Tunnelling guess 3

In a previous post I described a simulation of tunnelling I conducted to test a guess I made about quantum tunnelling. David Deutsch had guessed that some of the instances of a particle have energy above the energy of the barrier and they got though the barrier. I guessed that none of the instances of the particle had energy greater than that of the barrier and that tunnelling was just an interference effect. I conducted a simulation to test my guess guess and found that it was wrong. The probability of a particle having energy greater than that of the barrier increased for some energies greater than that of the barrier.

I have a new guess for what’s going on. The barrier reflects the instances of the particle that interact with it with a high probability, so the barrier is like a mirror. An accurate model of the barrier would take into account the fact that it is a finite but large physical system. The barrier would be modelled as having a mixed state with a range of positions and momenta. The interaction with the particle would slightly change the probabilities of those states. There would be a high probability of the before and after states of the barrier being indistinguishable since the probability of detecting it in a state with larger momentum than any of its previous states would be negligible. This is similar to the explanation of why mirrors interacting with photons doesn’t prevent interference in interferometers in The Beginning of Infinity, pp.296-297. Some instances of the particle gain momentum and others lose it as a result of the interaction, but the transmission or lack thereof is due to an interference effect rather than the loss of gain of momentum.