# Variable Speed of Light: Understanding Its Effects in Different Frames"

• lovetruth
In summary, In a frame S, there are two stationary objects A & B at a distance L in the x-direction. Object A is nearer to the observer than object B. Light will take time T to reach object B from A. Therefore in frame S, L/T = c. In another frame S’, both objects A & B are moving at velocity v in positive x-direction with respect to the observer. Therefore in frame S’, the distance between object A & B will be : L’ = L/(gamma) and the time for light to reach object B from A will be: T’ = T(gamma). An observer in frame S’ will calculate the speed
lovetruth
In a frame S, there are two stationary objects A & B at a distance L in the x-direction. Object A is nearer to the observer than object B. Light will take time T to reach object B from A. Therefore in frame S,
L/T = c

In another frame S’, both objects A & B are moving at velocity v in positive x-direction with respect to the observer. Therefore in frame S’, the distance between object A & B will be :
L’ = L/(gamma)
and the time for light to reach object B from A will be:
T’ = T(gamma)

An observer in frame S’ will observe that the total distance traveled by light in reaching object B from A will be:
L’ +v(T’)
Also, the time taken by light to reach object B from A will be: T’

Thus, an observer in frame S’ will calculate the speed of light to be:
[L’ + v(T’)]/T’ = (L’/T’) + v
= [c/(gamma)^2] + v
Thus, in frame S’, the speed of light will not be c. How?

lovetruth said:
In another frame S’, both objects A & B are moving at velocity v in positive x-direction with respect to the observer. Therefore in frame S’, the distance between object A & B will be :
L’ = L/(gamma)
OK.
and the time for light to reach object B from A will be:
T’ = T(gamma)
No. How did you deduce this?

FYI: You cannot simply apply the 'time dilation' formula here. That formula applies to time measurements made in a moving frame at a single location, but here you are concerned with the time to travel between two locations.

Last edited:
Doc Al said:
OK.

No. How did you deduce this?

time dilation

lovetruth said:
time dilation
See the note I added above.

Doc Al said:
See the note I added above.

I don't understand what you mean by 'Time dilation at a single point'. Time is just an interval. Also, I have read about derivation of time dilation by using 'light clock' in which the light travels between two points.

lovetruth said:
I don't understand what you mean by 'Time dilation at a single point'. Time is just an interval.
I spoke of time measurements made at a single point, such as by a clock.
Also, I have read about derivation of time dilation by using 'light clock' in which the light travels between two points.
Sure. As long as you take as your 'interval' the round trip time for the light to return to its starting point.

To figure out the time it takes light to travel from A to B in the primed frame, do this:

L/(gamma) + VT' = CT'

Lovetruth, the problem here is that you're trying to do a calculation that requires the Lorentz transformation, not just gamma factors for time dilation and length contraction. If you write the Lorentz transformation as an equation for (t',x') in terms of (t,x), there are four terms, one of which causes t' to depend on x. (This is all just a different way of saying what Doc Al said.) By finding an inconsistent result, what you've basically proved to yourself is that you need to learn about the Lorentz transformation.

Here are a couple of books that do the Lorentz transformation in detail:
Takeuchi, An Illustrated Guide to Relativity
Mermin, It's About Time: Understanding Einstein's Relativity

Doc Al said:
I spoke of time measurements made at a single point, such as by a clock.

Sure. As long as you take as your 'interval' the round trip time for the light to return to its starting point.

To figure out the time it takes light to travel from A to B in the primed frame, do this:

L/(gamma) + VT' = CT'

Why the 'interval' for the round trip and not for single trip. I thought time dilation holds for any event (which in this case is the journey of light from object A to B)

lovetruth said:
Why the 'interval' for the round trip and not for single trip. I thought time dilation holds for any event (which in this case is the journey of light from object A to B)
The simple time dilation formula, T = T'*gamma, only applies to time measurements made on a single moving clock (thus at a single location in the moving frame). If you want to apply 'time dilation' to an arbitrary time interval, you need the full Lorentz transformations.

Doc Al said:
If you want to apply 'time dilation' to an arbitrary time interval, you need the full Lorentz transformations.

Yep.

Lovetruth, the amount of time you've spent on this forum discussing relativity indicates an intense interest in the subject. That's great. But I'm frankly extremely shocked that you've spent that amount of time talking, calculating, and thinking about SR without apparently learning what the Lorentz transformation is or why it's necessary. Given the relative sophistication of the topics that you've been trying to discuss, like transformations of electric and magnetic fields between frames, it had never occurred to me that you hadn't built any kind of foundation beyond what one finds in popularizations.

It's a waste of your time and ours for you to keep posting things like this without taking some time to learn the fundamentals of the subject. PF isn't a substitute for reading books at the appropriate level. You cannot learn a nontrivial subject like relativity in the manner you've been doing, by repeatedly attempting calculations, getting them wrong, and then posting them and expecting other people to fix both the calculation and the underlying lack of background.

Doc Al said:
The simple time dilation formula, T = T'*gamma, only applies to time measurements made on a single moving clock (thus at a single location in the moving frame). If you want to apply 'time dilation' to an arbitrary time interval, you need the full Lorentz transformations.

Thank you.
I thought that time dilation is valid for any event

bcrowell said:
Yep.

Lovetruth, the amount of time you've spent on this forum discussing relativity indicates an intense interest in the subject. That's great. But I'm frankly extremely shocked that you've spent that amount of time talking, calculating, and thinking about SR without apparently learning what the Lorentz transformation is or why it's necessary. Given the relative sophistication of the topics that you've been trying to discuss, like transformations of electric and magnetic fields between frames, it had never occurred to me that you hadn't built any kind of foundation beyond what one finds in popularizations.

It's a waste of your time and ours for you to keep posting things like this without taking some time to learn the fundamentals of the subject. PF isn't a substitute for reading books at the appropriate level. You cannot learn a nontrivial subject like relativity in the manner you've been doing, by repeatedly attempting calculations, getting them wrong, and then posting them and expecting other people to fix both the calculation and the underlying lack of background.

You are right that I only read 'Popularization'. I am just an amateur not a full time physicist. Also, I try to read as much as I can. But you know that all academic books you prescribe to me are long and time-consuming. My lifetime would be too short to read all the books there are in physics, let alone science & math. Even in physics, people have specialized into classical, relativity, quantum mechanics, cosmology.. etc but not whole of physics. So don't construe my efforts to understand physics as insincere.

## 1. What is the variable speed of light?

The variable speed of light refers to the concept that the speed of light can vary depending on the frame of reference in which it is measured. This means that the speed of light may appear different to observers who are moving at different speeds relative to each other.

## 2. What is the theory of relativity?

The theory of relativity is a fundamental principle in physics that explains how the laws of physics are the same for all observers in uniform motion. It also explains how the laws of physics can appear different to observers who are moving at different speeds relative to each other.

## 3. How does the variable speed of light affect our understanding of the universe?

The variable speed of light has significant implications for our understanding of the universe. It allows us to reconcile seemingly conflicting observations and measurements, such as the constant speed of light and the relativity of time and space. It also helps us to better understand the behavior of light and its role in shaping the fabric of the universe.

## 4. Is the variable speed of light a proven concept?

Yes, the variable speed of light is a well-established concept in physics and has been confirmed through numerous experiments and observations. It is an integral part of the theory of relativity and has been extensively studied and supported by scientists.

## 5. How does the variable speed of light affect everyday life?

The effects of the variable speed of light are not noticeable in our everyday lives, as the differences in speed are extremely small and only become apparent at very high speeds. However, our understanding of the variable speed of light has led to advancements in technology, such as GPS systems, which rely on the precise measurements of time and space that are made possible by the theory of relativity.

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