# DBB and radioactive decay times

1. Jul 10, 2010

### skippy1729

Since it is deterministic, the deBroglie-Bohm theory needs a model, mechanism or story whereby complete information of the pilot wave, particle trajectories and other hidden variables will allow calculation of the decay time of a particular unstable atom. What progress has been made on this? Any references appreciated.

Skippy

2. Jul 12, 2010

### Demystifier

There is a general theorem that ALL measurable statistical predictions of dBB theory coincide with those of standard QM. However, this theorem assumes that the measured quantity is described by an OPERATOR. On the other hand, in the usual formulation QM, time is not an operator, which is why it is not so obvious how to apply the theorem to predictions on decay times.

Fortunately, there is a way to introduce a time operator in QM, in which case the general theorem can be applied to measurements of decay times as well. For general results on time operator in QM and the corresponding dBB theory, see
http://xxx.lanl.gov/abs/0811.1905 [Int. J. Quantum Inf. 7 (2009) 595]
http://xxx.lanl.gov/abs/1002.3226 [to appear in Int. J. Quantum Inf.]
The decay time in dBB is not specifically discussed, but the result of Sec. 3.2 of the second paper is general enough to include this case as well.

3. Jul 12, 2010

### vanesch

Staff Emeritus
I'm maybe very naive here, but I would think that "decay time" is actually just a way of expressing a probability of an event in a normalized way (a bit like "cross section"). You do not really measure a time: you measure the probability to have a certain channel after a (small but parametrically given) amount of time. In other words, exactly the same as "what's the probability that the photon hits detector X after t seconds", no ?