Questions about the Speed of Light, Time, etc.

[John Mcrain]

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 einstein? 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?

 

[phinds]

1. How much is acceleration of light?

That's not a meaningful question

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.

3.What is time by einstein? 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.

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.

 

[phinds]

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

 

[PeterDonis]

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.

 

[John Mcrain]

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...

 

[Ibix]

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.

 

[phinds]

@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.

 

[Dale]

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.

 

[John Mcrain]

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..

 

[Ibix]

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.

Speed is derived from distance and time..

Other way round - distance is derived from speed and time these days.

 

[Dale]

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.

 

[John Mcrain]

The reason you don’t understand is precisely because you continue to neglect the relativity of simultaneity.

Can you explain with example?

 

[Ibix]

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.

 

[PeterDonis]

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.

 

[Dale]

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.

 

[John Mcrain]

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?

 

[Ibix]

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.

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 $c$.

 

[John Mcrain]

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?

 

[Ibix]

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.

 

[John Mcrain]

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.

 

[Dale]

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.

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.

 

[John Mcrain]

$2L$ 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?
What do say about this?

 

[Ibix]

Did you look at my video at 1:22 - 1:28

1:22 still seems to be introductory comments.

 

[Dale]

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?
What do say about this?

See post 21

 

[John Mcrain]

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.

 

[Dale]

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.

 

[John Mcrain]

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?

 

[John Mcrain]

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?

 

[Dale]

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

 

[Nugatory]

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.