Exploring Possible Speeds of Photons in a Gravitational Field

[lfigo170]

Consider a photon moving in same direction with a gravitational field .
So the speed of photon must become greater than speed of light.
how its possible ?
please answer this then I'll ask my next questions.

 

[jtbell]

Consider a photon moving in same direction with a gravitational field .
So the speed of photon must become greater than speed of light.

Why do you think so?

 

[Polyrhythmic]

So the speed of photon must become greater than speed of light.

That's not correct, the photon doesn't get faster. Gravity can affect the frequency of light, and also change its direction, but it can't accelerate light beyond the vacuum velocity c, which is an absolute constant.

 

[Nabeshin]

Consider a photon moving in same direction with a gravitational field .
So the speed of photon must become greater than speed of light.
how its possible ?
please answer this then I'll ask my next questions.

No matter what the geometry of spacetime, light will always move along null geodesics, and objects moving on null geodesics are basically by definition moving at the speed of light.

 

[ApplePion]

That's not correct, the photon doesn't get faster. Gravity can affect the frequency of light, and also change its direction, but it can't accelerate light beyond the vacuum velocity c, which is an absolute constant.

This is not correct.

The speed of light in General Relativity is determind by setting the spacetime interval to zero for the path. The the amount of dx you get for the dt at any local point depends algebraically on the metric components. Thus dx/dt is not constant.

Light moving along the horizon of a massive body will be bent. One way to think of it is that the part of the bean moving at the higher altidude moves faster than the part at the lower altitude, causing bending, just as a bi-metallic strip with metals differing in coefficients of thermal expansion will bend under temperature changes.

 

[ApplePion]

Me <<the part of the bean >>

"Bean" (sic) should be "beam".

 

[Polyrhythmic]

This is not correct.
The speed of light in General Relativity is determind by setting the spacetime interval to zero for the path. The the amount of dx you get for the dt at any local point depends algebraically on the metric components. Thus dx/dt is not constant.

You're wrong, one has to differentiate between proper and coordinate speed. In a local frame, the proper speed of light will always equal to c, whereas the non-local coordinate speed may deviate from c.

 

[ApplePion]

<<You're wrong, one has to differentiate between proper and coordinate speed. In a local frame, the proper speed of light will always equal to c, whereas the non-local coordinate speed may deviate from c. >>

Your view is that because one *could* make a coordinate transformation to where the speed of light is c, that one *has* done that.

If one has a particle moving slower than the speed of c, one always *could* make a coordinate transformation so that it is at rest. But you don't think that all particles are at rest, do you?

 

[ApplePion]

You're wrong, one has to differentiate between proper and coordinate speed. In a local frame, the proper speed of light will always equal to c, whereas the non-local coordinate speed may deviate from c.

You should condider your earlier claim that gravity could change the frequency. But if you insist on using the local frame metrics rather than the actual metric, then the frequency would not change. So in one situation you use the actual metric, but in another use the local frame metric.

General Relativity is part of physics, not metaphysics. Quantities like metric have physical meaning. One must always use the actual metric in the coordinate system one is working in the.

 

[Polyrhythmic]

Your view is that because one *could* make a coordinate transformation to where the speed of light is c, that one *has* done that.

If one has a particle moving slower than the speed of c, one always *could* make a coordinate transformation so that it is at rest. But you don't think that all particles are at rest, do you?

My argument is not about rest frames, since for a particle moving at the speed of light, the concept of a rest frame is nonsense. It is about locality, the speed of light is locally a constant.
The frequency however can change, depending on the strength of the gravitational field. The phenomenon of gravitational redshift describes light with changed frequency, although constant velocity.

 

[ApplePion]

<< My argument is not about rest frames, since for a particle moving at the speed of light, the concept of a rest frame is nonsense.>>


That is why I specifically stipulated the particle was initially going slower than the speed of light. You seem to be responding to something I was very careful not to say.

<< It is about locality, >>

You are not arguing for locality. If we have a metric that is locally non-Minkowskian then locally the speed of light is not c. What you are arguing is that physical quantities take on values they have in different coordinate systems than the one employed. Just because you can make a coordinate transformation to make the speed of light c, that does not make the speed of light c in a DIFFERENT coordinate system.

From your argument you can just as well argue that gravity does not exist, being that you can always make a coordinate transformation to make the affine connection vanish. In reality if you have not made that transformation, gravity is still there. If you have not made a coordinate transformation to make the metric Minkowskian, the speed of light is not necessarily c.

<<The frequency however can change, depending on the strength of the gravitational field.>>

One can make a coordinate transformation to restore the frequency. (I'm not arguing that the frequency is thus shown not to change, I'm showing that from your erroneous argument one could reach that conclusion.)

 

[Polyrhythmic]

If we have a metric that is locally non-Minkowskian then locally the speed of light is not c.

That's just not true, the speed of light is locally c for any metric.

 

[ApplePion]

That's just not true, the speed of light is locally c for any metric.

Consider a photon moving in the radial direction in the standard Schwarzschild metric.

The spacetime interval along the beams path is zero.

This gives (g_rr)(dr)^2 + (g_00)(c dt)^2= 0

-1/ (1-2M/r)(dr)^2 + (1 - 2M/r)(c dt)^2 = 0

This gives dr/dt = c (1- 2M/r)

So it is not c.

One can make a coordinate transformation where the metric is Minkowskian at a point, and in that DIFFERENT new coordinate system the speed is c, but that is in a DIFFERENT coordinate system. The speed can change due to a coordinate transformation. Speeds are not scalar quantities.

You can also make the gravitational field at a point vanish. Does that make you think the statement "A mass distribution does not produce a gravitational field" seem reasonable?

A massive object changes the speed of light and it produces a gravitational field.

 

[Polyrhythmic]

What you're deriving there is not proper speed, but coordinate speed.

 

[lfigo170]

thanks for replies
but i found my answer
photon will be changed into Tachyon
http://en.wikipedia.org/wiki/Tachyon

 

[lfigo170]

That's not correct, the photon doesn't get faster. Gravity can affect the frequency of light, and also change its direction, but it can't accelerate light beyond the vacuum velocity c, which is an absolute constant.

But according to general relativity the speed of any massive body should be changed in a gravitational field.

 

[Polyrhythmic]

thanks for replies
but i found my answer
photon will be changed into Tachyon
http://en.wikipedia.org/wiki/Tachyon

No, it will not.

The speed of light is locally still a constant.

 

[WannabeNewton]

While for very large masses in free fall respective geodesics can be seen to diverge/converge, for general particles momentum along a geodesic will remain constant as long as the particle remains in free fall of course. If you are talking about a particle falling freely through flat space and then encountering space - time curvature due to some mass then I am sure the speed of the particle does not change; it simply follows the geodesics of said curved space - time.

 

[ApplePion]

<<The speed of light is locally still a constant>>

You are really misunderstandering the meaning of the term "local". You think "local" means "in local Minkowskian coordinates".

From your perspective there is no local gravitational field, being that in certain local coordinates the affine connection vanishes.

So do you want to say that there is no local gravitational field?

 

[ApplePion]

<<What you're deriving there is not proper speed, but coordinate speed. >>

So if I were to show you thatthe gravitational field in the Schwarzschild metric does not vanish, would you object, saying I was deriving the coordinate gravitational field, not the proper gravitational field?

 

[Polyrhythmic]

<<What you're deriving there is not proper speed, but coordinate speed. >>

So if I were to show you thatthe gravitational field in the Schwarzschild metric does not vanish, would you object, saying I was deriving the coordinate gravitational field, not the proper gravitational field?

Proper gravitational field? Are you even aware what the term proper in the context of relativity means? I rest my case, this discussion is pointless.