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A question in Quantum Theory


khaled
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I was reading about "Quantum Entanglement" .. and one explanation was saying that if we have two dices that are quantum entangled,

 

if we roll one for N times and it result in N ordered outcomes, if we roll the other N times, we will get the exact same outcomes ...

 

Not only I'm shocked by that example, but also confused .. my question is simple: what is quantum entanglement exactly ?

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In essence quantum entanglement means that the act of measuring some property of one particle automatically effects the other particle. It is a consequence of conservation laws and mixed states.

 

What your example really states is that the rolling of the first die, or really the outcomes of such rolling, determine the outcomes of the second die.

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not sure about quantum entangled dice, but putting that aside, wouldn't the act of rolling one die break any entanglement? can never get this straight in my head. if we have two quantum entangled things - we know that no matter how much we separate them that we know that if we measure an aspect of A, we now know B without measuring it; but if we deliberately perturb A and change it, we don't expect the same thing to happen to B at a distance. wouldn't this be the transfer of information - potentially faster than light and forbidden. or do I still have it wrong?

 

edit - and enjoy the coffee!

Edited by imatfaal
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Imagine quantum entangled clocks, they will be the perfect clocks in nature!

 

How so?

 

not sure about quantum entangled dice, but putting that aside, wouldn't the act of rolling one die break any entanglement? can never get this straight in my head. if we have two quantum entangled things - we know that no matter how much we separate them that we know that if we measure an aspect of A, we now know B without measuring it; but if we deliberately perturb A and change it, we don't expect the same thing to happen to B at a distance. wouldn't this be the transfer of information - potentially faster than light and forbidden. or do I still have it wrong?

 

edit - and enjoy the coffee!

 

For the analogy to work, the dice are already rolling — they are in an undermined state. When they land and you see how many spots, that's the measurement. The entanglement means you will know what the second die will show.

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Maybe another analogy is tossing two coins.

 

Lets say you and a friend toss two fair coins at the same time. When they land you both cover them, so that you do not know it it is HH, HT, TH or TT.

 

Classically each coin is either H or T, you just don't know which. So you do the experiment and you see that there is no correlation between values H and T the coins can take. That is each coin acts quite independently of the other.

 

Quantum mechanics says something far more bizarre than that. It states that each coin is in a superposition of H and T. It is both at the same time. It is only when you uncover your hand and look at the coin does it take the value H or T. This is very different to the classical case which says we just don't know if it is H or T.

 

Now we suppose we have "quantum coins" and that nature says that HT is conserved. That is when we look at any pair of coins one will always be H and the other T. As these are identical coins we cannot really say which one is which. These coins are entangled.

 

You do a similar experiment. While covered each coin is in a superposition of H and T. You uncover your coin and lets say you observe H. You know, without uncovering your friend's coin that it will be T.

 

The act of measuring the state of your coin to be H has forced your friend's coin to be T.

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What your example really states is that the rolling of the first die, or really the outcomes of such rolling, determine the outcomes of the second die.

 

This sort of phrasing leads people to the misunderstanding that there's a causation at a distance effect going on here. That's why people often think entanglement is so much weirder than it really is. For example, the terrible film "What the Bleep do we Know?" talks about applying a force to one entangled particle and having it felt by the other one. Unless I've completely misunderstood how entanglement works, that's not even close to what is going on.

 

From what I've been able to gather, entanglement is a type of linked uncertainty. You entangle particles by putting the two in superposition of states in such a way that they are linked (such as one will have spin up and the other will have spin down upon observation). One can then separate the two and if it is done in a way that does not measure the state which is in superposition, the entanglement holds. Upon measurement, the measurer will know the state of the other particle and the entanglement will be broken.

 

That's just my understanding of it based mostly from reading posts by Swansont. I've not formally studied QM, though.

 

For the analogy to work, the dice are already rolling — they are in an undermined state. When they land and you see how many spots, that's the measurement. The entanglement means you will know what the second die will show.

 

Posts like this are how I got my understanding as explained above. I may have completely misinterpreted them, though.

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Maybe another analogy is tossing two coins.

 

Lets say you and a friend toss two fair coins at the same time. When they land you both cover them, so that you do not know it it is HH, HT, TH or TT.

 

Classically each coin is either H or T, you just don't know which. So you do the experiment and you see that there is no correlation between values H and T the coins can take. That is each coin acts quite independently of the other.

 

Quantum mechanics says something far more bizarre than that. It states that each coin is in a superposition of H and T. It is both at the same time. It is only when you uncover your hand and look at the coin does it take the value H or T. This is very different to the classical case which says we just don't know if it is H or T.

 

Now we suppose we have "quantum coins" and that nature says that HT is conserved. That is when we look at any pair of coins one will always be H and the other T. As these are identical coins we cannot really say which one is which. These coins are entangled.

 

You do a similar experiment. While covered each coin is in a superposition of H and T. You uncover your coin and lets say you observe H. You know, without uncovering your friend's coin that it will be T.

 

The act of measuring the state of your coin to be H has forced your friend's coin to be T.

 

The drawback of this analogy* is that too often the caveat will be ignored and people think the coin is heads or tails all the time when you have it covered with your hand. A lot of the quantum weirdness is in the fact that the states are undetermined before the measurement is made. This misconception leads to incorrect statements like "changing the state of one instantly changes the state of the other"

 

One could also look at a single coin. The two sides are "entangled". If you flip it, you don't know what state it is in, but when you make the measurement, you instantly know what the other side of the coin is, even if the coin is ridiculously thick, e.g. a light-minute.

 

* Like models, all analogies are flawed. Some are useful.

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Agree with ydoaps - there is a lot of bad information out there. it is too easy to find pseudo-information that would lead one to believe that if you wiggle one entangled particle then the other one moves . I love the single very thick coin version.

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A lot of the quantum weirdness is in the fact that the states are undetermined before the measurement is made.

 

This is of course at the heart of entanglement.

 

The single coin is a good analogy. One can use this in another way.

 

Classically, if we flip and cover the coin we do not know what classical state the coin is in, either H up or T up. But we know it is in one of these, but we are not privy to this information.

 

Quantum mechanically the covered coin is not in a defined state of H up or T up. The coin is both H up and T up at the same time. It is when we look at the coin we force it to be in either H up or T up.

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I understand, that when two particles are entangled; then their wave-functions are spatially inter-mingled. And therefore, when you separate "the two particles"; then each particle, is partially present, in both locations. Each "partial particle" is also in the super-position state. So, in a coin analogy, each coin is half on one side, half on the other; and on each side, is partially H, and partially T. I read that in a book. I.e. "H+T" is conserved; and "L+R" is conserved:

 

[math]|\psi\rangle \sim |H,L\rangle_1 |T,R\rangle_2 + |T,L\rangle_1 |H,R\rangle_2 + |H,R\rangle_1 |T,L\rangle_2 + |T,R\rangle_1 |H,L\rangle_2[/math]

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