I Proper (and coordinate) times re the Twin paradox

[Herman Trivilino]

C's frame. A is traveling with velocity -v, B is traveling with velocity v.
(t,-vt,0,0) event 1, A has traveled a distance -vt ,
(t,vt,0,0) event 2. B has traveled vt,
(t,0,0,0) event 3. C has remained at rest.

Your descriptions don't make clear the fact that events have a duration of zero time.

(t,-vt,0,0) event 1, A is located at the position -vt ,
(t,vt,0,0) event 2. B is located at the position vt,
(t,0,0,0) event 3. C is located at the position zero.

Is it you're assertion that these three events are simultaneous in C's frame?

[Edit: Note they are simultaneous in C's rest frame given my descriptions of the events.]

At its simplest we can take C out of Peter's thought experiment above leaving us with two events A and B separated with coordinates (t, 0 , 0 , 0) and (t, vt, 0, 0) in A's frame [...]

Well, now you've lost me. I thought the events were labeled 1, 2, and 3. Now you seem to be labeling them A and B.

Anyway, Events 1 and 2 are not simultaneous in A's frame if they were simultaneous in C's frame.

 

[PeterDonis]

I will address Peter's suggestion

Yes, you did; and stevendaryl gave the correct response, that yes, you have described a perfectly consistent scenario in accordance with relativity, and there is no issue with it at all. So what's the problem?

If the problem is that you simply can't believe that the scenario as you've described it is consistent, I'm sorry, we can't help you with that. Relativity is an experimental fact.

If you have some other question, then, as stevendaryl asked you, what is it? What is the specific issue you are having with the scenario as you described it? So far nobody has been able to figure out what that is.

the proper time in A has the same duration as the proper time in B - as measured within each frame.

Yes, that's correct. Proper time along a specific path in spacetime, which is what you are referring to here (proper time along A's path, and proper time along B's path) is an invariant; it's the same for all observers and in all frames. It's just geometry; it's no different than saying that the distance from New York to Washington, DC is the same no matter what coordinate grid we put on the Earth's surface.

Everything is relative: A measures propertime on her clock, B measures proper time on his clock and C measures proper time on their clock

Yes, that's correct; each clock measures proper time along its own path in spacetime.

they each measure coordinate times on the other's clocks

This is not quite correct. Nobody can directly measure times of events that are not on their paths through spacetime. What they can do is calculate what those times are, based on measurements they can make directly. So A and B and C can each calculate what the times registered on the others' clocks will be, and can relate that to coordinate times in their own frames.

 

[Dale]

So as I see it ( and please explain where I am going wrong!) the proper time in A has the same duration as the proper time in B - as measured within each frame.

The proper time between the origin and events 1 and 2 are the same in every frame.

 

[Ebeb]

Yes, but any clock in its own reference frame is at rest and only measures time passing. And, in Spacial Relativity which as I understand it is where the twin paradox may be considered, identical clocks can be placed in any frame and will keep identical time - identical clocks; identical laws of science; identical conditions...
so how do they measure different times?

Because of relativity of simultaneity.
When both clocks move relative to each other, the 'identical time' you refer to, f.ex event 5 seconds proper time clock A and event 5 seconds proper time on clock B are not occurring simultaneously anymore. When they move relative to each other you are not allowed to say that "When I tick 5 seconds per my inertial ref frame, the other clock also ticks 5 times per his inertial ref frame." It's a statement that doesn't make sense anymore.
Per clock A ref frame clock B ticks slower. It means that f.ex. when clock A shows 5 seconds proper time, clock B shows only 4 seconds of its proper time (for gamma factor 1.25 for 0.6c). For clock A, clock B ticks slower, not because clock B ticks slower in its own inertial ref frame, but because of relativity of simultaneity clock A ref frame and clock B ref frame take different directions in 4D spacetime. This slows the popping up of clock B proper time events per clock A ref frame (and slows the popping up of clock A proper time events per clock B frame).

The 5 seconds clock A proper time is also a clock A coordinate time for 4 seconds clock B proper time.

You know how to read and draw spacetime diagrams?

 

[Grimble]

Those are the facts. What is the question? Why do you think there is anything paradoxical or unclear about all this?

That is exactly what I think is happening; I am not saying there is anything wrong, I am first checking that what I think is happening is correct.

Your descriptions don't make clear the fact that events have a duration of zero time.

I am sorry I did not think that was necessary, as it is a fundamental fact that events are instants in time...

 

[Grimble]

I agree, this thread is going nowhere - my fault as you say for not knowing just what I am asking.

I suggest it be closed.

I have now seen just where my confusion lies and I will open a new thread shortly which will be specific about the concerns I have.

Thank you all once again for your efforts!

 

[Herman Trivilino]

I am sorry I did not think that was necessary, as it is a fundamental fact that events are instants in time...

When you write "C has remained at rest" you describe something happening for a period of time, not something happening at a particular time. It is indeed fundamental, and therefore necessary for a full understanding. The only reason I mention it is because it's a documented source of learner confusion that poses a stumbling block to learning.

We write $t$ to refer to a particular time or clock-reading. We write $\Delta t$ to refer to a duration of time, or a difference between two clock-readings. This all seems pedantic until you realize its importance.

 

[Grimble]

When you write "C has remained at rest" you describe something happening for a period of time, not something happening at a particular time. It is indeed fundamental, and therefore necessary for a full understanding. The only reason I mention it is because it's a documented source of learner confusion that poses a stumbling block to learning.

We write $t$ to refer to a particular time or clock-reading. We write $\Delta t$ to refer to a duration of time, or a difference between two clock-readings. This all seems pedantic until you realize its importance.

Hmmm...

What I wrote was

(t,0,0,0) event 3. C is located at the position zero.

then, surely, my specifying the coordinates (t,0,0,0) where 't' is a "...particular time or clock reading..."
is specifying a particular time - 't' ?
The phrase ""C has remained at rest" is only describing how c arrived at that event, just as I specified

A has traveled a distance -vt [...]
B has traveled vt,

indicating how A and B arrived at their specified events (by traveling there)

I do appreciate being educated about points where my thinking or writing is a bit imprecise or wooly but it is disheartening to receive criticisms that appear to be unjustified...

 

[Herman Trivilino]

What I wrote was

(t,0,0,0) event 3. C is located at the position zero.

In Post #98 what you wrote was

(t,0,0,0) event 3. C has remained at rest.

And in Post #101 I replied

(t,0,0,0) event 3. C is located at the position zero.

You have somehow attributed to yourself what I wrote. But the point here is that events last for a duration of zero time and to a lot of people this is a stumbling block to learning.

I do appreciate being educated about points where my thinking or writing is a bit imprecise or wooly but it is disheartening to receive criticisms that appear to be unjustified...

Even if a correction is made in error, as you seem to think happened in this case, it's not a criticism. It's just a correction. A lot of people take corrections as criticisms. It's an obstacle to learning things like math and especially physics.

 

[Dale]

then, surely, my specifying the coordinates (t,0,0,0) where 't' is a "...particular time or clock reading..."
is specifying a particular time - 't' ?

I think this is just a bit of notational confusion. Usually the symbol $t$ is a variable referring to all times. It seems that you meant it as a constant, which often would be written something like $t_0$ to distinguish it. The former would typically be interpreted as a worldline while the latter would typically be interpreted as an event.

I don't think this is a mistake, just a miscommunication.

 

[sdkfz]

Notation issues aside, Grimble, you basically seem to be setting up a symmetrical scenario and expressing surprise at some symmetrical results.

Why is that useful? (Especially when the basic symmetry between two observers is well known).

I'm curious, do you still assert the idea you presented here? ... https://forum.cosmoquest.org/showthread.php?101237-Ontological-concepts(-)-Special-relativity

(i.e. is your post #98 here trying to set up a situation as in point 13 in the link I gave above?)

 

[Grimble]

Take a light clock A, with the mirror 1 light second from the lamp, now add any number of imaginary identical inertial light clocks moving at different relative velocities.
Every one of our imaginary clocks will tick at the same rate as clock A, measuring the local time within that clocks frame of reference.
Yet, even though they all measure time at the same rate, relativity of simultaneity means that they are not synchronised for there is no observer who can measure simultaneity for all those clocks.

After 1 second measured on clock A, the light in clock A will reach the mirror. The proper time measured for clock A will be 1 second; yet that will only be measured by observer A. Observers with any other clock, moving relative to clock A, have to calculate the proper time in clock A from the coordinate time they measure with their clock.
And the same is true of course for any of our imaginary clocks.

Relativity of Simultaneity means that an observer can only measure simultaneity for clocks moving with the equal relative velocity to that observer using the Lorentz equation.

I have merely been trying to make an observation to test my understanding. That an observer permanently at the mid point of two moving clocks, having equal relative velocity to each of those clocks, must calculate the same coordinate time for each of those moving clocks.

 

[Dale]

I have merely been trying to make an observation to test my understanding. That an observer permanently at the mid point of two moving clocks, having equal relative velocity to each of those clocks, must calculate the same coordinate time for each of those moving clocks.

Yes.

 

[Ibix]

Take a light clock A, with the mirror 1 light second from the lamp, now add any number of imaginary identical inertial light clocks moving at different relative velocities.
Every one of our imaginary clocks will tick at the same rate as clock A, measuring the local time within that clocks frame of reference.

Yes, but note that this is an assumption of special relativity. It's completely supported by experiment, but the idea that identical devices behave in identical ways when viewed under identical circumstances is a manifestation of the principle of relativity, aka Einstein's first postulate.

Yet, even though they all measure time at the same rate, relativity of simultaneity means that they are not synchronised for there is no observer who can measure simultaneity for all those clocks.

Well, they can be synchronised at one time (typically t=0), so we can agree that (for example) they all emitted their first pulse simultaneously. But time dilation means that they will drift out of synch. And the relativity of simultaneity means that if the clocks weren't co-located at synchronisation different frames won't, in general, agree that they were ever all synched.

After 1 second measured on clock A, the light in clock A will reach the mirror. The proper time measured for clock A will be 1 second; yet that will only be measured by observer A. Observers with any other clock, moving relative to clock A, have to calculate the proper time in clock A from the coordinate time they measure with their clock.

I disagree slightly with @Dale here. Your clock, as described, ticks once every two seconds, when the light returns to the starting point. You can't measure half a tick without some other finer-grained clock. This is important because the coordinate time for a whole tick of a light clock depends only on the time dilation, while the coordinate time for half a tick depends on time dilation, your synchronisation convention, and the orientation of the clock with regard to its velocity. And you can't really talk about the proper time for half a tick because you're relating null-separated events. You can talk about the event half way between the emission of the pulse and its return, but whether or not this is simultaneous with the reflection event depends on your synchronisation convention.

If the above seems pedantic, it is, but for good reason. You are struggling with simultaneity and the devil is in the details.

That an observer permanently at the mid point of two moving clocks, having equal relative velocity to each of those clocks, must calculate the same coordinate time for each of those moving clocks.

First, where the observer is located is irrelevant as long as both clocks have equal and opposite velocities.

As you described it, the result depends on details you didn't specify. If you had talked about a complete out-and-back tick of the clock then I would agree with Dale - the ticks of the clocks will be simultaneous always (in this frame and no other!) if they ever were. However you talked about a half tick. In that case, the time of the half-tick depends on the orientation of the light clocks. If both of them emit the flashes from their rear ends (or front ends) simultaneously then the half ticks will be simultaneous. If they emit the pulses from their -x ends simultaneously then the half ticks won't be simultaneous.

 

[Dale]

I disagree slightly with @Dale here. Your clock, as described, ticks once every two seconds, when the light returns to the starting point. You can't measure half a tick without some other finer-grained clock.

Yes, that is a good point. Hopefully @Grimble will understand

 

[Herman Trivilino]

After 1 second measured on clock A, the light in clock A will reach the mirror.

You'd need two clocks to reach that conclusion. One at the lamp and one at the mirror.

The proper time measured for clock A will be 1 second; yet that will only be measured by observer A.

That won't be a proper time. Proper time is the time that elapses between two events that occur at the same place. One event is the light leaving the lamp, and the other event is the light reaching the mirror. The lamp and the mirror are not in the same place, not for Observer A and not for any observer because it would require the observer to move at the speed of light. This is what @Ibix referred to as "null separated" events.

And I'm not sure what you mean by "only be measured by observer A". Do you mean it's only a measured time (as opposed to some other kind of time) or do you mean only Observer A will measure it?

Observers with any other clock, moving relative to clock A, have to calculate the proper time in clock A from the coordinate time they measure with their clock.

Why would they have to do it that way? If Clock A measures a certain amount of proper time (and any single clock always measures proper time) they could just read Clock A.

 

[Grimble]

Thank you Gentle folk for guiding me through the 'mine field' of expressing thoughts in scientific terms! (Note: My thanks are genuine, not sarcasm as they could be read, due to the 'mine field' of semantics - which is another whole ball game!)

I will rewrite my post, taking note of your comments, in order to avoid getting lost in analysis of all those excellent points and focus on the points I was trying to express.

So, to try again Take a light clock A, with the mirror 0.5 light seconds from the lamp, now add any number of imaginary identical inertial light clocks moving at different relative velocities with all clocks beginning their 'ticks' simultaneously, at the same Spacetime Event, event E₀ that is (0,0,0,0) in each clock's frame.
Every one of our imaginary clocks will tick at the same rate as clock A, measuring the local time measured within that clocks frame of reference.

Yes, but note that this is an assumption of special relativity. It's completely supported by experiment, but the idea that identical devices behave in identical ways when viewed under identical circumstances is a manifestation of the principle of relativity, aka Einstein's first postulate.

Yes, I understand, but are not Einstein's postulates fundamental to everything in Relativity? I just wonder why you feel that needs saying.

Yet, even though they all measure time at the same rate and were all synchronised at E₀, relativity of simultaneity means that they cannot remain synchronised for there is no observer who can measure simultaneity for all those clocks. Synchronisation is determined by each observer in relation to his view of Spacetime.

But time dilation means that they will drift out of synch.

I thought time dilation was the affect of relative motion on the remote measurements of a moving clock, not that it physically changed the clock as an inertial clock's motion is only "in the eye of the beholder" - one cannot determine if an inertial clock is moving by examining the clock's frame - it can only be determined to be moving when examined from another frame.
After 1 second measured on clock A, the light in clock A will have returned from the mirror. The proper time measured for clock A will be 1 second which will be measured and displayed only by clock A. Observers with any other clock, moving relative to clock A, have to calculate the proper time in clock A from their measurements.

And I'm not sure what you mean by "only be measured by observer A". Do you mean it's only a measured time (as opposed to some other kind of time) or do you mean only Observer A will measure it?

My apologies, poor semantics, what I meant was

be measured only by observer A

Why would they have to do it that way? If Clock A measures a certain amount of proper time (and any single clock always measures proper time) they could just read Clock A.

Yes that is what I understand too, yet so often I have read of different observers reading different times on the same clock, or of a clock displaying different times to different observers...

And the same is true of course for any of our imaginary clocks.

Relativity of Simultaneity means that an observer can only measure simultaneity for clocks moving with the equal relative velocity to that observer using the Lorentz equation.

I have merely been trying to make an observation to test my understanding. That an observer permanently at the mid point of two moving clocks, having equal relative velocity to each of those clocks, must calculate the same coordinate time for each of those moving clocks.

 

[Herman Trivilino]

Yes, I understand, but are not Einstein's postulates fundamental to everything in Relativity? I just wonder why you feel that needs saying.

It usually doesn't, but it was a response to your assertion that all of the clocks in your thought experiment keep time correctly, something that we usually assume without asserting.

I thought time dilation was the affect of relative motion on the remote measurements of a moving clock,

It's the effect of relative motion on the local measurements (emphasis on the plural) of a moving clock. You need two events to measure an elapsed time. If the two events occur in the same place (in some frame) then the time that elapses in that frame is a proper time. In the rest frames of observers who move relative to those events the time that elapses will not be a proper time, for them those two events occur in different places. They will therefore need two clocks, one located (local!) at each of the two events. And the time that elapses in those frames will always be larger than the proper time.

not that it physically changed the clock as an inertial clock's motion is only "in the eye of the beholder"

I would word this differently: "not that it changed the clock as inertial motion is relative". This takes us back to the assumption that @Ibix mentioned and noted is a consequence of the Principle of Relativity.

so often I have read of different observers reading different times on the same clock, or of a clock displaying different times to different observers...

I can see then why you'd be confused. Such a thing is simply not true. You don't by any chance recall where you read that? Or what you read that led you to believe that?

 

[Grimble]

It's the effect of relative motion on the local measurements (emphasis on the plural) of a moving clock. You need two events to measure an elapsed time. If the two events occur in the same place (in some frame) then the time that elapses in that frame is a proper time. In the rest frames of observers who move relative to those events the time that elapses will not be a proper time, for them those two events occur in different places. They will therefore need two clocks, one located (local!) at each of the two events. And the time that elapses in those frames will always be larger than the proper time.

I am sorry for the confusion but it is due to the way that I have been thinking about this. I have been mentally 'labelling' measurements in the clock's frame 'local' and those in other frames, in which that clock is moving, as 'remote' - i.e. made from outside the clock's frame...
So let me rephrase, I understood that time dilation was the affect of relative motion on the measurements from another frame... .

I would word this differently: "not that it changed the clock as inertial motion is relative".

Yes, that is the scientific way to say it...

This takes us back to the assumption that @Ibix mentioned and noted is a consequence of the Principle of Relativity.

(But to what extent is it an assumption? For isn't it the very basis of scientific experimentation that if one repeats an experiment, under exactly the same conditions, one would expect the same results... ? That Scientific Laws are immutable... ? Is it an assumption that 'c' is a constant... ?)

I can see then why you'd be confused. Such a thing is simply not true. You don't by any chance recall where you read that? Or what you read that led you to believe that?

Not that I believe that, but it is something often implied, at least, when people talk of 'moving clock's slowing'; as if the clock will display a different time to a moving observer when, in fact, what Einstein wrote was

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 [...] a somewhat larger time.

i.e. that, for the stationary observer, the clock ticked more slowly - each tick took longer - so the same time was measured but measured to take longer.
I had trouble with this at first because it seems like nonsense until one understands that the proper time, i.e the time displayed by the clock, is only part of the time measured by the non-moving observer; for they have to also factor in the time for the clock to travel between the two events the stationary observer measures the clock to travel between. Then the whole thing falls into place and we see why the proper time is the invariant Spacetime Interval,
S = √(ct)² - x²
or, as x = vt
S = √(ct)² - (vt)²
S = t√ (1 - v²/c²)
S = t/γ
where S is the Spacetime Interval = τ
and t is the coordinate time.

 

[Herman Trivilino]

I am sorry for the confusion but it is due to the way that I have been thinking about this. I have been mentally 'labelling' measurements in the clock's frame 'local' and those in other frames, in which that clock is moving, as 'remote' - i.e. made from outside the clock's frame...

But there is no such thing as outside of a frame of reference. A frame of reference assigns coordinates to every point so there are no points outside.

(But to what extent is it an assumption? For isn't it the very basis of scientific experimentation that if one repeats an experiment, under exactly the same conditions, one would expect the same results... ? That Scientific Laws are immutable... ? Is it an assumption that 'c' is a constant... ?)

To a full extent. Yes, it is also an assumption that the speed of light is the same in all inertial frames.

We assume they are valid unless we find evidence to the contrary. And even then we often retain the laws for use within the limits of their validity, if they are useful to us.

Not that I believe that, but it is something often implied, at least, when people talk of 'moving clock's slowing'; as if the clock will display a different time to a moving observer

It's not implied. It's not as if the clock displays different times to different observers. It displays the same time to all observers, it's just that it doesn't in general display the same time as their own clocks.

 

[Grimble]

But there is no such thing as outside of a frame of reference. A frame of reference assigns coordinates to every point so there are no points outside.

Yes, of course, but it seems to me that there is a difference between measurements made relative to one frame of reference and measurements made outside of that frame, relative to a different frame. The measurements exist in both frames but measurements in one, being based on a separate reference frame, are 'outside', that is not, based upon, the framework of the other frame of reference.
To put it another way, what I am saying is, they are not outside in terms of the scope of a frame of reference, so much as not related to a frame's coordinates. Not what they are measuring so much as where they are measuring it from.

To a full extent. Yes, it is also an assumption that the speed of light is the same in all inertial frames.

We assume they are valid unless we find evidence to the contrary. And even then we often retain the laws for use within the limits of their validity, if they are useful to us.

I suppose that at the deepest level one could say that about all scientific laws, facts and formulae - that they are all based upon assumptions that could be proven wrong at some time in the future - that science is all our best guess so far... But isn't that all a wee bit philosophical?

It's not implied. It's not as if the clock displays different times to different observers. It displays the same time to all observers, it's just that it doesn't in general display the same time as their own clocks.

I know it is not possible! A clock displays a time. I am answering your question as to where I had come across that (false) idea.
I have, been around on different forums for some time and have seen explanations that have described different observers reading different times from the same clock.

 

[Vitro]

A clock displays a time.

A clock displays a series of times, like 1:00:00, 1:00:01, 1:00:02, etc.

I have, been around on different forums for some time and have seen explanations that have described different observers reading different times from the same clock.

Sure, they could. Even the same observer can read different times on the same clock, depending when he takes the readings. When two relatively moving clocks A and B pass by each other and compare their readings one would read $t_A$ and the other $t_B$. How those times compare ($t_A>t_B$, $t_A<t_B$ or $t_A=t_B$) depends on a full description of the particular scenario.

 

[Grimble]

A clock displays a series of times, like 1:00:00, 1:00:01, 1:00:02, etc.

If you will excuse me being pedantic, a clock only displays one time, it does that repeatedly. It will have displayed many times and will display many more times (if it is working), but only one at a time.

Sure, they could. Even the same observer can read different times on the same clock, depending when he takes the readings. When two relatively moving clocks A and B pass by each other and compare their readings one would read $t_A$ and the other $t_B$. How those times compare ($t_A>t_B$, $t_A<t_B$ or $t_A=t_B$) depends on a full description of the particular scenario.

But in this case we are discussing a single clock being read by two observers. One at rest in the clock's frame and one in motion relative to the clock. And that I have seen it propounded that they would read different times on the same clock at a single event.

 

[Ebeb]

Let's hope this might help?

 

[Herman Trivilino]

Yes, of course, but it seems to me that there is a difference between measurements made relative to one frame of reference and measurements made outside of that frame, relative to a different frame.

Measurements aren't made relative to frames of reference. Measurements are made using frames of reference. Measurements are their raison d'être. And yes, you will sometimes get different measurements using different frames. The entire point of a theory of relativity is to relate those measurements to each other.

For example, you measure the length of a stick using one frame of reference and I measure it using another. We might get different results, we might get the same result. But the special theory of relativity gives us a way to relate those two measurements to each other. The stick is no more outside one of those frames than it is the other. The measurements aren't made relative to those frames of reference. The frames of reference exist so that we can use them to make these types of measurements.

The stick is an object. The frames of reference are abstractions, inventions of the human intellect.

 

[Ebeb]

And that I have seen it propounded that they would read different times on the same clock at a single event.

Events are absolute. If f.ex at event E of a clock, that clock shows 4 seconds, and another frame measures coordinate time 5 seconds between origin and event E, this doesn't mean the clock of event E shows 5 seconds in the other frame.
Different frames/different observers will measure different coordinate time, but the proper time displayed on the clock of the event that is being read won't change.
See also:

It's not as if the clock displays different times to different observers. It displays the same time to all observers, it's just that it doesn't in general display the same time as their own clocks.

 

[Ebeb]

In following case you do have different clock displays per different observer frames:
Event A: red and green clocks pass each other.
At event A, red frame reads a different proper blue clock display (blue clock event C) than green frame does (blue clock event B)
Note that here both green and red frame measure same coordinate time length (about 3.4 seconds).

 

[Grimble]

Events are absolute. If f.ex at event E of a clock, that clock shows 4 seconds, and another frame measures coordinate time 5 seconds between origin and event E, this doesn't mean the clock of event E shows 5 seconds in the other frame.
Different frames/different observers will measure different coordinate time, but the proper time displayed on the clock of the event that is being read won't change.
See also:

Yes, I agree. That is what I believe.
I was reporting what I have been told by 'experts' in forums in the past. Not, may I repeat, because I believe them, but in response to previous comments.
I do not believe that. I do not think that. I have never thought that.

 

[Grimble]

In following case you do have different clock displays per different observer frames:
Event A: red and green clocks pass each other.
At event A, red frame reads a different proper blue clock display (blue clock event C) than green frame does (blue clock event B)
Note that here both green and red frame measure same coordinate time length (about 3.4 seconds).
View attachment 206324

But they are reading the cock at different events! Is that due to relativity of simultaneity?
And why are the clocks that are 'time dilated' showing smaller durations?

The Behaviour of Measuring-Rods and Clocks in Motion][/B] 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 [...] a somewhat larger time. As a consequence of its motion the clock goes more slowly than when at rest.

I.E. the moving clock goes 'more slowly' in that each 'tick' takes longer... the display shewn by the clock must be the same (ref. previous post); which means it is only measured to be slow in relation to the observer's clock(?)

As a consequence of its motion the clock goes more slowly than when at rest.

implies that a moving clock is measured to 'tick' more slowly that the resting observer's clock.
The observer in the resting frame measures longer ticks for the moving clock = time dilation.

 

[Grimble]

I hasten to add that I am not disputing the science only saying that I find those diagrams rather confusing when I can draw it much more simply - which I will when I can manage to include a diagram...

 

[Herman Trivilino]

In following case you do have different clock displays per different observer frames:

That's not an example of what I'm talking about. A clock is present at an event and we note the reading on the clock. That's a relativistic invariant. All observers will agree on that clock-reading regardless of their position or velocity relative to that event.

Yes, if they are at different locations and are in motion relative to that clock then they may each disagree on what time it was on their clocks when the event occurred, but they will not disagree about what the clock that was present at the event read. In your diagram you note that two different clocks have different readings at events that are simultaneous with Event A, but Green and Red both agree that the clock that was present at Event A read 12 o'clock.

 

[Ibix]

If you have two spatially separated clocks and they both read 12 at the time they run down, everyone will agree that they both read 12 when they stopped. They will not, in general, agree on whether the clocks stopped simultaneously.

I suspect what people are getting at with "the clocks read different things" is that, as measured by different frames, at the same time as one clock stops the other may already have stopped, may stop simultaneously, or may not yet have stopped. I wouldn't say that this means that "the other clock reads different things" so much as "the frames disagree simultaneity so disagree on when it is appropriate to check the other clock".

 

[Ebeb]

That's not an example of what I'm talking about.

I never said it was. I gave an example where they do read different clock dispays. (I thought this being of interest in this topic about twin paradox...)
In post #126 I agreed with you a clock display of a clock event is absolute.

 

[Ebeb]

But they are reading the cock at different events! Is that due to relativity of simultaneity?

Correct

And why are the clocks that are 'time dilated' showing smaller durations?

What do you mean by "showing smaller durations"? A moving clock shows longer duraton of a time unit. Time dilation.
You mean on the diagram? Look at the green and red clock only: the time units have same length on their worldline. When red ticks 5, green ticks 4. Green clock ticks slower relative to red clock because of relativity of simultaneity.

I.E. the moving clock goes 'more slowly' in that each 'tick' takes longer... the display shewn by the clock must be the same (ref. previous post); which means it is only measured

Be careful with the "only measured". Readers might think the speed of the clock at rest is not a measurement, but the speed of the moving clock is. That's not correct. All speeds are a 'measurement'. And because there is no preferred reference frame, there is no time 'speed' that is more real than another speed of that clock. That's because there is no preferred reference frame to consider a speed of a clock more 'real' than another speed.

to be slow in relation to the observer's clock(?) implies that a moving clock is measured to 'tick' more slowly that the resting observer's clock.

Yes, to show you why 'measurement' is not only a feature valid for observing the moving clock, I could also write that "a reference frame measures the speed of a clock at rest to be different/ faster than a moving clock relative to that frame.

The observer in the resting frame measures longer ticks for the moving clock = time dilation.

Correct. You could also state that the resting frame measures the clock at rest to tick faster than the moving clock per that frame. It's not common to state it that way, but I mention it to be sure you don't overestimate your 'only measures'.

 

[Ebeb]

If you have two spatially separated clocks and they both read 12 at the time they run down, everyone will agree that they both read 12 when they stopped. They will not, in general, agree on whether the clocks stopped simultaneously.

I suspect what people are getting at with "the clocks read different things" is that, as measured by different frames, at the same time as one clock stops the other may already have stopped, may stop simultaneously, or may not yet have stopped. I wouldn't say that this means that "the other clock reads different things" so much as "the frames disagree simultaneity so disagree on when it is appropriate to check the other clock".

Correct. Special relativity is about relativity of simultaneity. If Grimble gets to that insight, he will understand coordinated time, proper time, reference frames, reading of clocks etc

 

[Ebeb]

I hasten to add that I am not disputing the science only saying that I find those diagrams rather confusing when I can draw it much more simply - which I will when I can manage to include a diagram...

Please do. If you are not familiar with photoshop, you can sketch something freehand, take a picture and upload (see upload button bottom right on this page).

 

[Dale]

And that I have seen it propounded that they would read different times on the same clock at a single event.

Where have you seen that? Please give an exact reference. It is wrong, so either you are misunderstanding the source or you have a very bad source.

I was reporting what I have been told by 'experts' in forums in the past

I suspect that you are misunderstanding what you were told.

 

[Dale]

Measurements are made using frames of reference.

@Grimble. I would even go further than @Mister T did and say that measurements are analyzed or described using frames of reference. You can analyze the same measurement using multiple frames so the frame is part of the analysis, not part of the measurement.

 

[Grimble]

Measurements aren't made relative to frames of reference. Measurements are made using frames of reference. Measurements are their raison d'être. And yes, you will sometimes get different measurements using different frames. The entire point of a theory of relativity is to relate those measurements to each other.

Thank you, of course we should never use the term 'relative'! It has such a special meaning here...
So what I could have said is: '...there is a difference between measurements made using the frame of reference of a resting observer and measurements made using the frame of reference of a moving observer.' ?

 

[Grimble]

@Grimble. I would even go further than @Mister T did and say that measurements are analyzed or described using frames of reference. You can analyze the same measurement using multiple frames so the frame is part of the analysis, not part of the measurement.

Thank you Dale, and maybe you can help me elucidate what I am trying to say? For I am getting lost here - it seems it doesn't matter how I try to say something, someone will find a way to say I am getting it wrong! Catch 22 really, because I can't ask how to say it without saying it wrong and the discussion then becomes all about how to use the right description while we never get to what I am saying or asking about...

What I am seeing is that we have an observer at rest in a frame - I wish there was a an easy way to refer to the frame of an observer holding a clock who measures the time difference between events on the worldline of the clock - measuring proper times; and the frame describing an observer for whom the clock is moving. For that observer not only reads the measurements from the clock (measures?) but also has to factor in the travel time of the clock, as measured in his frame, between those events. It is the same measurement, the spacetime interval, but to the resting observer it is the elapsed time (proper time) between two colocated events, while to the other observer the clock is moving and we not only have the elapsed proper time, but also the travel time between locations; so it seems to me there is a big difference between how something is measured depending on the frame used.
All I was trying to do was refer to that difference in those measurements

 

[Herman Trivilino]

Thank you, of course we should never use the term 'relative'! It has such a special meaning here...
So what I could have said is: '...there is a difference between measurements made using the frame of reference of a resting observer and measurements made using the frame of reference of a moving observer.' ?

Or simply measurements made using different reference frames.

 

[Herman Trivilino]

For I am getting lost here - it seems it doesn't matter how I try to say something, someone will find a way to say I am getting it wrong!

Instead of trying to describe generalities, try describing specific situations. Once you understand how the theory applies to various specific scenarios you can then make generalities. Every time I speak in generalities I'm thinking about a few different specific examples that apply to that generality.

 

[Dale]

For that observer not only reads the measurements from the clock (measures?) but also has to factor in the travel time of the clock,

So does any observer not co-located with the event, including other observers at "rest". The point is that your objection has little to do with the reference frame and more to do with the fact that it is not co-located with the event. Also, you can remove the travel time delay by using a system of synchronized clocks, one of which is co-located with the event.

 

[Dale]

Or simply measurements made using different reference frames.

I still say that the reference frame is part of the analysis, not the measurement. There is no need to use the reference frame where the measurement device is at rest.

 

[Herman Trivilino]

I still say that the reference frame is part of the analysis, not the measurement. There is no need to use the reference frame where the measurement device is at rest.

But you can use the reference frame to take your measurements.

 

[Dale]

But you can use the reference frame to take your measurements.

I am not sure how. I know how to use a measuring device to take a measurement. I don't know how to use a reference frame to take a measurement.

 

[Herman Trivilino]

I am not sure how. I know how to use a measuring device to take a measurement. I don't know how to use a reference frame to take a measurement.

You note that one end of your meter stick is adjacent to the 3-meter mark on your x-axis, and the other end is at the 4-meter mark. So you've measured its length to be 1 meter.

 

[Dale]

You note that one end of your meter stick is adjacent to the 3-meter mark on your x-axis, and the other end is at the 4-meter mark. So you've measured its length to be 1 meter.

Sure. That is how you use a meter stick to take a measurement. How do you use a reference frame instead of a meter stick?

 

[Herman Trivilino]

Sure. That is how you use a meter stick to take a measurement. How do you use a reference frame instead of a meter stick?

I was using the reference frame to measure the length of the stick. Suppose it was just a stick instead of a meter stick and I want to know how long it is. One end lines up the 3.0 meter mark on my x-axis, the other end lines up with the 4.2 meter mark on my x-axis. I therefore measure the length of the stick to be 1.2 meters.

 

[Dale]

One end lines up the 3.0 meter mark on my x-axis, the other end lines up with the 4.2 meter mark on my x-axis.

If there are marks that you can line up then that sounds like a measuring device, not a reference frame.

A reference frame is a mathematical object, a coordinate system, you can't make measurements with it. A measurement is the outcome of a physical experiment, and as such it is invariant.