P(i) = \lim_{N \rightarrow \infty} \frac{N(i)}{N}$).

As I said read Feller. Its a lot more complicated and subtle than that. The above is actually a theorem called the law of large numbers:
https://terrytao.wordpress.com/2008/06/18/the-strong-law-of-large-numbers/

Thanks
Bill