0.999999999c

[celox]

If EM radiation doesn't travel at c, Maxwell's equations don't work: you don't satisfy the wave equaton.

No? Even if EM radiation travel so close to c that we are currently unable to measure a difference? Du you have a pointer or an explanation why this is the case?

 

I think we can safely say that radio waves are still waves even if the car is in motion.

The difference in the waves would be so tiny, even if the car was driving at supersonic speed or beyond, that there would be no measurable visible/audible/whatever difference. Or is there a reason why something can't be a wave if traveling (slightly) below c? By my understanding, all matter are waves -- or are those waves a different thing altogether?

[Spyman]

Is it possible that the speed of light (in vacuum) is 0.999999999c (or some other number of 9's after zero) rather than 1c? Here I define "c" as the universal "speed limit", and obviously not as the speed of light itself. I know that it would have to be so close to c that we would (at least currently) be unable to measure any difference. But by my understanding, something accelerating very close to c (relative to us) would eventually move fast enought that it would seem to move at c[/i'] from all reference frames, as far as we would be able to measure it.

Interesting idea, would then gravity propegate at the correct "c" ?

 

If so one way would be to measure if there is a difference between the speed of gravity and light on a very large distance.

 

Also would such a difference imply that the speed of gravity is the cause for the universal speed limit ?

(If You try to move faster than Your own gravity it would pull You back.)

[swansont]

No? Even if EM radiation travel so close to c that we are currently unable to measure a difference? Du you have a pointer or an explanation why this is the case?

 

The difference in the waves would be so tiny' date=' even if the car was driving at supersonic speed or beyond, that there would be no measurable visible/audible/whatever difference. Or is there a reason why something can't be a wave if traveling (slightly) below [i']c[/i]? By my understanding, all matter are waves -- or are those waves a different thing altogether?

 

The solution to Maxwell's equations, which is a wave equation for EM radiation, fails if c depends on the speed of the source or observer. It doesn't matter if the difference is small - the solution fails. We see EM waves with high speed devices/particles as well as low speed ones.

 

Another implication of constant c is time dilation. This is also observed for high speed particles and lower speed devices.

[J.C.MacSwell]

Ok then you're fine.

 

 

Maybe I should say more than just that...

 

 

Suppose your speculation is correct.

 

Then i can switch reference frames' date=' and the same photon is moving faster than .99999c.

 

Speed is relative.[/quote']

 

OK Johnny, you know that some particles get up to pretty high speeds and presumably radiate EM.

 

Some of these particles are moving away from us.

 

Why don't we detect their radiation lazily strolling by from their direction?

[Severian]

To answer the original question, yes it is possible.

 

To travel at a speed less than c, the photon needs to have a non-zero mass. Current limits on the photon mass are that it is < 2x10^{-16} eV. That is extremely small (by contrast, the electron is 511,000 eV).

 

For the photon to have such a small mass would be very difficult to explain in a physics theory. Indeed, our current theory of QED requires that the photon be completely masses (and thus travel at c). Therefore there is a lot of circumstantial evidence that its mass is zero, but in principle this has not been proven (and never will be).

 

Edit: incidentally, if you put in the upper bound for the mass and work out the velocity of a photon with energy 1GeV (quite a high energy, but not too high, easily achievable with current tech) you would find a velocity of 0.99999999999999999999999999999999999999999999999999c (with about 50 9's in it) so it is definitely close to c (and would get closer with higher energies).

[celox]

The solution to Maxwell's equations, which is a wave equation for EM radiation, fails if c depends on the speed of the source or observer. It doesn't matter if the difference is small - the solution fails. We see EM waves with high speed devices/particles as well as low speed ones.

Interesting. However, I'm not saying that c depends on the speed of source or observer. I define c as an upper limit -- a constant (just as in SR). I define the speed of photons as seperate from, but very close to, c.

 

I guess the equation would still fail, however. Could the equation simply be an abstraction of a simpler or more complex one, the "real" equation?

 

Another implication of constant c is time dilation. This is also observed for high speed particles and lower speed devices.

As I'm not doing away with c as a physical constant, time dilation would still stand. The photon would also be subject to time dilation, as any other particle.

[celox]

Interesting idea, would then gravity propegate at the correct "c" ?

I don't know, as I have not thought much about gravity yet. If gravity is a property of space, probably. If it's a result of gravitons, probably not.

 

If so one way would be to measure if there is a difference between the speed of gravity and light on a very large distance.

Indeed. It will be interesting to see if more accurate measurements in the future will show a difference between the two. Definitely something I'll be keeping an eye on -- thanks!

 

Also would such a difference imply that the speed of gravity is the cause for the universal speed limit ?

(If You try to move faster than Your own gravity it would pull You back.)

Very interesting idea, I'll have to think this over. Thanks again!

[Severian]

Interesting idea' date=' would then gravity propegate at the correct "c" ?

[/quote']

 

If the graviton were massless, then yes.

 

Also would such a difference imply that the speed of gravity is the cause for the universal speed limit ?

(If You try to move faster than Your own gravity it would pull You back.)

 

No. Just as QED itself does not cause the speed limit (ie there would still be a speed limit even if the photon didn't exist), gravity cannot cause the speed limit either. It is a direct consequence of Special Relativity.

[celox]

Severian,

 

Exactly what I wanted to know, thank you!

 

I see your point, and why a sub-c speed of light is seen as improbable. However, I personally see the idea of anything moving at c as perhaps equally unbelievable. The same goes for a particle without mass. I know that human logic may not apply -- but as long as there is a possibility, I don't think we should entirely give up on the idea. Well, at least I won't.

[Severian]

I see your point' date=' and why a sub-[i']c[/i] speed of light is seen as improbable. However, I personally see the idea of anything moving at c as perhaps equally unbelievable. The same goes for a particle without mass. I know that human logic may not apply -- but as long as there is a possibility, I don't think we should entirely give up on the idea. Well, at least I won't.

 

Well, you have to ask what mass is first. In modern particle physics we think the fundamental mass of a particle is simply how strongly it interacts with a certain particle - called the Higgs boson. Since the photon doesn't (directly) couple to the Higgs boson, it has no mass. The Higgs boson (or rather, to be technically correct, the vaccuum expectation value of the Higgs field) holds the particle back, stopping it from travelling at c. Without the Higgs boson, all (fundamental) particles would be massless and travel at c (dynamical mass would still exist, but that is another story).

 

Now, with that definition, it is much easier to believe in massless particles - they are simply ones which don't directly interact with the Higgs boson. This happens all the time in particle physics - for example, the photon doesn't interact with the neutron either.

[celox]

Well, you have to ask what mass is first. In modern particle physics we think the fundamental mass of a particle is simply how strongly it interacts with a certain particle - called the Higgs boson. Since the photon doesn't (directly) couple to the Higgs boson, it has no mass. The Higgs boson (or rather, to be technically correct, the vaccuum expectation value of the Higgs field) holds the particle back, stopping it from travelling at c. Without the Higgs boson, all (fundamental) particles would be massless and travel at c (dynamical mass would still exist, but that is another story).

I understand. Then how does a massless particle in motion attain mass? Is that "kind" of mass also an interaction with the Higgs boson (I guess not, since you speak about dynamical mass without the Higgs)?

 

Now, with that definition, it is much easier to believe in massless particles - they are simply ones which don't directly interact with the Higgs boson. This happens all the time in particle physics - for example, the photon doesn't interact with the neutron either.

The Higgs boson is a hypothetical particle (I'm reading). Anyway, you're right -- it does make sense that way.

[Severian]

I understand. Then how does a massless particle in motion attain mass? Is that "kind" of mass also an interaction with the Higgs boson (I guess not' date=' since you speak about dynamical mass without the Higgs)?

[/quote']

 

The gaining of mass with increasing velocity is a result of the horrible way they teach relativity in high schools. What they call 'rest mass' in high school is the correct definition of mass. The problem is that the relation between momentum and velocity is not linear:

 

p = mv/sqrt(1-v^2/c^2)

 

In an attempt to maintain the classical equation p=mv, one could redefine 'mass' to be m/sqrt(1-v^2/c^2), but then it really is something completely different. It is much better to live with the non-linear relation between velocity and momentum.

 

By dynamical mass, I was meaning that (most of) the mass of composite particles is coming from the kinetic energy of the constituents, not their masses. (For example, a proton, which is two up quarks and a down quark, has a much larger mass than simply the sum of the down quark mass and twice the up quark mass. The extra 'mass' is coming from the quark's energies.)

 

The Higgs boson is a hypothetical particle (I'm reading).

 

Hopefully not for long. If it is there we will see it at the Large Hadron Collider, which is due to switch on in 2007.