Relation between coordinate time and proper time

[ash64449]

Hello friends,

If we consider ${T}$ as coordinate time and ${\tau}$ as proper time, the relationship between them is:

$\frac{T}{\tau}= \frac{1}{\sqrt{1-\frac{v^2}{c^2}}}$

so,

${T}= \frac{\tau}{\sqrt{1-\frac{v^2}{c^2}}}$

So we can consider this expression like this: If In IRF,An Observer "A" sees another Observer "B" moving,then ${T}$ of Observer B is dilated by the factor of $\frac{\tau}{\sqrt{1-\frac{v^2}{c^2}}}$ where ${\tau}$ is the proper time of Observer A

So we can consider the time dilation as the ratio of coordinate time of one observer to the proper time of another observer...

Am I correct?

 

[ash64449]

I found the earlier Relationship from this forum.. I just connected this equation and with the explanation of time dilation given in this article .

And then i got the conclusion that i posted in this thread.

Explanation of time dilation in that article is in Chapter 12

 

[ghwellsjr]

Hello friends,

If we consider ${T}$ as coordinate time and ${\tau}$ as proper time, the relationship between them is:

$\frac{T}{\tau}= \frac{1}{\sqrt{1-\frac{v^2}{c^2}}}$

so,

${T}= \frac{\tau}{\sqrt{1-\frac{v^2}{c^2}}}$

So we can consider this expression like this: If In IRF,An Observer "A" sees another Observer "B" moving,then ${T}$ of Observer B is dilated by the factor of $\frac{\tau}{\sqrt{1-\frac{v^2}{c^2}}}$ where ${\tau}$ is the proper time of Observer A

So we can consider the time dilation as the ratio of coordinate time of one observer to the proper time of another observer...

Am I correct?

No. The time on any clock is Proper Time. You should not think of Coordinate Time as the time on a clock but rather it is the time for the coordinate system. The Proper Time on any clock applies only to that one clock at whatever location it happens to be. The Coordinate Time applies simultaneously to every location in the coordinate system.

Of course, any clock that is stationary in the coordinate system and set to the Coordinate Time will also display the coordinate time and that is what Einstein does in his derivation of the ratio of Coordinate Time of one system (K) to the Proper Time on a clock fixed at the origin of another system (K') moving with respect to the first system.

And that is what I demonstrated to you in your other thread asking about the same thing. I thought we had made a lot of progress on that thread, including that one observer cannot see the Time Dilation of another observer's clock. We talked about Relativistic Doppler which describes what each observer sees of the other observer's clock.

So let's analyze your statement:

If In IRF,An Observer "A" sees another Observer "B" moving,then ${T}$ of Observer B is dilated by the factor of $\frac{\tau}{\sqrt{1-\frac{v^2}{c^2}}}$ where ${\tau}$ is the proper time of Observer A

The implication is that Observer "A" is stationary because you say that Observer "B" is moving. Therefore you should be talking about the Coordinate Time of System "A" not Observer "A". Then you should not be talking about the Coordinate Time, ${T}$, of Observer "B" but rather the Coordinate Time, ${T}$, of System "A" produces a larger time than the Proper Time, ${\tau}$, of Observer "B" by the ratio $\frac1{\sqrt{1-\frac{v^2}{c^2}}}$

 

[ash64449]

Yes.we have analysed what is time dilation but i didn't understand what is coordinate time and proper time.so i thought i have lots of things to learn..

 

[ash64449]

No. The time on any clock is Proper Time. You should not think of Coordinate Time as the time on a clock but rather it is the time for the coordinate system. The Proper Time on any clock applies only to that one clock at whatever location it happens to be. The Coordinate Time applies simultaneously to every location in the coordinate system.

Thank you for providing the definition of coordinate time and proper time. I really didn't understand what these terms meant but simply made assumptions based on that book of Einstein's.

Of course, any clock that is stationary in the coordinate system and set to the Coordinate Time will also display the coordinate time and that is what Einstein does in his derivation of the ratio of Coordinate Time of one system (K) to the Proper Time on a clock fixed at the origin of another system (K') moving with respect to the first system.

Thank you for providing more understandings from Einstein's Chapter.

And that is what I demonstrated to you in your other thread asking about the same thing. I thought we had made a lot of progress on that thread, including that one observer cannot see the Time Dilation of another observer's clock. We talked about Relativistic Doppler which describes what each observer sees of the other observer's clock.

I know that we made lots of progress in the other thread and then i got into these two new concepts and i got confused a bit.. I really agree that we cannot see Time dilation and instead see clocks ticking faster or slower because of relativistic Doppler Effect.

So let's analyze your statement:



The implication is that Observer "A" is stationary because you say that Observer "B" is moving. Therefore you should be talking about the Coordinate Time of System "A" not Observer "A". Then you should not be talking about the Coordinate Time, ${T}$, of Observer "B" but rather the Coordinate Time, ${T}$, of System "A" produces a larger time than the Proper Time, ${\tau}$, of Observer "B" by the ratio $\frac1{\sqrt{1-\frac{v^2}{c^2}}}$

Yes.This is Exactly what i meant but couldn't express as i don't know many important terms that is required in order to discuss Relativity..

 

[ghwellsjr]

EDIT: I see you delete the following post while I was responding so maybe you were able to figure it all out but I'm going to leave my response as is. Who knows? It might help someone else.

Wait, aren't they same??
What is wrong considering the way i considered first?
I am a bit confused on coordinate time and proper time. Can you explain How the ratio of coordinate time to proper time is time dilation? Also include who's coordinate time and who's proper time is that equation refers to..

Sometimes people talk about the rest frame of Observer "A" (or just the frame of Observer "A") and they mean a frame in which Observer "A" is at rest at the spatial origin of a frame which we could also call Frame "A" or System "A" or Coordinate System "A". But it's not Observer "A"'s frame just because he is at rest in it and being at rest in it does not provide him with any of the Coordinate Time information going on remotely to him. So, to make things clear, especially when discussing the ratio of Coordinate Time to Proper Time, I prefer to have just one frame and one clock. There doesn't have to be any observers involved at all, except us, of course.

I go back to the diagrams I provided earlier. They exactly correspond to Einstein's analysis of how the Proper Time on a clock is dilated when it is moving in an IRF. Here's the beginning of Einstein's analysis:

Let us now consider a seconds-clock which is permanently situated at the origin (x' = 0) of K'. t' = 0 and t' = 1 are two successive ticks of this clock.

And here is my diagram that corresponds to a clock at rest at the spatial origin of a frame that we will call frame K' to be consistent with Einstein's nomenclature:

Note that x'=0 is the Coordinate Distance of the clock which stays at 0. The first two blue dots at the bottom correspond to the Coordinate Times of t'=0 and t'=1. Any questions about this so far?

Next, Einstein uses the Lorentz Transformation process to see what the new Coordinates, x and t, are in a new frame, K, moving at speed v with respect to the first one. I used a specific value of v = -0.6c to make the second diagram for frame K:

Just in case you're not familiar with the Lorentz Transformation process, I will go through the details:

First we calculate gamma, γ, from the speed beta, β, the ratio of v/c, using the equation;

γ = 1/√(1-β²) = 1/√(1-(-0.6)²) = 1/√(1-0.36) = 1/√0.64 = 1/.8 = 1.25

Now we use the form of the LT where c=1 to calculate the new values of the coordinates:

x = γ(x'-βt')
t = γ(t'-βx')

Don't be confused by Einstein's interchanging of the prime and unprimed terms. We accomplish the same thing by changing the sign of the velocity.

So when x'=0 and t'=0 we get:

x = γ(x'-βt') = 1.25(0-(-0.6)*0) = 0
t = γ(t'-βx') = 1.25(0-(-0.6)*0) = 0

Just as Einstein got except he only did it for t. We need both x and t to be able to plot the events on the diagram. You can see that the first dot goes at the Coordinates of x=0 and t=0.

And when x'=0 and t'=1 we get:

x = γ(x'-βt') = 1.25(0-(-0.6)*1) = 1.25(0.6) = 0.75
t = γ(t'-βx') = 1.25(1-(-0.6)*0) = 1.25

Again, just as Einstein got if we plug the velocity into his formula. You can see that the next dot up is at the Coordinates of x=0.75 and t=1.25.

The Proper Time of the clock is dilated because it takes longer for it to tick out 1 second when it is moving. As Einstein said it:

As judged from K, the clock is moving with the velocity v; as judged from this reference-body, the time which elapses between two strokes of the clock is not one second, but

seconds, i.e. a somewhat larger time. As a consequence of its motion the clock goes more slowly than when at rest.

I think the issue that you are dealing with is that we say the ratio of Coordinate Time to Proper Time is gamma which is greater than 1 and indicates Time Dilation but yet we say the moving clock is ticking slower than a stationary clock so it seems like we should be saying the Coordinate Time is the one that is dilated. But we do it this way to be consistent with the concept of Length Contraction. When we depict objects and clocks on a spacetime diagram, we see that the length of a moving object takes up less coordinate space and the ticking of a moving clock takes up more coordinate time.

 

[Popper]

Yes.we have analysed what is time dilation but i didn't understand what is coordinate time and proper time.so i thought i have lots of things to learn..

The proper time between two events is the time as measured by a clock whose which moves through both events whereas coordinate time is the time measured by synchronized clocks and which the time between the two events is the difference between the readings on two different clocks.

 

[pervect]

Hello friends,

So we can consider the time dilation as the ratio of coordinate time of one observer to the proper time of another observer...

Except for the fact that proper-time is independent of any observer, that's exactly right.

Time dilation is the ratio of coordinate time to the observer-independent proper time. Hence time dilation is always coordinate dependent.

I see that another poster told you that you were wrong, I don't understand why he thinks it's wrong. I hope I can convince him civily not to post misinformation like that :-(.

 

[ash64449]

I think the issue that you are dealing with is that we say the ratio of Coordinate Time to Proper Time is gamma which is greater than 1 and indicates Time Dilation but yet we say the moving clock is ticking slower than a stationary clock so it seems like we should be saying the Coordinate Time is the one that is dilated.

Exactly.this is the one that confused me..That Coordinate time should be the one that is Time Dilated.Now i understand Time Dilation. It is the Proper Time that changes when It is moving with respect to coordinate system A... So this Proper Time needs 1.25 seconds in coordinate time of A to tick 1 second..

But we do it this way to be consistent with the concept of Length Contraction. When we depict objects and clocks on a spacetime diagram, we see that the length of a moving object takes up less coordinate space and the ticking of a moving clock takes up more coordinate time.

Can you explain How Arranging Time Dilation like this helps us to Explain the concept of length contraction easier?

 

[ash64449]

EDIT: I see you delete the following post while I was responding so maybe you were able to figure it all out but I'm going to leave my response as is. Who knows? It might help someone else.

Yes.Sorry that i deleted the post. I got the answer from your earlier comment itself.I thought a little bit hard. And Your presentation of answering the post is really great.

 

[ash64449]

Except for the fact that proper-time is independent of any observer, that's exactly right.

Time dilation is the ratio of coordinate time to the observer-independent proper time. Hence time dilation is always coordinate dependent.

I see that another poster told you that you were wrong, I don't understand why he thinks it's wrong. I hope I can convince him civily not to post misinformation like that :-(.

Ya.Proper Time is the one that change. But it appears invariant because we see co-ordinate time of our system relative to that observer change... That is why Time dilation is coordinate dependent..

 

[ghwellsjr]

The proper time between two events is the time as measured by a clock whose which moves through both events whereas coordinate time is the time measured by synchronized clocks and which the time between the two events is the difference between the readings on two different clocks.

I don't know why you would express Proper Time in this way. It makes it sound like there is a single Proper Time between two events but as you correctly point out, it is measured by a clock which moves through both events, but what you didn't point out is that it is dependent on the path of that clock between those two events so two different clocks taking two different paths can end up with different accumulated times on them.

It is sufficient to say that Proper Time is what any clock measures.

Also, when you are talking about coordinate time, you should not be connecting it with actual clocks. Of course, you could always put synchronized clocks at the two events in question but then when you do a Lorentz Transformation on the situation, those two clocks will not be synchronized and you will have to create two more synchronized clocks to put at those two events. And how will you know what time to put on them? You look at the Coordinate Times of the two events and you set the clocks accordingly. So what have you accomplished by this sort of explanation?

The whole point of Time Dilation is that it maintains the Proper Time of all events on real clocks even though the Coordinate Time of those events can be different.

 

[ghwellsjr]

Hello friends,

So we can consider the time dilation as the ratio of coordinate time of one observer to the proper time of another observer...

Except for the fact that proper-time is independent of any observer, that's exactly right.

Time dilation is the ratio of coordinate time to the observer-independent proper time. Hence time dilation is always coordinate dependent.

I see that another poster told you that you were wrong, I don't understand why he thinks it's wrong. I hope I can convince him civily not to post misinformation like that :-(.

Didn't you just point out that his statement wasn't completely correct? That's what I did, except I provided a great many more details.

If you think something in any of my posts is misinformation, you should quote it and point out what you think is wrong. You won't have any problem convincing me to not post misinformation but you have to point out specifically what it is. And please don't take anything out of context, read my entire posts.

 

[ghwellsjr]

But we do it this way to be consistent with the concept of Length Contraction. When we depict objects and clocks on a spacetime diagram, we see that the length of a moving object takes up less coordinate space and the ticking of a moving clock takes up more coordinate time.

Can you explain How Arranging Time Dilation like this helps us to Explain the concept of length contraction easier?

OK, here's a spacetime diagram for an IRF in which the observer and mirror are at rest showing one tick of a light clock:

At time 4 nanoseconds, the observer in blue at location 0 sends a flash of green light to a red mirror that is six feet away from him. He gets the reflection back at time 16 nanoseconds so each tick is 12 nanoseconds long.

Now let's see what happens if we view the same thing in an IRF moving at -0.6c with respect to the original IRF:

Now the observer and his mirror are moving at 0.6c. Notice that the distance to the mirror is Length Contracted. Instead of six feet it is only 4.8 feet. Be sure to measure this along a horizontal line where the Coordinate Time is a constant. Also notice that the observer's time is dilated, that is, it takes longer in the diagram to mark of the same Proper Time from the first IRF. Finally note that the flash of light propagates at c along a 45-degree angle in both diagrams and so the observer continues to experience exactly the same thing in this diagram as he did in the first one. He sends the light signal out at 4 nanoseconds of his Proper Time and receives the reflection at 16 nanoseconds of his Proper Time.

Does that answer your question?

 

[ash64449]

OK, here's a spacetime diagram for an IRF in which the observer and mirror are at rest showing one tick of a light clock:

At time 4 nanoseconds, the observer in blue at location 0 sends a flash of green light to a red mirror that is six feet away from him. He gets the reflection back at time 16 nanoseconds so each tick is 12 nanoseconds long.

Now let's see what happens if we view the same thing in an IRF moving at -0.6c with respect to the original IRF:

Now the observer and his mirror are moving at 0.6c. Notice that the distance to the mirror is Length Contracted. Instead of six feet it is only 4.8 feet. Be sure to measure this along a horizontal line where the Coordinate Time is a constant. Also notice that the observer's time is dilated, that is, it takes longer in the diagram to mark of the same Proper Time from the first IRF. Finally note that the flash of light propagates at c along a 45-degree angle in both diagrams and so the observer continues to experience exactly the same thing in this diagram as he did in the first one. He sends the light signal out at 4 nanoseconds of his Proper Time and receives the reflection at 16 nanoseconds of his Proper Time.

Does that answer your question?

Yes.This Answers my question. I have another question. Is Length Contraction Observed?

Well,You said Time Dilation is not observed.Instead Relativistic Doppler Effect..

 

[ghwellsjr]

Yes.This Answers my question. I have another question. Is Length Contraction Observed?

Well,You said Time Dilation is not observed.Instead Relativistic Doppler Effect..

No, Length Contraction is also not observed. How can it be? It can be different in different IRF's. Just look at the two examples in the above diagrams. Can the blue observer detect anything different as he looks for the reflection from his mirror as determined from either IRF?

 

[ash64449]

No, Length Contraction is also not observed. How can it be? It can be different in different IRF's. Just look at the two examples in the above diagrams. Can the blue observer detect anything different as he looks for the reflection from his mirror as determined from either IRF?

no.i said the other observer who observes the blue observer... Yes,like time dilation,length contraction changes with different frames of reference.
If length contraction is not observed,then what change is observed instead of it?
Just like this:time dilation is not observed,instead relativistic doppler effect...

 

[ash64449]

and i do agree that blue cannot identify length contraction.but i asked whether other observer in a coordinate system observe length contraction of the blue observer?

 

[ghwellsjr]

and i do agree that blue cannot identify length contraction.but i asked whether other observer in a coordinate system observe length contraction of the blue observer?

Usually when we are talking about Doppler and especially when it is shown on a spacetime diagram, we are only considering relative motion between observers that are directly in line with each other because the formula is very simple and because we can only show one dimension of space on a normal spacetime diagram.

If we do the same thing with Length Contraction, that is, only consider in line motion, it becomes very difficult to visually determine the length of an object along that dimension. So usually, when this subject comes up, we consider the appearance of an object that is traveling at right angles to our line of sight but some distance away. And it turns out that the analysis is extremely difficult to ascertain because we cannot just take the Length Contraction along the direction of motion and say that an object will appear the way it would be drawn on a diagram because the observer has to wait for the light signals coming from the different portions of the object to arrive at his eyes simultaneously and since the object is in motion at a speed comparable to that of light, it is a complicated subject.

However, the subject has been dealt with, most notably by Terrell, who has determined that the shape of a sphere traveling at high speed will still appear as a sphere. That is rather surprising, don't you think? Anyway, for more information you can read the wikipedia article or see this thread.

 

[ash64449]

Usually when we are talking about Doppler and especially when it is shown on a spacetime diagram, we are only considering relative motion between observers that are directly in line with each other because the formula is very simple and because we can only show one dimension of space on a normal spacetime diagram.

If we do the same thing with Length Contraction, that is, only consider in line motion, it becomes very difficult to visually determine the length of an object along that dimension. So usually, when this subject comes up, we consider the appearance of an object that is traveling at right angles to our line of sight but some distance away. And it turns out that the analysis is extremely difficult to ascertain because we cannot just take the Length Contraction along the direction of motion and say that an object will appear the way it would be drawn on a diagram because the observer has to wait for the light signals coming from the different portions of the object to arrive at his eyes simultaneously and since the object is in motion at a speed comparable to that of light, it is a complicated subject.
.

George,why can't we consider "real" situations?? Just like Einstein's Thought Experiment?

Whenever i am providing with examples,it means that i am considering "real" situations..

 

[ghwellsjr]

George,why can't we consider "real" situations?? Just like Einstein's Thought Experiment?

Whenever i am providing with examples,it means that i am considering "real" situations..

I thought I was considering "real" situations. Why did you think I wasn't?

 

[ash64449]

Einstein's Thought experiment helps us to understand length contraction.That is,he provided a method to help observe length contraction..

http://www.marxists.org/reference/archive/einstein/works/1910s/relative/relativity.pdf

Go to this chapter:On the Relativity of the
Conception of Distance.

This Chapter actually proves that length contraction can be observed..This is real situation..

 

[ash64449]

I thought I was considering "real" situations. Why did you think I wasn't?

You said this earlier:

"Usually when we are talking about Doppler and especially when it is shown on a spacetime diagram, we are only considering relative motion between observers that are directly in line with each other because the formula is very simple and because we can only show one dimension of space on a normal spacetime diagram.

If we do the same thing with Length Contraction, that is, only consider in line motion, it becomes very difficult to visually determine the length of an object along that dimension."

You said it is difficult to understand length contraction using space-time diagrams.I agree..But we can identify length contraction with the help of real situations..

 

[ash64449]

However, the subject has been dealt with, most notably by Terrell, who has determined that the shape of a sphere traveling at high speed will still appear as a sphere. That is rather surprising, don't you think? .

yes.George.It is surprising...

Well,will we obtain same result if that sphere was made to accelerate at high speed?!

 

[ghwellsjr]

Einstein's Thought experiment helps us to understand length contraction.That is,he provided a method to help observe length contraction..

http://www.marxists.org/reference/archive/einstein/works/1910s/relative/relativity.pdf

Go to this chapter:On the Relativity of the
Conception of Distance.

This Chapter actually proves that length contraction can be observed..This is real situation..

At first, I could not get your link to work. I was able to get to this page:

http://www.marxists.org/reference/archive/einstein/works/1910s/relative/index.htm

And from there to the chapter you referenced:

http://www.marxists.org/reference/archive/einstein/works/1910s/relative/ch10.htm

However, this chapter is not talking about observing or seeing a high speed object as length contracted, it's talking about an observer measuring the length of a high speed object, something that takes time for him to do and is based on assumptions that pinpoint the IRF in which he is making the measurements and doing the calculation.

I discussed this for the scenario of the observer and his mirror:

Thanks, I'm glad you liked them.

Now I want to take that same diagram that depicts the situation that adjacent described in his Opening Post (OP) and show you how it depicts the Length Contraction of the distance between the "person" in blue and the mirror in red which the "person" measured to be 6 feet with his ruler. There are a couple ways that other people, stationary in the IRF in which the "person" is moving can make this assessment. They both involve radar measurements. This is similar to the way a cop can clock you for speeding. It works by sending a light (or radar) pulse at an object and waiting for the return echo and then measuring how long the round trip took and dividing it by two and assuming that it took the same amount of time to get to the object as it took for the light to get back from the object. So we place the time of the measurement at the midpoint of the measurement and we consider the measurement of the distance to be how far the light traveled in the measured amount of time. By making successive measurements, we can establish a speed.

Here's the first spacetime diagram:

I have drawn the second observer as a black line at coordinate distance of 15 feet. At coordinate time of 1 nanoseconds, he happens to send out the first radar pulse in blue and a short time later he sends out the second radar pulse in green at 9 ns. He receives the first reflection at coordinate time of 13 ns and the second one at 15 ns. After doing the calculation I previously described, he calculates that the mirror was 6 feet away at time 7 ns and it was 3 feet away at 12 ns. The differences between these calculates establishes that the mirror is moving toward him at 3 feet in 5 ns. which is 0.6 feet per ns or just 0.6c.

So now, armed with the measurement of the mirror's speed of 0.6 feet/ns, he waits until the mirror reach him which happens at time 17 ns. Then he waits for the "person" to reach him which happens at time 25 ns. Since it took 8 ns for the object to pass him at 0.6 feet/ns, he concludes that its length is 0.6 times 8 or 4.8 feet, the same as the gamma process determined.

Now I want to show you another way. This involves measurements of both the "person" in blue and the mirror in red taken at the same "time":

First, the observer in black sends an orange radar pulse at time 4.2 ns and a second green one at time 9 ns. He receives the echoes at 15 ns and 19.8 ns. He concludes that the blue "person" is 7.8 feet away at time 12 ns and the red "mirrors" are 3 feet away at the same time leaving a difference of 4.8 feet.

All methods agree.

 

[ghwellsjr]

yes.George.It is surprising...

Well,will we obtain same result if that sphere was made to accelerate at high speed?!

I don't know but that's a different subject.

 

[ash64449]

However, this chapter is not talking about observing or seeing a high speed object as length contracted, it's talking about an observer measuring the length of a high speed object, something that takes time for him to do and is based on assumptions that pinpoint the IRF in which he is making the measurements and doing the calculation.

I cannot understand.Let me explain how length contraction can be observed. You can correct in what i have said so that i can understand what i have missed.

Determine the length of the rod when it is at rest relative to a coordinate system. Now let the rod move relative to that system. Let the rod be 10 meters long. mark two points that are 10 meters apart. Let us name the first point as 'A' and second point as 'B'.when rod passes the point 'B',Note whether the other end of the rod is at point 'A'. If the other end is at point 'A',then rods do not get contracted(or we can say that length contraction is not observed). And if the other end is not in point 'A',instead the other end is in between those two points,then rods contract when they travel(or length contraction is observed)..

What is wrong with this experiment??

I totally agree that Time Dilation is not observed.. I cannot think of any thought experiment that can prove that...

 

[Mentz114]

I cannot understand.Let me explain how length contraction can be observed. You can correct in what i have said so that i can understand what i have missed.

Determine the length of the rod when it is at rest relative to a coordinate system. Now let the rod move relative to that system. Let the rod be 10 meters long. mark two points that are 10 meters apart. Let us name the first point as 'A' and second point as 'B'.when rod passes the point 'B',Note whether the other end of the rod is at point 'A'. If the other end is at point 'A',then rods do not get contracted(or we can say that length contraction is not observed). And if the other end is not in point 'A',instead the other end is in between those two points,then rods contract when they travel(or length contraction is observed)..

What is wrong with this experiment??

I think the problem with this scenario is that one cannot observe A and B simultaneously in all frames.

If radar is used to measure the length ( along the direction of motion) of a moving rod, then the observed lengths transform exactly like the Doppler wavelength. So an approaching rod will be measured as $L_0\sqrt{\frac{1-\beta}{1+\beta}}$ and a receeding rod $L_0\sqrt{\frac{1+\beta}{1-\beta}}$.

 

[ash64449]

I think the problem with this scenario is that one cannot observe A and B simultaneously in all frames..

well,there is a way to do that. Take a camera,when the observer sees the rod reach at the points B,take the picture. In it i am sure that he can determine that.

 

[Mentz114]

well,there is a way to do that. Take a camera,when the observer sees the rod reach at the points B,take the picture. In it i am sure that he can determine that.

Explain exactly how. You are still saying 'when the observer sees ...' which is imprecise ( to me in any case).

 

[ash64449]

At first, I could not get your link to work. I was able to get to this page:

http://www.marxists.org/reference/archive/einstein/works/1910s/relative/index.htm

And from there to the chapter you referenced:

http://www.marxists.org/reference/archive/einstein/works/1910s/relative/ch10.htm

However, this chapter is not talking about observing or seeing a high speed object as length contracted, it's talking about an observer measuring the length of a high speed object, something that takes time for him to do and is based on assumptions that pinpoint the IRF in which he is making the measurements and doing the calculation.

I discussed this for the scenario of the observer and his mirror:

wait,,, so... You agree that length contraction is observed??

 

[ash64449]

Explain exactly how. You are still saying 'when the observer sees ...' which is imprecise ( to me in any case).

why do you say that 'seeing' is imprecise?
Look at the article that i linked to george,einstein was also used the method similar to what i said.
The reason why length contraction takes place is because light takes time to reach and as a result the word 'seeing' is very important..

 

[ash64449]

Mentz14, the reason why we cannot 'see' time dilation is because time is not something that we cannot 'see'. Instead we see time ticking faster and slower because of light and that is why relativistic doppler effect is seen..
Another reason why time dilation is not seen is because it not only involved proper time,coordinate time is too involved which we cannot in real situations cannot understand it because light has no role to play in coordinate time..

 

[Mentz114]

why do you say that 'seeing' is imprecise?
Look at the article that i linked to george,einstein was also used the method similar to what i said.
The reason why length contraction takes place is because light takes time to reach and as a result the word 'seeing' is very important..

It is 'when' that is imprecise ! What do you mean by 'when X sees Y' ? It has been stated many times on this forum that the LC phenomemnon is caused by the relativity of simultaneity - i.e. we cannot simultaneously perform two remote merasurements.

You have ignored the best part of my post ( the radar measurement).

I have to tell you that concentrating on LC and/or TD is not a good way to approach relativity. Stick to observables like radar and invariants like proper time. I've nothing more to say on this.

 

[Mentz114]

Mentz14, the reason why we cannot 'see' time dilation is because time is not something that we cannot 'see'. Instead we see time ticking faster and slower because of light and that is why relativistic doppler effect is seen..
Another reason why time dilation is not seen is because it not only involved proper time,coordinate time is too involved which we cannot in real situations cannot understand it because light has no role to play in coordinate time..

Sorry, I'm not involved in that discussion. Let's stick to 'seeing length contraction'.
(I've edited my post #34)

 

[ash64449]

You haven't understood my post. I said exactly what you said.

You said:LC phenomenon is caused by the relativity of simultaneity

And i said:The reason why length contraction takes place is because light takes time to reach and as a result the word 'seeing' is very important..

Both of them are same. You didn't understand that.

i.e. we cannot simultaneously perform two remote measurements.
.

Relativity of simultaneity doesn't mean the above statement. It means that events being simultaneous depends on reference frames.

 

[Dale]

YouYou said:LC phenomenon is caused by the relativity of simultaneity

And i said:The reason why length contraction takes place is because light takes time to reach and as a result the word 'seeing' is very important..

Both of them are same. You didn't understand that.

They are not both the same. The reason why length contraction takes place is because the speed of light is invariant, not because it is finite. If we had a universe where the speed of light were finite but there invariant speed was not then we would not have length contraction. Your statement is wrong.

IMO, Mentz114's statement is also wrong. Both length contraction and relativity of simultaneity are "caused" by the principle of relativity and the invariance of the speed of light. They don't cause each other.

 

[ash64449]

They are not both the same. The reason why length contraction takes place is because the speed of light is invariant, not because it is finite. If we had a universe where the speed of light were finite but there invariant speed was not then we would not have length contraction. Your statement is wrong.
.

DaleSpam,

see this thread: https://www.physicsforums.com/showthread.php?t=688843

Read the comment #8...

And You will find that Why speed of light is invariant even though light moves in a reference frame c+v and c-v relative to a observer by reading further...

So My statement holds true.

 

[ash64449]

IMO, Mentz114's statement is also wrong. Both length contraction and relativity of simultaneity are "caused" by the principle of relativity and the invariance of the speed of light. They don't cause each other.

Sorry DaleSpam,You are right in saying that Mentz114's statement is wrong.

Actually,i should say that they are closely related and not length contraction is caused by relativity of simultaneity..

I faced a similar problem like this when we first met and i made a similar assertion.. Now i understood it..

 

[Dale]

see this thread: https://www.physicsforums.com/showthread.php?t=688843

Read the comment #8...

And You will find that Why speed of light is invariant even though light moves in a reference frame c+v and c-v relative to a observer by reading further...

So My statement holds true.

The referenced post has nothing to do with the "cause" of length contraction. It simply assumes length contraction (and time dilation and relativity of simultaneity) in order to show a graph of a radar pulse.

References to random irrelevant comments is a bad habit of yours which you need to work on.

 

[ash64449]

The referenced post has nothing to do with the "cause" of length contraction. It simply assumes length contraction (and time dilation and relativity of simultaneity) in order to show a graph of a radar pulse.

Sorry,that is not what i was saying..in that thread you can see that to an observer,light moves c+v in one-way of the round trip and when it reflects back light moves c-v relative to observer. But one can only measure a full round trip and measuring full round trip will only come to the conclusion that light is invariant. See? Light speed is finite and even tough Light speed is invariant,because one can only measure full round trip.

I am extremely sorry if you felt that i linked that comment to say that length contraction is caused by relativity of simultaneity. I actually linked to show how light is invariant in different frames even though light travels finite speed and even if it moves c+v and C-v relative to observer too..


.

 

[ash64449]

And this "c+v" and "c-v" is same as telling that "Light takes time to reach" and that is what according to me Relativity Of simultaneity. I.e. I consider c+v and c-v as relativity of simultaneity.

 

[ash64449]

And i consider "hastening towards the beam of light" and "moving ahead of the beam of light" as light takes less time to reach and light takes more time to reach as it is said in this book:

http://www.marxists.org/reference/archive/einstein/works/1910s/relative/relativity.pdf.

Go to chapter Relativity of Simultaneity.

""he is hastening towards the
beam of light coming from B, whilst he is riding on ahead of the beam of light coming from
A. Hence the observer will see the beam of light emitted from B earlier than he will see that
emitted from A"".

and then he says ""Observers who take the railway train as their reference-body must therefore
come to the conclusion that the lightning flash B took place earlier than the lightning flash
A""

If you consider i have made a wrong conclusion,then help me correct it..

 

[Mentz114]

IMO, Mentz114's statement is also wrong. Both length contraction and relativity of simultaneity are "caused" by the principle of relativity and the invariance of the speed of light. They don't cause each other.

Can you be specific and say which of my several statements is wrong. I need to know to avoid the error in future.

[Edit]
I presume this is the one

It has been stated many times on this forum that the LC phenomenon is caused by the relativity of simultaneity - i.e. we cannot simultaneously perform two remote measurements.

I don't say that the oft quoted explanation is correct, merely that it was quoted many times (true).

Also, it is not possible to perform simultaneous remote measurements, is it ?

I apologise to the OP if I've confused the issue, but he does rather ignore most of what I posted.
I get impatient with people who think relativity is about LC and TD, and I suspect they have a hidden agenda.

 

[Dale]

I actually linked to show how light is invariant in different frames even though light travels finite speed and even if it moves c+v and C-v relative to observer too.

OK. That is also irrelevant to the topic. You stated "The reason why length contraction takes place is because light takes time to reach". That is false, and the fact that the closing speed is c+v or c-v is not relevant. There is no mention in the quote of anything which even remotely supports the claim that "length contraction takes place ... because light takes time to reach".

This posting of irrelevant and unresponsive quotes must stop.

 

[Dale]

Can you be specific and say which of my several statements is wrong. I need to know to avoid the error in future.

My apologies. I was reacting specifically the statement in ash64449's post which he attributed to you: "LC phenomenon is caused by the relativity of simultaneity". I didn't even check to see if the attribution was correct. The correct statement would be: "LC phenomenon and the relativity of simultaneity are both caused by the principle of relativity and the invariance of c"

I apologise to the OP if I've confused the issue, but he does rather ignore most of what I posted.
I get impatient with people who think relativity is about LC and TD, and I suspect they have a hidden agenda.

I have noted the same about the OP and agree with your impatience.

 

[ghwellsjr]

At first, I could not get your link to work. I was able to get to this page:

http://www.marxists.org/reference/archive/einstein/works/1910s/relative/index.htm

And from there to the chapter you referenced:

http://www.marxists.org/reference/archive/einstein/works/1910s/relative/ch10.htm

However, this chapter is not talking about observing or seeing a high speed object as length contracted, it's talking about an observer measuring the length of a high speed object, something that takes time for him to do and is based on assumptions that pinpoint the IRF in which he is making the measurements and doing the calculation.

I discussed this for the scenario of the observer and his mirror:

Thanks, I'm glad you liked them.

Now I want to take that same diagram that depicts the situation that adjacent described in his Opening Post (OP) and show you how it depicts the Length Contraction of the distance between the "person" in blue and the mirror in red which the "person" measured to be 6 feet with his ruler. There are a couple ways that other people, stationary in the IRF in which the "person" is moving can make this assessment. They both involve radar measurements. This is similar to the way a cop can clock you for speeding. It works by sending a light (or radar) pulse at an object and waiting for the return echo and then measuring how long the round trip took and dividing it by two and assuming that it took the same amount of time to get to the object as it took for the light to get back from the object. So we place the time of the measurement at the midpoint of the measurement and we consider the measurement of the distance to be how far the light traveled in the measured amount of time. By making successive measurements, we can establish a speed.

Here's the first spacetime diagram:

I have drawn the second observer as a black line at coordinate distance of 15 feet. At coordinate time of 1 nanoseconds, he happens to send out the first radar pulse in blue and a short time later he sends out the second radar pulse in green at 9 ns. He receives the first reflection at coordinate time of 13 ns and the second one at 15 ns. After doing the calculation I previously described, he calculates that the mirror was 6 feet away at time 7 ns and it was 3 feet away at 12 ns. The differences between these calculates establishes that the mirror is moving toward him at 3 feet in 5 ns. which is 0.6 feet per ns or just 0.6c.

So now, armed with the measurement of the mirror's speed of 0.6 feet/ns, he waits until the mirror reach him which happens at time 17 ns. Then he waits for the "person" to reach him which happens at time 25 ns. Since it took 8 ns for the object to pass him at 0.6 feet/ns, he concludes that its length is 0.6 times 8 or 4.8 feet, the same as the gamma process determined.

Now I want to show you another way. This involves measurements of both the "person" in blue and the mirror in red taken at the same "time":

First, the observer in black sends an orange radar pulse at time 4.2 ns and a second green one at time 9 ns. He receives the echoes at 15 ns and 19.8 ns. He concludes that the blue "person" is 7.8 feet away at time 12 ns and the red "mirrors" are 3 feet away at the same time leaving a difference of 4.8 feet.

All methods agree.

wait,,, so... You agree that length contraction is observed??

No, I never said that. What I said was that an observer can make some assumptions, take some measurements, do some calculations and from that determine the Length Contraction of a moving object as determined from his own rest frame. I showed you in the above two diagrams how the black observer can do this and I illustrated it in his own rest frame. Now I don't call that observing, do you?

Furthermore, you should not think that just because he is able to make some assumptions, take some measurements, do some calculations and come up with the same determination of the Length Contraction of a moving object as would be determined from his rest frame that he is actually determining a real Length Contraction because if he makes slightly different (but just as valid) assumptions, he can determine different Length Contractions.

The assumptions he is making is that the radar signal takes the same amount of time to propagate to an object as it takes for the echo to return to him, and that the time of the measurement applies at the midpoint in time between when he sent out the radar signal and when he received it. Are these valid assumptions? They are exactly the same assumptions that we use to define an IRF in SR, so it should be no surprise that they lead to the same determination of Length Contraction for a moving object in a particular IRF.

But rather than make some different assumptions, let me show you the same processes that the black observer makes but using the rest frame of the blue "person" and his red mirror (which we will assume are connected with a six-foot rod) and in which the black observer is now moving. We are going back to the original IRF from post #14 and you will note that the distance between the blue "person" and his red mirror is not contracted but is six feet.

Here is the first scenario where the black observer first measures the speed of the approaching (as far as he's concerned) rod and then times how long it takes for the rod to pass him:

Read the explanation above for the assumptions, measurements and calculation that the black observer performs to determine that the rod is Length Contracted to 4.8 feet, even though in this IRF it is not.

And for the second scenario where the black observer makes two different measurements but comes to the same conclusion:

I hope you can see that in neither IRF, can the black observer have any inkling what IRF is being used and therefore what the Length Contraction is. I hope you can also see that if the black observer had assumed that the radar signal took a different length of time to get to each target than it did to get back (something that cannot be known apart from an assumption or definition), he could have determined that the rod was not Length Contracted.

 

[ghwellsjr]

However, this chapter is not talking about observing or seeing a high speed object as length contracted, it's talking about an observer measuring the length of a high speed object, something that takes time for him to do and is based on assumptions that pinpoint the IRF in which he is making the measurements and doing the calculation.

I cannot understand.Let me explain how length contraction can be observed. You can correct in what i have said so that i can understand what i have missed.

Determine the length of the rod when it is at rest relative to a coordinate system. Now let the rod move relative to that system. Let the rod be 10 meters long. mark two points that are 10 meters apart. Let us name the first point as 'A' and second point as 'B'.when rod passes the point 'B',Note whether the other end of the rod is at point 'A'. If the other end is at point 'A',then rods do not get contracted(or we can say that length contraction is not observed). And if the other end is not in point 'A',instead the other end is in between those two points,then rods contract when they travel(or length contraction is observed)..

What is wrong with this experiment??

I totally agree that Time Dilation is not observed.. I cannot think of any thought experiment that can prove that...

What Einstein said to do in your referenced article is exactly what I described in post #14 after the second diagram. It's very easy to see on a spacetime diagram because the coordinates provide the means to know when the measurements of A and B are taken at the same time.

However, doing it in a real situation, as you requested and as Einstein described, is not easy. You basically would require a number of synchronized clocks all along the tracks that could record when each end of the rod reached them and then you would have to go back and examine the records to find two times on two different clocks that were the same and each indicated the passing of one end or the other of the rod.

Your method lacks any means to determine the same time at both events, but Mentz pointed this out already so I won't belabor the point.

 

[ash64449]

OK. That is also irrelevant to the topic. You stated "The reason why length contraction takes place is because light takes time to reach". That is false, and the fact that the closing speed is c+v or c-v is not relevant. There is no mention in the quote of anything which even remotely supports the claim that "length contraction takes place ... because light takes time to reach".

This posting of irrelevant and unresponsive quotes must stop.

i am sorry that i wrote ' length contraction takes place because light takes time to reach'.

 

[ash64449]

No, I never said that. What I said was that an observer can make some assumptions, take some measurements, do some calculations and from that determine the Length Contraction of a moving object as determined from his own rest frame. I showed you in the above two diagrams how the black observer can do this and I illustrated it in his own rest frame. Now I don't call that observing, do you?

Furthermore, you should not think that just because he is able to make some assumptions, take some measurements, do some calculations and come up with the same determination of the Length Contraction of a moving object as would be determined from his rest frame that he is actually determining a real Length Contraction because if he makes slightly different (but just as valid) assumptions, he can determine different Length Contractions.

The assumptions he is making is that the radar signal takes the same amount of time to propagate to an object as it takes for the echo to return to him, and that the time of the measurement applies at the midpoint in time between when he sent out the radar signal and when he received it. Are these valid assumptions? They are exactly the same assumptions that we use to define an IRF in SR, so it should be no surprise that they lead to the same determination of Length Contraction for a moving object in a particular IRF.

But rather than make some different assumptions, let me show you the same processes that the black observer makes but using the rest frame of the blue "person" and his red mirror (which we will assume are connected with a six-foot rod) and in which the black observer is now moving. We are going back to the original IRF from post #14 and you will note that the distance between the blue "person" and his red mirror is not contracted but is six feet.

Here is the first scenario where the black observer first measures the speed of the approaching (as far as he's concerned) rod and then times how long it takes for the rod to pass him:

https://www.physicsforums.com/attachment.php?attachmentid=58449&stc=1&d=1367619642

Read the explanation above for the assumptions, measurements and calculation that the black observer performs to determine that the rod is Length Contracted to 4.8 feet, even though in this IRF it is not.

And for the second scenario where the black observer makes two different measurements but comes to the same conclusion:

https://www.physicsforums.com/attachment.php?attachmentid=58450&stc=1&d=1367619642

I hope you can see that in neither IRF, can the black observer have any inkling what IRF is being used and therefore what the Length Contraction is. I hope you can also see that if the black observer had assumed that the radar signal took a different length of time to get to each target than it did to get back (something that cannot be known apart from an assumption or definition), he could have determined that the rod was not Length Contracted.

George,i cannot see the images that you posted in this post.

Anyway i understood the significance of this post-it says that you cannot conduct experiment by only observing.There always include assumptions and the fact that we cannot observe 'two' events at the same time. But please clarify a little bit by answering to the post that is present below to this one.