Simultaneity

Every experimental confirmation of Bell's Theorem shows the transmission of information at a speed faster than light. If a particle that is not in an eigenstate along a particular axis is measured along that axis, this automatically collapses the wavefunction for any particle that is entangled with it. For instance, an electron positron pair can be in a superposition of two states, one where the electron has positive z spin and the positron has negative z spin, and one where the electron has negative z spin and the positron has positive z spin. There is nothing special about the z axis: The same wave function can be expressed similarly with regards to the x axis. As soon as a measurement is taken along one axis, a measurement along that axis by another observer must show the same result. A measurement taken along another axis will show random results because of the Heisenberg Uncertainty Principle. Here is a good place to start your study of the matter, though there are a slew of other experiments which I linked earlier in the post: http://www.nature.com/news/2008/080813/full/news.2008.1038.html Note: The experimental apparatus I described in the original post is off by a bit, I realized, the measurements need to be taken in a bit more complex manner, using 45 degree angles and such. I linked a list to the experiments done to show the instantenous collapse of the wave function earlier in the thread, you can read about the methods researchers have used in those. But all point to the fact that a measurement can collapse a wave function simultaneously in two far away locations, and this does not jive with special relativity's disproof of the concept of simultaneity. OK, I think I have a more accurate version of the paradox that doesn't require fancy 45 degree measurements. So, a set of electrons and a corresponding set of entangled positrons are each put on opposing ends of the spaceship. These are in spin eigenstates along the x axis such that the electrons will read a positive spin and the positrons will read a negative spin. One machine measures the spin of its set along the x axis, and the other machine on the other side of the spaceship measures the spin of its set along the y axis. According to some observers, the y spin will be measured first, but according to other observers, the x spin will be measured first. Will the x spin read the definite measurements that were known "before" the y spin was measured, or will it read random measurements? It seems like this points to preferred frames of reference. But even preferred frames of reference can't be a solution, since a ship going in the other direction could be making corresponding measurements, with some paired electrons and positrons on different ships and some on the same ship. Immortal and IM, it seems to me like, whether either counterfactual definiteness, localism, counterfactual definiteness/localism, or superdeterminism is true, it can't explain why one of the measurements arbitrarily takes precedent over the other. I guess the paradox leads me toward a belief in superdeterminism, but this still doesn't explain the specifics of why the system acts as if it was measured by one of the observers first in a seemingly arbitrary fashion. I guess it might be some sort of inherent randomness of the Heisenber variety. Of course, to be technical, Heisenberg was only half right according to superdeterminism. Heisenberg said that the future outcome of a system can be such that it is not determined yet, and the measurement will be completely random. Superdeterminism says that the future outcome of a system cannot be such that it is not determined yet, but the measurement cannot be predicted. If the correctness of either observer's point of view is arbitrarily determined, it seems like Heisenberg's Uncertainty Principle and the more modern version, Ozawa's Inequality (see here: http://www.scientificamerican.com/article.cfm?id=heisenbergs-uncertainty-principle-is-not-dead), are both proven wrong by this paradox. Say both sets of particles are in spin eigenstates along the x axis. One observer then sees one of the sets being measured along the x axis and displaying its eigenstate. He then sees the other set of particles being measured along the y axis and showing random measurements. But another observer sees the measurement along the y axis taking place before the measurement along the x axis: This violates Ozawa's Inequality (and Heisenberg's Uncertainty Principle).

There's a list of the main published findings here. http://en.wikipedia.org/wiki/Bell_test_experiments

In quantum physics, a wave function instantaneously collapses once an observable is measured. For instance, if an electron's angular momentum in the z direction is measured, then the angular momenta in the x and y direction immediately become indeterminate due to the Heisenberg Uncertainty Principle. If two particles are entangled and described by a single wave function, such as two particles that are products of a previous particle that decayed and whose combined spin is known due to conservation of angular momentum, and an observable is measured on one of them, the wave function instantanously collapses on the other, no matter how far apart the particles are. Experiments can and have been done to show instantaneous transmission of information (such as which direction the measurement took place along). But special relativity says that there is no such thing as a universal "instant" for all observers in all frames of reference. So, suppose Observer A is watching a space ship pass by at a very fast constant velocity. Observer B is in the middle of the ship. Two light beams are emitted, one from the front of the ship (the edge of the ship farthest along the direction of motion according to Observer A), such that Observer B observes they have been simultaneously emitted at the same instant. Observer A sees that the light beam from the back of the ship takes longer to reach the middle than the light beam from the front, because it must catch up with the ship, while the ship is racing to meet the light beam emitted from the front. Both observers agree on the speed of light, which is universal. But if the light beams reach Observer B at the same time according to Observer B, Observer A must also see this: If Observer B sets up a machine that kills a cat if both beams reach him at the same time, Observer A would obviously agree that the cat is dead (physics thought experiments are a dangerous place for cats). So Observer A must see the beam of light being emitted from the back of the spaceship before the beam of light is emitted from the front of the spaceship in order for the beams to meet in the middle. If a series of clocks is placed along the length of the ship that Observer B sees as synchronized, Observer A will see the clocks that are further forward in the direction of motion as reading fractions of a second less, depending on how far forward they are. So, now we take our two particles that are entangled, and we put one at the front of the ship and one at the back of the ship. Two machines are set up that measure each particle's spins, and the machines each take a measurement along a different direction. Observer B sees the particle at the front of the ship being measured slightly before the particle at the back of the ship, while Observer A sees the opposite, because the back of the ship is further along in time for Observer A than it is for Observer B. So what happens to the wave function? Which axis does it collapse along? It seems natural that Observer B might be fundamentally correct, since he isn't moving with respect to the particles, but suppose we have four particles that are entangled, and the other two are in corresponding positions on the ship that Observer A is on. Observer B sees himself as being still and Observer A as moving, so neither observer is still with respect to the particles. This is not an extremely technical paradox: The mathematics only require an undergraduate level of physics education, but to my knowledge no one has ever resolved this paradox.