Since in quantum mechanics a particle can “borrow” energy to overcome a barrier. Can a photon for a very brief moment exceed the speed of light?
No, because in order to do so, it would have to “borrow” more than an infinite amount, which is clearly impossible.
But I thought any amount of energy could be borrowed? It was just the more energy the more improbable it became.
Does infinite energy = infinite improbability = impossible?
Basically. If a particle borrows energy, it must repay the “energy debt” in a time span inversely proportional to the amoun borrowed. In order to borrow an infinite amout of engery, it would have to repay it in an infinitely small amout of time. Plus, nature abhors infinities. If an infinity pops up in a calculation, it’s nature’s way of telling us we’ve done something wrong.
Don’t we get infinite results all the time when we bring quantum mechanics and general relativity together? Does this mean one (or both) have something wrong?
Yes, and yes. So far, superstring theory has done a wonderful job of bridging the gap between the two realms, however, so there is great hope amongst theoretical physicists that it might well be the long-sought Theory of Everything, or at least the firm foundation for the eventual final theory.
So it we leave relativity out it for a moment and only use quantum mechanics, could a photon exceed the speed of light?
Is this a stupid question?
No, quantum mechanics integrates Special Relativity quite well. It’s General Relativity that’s the problem. This is the point where the very small (quantum theory) meets the very large (gravity and General Relativity); and this is where those nasty infinities crop up, for instance in working out what’s happening inside a black hole. By itself, Relativity says the density should be infinite, which is silly.
Photons travel at the same speed regardless of energy. An x-ray photon has much more energy than a microwave photon, but both travel at the speed of light.
Quantum tunneling can lead to photons apparently traveling faster than photons traveling through a vacuum. What actually happens is that the peak of the wave of the tunneling photon arrives before the peak of the wave of the unobstructed photon. The wave fronts arrive at the same time. There was a thread about this: Quantum tunneling and information (NOVA episode). In the thread Ring provided a link to an explanation: Mike’s UFO and Superluminal Physics Page.