I Proper (and coordinate) times re the Twin paradox

[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.