How to resolve the contradiction in twin clocks?

[WannabeNewton]

I like Stephani's definition: time is what makes the laws of physics true.

Hehe.

 

[nitsuj]

No, the geometric symmetry of spacetime emerges from Einstein's first postulate, the PoR, and his second postulate, the propagation of light at c independent of its source.

wasn't spacetime there before it was modeled?

 

[ghwellsjr]

wasn't spacetime there before it was modeled?

No, spacetime is a model and it had no existence prior to Einstein's two postulates. There are other models just as viable that have existed.

 

[nitsuj]

No what? Everything after the comma agrees. anyways George this is silly...like I said earlier #86.

If you want to continue pm, let's not let me tarnish pf quality with you as my lead.

 

[Dale]

There are other models just as viable that have existed.

What do you mean by this?

 

[ghwellsjr]

What do you mean by this?

The same thing I presume you were referring to in post #78:

The term "proper time" is standard terminology. The term "local time" was used by LET to denote coordinate time in the non-aether frames, so I think that a different term is preferable. However, it is a purely semantic preference with no physical content whatsoever.

Namely LET which did not have relative space and relative time or spacetime but rather absolute space and time since it did not affirm Einstein's second postulate that light propagates at c in all IRF's but only in the rest IRF of the ether.

 

[Dale]

Oh, right. I forgot about LET.

 

[JM]

SR clocks

You don't understand--I am a beginner and most of what I've learned is from experts like these:
So I think you will have to agree, I'm not just sending beginners down the wrong track, I've been sent down there with them.

George: I think that the literature of SR is not clear, as I gather you do. With respect to Einsteins 1905 SR, these ideas make sense to me:
1 All clocks are ideal, in that they step off time in equal steps, i.e. the interval between 'ticks' is the same as time moves ahead.
2 Clocks that are at rest wrt each other are synched so that when one clock reads t = 10 e.g. all clocks read 10.
3 Clocks of two inertial frames in relative inertial motion start at zero and advance at the same rate. See Feynman's light clock analysis in Not so easy Pieces.
4 The Lorentz Transforms define the relation between the coordinates of the two frames, but leave room for many different ways to use the LTs.
5 Starting with x' = 0 and viewing the ticks of this clock as the events of interest, leads to the slow clock formula t' = t √( 1-v²/c². Since this clock is present at all the events ( the ticks ) it can be regarded as a proper clock reading proper time.
Note that this formula demands that t and t' be measured in the same units, and if there are clocks measuting the time , they must proceed at the same rate.
6 But there are other events that can be chosen; the relation x = f(t) can be chosen so that t' is zero, equal to t, or larger than t. And since the clocks are in synch all the clocks of K' read the same value, including the one at x' = 0. Its possible that none of the clocks are proper.
7 So a given clock can be proper or not proper depending on the particular events chosen for study.
Regards, JM

 

[ghwellsjr]

George: I think that the literature of SR is not clear, as I gather you do. With respect to Einsteins 1905 SR, these ideas make sense to me:
1 All clocks are ideal, in that they step off time in equal steps, i.e. the interval between 'ticks' is the same as time moves ahead.
2 Clocks that are at rest wrt each other are synched so that when one clock reads t = 10 e.g. all clocks read 10.
3 Clocks of two inertial frames in relative inertial motion start at zero and advance at the same rate. See Feynman's light clock analysis in Not so easy Pieces.
4 The Lorentz Transforms define the relation between the coordinates of the two frames, but leave room for many different ways to use the LTs.
5 Starting with x' = 0 and viewing the ticks of this clock as the events of interest, leads to the slow clock formula t' = t √( 1-v²/c². Since this clock is present at all the events ( the ticks ) it can be regarded as a proper clock reading proper time.
Note that this formula demands that t and t' be measured in the same units, and if there are clocks measuting the time , they must proceed at the same rate.
6 But there are other events that can be chosen; the relation x = f(t) can be chosen so that t' is zero, equal to t, or larger than t. And since the clocks are in synch all the clocks of K' read the same value, including the one at x' = 0. Its possible that none of the clocks are proper.
7 So a given clock can be proper or not proper depending on the particular events chosen for study.
Regards, JM

Since Einstein never used the term "proper clock" in his 1905 SR paper, I'm not sure why you referenced his paper with regard to your comments. And I'm sure most people don't know what the term "proper clock" means. This subject came up in your thread entitled Special Relativity Clocks at post #104 where the definition is of an inertial clock that passes through two events and so measures a time-like spacetime interval. So if you're still following that definition in your comments, a clock can only be proper if it is inertial during the interval under consideration so if a clock is inertial for some period of time and non-inertial during other periods, then, yes, "a given clock can be proper or not proper depending on the particular events chosen for study."

But this has nothing to do with the issue linked to in your quote of mine where the discussion was about Proper Time, not Proper Clocks. All clocks measure Proper Time all the time, even when they are non-inertial and can't be regarded as Proper Clocks.

 

[yuiop]

I am pretty confused in the following situation:

Two identical clocks moving at a constant speed v from each other in x-direction. If each clock is made up of a ball moving at a constant speed of 1 on a ruler in y-direction, then the position of the ball of a clock is the time of the clock. According to special relativity, y' = y no matter at what speed the two inertial reference frames move away from each other. Thus, the two clocks will always have the same time in both reference frames if they start from the same time at the same position, which contradicts the time conversion formula in the Lorentz Transformation.

Can anybody give me an explanation how to resolve the contradiction?

This thread is very long and I apologise if what I have to say has already been said and I missed it. Basically the situation described in the OP is almost identical to the classic light clock except we replace the balls with photons. If the classic light clock moves in the x direction, the photon bounces up and down along the y' axis, and the time recorded by the light clock is proportional to its accumulated distance up and down the y' axis. If we have two light clocks, A and B, with A at rest in irf S, and B moving relative to irf S. (Clock B is at rest in irf S'.) To observers at rest in S, when the photon in light clock A reaches the top where the mirror is, the photon in clock B is only part of the way up to its mirror. The speed of photons in the y direction is not the same for both clocks in either inertial reference frame S or S'. Note that to observers at rest with respect to irf S', the photon of clock B reaches its top mirror before the photon in clock A reaches its top mirror.

 

[JM]

But this has nothing to do with the issue linked to in your quote of mine where the discussion was about Proper Time, not Proper Clocks. All clocks measure Proper Time all the time, even when they are non-inertial and can't be regarded as Proper Clocks.

George- What definition of proper time and proper clock are you using? Moore says 'the time between two events measured by any clock present at both events is called a proper time between those events.' According to Taylor and Wheeler 'the special clock that records the proper time directly has the name proper clock for this pair of events.'
Do you use other definitions?
JM

 

[ghwellsjr]

George- What definition of proper time and proper clock are you using? Moore says 'the time between two events measured by any clock present at both events is called a proper time between those events.' According to Taylor and Wheeler 'the special clock that records the proper time directly has the name proper clock for this pair of events.'
Do you use other definitions?
JM

Those are both incomplete quotes and if you read the entire definitions in context, you will see why they are different, the first being general and the second being "special".

I don't have access to Moore's definition but the part you quoted is very similar to the first sentence for the definition of Proper Time from wikipedia:

In relativity, proper time is the elapsed time between two events as measured by a clock that passes through both events. The proper time depends not only on the events but also on the motion of the clock between the events. An accelerated clock will measure a smaller elapsed time between two events than that measured by a non-accelerated (inertial) clock between the same two events. The twin paradox is an example of this effect.

Doesn't Moore also have further explanation to point out that the Proper Time between two events depends on the motion of the clock?

Taylor and Wheeler's "special clock" is one that has a constant velocity as it travels between the two events. Look further up page 10 where you quoted and you will see:

We carry our wristwatch at constant velocity from one event to the other one.

So a Proper Clock (according to Taylor and Wheeler) is an inertial clock (one whose velocity is constant, in other words, non-accelerating) that passes between the two events in question. The point that Taylor and Wheeler are making is that a Proper Clock directly measures the invariant Spacetime Interval between two events.

In contrast, a clock that accelerates (changes it's velocity--that is, changes either its speed or its direction or both) on its way between the two events in question will measure a different time interval than a Proper Clock will (or another clock that accelerates differently).

So, no, I don't use other definitions except that to make it easier to understand for novices, I just say, "Proper Time is what any clock measures".

 

[JM]

So, no, I don't use other definitions except that to make it easier to understand for novices, I just say, "Proper Time is what any clock measures".

George- Thanks, that clarifies the definitions. So, now consider:
Given: Einsteins 1905 theory, and the Lorentz transforms.
Two events, (y,z = 00, v/c =0.8) first occurs at x,ct = 0,0 and the second at x = 5, ct = 10. The LT shows that ct' = 10. Since this time applies to all clocks of K', the time also applies to the clock at x' = 0. This clock is inertial, but not proper,because it is not present at both events, so its time is not a proper time.
But if ct = 10 and x = 8 then x' = 0 and this clock is present at both events so it is a proper clock and it reads proper time. Even if Einstein didn't use those terms.
So a given clock, such as the one at x' = 0, can be proper or not proper depending on the particular events chosen.
This suggests that there are significant differences between '1905' and the theory that you are using, wouldn't you say?
JM

 

[ghwellsjr]

So, no, I don't use other definitions except that to make it easier to understand for novices, I just say, "Proper Time is what any clock measures".

George- Thanks, that clarifies the definitions. So, now consider:
Given: Einsteins 1905 theory, and the Lorentz transforms.
Two events, (y,z = 00, v/c =0.8) first occurs at x,ct = 0,0 and the second at x = 5, ct = 10. The LT shows that ct' = 10. Since this time applies to all clocks of K', the time also applies to the clock at x' = 0. This clock is inertial, but not proper,because it is not present at both events,

True.

so its time is not a proper time.

Not true. You just quoted me as saying that "Proper Time is what any clock measures" so why would you say the time for this clock is not a proper time?

But if ct = 10 and x = 8 then x' = 0 and this clock is present at both events so it is a proper clock and it reads proper time. Even if Einstein didn't use those terms.

True.

So a given clock, such as the one at x' = 0, can be proper or not proper depending on the particular events chosen.

True.

This suggests that there are significant differences between '1905' and the theory that you are using, wouldn't you say?
JM

Do you still think there is any difference besides the insignificant terminology difference using the word "Proper" after fixing your earlier mistake?

 

[Dale]

This suggests that there are significant differences between '1905' and the theory that you are using, wouldn't you say?

No, it doesn't. Why would it?

 

[JM]

True.

Not true. You just quoted me as saying that "Proper Time is what any clock measures" so why would you say the time for this clock is not a proper time?

George: In post 102 you agreed, I think, with the definition that 'proper time is the elapsed time between two events as measured by a clock that passes through both events.' Are you now saying that a clock that does not pass through both events is also measuring proper time? JM

 

[Dale]

George: In post 102 you agreed, I think, with the definition that 'proper time is the elapsed time between two events as measured by a clock that passes through both events.' Are you now saying that a clock that does not pass through both events is also measuring proper time? JM

Yes, it is also measuring proper time, but along a different worldline. All clocks measure the proper time along their own worldline.

 

[ghwellsjr]

George: In post 102 you agreed, I think, with the definition that 'proper time is the elapsed time between two events as measured by a clock that passes through both events.' Are you now saying that a clock that does not pass through both events is also measuring proper time? JM

Yes, it's measuring the Proper Time between any two other events that it passes through. Clocks can only measure the time where they are, not somewhere else. It's kind of like saying that rulers can only measure lengths where they are, not somewhere else.

 

[JM]

Clocks can only measure the time where they are, not somewhere else.

Ah, but they do. Consider Einsteins watch, 1905,Part I,section1. In order to be useful a watch must be in synch with clocks at other locations. We synch with GMT in everyday life. So when the arrival of the train at the station (where Einstein is located) coincides with the hand of his watch pointing to 7, all the other watches/clocks also point to 7. So a person across town, who knows the schedule, and sees his clock point to 7 can conclude that the train has arrived.
In Einsteins theory the clocks of a given frame are synched by the exchange of light signals. So in my first example Post 103, when the clock at x' = -5 reads ct' = 10 then all the clocks of K' also read ct' = 10, including the one at x' = 0. For this specific example with these two events the clock at x' = 0 is not present at both, and is therefore not measuring Proper time, according to our agreed definition.
Other events can be specified as you suggest and as I did in my second example, but those other events don't change the analysis of my first example.
If there is a theory that doesn't allow for synch'ing of clocks then that theory is different from Einsteins 1905 theory.
JM

 

[Nugatory]

Clocks can only measure the time where they are, not somewhere else.

Ah, but they do. Consider Einsteins watch, 1905,Part I,section1. In order to be useful a watch must be in synch with clocks at other locations. We synch with GMT in everyday life. So when the arrival of the train at the station (where Einstein is located) coincides with the hand of his watch pointing to 7, all the other watches/clocks also point to 7. So a person across town, who knows the schedule, and sees his clock point to 7 can conclude that the train has arrived.

That's true, but I disagree that it follows that the clock at one location is measuring time at another location. I prefer to say that we're using the clock at one location to measure the proper time (precisely the proper time elapsed since some arbitrary zero event) at that location ("my clock says 7:00"), then using the Einstein synchronization process to map that value to coordinate time ("Hey guys, we all agree that it's 7:00 right now").

Much of the confusion here stems not from what the theory of special relativity is, but from how our language for discussing these concepts has evolved. When Einstein was writing in 1905 there was no distinction between coordinate and proper time as we understand the terms, so Einstein couldn't use them in his writing.

 

[ghwellsjr]

Ah, but they do. Consider Einsteins watch, 1905,Part I,section1. In order to be useful a watch must be in synch with clocks at other locations.

No, I can use my watch to measure how long I should brush my teeth, even if I'm on a fast moving train.

We synch with GMT in everyday life. So when the arrival of the train at the station (where Einstein is located) coincides with the hand of his watch pointing to 7, all the other watches/clocks also point to 7.

No, not my watch on a fast moving train (where I'm brushing my teeth).

So a person across town, who knows the schedule, and sees his clock point to 7 can conclude that the train has arrived.

But if that person is on another high speed train across town approaching the first train to make a transfer, he might be late by looking at his own watch.

In Einsteins theory the clocks of a given frame are synched by the exchange of light signals. So in my first example Post 103, when the clock at x' = -5 reads ct' = 10 then all the clocks of K' also read ct' = 10, including the one at x' = 0. For this specific example with these two events the clock at x' = 0 is not present at both, and is therefore not measuring Proper time, according to our agreed definition.

I think your problem is that you are equating Proper Time with a Proper Clock. If you had said, "the clock at x' = 0 is not present at both, and is therefore not a Proper Clock", then you'd be correct but as it stands, you are incorrect.

Other events can be specified as you suggest and as I did in my second example, but those other events don't change the analysis of my first example.
If there is a theory that doesn't allow for synch'ing of clocks then that theory is different from Einsteins 1905 theory.
JM

True, but I'm not aware of anyone proposing a theory that doesn't allow for synch'ing of clocks so I don't know why you would bring this up.

As I have told you before, you should quit thinking about a Proper Clock or its definition since it's not a commonly accepted term.

 

[pervect]

Ah, but they do. Consider Einsteins watch, 1905,Part I,section1. In order to be useful a watch must be in synch with clocks at other locations. We synch with GMT in everyday life. So when the arrival of the train at the station (where Einstein is located) coincides with the hand of his watch pointing to 7, all the other watches/clocks also point to 7. So a person across town, who knows the schedule, and sees his clock point to 7 can conclude that the train has arrived.

It appears to me that you've missed the point that simultaneity is relative. This is mentioned in for instance"Albert Einstein (1879–1955). Relativity: The Special and General Theory. 1920.", the section on "The Relativity of Simultaneity", which is online at http://www.bartleby.com/173/9.html.

Einstein's exposition is confusing to some readers, there are other expositions that may be clearer nowadays. The basic point is that there is *not* any universal way to synchronize clocks, according to Einstein.

You can find many other expositions online by looking up "The Relativity of Simultaneity" if Einstein's is too confusing. The biggest hurdle seems to be that Einstein doesn't motivate or provide a physical mechanism for making two lightning flashes occur "at the same time", he just presuposes that it occurred by chance.

Its not really necessary to consider the mechanism to make his point, but I've seen a lot of readers get tangled up over the issue.

 

[Dale]

Ah, but they do. Consider Einsteins watch, 1905,Part I,section1. In order to be useful a watch must be in synch with clocks at other locations. We synch with GMT in everyday life.

Only if you adopt a synchronization convention, as you point out here. If you have to use a synchronization convention then the measurement is no longer a measurement of proper time. Furthermore, the standard synchronization convention is frame variant, but measurements of proper time are frame invariant. Therefore it is clear that they are not the same.

You should pay attention to the comments by ghwellsjr. He has given you correct advice and information here. Your objections have been in error.

 

[ghwellsjr]

When Einstein was writing in 1905 there was no distinction between coordinate and proper time as we understand the terms, so Einstein couldn't use them in his writing.

I don't understand what you are saying here. Just because Einstein didn't use the terms Proper Time and Coordinate Time, he still talked about those two types of time as distinct from each other in section 4 of his 1905 paper with regard to the time on a moving clock compared to the time on the stationary clocks and he derived the formula for Proper Time, ?, as a function of the speed of the clock, v, and the Coordinate Time, t, (assuming that the clocks started out synchronized). He then proceeded to give an example of a constantly accelerating clock taking a circular path so it could not be construed as exhibiting Coordinate Time but rather Proper Time. I don't think Einstein saw the need to coin a special phrase like Proper Time for the time on a moving clock because it also applies to every clock, so why have a special name for it? But we do need the special name Coordinate Time because it applies where there are no clocks.

 

[Nugatory]

I don't understand what you are saying here. Just because Einstein didn't use the terms Proper Time and Coordinate Time, he still talked about those two types of time

I'm saying that Einstein didn't use those terms, we do, and this may be contributing to JM's confusion.

 

[ghwellsjr]

I'm saying that Einstein didn't use those terms, we do, and this may be contributing to JM's confusion.

Maybe, but I think his problem is the misuse of the term Proper Clock (thinking it is directly related to Proper Time).

 

[JM]

Yes, it's measuring the Proper Time between any two other events that it passes through.

George; Of course, when the events occur at the position of a clock, it measures proper time for those events, according to the definitions stated earlier, and the clock doesn't have to be a proper clock.
But post 103 identified two specific events, one occurring at x,ct = 0,0 and the other at x,ct = 5,10. And the question is 'does the clock at x' = 0 measure proper time for those two events.' My answer is no, because the clock at x' = 0 is not present at both of those events. Note that the idea of proper clocks isn't involved here.
Do you disagree?
JM

 

[ghwellsjr]

George; Of course, when the events occur at the position of a clock, it measures proper time for those events, according to the definitions stated earlier, and the clock doesn't have to be a proper clock.
But post 103 identified two specific events, one occurring at x,ct = 0,0 and the other at x,ct = 5,10. And the question is 'does the clock at x' = 0 measure proper time for those two events.' My answer is no, because the clock at x' = 0 is not present at both of those events. Note that the idea of proper clocks isn't involved here.
Do you disagree?
JM

No, I don't disagree but for a different reason.

Events don't have Proper Times. Clocks have Proper Times. Events have Coordinate Times. When you talk about two events, you can't just ask what is the Proper Time between them without specifying the path through spacetime of the clock that you have in mind which will be present at those two events.

Here is a spacetime diagram for K' as you specified it in post #103 (I'm using the speed of light to be one foot per nanosecond) along with a black Proper Clock:

Note the green clock at x'=0. Note the first green event at x',t'=0,0. Note the blue event at x',t'=-5,10.

Note that the Coordinate Time interval between those two events is 10 which is identical to the Proper Time interval on the green clock at x'=0 between the Coordinate Times of 0 and 10 (because this clock is stationary in this frame).

If you specify a Proper Clock (an inertial clock as I show in the diagram) to go between those two events, which is identical to specifying the Spacetime Interval between those two events, then the time interval is 8.66 which you can either calculate using the formula for the Spacetime Interval, √(Δt²-Δx²) = √(10²-5²) = √(100-25) = √75 = 8.66 (and you can do this from any frame), or you could actually have an inertial clock go between the two events and measure its Proper Time interval as depicted in the spacetime diagram.

But you can have a different non-inertial clock go between those two events and measure a different Proper Time as depicted in this spacetime diagram which measures 7:

This is no different than the issue with the so-called Twin Paradox where a non-inertial twin can have a shorter Proper Time between two events than an inertial twin. Here is another path for a clock which has an even shorter Proper Time interval beween the two events:

This Proper Time interval is just 2. You can make this interval as small as you like by having the clock travel close to the speed of light away from the first event and back to the second event.

I have tried to cover as much as I can on this subject so that it will answer all of your questions. Does it all make sense to you now?

 

[JM]

No, I don't disagree but for a different reason.

Events don't have Proper Times. Clocks have Proper Times. Events have Coordinate Times. When you talk about two events, you can't just ask what is the Proper Time between them without specifying the path through spacetime of the clock that you have in mind which will be present at those two events.

Here is a spacetime diagram for K' as you specified it in post #103 (I'm using the speed of light to be one foot per nanosecond) along with a black Proper Clock:

Note the green clock at x'=0. Note the first green event at x',t'=0,0. Note the blue event at x',t'=-5,10.

Note that the Coordinate Time interval between those two events is 10 which is identical to the Proper Time interval on the green clock at x'=0 between the Coordinate Times of 0 and 10 (because this clock is stationary in this frame).

If you specify a Proper Clock (an inertial clock as I show in the diagram) to go between those two events, which is identical to specifying the Spacetime Interval between those two events, then the time interval is 8.66 which you can either calculate using the formula for the Spacetime Interval, √(Δt²-Δx²) = √(10²-5²) = √(100-25) = √75 = 8.66 (and you can do this from any frame), or you could actually have an inertial clock go between the two events and measure its Proper Time interval as depicted in the spacetime diagram.

George; I applaud your presentation. It is clear and it applies to the points I posed. I appreciate that.
I note that there are two different meanings of 'Proper Time' used. The time of the green clock is called 'Proper time' even though this clock is not present at both of the events specified. This doesn't agree with the definitions cited earlier. Then you cite a clock going between the points and measuring Proper Time, in accordance with the definitons. I suppose it's OK, but isn't it confusing?
In the 1905 theory all the clocks of K' move at constant speed +v along lines parallel to the x axis. You allow clocks to move in many other directions. So your theory must be something different from his, mustn't it? What might a connection be?
Have you ever wondered where the 'Space-Time Interval' comes from? Did Minkowski pluck it from thin air, or what? And the term "interval'- isn't an interval zero only when two points coincide? Some things to think about.
Best Regards
JM

 

[Dale]

I note that there are two different meanings of 'Proper Time' used.
...
So your theory must be something different from his, mustn't it?

There are not two different definitions nor are there two different theories. You are asserting differences that simply don't exist. There is just one definition and one theory applied more generally than you are used to. Instead of asserting non-existent differences you would be better served to actually learn from the good material that has been presented.

In any case, this is all off topic, the OP is banned, and this thread is now closed. If you wish to discuss physics please do so in a new thread, but even if your comments about multiple definitions and multiple theories were correct (which they are not) they would be a semantic debate, not a physics debate, and the semantic debate is closed and should not be reopened.