|Jan8-07, 05:43 AM||#1|
Bell experiment would somehow prove non-locality and information FTL?
The famous Bell experiment would somehow proof non-locality and/or traveling of information faster then light.
A very simple explenation of the experiment is this: there is a subatomic event that creates a particle pair going opposite directions. The subatomic event determines the possible outcomes, as for example if one particle has spin up, the other must have spin down (conservation law).
But in the quantum mechanical sense, we don't know which particle has spin up and which has spin down.
So if we examine (observe) one particle and find it has spin down, this the determines the other observation, that the other particle has spin up.
But QM says both particles are in undefined states before observing.
Somehow then the act of observing one particle and indentifying it's spin causes the other particle to behave as determined by the other observation.
The two particles, before detection, can be at very long distance from each other at which no interaction could take place between the two observations, considering the speed of light.
This then somehow gets interpretated as non-locality or faster-then-light travel of information.
But there is a more simple explenation. The state of both particles are already determined when they get created in the experiment and from the physical laws we know one has spin up and one has spin down.
Just that we can't identify which particle has spin up and which has spin down. So, identifying one particle is in fact identifying both particles.
Nothing mysterious. It doesn't involve non-locality or faster-then-light travel of information.
(another way of looking it is this: instead of the unknown spin which gets detected, we could also say we already know which particle has spin up and which has spin down, the only thing we don't know if the spinup particele goes left or right, and likewise wether the spindown particle goes right or left, just that we know they go opposite directions. If we detect the spinup particle to go left, then we for sure we know the spindown partice went right.
In this way of interpreting this QM experiment, we see that there is nothing mysterious about it: no non-locality involved or faster-then-light travel of information.)
I don't know if the actual experiment involved measuring spin, it could also have been some other conserved quantity, like electric charge, for example the particle pair creation of electron and positron.
|Jan8-07, 07:20 AM||#2|
|Jan8-07, 07:41 AM||#3|
So instead of the two particles being in a superposition of a electron and a positron, it becomes now an electron and a positron in a superposition of two directions.
|Jan8-07, 10:11 AM||#4|
Bell experiment would somehow prove non-locality and information FTL?
It looks like you are discussing the EPR experiment, designed by Einstein as a refutation of QM. Bell's inequality showed that the quantum mechanical predictions of the results of the EPR experiment are incompatible with "local realism". Long after Einstein and Bell, the experiment has been performed and the results are in favor of QM, not local reality.
Here is a description of EPR:
Imagine that there is a pair of (literally) identical twin brothers who are interested in dating a pair of identical twin sisters. The brothers live together, but their dates live seperate lives on opposite sides of town.
Each brother has the same three evening suits, red, white and black. Thus, on any given date the only difference between the two brothers is their suit (possibly the same, as well).
Based on the color of his suit (and nothing else, since the brothers are otherwise identical and the sisters are identical), each brother gets either a slap or a smile from his date.
After many dates, the brothers compare notes:
1) If they wear the same suit, they get the same reaction.
2) Choosing suits at random, half the time the brothers share the same fate (both get slaps or both get smiles) and the other half of the time they recieve different fates.
(***this describes the basic EPR experiment with slap/smile corresponding to spin and the three suits corresponding to the three indepenent directions on which we analyze spin***)
Bell's theorem addresses the question: what selection shceme are the women using that produces the results above? The answers are grim for a local realist, either:
1) There is no sheme, its just a coincedence (unacceptable).
2) The women have non-local correlation i.e. telepathy, pheromones, etc.
Since the 1990s the experiments have been definitive; no physicist doubts the existence of nonlocality.
|Jan8-07, 08:09 PM||#5|
Your idea doesn’t support the experiment; it also doesn't explain the collapse of the wave function between entangled particles when they measured. (Why does the wave function collapses when we know through what slit particle went, when other times it behaves as a wave.) There is no simpler explanation to this and your idea suggests the theory of hidden variables, which was disproved long time ago ( see Bell’s inequality). The non-locality is indeed exists but not the idea of FTL travel also there is no information being transferred between entangled states. It is clear that you don't have the background knowledge on quantum mechanics and experimental physics, before you try to explain what is what and how I suggest you do some research on the subject otherwise this kind of discussions are pointless. http://en.wikipedia.org/wiki/EPR_paradox :)
|Jan8-07, 11:54 PM||#6|
I've often thought this way about QM.You have to realise that essentially, as boring and mundane as it sounds, nothing spooky is really happening. Just because you dont know or have not measured the spin or other undetermined property does NOT mean it exists in two at the same time and one determines the other. The particles have a precise spin when the event occurs and remain that way, nothing will change that. However given the 50/50 probability, the outcome is uncertain from a measurement and information point of few. This makes the line between what is 'actually true' aka reality, and what has been measured, rather fuzzy.
Hope that makes sense
|Jan10-07, 05:57 PM||#7|
The question wether - prior to observation - a particle is in a defined state, is something unknowable. Knowing the state of the particle requires an observation and this observation alters the state of the particle.
When we consider the experiment as explained http://en.wikipedia.org/wiki/Bell%27...ll.27s_theorem
it is obvious that the only factor of interest is not the respective angels of Alice and Bob, but only the difference between the angels is of relevance.
Further, the scores are somewhat illogical, because a series of scores like +1, -1, -1, +1 (which means: correlated scores and opposite correlated scores) add up the same as unrelated scores (0, 0, 0, 0).
From this one can already conclude that the angel which scores the most is at 45 and 135 degrees , since at angles of 0 and 180 degree the scores cancel each other and at 90 and 270 degrees the scores are also zero.
Although the set up looks like we have two measurements involved, which somehow miracelously (action-at-a-distance) influence each other, it can be asserted that this is in fact one measurement that takes place, although it involves two locations.
The only setting one can make is changing the angle between Alice and Bob. Alice and Bob could both change the angle at their location the same amount in the same direction, without this influencing the outcomes, simply because the difference of the angles stay the same.
And although the source emits the particles in random fashion, this does not contradict the fact that the particles are colerated. Same as I throw a dice, I don't know what side comes up, but I do know that the value summed with the opposite side of the dice always adds up to 7.
|Jan10-07, 06:14 PM||#8|
We have to understand what realy goes on, to predict the outcomes.
The fact is that on one hand it is totally random, but on the other hand it definately is not!
You need to make that subtle distinction here!
Suppose we design an experiment as follows: we have a dice throwing machine, and everytime we make an observation, the dice gets rolled. Now in this setup, two observers can chooce themselves which side they are going to inspect (let's name them: top, bottom, left, right, front and back). The two observers (A and B) on each observation can freely choose which side to inspect, they note the scores. Now miraculously, each time when A and B choose opposite sides, their scores total as 7. How does the dice know which side each observer chooses? And does the choice of the observers which side to inspect somehow influence the outcome?
In this case we know it is not.
We in fact do not have two random observations, but in fact only ONE observation (although we split the observation at two different points). The total scores of A and B together would otherwise not correlate when they choose opposites sides for inspection.
See, that is the same kind of correlations we have in quantum mechanics, just that it isn't miracalous at all upon further inspection. Like in the dice experiment above, the illusion is created that we do two seperate observations, which would somehow determine the outcome of the experiment, but we know in this case, the outcome was determined previously by the dice rolling machine. Only that in reality - on the qm level - we can not know how the dice rolled before we make the observation.
|Jan10-07, 07:50 PM||#9|
But what if Alice and Bob agree before the experiment that Alice will measure the number on the top of the dice (or the spin in the z-direction) and Bob measure the left-most number on the dice (spin in the x-direction). At a quantum level we can't do this (I think the spin operators for different directions don't commute)! If this dice has 1 on top and 6 on the bottom, it could have 2 (or 5) OR 3 (or 4) as the left most number. If 2 (or 5) is the left most number, then the top most could be 3 (or 4) OR 1 (or 6), but we can't know as we can only look at one side at a time!! (I think... I haven't actually studied spin at all... ) And yet they must both have definite answers, seeing as both Alice and Bob have measured them.....
Here is a very interesting (in my opinion...) paper on it: http://fr.arxiv.org/PS_cache/quant-p...04/0604064.pdf but what do I know. I haven't studied this stuff properly, so I wouldn't be surprised if there's something I haven't understood. It seems that one has to choose between Einstein's view of realism and locality though....
|Jan10-07, 08:22 PM||#10|
Here's a closer analogy. Suppose we have a machine that generates pairs of scratch lotto cards, each of which has three boxes that, when scratched, can reveal either a cherry or a lemon. We give one card to Alice and one to Bob, and each scratches only one of the three boxes. When we repeat this many times, we find that whenever they both pick the same box to scratch, they always get opposite results--if Bob scratches box A and finds a cherry, and Alice scratches box A on her card, she's guaranteed to find a lemon.
Classically, we might explain this by supposing that there is definitely either a cherry or a lemon in each box, even though we don't reveal it until we scratch it, and that the machine prints pairs of cards in such a way that the "hidden" fruit in a given box of one card is always the opposite of the hidden fruit in the same box of the other card. If we represent cherries as + and lemons as -, so that a B+ card would represent one where box B's hidden fruit is a cherry, then the classical assumption is that each card's +'s and -'s are the opposite of the other--if the first card was created with hidden fruits A+,B+,C-, then the other card must have been created with the hidden fruits A-,B-,C+.
The problem is that if this were true, it would force you to the conclusion that on those trials where Alice and Bob picked different boxes to scratch, they should find opposite fruits on at least 1/3 of the trials. For example, if we imagine Bob's card has the hidden fruits A+,B-,C+ and Alice's card has the hidden fruits A-,B+,C-, then we can look at each possible way that Alice and Bob can randomly choose different boxes to scratch, and what the results would be:
Bob picks A, Alice picks B: same result (Bob gets a cherry, Alice gets a cherry)
Bob picks A, Alice picks C: opposite results (Bob gets a cherry, Alice gets a lemon)
Bob picks B, Alice picks A: same result (Bob gets a lemon, Alice gets a lemon)
Bob picks B, Alice picks C: same result (Bob gets a lemon, Alice gets a lemon)
Bob picks C, Alice picks A: opposite results (Bob gets a cherry, Alice gets a lemon)
Bob picks C, Alice picks picks B: same result (Bob gets a cherry, Alice gets a cherry)
In this case, you can see that in 1/3 of trials where they pick different boxes, they should get opposite results. You'd get the same answer if you assumed any other preexisting state where there are two fruits of one type and one of the other, like A+,B+,C-/A-,B-,C+ or A+,B-,C-/A-,B+,C+. On the other hand, if you assume a state where each card has the same fruit behind all three boxes, like A+,B+,C+/A-,B-,C-, then of course even if Alice and Bob pick different boxes to scratch they're guaranteed to get opposite fruits with probability 1. So if you imagine that when multiple pairs of cards are generated by the machine, some fraction of pairs are created in inhomogoneous preexisting states like A+,B-,C-/A-,B+,C+ while other pairs are created in homogoneous preexisting states like A+,B+,C+/A-,B-,C-, then the probability of getting opposite fruits when you scratch different boxes should be somewhere between 1/3 and 1. 1/3 is the lower bound, though--even if 100% of all the pairs were created in inhomogoneous preexisting states, it wouldn't make sense for you to get opposite answers in less than 1/3 of trials where you scratch different boxes, provided you assume that each card has such a preexisting state with "hidden fruits" in each box.
But now suppose Alice and Bob look at all the trials where they picked different boxes, and found that they only got opposite fruits 1/4 of the time! That would be the violation of Bell's inequality, and something equivalent actually can happen when you measure the spin of entangled photons along one of three different possible axes. So in this example, it seems we can't resolve the mystery by just assuming the machine creates two cards with definite "hidden fruits" behind each box, such that the two cards always have opposite fruits in a given box.
|Jan10-07, 10:51 PM||#11|
|Jan10-07, 11:05 PM||#12|
The idea that the dice have locally predetermined values does not hold water. If it did, Bell's Theorem would be of no interest. Remember, experiments show the following:
1. When Alice & Bob are measured at the same angle, the results are perfectly correlated. This gives the illusion that the values are predetermined, true enough. This points you towards realism, and follows the reasoning of EPR.
2. But when Alice & Bob are measured at the different angles, the results are obey the cos^2 function. This, however, gives the "illusion" that locality is violated because the spin statistics don't follow the realistic assumption of 1. This follows the reasoning of Bell.
If you only look at 1. and not at 2., then of course it seems pretty simple. But that isn't the whole story.
|Jan10-07, 11:09 PM||#13|
Is the moon there when nobody looks? Reality and the quantum theory
|Jan11-07, 04:20 AM||#14|
Like for example: measuring from the same side, gives always the same outcome, measuring from opposite sides, always gives a sum total of 7.
And if we measure from two other sides (not same or opposite) means that the outcomes will be distinct and uncorrelated (don't add up to 7). In fact in that case the relative measurement position of A in respect to B then makes a difference. One way of looking at this is saying that this difference is "caused" by the measurement itself (the choice of what side to look at), but one also can explain it as that this is already "set" by the experiment (throwing the dice) itself, this two explenations (although they oppose each other) are not distinghuishable (we can't make any measurement which would show the right explenation). The cause of that is that both the throwing of the dice and the choice of what side to look at, are independend of each other.
Notice also that we (implictly) assumed the dice would always line up with facces in the exact measurement direction. So we use a somewhat abstract dice, that would never deviate from those positions, which is also different then a macro world experiment, in which the faces could in principle line up in any direction.
With experiments and observations you have to ask:
- Are the observations independend of each other?
- Does the act of observation disturb the outcome?
Translated to the quantum world, this means, what quantity or property is being measured, and how "fixed" is that quantity.
Measuring electron mass or charge would not alter that property, but measuing it's speed or spin status, would disturb the outcome, I guess.
|Jan11-07, 04:30 AM||#15|
Yes, but look a bit deeper. Alice and Bob can each pick an angle, but please discern that in fact only one angle is of interest, the difference between angle of Alice and Bob.
Further note that correlated scores (+1 , -1) add up to zero AS WELL as uncorrelated scores (0, 0).
This explains why angles of 0 / 180 and 90 / 270 degrees have minimum values, and because of symmetry, the maximum values are exactly in between.
Which already shows why that angle is 45 or 135 degrees.
And for measuring the outcomes, you take the sum total of squares for each angle, which add up to (1)^2 and (-1)^2, and then you take the square of that, which gives 1/2 sqrt(2) which is 0.71..
|Jan11-07, 04:41 AM||#16|
It's a shame you don't see that!!
(and btw. I have nothing revealed of the nature of the "machine" perhaps the "dice rolling" is an event based on some underlying quantum event).
Furter: I did't state that measuring a spin status is equivalent to my roling dice experiment, of course not.
A spin status is not a fixed observable, since I guess that in some cases we disturb that status. And possible in other cases, this quantity does not get disturbed.
So the error in your logic is to assume that either the spin status is something fixed, or it is not fixed (independend of the measurement).
While a real world anology can already show that such an assumption is not always true, but depends on the set up of the experiment.
But still there is the anology. If A and B choose to observe the dice from the same position or opposite position, they get somehow correlated results (the result is either the same or adds up to 7), but in other cases not!!!
It's same remarkable, I think!
Now please explain me, when A looks from the top, but B chooses neither the top, nor the bottom, he gets uncorrelated results (in fact in this case, the outcomes can be a selection of 4 distinct values, for each side).
But what determines the outcome of the result that B observes?
a. The experiment itself, rolling the dice, or
b. The choice of which side to observe
If we just assume that we don't know anything about the dice (as analogous to the quantum experiment) before we make these independend measurements, it is not determinable what causes this outcome. Was the number on the side that B chooses already fixed before B observes it, or does B somehow influence the outcome, just by the choise of the side to observe?
We can never know that, if the dice was realy a quantum experiment.
Only of course that in the macro world example, we can already know how the dice was lined up before the "measurements" take place, and in the quantum world, this is not possible.
|Jan11-07, 05:02 AM||#17|
Blog Entries: 27
I think you do not see the difference between:
1. A classical particle having an initial spin (say 0) angular momentum, and then at a later time split into two and move in opposite direction. You measure the spin angular momentum of one particle and immediately know the spin of the other one simply by invoking a conservaton of angular momentum.
2. The EPR-type experiment.
There IS a difference here and that is what Bell-type analysis is detecting. You missed an important factor that separates the classical (example 1) and the quantum (example 2) cases - SUPERPOSITION. The classical example has a definite angular momentum for each particle before they are measured. The quantum example does not. The superposition of all spin states is what makes the quantum scenario different. It is the very reason why you change the angle of polarization in those experiments - you are trying to detect the non-commuting component of that observable that isn't collapsed upon measurement.
The superposition aspect is what makes the EPR-type experiment different than a simple classical conservation-law measurement. One has to understand what superposition is, and how it is detected and how it makes itself known in our measurements.
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