Relation between coordinate time and proper time

[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.

 

[ash64449]

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.

No,You don't need a number of synchronized clocks all along the tracks that could record when each end of the rod reached them

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.

Yes.Now i understood the meaning of what Mentz was actually saying-You cannot measure at the same time,both events. Well,there is a way to measure both events at the same time:

Take a Snapshot.

Think that i have a detector in my hand,which immediately photographs the whole events taking place when the rod meets at point "A". Now whatever we see in that snapshot are the simultaneous events with the event of which one end of the rod meets at point A.

So,here we see that observing only 'one' event helps us to know all other events that are 'simultaneous' with other events.

What is wrong with this?

 

[Popper]

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.

Because the OP asked what the difference was between proper time and coordinate time. He didn't ask what the properties of proper time are. I was only attempting to explain what the definition is and that definitions I stated is precisely correct. In my opinion just because I didn't say that there are many ways for a clock to move between two clocks doesn't mean that my answer was wrong or lacking.

But if you insist on being complete; the proper time between two events is the time measured by a clock (or person attached to the clock/wristwatch) which travels on a timelike worldline between the two events.

Also, when you are talking about coordinate time, you should not be connecting it with actual clocks.

I disagree. Coordinate time refers to actual clocks so it was very important to mention them.

 

[ghwellsjr]

But if you insist on being complete; the proper time between two events is the time measured by a clock (or person attached to the clock/wristwatch) which travels on a timelike worldline between the two events.

It's not a matter of being complete--it's a matter of adding so much extraneous stuff. Let me take your definition and purge it of what isn't needed:

the proper time [STRIKE]between two events[/STRIKE] is the time measured by a clock[STRIKE] (or person attached to the clock/wristwatch) which travels on a timelike worldline between the two events[/STRIKE].

Since a clock can only travel on a timelike worldline, why do you include that? And why do you want to limit it to two events? Every clock continuously measures out Proper Time.

Also, when you are talking about coordinate time, you should not be connecting it with actual clocks.

I disagree. Coordinate time refers to actual clocks so it was very important to mention them.

If Coordinate Time refers to actual clocks and Proper Time refers to actual clocks, then what's the difference? Remember, you said:

Because the OP asked what the difference was between proper time and coordinate time.

 

[ghwellsjr]

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

You need to be logged on in order to see images that are uploaded to the Physics Forums.

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.

Please log on an study my post. It can teach you a lot. That's what you are badly in need of.

 

[ash64449]

You need to be logged on in order to see images that are uploaded to the Physics Forums.

Please log on an study my post. It can teach you a lot. That's what you are badly in need of.

George,i don't understand.Still i cannot find the images.

What do you mean i need to be logged on?

Shouldn't i need to log on to reply post? Do you mean that? Well,then i am logged on and still i cannot see them. The images that you posted on #47.I am not talking about the images in the quote.i am not seeing images that you posted..

 

[ash64449]

George,when i open the image in new tab,this message appears:

vBulletin Message

Invalid Attachment specified. If you followed a valid link, please notify the administrator

 

[ghwellsjr]

I re-uploaded them, even though I could see them. Can you see them now?

 

[ash64449]

I re-uploaded them, even though I could see them. Can you see them now?

YES! I can see them now.. I will read them very carefully and then reply

 

[ghwellsjr]

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.

No,You don't need a number of synchronized clocks all along the tracks that could record when each end of the rod reached them

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.

Yes.Now i understood the meaning of what Mentz was actually saying-You cannot measure at the same time,both events. Well,there is a way to measure both events at the same time:

Take a Snapshot.

Think that i have a detector in my hand,which immediately photographs the whole events taking place when the rod meets at point "A". Now whatever we see in that snapshot are the simultaneous events with the event of which one end of the rod meets at point A.

So,here we see that observing only 'one' event helps us to know all other events that are 'simultaneous' with other events.

What is wrong with this?

Mentz already pointed out what is wrong with taking a snapshot when you said the same thing way back in post #29:

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.

I don't know why you think a camera would be any better than an observer's eyeballs. Both are subject to the light travel time from each event to the camera/eye and since it is different for the two events in question, they will not see both events at the same time, even though we specify that they must be in order to determine the correct length of the rod.

Are you aware that if you set up a row of clocks and synchronized them and then looked at them, they would all have different times on them? Each further clock would be for an earlier time. That's why taking a picture won't help.

 

[ash64449]

George,in shorter terms,you were trying to show that Black observer cannot know which IRF he is using so as a result he cannot know what the length contraction is?(#47)

Makes sense to me!

 

[ash64449]

Mentz already pointed out what is wrong with taking a snapshot when you said the same thing way back in post #29:



I don't know why you think a camera would be any better than an observer's eyeballs. Both are subject to the light travel time from each event to the camera/eye and since it is different for the two events in question, they will not see both events at the same time, even though we specify that they must be in order to determine the correct length of the rod.

Are you aware that if you set up a row of clocks and synchronized them and then looked at them, they would all have different times on them? Each further clock would be for an earlier time. That's why taking a picture won't help.

oh,So RoS does not help us to make measurements in a right manner as a result we cannot determine what is the actual length of the rod. Because of RoS, We cannot perform and cannot understand by observing actually which events are simultaneous with which.Correct?

 

[ghwellsjr]

oh,So RoS does not help us to make measurements in a right manner as a result we cannot determine what is the actual length of the rod. Because of RoS, We cannot perform and cannot understand by observing actually which events are simultaneous with which.Correct?

The only time that two simultaneous events will be observed simultaneously is when the observer is equidistant from both events. (That's the definition of simultaneity.) But in terms of measuring the length of a moving rod, it's best to record as much information as possible and then go back and figure out which events taken at the two ends of the rod meet the criterion of being at the same time.

 

[Popper]

It's not a matter of being complete--it's a matter of adding so much extraneous stuff.

Different people are going to have different views and different ways of describing things. If something is unclear then its my experience that the person seeking the answer will ask about it.

Let me take your definition and purge it of what isn't needed:

That will be purely your opinion, of course.

the proper time [STRIKE]between two events[/STRIKE] is the time measured by a clock[STRIKE] (or person attached to the clock/wristwatch) which travels on a timelike worldline between the two events[/STRIKE].

I strongly disagree.

Since a clock can only travel on a timelike worldline, why do you include that?

The reason I referred to a timeline worldline was to intentionally be redundant for clarity. Who knows? Someone might think of a way to speak of the decay of a tachyon (a theoretical particle which travels faster than the speed of light) and perhaps it can decay. The one might want to speak of the proper time along a spacelike worldline so I made sure that I said timelike so that it's not used for tachyons. I'm not sure about proper time concerng tacyons and whether they can decay and what iwould mean to speak of the proper lifetime of a tachyon. So I leave it into make sure the tachyon people know that the definition I gave does not apply to tachyons.
In any case it doesn’t hurt it. If you disapprove then leave it out of the definition the nest time you post one.

And why do you want to limit it to two events? Every clock continuously measures out Proper Time.

Since proper time refers to the time interval between two events. That’s its very meaning. Please post an example of what you’re referring to.

Since proper times is path dependant this gives the integral the limits its required. A starting event and a terminal event so that the proper time has meaning. To speak merely of “proper time” as in “Hey frank! What’s the proper time along my worldline?” would have no meaning since the proper time refers to the integral of the proper time differential dT over the worldline and that integral must have two limits.

If you disagree then please post an example of the proper time pertaining to an arbitrary worldline.

If Coordinate Time refers to actual clocks and Proper Time refers to actual clocks, then what's the difference?

I guess I didn’t make that clear. Perhaps I wrongly assumed that the OP knew about how coordinate time was defined, i.e. in terms of an array of clocks. There is no requirement for anything to move between coordinate clocks.

Let me describe how to define coordinate time: Visualize a Cartesian coordinate system which is marked off with xy-axes and has tick marks which describe distances, like, for example, your everyday average meter stick has a series of lines marked on it with numbers above the marks telling you how far from the “origin” end of the meter stick to the mark on the meter stick. Now think of where these axes intersect and think of a clock placed at all intersections. Each clock has an identical construction to a clock used as a standard. Each clock will be set to start ticking when it receives a light signal from the systems origin. If the clock is at the location (x, y) then the distance from the origin to the clock is d = sqrt(x^2 + y^2). It will take a time t for the light to reach the clock. Since the speed of light is the same in all frames it’s the same in this frame and has the value c = d/t. Therefore when the clock at (x, y) receives a light signal it sets the time to t = d/c. The clock at the origin is the one that sends out the light signal (which is referred to as a timing signal). When the timing signal is sent the origin clock is set to read t = 0.

That is conceptually how you synchronize clocks. It’s all done in the imagination for purposes of solving problems. People don’t really build systems like that of course.

Now suppose we want to ask what the coordinate time interval was between two events. Here’s what we do. First we define the events.

Event #1 = (t1, x1, y1)
Event #2 = (t2, x2, y2)

Then we say that the coordinate time interval Dt between these two events is Dt = t2 – t1. If Dt > 0 then event #1 occurred before event #2. If Dt < 0 we say that event #1 occurred after event #2

 

[ghwellsjr]

The reason I referred to a timeline worldline was to intentionally be redundant for clarity. Who knows? Someone might think of a way to speak of the decay of a tachyon (a theoretical particle which travels faster than the speed of light) and perhaps it can decay.

But you said the Proper Time is measured by a clock and since no clock can travel faster than the speed of light, there is no need to be concerned about this extra stipulation. Saying a timelike worldline is the same as saying a clock's worldline. The redundancy implies the need for additional requirement which is never necessary.

The one might want to speak of the proper time along a spacelike worldline so I made sure that I said timelike so that it's not used for tachyons.

Anyone who talks about the proper time along a spacelike worldline doesn't know what they are talking about. Couldn't you dream up a whole lot of other impossible situations that you should guard against and include them in your definition of Proper Time?

I'm not sure about proper time concerng tacyons and whether they can decay and what iwould mean to speak of the proper lifetime of a tachyon. So I leave it into make sure the tachyon people know that the definition I gave does not apply to tachyons.
In any case it doesn’t hurt it. If you disapprove then leave it out of the definition the nest time you post one.

It doesn't help, which is why I asked you why you saw fit to include it and I'm still not getting a good reason.

Since proper time refers to the time interval between two events. That’s its very meaning. Please post an example of what you’re referring to.

Ok, look up coordinate time in wikipedia. There you will see:

In the special case of an inertial observer in special relativity, by convention the coordinate time at an event is the same as the proper time measured by a clock that is at the same location as the event, that is stationary relative to the observer and that has been synchronised to the observer's clock using the Einstein synchronisation convention.

Just like Coordinate Time is not an interval, so Proper Time is not an interval. If you want to refer to the Proper Time interval between two times on a clock, you just subtract them and call it a Proper Time interval.

Now of course we understand that the time on a clock is actually measuring a time interval between the time that the clock was set (or synchronized or reset) and some later time that we care about but we don't normally bother to call that a time interval, we just refer to the time that is on the clock. In this thread, I have drawn numerous spacetime diagrams in which I mark off Proper Time ticks with dots and label some of them with a Proper Time value. Are you suggesting that this is incorrect, that I should always make it clear that I'm talking about an interval between two events?

Since proper times is path dependant this gives the integral the limits its required. A starting event and a terminal event so that the proper time has meaning. To speak merely of “proper time” as in “Hey frank! What’s the proper time along my worldline?” would have no meaning since the proper time refers to the integral of the proper time differential dT over the worldline and that integral must have two limits.

If you disagree then please post an example of the proper time pertaining to an arbitrary worldline.

This is the same issue that I just discussed with regard to setting a clock and then referring to times on the clock later on. You can use the integral to determine what Proper Time is on the clock at the second event. Nothing wrong with that.

If Coordinate Time refers to actual clocks and Proper Time refers to actual clocks, then what's the difference?

I guess I didn’t make that clear. Perhaps I wrongly assumed that the OP knew about how coordinate time was defined, i.e. in terms of an array of clocks. There is no requirement for anything to move between coordinate clocks.

In physics, there's no such thing as coordinate clocks. Can you find a reference?

Let me describe how to define coordinate time: Visualize a Cartesian coordinate system which is marked off with xy-axes and has tick marks which describe distances, like, for example, your everyday average meter stick has a series of lines marked on it with numbers above the marks telling you how far from the “origin” end of the meter stick to the mark on the meter stick. Now think of where these axes intersect and think of a clock placed at all intersections. Each clock has an identical construction to a clock used as a standard. Each clock will be set to start ticking when it receives a light signal from the systems origin. If the clock is at the location (x, y) then the distance from the origin to the clock is d = sqrt(x^2 + y^2). It will take a time t for the light to reach the clock. Since the speed of light is the same in all frames it’s the same in this frame and has the value c = d/t. Therefore when the clock at (x, y) receives a light signal it sets the time to t = d/c. The clock at the origin is the one that sends out the light signal (which is referred to as a timing signal). When the timing signal is sent the origin clock is set to read t = 0.

That is conceptually how you synchronize clocks. It’s all done in the imagination for purposes of solving problems. People don’t really build systems like that of course.

Now suppose we want to ask what the coordinate time interval was between two events. Here’s what we do. First we define the events.

Event #1 = (t1, x1, y1)
Event #2 = (t2, x2, y2)

Then we say that the coordinate time interval Dt between these two events is Dt = t2 – t1. If Dt > 0 then event #1 occurred before event #2. If Dt < 0 we say that event #1 occurred after event #2

But can you tell me the Proper Time between those two events?

 

[Popper]

Tthe redundancy…

The ignore it. Don’t waste your time trying to convince me of something I already understand quite well and merely disagree with you. It’s not as if my goal is to force my viewpoints on you.


Just like Coordinate Time is not an interval, so Proper Time is not an interval.
[/quote]
That is quite incorrect. If I set the clock to read zero when it passes through event A and when it gets to event B it records 12 s have past then the proper time interval is 12 seconds. If I set the clock to read 350 s when it got to event A then it would read 362 and the proper time interval would be 12 s. Same idea as coordinate time. I’m stating this as a fact and not as a matter of opinion that this is how its defined, like it or not. But it’s quite meaningless to speak of time as an absolute. All times are referenced to something. Our calendar has a zero to it and it was supposed to reflect the event of the birth of Jesus and all times are time intervals between that event and now. When you read a clock all you’re doing is reading part of a time measurement since the calendar part is assumed.

Now of course we understand that the time on a clock is actually measuring a time interval between the time that the clock was set (or synchronized or reset) and some later time that we care about but we don't normally bother to call that a time interval, we just refer to the time that is on the clock. In this thread, I have drawn numerous spacetime diagrams in which I mark off Proper Time ticks with dots and label some of them with a Proper Time value. Are you suggesting that this is incorrect, that I should always make it clear that I'm talking about an interval between two events?

I haven’t looked at those diagrams but it sounds to me as if you’re doing exactly what I said above. You labeled events with a proper time and gave them a value. That value has a zero to it. If it reads 10 hrs then the proper time interval is the time between the event where the clock was set to zero and the time where there is a tick mark.

I’m going to leave it at that since anything more and we’re merely going to try to impose our views on each other and I understand what you’ve said.

In physics, there's no such thing as coordinate clocks. Can you find a reference?

There absolutely is. The reference is as I described it above where I explained how to synchronize clocks.

But can you tell me the Proper Time between those two events?

As I said, that is a meaningless question unless one makes an assumption about it such as the worldline is a geodesic (i.e. in this case a straight line). It’s very possible that one cannot define a proper time between two events. If the events have a spacelike spacetime separation than it can’t be done. Remember that if a single clock cannot be present at each event then a proper time cannot be defined. For example; suppose a firecracker goes off in Dallas Texas and t = 0 and at t = 1 s another firecracker goes off on Pluto. Then since no single clock could possible be present at both events then a proper time between those events cannot be defined. But know this – All times are time intervals. That must be kept in mind when you’re using the spacetime interval to determine either the proper distance or proper distance between two events.

If you want to disagree with me then that’s fine. But if you want me to view it all the same way that you do then you’re wasting your time. This is not my first clambake you know. :)

 

[Mentz114]

oh,So RoS does not help us to make measurements in a right manner as a result we cannot determine what is the actual length of the rod. Because of RoS, We cannot perform and cannot understand by observing actually which events are simultaneous with which.Correct?

Your earlier suggestion that one can use cameras with clocks synchronised in our stationary frame to 'observe' length contraction is correct. This is the same setup we would use to measure the length of the rod as it moves past. From our calculations (observations), the rod will appear to have shrunk. One reason is that the measurements we made were not simultaneous in the rest frame of the rod. So this experiment confirms what is predicted - that the the length of the rod in our coordinates is less than the length of the rod in it's rest frame coordinates. It does not mean that the rod shrank.

 

[Popper]

In physics, there's no such thing as coordinate clocks. Can you find a reference?

See http://openlibrary.org/books/OL15206606M/An_earth-based_coordinate_clock_network

It's not as if everyone uses the exact same words as everyone else. For example; Taylor and Wheeler use the term "far-away time" to refer to coordinate time and they refer to the clocks which keep such time as far-away clocks.

I use the term "coordinate clock" to refer to those clocks which keep coordinate time. This is pretty much standard terminology.

I recommend searching the internet for the terms "coordinate clock" and "coordinate time." using google.

 

[Fredrik]

Personally I find the term "coordinate clock" pretty weird, but it's probably because I spend so much time talking and thinking about the fundamentals, where everything is idealized. My first thought is that if the numbers displayed by a "clock" are time coordinates, then it's not really a clock.

But I guess that's why they call them "coordinate clocks" instead of "clocks". "Coordinate clock" is obviously a natural term for such a device, if they are useful at all. So the question is, are they useful? I think Pervect made a good case for that when he defended his usage of the term a couple of weeks ago, by mentioning international atomic time. (French acronym TAI).

In general the rate of the real, physical clock needs to be adjusted (because it keeps proper time) when one wishes to define a coordinate time. This is routinely done with TAI time, the atomic clocks that define TAI time are rate adjusted by height above sea level before being averaged into the TAI time standard.

I thought this was well known, and totally noncontroversial, in case there's some remaining doubt, I'll post a reference from wiki:

http://en.wikipedia.org/w/index.php?title=International_Atomic_Time&oldid=550649840

In the 1970s, it became clear that the clocks participating in TAI were ticking at different rates due to gravitational time dilation, and the combined TAI scale therefore corresponded to an average of the altitudes of the various clocks. Starting from Julian Date 2443144.5 (1 January 1977 00:00:00), corrections were applied to the output of all participating clocks, so that TAI would correspond to proper time at mean sea level (the geoid). Because the clocks had been on average well above sea level, this meant that TAI slowed down, by about 10^−12. The former uncorrected time scale continues to be published, under the name EAL (Echelle Atomique Libre, meaning Free Atomic Scale).[10]

 

[Nugatory]

Personally I find the term "coordinate clock" pretty weird, but it's probably because I spend so much time talking and thinking about the fundamentals, where everything is idealized. My first thought is that if the numbers displayed by a "clock" are time coordinates, then it's not really a clock.

The same device can be used both ways, and in daily life we switch between the uses almost without noticing it. I get on a plane when my wristwatch reads 4:00 PM, get off when it reads 6:00 PM, and my flight was two hours long and I used my watch to measure proper time. If I text someone right before takeoff to say "I land at 6:00; please meet my plane" I'm talking coordinate time for the landing event.

I expect that this is part of the difficulty with explaining coordinate and proper time to students. They have spent their entire lifetime drawing conclusions about proper time and about coordinate time from the same clock readings taken from the same device; it's hard to accept that the same number on the same display is two different statements about two different things.

 

[Dale]

Personally I find the term "coordinate clock" pretty weird, but it's probably because I spend so much time talking and thinking about the fundamentals, where everything is idealized. My first thought is that if the numbers displayed by a "clock" are time coordinates, then it's not really a clock.

But I guess that's why they call them "coordinate clocks" instead of "clocks". "Coordinate clock" is obviously a natural term for such a device, if they are useful at all. So the question is, are they useful? I think Pervect made a good case for that when he defended his usage of the term a couple of weeks ago, by mentioning international atomic time. (French acronym TAI).

Another example are the satellite clocks for GPS. Those measure cooridinate time, not proper time. And I wouldn't fight you on the claim that they aren't really clocks.