I'm confused about a premise implicit in the standard QM model of entanglement, which seems logically inconsistent.(adsbygoogle = window.adsbygoogle || []).push({});

I understand that entanglement arises when two or more particles interact in some way to become synchronized in their quantum states, which also must be indeterminate in terms of conjugate variables (e.g., spin or polarization), such that they share a common wave function that represents a superposition. When these particles then go their separate ways, the standard entanglement model states thatyou must continue to treat each particle as though it were a single particle with a common wave functionuntil a measurement is made, thereby collapsing the wave function and removing the entanglement between the two particles. Until the wave function collapses, the quantum state is indeterminate, and because it started out with the unknowns all mixed up between the two particles (entangled), you can't treat them as separate particles, but rather as an undivided whole.

Of course, the critical implication of this entanglement scenario is that you can actually perform a measurement on one of the two particles, and thereby make a prediction about the state of the other, because they share this common entangled state. For example, if you measure the spin on one particle and it is "up", then the other must be "down".

Here's my question: when we say that the particles have moved away from each other, thenwe seem to be saying something definite about the spatial decoupling of their wave functions: in a simple one dimensional Schrodinger wave propagation model, you would see two wave packets moving away from each other in opposite directions, leaving nothing in between. At this point, it would seem that even the standard model would have to predict that there is no way for these separate wave packets to produce any kind of single-particle entangled behavior: you are explicitly measuring two separate wave functions.

The very presumption of separation into separate particles seems to imply knowledge of the relative locations of the two particles. How can this happen in the absence of a measurement? If you truly did not know whether the two particles were still spatially intermingled or not, this would be represented by a superposition of the two particle wave functions over the shared range of uncertainty in their locations (providing plenty of opportunity for the wave functions to remain entangled). And then you would have tofirst conduct a measurement to determine if the two particles had in fact separated or not, before you could say anything specific about having performed a measurement on one particle or the other.

And once you did that measurement, if it indicated that you did in fact have two separate particles, then you would represent that state of the world with two separate wave functions, and entanglement would be broken.

So either way, it seems like the idea that physically separated particles could remain entangled is logically inconsistent with the standard QM formulation. In the first case you've setup the problem wrong if you know for sure that the two particle states will be physically separate, and in the second case you destroy the entanglement with the first measurement of position.

Concretely, in the case of photon polarization experiments used to test the EPR paradox, the photodetectors are placed some distance on either side of the direction vector of the incident photon that triggered the pair creation, so you definitely know that the two photons have nonoverlapping spatial locations. Why isn't this fact included in the structuring of the wave functions describing the setup, and why wouldn't that known spatial separation break the entanglement?

What am I missing?

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# Logical inconsistency in standard model of entanglement

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