Beating the Uncertainty Principle
Most recent answer: 09/12/2013
- Bryan Bentz (age 53)
Stonington, CT USA
Hi Bryan,
That's a good question. I think the simplest case to understand is basically the one you pointed out. Say a source particle decays into two photons; one shoots off generally upwards, while the other shoots off opposite. Of course, if you measure one photon's position on a film screen a meter away from the source, you will get a single blip corresponding to a rather definite location. Since you know almost exactly where the photon started (at the source, whose location can be measured before the emission), and you know almost exactly where the photon ended up (at the blip on the film), it would seem obvious that the particle's momentum was directed along the vector connecting these two points. As such, it seems that you precisely know what the particle's almost exact position and momentum were before it hit the screen.
That would definitely violate the uncertainty principle. Furthermore, if you repeat the experiment many times, you will find the photon in a new location on the screen each time, corresponding to a new momentum vector. You might think that there is some unknown difference between each trial, which tells the photons to have different momenta upon each emission. Such an instruction, or "hidden variable," is in violation of Bell's theorem, as you know, and has been experimentally disproven.
Instead, standard quantum theory says that the spread in your position and momentum measurement results IS an accurate portrayal of the photon, which was emitted into a superposition of many momenta, with mean values "up" and "down" for photons 1 and 2, respectively. The position of the particle also has an uncertainty, since the beam has a spread in space. When you do the position measurement, you randomly collapse the position of the particle, and you don't learn very much about the momentum of the particle. *
In no case, even if you use past information or measurements or entangled particles, can you beat the uncertainty principle. This is because, as you suspected, the principle doesn't apply just to human knowledge, but is actually a property of the physical state itself.
Hope that helps,
David Schmid
* As I understand it, the detection of the photon in a little region gives you very much the same sort of information about its past state as knowing that it came from a little region told you about its future state. The source info told you that the future state would be spread out leaving the source, in a simple case spherically spread out. The detection tells you that the past state was spread out, e.g. spherically, converging toward the little detection region. So now you have both types of info about the state that was present between emission and detection. The combination describes a state that spreads out from the source and then converges toward the detection.
But wait, you say. That's not a possible trajectory of any classical particle. It's not even a combination of many different classical trajectories. That's right, because there is no such thing as a classical particle. As David explained above, violation of the Bell Inequalities tells us that that quantum state is all that there was. Mike W.
(published on 09/12/2013)