# Questions about the Speed of Light, Time, etc.

• B
• John Mcrain
In summary, the speed of light in a vacuum is a constant, as stated by Einstein's theory of relativity. Time is what a clock measures and is not an illusion. The ratio of distance and time is known as speed, and in order to keep the speed of light constant, both distance and time must change in concert due to the relativity of simultaneity. This is explained by the Lorentz transforms, and it shows that even though distance and time may not be absolute, the speed of light remains absolute.

#### John Mcrain

Mentor Note -- Thread prefix level changed "A"-->"B".
1. How much is acceleration of light?

2. Why is speed of light constant if time is relative, to keep speed constant distance must be changed as well?

3.What is time by Einstien? If we state it is not absolute, it is illusion, dont exsit?

4. Can we say ratio between distance and time is constant for electromagentic waves(light) for every inertial frame?

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John Mcrain said:
1. How much is acceleration of light?
That's not a meaningful question
John Mcrain said:
2. Why is speed of light constant if time is relative, to keep speed constant distance must be changed as well?
I have no idea what confusion you have here. The speed of light in a vacuum is a constant.
John Mcrain said:
3.What is time by Einstien? If we state it is not absolute, it is illusion, dont exsit?
As Einstein said, time is what a clock measures. There is nothing mysterious about it and it certainly is not an illusion.
John Mcrain said:
4. Can we say ratio between distance and time is constant for electromagentic waves(light)?
The ratio of d/t is speed and the speed of light in a vacuum is constant, so yes.

I should add, "time is relative" is a vague statement. You need to specify a context for it to be meaningful.

John Mcrain said:
time is relative, to keep speed constant distance must be changed as well?
Both time and distance do change when you change inertial frames. So does simultaneity. All three change in concert to keep the speed of light the same in all inertial frames.

KobiashiBooBoo, dextercioby, russ_watters and 1 other person
phinds said:
I should add, "time is relative" is a vague statement. You need to specify a context for it to be meaningful.
Time is in denominator, speed will not be constant if in denominator is 40sec or 20sec, so to keep it constant you must reduce numerator(distance) as well...

John Mcrain said:
Time is in denominator, speed will not be constant if in denominator is 40sec or 20sec, so to keep it constant you must reduce numerator(distance) as well...
It's not that simple. You need to adjust the notion of simultaneity too. It's all encapsulated in the Lorentz transforms, which tell you what position and time coordinates you assign to an event given my coordinates and our relative velocity.

robphy and Dale
@John Mcrain what you should have gathered from all of the answers is that you are trying to apply classical physics to relativity and it just won't work. Best you get a good book on Special Relativity and study that before asking more questions.

robphy
John Mcrain said:
Time is in denominator, speed will not be constant if in denominator is 40sec or 20sec, so to keep it constant you must reduce numerator(distance) as well...
To “second” what @Ibix said, you are neglecting the relativity of simultaneity. The Lorentz transform has length contraction, time dilation, and relativity of simultaneity. Yes, both time dilation and length contraction occur, but they are insufficient. You need all three.

Dale said:
To “second” what @Ibix said, you are neglecting the relativity of simultaneity. The Lorentz transform has length contraction, time dilation, and relativity of simultaneity. Yes, both time dilation and length contraction occur, but they are insufficient. You need all three.
I dont understand why is speed of light absolute if distance and time are not, how we can get something absolute from something that is not absolute?
Speed is derived from distance and time..

John Mcrain said:
I dont understand why is speed of light absolute if distance and time are not, how we can get something absolute from something that is not absolute?
Look up the Lorentz transforms. Write down arbitrary x,t coordinates, say ##x_0,t_0##. Work out where a light ray would be ##\Delta t## later if it was emitted there (i.e. ##x_0+c\Delta t, t_0+\Delta t##). Feed both sets of coordinates through the Lorentz transforms to get the coordinates in the other frame. Calculate the distance and time between the transformed coordinates and divide to get the transformed speed.

Keep repeating that until you convince yourself it's possible for the distance and time to change but the speed not. You do not need any maths more complicated than a square root.
John Mcrain said:
Speed is derived from distance and time..
Other way round - distance is derived from speed and time these days.

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russ_watters
John Mcrain said:
I dont understand why is speed of light absolute if distance and time are not,
The reason you don’t understand is precisely because you continue to neglect the relativity of simultaneity.

Ibix
Dale said:
The reason you don’t understand is precisely because you continue to neglect the relativity of simultaneity.
Can you explain with example?

John Mcrain said:
Can you explain with example?
Google Einstein's train. Or look up the Lorentz transforms and feed in two events with the same ##t## coordinate (so, simultaneous) but different ##x## coordinates. Are the resulting ##t'## coordinates the same? If not, then the claim "these two things are/are not simultaneous" depends on your frame - i.e. simultaneity is relative.

John Mcrain said:
Speed is derived from distance and time.
Not in relativity. In relativity it's the other way around: the behavior of distance and time (and simultaneity) is derived from the fact that the speed of light is invariant.

John Mcrain said:
Can you explain with example?
Sure. Suppose we have a light source and two detectors that are each a distance ##L## from the light source, one in the ##+x## direction and the other in the ##-x## direction. The light source flashes at ##t=0##, so the equations of motion for the light pulses and the detectors can be written as follows: $$x_{+light}(t)=ct$$$$x_{-light}(t)=-ct$$$$x_{+detector}(t)=L$$$$x_{-detector}(t)=-L$$ We can easily see that $$|\dot x_{+light}|=|\dot x_{-light}|=c$$ and we can also easily see that the separation between the detectors is $$x_{+detector}(t)-x_{-detector}(t)=2L$$ If ##t_+## is the arrival of the light at the ##+## detector and ##t_-## is the arrival of the light at the ##-## detector then $$x_{+detector}(t_+)=x_{+light}(t_+)$$$$t_+=\frac{L}{c}$$$$x_{-detector}(t_-)=x_{-light}(t_-)$$$$t_-=\frac{L}{c}$$ The light arrives simultaneously at both detectors.

Now, consider a primed reference frame moving at ##v## with respect to the unprimed frame. The equations of motion in the primed frame are obtained from the unprimed frame using the Lorentz transform. With that we can find $$x'_{+light}(t')=ct'$$$$x'_{-light}(t')=-ct'$$$$x'_{+detector}(t')=\frac{L}{\gamma}-vt'$$$$x'_{-detector}(t')=-\frac{L}{\gamma}-vt'$$ Again, we can easily see that$$|\dot x'_{+light}|=|\dot x'_{-light}|=c$$, so the speed of light is the same in both frames. We can also easily see that the separation between the detectors is $$x'_{+detector}(t')-x'_{-detector}(t')=\frac{2L}{\gamma}$$ meaning that lengths are contracted. Again, if ##t'_+## is the arrival of the light at the ##+## detector and ##t'_-## is the arrival of the light at the ##-## detector then $$x'_{+detector}(t'_+)=x'_{+light}(t'_+)$$$$t'_+=\frac{L}{(c+v)\gamma}$$$$x'_{-detector}(t'_-)=x'_{-light}(t'_-)$$$$t'_-=\frac{L}{(c-v)\gamma}$$ The light arrives at each detector at a different time.

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hutchphd, John Mcrain and Ibix
Dale said:
Sure. Suppose we have a light source and two detectors that are each a distance ##L## from the light source, one in the ##+x## direction and the other in the ##-x## direction. The light source flashes at ##t=0##, so the equations of motion for the light pulses and the detectors can be written as follows: $$x_{+light}(t)=ct$$$$x_{-light}(t)=-ct$$$$x_{+detector}(t)=L$$$$x_{-detector}(t)=-L$$ We can easily see that $$|\dot x_{+light}|=|\dot x_{-light}|=c$$ and we can also easily see that the separation between the detectors is $$x_{+detector}(t)-x_{-detector}(t)=2L$$ If ##t_+## is the arrival of the light at the ##+## detector and ##t_-## is the arrival of the light at the ##-## detector then $$x_{+detector}(t_+)=x_{+light}(t_+)$$$$t_+=\frac{L}{c}$$$$x_{-detector}(t_-)=x_{-light}(t_-)$$$$t_-=\frac{L}{c}$$ The light arrives simultaneously at both detectors.

Now, consider a primed reference frame moving at ##v## with respect to the unprimed frame. The equations of motion in the primed frame are obtained from the unprimed frame using the Lorentz transform. With that we can find $$x'_{+light}(t')=ct'$$$$x'_{-light}(t')=-ct'$$$$x'_{+detector}(t')=\frac{L}{\gamma}-vt'$$$$x'_{-detector}(t')=-\frac{L}{\gamma}-vt'$$ Again, we can easily see that$$|\dot x'_{+light}|=|\dot x'_{-light}|=c$$, so the speed of light is the same in both frames. We can also easily see that the separation between the detectors is $$x'_{+detector}(t')-x'_{-detector}(t')=\frac{2L}{\gamma}$$ meaning that lengths are contracted. Again, if ##t'_+## is the arrival of the light at the ##+## detector and ##t'_-## is the arrival of the light at the ##-## detector then $$x'_{+detector}(t'_+)=x'_{+light}(t'_+)$$$$t'_+=\frac{L}{(c+v)\gamma}$$$$x'_{-detector}(t'_-)=x'_{-light}(t'_-)$$$$t'_-=\frac{L}{(c-v)\gamma}$$ The light arrives at each detector at a different time.
Thanks for explanation.
So Newton thought that speed of light in the train from ground frame is c+ train speed and c-train speed?

He say at 1:22 if distance between two observers is far enough, time will also be very different even for low speeds.
So distance between observers also make a difference?

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John Mcrain said:
So Newton thought that speed of light in the train from ground frame is c+ train speed and c-train speed?
There were several theories of light, and that was one, yes. Another was that light was a wave in a medium called the ether, so would always travel at ##c## relative to that. None of them stood up to experiment. Relativity did.
John Mcrain said:
So distance between observers also make a difference?
Yes, as is obvious from Dale's maths. Just let ##L## be very large and the difference between ##t'_-## and ##t'_+## can be large even if ##v## is very small compared to ##c##.

Dale
Ibix said:
There were several theories of light, and that was one, yes. Another was that light was a wave in a medium called the ether, so would always travel at ##c## relative to that. None of them stood up to experiment. Relativity did.

Yes, as is obvious from Dale's maths. Just let ##L## be very large and the difference between ##t'_-## and ##t'_+## can be large even if ##v## is very small compared to ##c##.
But L is distance from light source to detector in train, not distance from how far I observe train?

John Mcrain said:
But L is distance from light source to detector in train, not distance from how far I observe train?
Yes. The distance between events you are observing is important, but where you are does not matter (unless one of the events is something that happens where you are, of course). Greene isn't always particularly careful about how he says what he says, but I doubt he says anything else here.

Ibix said:
Yes. The distance between events you are observing is important, but where you are does not matter (unless one of the events is something that happens where you are, of course). Greene isn't always particularly careful about how he says what he says, but I doubt he says anything else here.

How is it possible that he is just not careful if he made animation(look at my video at 1:22) where he show how even for low velocity if distance between two observers is big enough, change in time is big.

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John Mcrain said:
But L is distance from light source to detector in train, not distance from how far I observe train?
##2L## is the distance between the two detectors in the unprimed frame. ##2L/\gamma## is the distance between the two detectors in the primed frame.

John Mcrain said:
So distance between observers also make a difference?
As the distance between the detectors in the primed frame increases the time difference ##\Delta t’=t’_+ - t’_-## also increases. That is the relativity of simultaneity that Greene is talking about.

Dale said:
##2L## is the distance between the two detectors in the unprimed frame. ##2L/\gamma## is the distance between the two detectors in the primed frame.As the distance between the detectors in the primed frame increases the time difference ##\Delta t’=t’_+ - t’_-## also increases. That is the relativity of simultaneity that Greene is talking about.
Did you look at my video at 1:22 - 1:28 where Green show how even for low velocity if distance between two observers is big enough, change in time is big?

John Mcrain said:
Did you look at my video at 1:22 - 1:28
1:22 still seems to be introductory comments.

John Mcrain said:
Did you look at my video at 1:22 - 1:28 where Green show how even for low velocity if distance between two observers is big enough, change in time is big?
See post 21

Dale said:
See post 21
Here Green is talking about distnace between two observers/frames, your post 21 talk about distance between two detectors/lenght of train.

Green tell if you observe train from bigger distance, change in time will be bigger.

John Mcrain said:
Here Green is talking about distnace between two observers/frames, your post 21 talk about distance between two detectors/lenght of train.

Green tell if you observe train from bigger distance, change in time will be bigger.
Observers, detectors, whatever. It is the same effect.

Dale said:
Observers, detectors, whatever. It is the same effect.
So you agree if you observe einstein train for grater distance, change in time will be bigger?

Ibix said:
Yes. The distance between events you are observing is important, but where you are does not matter (unless one of the events is something that happens where you are, of course). Greene isn't always particularly careful about how he says what he says, but I doubt he says anything else here.
What do you mean by "where you are"?

If you observe einstein train from 100m or from 100km, isnt the same?
From 100km ,change in time will be bigger?

John Mcrain said:
So you agree if you observe einstein train for grater distance, change in time will be bigger?
See post 15. The larger the distance between two events that are simultaneous in one frame, the greater the difference in time between those same events in another frame. This is the relativity of simultaneity, regardless of how you dress it up in different scenarios

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John Mcrain said:
Can you explain with example?
The length of an object is the distance between where its ends are at the same time. Relativity of simultaneity means that “at the same time” is frame-dependent; therefore lengths are also frame-dependent.

When I say that clock A is running slower than clock B, I’m actually saying something about what clock B reads at the same time that clock A says that one second has passed. Again, relativity of simultaneity - different notions of “at the same time” lead to different notions of what the relative clock rate is.

Learn to use the Lorentz transformations. There is no other way.

John Mcrain said:
If you observe einstein train from 100m or from 100km, isnt the same?
The result is the same whether you are next to it or miles away.

Your time stamp didn't take me to anything relevant in the video, but my guess is that in the bit you are talking about Greene was referring to the Andromeda Paradox. In that case, one of the events is defined to be at your location. That's why how far away from you the other event is matters in that case - because one of the events being compared is at your location. In Einstein's train the events being compared are at opposite ends of the train, and where you are is irrelevant.

So it's always the distance between events of interest that matters. Where you are is only relevant if one of the events of interest is defined to be at your location.

John Mcrain and Dale
Ibix said:
The result is the same whether you are next to it or miles away.

Your time stamp didn't take me to anything relevant in the video, but my guess is that in the bit you are talking about Greene was referring to the Andromeda Paradox. In that case, one of the events is defined to be at your location. That's why how far away from you the other event is matters in that case - because one of the events being compared is at your location. In Einstein's train the events being compared are at opposite ends of the train, and where you are is irrelevant.

So it's always the distance between events of interest that matters. Where you are is only relevant if one of the events of interest is defined to be at your location.
If inside train is clock and I have my clock at station, then distance between station and train matters, further the station from the train, bigger will be difference in time between my and clock in train?

I read that Lorenz and Poicare set this equations before Einstein, they knew that c=const. so what Einstein discoverd new?
Why his theory was laughed for decades, if other geniuses didnt understand his theory why people wonder how normal person cant understand this?

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John Mcrain said:
Why his theory was laughed for decades, if other geniuses didnt understand his theory
Einstein proposed special relativity in 1905 as the solution to a problem that had tormented physicists for almost a half-century: the laws of E&M, discovered in the early 1860s, suggested that the speed of light ought to be constant but no one could figure out how that could be. He was not ”laughed at for decades”; instead (after a fairly normal period of checking the math and verifying the internal consistency) the theory was accepted with the same relief that you or I would accept the key missing piece of a jigsaw puzzle.
why people wonder how normal person cant understand this?
Special relativity is well within the grasp of a STEM-focused high school student. People make it unnecessarily hard for themselves by refusing to study it an systematic way, and by insisting that the math should conform to their misunderstandings instead of allowing it to guide their understanding.

russ_watters, John Mcrain and Dale
John Mcrain said:
I read that Lorenz and Poicare set this equations before Einstein
Lorentz not Lorenz - different people, similar names - he had the equations but misinterpreted their significance so didn’t have the answer to the big question In the previous post.

Poincare was close to the solution, so close that had Einstein fallen in front of a bus (I suppose a train would be a more historically appropriate hypothetical?) before he could present the solution, Poincare would likely have found it and received the credit.

Dale said:
The light arrives at each detector at a different time.
This is how I at first look at this; fur sure light need more time to reach detector that is moving away for it, because light must travel longer distance to reach this detector.

From frame at rest, distance L2 is longer then L1. So I would say distance "change" and that is reason why light need more time to reach right detector.
So light has speed c in both direction, time is absolute, but distance is changed in frame at rest.

Where I am wrong?