Particles as wave packets - why they don't dissipate?

[Duda Jarek]

Particles in quantum mechanics are often seen as wave packets - linear superpositions of plane waves summing to a localized excitation.
But wave packets dissipate - for example passing such single photon through a prism, its different plane waves should choose different angles - such single photon would dissipate: its energy would be spread on a growing area ... while we know that in reality its energy remains localized: will be finally adsorbed as a whole by e.g. a single atom.
Analogously for different particles like electron - any dependence on momentum while scattering would make such wave packet dissipating (e.g. indivisible elementary charge).

How is this problem of dissipating particles solved?
Aren't there some additional (nonlinear?) mechanisms needed to hold particles together, make these wave packets maintaining their shapes - being so called solitons?

[swansont]

Not all waves dissipate, but beyond that, you can't say you know the energy remains localized — you only know the energy is localized when you detect the photon. You don't know what's happening to it before then.

[Duda Jarek]

So imagine a single excited atom produces single optical photon, which comes through a prism and finally is absorbed by another single atom - suggesting that energy has traveled localized through a concrete trajectory between them.

While if it would be a wave packet, this energy should be dissipated - especially after the prism.

 

Don't we need some additional mechanisms to hold this wave packet together - make it maintain its shape (become a soliton)?

[swansont]

So imagine a single excited atom produces single optical photon, which comes through a prism and finally is absorbed by another single atom - suggesting that energy has traveled localized through a concrete trajectory between them.

While if it would be a wave packet, this energy should be dissipated - especially after the prism.

 

Don't we need some additional mechanisms to hold this wave packet together - make it maintain its shape (become a soliton)?

 

QM rejects the notion that there is a definite trajectory, making the rest of this moot.

[Duda Jarek]

Even for Mach-Zehnder interferometer we draw two classical trajectories, saying only that we don't know which one is chosen.

Here situation is even simpler - no interference.

I think you are referring to Feynman path integrals? But the basic their approximation is taking the classical trajectory and small variations around it (van Vleck formula) - in QM energy travels through a bit fuzzed classical trajectories.

[swansont]

You are still trying to shoehorn a classical idea, that you know details of the light, into a quantum situation.

 

Why is it required that an outside interaction keep the wave from spreading?

[Enthalpy]

Even for Mach-Zehnder interferometer we draw two classical trajectories, saying only that we don't know which one is chosen.

It's worse than that: we know the photon has taken both paths. That's why interferences are built.

 

If you try to imagine a point-like photon (or electron, or any particle) propagating, you'll make wrong conclusions. They are waves and propagate as such.

 

These waves are also particles in the sense that they're absorbed once, as locally as is necessary.

(1) So imagine a single excited atom produces single optical photon, which comes through a prism and finally is absorbed by another single atom -

(2) suggesting that energy has traveled localized through a concrete trajectory between them.

(3) While if it would be a wave packet, this energy should be dissipated - especially after the prism.

(1) yes

(2) no

(3) It doesn't even need a prism. A single atom emits light very broadly, because an atom is small. Farther from the emitter, the energy spreads in more volume. Accordingly, the number of photons is constant, but the probability to detect the photon in a give small volume element diminishes.

 

For instance, a distant star emits many photons, but the chances to detect one in a camera pixel are faint. We need a big telescope mirror to concentrate light in the pixel and improve the chances.

[Duda Jarek]

Reflecting from a mirror means changing momentum of photon and so of the mirror - if you are saying that photon literally goes both ways, does it mean that it has changed momentum of both mirrors?

How much? - like there was complete photon going both ways or (as there was initially only single photon) maybe there were two "halves of photon" (or charge in electron interference)?

 

And generally if you want particle/photon go a more complex trajectory, every change of direction needs a momentum transfer with something (vacuum???)

Edited November 4, 2013 by Duda Jarek

[swansont]

If you detect the mirror's recoil, you have "which path" information and you would only get one result.

[Delta1212]

It's probably better to think of a photon as a smeary blob of probability spreading out from the source that condenses to a single location upon interacting with something than as a tiny billiard ball hurtling from source to destination.

[Duda Jarek]

swansont, I am not talking about detecting the event by an subjective observer, but what is objectively happening there ... physics is still working without observers (e.g. millions of years ago).

 

Delta1212, I am asking about something more concrete than probability: e.g. energy or charge distribution.

Can energy of a single photon or charge of elementary charge dissipate? It is what would happen if you would see them as pure wave packet (without a mechanism to prevent dissipation - make them soliton).

[Delta1212]

"Observer" is more accurately understood in QM "anything being interacted with" rather than "person looking at results."

 

If a photon reflects off a mirror and the mirror recoils, then that mirror "observed" the photon and it is no longer available to interact with the other mirror.

[Duda Jarek]

So any of two paths this photon will choose, it will change momentum of corresponding mirror - be "observed" as you say ... so how can we get interference?

[swansont]

swansont, I am not talking about detecting the event by an subjective observer, but what is objectively happening there ... physics is still working without observers (e.g. millions of years ago).

 

 

Knowing what objectively is happening is not physics. Physics makes no claim to know objectively what is happening. It only claims to have models which tell us how nature behaves. If it happens to be objectively true that's a bonus.

[Duda Jarek]

 

Knowing what objectively is happening is not physics. Physics makes no claim to know objectively what is happening. It only claims to have models which tell us how nature behaves. If it happens to be objectively true that's a bonus.

Interesting, so why e.g. cosmologists bother what was happening before us, astrophysicists bother what is happening inside a star - where we will never be able to directly measure ...

... or what is the solution of Schrodinger equation for hydrogen - for which we cannot measure the whole wavefunction, we can observe only its far consequence: energy spectrum.

 

Indeed modern physics has lost the objectivity - everybody has own subjective physics ... about which real physics doesn't care about - just making that the world objectively works as it works ...

[Enthalpy]

Delta1212, I am asking about something more concrete than probability: e.g. energy or charge distribution.

You can detect a particle once (... recent experiments did better, but let's forget that). So "the energy or charge distribution" is not measurable, hence a theory doesn't need to answer it.

If using many particles, if needed successively, then the probability distribution can be observed, and QM does predict it.

Can energy of a single photon or charge of elementary charge dissipate? It is what would happen if you would see them as pure wave packet.

Please read again my previous answer. The particle spreads more and more, there is still one (1) particle.

[...] everybody has own subjective physics ... [...]

Every serious physicist has QM, because this is what works, and damned well.

If you wish to have something else, that's your problem.

[...] solution of Schrodinger equation for hydrogen - for which we cannot measure the whole wavefunction, we can observe only its far consequence: energy spectrum. [...]

For several years, we see the shape of wavefunctions for atoms and molecules, using atomic force microscopes and the like.

QM not only predicts spectra with fantastic accuracy, using no free fitting parameter - in itself an absolute proof of correctness. It also explains why matter has a volume, as an immediate and concrete consequence.

So any of two paths this photon will choose, it will change momentum of corresponding mirror - be "observed" as you say ... so how can we get interference?

This depends on how much momentum the photon loses upon reflection. And if it loses equally much at both mirrors, no worry at all - which looks like the proper answer. The photon is reflected by both mirrors.

 

Simple descriptions like "know through which slit" usually involve a detector that destroys the photon, and then interference is lost. With only a small modification of the photon (mirror recoil reduces the photon's frequency a little bit), one would have to check how much recoil is necessary to make a detection, how much it changes the photon, and whether interference is still possible then.

 

An interaction is not always as binary as an absorption by a camera pixel. When electrons are diffracted by a crystal, they interfere with many atoms without being absorbed.