Does Gravitational Time Dilation Affect the Speed of Light in Outer Space?

[jeremyfiennes]

TL;DR Summary

Due to gravitational time dilation, the speed of light in outer space will be higher than on Earth. Do astronomers use the corrected value?

Due to gravitational time dilation, the speed of light in outer space will be higher than on Earth. Do astronomers use the corrected value?

 

[Vanadium 50]

Due to gravitational time dilation, the speed of light in outer space will be higher than on Earth.

That is not true.

 

[jeremyfiennes]

Does the GPS not have a gravitational clock-speed correction based on this principle?

 

[Ibix]

I don't think there's a "corrected value", because the speed of light is always $c$. You may find that the coordinate speed varies, but that would depend on your coordinate system (it's one possible interpretation of Shapiro delay, for example).

What measurement did you have in mind?

 

[Ibix]

Does the GPS not have a gravitational clock-speed correction based on this principle?

No. That's gravitational time dilation, which isn't the same thing as a speed of light measurement.

 

[Vanadium 50]

If this is a thread on gravitational time dilation, it really needs to be retitled.

 

[jeremyfiennes]

So when the wikipedia says "(..) according to the general theory, the speed of a light wave depends on the strength of the gravitational potential along its path" (https://en.wikipedia.org/wiki/Shapiro_time_delay), that is wrong?

 

[Janus]

Even if you were considering the coordinate speed of light in deep space compared to that measured at the surface of the Earth, the difference only comes out to be ~ 20 cm/sec. That works out to about a 1/10 of a sec difference in travel time from Alpha Centauri to Earth. However, we don't know the distance to Alpha C to enough degree of accuracy for that to matter. With a star like Betelgeuse, the margin of error for its distance measurement is almost 150 light years.
The point being that with any measurements we make, there is going to be measurement error range that would far exceed that of not considering the coordinate speed for light.

 

[jeremyfiennes]

Ok. So it is basically correct, but irrelevant. Query answered. Thanks.

 

[Nugatory]

So when the wikipedia says "(..) according to the general theory, the speed of a light wave depends on the strength of the gravitational potential along its path" (https://en.wikipedia.org/wiki/Shapiro_time_delay), that is wrong?

It’s not exactly wrong, but very misleading. It’s worth taking a moment to understand what measured quantity they are calling “the speed of a light wave” (I will give them full credit for not saying “photon” though), compare with how that term is usually understood.

 

[Drakkith]

So when the wikipedia says "(..) according to the general theory, the speed of a light wave depends on the strength of the gravitational potential along its path" (https://en.wikipedia.org/wiki/Shapiro_time_delay), that is wrong?

No, they are just talking about something more like an 'apparent' speed than 'actual' speed, but the details are a bit complicated and involve different coordinate systems and such. The speed of light, from our point of view, appears slower when passing by massive objects because the light has a longer path to travel, not because its local speed at any point has changed.

 

[andrew s 1905]

I came across this that my help clarify the situation for the OP https://link.springer.com/article/10.1007/s13370-020-00761-w
Regards Andrew
PS the link goes to a paid for download. If you Google the title you can read it on line for free. "On the distinction between coordinate and physical speed of light in general relativity" Sorry even that does not seem to work now.

 

[jeremyfiennes]

I tried but got the same result. Abstract but no content. Never mind. Janus explained that what I thought was in principle correct, but that the effect was too small to be worth considering. Thanks.

 

[Ibix]

It’s not exactly wrong, but very misleading. It’s worth taking a moment to understand what measured quantity they are calling “the speed of a light wave” (I will give them full credit for not saying “photon” though), compare with how that term is usually understood.

@jeremyfiennes - this is the point that I was trying to make earlier. It's not that there's a "corrected value" that astronomers should or should not be using. It's that, in vacuum, "the speed of light" either means $c$ or it means "the coordinate speed of light". The latter is a quantity that depends on your choice of coordinates and can take a wide range of values, given a sufficiently malicious coordinate system.

In practice, however, as Janus noted, in many applications any non-malicious coordinate choice will yield a value of the coordinate speed of light that is close enough to $c$ that other error sources are much more important, so exactly what "speed of light" we are using doesn't matter. That is not always the case, though. For example, Shapiro delay can be interpreted in terms of a reduced coordinate speed (or not, as Drakkith noted), which is why I asked what measurements you were interested in.

 

[jeremyfiennes]

This discussion is getting ever profounder! My initial query - more a thought that passed my mind - was simple. Namely that since the speed of light varies with gravitational potential, and since on Earth we have a non-zero potential, in an earthly coordinate frame - which is presumably what astronomers use - the speed of light in outer space should be higher than on earth. So I wondered whether they based their calculations on this rather than the earthly 300 km/s. I should maybe have called it an "adjusted" rather than a "corrected" value.

 

[Ibix]

My initial query - more a thought that passed my mind - was simple. Namely that since the speed of light varies with gravitational potential

And the problem is that this isn't true, not without a lot of caveats. So it isn't a simple question, even if it looks like it ought to be.

Edit: there are some missing zeros here, by the way:

300 km/s

 

[Vanadium 50]

Namely that since the speed of light varies with gravitational potential

You keep saying that. It is not true. It does not become true by saying it again.

 

[jeremyfiennes]

My original google that set all this off told me:
"Spatial variation of the speed of light in a gravitational potential, as measured against a distant observer's time reference, is implicitly present in general relativity. The apparent speed of light will change in a gravity field and, in particular, go to zero at an event horizon as viewed by a distant observer."

 

[phinds]

The apparent speed of light will change ..

Exactly. The APPARENT speed, which as others have pointed out can be a co-ordinate based quantity as opposed to the ACTUAL speed (locally)

 

[andrew s 1905]

Have a look at the series by @PeterDonis https://www.physicsforums.com/insights/schwarzschild-geometry-part-1/

It explains how the coordinate speed of light can vary in a specific GR example but there is a "local" invariant speed of light c that is constant. It is this speed of light that is being referred to as constant.

Regards Andrew

 

[Ibix]

My original google that set all this off told me:
"Spatial variation of the speed of light in a gravitational potential, as measured against a distant observer's time reference, is implicitly present in general relativity. The apparent speed of light will change in a gravity field and, in particular, go to zero at an event horizon as viewed by a distant observer."

Yeah - and it's talking about coordinate speed, in Schwarzschild coordinates (I infer) that don't actually work at the event horizon, so the last clause isn't really valid. Some coordinate systems (e.g. Kruskal-Szekeres) are specifically designed so that the coordinate speed of light is the same everywhere throughout a black hole spacetime.

The whole topic is sensitive to what you want to measure, how you measure it, and how you interpret your measurements.

 

[nnunn]

This discussion is getting ever profounder! My initial query - more a thought that passed my mind - was simple. [. . .]

Since the (simple ) question was about "speed of light in outer space", and since $c \equiv 1/\sqrt{\epsilon_0 \mu_0}$, a possible complication would be if the permittivity and permeability of space between superclusters turns out not to be the same as those constants we use in the lab (i.e., as we define $\epsilon_0 \mu_0$ deep within the local condensate of weak hypercharge (Higgs-type field) peculiar to our Milky Way.

As OP said, just "a thought that passed my mind"

 

[Ibix]

Since the (simple ) question was about "speed of light in outer space", and since $c \equiv 1/\sqrt{\epsilon_0 \mu_0}$, a possible complication would be if the permittivity and permeability of space between superclusters turns out not to be the same as those constants we use in the lab (i.e., as we define $\epsilon_0 \mu_0$ deep within the local condensate of weak hypercharge (Higgs-type field) peculiar to our Milky Way.

This would be a local measure of the speed of light. As such, it would always be $c$ following the 2018 redefinition of the SI units.

 

[nnunn]

This would be a local measure of the speed of light. As such, it would always be $c$ following the 2018 redefinition of the SI units.

Indeed! But wouldn't that local $c$ (as measured in an inter-cluster void) be a different number of local $km/s$?

 

[Ibix]

Indeed! But wouldn't that local $c$ (as measured in an inter-cluster void) be a different number of local $km/s$?

No. One kilometre is defined to be the distance light travels in 1/299792.458 seconds, so the locally measured speed of light is exactly 299792.458 km/s always, everywhere, by definition.

 

[nnunn]

Hi Ibix,

"... so the locally measured speed of light is exactly 299792.458 km/s always, everywhere, by definition."

Since all media have well-defined permittivity and permeability, and the speed of light through those media is dependent on that permittivity and permeability, I had to wonder... if that ratio of 299792.458 km/s were in fact dependent on the local value of $\epsilon$ and $\mu$, i.e. if $(\epsilon_0 \mu_0)$ is affected by variation in the local value of weak hypercharge (or Higgs-type field), then astronomers may need to accommodate such a variation.

Recall how the standard model unifies the electromagnetic and weak interactions; which got me wondering if some unexpected variation in the standard model's Higgs-type field (i.e. some variation in the distribution of primitive weak hypercharge) might have some effect on electromagnetic propagation?

I mean, should we assume that all the properties of space within a galaxy (deep within a supercluster) are the same as those properties between superclusters?

Thanks for helping me to think through this,
Nigel

 

[Ibix]

if that ratio of 299792.458 km/s were in fact dependent on

It's dependent on a decision of the SI committee and nothing else. Attempting to have it vary by changing some other dimensionful constant inevitably ends up in a circular argument.

If you want to consider a meaningful variation in physical constants then you need to look at dimensionless constants - in this particular case, the fine structure constant. As far as I'm aware no one has ever seen any evidence of such variation, despite active searching.

 

[nnunn]

If you want to consider a meaningful variation in physical constants then you need to look at dimensionless constants - in this particular case, the fine structure constant. As far as I'm aware no one has ever seen any evidence of such variation, despite active searching.

Thanks Ibix - understood. I'll switch to wondering about what sort of mechanism might allow for variation in the global distribution of weak hypercharge, and what (if any) effect this could have on electromagnetic propagation. I'll take this where it belongs

 

[snorkack]

Is it better to visualize this through "speed of light" or "amount of space"?
Would it instead be better to say "A region of space in which there is a large gravitational potential is bigger inside than outside"?

 

[sophiecentaur]

Is it better to visualize this through "speed of light" or "amount of space"?
Would it instead be better to say "A region of space in which there is a large gravitational potential is bigger inside than outside"?

That's counter-intuitive enough to make people think very hard but I guess it could be fair enough.

 

[Gardiananj]

I don't think there's a "corrected value", because the speed of light is always $c$. You may find that the coordinate speed varies, but that would depend on your coordinate system (it's one possible interpretation of Shapiro delay, for example).

What measurement did you have in mind?

ooops...the speed of light in an absolute vacuum is c, that can only be calculated, never measured because there is no place in this universe that is an absolute vacuum. The speed of light is dependent on the permitivity of the substance it is traveling through and even extragalactic space is not empty. Einstein always was careful to say "near light speed". As an aside...in an absolute vacuum there would be no electromagnetic waves, i.e. no light from which to calculate it's speed. Please correct me if I am wrong.

 

[Ibix]

ooops...the speed of light in an absolute vacuum is c, that can only be calculated, never measured because there is no place in this universe that is an absolute vacuum.

$c$ is a defined quantity these days, so it can't be measured even in principle. You are welcome to calculate the effect of a hydrogen ion per cubic meter on the propagation of light if you wish. You will need a lot of decimal places, and it has nothing to do with time dilation which is what the OP asked about.

in an absolute vacuum there would be no electromagnetic waves,

Unless you are defining space that contains only an electromagnetic wave as not an absolute vacuum because it contains an electromagnetic wave then your statement is not correct. Electromagnetic waves do not require a medium in which to travel.

 

[PeterDonis]

This thread has run its course and is now closed.