Acceleration in quantum theory

[geordief]

Are there examples of how acceleration is treated in quantum theory?

If a classical system is accelerated I have a picture of a wave traveling through the system like if you were to pull a string or push a rod.

What happens in "comparable" situations  when the systems are quantum?

Does "acceleration" mean anything under those circumstances? 

[swansont]

1 hour ago, geordief said:

What happens in "comparable" situations  when the systems are quantum?

What would be a comparable situation?

Cases I can think of where acceleration matters are where you’d treat the particle classically. 

In quantum systems you’d look at the energy of an interaction.

[Sensei]

1 hour ago, geordief said:

Are there examples of how acceleration is treated in quantum theory?

Aren't CERN and the LHC examples of accelerators that accelerate quantum particles to near the speed of light?

New (usually short-lived) particles appear, and other particles are destroyed into smaller components, etc. etc.

[geordief]

1 minute ago, Sensei said:

Aren't CERN and the LHC examples of accelerators that accelerate quantum particles to near the speed of light?

New (usually short-lived) particles appear, and other particles are destroyed into smaller components, etc. etc.

That example occurred to me after I had asked the question.

So the particles collide and as a result new particles result.

Do they accelerate away from the region where the "parent" particle was?

Or do they  travel like  a photon ,either at zero velocity or at c?

If the latter then they don't accelerate  and the acceleration as in "particle accelerator " is a classical  process.

28 minutes ago, swansont said:

What would be a comparable situation?

That is why I put it in quotes.As "comparable" as possible ,I suppose.

Are there any situations where a quantum system undergoes anything like what a classical system does when it is subject to accelerating  forces?

I think you are saying there aren't?

 

Is it possible to treat a quantum particle (system?) classically?

Does that introduce error?

[swansont]

14 minutes ago, geordief said:

So the particles collide and as a result new particles result.

Do they accelerate away from the region where the "parent" particle was?

I’m not sure why they would accelerate away.

There could be an electrostatic force, but this typically has a small energy compared to the interaction energy. e- and e+ for example (creation or annihilation) - the mass energy is around 1 MeV but the electrostatic PE is of order 10 eV

 

14 minutes ago, geordief said:

Are there any situations where a quantum system undergoes anything like what a classical system does when it is subject to accelerating  forces?

I think you are saying there aren't?

Owing to the uncertainty principle(s) you don’t get to “look” at the interaction in arbitrarily fine detail of whatever variable (e.g. position, momentum) You look at the start and end of the interaction and apply conservation laws - momentum, energy, charge, angular momentum

Quote

Is it possible to treat a quantum particle (system?) classically?

You can treat the acceleration of a free electron classically.

[MigL]

Your notion of acceleration is not totally valid even for classical systems.
Your 'push'/'pull' analogy only works for contact forces; it does not work in the case of gravity, or electromagnetic forces, where the whole body interacts with the force, not just the contact surface.

Quantum mechanically things are no different.
Contact forces, such as the LHC, are treated the same because the EM part of the interaction is small/weak compared to the collision part.

One slight difference is that, classically, most people use Newtonian mechanics, but any 'advanced' treatments, including Quantum mechanical and Relativistic, use Lagrangian or Hamiltonian mechanics ( energy of the system ), as Swansont alluded to previously..

[geordief]

1 hour ago, MigL said:

Your notion of acceleration is not totally valid even for classical systems.
Your 'push'/'pull' analogy only works for contact forces; it does not work in the case of gravity, or electromagnetic forces, where the whole body interacts with the force, not just the contact surface.

Quantum mechanically things are no different.
Contact forces, such as the LHC, are treated the same because the EM part of the interaction is small/weak compared to the collision part.

One slight difference is that, classically, most people use Newtonian mechanics, but any 'advanced' treatments, including Quantum mechanical and Relativistic, use Lagrangian or Hamiltonian mechanics ( energy of the system ), as Swansont alluded to previously..

Thanks.

Is it possible for two particles to collide without new  sub particles being created ?

Does "particle dodgems" or "particle pinball" exist in practice?

Can one particle influence the trajectory of another without the  fireworks? (do their waves just superimpose in a continuous way?)

[swansont]

1 hour ago, geordief said:

Thanks.

Is it possible for two particles to collide without new  sub particles being created ?

Yes. If there isn’t enough energy then you can’t create new particles. 

1 hour ago, geordief said:

Does "particle dodgems" or "particle pinball" exist in practice?

Yes.

1 hour ago, geordief said:

Can one particle influence the trajectory of another without the  fireworks? (do their waves just superimpose in a continuous way?)

Yes. Particles scatter all the time.

[Sensei]

On 1/22/2024 at 2:57 AM, geordief said:

 

On 1/22/2024 at 2:51 AM, Sensei said:

Aren't CERN and the LHC examples of accelerators that accelerate quantum particles to near the speed of light?

New (usually short-lived) particles appear, and other particles are destroyed into smaller components, etc. etc.

That example occurred to me after I had asked the question.

So the particles collide and as a result new particles result.

Do they accelerate away from the region where the "parent" particle was?

Or do they  travel like  a photon ,either at zero velocity or at c?

If the latter then they don't accelerate  and the acceleration as in "particle accelerator " is a classical  process.

Calculations at CERN/LHC or any other particle accelerator, or near the speed of light, are done in CoM (Center-of-Mass/Center-of-Momentum) FoR (Frame-of-Reference).

https://en.wikipedia.org/wiki/Center-of-momentum_frame

https://en.wikipedia.org/wiki/Center_of_mass

In this FoR, all kinetic energies of all particles participating in this collision, must exceed the masses-energies of the all newly formed particles after the collision.

The remaining energy (if it exceeds the threshold *) is carried by the newly formed particles as their kinetic energy (including photons and neutrinos).

Calculations made in CoM are translated into laboratory ("lab frame", "local") FoR, to learn to what velocity particles are required to accelerate at particle accelerator.

https://en.wikipedia.org/wiki/Local_reference_frame

 

 

*) in the case of Pion meson  it is called "pion threshold creation"

https://www.google.com/search?q=pion+threshold+creation

If you look at my 2017+ posts, you should find that I have repeatedly attached the URL to an article where physicists showed how to calculate pion threshold creation and how to convert from CoM to lab frame..

Check this out https://galileo.phys.virginia.edu/classes/252/particle_creation.html

 

Quote

Do they accelerate away from the region where the "parent" particle was?

Acceleration means change of velocity. Fly through vacuum ("near vacuum conditions") with no interactions is continuous without disruptions and at constant velocity, until some interaction happens. The more particles, the more interactions, thus slowing down and losing (kinetic) energy.

In particle accelerators, physicists specifically place strong magnetic fields to find out what are charges of the newly created short-living particles. This forces charged particle flying in "circles", which directions and radius depends on applied magnetic field, particle kinetic energy/velocity/momentum, charge, etc.