Energy levels in atoms & speed of interaction

[DanMP]

Which "force carrier"? You are only proposing changing the EM interaction, aren't you?

The speed of all force carriers and the speed of light "become" (is, in the other universe) Fc, instead of c.

I'm simply using your faulty logic in which you think by changing one fundamental constant, you keep everything else the same (which, if you are able to follow what has transpired in this thread, is a fallacy!).

I was able to follow that, in order to find the answer to my question, we cannot just use the equations proposed, with Fc instead of c.
So another approach is needed, something that deals with force carriers moving between electrons and protons. Do you know such an approach?

This thread has gone WAY beyond speculation.

What speculation? I just want to see if/how the atoms are influenced by the speed of force carriers.

 

[mfb]

The speed of all force carriers and the speed of light "become" (is, in the other universe) Fc, instead of c.

As discussed, this alone does not make sense.

You need measurements you can do within the universes, with answers that are dimensionless. Those are the only measurements you can reasonably compare between different physics. Usually those measurements are ratios. The fine-structure constant is something like a ratio, the ratio between different transitions in atoms is such a ratio (and it depends mainly on the fine-structure constant).

 

[DanMP]

As discussed, this alone does not make sense...

Well, I'm not convinced that it is impossible to see if/how the atoms are influenced by the speed of force carriers. I agree that to change from c to Fc in QM equations doesn't make sense, but it must be a way to see how the atoms are influenced by the speed of force carriers in one (our) universe, as I said, probably by making a computer model where force carriers traveling between electrons and protons are considered. Maybe it would be easier to consider in such a way (by using force carriers) something else, like a particle decay mediated by the weak force. What would happen with the half-life of a particle if weak force carriers "slow down"?

 

[mfb]

That speed on its own has no physical relevance, unless you have something to compare it with.
Give photons a mass, and you do change the energy levels.

What would happen with the half-life of a particle if weak force carriers "slow down"?

More massive W and Z? Most lifetimes should increase (for particles where weak decays are relevant).

 

[ZapperZ]

Well, I'm not convinced that it is impossible to see if/how the atoms are influenced by the speed of force carriers. I agree that to change from c to Fc in QM equations doesn't make sense, but it must be a way to see how the atoms are influenced by the speed of force carriers in one (our) universe, as I said, probably by making a computer model where force carriers traveling between electrons and protons are considered. Maybe it would be easier to consider in such a way (by using force carriers) something else, like a particle decay mediated by the weak force.

When you have made such a model and published it in PRL, do let me know.

Zz.

 

[DanMP]

More massive W and Z? Most lifetimes should increase (for particles where weak decays are relevant).

How an increase in mass for W and Z bosons would affect their speed? You can calculate, for instance, what mass they should have in order to decrease their speed to 1/3 of their usual/normal speed? And then, you can calculate how their new mass would affect the lifetime of a particle where weak decays are relevant?

By the way, I made a mistake saying that "the speed of all force carriers and the speed of light "become" (is, in the other universe) Fc, instead of c". I ignored that W and Z bosons have speeds lower than c, because they have mass. Sorry for that.

Give photons a mass, and you do change the energy levels.

You can calculate how a massive force carrier photon, traveling with 1/3 c, would affect an atom (energy levels, electron speeds, atomic radius)?

 

[mfb]

How an increase in mass for W and Z bosons would affect their speed? You can calculate, for instance, what mass they should have in order to decrease their speed to 1/3 of their usual/normal speed?

They do not have a "usual/normal" speed, but if you keep the energy constant, a larger mass means particles are slower. In the rare cases where you have real W and Z, otherwise speed is not a meaningful concept.

And then, you can calculate how their new mass would affect the lifetime of a particle where weak decays are relevant?

I would have to look up the formulas, but it is possible to calculate that.

You can calculate how a massive force carrier photon, traveling with 1/3 c

You cannot fix the speed to some number, the speed of massive objects depends on their energy, and virtual particles (which would be relevant for the atom energy levels) do not even have a well-defined speed.
A non-zero photon mass would change the field of the nucleus to a Yukawa potential, those have different energy eigenstates than 1/r potentials.

 

[DanMP]

You cannot fix the speed to some number, the speed of massive objects depends on their energy, and virtual particles (which would be relevant for the atom energy levels) do not even have a well-defined speed.

I thought that force carrier photons are virtual particles and do have a well-defined speed, c.
Anyway, my intention was/is to see how a change in force carriers speed would affect the atom, so, if we cannot "fix" the speed by changing the mass, maybe this mass increase/addition is not the solution to my problem.

They do not have a "usual/normal" speed, but if you keep the energy constant, a larger mass means particles are slower. In the rare cases where you have real W and Z, otherwise speed is not a meaningful concept.
I would have to look up the formulas, but it is possible to calculate that.

Although you/we cannot tell exactly how much week force carriers speed would decrease if their mass increases, it is interesting to see/calculate how the lifetime of a particle (where weak decays are relevant) would be affected.

 

[mfb]

I thought that force carrier photons are virtual particles and do have a well-defined speed, c.

Virtual particles do not have a position or speed. And you can argue that they do not exist at all.

The muon lifetime for example can be expressed as
$$\tau = \frac 1 \Gamma$$
with the decay width
$$\Gamma=\frac{G_F^2 m_\mu^5}{192\pi^3}I\left(\frac{m_e^2}{m_\mu^2}\right)$$
which uses the Fermi coupling constant
$$G_F=\frac{\sqrt{2}}{8}\frac{g^2(\hbar c)^3}{m_W^2}$$
where m_W is the W boson mass.
If you increase the W mass, you decrease the coupling constant, which decreases the decay width, which increases the lifetime. The lifetime is proportional to the fourth power of the W mass if we keep all other constants the same.

 

[DanMP]

...
If you increase the W mass, you decrease the coupling constant, which decreases the decay width, which increases the lifetime. The lifetime is proportional to the fourth power of the W mass if we keep all other constants the same.

Thank you.

Virtual particles do not have a position or speed. And you can argue that they do not exist at all.

Yes, I just read 2 articles about that (1 and 2), but still, is the EM force "carried" faster or slower than c?

 

[mfb]

Changes in the field do not propagate faster than c.

 

[DanMP]

Changes in the field do not propagate faster than c.

Of course not faster then c, but how fast?
And how? If virtual (force carrier) photons do not exist at all, how is EM force transmitted?

 

[mfb]

Of course not faster then c, but how fast?

With c. This does not change if you give photons a mass, but changes that spread out that fast will be negligible then.

And how? If virtual (force carrier) photons do not exist at all, how is EM force transmitted?

Via changes in the field. The field is the fundamental concept, particles (both real and virtual) are just things we make up to make calculations easier.

 

[DanMP]

With c. ...
Via changes in the field. The field is the fundamental concept, particles (both real and virtual) are just things we make up to make calculations easier.

Ok, thank you very much for all your answers.