Causality in Copenhagen…

Editor, Scientific American Magazine; Dear Sir:

Thank you for your recent article about quantum mechanics and special relativity (Albert & Galchen, March 2009). While it was good to read an in-depth treatment of a fascinating subject I think it failed to state its case succinctly or cover it completely.

Many years ago studying physics as a mere undergraduate it was clear to me that Bohr and Einstein were fundamentally in conflict. An isolated part of a quantum mechanical system, like an individual particle, can be described by a wave function expressing a range of probabilities about that particle, including where it’s located. In practice, however, when a particle is measured it can be found at only a single specific place. The Copenhagen interpretation, if taken literally, says that at the instant of measurement the wave function “collapses” and the position of the particle is known everywhere. But such an “instant of measurement” must be a moment in absolute time in contradiction to special relativity. If we know that a particle is here and that it’s “simultaneously” not there, we’re potentially violating causality in opposition to all our intuitions (and theory).

But this is a general problem for the very concept of wave function collapse, not a special feature of quantum entanglement on which the article unnecessarily focused. Entanglement just allows a wave function involving multiple particles to grow to macroscopic scales where we can all be freaked out about its instantaneous collapse. I also don’t feel that the article’s alarmist tone about the end of physics was justified. There may be many ways to resolve this issue without having to retreat to some contrived, neo-classical interpretation:

1) Given that there is no inherent difference between an entangled particle and a non-entangled particle except its history, perhaps knowing a particle is entangled makes the observer “entangled” in its history in a similar way. Treating observers as godlike and objective has been a prejudice of physics that perhaps should be questioned. After all the “knowledge” of entanglement had to move at no more than the speed of light just like the particle itself.

2) More fundamentally (and of course I am a relative layman here) perhaps the wave function shouldn’t be computed in absolute time in the first place. That’s an acceptable Newtonian approximation for small-scale events, but as we all well know it can’t be correct. Just as there is spatial uncertainty in quantum events, there should be a level of temporal uncertainty as well, probably with a factor of c in there someplace. Instead of throwing bricks at Einstein maybe quantum theorists should try to incorporate our basic knowledge of unified spacetime into their formulations from the ground up.

- jack*

Comments

[01d55]

I've never understood how quantum physics defined "observer," assuming of course that the term is well defined.