I Speed of light not an invariant in GR

[Pyter]

Take a look at this:

https://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/speed_of_light.html

Then I'm citing from your link (emphasis mine):

None of the preceding discussion actually depends on the distances being large; it's just easier to visualise if we use such large distances. So now transfer that discussion to a rocket you are sitting in, far from any gravity and uniformly accelerated, meaning you feel a constant weight pulling you to the floor. "Above" you (in the direction of your acceleration), time speeds up and light travels faster than c, arbitrarily faster the higher up you want to consider. Now use the Equivalence Principle to infer that in the room you are sitting in right now on Earth, where real gravity is present and you aren't really accelerating (we'll neglect Earth's rotation!), light and time must behave in the same way to a high approximation: light speeds up as it ascends from floor to ceiling, and it slows down as it descends from ceiling to floor; it's not like a ball that slows on the way up and goes faster on the way down. Light travels faster near the ceiling than near the floor. But where you are, you always measure it to travel at c; no matter where you place yourself, the mechanism that runs the clock you're using to measure the light's speed will speed up or slow down precisely in step with what the light is doing. If you're fixed to the ceiling, you measure light that is right next to you to travel at c. And if you're fixed to the floor, you measure light that is right next to you to travel at c. But if you are on the floor, you maintain that light travels faster than c near the ceiling. And if you're on the ceiling, you maintain that light travels slower than c near the floor.

The observed speed of a faraway light beam depends on the metric, and if the latter depends on time, also the light speed does.

 

[PeroK]

Then I'm citing from your link (emphasis mine):
The observed speed of a faraway light beam depends on the metric, and if the latter depends on time, also the light speed does.

Okay, but it's impossible to keep up with this. You posted a completely different text previously (claiming you were referencing that). Now you're posting a different text altogether. The key point is that you are still paraphrasing and extrapolating what Baez says.

There is a huge difference between quoting Baez directly (a citation) and taking something he said and applying your own logical reasoning to it and claiming it's something Baez says.

To put it in simple terms: Baez does not say that the speed of light changes with time. He simply does not say that.

 

[Pyter]

@PeroK Baez says that the speed changes with the metric.
I'm arguing that if the metric changes with time, also the speed does.

 

[PeterDonis]

What's its shape exactly?

Topologically, it's a double cone--two conical null surfaces (one future, one past) joined at the apex, which is the chosen event.

Null surfaces don't really have an invariant "shape" in the ordinary geometric sense. How they are represented in a diagram depends on what coordinates you choose.

If the metric changes with time, the light speed also changes, so you might say that the cone is not "static" (in time) and is not a "cone", in the sense that its surface is not regular but bent here and there by the massive bodies?

None of this is correct, no.

Remember that there is a light cone attached to every event--every point in spacetime. Each point has its own, and they are all different.

It makes no sense to say the light cone of a particular event "changes with time" or is "static". The light cones are invariant features of the 4-dimensional spacetime geometry; there is no "change" in the 4-dimensional geometry, it just is.

Which events are in the light cone for a given event is of course determined by the spacetime geometry, which in turn is determined by the presence of stress-energy; but to say the cone's surface is "bent" by the presence of massive bodies is an oversimplification.

Also, the term "cone", as my statement at the start of this post indicates, refers to the topology of the light cone, not its geometric shape; as I noted, null surfaces don't really have a geometric "shape" in the ordinary sense.

 

[PeterDonis]

The measured speed of a faraway light beam

There is no such thing. You can't directly measure the speed of something that is far away from you. You can calculate various "speeds", but those calculations will depend on your choice of coordinates.

Baez says that the speed changes with the metric

He's talking about the coordinate speed of light, not anything that is directly measured. The coordinate speed he is talking about is a calculation and depends on your choice of coordinates.

 

[PeterDonis]

The OP's questions have been answered, repeatedly. Further repetition of the same misunderstandings and the same responses to them is pointless. Thread closed.