"If you have a particle (such as a photons, electrons, or molecule) and have it physically interact with another particle, and then separate them, the result is that they can then both be described as being in the same quantum mechanical state. Basically, they are now the same, in factors such as position, momentum, spin, polarization, etc.
However, because we are dealing with quantum mechanics, the state of those particles remains undefined until measured (because it would then be forced to assume a specific state)."
No they are NOT in the same quantum mechanical state at the moment of entanglement. They are, as you said later, undetermined until measurement (or better, until the collapse of the wavefunction). So they are not the same before, unless you accept the completely discredited theory of local hidden variables (cf. Bell's Theorem). They are connected, by the spooky action at a distance, and at the moment of measurement of one, the other will react accordingly. But before that measurement neither are in any state at all.
But at least I've pinpointed the point where you got QT wrong : "Say you had a binary bit you wanted to transfer. First, you must entangle the bits. Then, put one of them on the other side of the globe. Observe one of them, forcing it to assume a certain state, and the other will instantly change. Like magic."
The problem, see, is that, by definition of quantum mechanics, the collapse of the wavefunction is completely random. You can't force a photon to assume the state you want, it'll assume a random state. Then the other photon will indeed assume the symmetrical state. But that's still be the product of the randomness of the first measurement.
In other words, causality has not been violated because no information is transmitted, only randomness. It's like having two connected dices separated by hundred of miles, when you roll a 1, the other rolls a 6, when you roll a 2 the other will roll a 5 etc. So you roll your dice, and you look at it. You got a 4 ! Great. Now you know that somewhere around in the world someone is looking at his own dice and seeing a 3. Did you transmit any kind of information ? No you knew beforehand that the guy would have a symmetrical result. And you can't tell him a message, because it's completely random. How would you say to your friend on the other side of the planet "Hello" ? You just got 5 fours in a row on the dice... Your friend know it. But that has no meaning at all.
Now, of course, you can imagine local hidden variables, that could be read beforehand to influence the result. Or use another way of influencing the result of the wavefunction collapse, so that a message could be transmitted. But that's what I was speaking of when I said that you had first to reinvent the laws of physics. Cause the Bell's theorem and the No Communication Theorem forbid it in the actual understanding of science. Boy I would love to live in an universe where we can so easily violate causality. That would be FUN !
You're talking about old things like Bell's theorem to support your straw man fallacy, but neglect your own saying. States are transmitted instantly and you still misunderstand either willingly or not the possibility of information transmission by this method.
Your words >> "Then the other photon will indeed assume the symmetrical state."
Your causality argument is void, because in no way has this to do with a paradox. That's high-school physics you use to draw the straw man here. You have no references that back your claims and have you even looked at the scientific journals I have sent you? Try to formally disprove those. And I'm all ears again, but here you only defend your position no matter what.
Ok. So I'm doing a strawman... But you're not doing an argument from authority ?
So let's be clear. Bell's theorem is not an "old thing". I mean, what serious scientist argue something like that... (Yep, that's a No true Scotsman ;-) ) I've never encountered any argument in that direction. Of course some people argue against some of the derivations of Bell's theorem, and his test, but against the soundness of the theorem in itself ? For the record : "No physical theory of local hidden variables can ever reproduce all of the predictions of quantum mechanics."
Then people who challenge the consequences of Bell's Theorem, argue for Non Local Hidden Variables (http://arxiv.org/pdf/quant-ph/9906036v1.pdf). But frankly, non locality is not at all in the actual consensus of quantum physicists. It would have huge consequences on special relativity.
So, again, if you want to argue that Non locality is true, welcome to a completely new world of physics. As of today, no one have any proof that non-locality is real. The scientific consensus is that No communication theorem is a much more credible solution to the EPR paradox. I mean of course some people say that proof of NCT are circular. But most only do because they think we can find a better proof of it.
How many serious scientists work on disproving the Non Communication Theorem ? John Cramer ? Some people in his lab ? That's mostly it. And as of today... they found nothing I am aware of.
And then what are your references ? A nature article, published in the vulgarization part of the review and non peer reviewed ? That short blog post that show very limited understanding of the problems with Quantum Entanglement ?
Anyway, if No Com Theorem is false, boy what a world, time traveling become possible, teleportation, several other sci-fi things. That would be great. But probably will never happen.
However, because we are dealing with quantum mechanics, the state of those particles remains undefined until measured (because it would then be forced to assume a specific state)."
No they are NOT in the same quantum mechanical state at the moment of entanglement. They are, as you said later, undetermined until measurement (or better, until the collapse of the wavefunction). So they are not the same before, unless you accept the completely discredited theory of local hidden variables (cf. Bell's Theorem). They are connected, by the spooky action at a distance, and at the moment of measurement of one, the other will react accordingly. But before that measurement neither are in any state at all.
But at least I've pinpointed the point where you got QT wrong : "Say you had a binary bit you wanted to transfer. First, you must entangle the bits. Then, put one of them on the other side of the globe. Observe one of them, forcing it to assume a certain state, and the other will instantly change. Like magic."
The problem, see, is that, by definition of quantum mechanics, the collapse of the wavefunction is completely random. You can't force a photon to assume the state you want, it'll assume a random state. Then the other photon will indeed assume the symmetrical state. But that's still be the product of the randomness of the first measurement.
In other words, causality has not been violated because no information is transmitted, only randomness. It's like having two connected dices separated by hundred of miles, when you roll a 1, the other rolls a 6, when you roll a 2 the other will roll a 5 etc. So you roll your dice, and you look at it. You got a 4 ! Great. Now you know that somewhere around in the world someone is looking at his own dice and seeing a 3. Did you transmit any kind of information ? No you knew beforehand that the guy would have a symmetrical result. And you can't tell him a message, because it's completely random. How would you say to your friend on the other side of the planet "Hello" ? You just got 5 fours in a row on the dice... Your friend know it. But that has no meaning at all.
Now, of course, you can imagine local hidden variables, that could be read beforehand to influence the result. Or use another way of influencing the result of the wavefunction collapse, so that a message could be transmitted. But that's what I was speaking of when I said that you had first to reinvent the laws of physics. Cause the Bell's theorem and the No Communication Theorem forbid it in the actual understanding of science. Boy I would love to live in an universe where we can so easily violate causality. That would be FUN !