# Speed of light in non inertial conventions

## Main Question or Discussion Point

Hello guys, I just had to ask a quick question about the nature of light. In different synchronization parameters regarding inertial frames (other than 1/2) light can take value between c/2 and infinity. So far, so good for inertial frames. But considering non-inertial frames, what are the boundaries between max and min speed of light in an arbitary direction? Are they the same as in the inertial case, and if not what is their value. An almost absurd thought came to my mind that light may have a velocity so small that it takes very much time to propagate even to our eyes for objects in vicinity, let's say if it's 1 m/s that in takes much more time to reach our eyes, since we are in a non-inertial reference frame. After all, it seems absurd since everybody is saying that light is so quick that the things that we see in our vicinity are so close in time to us that we can almost consider them present even if they are in our past.

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bcrowell
Staff Emeritus
Gold Member
In different synchronization parameters regarding inertial frames (other than 1/2) light can take value between c/2 and infinity.
I haven't thought this through in detail myself, but I believe this is incorrect. Picking ϵ≠1/2 is equivalent to defining simultaneity in a noninertial frame. Assuming I've got that right, then it doesn't make sense to ask how to extend ϵ≠1/2 from inertial to noninertial frames; you were already dealing with a noninertial frame.

An almost absurd thought came to my mind that light may have a velocity so small that it takes very much time to propagate even to our eyes for objects in vicinity, let's say if it's 1 m/s that in takes much more time to reach our eyes, since we are in a non-inertial reference frame. After all, it seems absurd since everybody is saying that light is so quick that the things that we see in our vicinity are so close in time to us that we can almost consider them present even if they are in our past.
An observer with a constant proper acceleration has an event horizon. Light emitted from the event horizon will take an infinite time to reach the observer.

Dale
Mentor
I haven't thought this through in detail myself, but I believe this is incorrect. Picking ϵ≠1/2 is equivalent to defining simultaneity in a noninertial frame.
I agree. I would call any other convention non-inertial. The second postulate requires inertial frames to have speed of light equal to c.

I think there are other definitions of inertial that you could use, but this one makes sense in a special relativity forum.

To the OP, there is no limitation on the coordinate speed of light in general non inertial coordinates.

I agree. I would call any other convention non-inertial. The second postulate requires inertial frames to have speed of light equal to c.

I think there are other definitions of inertial that you could use, but this one makes sense in a special relativity forum.

To the OP, there is no limitation on the coordinate speed of light in general non inertial coordinates.
So could you explain to me the example I mentioned in my previous post, for instance I have an object in front of myself and I'm a non-inertial frame. If I was inertial, the speed of light would be c and I could deduce how many time units have passed before the light from the object hit my eyes.

In a non-inertial frame, if light was very very slow in our vicinity, it seems absurd that the objects that are close to us as we perceive them could be in the distant past relative to us. That thought gives me trouble and I still believe that the speed of light is actually very quick even in non-inertial frames, so that the transimission of information via light takes little time. Could you explain this DaleSpam? In inertial frames, everything makes perfect sense, light has the speed of c and by that speed the information is transmitted to our percepts so we don't lag behind the 'now' of events too much. What is the situation from the perspective of non-inertial frames?

I can't edit my previous post for some reason, so I will post a new reply, I hope it isn't a problem.

It is often said that the light from the sun takes 8 minutes to reach us, of course people take its velocity to be c in this case. If the speed can be as low as few meters per second, this simply doesn't make sense to me (since Earth is non-inertial). So I don't understand how its velocity can be 'anything'.

bcrowell
Staff Emeritus
Gold Member
It is often said that the light from the sun takes 8 minutes to reach us, of course people take its velocity to be c in this case. If the speed can be as low as few meters per second, this simply doesn't make sense to me (since Earth is non-inertial). So I don't understand how its velocity can be 'anything'.
To make light have a velocity very different from c, you have to have a highly noninertial frame. A frame defined relative to a point on the earth is only slightly noninertial.

Dale
Mentor
So could you explain to me the example I mentioned in my previous post
No, I cannot. The question is insufficiently well specified. You would need to provide the metric in your non inertial coordinates.

All I can do without that is tell you that in general the coordinate speed of light is not limited in non inertial coordinates.

No, I cannot. The question is insufficiently well specified. You would need to provide the metric in your non inertial coordinates.

All I can do without that is tell you that in general the coordinate speed of light is not limited in non inertial coordinates.

The question seems very straightforward, you said that the coordinate speed can be as low as we can imagine. So I asked why it isn't so low in our everyday lifes, and I mentioned the example that the light from the Sun takes 8 minutes to reach us. In which conditions is the light much slower than the regular c?

pervect
Staff Emeritus
The question seems very straightforward, you said that the coordinate speed can be as low as we can imagine. So I asked why it isn't so low in our everyday lifes, and I mentioned the example that the light from the Sun takes 8 minutes to reach us. In which conditions is the light much slower than the regular c?
Relativistic effects are often tiny in "everyday life". However, with modern technology (especially clocks) they are easily measurable.

As far as an example goes, the coordinate speed of light in one of the natural coordinate systems for an accelerated observer, called Rindler coordinates, has the property of varying from zero to infinity. I'm not sure what use that more specific info will be - I don't mean to be insulting, but I don't think you have enough background that it would be useful to go into any more technical details, and I don't really think giving the name of the coordinates adds much over the statements already made.

Probably the most important point is that if you realize that GR allows arbitrary coordinates, you don't even need to ask the question, because by the nature of arbitrary coordinates, the coordinate speed can be anything. Since you did ask the question, you probably don't realize that GR allows arbitrary coordinates, or don't realize the significance of this fact.

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Dale
Mentor
The question seems very straightforward, you said that the coordinate speed can be as low as we can imagine. So I asked why it isn't so low in our everyday lifes, and I mentioned the example that the light from the Sun takes 8 minutes to reach us. In which conditions is the light much slower than the regular c?
What is the metric in our "everyday life" coordinates?

I'm sorry, but if you ask a partial question then you will have to be satisfied with a partial answer, regardless of how straightforward it may seem to you. If it were actually straightforward then wouldn't you be able to answer it yourself?