# Speed of light same as light speed?

1. Oct 24, 2008

### Naty1

My question is whether the speed of light, as defined below, is precisely the same as the speed of light in free space, without gravity.

DISCUSSION
I'm trying to figure out if the standard value for "c" is or is not corrected for the very,very slight influence of earth's gravitational field (potential) for a stationary observer relative to earth's surface.

The definition appears to occur at the surface of the earth where there is a weak gravitational field; if the speed of light is defined from the frame of reference of a stationary observer on the earth's surface, the gravitational field will make the speed appear slightly different (slower) than if the observer were in gravitational free fall...or the definition were in a gravity free location.

So it seems like that gravitational acceleration (crude estimate below) may be enough to change the last few integers in the definition of light speed...but I did not do any calculations. In any event, even if all nine digits of light speed remain the same, there is still a slight possible theoretical difference. (In other words, a fixed frame of reference at the earth's surface is a coordinate type reference frame, right, where different speeds of light will generally be observed.)

DEFINITION
From http://math.ucr.edu/home/baez/physic..._of_light.html

Quote:

from Peter Bergmann's THE RIDDLE OF GRAVITATION,:

Quote:
....

2. Oct 24, 2008

### Jonathan Scott

Re: Lightspeed

Wherever you are, the speed of light at your own location is the standard value. That is the key point in relativity.

The variation with gravitational potential means that if you look at the apparent speed of light at some other location, it may appear to be slightly faster or slower than the standard value. The exact result depends on the coordinate system used to compare the speed, but in isotropic coordinates (which are normally the most practical ones for astronomical purposes), the apparent speed of light varies by a fraction equal to twice the change in gravitational potential, -GM/rc^2, at the points being compared.

3. Oct 24, 2008

### MeJennifer

Re: Lightspeed

Exactly, that is the only factor to hold on in understanding spacetime.

4. Oct 24, 2008

### Naty1

Re: Lightspeed

yes, you are both right...had I worded my question more carefully I would have been able to answer it myself....I should have asked:

ah,well, live and learn...or not...

5. Nov 11, 2008

### Naty1

Re: Lightspeed

Rereading this I now have some uncertainty...

Do the above answers imply that even an accelerating observer, such as one standing "stationary" at a point on earths surface, always observes local light at "c"? It looks that way from the answers.

Then why is the speed of light postulated as c, locally, only in a freely falling (non accelerating) frame? It sounds like this frame is necessary to observe constant c locally irrespective of gravitational potential.

I'm now have difficulty reconciling these two ideas.

6. Nov 11, 2008

### RandallB

Re: Lightspeed

Remember what Scott said about “the apparent speed of light at some other location” may be fast or slow.
The key word here is apparent.

All local locations will define a common physics where:
Every local observer will use these same physics definitions and that results in “c” for local light.

And when any “other location” looks at what you are using for “Meter” and “Second” (Including IMO even if you are an “accelerating observer” relative to them) and see your defined “c” as apparently slow or fast wrt to what they know to be “c”. When they apply all appropriate transforms to redefine their time and length to your reference frame they will get the same results as you from making the above physical measurements to establish the standards for meter & second to define a local values and thus for “c” as well.
(Granted if you are an accelerating observer those transforms will be difficult, and not something I want to try)

7. Nov 12, 2008

### DrGreg

Re: Lightspeed

All observers, accelerating or not, measure the local speed of light to be c.

Although the metre is officially defined as 1/299792458 light-seconds, that definition strictly works only in the infinitesimal limit. An observer measures the distance to an object by radar: time how long it takes for a there-and-back reflected signal and multiply the seconds by (299792458/2) to get metres. But, for an accelerating observer, or any observer in curved spacetime, that procedure is accurate only in the limit as the time interval $\Delta t \rightarrow 0$. In flat spacetime the true answer is defined to be the radar distance measured by a co-moving inertial observer (an inertial observer travelling at the same speed as the accelerating observer at the moment the measurement is made). In curved spacetime there is no unique answer because there are no globally-inertial frames, only locally-inertial frames. You could say distance is only a local concept, although it's nevertheless possible to integrate local distances to get longer distances, but you need to specify how the integration is performed.

What has that got to do with the question? Well, the local speed of light is c by definition. But if an accelerating observer, or any observer in curved spacetime, tries to measure the average speed of light over a distance, the answer might not be c, but the answer will converge to c as the distance converges to zero.

8. Nov 15, 2008

### Naty1

Re: Lightspeed

"But, for an accelerating observer, or any observer in curved spacetime, that procedure is accurate only in the limit as the time interval . In flat spacetime the true answer is defined to be the radar distance measured by a co-moving inertial observer (an inertial observer travelling at the same speed as the accelerating observer at the moment the measurement is made). In curved spacetime there is no unique answer.."

I think I understand...BUT it seems to conflict with Einstein/s needd for inertial frames to view "c".

If even accelerating observers (standing till on earth's surface) see light locally at "c" then why did Einstein specify local free falling frames as the inertial frames for measuring local light speed with gravity and inertial frames (generally) for special relativity. Is your description an "update" from Einstein's understanding?

My understanding is that when measuring light we observe "c" in flat spacetime, both locally and distant as space is uniform. That means when we freely fall in the presence of gravity locally: Standing on earth's surface , we are not in free falling frame, but an accelerating frame (g)...a coordinate frame where "c" seems to depend on gravitational potential (curvature). The difference is minor because gravity is low, I know, but this is a question of principle.

Does anyone standing in any gravitational potential see light locally as "c"?? Apparently "yes" if it's instananeous, as you say. But Einstein said Only a free falling observer sees "c" locally.

Another way to phrase the question, I think, would be this: If we can observe a distant speed of light apparently slowing, say approaching a black hole event horizon, due to distant curved space and the fact we observe from a coordinate frame, why would we not also observe a different speed of light from "c" locally in curved space when in the same coordinate frame? I would think we'd measure two different values from "c", slower for the distant, closer to "c" for the local....

Last edited: Nov 15, 2008
9. Nov 15, 2008

### Naty1

Re: Lightspeed

Finally I got to one piece of my own puzzle....the test particle in GR:

(from http://math.ucr.edu/home/baez/einstein/node2.html )

10. Nov 17, 2008

### DrGreg

Re: Lightspeed

If you look at what I said, I first of all defined things for inertial (= free-falling) observers, and then extended the concept to a non-inertial observer defined in terms of a local co-moving inertial observer. The non-inertial point of view arises by definition.

I am working from memory and my own understanding and haven't looked up the exact words Einstein used. Just because we choose to use inertial observers to make certain measurements doesn't always mean we couldn't have chosen non-inertial observers in some circumstances. The theory is built around inertial observers but later we find that some (but not all) concepts may still work (locally) for non-inertial observers.
That's all correct. (But remember, someone at the top of a skyscraper will have their own frame that differs slightly from someone at street level, so each measures light at c at their own location, but slightly different at each other's location.)
I don't know what Einstein actually said without looking it up, but I'd omit the word "only"!
Sorry, I'm not sure I understand what you ask here.

11. Nov 17, 2008

### Kopachris

Re: Lightspeed

c is defined as the speed (it's not usually a vector, but sometimes is) of light in a vacuum, 299,792,458 m/s. Special Relativity says that all velocities are relative to each other except the velocity of light. Light in a vacuum always goes at c to an outside observer. If you shoot a beam of light in front of you while you're going at 90% the velocity of light, you will see the light going 10% the speed of light while an outside observer will see it going at c. Light is always globally c, not locally c. Einstein concluded from that that time becomes dilated as a moving object approaches c.

Last edited: Nov 17, 2008
12. Nov 17, 2008

### MeJennifer

Re: Lightspeed

You are mistaken, you will see light going at 100% of the speed of light.

13. Nov 17, 2008

### Kopachris

Re: Lightspeed

Woops! I forgot about time dilation. Duh!

14. Nov 17, 2008

### Naty1

Re: Lightspeed

Dr Greg posts:

I appreciate your patience discussing this!!!! Using your definition, I understand how you reach your conclusions. Everybody sees local light at "c" with your conventions.

Is this a generally accepted and understood convention? I can't reconcile other things I read with your perspective. Other descriptions are not as clearly defined as yours.

This thread is becoming painfully close to a prior one:
How does light slow in the presence of gravity?

I am basically still asking if all observers, inertial and non inertial as well , observe light locally at "c" in conventional physics discussions.

I'd like interpretations on the following, and then I'll stop asking this same question.

(http://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/speed_of_light.html)
This includes consecutive paragraphs, no omissions, which to me appear inconsistent.

My comment:This sounds like all observerssee light at "c"...inertial and noninertial.

Thanks to all for input!!!

Last edited: Nov 17, 2008
15. Nov 18, 2008

### DrGreg

Re: Lightspeed

The answer should be "yes" but there is a catch. It depends what coordinate system you use. If you use your own proper time as the 0th coordinate (locally) and three orthogonal "physical distances" as your 1st 2nd & 3rd coordinates (locally), the answer is "yes" (locally). But in GR you are free to use any coord system you like, so you could choose the "wrong" coords and the answer could be "no".

I think in discussions people sometimes "play safe" and discuss inertial observers only to avoid complications with non-inertial frames.

I'm in a hurry and haven't had time to properly read the quote you gave, but I think the differences you found in your quote are probably referring to non-local measurements when they say the speed of light might not be c.

16. Nov 23, 2008

### Naty1

17. Nov 23, 2008

### JesseM

Re: Lightspeed

Why do you say that? The sentence immediately after the one you put in bold mentions that in the frame of the observer "at rest relative to a source of gravity" (i.e. not a freely-falling frame and therefore not locally inertial), "the speed of light can differ from c". Only in an inertial frame is the speed guaranteed to be c.

18. Nov 24, 2008

### Naty1

Re: Lightspeed

Hi JesseM: MY post:

was intended to addresss my interpretation of item #5, post 14:

I am unsure what to make of (5)...seems like there are no restrictions.

19. Nov 24, 2008

### Naty1

Re: Lightspeed

Here is what clears this situation up for me:

Under another thread, Light Velocity Measurements, I posted my conclusion:

George's post, # 2:

(and this was confirmed by MeJennifer)

is by convention measured according to DrGreg's definition, post #7

.

In the above thread, DrGreg explained:

* meaning physical curvature

The thing that had me stymied all this time was my strong suspicion that an accelerating observer would encounter apparent curvature when making observations (called visible by DrGreg,above) due to the equivalence principle; in the popular physics books I have been reading the past few years they only say inertial observers measure "c", not accelerating observers, but the context of their assertion was never made clear. I now suspect that others who have read books by Greene,Smolin, Kaku, etc, are, like me, the source of so many repeated questions on this forum about the speed of light. If we all use DrGregs "summary" above on this forum I'm all set....
and really aprpeciate the feedback to help me.

I'd like to find the FAQ for constant light speed (an item in discussion under general physics at the moment) and see if this is addressed there.....if somebody will confirm the above explananation I'll try to include it in the FAQ....