# Jumping between quantized values

## Main Question or Discussion Point

If you have a particle spinning at some quantized value and it makes a jump to the next energy level so it's spinning faster, what happens in the in-between time? If it happens immediately I'd think that would imply an infinite acceleration...

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Measuring something in QM is sort of like taking a sledgehammer and whacking the system, then seeing what you get. For whatever reason, you always whack it into one of these quantized energy levels, or spin states, or whatever. So a measurement always gives you a quantized energy level, and you never see it in between. So there isn't really an in-between time, or rather, you can't see what's going on in the in-between time. Seeing as you can't know what's going on 'in-between', it doesn't make much sense to talk about it. I suppose that's not all that satisfying, but that seems to be how the world works.

CarlB
Homework Helper
The nature of the measurement process is that it is not complete until the result has registered on the output of some macroscopic device. That could take milliseconds.

QM is related to statistical mechanics in a way. A quantum state is represented by a collection of possible states, similar to the "ensemble" of statistical mechanics. Measurement means that one of those states turned out to be the one.

Where QM is different from statistical mechanics is that the states in the ensemble interact. In the two-slit experiment, the fact that the other slit is open influences what the particle does even though the particle can travel only through one slit.

None of what I've described here suggests particle movement that is fast. What apparently happens in a measurement is that one of the states gets picked out. We can't place a speed on how fast that state gets picked out because all the states already describe the same points in space time. The transition speed is in the measurement, not in the particle.

Carl

Wouldn't the idea of a "seamless whole" produce ridiiculous results though? How can a state change instantaneously? Of course I'm only referring to states in a 3+1 dimensional well.

You're falling into a rather simple error: you're assuming that the particle can be said to be "in an energy level" before you make a measurement. To say that a particle is in a state
$$|\alpha \rangle = 1/\sqrt{2} ( |n \rangle + |m \rangle )$$
means that I have an equal probability of measuring the system to be in n or m when I measure it. But I can't say that the particle is in the state n because that's what I measured, because that isn't the case.

The particle is in neither n nor m before you make the measurement, and afterwards it is in one or the other state with certainty (state vector collapse). But it doesn't make sense to talk about the particle being in the state n or m definitely before the measurement.