-1

The speed of light in special relativity is a constant, 186,000 miles per second, but in general relativity, "the speed of a light wave depends on the strength of the gravitational potential along its path" (Shapiro, qtd. in Wikipedia).

How much energy or mass would be needed to have a gravitational potential strong enough to slow the speed of light down to 1 mile per second?

For context: This is to amplify gravitational waves because, based on research, if the speed of light were slowed so much and a gravitational wave is generated from black holes colliding, the gravitational waves will have a prominent effect.

Mikayla Eckel Cifrese
  • 2,297
Khepera
  • 29
  • 1
    Why do you claim that mass changes the speed of light? Are you talking about the Shapiro time delay? – PM 2Ring May 16 '23 at 03:14
  • No, but I mean having enough energy or mass in a space to slow down the speed of light to 1 mile per second. – Khepera May 17 '23 at 02:14
  • 2
    As Eric says, a local observer will always measure the speed of light to be c. A distant observer can calculate the speed of light near a massive object to be slower, as measured in Schwarzschild coordinates, see https://physics.stackexchange.com/a/77280/123208 for details. – PM 2Ring May 17 '23 at 03:05
  • 2
    To get a significant reduction the light has to be very close to the event horizon of a black hole. Eg, for a 10 solar mass BH (which has a Schwarzschild radius of ~29.5 km), to drop the speed to 1 mile per second, the light has to be about 6¼" from the event horizon. – PM 2Ring May 17 '23 at 03:06
  • Can the speed of light be changed, definitely, I mean without the influence of the location of the observer? – Khepera May 17 '23 at 03:20
  • No. Nothing can ever change the local speed of light in a vacuum. Any apparent slowdown is only due to the difference in the spacetime curvature at the location the light beam is traversing vs the spacetime curvature at the location of the observer. – PM 2Ring May 17 '23 at 03:49

3 Answers3

4

It's not the mass that matters, it's the gravitational potential, which depends both on mass and on distance.

Also, the Wikipedia quote is a bit misleading if taken out of context. The speed of a light beam as measured by a distant observer depends on the gravitational potential, but the speed of light as measured by a local observer (next to the beam of light) is always $c$.

Finally, to answer your question more concretely, the only place in the universe where a distant observer would measure such a slow speed of light would be just outside the event horizon of a black hole, where gravitational time dilation would make all processes appear slow (again, for a distant observer, local observers would not observe anything different).

Eric Smith
  • 9,064
  • So a change in the gravitational potential is needed to alter the speed of light? – Khepera May 17 '23 at 02:13
  • I think it's more accurate to say that the speed of light depends on time, and time is relative and depends in part on the curvature of spacetime. Near a massive object clocks appear to tick more slowly, compared to distant clocks. – Eric Smith May 17 '23 at 11:58
0

No amount of mass can change the speed of light. Mass corresponds to a change in the direction of the geodesics in which light can travel and along which light always travels at $c$, not a change in the value of $c$. Geodesics are analogous to straight lines in curved space.

g s
  • 13,563
  • Thank you, so a change in mass only changes the direction of light? – Khepera May 16 '23 at 12:10
  • 2
    This isn't quite accurate, if you look at the coordinate speed of light it will indeed be different -- consider for example two light clocks ticking, one on the surface of the Earth and one high above the Earth. They will be ticking at (very slightly) different rates, indicating that they disagree on the speed of light. Locally spacetime is flat and $c$ is constant, but that need not be true globally. – Eric Smith May 16 '23 at 12:40
  • How can the local speed of light be decreased then? – Khepera May 18 '23 at 00:11
0

For photons, $E = h\nu$ where $\nu =$ frequency. Any change in photon energy does not change the photon velocity it changes the photon frequency. Inside the sun, the intense density means photons only travel by absorption and remission. In this process, photons can take 100,000 years to reach the surface but technically it's not the same photon that started the process.

Stevan V. Saban
  • 1,720
  • 3
  • 17
  • Thank you, so in the sun photons speed are limited, however technically they are not the same photon? – Khepera May 17 '23 at 01:55
  • @KeithReid A photon is absorbed and then a photon of the same energy is emitted. It's not really possible to determine if the same photon absorbed is the same photon that is emitted. It is not the same as a single photon traveling in a vacuum. – Stevan V. Saban May 17 '23 at 02:20