Ziggurat
Penultimate Amazing
- Joined
- Jun 19, 2003
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At the risk of derailing and confusing timf1234, I'm going to interject and say that the above isn't true. Radioactive decay is very much dependent on the uncertainty principle (in the deltaE*deltat~hbar form). It plays a huge role in determining the lifetime of an unstable atomic nucleus against alpha and/or beta decay. Eg in alpha decay the alpha particle has to tunnel through the potential barrier of the residual nucleus. The probability of tunneling is dependent on the height of the barrier (and hence the energy that needs to be 'borrowed') and the extent of the barrier (hence the time said energy needs to be borrowed for).
This is a common but incorrect interpretation of the energy/time uncertainty relationship, which (in non-relativistic QM) is completely distinct from all the other uncertainty relationships. deltaE does not represent borrowed energy (it isn't borrowed), but merely the standard deviation for measurements of the energy. deltat does not represent the time that energy is borrowed for, but the time it takes for an observable (such as position) to change by one standard deviation. It is true that this relationship is relevant to radioactive decay (the particle's expectation position can change because it's not in an energy eigenstate, and the greater the spread in energies, the faster that change can happen), but your understanding of that relationship is wrong.