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.(adsbygoogle = window.adsbygoogle || []).push({});

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?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Tunneling past the speed of light

**Physics Forums | Science Articles, Homework Help, Discussion**