What is the Difference between the lottery and QM?

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It seems to me that so far in quantum mechanics, because we have yet to establish probability patterns for, say, what the spin of a photon is, we have made it some mystical thing that we can only know by measuring it. I don't really buy that; is the result of a lottery impossible to know until it is done? No, because we know the probability of different results. So why could it not be that we just have yet to find a probability function for the spin of a photon?
 

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  • #2
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Thanks for your reply! So I understand that there are no hidden variables, but could you help me understand what the experiment that has been done is? As I understand it, if two particles become entangled and they are measured, then they will be the opposite of eachother; in this case, what is to say that they weren't just that way since the time they became entangled instead of what is currently asserted which is that it is the act of observing that brings them from a state of uncertainty and randomness to a solid state?
 
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Further on how these experiments have been carried out, are the particles constantly changing after the entanglement or are they a solid state? If they are solid state, have we tried making stuff entangled, measuring it, changing one, measuring the originally changed one, and then measuring the other one?
 
  • #5
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I don't think we can answer the question of the changing or remaining constant state without measuring the state which then changes the state. We can say that the system is entangled if we measure the state of A and then measure the state of B and see that they are in complementary states.

However doing this measurement doesn't mean we will always get this answer when they are entangled only that we get the answer with a high probability of the time. This is why we can't say we have superluminal communications between two entangled particles because one measurement doesn't answer the question, we must make many measurements and compare results later on.

Here's a video on Bell's Theorem that you might interesting:


and one on Quantum Entanglement:

 
  • #6
PeterDonis
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we have yet to establish probability patterns for, say, what the spin of a photon is
Where are you getting this from? We have very detailed quantum descriptions of how photons behave, including their spins, that have been confirmed to many decimal places in experiments.
 
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I will have to look into those videos. I guess what my question boils down to is: How do we know that these particles just aren't in complementary states from the start? It seems like we are saying that there is some connection between two entangled particles when in reality they were the same the entire time.
 
  • #8
PeterDonis
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I guess what my question boils down to is: How do we know that these particles just aren't in complementary states from the start?
Because the particles don't have definite states until they're measured. Only the overall system consisting of both particles has a definite state.
 
  • #9
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what is to say that they weren't just that way since the time they became entangled instead of what is currently asserted which is that it is the act of observing that brings them from a state of uncertainty and randomness to a solid state?
If entangled particles had their definite values from the beginning, then spin measurements at angles other than exactly opposite must obey an inequality called "Bell's Inequality". However, quantum mechanics predicts that Bell's inequality will be violated, and experiments have confirmed the quantum mechanical prediction. Therefore, no theory in which the entangled particles have their definite values from the beginning can be right, or can reproduce all the predictions of quantum mechanics.

For more about Bell's theorem, you could start with https://static.scientificamerican.com/sciam/assets/media/pdf/197911_0158.pdf and the website maintained by one of our members: http://www.drchinese.com/Bells_Theorem.htm

Further on how these experiments have been carried out, are the particles constantly changing after the entanglement or are they a solid state? If they are solid state, have we tried making stuff entangled, measuring it, changing one, measuring the originally changed one, and then measuring the other one?
Do remember that you only get one measurement: A and B are entangled; I measure A then I know what the result of the corresponding measurement of B will be; but that measurement of A also ends the entanglement so that subsequent measurements will not be correlated.

Thus, the only way to even detect entanglemet is to work with a large number of entangled pairs. I measure A and get spin up and then measure B and get spin down; that might mean that they were entangled, or I might have just gotten lucky - random chance will give me a mismatch 50% of the time. So I prepare another pair of particles the same way and I get a mismatch again. I do this a few thousand times and I get a mismatch every single time. The probability of this happening with random unentangled pairs producing a mismatch every single time is negligible (would you think a coin was honest if it landed heads ten thousand times in a row?) so I conclude that my source is generating entangled pairs.

Variations of this experiment have been done in countless different ways by many different groups in the half-century since Bell first published his inequality. At this point, the evidence is as convincing as anything in science.
 
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If entangled particles had their definite values from the beginning, then spin measurements at angles other than exactly opposite must obey an inequality called "Bell's Inequality". However, quantum mechanics predicts that Bell's inequality will be violated, and experiments have confirmed the quantum mechanical prediction. Therefore, no theory in which the entangled particles have their definite values from the beginning can be right, or can reproduce all the predictions of quantum mechanics.

For more about Bell's theorem, you could start with https://static.scientificamerican.com/sciam/assets/media/pdf/197911_0158.pdf and the website maintained by one of our members: http://www.drchinese.com/Bells_Theorem.htm

Do remember that you only get one measurement: A and B are entangled; I measure A then I know what the result of the corresponding measurement of B will be; but that measurement of A also ends the entanglement so that subsequent measurement will not be correlated.

Thus, the only way to even detect entanglemet is to work with a large number of entangled pairs. I measure A and get spin up and then measure B and get spin down; that might mean that they were entangled, or I might have just gotten lucky - random chance will give me a mismatch 50% of the time. So I prepare another pair of particles the same way and I get a mismatch again. I do this a few thousand times and I get a mismatch every single time. The probability of this happening with random unentangled pairs producing a mismatch every single time is negligible (would you think a coin was honest if it landed heads ten thousand times in a row?) so I conclude that my source is generating entangled pairs.

Variations of this experiment have been done in countless different ways by many different groups in the half-century since Bell first published his inequality. At this point, the evidence is as convincing as anything in science.
Thank you for the response, this was really helpful! A question I have then is what if you measure them at the exact same time?
 
  • #11
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The difference is: You're never going to become a millionaire from quantum mechanics.
 
  • #12
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I have then is what if you measure them at the exact same time?
It makes no difference which measurement is first or whether they are simultaneous. In fact, since we are typically working with particles that are moving between source and detectors at close to the speed of light, relativity of simultaneity (Google for that if you're not familiar with it already - it's an essential part of Einstein's theory of relativity) often means that there is no unambiguous way of saying which measurement came first or whether they were made at the same time - different observers moving at different speeds relative to one another will disagree about the relative ordering of the two measurements.

The quantum mechanical prediction comes out the same either way. We can can explain the observed 100% mismatch by saying that when we measured A and got spin-up, we collapsed the wave function into the state "A is is spin-up and B is spin-down" so of course a subsequent measurement on B will be spin down; but we could just as easily say that it was the measurement of B that caused the system to collapse into that state so of course the measurement of A has to be spin-up. But the only thing that QM says is that when we compare the two measurements after the fact they will always mismatch if the particles are entangled.
 
  • #13
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A question I have then is what if you measure them at the exact same time?
An entangled pair share one wave function - they are always measured at the same time.
 
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So once a wave function has collapsed by the observation of A, B is permanently the opposite from then on? So is this ultimately saying: everything is random until we measure it, then it is a certainty; that there is no way to know anything before?
 
  • #15
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So once a wave function has collapsed by the observation of A, B is permanently the opposite from then on?
Not quite.... For example I could measure A's spin on the vertical axis and B's spin at an angle of 45 degrees from the vertical, and then I'd find a different correlation than exactly opposite. Again, I'd have to do this with many pairs before the statistical pattern emerges. In any case, once the wave function has collapsed (and it is irrelevant which of the two measurements I consider to be the one that came first and "caused" the collapse) the entnglement is broken and the two particles evolve independently.
So is this ultimately saying: everything is random until we measure it, then it is a certainty; that there is no way to know anything before?
As far as the mathematical formalism of quantum mechanics is concerned - and there's not much else on the table - yes. It's actually even stronger than what you said. "No way to know" implies the possibility that the spin has a definite value but we don't know what it is; it would be more in the spirit of the mathematical formalism to say that there is no value before the measurement, the same way that I have no lap before I sit down.
 
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Alright, but if they evolve separately, do they just not evolve fast enough for us to not know if the spin has changed since the entanglement stopped?
 
  • #17
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Alright, but if they evolve separately, do they just not evolve fast enough for us to not know if the spin has changed since the entanglement stopped?
If you're setting up an experiment to test spin entanglement, you design your setup so that the evolution of the wave function doesn't change the direction of the spin before the particles reach their respective spin-measuring devices. As a practical matter, this means that the particles are moving through a hard vacuum and we don't have any stray magnetic fields in our apparatus.

(As an aside, note just how hard it is to talk about quantum mechanics without using the math. Both your "if the spin has changed" and my "doesn't change the direction of the spin before [measurement]" are speaking of a pre-measurement spin - and there's no such thing. It would be more accurate to say "doesn't change the probabilities of getting various measurement results at various angles, including the 100% probability of a mismatch if we measure both spins along the same axis")
 
  • #18
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The difference is: You're never going to become a millionaire from quantum mechanics.
Unless you get a Nobel Prize for work in quantum mechanics, perhaps by definitely answering the question where do quantum probabilities come from. :wink:
 
  • #19
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Unless you get a Nobel Prize for work in quantum mechanics, perhaps by definitely answering the question where do quantum probabilities come from. :wink:
The Nobel Prize is a kind of lottery, you might say.
 
  • #20
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It seems to me that so far in quantum mechanics, because we have yet to establish probability patterns for, say, what the spin of a photon is, we have made it some mystical thing that we can only know by measuring it. I
You have received some good answers here.

I just want to say there is nothing mystical about any part of QM.

Thanks
Bill
 

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