Entangled electrons and time dilation where each observer opens box first to cause random collapse ("cause"/random selection paradox?)

Question

Suppose two entangled electrons are put into separate boxes, and these boxes are made to travel in separate frames close to the speed of light (relative to the other frame). A person traveling with each frame observes time dilation in the other frame. Further suppose that each person open the box in their frame before they observe the other person to do so. When each person opens the box (i.e., performs a measurement), the entangled electron randomly collapses to a state, immediately causing the other electron to collapse accordingly. But each person observes the other person to open their box after the collapse of the electron has already occurred. So both people observer that the other person open a box where the state is no longer a random selection? So is there an observer here who can initiate the random collapse of the entangled electron to a state? (Maybe this is not well-stated, but there does seem to be a paradox).

Answer 1

Yes, this issue is the basis of the Einstein-Podolsky-Rosen (EPR) Paradox. The idea of "instantaneous" collapse conflicts with special relativity. Different observers have conflicting definitions of when events are simultaneous, and the 'collapse' hypotheses generally offers no coherent explanation of how the collapse propagates through spacetime (or what triggers it, or how it works, or why it leads to the probabilities it does, or anything much). Any objective collapse process that propagates through space faster-than-light will also be travelling backwards-in-time for some moving observers.

The trouble is that wavefunction collapse has no observable consequences, so there is no way experimentally of finding out how fast it actually moves. It's not a scientific question, it's a metaphysical one. We have several different 'interpretations' of quantum mechanics, which all make exactly the same predictions regarding experiments, but differ in what they think is 'really going on' behind the scenes (what philosophers call the 'ontology'). We can only choose between them on non-scientific grounds like aesthetic elegance, simplicity, parsimony, or calculational convenience.

There are two processes in the common interpretation of quantum mechanics by which things change: the smooth, reversible unitary evolution between measurements, and the discontinuous, irreversible 'collapse' onto a randomly-selected eigenstate. The Everett Interpretation points out that the unitary evolution of interacting systems naturally causes them to enter a joint superposition of mutually non-interacting sub-states, each representing an observer seeing a single possible outcome, none of them able to see any of the others. All the other alternative outcomes still exist but are are mutually invisible. The collapse process asserts that all but one of these alternatives are suddenly deleted (without really saying how, or why, or how the change propagates through spacetime). Since they were unobservable anyway, their disappearance is unobservable too.

So, one hypothesis predicts trillions of invisible alternative versions of ourselves seeing all the other possible outcomes of a quantum measurement. The plus points are that it is local (no faster-than-light backwards-in-time paradoxes such as you mention), reversible, deterministic, information-preserving, and has complete, clear and simple rules. There is no ill-defined division of the universe into 'quantum' and 'classical' realms. The minus points are that it is considerably less intuitive to work with practically, and seems to violate Occam's Razor with all these invisible alternatives.

The other main alternative predicts 'instantaneous' propagation of effects faster than light, with ambiguous or inconsistent causal relationships, and leaves a whole lot of questions unanswered (and probably unanswerable). Although easier to calculate with, the paradoxes mean that any attempt to understand the theory on a deeper level runs into all sorts of 'weird' unintuitive behaviour, leading many to abandon all hope of getting any comprehensible explanation in despair. This is sometimes called the "Shut Up and Calculate" school of thought.

In summary, yes, 'instantaneous' wavefunction collapse is ontologically paradoxical, collapse theories generally don't specify how to resolve it, but they say it doesn't matter because it cannot result in any observable causality-violating effects. Faster-than-light transmission of any experimentally observable information is still forbidden.

--

I should note, there are a number of physicists who have tried to construct alternatives to quantum mechanics with tiny non-linearities that would have the effect of looking linear on the small scale (thus matching experiments), but where the non-linearities cause all but one of the alternatives to actually disappear under their almost-unitary evolution at larger scales. (e.g. Roger Penrose proposing that quantum gravity would do so.) These are in principle experimentally distinguishable from quantum mechanics. However, I have heard that it is extremely difficult to fill in the details consistently, it is even harder to motivate why the tiny non-linearities should take the forms proposed, and so far there is zero experimental evidence either for or against any of them, compared to the linear alternative. I don't actually know how they propose to deal with the EPR-type causality paradoxes - but I should think they would still have the same problem that any sort of faster-than-light collapse process implies something travelling backwards-in-time.