Recoil of a hydrogen atom emitting Lyman alpha photon

[Geoff Simmons]

I am interested in what the recoil velocity of an initially stationary hydrogen atom in free space would be when it emits a Lyman alpha photon. I tried to do the calc and got about 3 metres per second which seems rather high.

 

[NascentOxygen]

Hi Geoff.

Perhaps our General Physics would be a suitable forum where you could post your question. If this is a homework exercise, you will need to use our physics homework forum and include your calculations/attempt.

This Introductions forum is just for saying "Hi".

EDIT: I see someone has moved the thread for you

 

[Bystander]

seems rather high.

Other than offending your intuition, what's bothersome about that result?

 

[Geoff Simmons]

Other than offending your intuition, what's bothersome about that result?

Errr... Thanks for the respectful response. A hydrogen atom in a nebula emits Lyman alpha. It recoils at 3 m/s. The photon travels through space for 5 years say, before being absorbed into an observer;s retina. In the meantime the hydrogen atom has recoiled hundreds of thousands of kilometers. When the photon is eventually absorbed, who is to say that the hydrogen atom recoiled in the right direction? It;s a failing of the standard model.

 

[e.bar.goum]

I am interested in what the recoil velocity of an initially stationary hydrogen atom in free space would be when it emits a Lyman alpha photon. I tried to do the calc and got about 3 metres per second which seems rather high.

That's about the same answer I get. I don't see any issue with it.

And the standard model doesn't even come into this problem, so I'm wondering how you got the idea that that is an issue.

 

[Geoff Simmons]

Thanks v much. The standard model produces the EPR paradox, photon entanglement and other quantum weirdness. The issue of photon momentum that I mentioned is just another problem with the standard model. We build our physics ever higher but should be ready to accept it may be built on ideas that just "seemed to work" at the time.

 

[nasu]

You fail to explain (so far) how is this a problem at all.
And this recoil is not really a matter of standard model. Unless you mean by it just "standard physics" or "current theories of physics".

Edit. Do you imagine the atoms in the hydrogen gas at rest before emitting a photon?
If not, what do you think are their average speed for a gas at the temperatures that make emission likely?

 

[Nugatory]

The issue of photon momentum that I mentioned is just another problem with the standard model.

Could we ask you to clarify what you mean when you say "the standard model"? The term has a generally accepted meaning (https://en.wikipedia.org/wiki/Standard_Model), but that meaning makes no sense here.

It's also not clear to me what problem you're seeing. The atom emits some electromagnetic radiation; this radiation carries some momentum so the atom recoils in the opposite direction and momentum is conserved.

 

[Geoff Simmons]

Sorry that my explanation was so incomplete. In the photon-as-a-particle (standard) model there is no problem. Momentum and energy are conserved. I was referring to the problem that the photon behaves as a widely dispersed wavefront while the atom recooils in a very precise direction. It's the counterpart of the "wave function collapse" problem, although it happens long before the wave function collapses. Apologies for the lack of clarity. It's easy to set up an experiment, for example by placing the atom at a focal point of an ellipsoidal mirror and observing the light focused at the other focal point, to prove that the photon behaves as if the wavefront disperses in a spherical form.. How then does the atom know what direction to recoil without knowing where the photon will finally be absorbed? It strikes me there is an interesting issue here. It's similar to the EPR paradox.

 

[e.bar.goum]

Sorry that my explanation was so incomplete. In the photon-as-a-particle (standard) model there is no problem. Momentum and energy are conserved. I was referring to the problem that the photon behaves as a widely dispersed wavefront while the atom recooils in a very precise direction. It's the counterpart of the "wave function collapse" problem, although it happens long before the wave function collapses. Apologies for the lack of clarity. It's easy to set up an experiment, for example by placing the atom at a focal point of an ellipsoidal mirror and observing the light focused at the other focal point, to prove that the photon behaves as if the wavefront disperses in a spherical form.. How then does the atom know what direction to recoil without knowing where the photon will finally be absorbed? It strikes me there is an interesting issue here. It's similar to the EPR paradox.

Simple: The atom also doesn't have a definite direction.

 

[Geoff Simmons]

Thanks. However the uncertainty principle doesn't solve this. In the case that the atom is as far away as Alpha Centauri, then it will have recoiled hundreds of thousands of kilometres before the photon reaches Earth. I think that a committed QM expert would be reduced to saying that the atom and the photon are "entangled". When the photon is finally absorbed, the position of the atom is suddenly communicated instantaneously. Not simple.

 

[Nugatory]

I think that a committed QM expert would be reduced to saying that the atom and the photon are "entangled". When the photon is finally absorbed, the position of the atom is suddenly communicated instantaneously. Not simple.

For better or for worse, you've restated the EPR problem - which I'll grant is not simple.

It's worth noting that observers in motion relative to one another may describe the interaction differently. One will say that the electron measurement comes first, "causing" the wave function of the photon to collapse; thanks to the relativity of simultaneity the other may just as correctly say that the photon measurement comes first causing the wave function of the electron to collapse first. Thus, whatever is happening doesn't remotely resemble anything that we'd naturally call "communication" - there is no sensible definition of the sender, the receiver, or the content of the communication.

 

[Nugatory]

In the photon-as-a-particle (standard) model there is no problem.

It's a bit of a digression here, but the photon-as-a-particle model is a red herring. No matter how we think about the emitted radiation, we end up in the EPR place: We know the total momentum of the system is zero so the momentum vectors of the two particles will be equal in magnitude and opposite in direction... But as far as the formalism of quantum mechanics is concerned, the direction of the two vectors is not determined until we've measure one them, even at an arbitrarily large distance from the other.

And PLEASE stop calling it the "standard model", if only because you're going to mess up other people's search queries.

 

[Vanadium 50]

but the photon-as-a-particle model is a red herring

So is the specific question asked: this question doesn't depend on the magnitude of the recoil.

 

[e.bar.goum]

Thanks. However the uncertainty principle doesn't solve this. In the case that the atom is as far away as Alpha Centauri, then it will have recoiled hundreds of thousands of kilometres before the photon reaches Earth. I think that a committed QM expert would be reduced to saying that the atom and the photon are "entangled". When the photon is finally absorbed, the position of the atom is suddenly communicated instantaneously. Not simple.

I was actually invoking entanglement, not the HUP. Sorry to be unclear.