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Alex, Here's A Paradox That Troubles Me...

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Posted by Mark on October 24, 2001 21:19:52 UTC

Perhaps you know the resolution since you're the expert in the field.

I thought about this the other night, and I cannot seem to come up with an answer; hopefuly you can...

We have, say, an electron in some arbitrary orbital. All of the sudden, the electron spontaneously emits a photon and dissapears from one position while instantaneously materializing in a lower energy state. The electron does not traverse the distance between orbitals in a "classical" fashion; this is a quantum event.

However, the thing I find most troubling is not "quantum jumps", but the causual paradox this creates.

When I think of an electron as having mass, I immediately equate that to having gravity. But gravity, like electromagnetism, propogates with finite speed c. Therefore, if the electron vanishes and instantaneously reappears (allowed by uncertainty principle)... gravitational influences must propogate away from the initial position of the electron with finite speed, only to later encounter that same electron which jumped ahead of its own field emission. So can a particle interact with itself via uncertainty?

If a proton vanishes and reappears at a different location (point A to point B), then all causual influences will take time to travel from point A to point B, only to find that the proton "beat them to the punch" because of the quantum uncertainty in its position. So a graviton emmited by the proton at point A, will find this same proton at point B a short while later, and then proceed to exert a gravitational tug on this proton. The direction of force points toward the location of A, therefore the proton imparted a momentum upon itself in the direction of A. Does this spoil momentum conservation? What gives?

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