# The C is the speed of photon ( light ) ?

1. Aug 5, 2011

### dailydc

Hello everyone .
In Einstein's famous formula E=mc^2 , the C is speed of photon in Vacuum or is different ?

2. Aug 5, 2011

### DaveC426913

A photon does move at c in a vacuum, yes. But c is a fundamental constant of the universe; it is not specific to the speed of photons.

3. Aug 5, 2011

### Pengwuino

Just to clarify something in case the OP gets tripped up here, 'c' is specifically the speed that a massless particle must travel at - it is indeed something fundamental to the universe. The photon has been measured to be massless to some very high precision though so people say 'c is the speed of light' with the pretty much universal implication that photons are massless.

4. Aug 5, 2011

### dailydc

Sorry for my English .

Yes , i know "C" could be attributed to the speed of gravity and other energy in vacuum .

But Someone said to me "C" is not exactly equal to the speed of photons in vacuum .
Rather "C" is limited a speed of photon in a vacuum
That Means "C" is higher that speed of photon in vacuum because a photon in vacuum arrest in bending of space .
I got confused

5. Aug 5, 2011

### HallsofIvy

Well, that someone was wrong. "c" is the speed of photons in vacuum. (Strictly speaking you should use "c", not "C".)

So am I. I have not idea what "a photon in vacuum arrest in bending of space".

6. Aug 5, 2011

### GrayGhost

My best guess, is that your "someone" was pointing out that light's speed can be measured as "slower than c" thru a gravity well, per an observer far removed fromm the well. Since gravity exists everywhere, then he may have been thinking that light should technically appear to travel just under c wrt any distant POV when considered over a very very large expanse. However no matter where one is in vacu, whether inside a gravity well or not, when light is measured in one's local area it is always precisely c.

GrayGhost

7. Aug 5, 2011

### WannabeNewton

How is that possible: one cannot even define velocity globally in arbitrary space - times.

8. Aug 5, 2011

### GrayGhost

Well, spacetime is warped by rest mass. The photon travels along the curvature within a gravity well. Although we know the curvature is there, we don't see the dent in space. In fact, we don't even see space, as it's transparent. Instead, we see the POE appear to reside in a place that it really does not ... as a brick at the bottom of a swimming pool. Ie, lensing effects. The curved pathlength light traverses thru a gravity well is longer than the straight euclidean path it appears to take. Since it always travels at c, and since the longer curved path appears "as a shorter euclidean straight path", the photon must appear to slow down as it traverses the well, and thus it "only appears" to travel slower than c, while in reality it always exists at c everywhere, all the time, at any local spot measured.

GrayGhost

9. Aug 5, 2011

### WannabeNewton

I'm saying your point doesn't make sense because you can't unambiguously define the velocity of a photon if you are making global measurements.

10. Aug 6, 2011

### GrayGhost

Hmmm. Well, velocity is defined wrt your own coordinate system as stationary. It seems to me that spacetime is flat, with wells here and there due to mass. All the wells are in the same direction wrt flat spacetime. All wells must create a longer pathlength (non-euclidean) than what is apparent (since we perceive them as euclidean). This concept should apply globally.

Here's a couple supporting links ...

http://www.speed-light.info/speed_of_light_variable.htm" [Broken] ...

In 1915 (10 years after Special Relativity) Einstein developed another theory called General Relativity that deals with gravitational fields and according to this latest theory the velocity of light appears to vary with the intensity of the gravitational field. For example, an observer outside gravitational fields measures the speed of light locally (in his location) at 299792.458 km/s but when he looks towards a black hole he sees the speed of light there to be as slow as a few meters/sec.​

A non-mathematical discussion of this can be found in:

'The Riddle of Gravitation,' Peter G. Bergmann, Charles Scribner's Sons, NY (1987).

See, in particular, pages 65-66 and, especially, the first full paragraph on page 66. Here, Bergmann takes the deflection of light by the gravitational field of a star as evidence of the decreased speed of light in a gravitational field.

The speed of light is _not_ constant in a gravitational field, but depends upon the reference frame of the observer. An observer anywhere in free fall will measure (locally) the traditional value of c. An observer sufficiently far away from the source of the field will conclude likewise that the speed of light is c (locally). But, the observer far away from the source will likewise conclude that the speed of light closer in to the source decreases as the source is approached.​

Also ...

http://www.speed-light.info/speed_of_light_variable.htm" [Broken] ... Suppose that you have a clock and a ruler (which is not rotating with respect to stars) and that you are not accelerating (inertial). Locally (where you are) you will always measure the speed of light at 299792.458 km/sec. However in the presence of gravity if I am at a different location than yours then I could measure the speed of light at your location to be any value smaller than or greater than 299792.458 km/sec. It depends on where I am and where you are (it depends on locations). So in the presence of gravity the speed of light becomes relative (variable depending on the reference frame of the observer). This does not mean that photons accelerate or decelerate. This is just gravity causing clocks to run slower and rulers to shrink.

GrayGhost

Last edited by a moderator: May 5, 2017
11. Aug 6, 2011

### harrylin

Yes, c is a vacuum constant which can be slightly different at different places as determined with a non-local measurement. In particular:

The average speed of light (= distance / propagation time ) is measured to decrease in the presence of the Sun,
- http://en.wikipedia.org/wiki/Shapiro_delay
(Note that this does mean that light decelerates and accelerates according to the definitions of such a standard measurement system.)

Einstein predicted the bending of light near the Sun due to the gradient in c (this made him famous),
- http://www.alberteinstein.info/gallery/gtext3.html [Broken]

Harald

Last edited by a moderator: May 5, 2017
12. Aug 6, 2011

### dailydc

hello

In other words,
He said if space was flat A photon does move at "c" in a vacuum
like left of picture

But we know space is not flat and is flexible , bending , warped or something like that In an overview .
like right of pictue

So the feature of space causes Photons can not easily move at "c" in vacuum and decrease their speed . is that true ?

13. Aug 6, 2011

### HallsofIvy

I believe Harrylin's post #11 addresses that.

14. Aug 6, 2011

### WannabeNewton

Parallel transport of vectors is path dependent in curved space - time ($\bigtriangledown_{\mu } \bigtriangledown_{\nu }U^{\alpha }\neq \bigtriangledown_{\nu } \bigtriangledown_{\mu }U^{\alpha }$) so you can't unambiguously define the velocity of something globally.

Last edited: Aug 6, 2011
15. Aug 6, 2011

### GrayGhost

Well, I would agree in that you will likely never get the result totally accurate. You should be able to approximate it well enough though. You do the best you can.

When we consider the path of a photon, it travels the shortest energy-free'est path thru spacetime. IOWs, stretch a string across the surface of a globe between London and Los Angeles, pull the string taut. It will be the shortest possible path between 2 points on a curved space. We don't care about the other possible curved paths between the 2 cities. The photon always takes that energy free'est path, a straight "and shortest possible" path thru curved space between emission and detection.

The avg speed of the photon is based upon a number of assumptions, which we assume are correct, or at least most correct compared to any other competing theory. There are many issues here. First, the assumed distance the photon appears to traverse. Then the assumption regarding the precise curvature of space on the grand scale. Add, the assumption as to the extent of gravitation the photon passed thru from there to here. The photon was emitted from a point in spacetime, and thus "from an earlier epoch" ... and thus travels thru space and time "as spacetime itself expands" during its trek. All such things need taken into account.

GrayGhost

Last edited: Aug 6, 2011
16. Aug 6, 2011

### WannabeNewton

I agree with you that global measurements of a photon's speed need not return c. All I'm saying is that due to that path dependence different observers making those global measurements will all get different values from one another so there won't be one single deviated velocity for the photon as per the global measurements (all made at the same time).

17. Aug 6, 2011

### bcrowell

Staff Emeritus
WannabeNewton is right. Sources like those in GrayGhost's #10 are referring to coordinate velocities, which are fundamentally meaningless. Those sources are making true statements about quantities that are of no physical interest.

18. Aug 6, 2011

### GrayGhost

Well, I suppose what you say here is true. The result of observers traveling different inertial paths thru curved spacetime is (generally speaking) relative motion. 2 different observers moving relatively measure space and time differently, no matter where they are. I'm not proficient in GR, so I'll defer to another here who knows more than I do. Harrylin seems to have a handle on this, maybe he can weigh in on your response here.

GrayGhost

19. Aug 6, 2011

### GrayGhost

While I agree they are coordinate vs proper, I'm not so sure I agree that coordinate values are "fundamentally meaningless". They exist, and they have their role in physics, which cannot be ignored. To say they are meaningless is to say that the difference between 2 observer's sense of NOW is meaningless. The transmission of light signals prove that coordinate values are something more than unreal or meaningless. It's merely a matter of understanding the difference between proper vs coordinate, IMO.

GrayGhost

20. Aug 6, 2011

### WannabeNewton

Physically meaningful quantities are those that remain invariant under a change of coordinates. Simple as that.