Yeah, so, I was thinking about how M-Theory would explain quantum entanglement, and considered that when, say, a photon is separated symetrically, in quantum mechanics, the photon string is still a whole, but is vibrating in such a way that we could only tell this if we could see its movement through the entire calabi-yau shape. This would get rid of the need to move back and fourth through time.
Is this a plausible guess? Does anybody know some good material for an answer to this problem?
Well, let's investigate a little further. I don't think this is a good way to think about it. I think there may be a better model available. See how this grabs you:
"Entanglement" means specifically that there is some variable of one quantum (i.e. string) whose value is dependent upon the value of the same variable of another quantum. Specifically, in the Aspect experiment, the variable is "spin angular momentum." In other words, when two particles manifest from a common source, then conservation of angular momentum dictates that they should have spin angular momenta that add up to the difference in spin angular momentum between the states of the source before and after the emission of these two particles. In most enactments of the experiment, that means that the spin angular momenta of the two particles should be opposite.
Now, quantum mechanics says that if the spin angular momentum of a particle is known beyond question (i.e. "measured") in one plane, its value
must be random in any other plane. To put it another way, you can only measure the spin angular momentum of one particle in one plane at one time. And once you have done so, you not merely
don't know what the spin angular momentum is in any other plane; you
in principle cannot know it.
Now, the spin angular momentum of a particle in one plane
should have an effect on what spin angular momenta
could be measured in other planes,
if it were possible to measure them, but that is true
if and only if the spin angular momentum in the second plane actually has some definable value, even though we cannot measure it. And if this were true, then there would be a
correlation between the spin angular momenta in the different planes. But what quantum physics says is, the spin angular momentum in another plane of measurement
has no definite value under these circumstances.
The Aspect experiment has found a way to indirectly measure the spin angular momentum of a particle in two planes. Because the spin angular momenta of particles emitted from a common source are correlated, we merely measure one plane on one particle and another plane on the other particle. This should, theoretically,
supposing that the second plane has a definite value correlated to the measurement on the first, and note please that this is a
second correlation, separate and distinct from the correlation between the "entangling" correlation between the two particles, give us the spin in two axes, a number that the Heisenberg Uncertainty relation says we should not be able to find.
That means there are two statistical possibilities:
1. We will successfully find a correlation between the spins on two axes, indicating that the spin on the second, unmeasurable axis has a definite value, even though we cannot measure it.
2. We will not find any correlation between the spins on the two axes, indicating that unmeasurable values
do not have definite values.
Finally, as an experimental control, the axes of measurement are randomly determined. In other words, sometimes the two measurements are on the same axis, and sometimes they are on different axes. This controls for defects in the concept of the experiment, or in its implementation, since we should
always find correlation in this case, whether alternative 1 or alternative 2 is true.
So what are the results? They strongly support alternative 2. In other words, if a variable is unmeasurable under the Heisenberg Uncertainty relation, that is, if its complementary value has been measured, the results of the Aspect experiment indicate very strongly that that variable has no definite value.
OK, so how does this relate to strings? Well, the variables that we assign to these "particles" are theorized under string theory to correspond to "modes of vibration" of the strings on various planes of the Calabi-Yau space that they manifest in. Thus, what this means is that if we measure a string to have a particular vibration mode in a particular plane, then the vibration mode potentially in a different plane that corresponds to a variable that is complementary under uncertainty to the first variable has no definite value, and is intrinsically undefined.
We don't precisely know what that means, because we have not managed to connect very much about these vibration modes or these planes of Calabi-Yau space to measurable variables of the particles. However, the fact that these complementary variables exist will probably wind up constraining the Calabi-Yau spaces that produce the physics we see, once we can find a prescription for choosing among the Calabi-Yau spaces on the basis of other criteria.
Hope that helps; it's rather a long journey.
