Quantum Entanglement at Point of Creation
Date: Spring 2013
In my physics class, the process of quantum entanglement was brought up at a very superficial level with something that sounds like this: if two particles emerge and we separate them spatially, and we measure the spin of one particle, the other automatically assume the opposite spin. My understanding of quantum physics is superficial, but I have the following questions: what if they are measured simultaneously? If that is not possible, how about this: in Earth's frame, S, I measure one particle (A) and at t later I measure the other (B), t is such that the separation between two events is space-like. Now in S the event at A causes the spin of B to assume a state, now in another reference frame B precedes A (since their separation is space-like) hence the two events cannot be causally related? Does this make sense? The best I can come up with in my head is that the process of entanglement occurs at the point of creation, so later measurements have no effect on their states. Please help me understand this.
What you are describing is what others refer to as, “Quantum Weirdness.” It is more formally known as the “EPR Paradox” after the scientists (Einstein, Podolsky, Rosen) who originally used some of your thought processes as an argument against the reality of Quantum Mechanics. Subsequent experiments have shown quantum entanglement to be real. One of the ways to think of the problem is to view the entangled particles as a single system. The particles do not exist separately with one spin ‘up’ and the other ‘down.’ Rather, they exist as a single unit with a combination of ‘up’ and ‘down.’ When you make a measurement, the particles in a sense become distinct with opposite spins. Measuring the two simultaneously somehow would not change the system in that the spins would be opposite. One would be measured ‘up’ and the other ‘down.’ Where I would disagree with your statement is in the idea that at the point of entanglement that the states are determined. It is in precisely the fact that the system of entangled particles are in a combination of states (up/down) that causes the seeming paradox. I say seeming because the difficulty is in the way we state the result: ‘measuring the spin of particle A causes the spin of particle B to be in the opposite spin.’ ‘Cause’ implies that somehow information on the state of the particle A passes to B and causes its state to be the opposite. In this sense, the information of state A would have to pass through space somehow and affect state B. It is possible to set up an experiment in which such information exchange would violate Einstein’s Special Theory of Relativity by having this information travel faster than the speed of light; however, this violation does not occur. Thus, causality in this sense is not the right way to look at it: information is not exchanged from particle A to B so far away. Indeed, as you observed, it is possible not even to agree on the simultaneity of the measurements in different frames of reference through relativity. However, relativity is not violated because measurement of the spin of particle A does not cause (force) the spin of particle B to change.
Kyle Bunch, PhD, PE
You are treading in waters that are deep and not fully understood. Like you, I am not an expert in this area by any means, but I will throw out some ideas for your thinking. First warning bell: ?Now in S the event at A causes the spin of B?. Entanglement is not a cause / effect relationship. ?A? and ?B? occur simultaneously, but in different places. That is where the ?weirdness? takes place. You correctly point out that the two ?events? do not occur in a cause/effect way, in the classical sense. Their different ?states? occur because the laws of quantum mechanics demands that if ?A? has property ?A?(+), the laws of quantum mechanics requires that ?B? has the property ?B?(--). The option of ?A?(--) and ?B?(+) is not allowed by the laws of symmetry. This relation of ?A?(+) and ?B?(--) is demanded by the quantum symmetry, not by any physical laws of motion etc., only by the laws of symmetry, which are not governed by any laws of quantum mechanical physical laws.
I hope I did not toss more confusion into the ?fire? but this whole topic is not simple.
Thanks for the question. The spins of two particles are not necessarily opposite or parallel. The identity of the particle and how it was created will determine whether the spins are parallel or opposite (anti-parallel).
Here is a general principle of quantum theory that will help you to understand (and predict) the outcomes of experiments: If I measure the system, the system collapses into a single state and the system stays in that state for all time (with the exception of time-dependent perturbations, which we aren't considering anyways.) If I measure the system again, I will find that system in the same state as before. We call this process "the collapse of a superposition into a single eigenstate of the operator corresponding to the measurement."
I hope this helps. Please let me know if you have more questions.
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