Particle Stability: Wave Packets & Target Interactions

[sphay]

If particles consist of wave packets, and thus a range of frequencies, how does the partciel stay intact after interacting with a target?

Wouldn't the different frequencies diffract at different angles thereby destroying the stability of the particle? Whilst I realize this problem was recognised a long time ago, I am finding it hard to recognise a coherent answer to this problem in the literature. Any views, pointers or clarification appreciated.

 

[vanesch]

Wouldn't the different frequencies diffract at different angles thereby destroying the stability of the particle? Whilst I realize this problem was recognised a long time ago, I am finding it hard to recognise a coherent answer to this problem in the literature. Any views, pointers or clarification appreciated.

Well, the answer is that the "wave packet" is not the particle itself, but its quantum state. And indeed, its quantum state will diffract all over the place. In quantum mechanics, this then means simply that the particle can now be found in different places, and that the amplitude of this quantum state, squared (in the position basis) will give you the probability of finding it in different places, and not that you will find "fractions" of the particle splattered all over the place.

 

[Ratzinger]

If particles consist of wave packets, and thus a range of frequencies, how does the partciel stay intact after interacting with a target?

The wave description applies for dynamic observables, i.e. position, momentum, energy, direction of spin. Mass, charge, magnitude of spin and other static observables remain constant.

 

[sphay]

And indeed, its quantum state will diffract all over the place. In quantum mechanics, this then means simply that the particle can now be found in different places

OK, then if I make an observation at B, the wave function collpases at that position, right?

The wave description applies for dynamic observables, i.e. position, momentum, energy, direction of spin. Mass, charge, magnitude of spin and other static observables remain constant.

OK, so mass diffracts to one position at say A, (is not "splattered"), and A in general will be at a different location to B.

So how do we then reconcile an observed momentum at B, with the mass at A?

 

[vanesch]

OK, then if I make an observation at B, the wave function collpases at that position, right?

That's a way to look upon it. It is not my way, but it is the "standard" way for sure. Especially for starters, it is the best way to see it.

OK, so mass diffracts to one position at say A, (is not "splattered"), and A in general will be at a different location to B.

So how do we then reconcile an observed momentum at B, with the mass at A?

Eh, you do not have different wavefunctions for different "aspects" of the particle. You will not have "momentum" in A, "mass" in B or something of the kind if that's what you want to suggest.

I think that the main confusion comes about by thinking that somehow the particle IS the quantum state. No, the quantum state is the DYNAMICAL DESCRIPTION of the particle. In the same way as "position and momentum" are the dynamical description of a particle in classical mechanics, but is not the particle itself, which is a postulated entity, in both theories. As such, it will keep all its "particle properties" *by postulate*. The wavefunction is just a means to find out where you'll find it after a measurement, or how fast you will find it moving, or so (in the same way as in the case of a classical dynamical state, except that there's now a random aspect to it).

 

[Farsight]

If particles consist of wave packets, and thus a range of frequencies, how does the particle stay intact after interacting with a target?

Are some of these conceptual problems to do with words like "particle"? It suggests tiny billiard balls, and it just can't be like that. A photon is a propagating electromagnetic variation. It doesn't have a surface, or an edge. You can't pin it down. It isn't something intact in the first place.

Can anybody advise me on what a "particle" is?

 

[sphay]

OK, then if I make an observation at B, the wave function collpases at that position, right?

That's a way to look upon it. It is not my way, but it is the "standard" way for sure.

I am curious then how you look upon it?