Quantum Mechanics & Relativity: Vacuum Connection?

[DaTario]

Hi All,

Once in the past I have heard that the vacuum in quantum mechanics, having its energy given by
$\sum_n \frac{1}{2}\hbar \omega_n$
was also obtained by methods of Einstein's relativity, through the claim that the vacuum should be a field which is invariant under a boost transformation. This means that there may be a certain EM field configuration where an observer, traveling in some velocity, will not perceive any change in its spectrum due to the Doppler effect. This field, thus, would have the same energy (spectrum) of the QM vacuum field.

Is this correct? Is there any reference to this result (in case it is correct )

Best wishes,

DaTario

 

[PeterDonis]

Once in the past I have heard that the vacuum in quantum mechanics, having its energy given by
$$\sum_n \frac{1}{2}\hbar \omega_n$$
was also obtained by methods of Einstein's relativity

Can you give a reference for this statement? Just saying "I have heard" is not enough; you need to say specifically from what source you heard it. And that source should be a valid reference--textbook or peer-reviewed paper--not a pop science article or TV special.

This means that there may be a certain EM field configuration where an observer, traveling in some velocity, will not perceive any change in its spectrum due to the Doppler effect.

A vacuum EM field configuration has no "spectrum" except in the vacuous (!) sense that all of the possible frequencies have zero amplitude.

This field, thus, would have the same energy (spectrum) of the QM vacuum field.

No, it means that EM field configuration you are describing is the QM vacuum field.

 

[DaTario]

Hi Peter,

An equivalent form of this question (without the " I have heard" part ) would be:
"Is it true that the an invariant EM field under boost tranformation can be put in equivalence to the vacuum defined in quantum mechanics?"

I would like this forums participants to help me tan eventual references.
I have a fuzzy ideia about such references, however. It seems that the group associated with this research works in Spain.

Anyway, if my question doesn't meet the requirements of this forum, I will agree with its removal.

Best wishes,

DaTario

 

[PeterDonis]

"Is it true that the an invariant EM field under boost tranformation can be put in equivalence to the vacuum defined in quantum mechanics?"

A vacuum EM field certainly can. An EM field that is not vacuum cannot, because it's not vacuum.

It seems that the group associated with this research works in Spain.

Once again, can you give a specific reference? What group? How do you know about them? We can't help you if we have no information.

 

[DaTario]

Dear Peter,

Excuse me, but I respectfully disagree. You may speak in the name of some of the staff members when you say that I have to give a reference for you to help me. But being a forum where others may contribute, you should not speak in the name of all, for someone may help me providing the references I am searching for. The OP is a quest for a reference on some result in science. It is not logical to require that I enter the very references I am searching for. If you understand this forum as a free area for contributions in science, you should allow for others to eventually make contributions with such a small hint given in the OP.

Hoping to have shown my point with the due respect,

Best wishes,

DaTario

 

[PeterDonis]

Hoping to have shown my point with the due respect,

All you have shown me is that you want other people to do the hard work of finding references for you. You said you "have heard" about a particular result. Where did you hear of it? You mentioned a group that you think works in Spain. How do you know about this group's existence? Where did you hear of it?

Instead of complaining, you could simply have answered these questions, which I have already asked you in previous posts, giving us all the information you do have, in order to help us help you find information that you don't have. But if you can't even give us the information you do have, how do you expect anyone to help you find more?

In any case, it looks to me like the only actual substantive question you asked has been answered. So this thread is closed. Please don't open another thread on this topic unless you are willing to provide more information than just "I heard" or "some group".