Einstein and "spooky actions"

[Skwim]

I guess the discussion with you is over.

Come on zaybu, I'm rooting for you.

 

[zaybu]

Come on zaybu, I'm rooting for you.

Thanks, but it would be a waste of time, and besides post 58 pretty much sums it up. You can do QM without mentioning nonlocality and there would be no lost. Those who are working in that field are wasting their time. Unfortunately, the internet abounds with misguided fans. Had anyone else but Einstein spoken of spooky action at a distance, no one would have paid attention. And this thread wouldn't exist. However if you want to know the math behind, here's a good place to start. Let me know what you think:

Violation of Bell’s theorem | Lecture 5 - Quantum Entanglements - Susskind Lectures - Lecture Notes

Any physisict who understands Susskind lecture and continues to work on this topic is a fool. Spooky action at a distance is for the nutjob.

 

[PolyHedral]

Not nessarily. I don't know what you mean by "interactions", but if you mean signals even here there are arguments that it is possible and even that it doesn't violate relativity constraints. In a paper by Steve Weinstein, "Superluminal signaling and relativity", we find one of many arguments against the no-signalling constraint".

To be clear, when I say that it breaks Relativity, I don't mean that it's not valid within Relativity, but that it produces unreal results, i.e. backwards time-travel. Which wrecks physics in a very practical sense: you can't make predictions about the effects of causes that haven't happened yet.

Weinstein first points out that the "existence of a finite, invariant speed of light in vacuum suggested early on that it would be impossible to send signals faster than light, and Einstein’s attribution of this limit to the structure of space-time itself suggested that in fact all physical fields would be subject to this limitation. Yet arguments to this effect are nowhere to be found in Einstein’s original work"

You can, however, use the original work to show that a faster-than-light signal looks like time travel from some frame.

But this paper, like others (some which are rather far "out there" in terms of wildly speculative), is about possibilities. Perhaps this kind of "signal" is possible, or perhaps some aspect of relativitstic quantum physics makes superluminal signals possible, or perhaps we can travel back in time in a Delorean (providing, of course, we have the flux capacitor and plutonium). And while I think it important not to repeat Einstein's mistake and rule out what appears to be counter-intuitive, impossible, and/or inconsisten with current knowledge, that doesn't make a bunch of arguments that superluminal signals are possible necessarily plausible arguments.

It is absolutely necessary not to say, "That is absurd, therefore it's impossible!" That's why I'm perfectly fine with the actual observable result of entanglements, i.e. that the spins are correlated more than one would expect. The part I object to is interpreting this as one particle "messaging" the other when it's observed, regardless of the fact that one can't use it to send a coherent signal. I feel it's more sensible to interpret it as "collapses" which propagate from the measurement at c-or-less, with the kludge that (by virtue of entangling, which is a local process) there are only two different combinations of collapse possible, instead of four.

(This is in the framework of collapse interpretations, which shouldn't really be used, but since the "simplest" interpretation is "Everything gets entangled with everything else!" that doesn't really help solving the problem of what entanglement does.)

 

[LegionOnomaMoi]

If you go through the derivation of Bell's theorem (at the end of the text), Bell uses only classical logic. That was one of his assumption.

If you look on pg. 377 of the document kindly provided by Mr Sprinkles, you'll notice a footnote. It says that even before we get to the inequality itself, we've already abandoned classical physics (which is deterministic).

Bell did not rely on classical logic. Not only that, but even before you get to his inequality he is defining the a "particle" in terms of states which, by classical physics/logic, are mutually exclusive and therefore cannot happen.

I'm not going to go over what Einstein said, as his words are a mass of confusion. But what Aspect established is that Bell's inequalities are violated, meaning that classical logic doesn't apply to quantum system

No one is disputing that classical logic doesn't apply to a quantum system. In fact, that's what Einstein and Bell were trying to show (in different ways).

The issue is this:

Take the example of tossing a fair coin, with probability 1/2 for heads, and 1/2 for tails.

Classically:

1. the word "and" means multiply. What's the probability of tossing a heads and tossing a heads again? Answer (1/2 ) * (1/2) = 1/4
2. the word "or" means add. What's the probability of tossing heads or tails? Answer 1/2 + 1/2 = 1

In QM: we do not perform these operations on the probabilities but on the "probability amplitude", then we square the amplitude to get the probability.
Example, If a particle is in a spin state (up or down), we write:

|ψ>= a|+1> + b|-1>, with a^2 + b^2 = 1

If we want to know what's the probability it is in one state say, up, then we calculate the probability amplitute <&#968;|+1>, after which the probabilty will be P = <&#968;|+1>^2. In doing so, you will get mix terms. And it's with that we can explain the double-slit experiment, and many other features that classical physics can't.

The problem, or at least a big part of it, is how you are describing the difference between classical and quantum logic, and what this entails.

A coin, like you state, can in classial logic only be heads or tails. It cannot be both. That's the classical "or" logic you have as #2 below "Classically: ". The same is true of the double-slit experiment.

If classic logic held, we'd be able to find the probability that particles will hit the detection screen at certain points having traveled through the double-slit screen by adding the probabilities that they traveled through slit A and the probabilities that they traveled through slit B.
A bit more formally, albeit without bras and kets (as those of us who studied linear algebra and abstract algebra for some time before quantum physics were rather annoyed to have to get used to an entirely different notational schema), classical logic demands we obtain the probability distribution, or P(x), that we detect the particle at some point x on the detection screen by adding P(A) + P(B), the sum of the two possible and mutually exclusive probabilities:

P(x) = P(A) + P(B)

This doesn't work, because classical logic doesn't work. In order to get the right distribution P(x) we require the following:

P(x) = | P(A) + P(B) | ^2

(I'm being a bit cavalier with the formalism as you no doubt noticed, but it's simpler and I'm sure you undersand it).
If we calculate the squared amplitude as above, we'd get the classical "or" result, but also with a certain "something else" added. This is easily represented mathematically (in more than one way), but boils down to this notion: the probability that the particle traveled through either one of the slits and in addition two further values (both the probability functions added with their complex conjugates). Both additional terms can of course be made one (e.g., rather than add both just add twice the real part with one complex conjugate). It doesn't really matter for us here.

It doesn't matter because we agree that this is not how classical physics or classical logic works. We shouldn't need extra terms, whatever they are. Yet that's the only way to obtain the right probabilities.

What, though, does that mean about the physical system itself? We are saying that, given a situation in which there are two mutually exclusive routes, we cannot simply say that the particle took one or it took the other. Which is logically equivalent of saying that a single particle cannot be treated as going through just one of the two slits or (alternatively) as taking just one of the two routes.

We've discovered something without even resorting to Alice and Bob and their endless quests to read spins (which, unfortunately, both started their romantic involvement and ended it; although they had no children, they battled over everything from the pet fishes to who should be able to stay in their home).

We've discovered that a single particle, which is supposed to be localized in space, cannot be treated as localized in space. If it could be, then it would simply take one of the mutually exlusive routes and we'd be able to use normal probability rules.

What does it mean to not be localized in space? And how would we represent the spatial coordinates of the particle?

 

[PolyHedral]

This doesn't work, because classical logic doesn't work.

Sure it does. However, you sneakily re-defined P(A) and P(B) to be complex, not real values! Those aren't probabilities at all!

Also, you're quoting the simplified form of a theorem that actually says P(A and B)=P(A)+P(B)-P(A or B), which... might give you the right answer for non-mutually-exclusive A and B? I'll try the math later when its not 4am.

 

[LegionOnomaMoi]

I guess the discussion with you is over.

That's it? This entire dispute started on another thread because you said that there is no "spooky action at a distance". That's why this thread has as a title "Einstein and 'spooky actions'". It is because you state that spooky actions at a distance do not occur. If you cannot simply tell us (or me; however you wish to think about it) what Einstein meant by "spooky action at a distance" (or the German; either one is fine), then how can you assert it doesn't happen?

Simply put, you've made (among other things) two statements so far:

1) There is no "spooky action at a distance"

2) That because I asked you to define what it is you are claiming does not exist (i.e., "spooky action at a distance"), the discussion is over.

You've clearly stated multiple times that there is no "spooky action". I have stated there is, not because there actually is something "spooky" about the phenomena Einstein referred to, but because these phenomena have been experimentaly realized in a wide variety of ways for about three decades.

How can you deny that whatever it is Einstein meant by "spooky action at a distance" does not occur if you cannot put into words what "actions" or"activity" he claimed were "spooky"?

Let's imagine I claim that "survival of the fittest" was wrong because Darwin was wrong and therefore there's no evolution. Now let's further imagine that, rather than try to explain why I'm wrong first, you try to clarify what I mean by "survival of the fittest" and how I believe this relates to evolution. After all, I might be saying this because I don't understand that "fittest" is specific to an environment, or what "fit" actually means (perhaps I'm thinking that being more "fit" means being more "evolved" and that means greater complexity).

If, when you asked "what do you think survival of the fittest means?" I say "I guess that's the end of our discussion", wouldn't you find that a bit odd? I am claiming something doesn't exist but as soon as you ask me to define what that something is, I tell you "that's it, no more discussion".

 

[Reptillian]

I got bored reading all of this, so I skimmed ahead.

...Go over that one again? I always took "non-local" to mean "involves faster than light propagation," which doesn't have anything to do with quantum superposition.

I've always taken locality to mean that you can isolate and describe bits of the universe without referencing the whole. For example, I can talk about the physics of a game of pool without factoring in the exceptionally loud fart of a dinosaur on December 2 of the year 70,061,281 B.C. I don't have to worry about the fact that Jupiter is in the constellation Scorpio, or whether some alien will be picking his nose in the Andromeda galaxy 1000 years from now.

 

[LegionOnomaMoi]

Sure it does. However, you sneakily re-defined P(A) and P(B) to be complex, not real values! Those aren't probabilities at all!

You do realize that that's how probabilities are defined in quantum mechanics, right? That probabilities are never directly obtained but are derived through amplitude?

Also, you're quoting the simplified form of a theorem that actually says P(A and B)=P(A)+P(B)-P(A or B), which... might give you the right answer for non-mutually-exclusive A and B? I'll try the math later when its not 4am.

If P( A &#8745; B ) = 0, then P( A &#8746; B ) = P(A) + P(B)

What you're using is something like the equation to figure out the probability of obtaining an event when the union of A and B share elements or overlap (that is, their union is not 0). In that case, we'd need
P( A &#8746; B ) = P(A) + P(B) - P( A &#8745; B )

 

[PolyHedral]

I got bored reading all of this, so I skimmed ahead.



I've always taken locality to mean that you can isolate and describe bits of the universe without referencing the whole. For example, I can talk about the physics of a game of pool without factoring in the exceptionally loud fart of a dinosaur on December 2 of the year 70,061,281 B.C. I don't have to worry about the fact that Jupiter is in the constellation Scorpio, or whether some alien will be picking his nose in the Andromeda galaxy 1000 years from now.

I think they're essentially equivalent. In Relativity, the maximum speed any change in anything can move is c, and therefore, one can always describe some event in terms of the region around it which is c*t distance away and t time ago.

 

[Reptillian]

As I see it, Bell has left us with abandoning; realism, locality, quantum mechanics or some combination thereof. I'm a fan of number three since we don't have a general relativistic quantum theory and we seemingly need one. Quantum physics makes predictions that conflict with relativity for the same reason that Newton's mechanics conflict with relativity. The majority of our quantum experiments have been performed here on the Earth's surface where we know we're in a non-inertial frame. We need to do more quantum experiments in orbit and in low gravity environments like on the surface of the moon or Mars. Most of the "big mysteries" confronting modern physics can be attributed to a lack of understanding when it comes to the blend of GR and QM. The solar neutrino problem, the prevalence of matter over antimatter, cosmic inflation, or even the dark matter problem might be better understood in light of a general relativistic quantum theory.

 

[Reptillian]

I think they're essentially equivalent. In Relativity, the maximum speed any change in anything can move is c, and therefore, one can always describe some event in terms of the region around it which is c*t distance away and t time ago.

Yes! You can always split the universe into past, present, future, and elsewhere.

 

[PolyHedral]

You do realize that that's how probabilities are defined in quantum mechanics, right? That probabilities are never directly obtained but are derived through amplitude?

I'm saying that probabilities are always positive real numbers. I know that you get those probabilities by adding the complex-valued wavefunctions together and then mod-squaring the result. (And then normalizing if you're picky.) Adding together complex values doesn't produce the same behaviour as adding together reals, and that's where the weird double-slit behaviour comes from.

If P( A &#8745; B ) = 0, then P( A &#8746; B ) = P(A) + P(B)

What you're using is something like the equation to figure out the probability of obtaining an event when the union of A and B share elements or overlap (that is, their union is not 0). In that case, we'd need
P( A &#8746; B ) = P(A) + P(B) - P( A &#8745; B )

...you just repeated what I said?

 

[LegionOnomaMoi]

Thanks, but it would be a waste of time, and besides post 58 pretty much sums it up.

I addressed your post and the idea that Bell was using "classical logic". But apparently that was a waste as you already just proved yourself wrong:

Violation of Bell’s theorem | Lecture 5 - Quantum Entanglements - Susskind Lectures - Lecture Notes

Any physisict who understands Susskind lecture and continues to work on this topic is a fool. Spooky action at a distance is for the nutjob.

From your link:
"Later, Alan Aspect proved the result for entangled photons rather than electrons. The measurements made on the photons were sufficiently simultaneous so that no light signal (information) could travel between them, hence completely eliminating any chance that the result was due to anything other than entanglement."

This is nonlocality.

 

[Reptillian]

Another side note, one shouldn't be surprised when physicists abuse mathematics. I've always thought of math as grammar and physics as poetry. Sometimes poets abuse the rules of grammar to get an idea across. Math is the language that physicists use to describe the universe. Some physicists talk about their preference for mathematical beauty in physics. You can use beautiful language to describe a garbage dump (bad theory). You can also use horrific grammar to convey a great idea.

 

[LegionOnomaMoi]

I'm saying that probabilities are always positive real numbers. I know that you get those probabilities by adding the complex-valued wavefunctions together and then mod-squaring the result. (And then normalizing if you're picky.) Adding together complex values doesn't produce the same behaviour as adding together reals, and that's where the weird double-slit behaviour comes from.

It does. But in order to show that:

Sure it does. However, you sneakily re-defined P(A) and P(B) to be complex, not real values! Those aren't probabilities at all!

I didn't define that at all.

P(x) = P(A) + P(B)

This doesn't work, because classical logic doesn't work.

As I said, I was cavalier with the formalism, but I thought it would remain clear. I've conflated probability of exclusive events with the probabilities that these events lead to. But that was because I wanted to give a demonstration of failure of classical logic to hold using the double-slit experiment.

It is not true that the probabilies P(A) + (PB) are mutually exclusive if we treat them as points over some area on the detection screen. Rather, the routes are mutually exclusive.

To be less cavalier:
I have slits A and B. Classical logic tells me the particle can't go through both. For each slit, there exists some area on the detection screen giving me the expectation values (probability distributions over suitable trials) of finding the particle at point x given that A occured or y given that B occurred (by "occured", I mean that the particle arrived at x through a route from that slit). Classical logic tells me that I need only add the expectation values:

E( x + y) = E(x) + E(y)

This fails to give me the right results.

So I alter my method of deriving a probability, but still recognize that I have two slits, A and B, that the particle can travel through, and thus can arrive at some point x via paths A(p1) and B(p2). So instead of using expectation values or averages or whatever, I use the mod square like so:
P(x) = | A(s1) + B(s2) | ^2

which becomes | A(s1) |^2 + | B(s2) |^2 + A(s1)B*(s2) + A*(s1)B^(s2)

and I can simplify the last terms into 2 times the real part of { A(s1)B*(s2) }

Then

...you just repeated what I said?

No, because "and" doesn't mean union. P (A & B ) means what is the probability of getting A and B, but I can't get A and B because they are mutually exclusive. If I roll dice, the probability that I will get a 2 and a 4 is not a is not calculated by 1/6 +1/6 -...? They are independent events. The probability is 1/6* 1/6.

 

[Curious George]

...

P(x) = P(A) + P(B)

This doesn't work, because classical logic doesn't work. In order to get the right distribution P(x) we require the following:

P(x) = | P(A) + P(B) | ^2

I am sorry, I still do not see it. Why could we not say that the first doesn't work because we are dealing with vectors instead of events.

But were we to simply focus on the event- Then we have an assumption of mutual exclusivity with your first probability determination. In logic, such an assumption could be viewed as a true dichotomy or a false dichotomy. If it is a false dichotomy then we would certainly expect that your first equation would yield different results.

Perhaps you could recommend some reading so I can clear up my misunderstanding.

 

[Mr Spinkles]

To be clear, when I say that it breaks Relativity, I don't mean that it's not valid within Relativity, but that it produces unreal results, i.e. backwards time-travel. Which wrecks physics in a very practical sense: you can't make predictions about the effects of causes that haven't happened yet.

You can, however, use the original work to show that a faster-than-light signal looks like time travel from some frame.

It is absolutely necessary not to say, "That is absurd, therefore it's impossible!" That's why I'm perfectly fine with the actual observable result of entanglements, i.e. that the spins are correlated more than one would expect. The part I object to is interpreting this as one particle "messaging" the other when it's observed, regardless of the fact that one can't use it to send a coherent signal. I feel it's more sensible to interpret it as "collapses" which propagate from the measurement at c-or-less, with the kludge that (by virtue of entangling, which is a local process) there are only two different combinations of collapse possible, instead of four.

(This is in the framework of collapse interpretations, which shouldn't really be used, but since the "simplest" interpretation is "Everything gets entangled with everything else!" that doesn't really help solving the problem of what entanglement does.)

In case you missed it, I direct your attention to this post, which was a response to your concerns about nonlocality vs. special relativity.

 

[LegionOnomaMoi]

I am sorry, I still do not see it. Why could we not say that the first doesn't work because we are dealing with vectors instead of events.

Because we are dealing with events. We have a particle that can arrive at a point x via two ways: slit A, or slit B. You can refer to these as events or paths or whatever you wish, but what you cannot do is treat the particle as if it could arrive at some point x via a path through A OR a path through B.

Does that make more sense? If not, then I can recommend books or try to explain better or both.

EDIT: I just realized you were responding to my first simplified version. I've re-written it to clear that up. As I was responding to one member in particular, and one of the few things we agree on is that classical logic doesn't work here, I thought I could just focus on the way in which it does not work (the normal methods of obtaining probabilities when you have mutually exclusive ways in which something can happen)

 

[Curious George]

Because we are dealing with events. We have a particle that can arrive at a point x via two ways: slit A, or slit B. You can refer to these as events or paths or whatever you wish, but what you cannot do is treat the particle as if it could arrive at some point x via a path through A OR a path through B.

Does that make more sense? If not, then I can recommend books or try to explain better or both.

Books would be helpful.

but this last portion of your statement seems to imply that we cannot treat the events as mutually exclusive. So, why would we consider using the P(x)=P(a)+P(b) approach.

And, I might be completely off base but if you are dealing with a mutually exclusive event- the probability that the event will occur is that of the parts added together which = 1.

I just found it a little confusing to toss in "point X" since we were talking about the probability of x, P(x). In the double slit experiment the point at which the "particle" goes is synonymous with the path traveled, since that is how we "see" the particle in the first place.

But again, I might be getting confused. Perhaps just the books, then?

 

[Mr Spinkles]

I wish it would be my personal view - that would make me very smart. LOL.

No, that Bell's theorem is based on classical logic and its violations demonstrate that classical logic fails to describe quantum systems comes from Leonard Susskind. In a lecture, many years ago I can't recall the year, he derived Bell's theorem by using exclusively Venn's diagrams -- you cannot get any closer to classical logic then with Venn's diagram. And he then showed with quantum logic, that Bell's theorem will be violated. There Was no need to invoke non-locality.

I believe you are confused. First, nonlocality--whether you agree with it or not--is not put forward by anyone as a fundamental principle to be invoked. Rather, it's a prediction or consequence to be derived from fundamental principles, especially the principles of QM, in certain experimental situations. Notice that we do not invoke locality in QM, either: that is, QM says that a measurement on one entangled particle affects a measurement on its partner entangled particle, without imposing any additional local restrictions on how far apart the particles or measuring devices were at the time of measurement. So if we're talking about fundamental QM principles, it's really the absence of locality as a principle, that makes nonlocal effects allowable as a consequence.

By analogy, you don't need to "invoke" any principle of nonlocality in Newton's theory of universal gravitation, either. In that theory, as in QM, nonlocality arises as a consequence of the absence of any principle at the beginning enforcing locality. Newton says F = G m1*m2/r^2, without any reference to how fast a force travels from mass m1 to mass m2. As a consequence, Newtonian gravitation predicts nonlocal effects. Specifically: change the position or mass of the Earth, and it has an effect on the acceleration of the Sun a large distance away, instantaneously. By definition, such an effect would be nonlocal (although it would be a stronger form of nonlocal influence than allowed by QM, namely a deterministic or causal influence). And in Newton's theory, as in QM, whether there is actually locality hiding in there somewhere is not a critical issue that every researcher or theorist must be concerned about; you can do advanced Hamiltonian or Lagrangian dynamics without worrying about the nonlocality implied at a more basic level by Newton's laws. And similarly, you can do research on what goes on in a high-energy particle accelerator, you can do QCD or QFT in curved spacetimes, without worrying about what happens when entangled cold atoms or low-energy photons are simultaneously measured on an optics table at great distances from each other.

Second, you realize that Bell's theorem was expected to be violated on the basis of QM and nonlocality, right? You seem to be suggesting (incorrectly) that disproving Bell's theorem is a blow against nonlocality. In fact if Bell's theorem was not violated, then the apparently nonlocal experimental outcome might have been explained as just a misleading artifact, due to QM being an incomplete theory of what are really local interactions. You realize that the only LOCAL option from the get-go was locality + hidden variables, right? There is no locality-without-hidden-variables option, as far as I know. The two remaining contenders in light of Bell violations are (1) nonlocal + hidden variables, and (2) nonlocal and no hidden variables either (orthodox QM).

Thanks, but it would be a waste of time, and besides post 58 pretty much sums it up. You can do QM without mentioning nonlocality and there would be no lost. Those who are working in that field are wasting their time. Unfortunately, the internet abounds with misguided fans. Had anyone else but Einstein spoken of spooky action at a distance, no one would have paid attention. And this thread wouldn't exist. However if you want to know the math behind, here's a good place to start. Let me know what you think:

Violation of Bell&#8217;s theorem | Lecture 5 - Quantum Entanglements - Susskind Lectures - Lecture Notes

Any physisict who understands Susskind lecture and continues to work on this topic is a fool. Spooky action at a distance is for the nutjob.

Those notes don't support your argument. In addition, you've made a number of mistakes. The most straightforward mistake can be seen by comparing what you said about the singlet state, to what the link you cited says about it.

In the link you cite, the singlet state is described as "the simplest quantum system that exhibits entanglement" and this state is used as the example for demonstrating everything that follows. And the way the singlet state is written in your link is correct (see bottom of this post), and it agrees with the way I wrote it in a previous post, below (to see this, consider what basis your link is using to write out the ket in matrix form):

But your link does not agree with the state you wrote, below. (Can you see why?)

It is a singlet state but if you want to deal with entanglement, it is in the wrong format. Entanglement means that is you know the state of one particle, you know automatically the state of the other.

What you need is

|&#968;>=|+1,u> + |-1,d>.

The +1,-1 would indicate that one particle is going to the right, the other to the left. The u and d would indicate that one has an up-spin, the other, a down-spin.

Notice that according to what you wrote down, we know the precise spin state of both particles before a measurement is done. In other words, what you wrote down is not an entangled state. (In fact it's not a sensible two-particle state of any kind, as far as I can tell, which should involve products of terms like those you wrote down, not a simple sum. See Griffiths, Shankar.) What I wrote down, and what appears in your link, is a proper entangled state because it's only AFTER a measurement alters the entangled state, and determines the spin state of one particle, that the spin state of the other particle is determined as well. So one measurement affects another. And how long does it take for a measurement to change the state? QM doesn't say it takes any time at all. And how far away can the measuring devices be located? QM doesn't place any local restrictions there. Hence, the principles of QM predict nonlocal influences in certain experiments where entangled particles are separated and measured simultaneously.

By the way, it's useful to repeat that it is a consequence which, as far as I know, isn't experimentally significant at the level of high-energy subatomic particles and hence, discussion of this experimental consequence would probably add unnecessary complexity to QFT or QCD or SM textbooks.