A Gedanken Experiment Regarding Bell's Theorem and Nonlocality

In summary, the conversation revolves around a thought experiment involving entangled boxes and the possibility of observing different colored socks when randomly opening compartments. The results show that different outcomes can be obtained depending on whether the sock colors are predetermined or indeterminate, which relates to Bell's Theorem and the concept of nonlocality. However, there are some discrepancies and uncertainties in the example, making it difficult to draw a clear conclusion.
  • #1
Gary Boothe
15
0
A GEDANKEN EXPERIMENT REGARDING BELL'S THEOREM AND NONLOCALITYLet’s say I have four boxes with three compartments in each one, and each compartment contains either a white sock or a black sock. This is analogous to photons having spin components either clockwise or counterclockwise (black or white socks) around three perpendicular axes (the three compartments).

There are only four different sets of possible “entangled” boxes, analogous to entangled photons. I can represent the four sets of entangled boxes as:

Set 1 Set 2 Set 3 Set 4

B W B W B W B W

B W B W W B W B

B W W B B W W B

The boxes are "entangled" in that if a black sock is in the left top compartment of a box, the sock must be white in the right top compartment of the other box, and so on for each of the four possible sets of boxes.

Let’s say I keep one box in a set and mail the other one to you. For this box and every one I send to you, we open only one compartment at a time at random. After opening our compartments at random, we then compare the colors of our socks.

With the first possible set of boxes, If I open the top left box, you may open any of the three compartments to get a white sock, and the possible outcomes are BW,BW,BW, and of course this is repeated three times for a total of nine possible outcomes:

BW,BW,BW,BW,BW,BW,BW,BW,BW.

So, we get different colored socks 100% of the time.

For the second set of possible boxes, the possible outcomes when I open a compartment at random, and you open a compartment at random are:

BW,BW,BB,BW,BW,BB,WW,WW,WB.

So, we get different colored socks only 5 times out of 9, or 55.55% of the time.

For the third and fourth set of boxes, we also get different colored socks 55.55% of the time. So, if we randomly opened thousands of "entangled" boxes with predetermined colored socks, on average we will see different colored socks 66.67% of the time.

(100% + 55.55% + 55.55% + 55.55%)/4 = 66.67%

But what happens if the sock color is not predetermined, as quantum theory asserts? Would we get a different percentage of different colored socks? Yes, it is obvious that we would get different colored socks 100% of the time.

What I have shown above is that different results (66.67% and 100%) are obtained for entangled boxes when the colors of the socks are either predetermined (as in classical physics) or indeterminate (as in quantum theory). Isn't this the principle behind Bell's Theorem and the case for nonlocality, or am I completely off base? Any response would be greatly appreciated.
 
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  • #2
Gary,

There are a lot of issues with your question that make it impossible to answer in its current form. Usually for an example of this type, there are 2 entangled particles. So I don't follow what there is 4 of.

Also, electrons have spin along 3 non-commuting axes, but photons I would call it 2 instead. Probably we should shift to an example that we can all discuss, ok?
 

1. What is Bell's Theorem and why is it important in physics?

Bell's Theorem is a mathematical proof that shows the limitations of local hidden variable theories in explaining the results of quantum mechanics experiments. It is important because it challenges the traditional notion of causality and locality in physics, and has significant implications for our understanding of the fundamental principles of the universe.

2. What is a Gedanken experiment and how is it used in Bell's Theorem?

A Gedanken experiment (German for "thought experiment") is a hypothetical scenario used to explore the consequences of a particular scientific theory. In Bell's Theorem, a Gedanken experiment is used to demonstrate the nonlocal nature of quantum entanglement and the violation of Bell's inequality, which supports the predictions of quantum mechanics over local hidden variable theories.

3. How does the nonlocality of quantum entanglement challenge our understanding of space and time?

According to classical physics, information cannot be transmitted faster than the speed of light. However, the phenomenon of quantum entanglement, where two particles can be connected in such a way that the state of one particle can instantly affect the state of the other regardless of the distance between them, challenges this notion of locality. This suggests that space and time may not be as fundamental as previously thought.

4. Can Bell's Theorem and nonlocality be experimentally tested?

Yes, numerous experiments have been conducted to test the predictions of Bell's Theorem and the nonlocal nature of quantum entanglement. These experiments have consistently shown violations of Bell's inequality, supporting the principles of quantum mechanics and nonlocality.

5. What are the implications of Bell's Theorem and nonlocality for practical applications?

The implications of Bell's Theorem and nonlocality are still being explored and debated by scientists. However, some possible applications include the development of new quantum technologies, such as quantum cryptography and quantum computing, which could have significant impacts on fields such as communication and security.

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