Lorentz violating severely restricted: Mqg/Mplank > 1200

[atyy]

What, if the single photon was due to a detector malfunction? Do you know all of its inner workings to be sure?

In the real world you never get 100% security, yes. But if a different group with a different detector got the same result, then I think people would start to accept a strong word like "falsify". This is exactly not about betting, but about careful language.

The LHC has two technically completely different detectors constructed and operated by different groups. Is it a waste of resources?

This is an interesting question - the experiment should be done by a "competent" group - but the competence can only be verified by another "competent" group(s) repeating their results. But if the competence is verified, then the first observation would constitute the the falsification.

Like the proof of Fermat's last theorem - when is it proved?

It's like the event horison - forms in the past but known only in the future?

Edit: I guess Perelman's proof would illustrate the sociological issues better?

 

[ensabah6]

Would quantization of time break lorentz invariance? does string theory posit that time is infinitely continuous?

Would it break Lorentz invariance if both space and time are quantized, and all photons of all frequencies can travel one Planck length per Planck time?

 

[Micha]

This is an interesting question - the experiment should be done by a "competent" group - but the competence can only be verified by another "competent" group(s) repeating their results. But if the competence is verified, then the first observation would constitute the the falsification.

Like the proof of Fermat's last theorem - when is it proved?

It's like the event horison - forms in the past but known only in the future?

Edit: I guess Perelman's proof would illustrate the sociological issues better?

I consider these questions to be mostly artificial, created by our language.

Proof, falsification and so on, these words work like Boolean algebra, either true or untrue. Anything in the real world however, like collecting evidence, is a continuous process. Only our impatient mind wants to put labels. And they are useful for orientation.

I just think, Lubos is a little impatient to put them, which brings critics and discussion, where unnecessary.

 

[atyy]

Proof, falsification and so on, these words work like Boolean algebra, either true or untrue. Anything in the real world however, like collecting evidence, is a continuous process. Only our impatient mind wants to put labels. And they are useful for orientation.

Yes, continuous is better than discrete - otherwise you violate Lorentz invariance

 

[Micha]

Yes, continuous is better than discrete - otherwise you violate Lorentz invariance

 

[lumidek]

Hi, Lubos

I see you went into this issue by answering ensabah6's post. Thank you for doing so.

Nevertheless, the propagation speed of massless particles, in this case the photon,
is often not equal to c even if the theory is Lorentz, invariant, with the best know
example the flat spaces with an even number of spatial dimensions which have photon
Green functions which are non-zero inside the light cone. (Figure 1 http://physics-quest.org/Higher_dimensional_EM_radiation.pdf" )

Gravitational lensing is another case where you get a dispersion of the photon propagator.

So it doesn't seem that easy for string theory to escape dispersion due to its complicated
geometry paths at Planck scale (except for the trivial Brane world case of course)

Do you want to say that you expect that the holonomy requirements which lead to
CY and G2 manifolds should be responsible for the cancellations of the non-light cone
paths? and if so do you have any interesting links?

Regards, Hans

Dear Hans, the constancy of the speed of light in the vacuum - regardless of the motion of the source, observer, or frequency - is a postulate of special relativity, so it's valid everywhere as long as relativity is taken seriously.

One may produce theories with a "different light", building upon special relativity. Massive light will obviously move slower than the "speed of light" (= the ultimate cosmic speed limit). There are good theoretical and experimental reasons to think that light can't be massive. Also, in string theory, one can slow the light down by the B-field two-form.

If there's one, gravitons continue to move by the maximum speed - which is often misleadingly called "speed of light" - while the photons may become slower. But the B-field in the (realistic) vacuum must be zero because of many other reasons, within string theory or independently of string theory.

In the context of a curved space, the motion "by the speed of light" is generalized to "motion along null trajectories". All light in GR is moving along null trajectories. Nothing is changed about it in the case of light bending (quite on the contrary, the light-like shape of the trajectory is crucial in any calculation of light bending), and nothing is changed about it because of G2 holonomy of compact manifolds in string theory, other shapes, embedded branes or fluxes, or any other feature of string theory.

The constancy of the speed of light is a fundamental and universal law of physics and you're confusing yourself if you want to think that any of the things you mentioned - or almost any other effect - destroys the validity of this postulate of relativity. It doesn't. And it doesn't destroy the validity of any consequence of relativity, either. It remains true in string theory as well as any other theory that is compatible with the observations of spacetime geometry as known in 2009. Relativity is a universal set of rules about the relationships between space and time, momentum and energy, electricity and magnetism, and other things. It's valid at all distance scales.

 

[Dmitry67]

I wonder what superstring theories tell about this: http://en.wikipedia.org/wiki/Faster...t_.28Casimir_vacuum_and_quantum_tunnelling.29
-- Scharnhorst effect

Is it always so small? Even on the planks scale?
ALso no matter how small is the difference, the "c" in all formulas is the apparent light speed (reduced by the vacuum) or the fundamental one?

 

[Hans de Vries]

Hi, Lubos

Thank you for replying, I do appreciate it.

Dear Hans, the constancy of the speed of light in the vacuum - regardless of the motion of the source, observer, or frequency - is a postulate of special relativity, so it's valid everywhere as long as relativity is taken seriously.

One may produce theories with a "different light", building upon special relativity. Massive light will obviously move slower than the "speed of light" (= the ultimate cosmic speed limit). There are good theoretical and experimental reasons to think that light can't be massive. Also, in string theory, one can slow the light down by the B-field two-form.

I was referring here to the standard theory where the Green's functions of the photon
in even dimensional spaces (2n+1d) are non zero inside the light-cone. (although still
expressed in the Lorentz invariant parameter t²-r²)

So, although the Green's functions are mostly concentrated on the lightcone, they
are not 100% so, and there is dispersion. This is the origin of the fact that Huygens
principle is not valid for (2n+1d) spaces. There was a discussion on this a while ago
at sci.physics.research.

You may find my old derivation the most accessible which is http://physics-quest.org/Higher_dimensional_EM_radiation.pdf" , but it was not the
first. Some relevant links:
[1] S. Hassani, Mathematical Physics, (Springer-Verlag, New York, 1998)
Is mentioned to contain a complete derivation of the massless propagators in the space-time domain in any dimensional space.

[2] D. V. Gal'tsov, Radiation reaction in various dimensions, Physical Review D 66, 025016 (2002). hep-th/0112110
http://arxiv.org/abs/hep-th/0112110

[3] Cardoso et. al. Gravitational Radiation in D-dimensional Spacetimes, Physical Review D 67 064026 (2003). hep-th/0212168
http://arxiv.org/abs/hep-th/0212168Regards, Hans

 

[lumidek]

I wonder what superstring theories tell about this: http://en.wikipedia.org/wiki/Faster...t_.28Casimir_vacuum_and_quantum_tunnelling.29
-- Scharnhorst effect

Is it always so small? Even on the planks scale?
ALso no matter how small is the difference, the "c" in all formulas is the apparent light speed (reduced by the vacuum) or the fundamental one?

Dear Dmitry, good points.

These Casimir changes to the speed of light are correctly derived from low-energy approximate physical theories, and because string theory reduces to them at distances longer than the Planck scale, it also reproduces the conclusions about the speed-up in the Casimir context.

The constancy of the speed of light refers to the vacuum, and when you have the Casimir plates, it's no longer considered "vacuum". Still, if one properly calculates how quickly the "information" in the light can be transmitted, this speed never exceeds the speed of light in the vacuum.

 

[lumidek]

Hi, Lubos

Thank you for replying, I do appreciate it.

I was referring here to the standard theory where the Green's functions of the photon
in even dimensional spaces (2n+1d) are non zero inside the light-cone. (although still
expressed in the Lorentz invariant parameter t²-r²)

So, although the Green's functions are mostly concentrated on the lightcone, they
are not 100% so, and there is dispersion. This is the origin of the fact that Huygens
principle is not valid for (2n+1d) spaces. There was a discussion on this a while ago
at sci.physics.research.

You may find my old derivation the most accessible which is http://physics-quest.org/Higher_dimensional_EM_radiation.pdf" , but it was not the
first. Some relevant links:

[1] S. Hassani, Mathematical Physics, (Springer-Verlag, New York, 1998)
Is mentioned to contain a complete derivation of the massless propagators in the space-time domain in any dimensional space.

[2] D. V. Gal'tsov, Radiation reaction in various dimensions, Physical Review D 66, 025016 (2002). hep-th/0112110
http://arxiv.org/abs/hep-th/0112110

[3] Cardoso et. al. Gravitational Radiation in D-dimensional Spacetimes, Physical Review D 67 064026 (2003). hep-th/0212168
http://arxiv.org/abs/hep-th/0212168


Regards, Hans

Dear Hans, very good points. Indeed, the Green's functions are zero or nonzero inside the light cone depending on the dimension. But this fact doesn't mean that the light doesn't move by the speed of light.

There are several kinds of Green's functions and they differ in details of their interpretation and behavior. Generally, they're the response functions, and any point inside the future light cone of P is allowed to "respond" to changes at point P.

But the propagation of physical photons is only governed by the so-called "on-shell physics", namely the behavior of the Fourier-transformed Green's functions - which are functions of energy and momenta - near the on-shell loci of the momentum space, e.g. near E^2=p^2.c^2 in this case.

If you change the momentum Green's functions away from this locus arbitrarily, the propagation of the light won't be affected, but the behavior of the spatial Green's functions inside the light cone will. This proves that not all information in the Green's functions is relevant for questions about the propagation of physical particles: for example, field redefinition leads to completely different Green's functions but completely the same propagation of physical particles. So you must be very careful when you try to extract conclusions about the propagation from the Green's functions. You have apparently used an algorithm that was oversimplified - well, it was incorrect.

Well, it's true that the strong quantitative version of the Hyugens principle fails in odd spacetime dimensions because of the comment you wrote.

 

[Eelco]

Dear Hans, the constancy of the speed of light in the vacuum -
The constancy of the speed of light is a fundamental and universal law of physics and you're confusing yourself if you want to think that any of the things you mentioned - or almost any other effect - destroys the validity of this postulate of relativity. It doesn't. And it doesn't destroy the validity of any consequence of relativity, either. It remains true in string theory as well as any other theory that is compatible with the observations of spacetime geometry as known in 2009. Relativity is a universal set of rules about the relationships between space and time, momentum and energy, electricity and magnetism, and other things. It's valid at all distance scales.

Or so you assert.

I agree with you, that the role of science is to reduce a mess of observational data to a minimum of elegant principles, that reproduce the observational data as an emergent feature.

Sometimes, one makes missteps along the way. One embraces fundamental truths, which turn out to be only approximate truths in retrospect. Euclidian geometry, gallilean relativity, to name just a few.

Sometimes, the way forward, is to take a step back. Lorentz invariance may be just such a case. You seem to treat it as an article of faith. << personal insult removed by Mentors >>

 

[Hans de Vries]

Sometimes, the way forward, is to take a step back. Lorentz invariance may be just such a case. You seem to treat it as an article of faith.

Well, if religion is a belief without sufficient proof then Special Relativity
is certainly no religion, to say the least...

For string theorists any proof that Lorentz invariance holds at "all" length
scales is of course welcome. Otherwise they would not only have to deal
with a complex geometry at Planck scale but also with a deviation of one
most elementary principles of physics. Not really a workable situation...

Regards, Hans

 

[MTd2]

Well, if religion is a belief without sufficient proof then Special Relativity is certainly no religion, to say the least...

As you say in the following paragraph, he implies invariance at all scales. So, that is religion for you too, since you imply doubt Lorentz invariance at all scales.

 

[Eelco]

Well, if religion is a belief without sufficient proof then Special Relativity
is certainly no religion, to say the least...

Neither was Euclidian geometry. Euclidian geometry is no religion, but asserting that geometry could only ever possibly be Euclidian, because you say so, is a religious attitude, even without any observational evidence to the contrary.

Does the fact that you cannot conceive of any other possibility prove it must be so, or is it evidence of your own limitations?

For string theorists any proof that Lorentz invariance holds at "all" length
scales is of course welcome. Otherwise they would not only have to deal
with a complex geometry at Planck scale but also with a deviation of one
most elementary principles of physics. Not really a workable situation...

Ditching euclidian geometry could even more aptly be described as 'not really a workable situation'.

It is ofcourse perfectly workable, the trick is finding an alternative paradigm. Or maybe, the real trick is wanting to find an alternative paradigm, which indeed probably isn't that welcome, if youve invested the best years of your life into one already.

 

[Dmitry67]

Dear Dmitry, good points.

These Casimir changes to the speed of light are correctly derived from low-energy approximate physical theories, and because string theory reduces to them at distances longer than the Planck scale, it also reproduces the conclusions about the speed-up in the Casimir context.

The constancy of the speed of light refers to the vacuum, and when you have the Casimir plates, it's no longer considered "vacuum". Still, if one properly calculates how quickly the "information" in the light can be transmitted, this speed never exceeds the speed of light in the vacuum.

Thank you
Whats about different sorts of very dense "false vacuum" very soon after the Big Bang?
In the reply above, by "vacuum" do you mean
* the lowest energy vacuum, like ours (but it is not guaranteed to be the lowest one!)
* the 'current' vacuum in the Universe (so at a time of the false vacuum we should use the false vacuum)?
* Could be the Casimir effect (and FTL between plates) much stronger in the false vacuum?

 

[Hans de Vries]

As you say in the following paragraph, he implies invariance at all scales. So, that is religion for you too, since you imply doubt Lorentz invariance at all scales.

The difference between All length scales and "All" length scales
(all relevant length scales) is an altogether different discussion.

I would think that Lorentz invariance can be an emergent effect but
it's certainly not trivial because of the extreme accuracy and specifically
in this case: The total lack of dispersion.

Regards, Hans

 

[lumidek]

Or so you assert.

I agree with you, that the role of science is to reduce a mess of observational data to a minimum of elegant principles, that reproduce the observational data as an emergent feature.

Sometimes, one makes missteps along the way. One embraces fundamental truths, which turn out to be only approximate truths in retrospect. Euclidian geometry, gallilean relativity, to name just a few.

Sometimes, the way forward, is to take a step back. Lorentz invariance may be just such a case. You seem to treat it as an article of faith. << personal insult removed by Mentors >>

Except that the local Lorentz symmetry can't be an approximation, unless the whole structure collapses - a fact that Einstein realized very well and emphasized in all his essays. He's made many mistakes but this was not one of them, we know 1 century later. There exist approximate truths but there also exist generally valid principles, and relativity is clearly the latter (much like a few conservation laws, the general postulates of quantum mechanics, and, in the macroscopic context, the laws of thermodynamics).

The right religious analogy is between Lorentz violation and Allah. The difference between the Lorentz violation and Allah is that Allah has already been seen twice. ;-)

Making the bold and loud statements of your kind without any glimpse of any violation of relativity is, well... fails to be sensible at the basic level. Lorentz symmetry is a fact of Nature, regardless of the volume that you or someone else invests into the denial of the basic and most important laws of physics. These principles are the insights that the true physics knowledge is all about, and who doesn't understand them and their inevitability, just doesn't understand the core of the 21st century physics.

Incidentally, effective field theories are meant to be approximations but string theory can't be an approximation, either. If the world is described by string theory, there can't be any "small corrections" that can be added to physics of string theory. String theory can't be deformed, a fact that is demonstrated in the major textbooks of the subject. I know that the universal validity of some laws is extremely unpopular with the postmodernists who want everything to be "relative", but it's true, anyway.

 

[MTd2]

specifically in this case: The total lack of dispersion.

When you spoke about the gravitational lensing, I thought you were referring to the idea that some of the photons could go through slightly larger paths due to quantum fluctuation, and that the smaller the wavelength the more frequently it would go through such fluctuations and
the longer there would be the path. Speed of light would not be violated, but it would bring an apparent stochastic element to the time of arrival of such photons.

 

[lumidek]

Thank you
Whats about different sorts of very dense "false vacuum" very soon after the Big Bang?
In the reply above, by "vacuum" do you mean
* the lowest energy vacuum, like ours (but it is not guaranteed to be the lowest one!)
* the 'current' vacuum in the Universe (so at a time of the false vacuum we should use the false vacuum)?
* Could be the Casimir effect (and FTL between plates) much stronger in the false vacuum?

Dear Dmitry,

the false vacuum e.g. during inflation may have a higher curvature, i.e. it is a de Sitter space. So is the vacuum in our world. The isometry of the de Sitter space is the de Sitter group. Its contraction is the Poincaré group - and the latter is thus relevant for physics at distances much shorter than the radius of de Sitter curvature.

To make the sentence about the Lorentz symmetry strict, "vacuum" should be the lowest energy state of an asymptotically Minkowski superselection sector of the Hilbert space - an empty flat spacetime.

But that doesn't mean that the statement is completely wrong in any other context. It can be seen that the empty de Sitter space with the cosmological constant 10^{-120} in Planck units preserves the same statements, up to corrections of order 10^{-120} (or zero, in properly formulated statements).

The vacuum with some matter inside conserves the Lorentz symmetry, too. In fact, the Lorentz symmetry is supposed to act on all the states in the same superselection sectors, to make any sense and to be useful.

There are all kinds of "variations" of the idealized situation of the empty Minkowski space, and many conclusions from the empty space are still exactly valid while many others are valid up to corrections that can be shown to be small.

I can't enumerate all related statements in all conceivable contexts in this comment because that would be like listing all facts about physics: all of physics is, in some sense, encoded in the physics of the vacuum. Your question is just not specific enough to have a good answer.

The Casimir forces and the vacuum energy from a false vacuum are, at least in the first approximation, two independent corrections to the flat Minkowski space that simply add up. In the second order, their effects are nonlinear and don't just add up, but the addition is surely sufficient for virtually all situations worth considering (or measurable in practice).

Is there some reason why you're asking this completely technical question? I don't think it has any far-reaching consequences.

 

[lumidek]

The difference between All length scales and "All" length scales
(all relevant length scales) is an altogether different discussion.

I would think that Lorentz invariance can be an emergent effect but
it's certainly not trivial because of the extreme accuracy and specifically
in this case: The total lack of dispersion.

Regards, Hans

Well, Lorentz symmetry could have a priori been an emergent effect, an approximate fact that only arises in the long-distance approximation. Except that one can

1) show theoretically that unlike the baryon charge conservation, and its U(1) symmetry (which hold in the Standard Model because no Lorentz-symmetry gauge-symmetric renormalizable term involving the SM fields can be written down - but nonrenormalizable ones can!), the Lorentz symmetry can't be an accidental symmetry for complicated systems with many fields. The amount of fine-tuning needed to obtain a Lorentz-invariant long-distance limit from a Lorentz-violating short-distance fundamental theory is effectively infinite if there are many fields (and particle species). There is no reason - neither "dynamical" nor "anthropic" reason - why Nature would make such a huge amount of fine-tuning just in order to confuse us about the composition of the symmetries in Her physical laws.

2) show experimentally that the Lorentz symmetry holds not only at long distances, something that was shown by 100+ years of successful tests of relativity, but even at the Planck scale, as Fermi has just showed. The probability that the Lorentz violation is visible for other effects - so that it physically exists - but it just happens to be invisible for the propagation of photons, with a 1% accuracy, is negligible. Why would Nature play these silly games with us all the time?

Isn't the assumption of such games equivalent to the belief that there are elephants flying everywhere in the skies on Sunday evening but the laws of physics just prevent us from looking at them on Sunday evening and no one has noticed? All these possibilities are silly conspiracy theories, not legitimate hypotheses that should be put on par with relativity or other justified laws of Nature. Such conspiracy theories may always be made even more awkward to avoid a falsification at a new level, so you can never "quite" falsify all of them, but the goal of science is not to create increasingly artificial conspiracy theories, but rather increasingly unified theories that actually describe an increasing set of observations with a decreasing collection of input (assumptions, independent concepts, and parameters).

I just don't understand why you still treat this question - about the emergent and/or fundamental character of the local Lorentz symmetry - as an open one. It is no longer open in August 2009, much like the creationism vs evolution is no longer open. The Lorentz invariance holds at the Planck scale, too. Consequently, it can't be an emergent symmetry resulting from a high number of degrees of freedom conspiring in a way. This is an empirical fact by now. Get used to it.

 

[lumidek]

Neither was Euclidian geometry. Euclidian geometry is no religion, but asserting that geometry could only ever possibly be Euclidian, because you say so, is a religious attitude, even without any observational evidence to the contrary.

Does the fact that you cannot conceive of any other possibility prove it must be so, or is it evidence of your own limitations?

Ditching euclidian geometry could even more aptly be described as 'not really a workable situation'.

It is ofcourse perfectly workable, the trick is finding an alternative paradigm. Or maybe, the real trick is wanting to find an alternative paradigm, which indeed probably isn't that welcome, if youve invested the best years of your life into one already.

I have never said that the Euclidean geometry is the only possible geometry in mathematics. In fact, despite your dishonest and untrue indications otherwise, I have never made any similar wrong - and therefore unprovable - statement.

But it is simply true that there are only a few solutions (symmetry groups) to the principle that different inertial observers see the same laws of physics. Galilean symmetry, Lorentz symmetry, and Euclidianized Lorentz symmetry. This is a fact of group theory. The global geometry of space can be curved and the quantum phenomena in the spacetime may be quantum and may have a lot of corrections from different length scales (as measured by proper distances and times), but it's just a mathematical fact that the very kinematics of the spacetime can't be "deformed" without changing the amount of symmetry and physical degrees of freedom.

Quantum groups - special deformations of groups - may be a counterexample but it is almost certainly unphysical above 2+1 spacetime dimensions.

Different questions have different answers. Corrections to the laws of physics can't have "any form" you invent and can't influence "any aspect" of the laws of physics. Physics is simply not an "anything goes" business and silly conspiracy theories about "best years of life" by people who have no idea about physics can't change a Planck length about this fact.

 

[lumidek]

When you spoke about the gravitational lensing, I thought you were referring to the idea that some of the photons could go through slightly larger paths due to quantum fluctuation, and that the smaller the wavelength the more frequently it would go through such fluctuations and
the longer there would be the path. Speed of light would not be violated, but it would bring an apparent stochastic element to the time of arrival of such photons.

That's nice except that not only good theoretical reasoning but also *observations* unambiguously show that no such stochastic component in the arrival time of photons exists, and if they do, the coefficient controlling the width of such a "stochastic component" is smaller than 1 Planck length (or its positive power). Every person who actually looks around, instead of holding his head in the sand, knows that every single possibility and sentence you have written down has been ruled out by now.

 

[MTd2]

That's nice except that not only good theoretical reasoning but also *observations* unambiguously show that no such stochastic component in the arrival time of photons exists, and if they do, the coefficient controlling the width of such a "stochastic component" is smaller than 1 Planck length (or its positive power).

While a dispersion relation was ruled out in the way you describe, what you comment about a stochastic component was not.

 

[Fra]

I'm not speaking on behalf or Hans or anyone else, but I have a comment on this question of what's the point of coming up with these "weird" ideas such as emergent symmetries.

I just don't understand why you still treat this question - about the emergent and/or fundamental character of the local Lorentz symmetry - as an open one. It is no longer open in August 2009, much like the creationism vs evolution is no longer open. The Lorentz invariance holds at the Planck scale, too. Consequently, it can't be an emergent symmetry resulting from a high number of degrees of freedom conspiring in a way. This is an empirical fact by now. Get used to it.

FWIW, from my point of view this issue of emergent symmetries is much larger than just the local lorentz symmetry. The issues has IMO to do with the nature of physical law, as inferrable from real interactions and representable by a physical observer (which means I reject a mathematical reality where the laws of physics are written by some God).

There isn't a lot of mature research programs looking into this, but some philosophical arguments that can motivate is what smolin has tried to convey in his books, writings and talks about the reality of physical law.

There is a connection between the suggestion here that a sufficiently probable conclusion is true, and that observed laws (meaning inferred from a histoty of physical interactions) are timeless, and the objection to fundamental symmetries, since it seems not possible for an observer or system of finite complexity, to with certainty infer by means of a finite physical process (finite time) learn the truth about it's entire universe.

Smolin in one talk at perimeter raised the point of what is the justification of talking about eternal laws (or eternally certain laws, such as perfect objective realist minded symmetries) when the universe is as it seems, not infinitely old?

IMHO, there is a similarity between deductions in nature (like some suggest here that lorentz symmetry is known to be perfect) and the belief in perfect eternal laws (which are often represented/encoded in our mathematical models as symmetries).

Somehow observerd/inferred symmetries could be thought of as constraints on the systems actions, if we could understand the origin of symmetries better as processes I think it would hold a great potential to help solve unification and fine tuning problems.

But to just be able to THINK about this, we must be allowed to get our heads out of some of the current frameworks. Maybe this will lead somewhere, maybe not. But for sure no one can claim that there is nothing to see here.

/Fredrik

 

[Dmitry67]

Is there some reason why you're asking this completely technical question? I don't think it has any far-reaching consequences.

I am asking because your answer was unexpected.

I was thinking that there is a "fundamental" c. But as photons pass some time in a form of virtual pairs, then move slightly SLOWER then c.

You were saying that the apparent speed of light in vacuum (including the corrections from virtual particles) IS c, and between Casimir plates it is moving faster then c.

That sounds very strange. For example, if there are different massless particles with different probabilities to be slowed down, then they would move with slightly different "c" speed. Then what is a right one?

 

[Eelco]

I have never said that the Euclidean geometry is the only possible geometry in mathematics. In fact, despite your dishonest and untrue indications otherwise, I have never made any similar wrong - and therefore unprovable - statement.

I never made any such indications, I made an analogy. A perfectly valid one. People like you are the Kant of the 21th century. He 'proved' space was Euclidian, didnt you know? After all, how could it be any different?

You are bringing forth the exact same kind of arguments with respect to Lorentz symmetry.

But it is simply true that there are only a few solutions (symmetry groups) to the principle that different inertial observers see the same laws of physics. Galilean symmetry, Lorentz symmetry, and Euclidianized Lorentz symmetry. This is a fact of group theory.

Yeah. That is, assuming a continuous space-time: the very point of contention.

 

[Fra]

I'd like to add one more comment that I personally think is relevant to the general reasoning and arguments in is discussion that adds on to my previous comment.

About the reality of law, a common reasonable principle is that the laws of physics should look the same to all observers. Then fairly simple ideas on howto generate all observers give rise to various symmetries.

But this simple approach ignores the process of inference of the laws, from the point of this observer. Ie. how does a given arbitrary observer actually _infer_ the laws. Clearly a simple single observation isn't enough. And in this picture, how are laws distinguished from just any information this observer has about it's environment?

Also, how does the complexity of the observer, scale the above description? ie. how are the RULES of inference constrained by say the complexity of the observer?

I think these are relevant questions, that does put the nature and physical basis of what a symmetry is from a physical inference point of view - and not just from the point of pure mathematics.

IMHO, a possible result of this reasoning, is that not only does differences in states give rise to interactions as a result of a given symmetry, it is not posible to distinguish clearly the state of a symmetry and the state of anything, it seems to just be a matter of difference in stability and that law is in a certain sense the most stable state we see, but still generally possibly evolving.

/Fredrik

 

[atyy]

But this simple approach ignores the process of inference of the laws, from the point of this observer. Ie. how does a given arbitrary observer actually _infer_ the laws. Clearly a simple single observation isn't enough. And in this picture, how are laws distinguished from just any information this observer has about it's environment?

"The universe is secretly acausal"
http://arxiv.org/abs/0805.2183

"The universe may be in a zero entropy state, even though it appears (to us, internal observers) to possesses a higher entropy"
http://arxiv.org/abs/0802.0438

 

[lumidek]

I am asking because your answer was unexpected.

I was thinking that there is a "fundamental" c. But as photons pass some time in a form of virtual pairs, then move slightly SLOWER then c.

You were saying that the apparent speed of light in vacuum (including the corrections from virtual particles) IS c, and between Casimir plates it is moving faster then c.

That sounds very strange. For example, if there are different massless particles with different probabilities to be slowed down, then they would move with slightly different "c" speed. Then what is a right one?

Dear Dmitry, there surely *is* a fundamental speed of light "c", and it represents the speed of light in the vacuum. It defines the null trajectories in spacetime and the light cones. A configuration with Casimir plates is not a vacuum.

There can't be any paradoxes with causality arising in QED, not even in the presence of Casimir plates: every physicist who has studied this question agrees with that. And as far as I can say, it is impossible for the real information to propagate faster than the speed of light in the vacuum, either, as long as this speed is measured properly. That's a subtle question, however, because the electromagnetic field around Casimir plates is "preprogrammed" by entanglement relating different points in space, so the information can propagate faster, if you wish, if you forget that the distant places already knew about the information, too. One shouldn't forget such things.

Different, less physical speeds - such as phase velocity and even group velocity - may exceed "c", the speed of light in the vacuum. It's not in a direct contradiction with the universal speed limit because the objects that may be moving superluminally are not quite "physical". The information, when its location is correctly determined including all the entangled regions, can never propagate faster than "c", the speed of light in the vacuum.

 

[lumidek]

I never made any such indications, I made an analogy. A perfectly valid one. People like you are the Kant of the 21th century. He 'proved' space was Euclidian, didnt you know? After all, how could it be any different?

You are bringing forth the exact same kind of arguments with respect to Lorentz symmetry.

Yeah. That is, assuming a continuous space-time: the very point of contention.

Well, if the answer to question #1 is No and the answer to question #2 is Yes, then the analogy between #1 and #2 is likely not to be perfectly valid, right? In fact, it is perfectly invalid.

Again, I have never proved any wrong far-reaching statement of the kind you indicate, and I am not analogous to any person who has made such mistakes. The only person in the conversation of two of us who produces rubbish is you - and it's perfect rubbish, indeed.

I have explained why my statement was correct and your perfectly invalid and extraordinarily misguided analogies with some completely unrelated questions in the history of physics can't change this fact at all.