Scharnhorst, faster than light

[exponent137]

In http://www.nat.vu.nl/~scharnh/m16newsc.htm
it is described correction to the speed of light, if a measurement is made on 1 um. But, let us ignore practical problems: what happens at very small distances. Does speed of light converge or diverge? What QED calculations show?

 

[Dmitry67]

BTW I have another explanation why it won't break causality.
Light (between 2 plates) is in gravitational well (because plates can't be massless in order to resist Casimir tension), hence it is propagating SLOWER than C. Magnitude of this effect is superior than Scharnhors effect itself

 

[exponent137]

Maybe it is so.
But I asked only about theory of Scharnhors. Is it his calculation of c convergent or divergent. At 1 um it is larger 1 part in 10^36. How it is at still smaller distances?

 

[Creator]

In http://www.nat.vu.nl/~scharnh/m16newsc.htm
it is described correction to the speed of light, if a measurement is made on 1 um. But, let us ignore practical problems: what happens at very small distances. Does speed of light converge or diverge? What QED calculations show?

Hello exponent;
I took an interest in this some years ago...

First; the article is misleading. The increase in c doesn't just kick in at 1 u-meter; it goes as the inverse 4th power of plate seperation.

I haven't reviewed recently Scharnhorst's derivation (derived independently also by G. Barton), (I have it somewhere among a gazillion files), but I can tell you that the resultant formula for the velocity of light, v, between two Casimir conducting plates goes as c plus a constant times the cos^2 times the inverse of the 4th power of the plate seperation, (your interesting question forced me to look it up among my hard copies).

Obviously, this formula shows an increased c based on the modified vacuum energy density between the plates and shows that the max. velocity is normal to the plates, (cos^2 factor being the angle between the light ray propogation direction and the normal to the plates).

So in that sense any convergence is somewhat of a moot point.

(There is a factor of the inverse of the mass of electron to the 4th power in there also, making its value very tiny; and its applicablility is for the low frequency range).

More if interested.

Creator

 

[Demystifier]

BTW I have another explanation why it won't break causality.

But why are you afraid of breaking causality in the first place? If you accept the block-universe view of relativity (which you do), then the break of causality does not make any troubles.

 

[Demystifier]

An effect similar to the Scharnhost effect can also be obtained when Casimir plates are replaced by finite-temperature effects:
http://xxx.lanl.gov/abs/hep-ph/0301275 [Phys.Rev.D68:085008,2003]

 

[nismaratwork]

An effect similar to the Scharnhost effect can also be obtained when Casimir plates are replaced by finite-temperature effects:
http://xxx.lanl.gov/abs/hep-ph/0301275 [Phys.Rev.D68:085008,2003]

Thanks for the link, that was one of the best reads (in QM) I've had in a while.

 

[Creator]

BTW I have another explanation why it won't break causality.
Light (between 2 plates) is in gravitational well (because plates can't be massless in order to resist Casimir tension), hence it is propagating SLOWER than C. Magnitude of this effect is superior than Scharnhors effect itself

It may interest you to know that in an oft quoted seminal paper Drummod and Hathrell have shown that in a gravitational background just the opposite can be true.

http://link.aps.org/doi/10.1103/PhysRevD.22.343

"We calculate in QED the contribution to the photon effective action from one-loop vacuum polarization on a general curved background manifold, and use it to investigate the corrections to the local propagation of photons. We find that the quantum corrections introduce tidal gravitational forces on the photons which in general alter the characteristics of propagation, so that in some cases photons travel at speeds greater than unity. The effect is nondispersive and gauge invariant."

Furthermore, there is no need to make a supposition based on presumed causality violation. Here's an interesting note from CERN referencing Drummond and Hathrell and stating why it doesn't necessarily imply causality violation...
http://cerncourier.com/cws/article/cern/28606

Others have come to a similar QED conclusion...

http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6TVN-3YMWNY4-8S&_user=10&_coverDate=03%2F09%2F1995&_rdoc=1&_fmt=high&_orig=search&_sort=d&_docanchor=&view=c&_searchStrId=1436245201&_rerunOrigin=google&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=ee22b3b79052164d06751dbad6ef2db4

Creator

 

[exponent137]

Çreator, thanks for answer.
So this divergent(!) speed of light needs similar renormalisation as mass in charge.

Feynman proposes also other aspects of changed speed of light. He also uses it at calculation of renormalisation. He mentioned this also in his book "strange theory of matter and light". He uses only a few sentences.

What happens if we measure speed of light on a very tiny distance (let say 10^-30 m) without Casimir plates. What the measurements will give?

My opinion is that microscopic speed of light is infinite. Virtual particles give it finite speed.
This variable c gives also different view on Duff, that speed of light does not exist.

 

[nismaratwork]

Çreator, thanks for answer.
So this divergent(!) speed of light needs similar renormalisation as mass in charge.

Feynman proposes also other aspects of changed speed of light. He also uses it at calculation of renormalisation. He mentioned this also in his book "strange theory of matter and light". He uses only a few sentences.

What happens if we measure speed of light on a very tiny distance (let say 10^-30 m) without Casimir plates. What the measurements will give?

My opinion is that microscopic speed of light is infinite. Virtual particles give it finite speed.
This variable c gives also different view on Duff, that speed of light does not exist.

If that is the case, I wouldn't expect to see the divergence until or beyond the Planck scale.