Progress on Explaining Bell's Inequality

[atyy]

I would object to naming this "more fundamental". Instead, I would name it "less fundamental", because it has a much more direct connection with observation.

Fundamental from an operational point of view :D which of course is not what is being asked in this thread.

I guess two possibilities are some Bohmian version of QED, or http://arxiv.org/abs/1111.1425?

 

[Elroy]

Superposition is not the best way of expressing it - entangled is much better.

I haven't read the Dr. Chinese page in detail, but I have scanned it. However, I thought I would ask some questions of you regarding this statement.

My agenda is to attempt to formalize a language that can be used for programming and understanding quantum computers. Just to explain a bit further, regarding classical computers, there is a rather sharp distinction between the electronic engineers who design and build them, and the programmers who make them do all the wonderful things we use them for. Sure, it's not a "perfectly" sharp divide, but it's fairly clear. My interests are clearly on the programming side. I'll just assume that the quantum engineers will figure out how to create, transmit (i.e., move), and entangle qubits. I will further just assume that they will figure out how to send them through Pauli gates of any selected angle (which is little more than just rotating the laser that would "read" them).

Given this, I find it useful to think of superposition and entanglement as separate things.

For me, superposition is any qubit that is in a state other than |0〉 or |1〉. It has to do with one, and only one, qubit.

Entanglement, on the other hand, requires a minimum of two qubits (and possibly a large number of qubits). Also, superposition is a yes-or-no thing (although the square of the absolute value probability amplitudes need not be 50/50). However, in contrast, entanglement is a matter of degree (from none to perfect correlation).

(Again, we must remember that when reading pairs of qubits (entangled or not), they will agree with each other 50% of the time by chance alone.)

So here's my definition of entanglement (which I hope agrees with most others). If you have pairs of qubits (with a large number of pairs prepared and measured the same way) and you can find some axis on which to measure them such that (over the long run) they will have greater than a 50% agreement (i.e., absolute value correlation greater than zero), then they are entangled.

It's interesting to think about whether you can have entanglement without superposition, or vice-versa. Also, it's interesting to realize that both entanglement and superposition are lost "instantaneously" faster than C.

Also, if others feel like my definitions of entanglement and superposition are not at least somewhat accepted definitions, I welcome critique.

Regards,
Elroy

 

[atyy]

It's interesting to think about whether you can have entanglement without superposition, or vice-versa.

It is not possible to have entanglement without superposition. A product state is something like |01>. Entanglement means the state cannot be written as a product state in any basis*, so |00> + |11> is an entangled state. So the entangled state is a superposition of the product states |00> and |11>.

*I gave an old-fashioned definition of entanglement there. It means the entanglement entropy is not zero.

 

[Elroy]

Yeah atty, I was pretty much there in my own head, and it makes sense that you can't have entanglement without superposition.

Also, after re-reading it, I can find holes in my definition of entanglement. For instance, if we prepare a large number of qubits, all with a value of |1〉, then separate them into pairs, they will have a perfect correlation, but they won't be entangled. That actually again makes your case that you can't have entanglement without superposition. The value of Alice's qubit must be unknown (i.e., in superposition) before we can even talk about entanglement.

 

[bohm2]

The problem is that they could be explained with some type of information transfer much much faster than the speed of light, but nonetheless with finite maximal speed. In such an explanation everything would be similar to what is named today "local", only the maximal speed has another value, not c but say 10000000000000 c.

According to this paper, the hidden/private quantum signals that exist between entangled particles/systems cannot remain hidden if the speed is anything less than instantaneous:

The new hidden influence inequality shows that the get-out won't work when it comes to quantum predictions. To derive their inequality, which sets up a measurement of entanglement between four particles, the researchers considered what behaviours are possible for four particles that are connected by influences that stay hidden and that travel at some arbitrary finite speed. Mathematically (and mind-bogglingly), these constraints define an 80-dimensional object. The testable hidden influence inequality is the boundary of the shadow this 80-dimensional shape casts in 44 dimensions. The researchers showed that quantum predictions can lie outside this boundary, which means they are going against one of the assumptions. Outside the boundary, either the influences can't stay hidden, or they must have infinite speed.

Quantum nonlocality based on finite-speed causal influences leads to superluminal signaling
http://arxiv.org/pdf/1110.3795v1.pdf
http://www.nature.com/nphys/journal/v8/n12/full/nphys2460.html

The experimental violation of Bell inequalities using spacelike separated measurements precludes the explanation of quantum correlations through causal influences propagating at subluminal speed. Yet, it is always possible, in principle, to explain such experimental violations through models based on hidden influences propagating at a finite speed v>c, provided v is large enough. Here, we show that for any finite speed v>c, such models predict correlations that can be exploited for faster-than-light communication. This superluminal communication does not require access to any hidden physical quantities, but only the manipulation of measurement devices at the level of our present-day description of quantum experiments. Hence, assuming the impossibility of using quantum non-locality for superluminal communication, we exclude any possible explanation of quantum correlations in term of finite-speed influences.

Quantum Nonlocality Based on Finite-speed Causal Influences Leads to Superluminal Signalling
http://pirsa.org/displayFlash.php?id=11110145

 

[bhobba]

Given this, I find it useful to think of superposition and entanglement as separate things.

There are standard definitions of superposition and entanglement in QM. I suggest you stick to those.

They are:

1. Superposition reflects the vector space structure of so called pure states. That is if you have a system that can be in state state |a> and state |b> then it can be in a superposition of those states ie c1*|a> + c2*|b> where c1 and c2 are complex numbers. This is called the principle of superposition and is a fundamental principle of QM. It is not an axiom because it follows from something else - but no need to go into that here.

2. Entanglement applies the principle of superposition to separate systems. Suppose you have a system that can be in state |a> or |b> and another system that also can be in state |a> or |b>. If system 1 is in state |a> and system 2 in state |b> that is written as |a>|b>. Conversely if system 1 is in state |b> and system 2 on state |a> that is written as state |b>|a>. But we can apply the principle of superposition to give a state c1*|a>|b> + c2*|b>|a>. The two systems are then said to be entangled. It is a peculiar non classical situation - system 1 is no longer in state |a> or |b> and the same with system 2 - they are entangled with each other. If you observe system 1 and find it in state |a> by the principles of QM the combined system is in state |a>|b> - so system 2 is in state |b> and conversely. Observing one system immediately has told you about another due to entanglement.

This is the weirdness of entanglement - observing one system immediately tells you about the other system and conversely. The difference classically is that the principle of superposition does not hold and you don't have this peculiar relationship involving complex numbers between states. You can in fact have something similar to entanglement classically (by, for example, putting coloured papers in two envelopes - look at one envelope and you know the colour of the other) but its this complex number thing that distinguishes it. The reason you have complex numbers involved, which distinguishes it from classical probability theory, is the requirement for continuity between pure states:
http://www.scottaaronson.com/democritus/lec9.html

This is the background to my statement right at the beginning of this thread that progress has been made in understanding bells inequalities. We understand this essence of QM is the requirement of continuous transformations between pure states and directly leads to entanglement which simply can't be explained classically - in fact it leads to the overthrow of naive reality.

Thanks
Bill

 

[bhobba]

According to this paper, the hidden/private quantum signals that exist between entangled particles/systems cannot remain hidden if the speed is anything less than instantaneous:

Of course if it was merely very very large rather than instantaneous that would be detectable. What Ilja is saying is that it may be undetectable within current, or even future, experimental technique. Also if true it would likely mean there was a sub-quantum theory to which QM is simply an approximation as classical physics is an approximation to QM. It would fulfil Einstein's belief that QM was incomplete.

Such is not the only proposal along those lines eg primary state diffusion (which I suspect would also require such very very large, but not infinite, superluminal influences):
http://arxiv.org/pdf/quant-ph/9508021.pdf

Thanks
Bill

 

[Elroy]

Oh gosh, bhobba, I wholeheartedly agree. I certainly wasn't attempting to alter the definition of either superposition or entanglement, and thanks outlining standard definitions. I suppose, more than anything, I'm just developing my own way of "saying" those definitions. It's important to me that I'm able to "say" them (possibly with slightly different words but the same meaning). It's also important that the definitions are thoroughly "nailed down."

Regarding your definition of superposition, I have absolutely no argument. It's the standard...
|\psi \rangle = \alpha |0\rangle + \beta |1\rangle
...that is so often stated, where |ψ〉 is the qubit's state, α and β are complex, |α|² + |β|² = 1, and α and β are defined as probability amplitudes.

However, entanglement would seem to be even more complex than what you've stated. (Shucks, I'm being called away but will return tomorrow. I'll say a bit though.) I suppose the primary thing I'd like to say is that it seems that entanglement can be framed in terms of correlations among the qubits as well as superposition across the system of qubits. I did a somewhat poor job with my definition in post #32, but I'll give a more formal definition (in terms of correlations) tomorrow.

Also, I think a definition of entanglement also has to address the situation where qubit #1 is measured on one axis (say Z), but qubit #2 is measured on some other axis (say 45° from Z in either X or Y). This would be the equivalent of rotating qubit #2 by 45° before "reading" it.

Take Care,
Elroy

 

[bhobba]

Also, I think a definition of entanglement also has to address the situation where qubit #1 is measured on one axis (say Z), but qubit #2 is measured on some other axis (say 45° from Z in either X or Y). This would be the equivalent of rotating qubit #2 by 45° before "reading" it.

The standard definitions I gave fully explains Bell. There is no need to go any further.

Dr Chinese's superb link on it gives the detail - and even with easy math:
http://www.drchinese.com/Bells_Theorem.htm

It a result of that damnable principle of superposition with complex numbers.

Thanks
Bill

 

[Jimster41]

I'm reading the book mentioned above. "Quantum Chance" Nicholas Gisin (been mind boggled by EPR and Bell for a long time).

I am a bit confused about the wave collapse between entangled entities. I worry I've been carrying around an incorrect picture of a two slit interference pattern shining on the wall of a dark classroom - The pattern is made up pointillist-like of dots representing samples taken by the screen periodically over some period of time say like over the 6 hours between noon and 6pm. To keep the non-locality notion handy and ready for rumination, I have always held onto the explanation - "The photons that were sampled at 2pm were apparently interfering with the photons sampled at 3 pm"

Now I think I might have that wrong. It really was that every sampling at time t throughout the afternoon, the photon sampled through the left slit was interfering with (uh, itself?) going through the right slit. Still crazy but the entanglement doesn't cross time. I always remembered it as the pattern wasn't visible until the parade of entangled photons were through the slits over time. Maybe I'm just getting confused by the fact that the wall wouldn't look very interesting after only a couple of pairs were sampled - even though the pattern that would eventually be painted was there with each sample. But I think I've asked myself about this and answered myself with "how would you see the pattern with only one pair. It would just be a dot on the wall. Maybe if you had drawn an expected wave interference pattern on the wall you'd notice it was on a trough or a valley but what would that tell you"

I got thrown off into this possibly justified worry again, just now by someone's thought experiment above where Bob reads his detector or let's say flips his "entangled photon pair 1" coin and gets "heads". He then drives over to Alice's house where the the other "entangled photon pair 1' coin is (which hasn't been flipped?) and bets Alice that when she flips it she'll get "heads". Alice still gets to toss her coin right? Or is it laying there dead, stuck to the floor, with only a "heads" side to be had, because Bob already flipped it's entangled twin? And it did this to iteslf, flipped itself, automatically the instant Bob flipped his?

Is there such a thing as an entangled wave collapse that can be smeared across some frame of non-zero time? Or is that kind of the special thing about entangled wave collapse and time, that somehow, though it is not helpful to us in synchronizing our reality across space-time the entangled wave collapse is THE or at least A fundamentally simultaneous thing. I just don't see how if Bob is standing there, obviously having flipped his half of the tangled coin pair and driven all the way over, Alice still has a coin to flip.

I'm totally excited to find this whole PF site. I find it's tough to be alone with this stuff, only books and such. It's just too strange and interesting not to talk about, ask questions about. And my wife's patience with it is... way past flipped.

 

[Elroy]

Hmmm, I really should take this time to mathematically formalize entanglement, so I don't get into (more) trouble with bhobba. But I'll take a shot at some of this.

In my mind, the two-slit experiment is more about superposition than entanglement. It just illustrates the oddities (wave-particle-duality) of a photon quite well. In fact, I've actually done this one here at home. You can take a piece of glass and thoroughly stain it with candle smoke. Then take two very thin razors (like old-fashioned two-sided razors), put them together and then run them down the smoke on the glass (making two very small slits in the smoke). Then, take any laser pointer and shine it at the slits and let it go through onto another surface. You can see the sinusoidal pattern in the light. It's quite cool.

And Jimster, yes, I've always interpreted this as a photon interfering with itself. It has nothing to do with one photon interfering with another photon. In fact, there have been versions of this done where a single photon is emitted every second (temporally very slow in terms of photons). Over time, the interference (sinusoidal) pattern still emerges (so long as there's no way to know which slit the photon went through).

I think I'll hit "post" and make other replies to your comments in another post, so that others don't get woven in.

 

[Jilang]

Elroy, I read your post #22 with interest. Is the difference between the straight lines in the graph and the curved line related from going from 2 dimensions to three? Angles in three dimensions tend to be less than their projections in two dimensions etc.

 

[atyy]

Hmmm, I really should take this time to mathematically formalize entanglement, so I don't get into (more) trouble with bhobba.

There is an old fashioned definition of entropy: not a product state in any basis. This can be formalized using the entanglement entropy.
http://www-thphys.physics.ox.ac.uk/people/JohnCardy/seminars/statphys.pdf

There are other measures, and some proposals are basis dependent.
http://arxiv.org/abs/quant-ph/0507189

 

[Elroy]

Jilang,

Please be sure to read my post #23 as well. You've posted an excellent question and I hope to come up with a well formulated answer that isn't too mathematical, and is also intuitive (at least as intuitive as QM can be).

However, in the interim, here are a couple of good threads:
https://www.physicsforums.com/threa...variables-imply-a-linear-relationship.589923/
http://physics.stackexchange.com/qu...-bells-experiment-be-a-linear-function-of-ang

Also, the Wikipedia page is good: http://en.wikipedia.org/wiki/Bell's_theorem

Regards,
Elroy

 

[Elroy]

I'd like to say a bit more about the two-slit experiment. I think we all agree that a photon is the smallest quanta of light that can be "detected". Anything smaller is rather theoretical, and this is where we must think of waves (rather than particles). The reason the sinusoidal pattern of photons comes about is because each photon (as a wave) goes through both slits simultaneously and then interferes with itself before hitting a back-surface:

What's quite fascinating is that we can put a photon detector at each slit (that minimally "observes" which slit it goes through, still letting it pass), and this destroys the sinusoidal pattern.

One of the most counter-intuitive things about this is that forcing the photon to be a particle at the slits actually increases its options as to where it goes. If the photon is observed going through "one slit or the other" (and not both), then it can hit the darkened stripes on the above figure. Whereas if it has both options, it can not.

Said differently, if we have just one slit, it can get onto the darkened stripes. Two slits (two options) creates areas of decreased probability (with zero probability at the center of the darkened stripes), whereas only one slit allows the photon to go to those areas. Very counter-intuitive compared to classical Newtonian (or even Einsteinian) physics.

 

[bhobba]

I am a bit confused about the wave collapse between entangled entities.

That may be because, popularisations not withstanding, QM does not require collapse. What happens in EPR is you have entangled particles - as soon as one is observed it becomes entangled with the observational apparatus and is no longer entangled with the particle. Collapse is not necessarily involved.

I worry I've been carrying around an incorrect picture of a two slit interference pattern shining on the wall of a dark classroom - The pattern is made up pointillist-like of dots representing samples taken by the screen periodically over some period of time say like over the 6 hours between noon and 6pm. To keep the non-locality notion handy and ready for rumination, I have always held onto the explanation - "The photons that were sampled at 2pm were apparently interfering with the photons sampled at 3 pm"

Interference as in wave-particle duality (which is wrong anyway - it was overthrown when Dirac came up with his transformation theory at the end of 1926 - and likely sooner - but certainly by then) isn't really what's going on in the double slit experiment:
http://arxiv.org/ftp/quant-ph/papers/0703/0703126.pdf

What happens is each slit acts as a position measurement which means there is an uncertainty in direction after the slit. We have two slits so the state of the particle after the slits is a superposition of the state at each slit as per equation 9 in the above paper due to the symmetry of the situation. The interference pattern is a result of the uncertainty principle and superposition principle.

Is there such a thing as an entangled wave collapse that can be smeared across some frame of non-zero time

I think you are a bit confused about some fundamental ideas and need to read a good book on QM. Unfortunately that will require a bit of math:
https://www.amazon.com/dp/0471827223/?tag=pfamazon01-20
https://www.amazon.com/dp/0465075681/?tag=pfamazon01-20
https://www.amazon.com/dp/0465036678/?tag=pfamazon01-20

There are also some video lectures:
http://theoreticalminimum.com/

If you are dead against math at all check out the following - but your understanding will not be as good:
https://www.amazon.com/dp/0473179768/?tag=pfamazon01-20

Thanks
Bill

 

[bhobba]

I'd like to say a bit more about the two-slit experiment. I think we all agree that a photon is the smallest quanta of light that can be "detected". Anything smaller is rather theoretical, and this is where we must think of waves (rather than particles)

Both theory and observation say the same thing - the smallest quanta of light is the photon. It's the quanta of the underlying EM field. But what field quanta are is not simple - unless its from a textbook on Quantum Field theory its almost certainly wrong - and QFT is a difficult advanced subject - although some good books at the undergraduate level are appearing:
https://www.amazon.com/dp/019969933X/?tag=pfamazon01-20

It is doable after the Susskind books I mentioned in my previous post.

You need to forget this wave particle duality stuff - it was overthrown in 1926 by Dirac - you can do a search on physics forums and find many posts giving the detail. Also see the FAQ:
https://www.physicsforums.com/threads/is-light-a-wave-or-a-particle.511178/

In my previous post I gave the correct explanation of the double slit experiment - it's also very elegantly explained by Feynmans path integral approach - but wave particle duality is a left over from De-Broglies hypothesis that was simply a stepping stone to the correct quantum theory and was quickly done away with.

Thanks
Bill

 

[DrChinese]

One of the most counter-intuitive things about this is that forcing the photon to be a particle at the slits actually increases its options as to where it goes.

The interference pattern shows fringes, while the other pattern does not. So you may have that backwards, not really sure what you mean.

However, you do not need to force a photon to be a "particle" (using that analogy) at the slits to eliminate the interference pattern. Place polarizers at both slits. If they are aligned parallel, there WILL be interference. If they are oriented perpendicular, there will be NO interference pattern.

 

[Elroy]

The interference pattern shows fringes, while the other pattern does not.

I was just trying to convey the idea that, without two slits (with only one slit) (classically, seemingly like fewer options for the photon), it would then be able to get to the center of the troughs in the above sinusoidal (interference pattern) image.

you do not need to force a photon to be a "particle" (using that analogy) at the slits to eliminate the interference pattern

And yes, I didn't mean to imply that detecting the photon going through the slit was the only way to eliminate the interference (sinusoidal) pattern. Simply having only one slit also does it. I'm sure others can come up with a variety of ways to do it.Jilang asked a good question in post #42, which rather directly relates to Bell's inequalities. I see that Dr. Chinese has a page on this (which I admittedly haven't thoroughly read). It seems that there should be a straightforward answer to this question, with an appropriate logical explanation. The two-slit stuff was a bit of a distraction, and I wouldn't mind if we pushed that to another thread.

I'm just working on the easiest way possible to explain the empirically validated violations of Bell's inequalities, showing how the linearity should be replaced with the cosine function when we're dealing with entanglement.

(But got to go for the evening. Y'all take care.)

 

[DrChinese]

I'm just working on the easiest way possible to explain the empirically validated violations of Bell's inequalities, showing how the linearity should be replaced with the cosine function when we're dealing with entanglement...

There really is nothing which is linear at any level that matches the graph. The graph shows a hypothetical local function which most closely approaches the quantum prediction (for entangled cases) and also provides for so-called "perfect" correlations. There aren't any serious models that do this (as they immediately fail to explain Malus). So there is nothing to "replace" per your comment. In other words, forget the linear portion, the graph is just illustrating a concept. You could actually replace it with many different shapes (all of which would be even more ridiculous). For example, a common alternative is: 1/4+(cos^2(theta)/2) which varies between .25 and .75. This matches Malus but is further away on entangled pairs.

If you want a visual, there is one class that most closely matches experiment. Most people reject these because causality is not respected. These are the time symmetric group of interpretations. In these, you have the following 2 key elements:

a) Both the past and the future are elements of the experimental context. So Alice's setting and Bob's setting are both part of the equation when particle pairs are created, even though they are set in the future.

b) Otherwise, locality (c) is always respected. Despite the "non-local" appearance of entangled pairs (which I don't dispute in any way): in these interpretations, everything is cleanly connected by local action.

One of the advantages of this visual is that it naturally explains entanglement which occurs after detection. Sophisticated experiments allows after-the-fact entanglement (hard to believe but true - you can entangle particles that no longer exist). Such is not natural in many other mechanistic explanations.

 

[Jimster41]

Thanks for that great list of resources! I have ordered a couple of the books, and as of this morning I am planning to take one of those Susskind courses.

I'm not against math. I love math. But, I have no talent for it.

The other image I have carried around is of this almost transparent octopus looking Probability wave-function spread between the laser and the slits and poking through both slits hovering right in front of the screen, but not touching it - just yet. Then when one tentacle touches the screen - all of a sudden you can see the octopus - how's that for an understanding! ;-)

 

[bhobba]

I'm not against math. I love math. But, I have no talent for it.

That's not important. What is more important is perseverance. Take your time and don't give up - its not a race. Post here with any queries - that's what this forum is all about. Soon you will have an understanding way beyond popularisations.

Thanks
Bill

 

[Elroy]

Yes, I'd like to wholeheartedly second bhobba's above comment. For me, it's important that we can develop an (accurate) "conceptual" understanding of these phenomena, possibly with a great deal of use of "everyday" language. Everyday language has the problem in that it's sometimes slippery around the edges, so we do need to be concise with our definitions. However, for me, that's what a great deal of this is about: The development (and acquisition) of the precise language of physics.

Also, I think this approach is important for these concepts to "stick". If they are "purely" abstract, our minds seem to struggle to attach them to the rest of our knowledge. However, this is where a great deal of the struggle comes in. As far as can be understood, all of our "concrete" perceptions are in three spatial dimension and one temporal dimension. As an example, relativity often talks about Minkowski space as a four-dimensional static visual space (including time) to talk about things. It collapses the dynamic dimension of time into a static spatial dimension.

In this depiction, the actual three observable spacial dimensions are only given two dimensions, so the third can be given to time. (Just FYI, the cones are where "causal" events can take place, assuming speed of light limit is obeyed.) To make sense of this depiction, we must "stretch" our minds to recognize that the 2D space is truly attempting to represent the 3D spatial space in which we live. That is why it is labeled a "hypersurface".

Regarding math, we can quite easily represent vectors (or even tensors or spinors) in space (spacial, temporal, or otherwise) of as many dimensions as we like. However, we do often lose the ability to "grasp" the underlying concepts. Furthermore, math can be wrong. In the end, math is yet another (hopefully more accurate and concise) language in which to outline this stuff. As with any other language, it can tell lies. I'm tempted to also include the math-thought-reality tri-image developed by Penrose, but I'll leave it to others to explore that.

p.s. I'm still working on a pictorial way to represent the transition from classical probability theory to the correlations observed with quantum superposition and entanglement (focusing specifically on complete entanglement with EPR pairs, as a first pass). I'm having fun with it.

 

[bhobba]

Relativity is a good example of math giving deep insight.

Check out the following derivation of the Lorentz transformation:
http://www2.physics.umd.edu/~yakovenk/teaching/Lorentz.pdf

It's premises are so plausible and fundamental no-one would care to doubt them. In fact we see the speed of light thing in SR is simply fixing a constant that naturally occurs from other more basic symmetry considerations. Yet it has these startling consequences. Its the power and beauty of math.

Math is not about long boring calculations - it about concepts and their consequences.

Thanks
Bill

 

[Jimster41]

Nothing in that Lorentz transform derivation that I'm unanle to follow. I am up on that level of math. And I believe it all. It's just not very portable or compact, at least for me, in terms of trying to get to the next part, or having something I can walk down the sidewalk thinking about. Elroy's 3d space-time diagram (that's what they are called right?) on the other hand, I was already pretty comfortable with...

Reading Penrose' Cycles of Time. I feel like I almost get Confirmal Diagrams, but the strict Conformal Diagrams "don't stick" quite yet.

I did read Dr Chinese' page and I'm enjoying Gisin's "Quantum Chance" Maybe where my question about Alice and Bob went wrong... Gisin's uses The Joystick Metaphor rather than the "coin toss". My confusion is with regard to how a decision made far away/earlier by Bob's Joystick seems to me to be determining what's going to happen to Alice. Bob is standing there betting her what's going to happen (he knows) just to represent the discomfort implied (I'm having) from non-local determinism? Once Bob has moved his joystick, Alice's outcome is set, and her joystick doesn't do what she thinks it does anymore - Or does she always have to move her joystick exactly when Bob does - for the metaphor to be consistent with the math? I get that Bob couldn't control the result of his joystick - it's just that whatever he got the instant He jumped the gun is now some non-local thing playing a deterministic role in Alice's present and future? Is it just the fact that the non-local influence causes an outcome that seems just as random, as far as Aluce can tell, as her Joystick would have given anyway? This is why I wanted to have Bob there gloating, just to drive home the idea that what she thought was random, and looks just like the usual random stuff, from Bob's perspective, which represents another place, in the past, is determined.

Well now that I say it like that, what could be less weird. But then it's an influence out of all causal norm. As far as Alice knows (can tell) nothing causal has happened to her joystick to make it deterministic, rather than random

Crap, what a headache.

In entanglement experiments, I vaguely recall hearing the phrase "delayed choice" is that all this is? Anyway just trying to grok the concept at some level I can enjoy in daily life - which of course may not be possible...

I realize I have a surprising and possibly ridiculous notion that entanglement is somehow a significant, frequent, dispersed, even ubiquitous thing out there. Which is why Bob's gloating is sort of disturbing. I can imagine this is not at all interesting if Bob and Alice's joysticks are so rare, co-located, and short lived, as to be pretty much irrelevant phenomena to existence.

 

[Jimster41]

If you want a visual, there is one class that most closely matches experiment. Most people reject these because causality is not respected. These are the time symmetric group of interpretations. In these, you have the following 2 key elements:

a) Both the past and the future are elements of the experimental context. So Alice's setting and Bob's setting are both part of the equation when particle pairs are created, even though they are set in the future.

b) Otherwise, locality (c) is always respected. Despite the "non-local" appearance of entangled pairs (which I don't dispute in any way): in these interpretations, everything is cleanly connected by local action.

One of the advantages of this visual is that it naturally explains entanglement which occurs after detection. Sophisticated experiments allows after-the-fact entanglement (hard to believe but true - you can entangle particles that no longer exist). Such is not natural in many other mechanistic explanations.

I totally need a picture. The above (I hadn't understood this post at all the firsttime I read it) is exactly what I mean I think. What I am amazed and confused by. Strange how the sentence "Both the past and the future are elements of the same experiment" Gives me a connotation rich image I can sort of hold onto to represent the meaning the amazing math has uncovered? I just hope it's sort of correct...

So now I would love to have just a couple of more pieces squared away.

Is there any sense in which entanglement is significant feature of space time evolution as we experience it? Or is it an utterly fleeting and rare exception? Or do we not know?

Does the bizarre non-causal a-temporal sounding statement a) above turn out to be utterly innocuous because the "experiment" always provides random results - leading to a conclusion like "well the future is already set, but the result is random". In which case what's the difference between random and uncertain? I'd guess it's about 1 big beer.

But then random seems unsatisfactory, if entanglement is a phenomenon that is involved in our evolution? this feels almost completely fuzzy, but I get this icicle in brain that's asking "where does all the structure come from"

 

[Jimster41]

Someone asked if the photon probability wave front hit the slits at the same time. An innocuous question... That as I try to answer it for myself has me pretty much confused.

Position was uncertain
Can't go faster than c
It was entangled with all the stuff around it forward and backward in time and out to freaking infinity but that matters not because baseballs are made of quantum sh--- and we can manage those pretty good

 

[bhobba]

It was entangled with all the stuff around it forward and backward in time and out to freaking infinity but that matters not because baseballs are made of quantum sh--- and we can manage those pretty good

Where are you getting this from?

Here is a much better analysis:
http://arxiv.org/ftp/quant-ph/papers/0703/0703126.pdf

Thanks
Bill

 

[Jimster41]

Where are you getting this from?

Here is a much better analysis:
http://arxiv.org/ftp/quant-ph/papers/0703/0703126.pdf

Thanks
Bill

Thanks, it looks good. I am pretty weak on the bracket notation, but it's sort of reads intuitively. I understand the setup and the three cases, seems very helpful to break it down that way. I'm going to study it for awhile.

The math defines some pieces of my limit. e, i and \pi, combinations thereof especially { e }^{ -i }. I have an easier time with Planck's constant of Position and Momentum Relation and Boltzman's constant of Energy Temperature relation. Not that they aren't utterly puzzling. But they don't break my read of equations the way e, i and \pi do. I wonder often if you guys really "feel" or "see" those when you read them. I imagine you do but maybe that's not true.

Trying to read this has already been helpful because I remembered this morning how in my DiffEq class and then later in Signals and Systems, we learned how Fourier's theorem shows you can create arbitrary signals by adding together sin waves written in that { e }^{ -i } notation. Fourier really stuck, even though I was and am still baffled by how you use { e }^{ -i } to make sin waves. It's the periodicity of -i or something like that and then \pi gets in there with the wack-ness of the very circle itself. I need to refresh my memory on it. So do I understand correctly that those terms represent the points on Schrodinger's Wave Equation, for purposes of integrating over it's point-wise interaction with the... Eigen things...

Eigenstates and Eigenfunctions. I made the grade in Linear Algebra but frankly it was frustrating... because I walked away feeling like it was just dutiful plug and chug, doing the homework, taking good notes. I have almost no 'feel' for what Determinants, Eigenstates and Eigenfunctions mean as operators. They turn matrices into scalars, and ... functions, or vectors of scalar points, or functions of points. I need to drill into that one. It's a real obstacle to reading math.

I can pick it up later with the linearity of the QM operations

So thanks this is helpful. I am still curious at the end of the day about the philosophical implications of this stuff - and I wonder sometimes if maybe you all are saying there really aren't any. Or is it more that it gets weirder the more precise one's understanding?

Sorry for going on and on, and I didn't mean to hijack this thread.

 

[bhobba]

So thanks this is helpful. I am still curious at the end of the day about the philosophical implications of this stuff - and I wonder sometimes if maybe you all are saying there really aren't any. Or is it more that it gets weirder the more precise one's understanding?

There are philosophical implications all right - just not the things you read in some populist accounts eg the overthrow of naive reality by Bells theorem - but not rubbish like conciousness created reality and other mystical twaddle found in trash like What The Bleep Do We Know Anyway.

Thanks
Bill