Inertial Frames distinguished by proper times

[Ich]

Real time on a clock is proper time - proper time is local time - that read by an observer at rest wrt the clock.

"proper time is local time" is ok with me.
"that read by an observer at rest wrt the clock" is wrong and not compatible with SR.
What do you mean with "local"? 50 ly?

It might appear possible to overcome all the difficulties attending the definition of "time'' by substituting "the position of the small hand of my watch'' for "time.'' And in fact such a definition is satisfactory when we are concerned with defining a time exclusively for the place where the watch is located; but it is no longer satisfactory when we have to connect in time series of events occurring at different places, or--what comes to the same thing--to evaluate the times of events occurring at places remote from the watch.

You don´t have to be at rest with the clock to read it. You have to be near it.
This is about the 6th time I tell you that you can´t compare times at different locations unambiguously. Even if they are at rest. My post #67 shows that explicitly.
It makes no sense to continue the discussion until we clear this point.
Do you agree or not?
If not, address the points in #67.

 

[yogi]

Also from the same paper:


If at the point A of space there is a clock, an observer at A can determine the time values of events in the immediate proximity of A by finding the positions of the hands which are simultaneous with these events. If there is at the point B of space another clock in all respects resembling the one at A, it is possible for an observer at B to determine the time values of events in the immediate neighbourhood of B. But it is not possible without further assumption to compare, in respect of time, an event at A with an event at B. We have so far defined only an ``A time'' and a ``B time.'' We have not defined a common ``time'' for A and B, for the latter cannot be defined at all unless we establish by definition that the ``time'' required by light to travel from A to B equals the ``time'' it requires to travel from B to A. Let a ray of light start at the ``A time'' from A towards B, let it at the ``B time'' be reflected at B in the direction of A, and arrive again at A at the ``A time'' .


We assume that this definition of synchronism is free from contradictions, and possible for any number of points; and that the following relations are universally valid:--

If the clock at B synchronizes with the clock at A, the clock at A synchronizes with the clock at B.
If the clock at A synchronizes with the clock at B and also with the clock at C, the clocks at B and C also synchronize with each other.
Thus with the help of certain imaginary physical experiments we have settled what is to be understood by synchronous stationary clocks located at different places, and have evidently obtained a definition of ``simultaneous,'' or ``synchronous,'' and of ``time.'' The ``time'' of an event is that which is given simultaneously with the event by a stationary clock located at the place of the event, this clock being synchronous, and indeed synchronous for all time determinations, with a specified stationary clock.

 

[Ich]

Yes, that´s the definition of coordinate time. Einstein shows how you can establish an inertial frame with position and time coordinates.
Note that he says:
We "have evidently obtained a definition of 'simultaneous' "
Now add what I posted before:

So we see that we cannot attach any absolute signification to the concept of simultaneity, but that two events which, viewed from a system of co-ordinates, are simultaneous, can no longer be looked upon as simultaneous events when envisaged from a system which is in motion relatively to that system.

And you find out why he said "a definition" and not "the definition".
There are as many definitions of simultaneity as there are reference frames. They all are different.
So you have to conclude that when you say in our example "D reads more than A when they meet", that´s an "universal truth", because everyone will agree on that.
But when you say "B reads the same as D all the time", that is no universal truth. It is (by the above definition) true in the B-D frame, but obviously wrong in the A-E frame. And the A-E frame is just another inertial frame, just as valid as B-D.
So when you compare A to B (at the time A meets D) you get different results, depending on the frame.
Do we agree on that?

 

[yogi]

I am comparing D and B only in the BD frame - I do not say that B reads the same as D after B is put in motion - where did you get that idea - after B is put in motion, the longer he travels the more out of sync B will be with D. But when B is first put in motion - the local time on his clock will not have changed much from what it read before he (B) accelerated

I missed something - what is the AE frame? What post did you introduce E?

Anyway, to continue

B and D each read 100 years when A arrives at D, and A reads 86.6 years. All readings are made when the guy holding the clock looks at it. A and D know when to look at their clocks because A see's D and yells ahoy. B knows that D's clock reads the same as his and he knows that A's trip will take 100 years in the BD frame - so the observer holding the B clock reconds A should arrive at D when his own clock (B) reads 100 years.

So are we in agreement as to the local readings before B accelerates?

 

[pervect]

We've been over this a lot. Here's my suggestion - if you draw a space-time diagram with jpicedt http://jpicedt.sourceforge.net/ or some other tool, and draw the wordline of every clock you are interested in on the diagram, there is at least some chance that you will receive enlightenment.

If not, if you go through all the trouble of drawing the diagram, I'll be willing to take the time to compute as best I can, what any specific clock on said space-time diagram will read, if you give the beginning point, the ending point, and the path that the clock takes on the diagram.

Since we may have clocks that accelerate on this diagram, I'd need to konw either a specific acceleration, or some general guideline like "in the limit of high acceleration" if you don't need that level of detail. (The high-acceleration limit is a lot easier to compute, please use it if you don't need the detailed effect of finite accelerations). The start and ending velocity would specify the world-line for the high-acceleration limit, the start and end velocity plus the proper acceleration would be one way of specifying the world-line for a finite acceleration case.

Note that I am going to insist that if you want to know the interval reading of a clock, that you specify its path in space-time, and the two points which mark the beginning and ending of the interval. The points can be specified by the receipt of specific light signals (you need to draw the appropriate light-beam on the diagram).

I'm assuming that all of this occurs in flat-space time (no massive bodies).

 

[Ich]

Yes, spacetime diagrams could help.
And, yogi, what would help even more: read my posts before answering.
In #67, I introduced clock E to show you where you run into contradictions. All my posts since then rely on that.
Besides that, we agree that B reads 100 years when he starts accelerating. That´s how we defined it.

 

[Ich]

pervect, I think you could help even w/o diagrams.

I spent the last ~20 posts explaining why SR gives a certain result, but now it occurs to me that yogi still does not believe the result at all.
Maybe he will believe you.

Gedankenexperiment:
Twins A and B are at the same position.
A accelerates quickly to v=+0.6c (0.6 is easier to calculate than 0.5).
After 100 years (proper time), B also accelerates to v=+0.6c.
Then, A and B are brought slowly together.

Yogis claim: A will be younger than B, because he accelerated first.

 

[pervect]

Nah, yogi and I have been over this ground before. (He's been over this ground with other people like robphy, too.)

Drawing the space-time diagrams has the potential to help yogi a lot more than it does me.

If yogi finds the motivation to draw the diagrams, I'll find the motivation to do the calculations. If you want to try answering his questions without the diagrams, go ahead and try.

But I'll predict that that won't work. The exercise of formulating the problem in geometric terms (as a specific line on the diagram) is probably essential for yogi to understand the point that we are trying to make.

[add]
My prediction, based on past experience, is that the problem that you will find in trying to answer the questions without a diagram is that the questions themselves will become "slippery" and/ or contain hidden assumptions.

 

[Hurkyl]

B and D each read 100 years when A arrives at D, and A reads 86.6 years. All readings are made when the guy holding the clock looks at it. A and D know when to look at their clocks because A see's D and yells ahoy. B knows that D's clock reads the same as his and he knows that A's trip will take 100 years in the BD frame - so the observer holding the B clock reconds A should arrive at D when his own clock (B) reads 100 years.

So are we in agreement as to the local readings before B accelerates?

I'm not sure -- are you claiming all of these are local readings? I object to:

B ... read 100 years when A arrives at D

B knows that D's clock reads the same as his

so the observer holding the B clock reconds A should arrive at D when his own clock (B) reads 100 years.
​

none of these are local readings. The only have meaning through the construction of the mathematical abstraction called the "BD inertial reference frame". But relative to that frame, I agree.

(At least I assume that you meant all three of those statements relative to the BD inertial reference frame -- it's rather irritating that you habitually omit such qualifications)

 

[yogi]

Hurkyl - this was not my problem - Ich introduced it - so I interpreted it to mean what I have said in post 74 - D is taken as the at rest frame since D does not accelerate at any part of the experiment. A, B and D are all at rest initially in the D frame and synchronized - in the first part of the problem A and B are together and separated from D - so the analysis is straightforward - A quickly accelerates to a velocity v and maintains this velocity for the rest of the journey - this is right out of Einsteins 1905 paper Part 4 - Einstein didn't draw any spacetime diagrams, they are not necessary - When A arrives at D, A clock will read less than D. B and D are stilll at rest in the D frame - so B must read the same as D.

Or if you insist, draw A and B at the X-T origin and D at some distance X_d along the positive X axis - initialy B and D both move vertically parallel to the T axis to the time 100 years (their world lines are vertical). The plane of simultaneity of B and D is still parallel to the X axis - A's world line starts at the origin and slopes upwardly to intersect the event D = 100 years with a space coordinate X_d. A's time will be less than D's time by the gamma factor. and since B and D have not moved since being synchronized, B will also read 100 years. All times are read by the guy accompanying the watch (proper times only) - What A reads for the B watch when A has reached D is an apparent time -

 

[yogi]

Ich - your post 67 - I recall now - I still don't understand the need to introduce all kinds of ultrafast observers to answer the question of what does B clock read at instant before it is accelerated - proper time is not dependent upon the distance or velocity of a relativly moving observer. Apparent times are misleading - and while it is true you can make measurments in a relatively moving frame and arrive at correct results if you do the proper book-keeping - the measurments themselves are not physical reality - e.g., this is the difficulty with attempting to explain the twin paradox by saying the clock of the stay at home twin appears to advance very fast when the traveling twin turns around - the reality of the situation is otherwise - clocks don't suddenly increase their readings because some other clock executes an acceleration. Einstein attempted to explain the twin paradox in 1918 by introducing a pseudo G field - if you get the correct answer - maybe it doesn't make any difference.

 

[Hurkyl]

so I interpreted it to mean what I have said in post 74 - D is taken as the at rest frame since D does not accelerate at any part of the experiment.

That is the point I wanted to make. Those three measurements I quoted are not local. They only make sense relative to a coordinate chart, so they are all "apparent", according to how you seem to be using the word.

 

[Ich]

Ich - your post 67 - I recall now - I still don't understand the need to introduce all kinds of ultrafast observers to answer the question of what does B clock read at instant before it is accelerated - proper time is not dependent upon the distance or velocity of a relativly moving observer.

But you did not ask about the instant before B is accelerated. You asked:

tell me what you think B clock will read at the time A arrives at D.

Do you really think that is the same?

And to make some progress:

Please answer these questions:
1. What time is the event "B accelerates" (t=100,x=0) in the A frame? (use v=.6, then gamma=1.25)

2. There is a difference between this time and B´s reading of 100 years. Will this difference remain unchaged if A and B then move slowly to meet each other?

3. Do we agree now?

 

[yogi]

Question 1 - if A stops when he reaches D, then B,A and D are all in the same frame (prior to B accelerating). When the owner of the A clock reads the A clock, it will read less than the reading made by the owner of the D clock when the D clock owner reads the D clock at the spacetime event marking the arrival of A.

B and D have remained at rest in the same frame and each will read the clock he owns as 100 years. D owner knows when to read D clock because he sees A arrive, A owner knows when to read A clock because he sees D. B owner checks the time on the B clock and makes sure he does not accelerate until his clock reads 100 years.



So the B and D clocks are running in sync until B accelerates, The A clock is now running at the same rate as B and D, but it is out of phase in the amount (100 years)/1.25 The world line of A is now vertical in the coordinate system of D, as are the world lines of B and D. Prior to pulling up to a stop at D, A would judge B clock to be running behind. ... But that is an apparent observation - analogous to the outbound twin mistakenly observing the stay at home twin to be aging more slowly by assuming the traveling frame to be at rest - but my whole purpose in starting this discussion is to avoid this type of analysis - as I have said - you get the correct answer if you translate the observations propertly - but it does not reveal anything about the physics - and that is what interest me.

Hurkyl and Ich ...What i am saying is that the times are local - the intent of this thread was to pose the question of whether clocks can be differentiated in relativly moving reference frames - In other words, does real time dilation involve local changes in the quantities that determine proper times.

As I stated in a previous post, you can do an experiment with lab generated pions and instantly accelerate some of the them (A pions) and delay the acceleration of some (B pions) and measure the average distance traveled by the A and B pions If any of you who wish to bet on the B pions traveling further (as per Ich) I will cover any and all takers.

Unfortunately, This thread got side-tracked and I am leaving for vacation w/o my computer.

Yogi