# Tunneling past the speed of light

1. May 29, 2007

### michael879

correct me if Im wrong, but from what I remember, standard tunneling occurs because of the heisenberg uncertainty principle. There is some known error in the position of a particle (probably a 3d gaussian distribution centered on the mean and with a standard deviation equal to this error although Im not sure) and it is impossible to measure with less than this error because the particle's position isnt actually deterministic, and has this error associated with it.

The formula is momentum * position >= h-bar where momentum is the error of the momentum and position is the error of the position. There is also a similar equation for energy and time.

Because particle's have this error associated with their position, there is some non-zero probability of the particle being in any point of space. Of course this probability falls rapidly as you get farther from the mean position (like a gaussian curve if not exactly one). Putting a particle with some energy in a potential well with a greater escape energy, the particle will be able to tunnel out with some probability. This goes against the deterministic classical view.

However, particle's also have an error associated with their momentum. Wouldnt this mean that as a particle's speed approaches the speed of light, there would be some probability of its speed actually being greater than the speed of light? The probability of it being exactly c would still be 0 of course (similarly the probability of a particle being at a specific point is essentially 0), but there would be some non-zero probability of it moving at faster than c. This would imply that accelerating a particle close enough to c would allow it to actually tunnel through this boundary.

This doesn't sound right to me, but I dont see any flaws in my logic... can anyone help?

2. May 29, 2007

### JesseM

You're thinking of how the probability of finding a particle at different locations works in nonrelativistic QM; apparently it works differently in quantum field theory, with there being zero chance of detecting a photon at a distance x from its previous detection if the time is less than x/c. See this older thread for details.

3. May 29, 2007

### michael879

Im not talking about photons.. Ive heard the problem asked in that post, and Ive seen the answer before. Im talking about massive particles tunneling past the speed of light. I dont see why its not possible, especially since it doesnt conflict with relativity at all.

4. May 29, 2007

### JesseM

I'm pretty sure massive particles are also treated differently in quantum field theory than in nonrelativistic quantum mechanics, so it seems plausible that the nonrelativistic notion of a position wavefunction which assigns a nonzero probability to the particle being detected anywhere in the universe is also not perfectly accurate in QFT. That's the impression I got from the post on the thread I linked to where Ambitwistor said:
I could be wrong in my reading of that quote though, hopefully someone more knowledgeable will weigh in.

5. May 30, 2007

### Fra

Unlike the normal QM tunneling through classically forbidden configurations, forcing the light speed barrier would require an infinite energy. There is no classical tunneling through infinite energy barriers because the tunneling probability goes to zero, only finite (but arbitrarily large) barriers give non-zero probability.

Classically the heavy particle doesn't just need "a little more energy" to reach light speed, it needs *infinite* energy. I think that's the missing point in your reasoning.

The classical observables, are more like expectations when noisy fluctuations are marginalized. It means that in QM the classical conservations are "on average" conserved. Average refers to the average of a imagined statistical ensmeble, or an optimal bet, given any incompleteness. One can basically assign probabilities to a deviation from the expectation. But if the deviation goes to infinity, so does the probability for it.

/Fredrik

6. May 30, 2007

### RandallB

Are you you reffering to some new version of Relativity.

Realtivity uses as a given that:
Vtotal = (V1 + V2) / (1 + V1V2 /c2)

Anything going past the speed of light would be in conflict with that realativity principle
Unless there is something new.

7. May 30, 2007

### JesseM

That formula is just for translating between velocities as seen in different frames, and it shows that something moving at some speed V1 <= c in one frame cannot move faster than light in another frame moving at V2 relative to the first frame, but that's not what the OP was talking about (and the formula also doesn't rule out things like tachyons which move faster than c in all frames, although they're considered very unlikely for other reasons).