Clocks, rulers... and an issue for relativity

[michel123456]

Multiplication and division just depend on how you write the equation down If z=xy, x = z/y (or y = z/x). Reverse the order in 1 and 2, to be consistent in going from one frame to the other.

 

1. The time in the Earth's rest frame divided by γ gives you the time in the moving frame

OK, The time in the Earth's rest frame divided by γ. Well understood

The travel length in the Earth's rest frame divided by γ gives you the travel length in the moving frame.

OK, The travel length in the Earth's rest frame divided by γ. Well understood

The length of the moving object as observed in the Earth's rest frame is the object's rest frame length divided by γ.

Here is my problem: why have you replaced "The length of the moving object as observed in the Earth's rest frame" by "the object's rest frame length" in the same sentence?

Why is it not simply "The length of the moving object as observed in the Earth's rest frame divided by γ gives you the length of the moving object in the moving frame " ?? How do you know the object's rest frame length in the first place?

 

If I understand correctly, Relativity presents a set of equations that transform what is experienced in one frame to another.

[Tim88]

Very nice Celeritas

 

Indeed, your introduction is simpler than the Wikipedia one that I referred to with the same purpose.

 

After a quick glance I noticed a glitch: you forgot to mention that after acceleration the clocks in S' should be synchronized to S' before doing measurements. That makes your presentation not erroneous, I think, but perhaps this is by mere chance:

 

Your example concerns measurements between two pairs of spatially separated clocks. After acceleration the clocks of S' are not all synchronized to S'. In particular, the clocks along X' must be "Einstein synchronized" to S' in order to "directly measure", as you call it, similar relationships along X and X'. And of course, all the times that are measured are directly affected by the synchronisation convention of S.

 

As clocks along the Y' axis remain simultaneous with each other under acceleration in X direction, the fact that S' is not a fully valid SR reference system has no effect on your example.

 

PS. One can get rid of clock synchronisation issues and obtain more "direct" measurements by means of using only one clock and mirror per system for two-way measurements, from the clock to the mirror and back to the same clock.

Edited September 10, 2016 by Tim88

[michel123456]

I mean: (on the basis of the following)

Since the atmosphere is stationary wrt the earth, earth-frame rulers directly measure the atmosphere's thickness at its PROPER LENGTH (10km). Earth-frame rulers cannot measure the atmosphere's contracted-length directly, because the atmosphere does not move wrt the muon. The contracted-length measurable directly by the muon's ruler must be calculated by earth-frame observers ... contracted-length = proper-length / gamma = 10km / 5 = 2km.

 

Here the proper length of the atmosphere is the directly measurable length as seen from Earth.

Why don't we take the directly measurable length of the moving object, as measured in Earth's frame, and divide this measure by γ?

[swansont]

OK, The time in the Earth's rest frame divided by γ. Well understood

 

OK, The travel length in the Earth's rest frame divided by γ. Well understood

 

Here is my problem: why have you replaced "The length of the moving object as observed in the Earth's rest frame" by "the object's rest frame length" in the same sentence?

Why is it not simply "The length of the moving object as observed in the Earth's rest frame divided by γ gives you the length of the moving object in the moving frame " ?? How do you know the object's rest frame length in the first place?

If I understand correctly, Relativity presents a set of equations that transform what is experienced in one frame to another.

You don't have to know it. It's part of an equation. You could be solving for it. But that's the length you would be solving for.

[Tim88]

OK, The time in the Earth's rest frame divided by γ. Well understood

OK, The travel length in the Earth's rest frame divided by γ. Well understood

Here is my problem: why have you replaced "The length of the moving object as observed in the Earth's rest frame" by "the object's rest frame length" in the same sentence?

Why is it not simply "The length of the moving object as observed in the Earth's rest frame divided by γ gives you the length of the moving object in the moving frame " ?? How do you know the object's rest frame length in the first place?

 

If I understand correctly, Relativity presents a set of equations that transform what is experienced in one frame to another.

 

Because the object is moving according to the Earth's rest frame, so that according to SR it is length contracted by factor γ according to our measurements.

From that knowledge we can deduce that according to the object's rest frame, the object is in rest and thus not length contracted but a factor γ longer than what we measure (or infer, as it's practically impossible to measure).

It is therefore just the opposite of what you ask for: it is simply "The length of the moving object as observed in the Earth's rest frame multiplied by γ gives you the length of the moving object in the moving frame".

 

Edit, addition:

 

By the relativity principle it is just the same for a moving object in the object's rest frame: as you surely remember in the muon example, an observer in the muon's rest frame will measure the lower atmosphere as 2 km high, and may deduce that the height of the atmosphere in the Earth's rest frame must be 2x5=10 km.

 

And just to make sure that terminology did not contribute to confusion: "the moving frame" = "the moving object's rest frame"

Edited September 10, 2016 by Tim88

[michel123456]

 

Because the object is moving according to the Earth's rest frame, so that according to SR it is length contracted by factor γ according to our measurements.

From that knowledge we can deduce that according to the object's rest frame, the object is in rest and thus not length contracted but a factor γ longer than what we measure (or infer, as it's practically impossible to measure).

It is therefore just the opposite of what you ask for: it is simply "The length of the moving object as observed in the Earth's rest frame multiplied by γ gives you the length of the moving object in the moving frame".

 

Edit: just to make sure that terminology did not contribute to confusion: "the moving frame" = "the moving object's rest fr

So you get 3 measurements from Earth.

You divide the first (path length), you divide the second (time) and you multiply the third (object length).

And those 3 results combined give you the "reality" in the frame of the object.

IOW it has nothing to do with a kind of scaling: it is not a "short reality" to compare with a "large reality".

It is a short "path&time" with a large object that transforms into a large "path/time" with a small object (contracted object). If you understand what I mean.

[Tim88]

So you get 3 measurements from Earth.

You divide the first (path length), you divide the second (time) and you multiply the third (object length).

And those 3 results combined give you the "reality" in the frame of the object.

IOW it has nothing to do with a kind of scaling: it is not a "short reality" to compare with a "large reality".

It is a short "path&time" with a large object that transforms into a large "path/time" with a small object (contracted object). If you understand what I mean.

With the Earth's "frame" (standard inertial reference system) one can easily measure the height of the lower layer of the atmosphere as well as the speed of the muon, which is deduced from the measurements of path length and two coincidence times. That's 4 measurements in practice.

 

... I don't really recognize the formula for gamma in your summary, but it does have to do with a kind of scaling. Only, due to relativity of simultaneity, it's not a simple kind of scaling except in some special examples. In particular, due to relativity of simultaneity the effects are mutual: each system considers the other system to be length contracted and time dilated.

[michel123456]

If it is about a kind of scale factor, then there is something abnormal about it.

[Mordred]

What is abnormal about a scale factor? It is just an assigned variable to represent a ratio of change of measurement scales in the formulas.

 

In the Lorentz formulas both length contraction and time dilation have the same ratio of change. The assigned variable is gamma. [latex]\gamma [/latex]

 

In cosmology for an expanding volume it is a(t). They are both scale factors but the cause of the change is different.

 

If you ever used a draftsman ruler, you will note that there is a scale factor for each edge. Each edge has its own scale factors in terms of the marked lengths.

 

ie 1:1, 1:0.5, etc. Scale factors denote changes in measurement scales from one geometry to another. This is the same in the above two metric examples. Just like a draftsmans ruler. Just like any map you buy in a store. On that map is a scale factor used to measure off and calculate distances.

 

Its usage is no different in GR nor SR. Provided you pay attention to what the map or graph represents.

Think of it this way. Every reference frame has his own map. The differences in measurement scales between any two maps is the scale factor. This is what the Lorentz formulas allow us to calculate.

 

To be 100% honest with you. The easiest way in my opinion to understand GR and SR is to understand each individual "Reference frame maps" and how one map scales (scale factor) to the other.

 

In the lorentz formulas you can assign a value of gamna to represent an individual reference frame map. (sort of like a page number. If gamma = 0.5 goto this reference frame map.)

 

the at rest frame gamma=0. use scale 1:1

Edited September 10, 2016 by Mordred

[Celeritas]

Very nice Celeritas

 

Indeed, your introduction is simpler than the Wikipedia one that I referred to with the same purpose.

 

After a quick glance I noticed a glitch: you forgot to mention that after acceleration the clocks in S' should be synchronized to S' before doing measurements. That makes your presentation not erroneous, I think, but perhaps this is by mere chance:

 

Your example concerns measurements between two pairs of spatially separated clocks. After acceleration the clocks of S' are not all synchronized to S'. In particular, the clocks along X' must be "Einstein synchronized" to S' in order to "directly measure", as you call it, similar relationships along X and X'. And of course, all the times that are measured are directly affected by the synchronisation convention of S.

 

As clocks along the Y' axis remain simultaneous with each other under acceleration in X direction, the fact that S' is not a fully valid SR reference system has no effect on your example.

 

PS. One can get rid of clock synchronisation issues and obtain more "direct" measurements by means of using only one clock and mirror per system for two-way measurements, from the clock to the mirror and back to the same clock.

 

Thanx,

 

I understand your points, and agree.

I did forget to make a statement regarding clock sync. I'll enhance the post for future readers with an EDIT per your comments here. I'm thinking I'll state it this way ... no setting into motion, and the 2 inertial systems coincidentally read t=t'=0 at the momentary co-location of their spatial origins. The purpose of the figure was regarding how relative time (per LTs) arises, not what impacts from proper acceleration eg in the twins scenario.

However, if I were to keep the scenario as stated (I won't), I would (for simplicity) just state that the proper acceleration of the primed system (that puts it into inertial motion) is "virtually instant". Then, there would be no need to re-synchronize the clocks upon completion of the acceleration, since x' in t = γ(t'+vx'/c²) is essentially zero, and the time is essentially t=t'=0. It's a trade-off of detail for simplicity for sake of point. Nonetheless, for any proper acceleration that is "not so instant", the primed system would indeed have to re-synchronize their clocks immediately upon completion of their own proper acceleration, and what happens during the non-inertial period of relative motion would need accounted for. Thanx.

Best regards,

Celeritas

************************************

EDIT ... Well, I updated the figure for my prior post, I deleted the old image, and went to insert the new image's link. However, I then found that my EDIT period expired apparently, as the EDIT button no longer exists for that post. So, I could not edit it, AND my original post lost its image. So, I will repost that prior post with updated figure. Sorry about that !

How long does the EDIT opportunity last? 24 hr or so, maybe?

Edited September 10, 2016 by Celeritas

[VandD]

Only, due to relativity of simultaneity, it's not a simple kind of scaling except in some special examples. In particular, due to relativity of simultaneity the effects are mutual: each system considers the other system to be length contracted and time dilated.

 

Indeed. Length contraction (and time dilation) is not about different scaling. It's about relativity of simultaneity.

Talking about gamma factor is one thing, but knowing what you measure is more important to understand SR: a guy sitting on the muon measures the length(distance) of a completely different set of simultaneous events of the atmosphere than a guy at rest relative to the atmosphere does. Different 3D sections through 4D spacetime.

Edited September 10, 2016 by VandD

[Mordred]

 

It's about relativity of simultaneity.

Talking about gamma factor is one thing, but knowing what you measure is more important to understand SR:.

Excellent point,

[Celeritas]

I mean: (on the basis of the following)

Here the proper length of the atmosphere is the directly measurable length as seen from Earth.

Why don't we take the directly measurable length of the moving object, as measured in Earth's frame, and divide this measure by γ?

 

michel123456,

 

I'm not sure what you mean here, as written?

 

The moving object is the atmosphere. The earth frame does not hold the atmosphere in motion, and so a direct measurement by the earthbound observer records only the proper length. The earth frame observer cannot directly record the moving contracted-length that an observer moving wrt the earth (eg the muon) would measure. The earthbound observer must divide that proper length by gamma to determine how observers who move wrt the earth measure the moving atmosphere's thickness.

 

If I may make a point here. This is off topic, but it might relate to one interpretation of your statement above (not sure), but I'll mention it anyway ...

 

The muon holds the atmosphere in motion, and so the atmosphere directly measured by the muon is length-contracted (to L=2km) wrt its proper length (L₀ = 10km), given the velocity v = 0.98c. Let's say the muon holds up his wonder ruler, and takes an instantaneous measurement of the moving earth atmosphere. His ruler measures it at 2km. Let's say the muon used a ruler precisely 2km long to make that measurement, ie its proper length. The muon might then consider what an observer (in a system x",y",z",t") moving at u=-0.98c (in the opposite direction wrt himself) would measure for his ruler's length. In that case, the muon can simply divide his ruler's own proper length by gamma, so L" = 2km / 5 = 0.4 km. That's the muon's moving-ruler-length per the dbl-primed system. However, this does not lead that the earth's atmosphere is 0.4 km thick per that other dbl-primed system. One must apply the Composition of Velocities formula first to determine the velocity between the earth's atmosphere and the dbl-primed system, then determine the gamma factor for that velocity. That calculation is ...

 

u = (w+v)/(1+wv/c²)

u = (.98+.98)/(1+.98(.98)/1²)

u = 0.99979 ... velocity of earth's atmosphere wrt the dbl-primed frame

 

Then one determines gamma for that velocity u ...

 

γ = 1/√(1-u²/c²)

γ = 1/√(1-.99979²/1²)

γ = 49.5

 

The earth's atmosphere is contracted per the dbl-primed system since it moves, and so its moving contracted-length is given by ...

 

L" = L₀ / γ

L" = 10km / 49.5

L" = .202km ... thick

 

So while the muon may hold his own ruler (proper length = 2km) as the same length as the moving earth atmosphere, he divides his ruler's proper length by γ = 5 to determine the length of his own ruler per the other dbl-primed system ... 2 km / 5 = .4 km. However, he must divide the earth-atmosphere's proper length (10km) by γ = 49.5 to determine the length of the earth's atmosphere per the other dbl-primed system ... 10 km / 49.5 = .202 km.

 

I mention this, only because many have difficulty in keeping the frames of consideration straight. Also, as to what is invariant and what is not. The proper-length (L₀) of the earth's atmosphere is invariant. Any frame that moves relatively wrt earth can directly measure only what exists per they, ie a moving length-contracted earth atmosphere, which in relation to the direct measurement per earth observers is L = L_{0 /} γ.

 

Best regards,

Celeritas

Edited September 11, 2016 by Celeritas

[Tim88]

 

Thanx,

 

I understand your points, and agree.

I did forget to make a statement regarding clock sync. I'll enhance the post for future readers with an EDIT per your comments here.

I'm thinking I'll just state ... the 2 inertial systems coincidentally read t=t'=0 at the momentary co-location of their spatial origins. The purpose of the figure was regarding how relative time (per LTs) arises, not what impacts from proper acceleration eg in the twins scenario.

However, if I were to keep the scenario as stated, I would (for simplicity) just state that the proper acceleration of the primed system (that puts it into inertial motion) is "virtually instant". Then, there would be no need to re-synchronize the clocks upon completion of the acceleration, since x' in t = γ(t'+vx'/c²) is essentially zero, and the time is essentially t=t'=0. It's a trade-off of detail for simplicity for sake of point. Nonetheless, for any proper acceleration that is "not so instant", the primed system would indeed have to re-synchronize their clocks immediately upon completion of their own proper acceleration, and what happens during the non-inertial period of relative motion would need accounted for. Thanx.

Best regards,

Celeritas

************************************

EDIT ... Well, my EDIT period expired apparently, as the EDIT button no longer exists for that post. So, I could not edit it. As such, the interpretation required "as written", is this ...

Assume the proper acceleration of the primed system is virtually instant. Then, the loss of synchronisation of primed-frame clocks during their proper acceleration is negligible, and those clocks remain in sync (similarly as in all inertial scenarios). Add, it should be assumed that all clocks are synchronised in both frames from scratch, which is generally assumed in most all scenarios.

 

I'm glad that you agree that it should be mentioned as it is of general importance, and that nevertheless, by chance your calculation as stated is not (very) wrong. But, sorry, it seems to me that you do not fully understand it:

 

"Assume the proper acceleration of the primed system is virtually instant. Then, the loss of synchronization of primed-frame clocks during their proper acceleration is negligible, and those clocks remain in sync (similarly as in all inertial scenarios)", is faulty.

 

[edit:] And I had overlooked that you started the pulse at the same time as the acceleration. That is too messy...

What will make it correct without effort, is to simply add, like Einstein did*, that first S' is accelerated and after acceleration the clocks are being synchronized according to the standard operating procedure. And put then all coordinates and times to 0 as per the picture, with a light flash at t=0.

 

The synchronization issue between clocks of S and S' was not my point, as I had not noticed that glitch. What I tried to convey, is the synchronization between moving clocks C1' and C2' along X'. For acceleration to a medium speed of <0.1c, C1' and C2' remain approximately synchronized to S, because their trajectories are almost identical - considering displacement, your added equation in your last post applies to both C1' and C2'. Consequently they are not synchronized to S'.

 

At higher final speed also length contraction plays a role, but it works the wrong way(!) for synchronizing those clocks to S'. You can easily figure out for yourself that the moving rear clock will slightly delay on the moving front clock according to S. For correct synchronization to S', the moving rear clock must instead advance on the moving front clock. That is a task for the observers of S'.

 

*compare: §3 of http://www.fourmilab.ch/etexts/einstein/specrel/www/

 

PS comment on the following post by Celeritas: Yes, that's a smart solution!

Edited September 10, 2016 by Tim88

[Celeritas]

This is a re-post of my original related post, necessary because the prior post's IMAGE LINK was deleted, and the prior post is no longer EDIT'able. For reference, my prior post ... post 225

 

I can understand for the question: How much time did the travelling clock lose? But what if the question is: How did the travelling clock lose time? What is the answer (with certainty) to that question?

 

robinpike,

So the LTs explain the relative measure of time for any 2 observers moving relatively. Per your study of that math, you do not yet understand WHY the LTs do what they do. A derivation of the LTs from scratch (on your own) would help you considerably in that regard. Usually, if one understands the derivation then one envisions the mechanism, and your answer lies therein. Also, the fine spacetime diagrams presented thus far in this thread, have apparently not gotten you there. I would recommend you spend a good week studying spacetime figures, if you haven't already. Often, they are the ticket for a more expedient and complete understanding of WHY the relativistic effects exist, as they present the abstract math per the LTs both geometrically and visually.

Ok, that said, I will try and attempt answering your question using only a 2-spacetime figure (with time implied), which most folks are plenty familiar with. Read this carefully, think about it before responding, and let me know if it helps any ...

*************************************************************************************

Note: scenario description was modified to include statement for clock synchronization, and to delete the instantaneous proper acceleration of the primed system at co-located origins. The systems are now defined as purely inertial, to simplify the description for sake of point (ie. why relative time exists). Corrections per Tim88 review.

Best regards,

Celeritas

Edited September 11, 2016 by Celeritas

[VandD]

 

To visualize the importance of relativity of simultaneity for the symmetry of length contraction, I added a long spaceship, length at rest = length of atmosphere at rest.

The muon sits on the nose (or flies alongside rocket's nose). Relative speed of rocket = relative speed muon

Mr Green is in rocket, Mr Red at rest in atmosphere.

 

First diagram: In Mr Green"s 3D space of simultaneous events "the collection of simultaneous rocket events" has rest length. The collection of simultaneous atmosphere events in Mr Greens 3D space has shorter length than the collection of simultaneous events of the "at rest" atmosphere in Mr Red's 3D space.

 

Second diagram: In Mr Red's 3D space of simultaneous events the "collection of simultaneous atmosphere events" has rest length. The collection of simultaneous rocket events in Mr Red's 3D space has shorter length than the collection of simultaneous events of the "at rest" rocket in Mr Green's 3D space.

 

The "at rest rocket" for Mr Green and the "at rest atmosphere" for Mr Red have different slope in 4D spacetime. I.o.w. they are not part of the same 3D space of simultaneous events.

 

Event C (for example a baby born on earth surface/lower atmosphere) happens after event B (a bird sits a split second on the roof).

For Mr Green the nose of the rocket (= muon) hits the atmosphere (=event A) when the baby is born (event C). No bird on the roof (the bird was on the roof some time ago).

For Mr Red the nose of the rocket (= muon) hits the atmosphere (=event A) when the bird sits on the roof (event B). No baby is born (yet).

[Celeritas]

 

I'm glad that you agree that it should be mentioned as it is of general importance, and that nevertheless, by chance your calculation as stated is not (very) wrong. But, sorry, it seems to me that you do not fully understand it:

 

"Assume the proper acceleration of the primed system is virtually instant. Then, the loss of synchronization of primed-frame clocks during their proper acceleration is negligible, and those clocks remain in sync (similarly as in all inertial scenarios)", is faulty.

 

[edit:] And I had overlooked that you started the pulse at the same time as the acceleration. That is too messy...

What will make it correct without effort, is to simply add, like Einstein did*, that first S' is accelerated and after acceleration the clocks are being synchronized according to the standard operating procedure. And put then all coordinates and times to 0 as per the picture, with a light flash at t=0.

 

The synchronization issue between clocks of S and S' was not my point, as I had not noticed that glitch. What I tried to convey, is the synchronization between moving clocks C1' and C2' along X'. For acceleration to a medium speed of <0.1c, C1' and C2' remain approximately synchronized to S, because their trajectories are almost identical - considering displacement, your added equation in your last post applies to both C1' and C2'. Consequently they are not synchronized to S'.

 

At higher final speed also length contraction plays a role, but it works the wrong way(!) for synchronizing those clocks to S'. You can easily figure out for yourself that the moving rear clock will slightly delay on the moving front clock according to S. For correct synchronization to S', the moving rear clock must instead advance on the moving front clock. That is a task for the observers of S'.

 

*compare: §3 of http://www.fourmilab.ch/etexts/einstein/specrel/www/

 

PS comment on the following post by Celeritas: Yes, that's a smart solution!

 

Well, I do realize there would be a sync problem globally, for clocks scattered at differing x' values. Also, for (say) a thick ruler, where the ruler has a non-ignorable thickness wrt x'. Primed clocks would exist at different values of x'. But as you just mentioned in your prior post, there should be no sync problem for various clocks at rest on the y’-axis that reside only on a specific single x' value x'=0 at t'=t=0 (they remain in sync per themselves during the instant proper acceleration). That's what I intended when I showed the time LT for x'=0 at t'=t=0. For simplicity, my ruler may be taken as a string of wonder point-clocks along the y'-axis at x'=0, the proper acceleration being instantaneous at t'=t=0. Does this sound reasonable, or no? At any rate, I had just re-posted that diagram, which now essentially says ... the systems are purely inertial, and coincidentally their origins align at t=t'=0.

 

When trying to keep a figure and its verbiage "non-lengthy" and "busy-minimal" (yet complete enough for sake of point), its does get tricky at times trying to balance those, ie detail is traded off for simplicity

 

I do understand that (in the primed system) aftward clocks would need advanced to become synchronous with forward clocks of the primed system, after proper acceleration completes, and inertial motion commences. I have a nice Rindler diagram that depicts this, for clocks at each end of a Born-rigid body of single point acceleration. All very good points, thanx Tim88.

 

Best regards,

Celeritas

Edited September 11, 2016 by Celeritas

[Celeritas]

In regards to my prior post 223 ... which addressed proper length, contracted length, proper time, and coordinate time (partly shown below) and as in relation to the muon scenario, I had a blunder on 1 word there. Correction shown below ...

 

 

 

1) wrt SPATIAL LENGTHs ...

 

PROPER LENGTH ... If a length measured by an observer does not move over duration, it is a stationary length. This is referred to as a proper length, and is the longest length measurable for the said length. He divides his measured stationary-length by gamma if he wishes to know what an observer in relative motion would measure that length as (ie its contracted-length, per POV).

 

Since the atmosphere is stationary wrt the earth, earth-frame rulers directly measure the atmosphere's thickness at its PROPER LENGTH (10km). Earth-frame rulers cannot measure the atmosphere's contracted-length directly, because the atmosphere does not move wrt the muon. The contracted-length measurable directly by the muon's ruler must be calculated by earth-frame observers ... contracted-length = proper-length / gamma = 10km / 5 = 2km.

 

 

wrt the word MUON (in brown highlight) in the text referenced above, it should have said EARTH. Very sorry for any confusion that may have caused.

 

Best regards,

Celeritas

Edited September 11, 2016 by Celeritas

[michel123456]

What is abnormal about a scale factor? It is just an assigned variable to represent a ratio of change of measurement scales in the formulas.

 

In the Lorentz formulas both length contraction and time dilation have the same ratio of change. The assigned variable is gamma. [latex]\gamma [/latex]

 

In cosmology for an expanding volume it is a(t). They are both scale factors but the cause of the change is different.

 

If you ever used a draftsman ruler, (...)

Yes I use a draftman ruler constantly, I am an architect.

 

About scale factor, a very simple example:

here below a back of the envelope sketch made on my coffee table at breakfast this Sunday morning.

You have a stool Sp close to you with a sphere M.

An identical stool Sp' a few meters away with an identical sphere M'

At the same instant, the 2 spheres fall out of the stool.

 

It is evident that as seen from Sp and Sp', the 2 phenomena will be seen as identical:

1.Distance d = d'

2.Time T=T'

3.So from each Point of Vue (POV), velocity is conserved d/T = d'/T'

 

However, as it is drawn on the paper & as it is observed)

4.M' is apparently smaller than M

5.d' is apparently smaller than d

6.T' is conserved T=T'

7.Which means that apparent Velocity is not conserved. At the horizon, d'=0 and apparent velocity 0/T'=0/T=0

However, as per point 3, velocity is the same from each point of vue.

 

Also it is remarkable that the point of vues of Sp and Sp' can be interchanged. It is fully symmetrical

 

That is an example of scale factor.

 

---------------

 

Now, what are the differences with Relativity:

In order to introduce the velocity conservation in each frame, it is stated that

8. d' is smaller than d d'<d (no problem with that)

9. because d' < d, it means that Time has changed T'<T so that d/T=d'/T' (in the above example it is unnecessary)

10. M is observed smaller than M' !!!!**

 

So maybe you understand my scepticism. Especially concerning point 10.

 

Point 9 is also interesting.

 

Edited the labeling in the text to correspond to the sketch.

 

** I forgot to mention that Relativity states that the moving object is smaller (contracted) only in the direction of motion. That is another substantial difference when one talks about scale factor. Usually, a scale factor concerns all the 3 dimensions.

Edited September 11, 2016 by michel123456

[Celeritas]

Tim88,

 

I see I never got back to you in relation to one of my early posts in this thread ...

 

 

... No matter what can be read into a diagram, length contraction and time dilation go hand in hand in SR and are a function of speed only.

 

As was elaborated in the spun-off thread starting from http://www.scienceforums.net/topic/98048-relativity-and-shared-realities-split-from-clocks-rulers/?p=941488 , pretending that a clock remains length contracted but temporarily ticks faster due to what is done to another far away clock is not a valid physical description in SR. If you think otherwise, please comment there as it relates to claims about physical reality.

 

If I had actually said what you paraphrased here, I’d agree with your assessment …

It’s not about something being done to a far away clock. It’s about how the remotely located (and inertial) twin A clock exists within the non-inertial twin B spacetime system …

 

Here's my understanding ...

 

During B’s virtually-instant turnabout, the twin A worldline shifts wildly (even superluminally) within the B spacetime system, and twin A also advances wildly along his own worldline as it exists within the B spacetime system. This, the result of twin B’s line-of-simultaneity (sense-of-now across B-space) rapidly rotating within spacetime wrt inertial spacetime systems (eg twin A’s). Within the B spacetime system, the A clock time-readout must tick wildly forward, relative to B’s normal steady-ticking clock rate (per B). Twin B never sees this happen by the receipt of light signals, but can deduce this (1) per the measured doppler shift of light from A, and per the LTs ... for example, I consider the collection of momentarily co-located and co-moving inertial observers wrt twin B. Twin A never experiences anything unusual, time passing steadily per he as normal. B's clock ticks normal per himself. I'm talking only about how the twin A clock exists within in the B spacetime system. This must happen in the B system, for otherwise B could not predict (or agree) that A must age more than himself over the round-trip, as twin A is in motion per B over the entire interval.

 

However, geometrically, a rotation of B's spacetime system by his own proper acceleration cannot ever cause moving-lengths to become non-length-contracted, within B's own system.

What I say here is not about optical effects. It's about how remotely located clocks exist within the non-inertial spacetime system, during a virtually-instant proper acceleraton (B's turnabout).

Now, does what I say here change your stated position at all?

Best regards,

Celeritas

Edited September 11, 2016 by Celeritas

[Mordred]

** I forgot to mention that Relativity states that the moving object is smaller (contracted) only in the direction of motion. That is another substantial difference when one talks about scale factor. Usually, a scale factor concerns all the 3 dimensions.

Yes the scale factor in the case of relativity only affects the x axis and time axis. This is where it differs from Euclidean geometry change.

 

Just try to remember an observer measuring within his own frame of reference his scale factor is 1 for 1. No length or time dilation gamma equals zero.

 

If you remember that rule and keep track of reference frames you have an easier time.

 

(particularly if you start studying GR.)

 

Some of the terminology changes from SR to GR. In particlular proper time becomes coordinate time. Just a side note...

Edited September 11, 2016 by Mordred

[Tim88]

 

Tim88,

 

I see I never got back to you in relation to one of my early posts in this thread ...

 

 

If I had actually said what you paraphrased here, I’d agree with your assessment …

It’s not about something being done to a far away clock. It’s about how the remotely located (and inertial) twin A clock exists within the non-inertial twin B spacetime system …

 

Here's my understanding ...

 

During B’s virtually-instant turnabout, the twin A worldline shifts wildly (even superluminally) within the B spacetime system, and twin A also advances wildly along his own worldline as it exists within the B spacetime system. This, the result of twin B’s line-of-simultaneity (sense-of-now across B-space) rapidly rotating within spacetime wrt inertial spacetime systems (eg twin A’s). Within the B spacetime system, the A clock time-readout must tick wildly forward, relative to B’s normal steady-ticking clock rate (per B). Twin B never sees this happen by the receipt of light signals, but can deduce this (1) per the measured doppler shift of light from A, and per the LTs ... for example, I consider the collection of momentarily co-located and co-moving inertial observers wrt twin B. Twin A never experiences anything unusual, time passing steadily per he as normal. B's clock ticks normal per himself. I'm talking only about how the twin A clock exists within in the B spacetime system. This must happen in the B system, for otherwise B could not predict (or agree) that A must age more than himself over the round-trip, as twin A is in motion per B over the entire interval.

 

However, geometrically, a rotation of B's spacetime system by his own proper acceleration cannot ever cause moving-lengths to become non-length-contracted, within B's own system.

What I say here is not about optical effects. It's about how remotely located clocks exist within the non-inertial spacetime system, during a virtually-instant proper acceleraton (B's turnabout).

Now, does what I say here change your stated position at all?

Best regards,

Celeritas

 

 

Red bold face mine. What you say here above strengthens my stated objection, but perhaps it was not sufficiently clear what I objected to for the sake of michael and robin.

 

I commented on the claim that "during periods of non-inertial relative motion, the twin A clock ticks faster than B's own clock within the B spacetime system", saying that it is not a valid physical description as it leads to messing with the laws of physics, even causality.

 

Apparently "the B spacetime system" referred to a reference system for physical measurements of the accelerating twin in which the twin is constantly in rest. If I misunderstood that, then my comment may have been misdirected; but from your above clarification I think that I correctly understood you.

 

In SR the laws of physics hold "in" (with respect to) inertial frames. The laws of physics do not hold with respect to non-inertial frames, as you apparently acknowledge here above, as according to the laws of physics according to SR clocks do not tick wildly, and there can be no superluminal speeds. In SR the kind of "accelerated frame" that you discuss is not suitable for physical inferences, as you nevertheless appear to do; the term is even misleading as it relates to an ensemble of an infinite number of Lorentz transformed inertial reference systems. Such a virtual "accelerated frame" does not even correspond to measurement results obtained with a real, extended physical system. But any of those inertial reference systems is suited for physical descriptions, without things like breaking the speed of light or the fictitious speeding up of far away clocks.

 

According to SR, the twin who turns around observes a Doppler effect due to his turnaround; no laws of physics are messed up, nor does any law of physics need to be messed up to understand the observation of the correct number of ticks of the stay-at-home's clock by the traveler.

Compare Langevin's description on p.51 of https://en.wikisource.org/wiki/Translation:The_Evolution_of_Space_and_Time

 

It's similar in classical mechanics. For example, on a fair there is a merry-go-round on which people may freely move. It can then happen that a guy looses contact and flies outward until crashing against the outer rim. Geometrically he observed coordinate acceleration relative to the merry-go-round, until hitting the outer rim (as a matter of fact it happened to me once, with one rib broken).

Suppose that this is discussed in a thread in which one desires to get better physical insight in how this should be interpreted according to classical mechanics.

In that thread someone states that whatever is measured is real, and in the merry-go-round space-time system, a force acts on the guy that accelerates him towards the rim. Would you not object, and clarify that in classical mechanics such a magical force is merely fictitious, due to pretending that the rotating platform is not rotating, but in rest? Or would you claim that textbooks are wrong as fictitious force should be called real force? Even that forces which originate from nothing that could be their cause, are not a hindrance for physical insight?

 

PS. One more illustration that I thought of, as in this discussion there was a comparison with using maps (e.g. #234 by Mordred).

Imagine the captain of an airplane using a series of country maps (Mercator) when flying around the world. His copilot remarks that coastlines change shape when they are flying over them. Really? Is that a good physical description to explain what is happening?

Edited September 12, 2016 by Tim88

[Tim88]

 

Red bold face mine. What you say here above strengthens my stated objection, but perhaps it was not sufficiently clear what I objected to for the sake of michael and robin.

 

I commented on the claim that "during periods of non-inertial relative motion, the twin A clock ticks faster than B's own clock within the B spacetime system", saying that it is not a valid physical description as it leads to messing with the laws of physics, even causality.

 

Apparently "the B spacetime system" referred to a reference system for physical measurements of the accelerating twin in which the twin is constantly in rest. If I misunderstood that, then my comment may have been misdirected; but from your above clarification I think that I correctly understood you.

 

In SR the laws of physics hold "in" (with respect to) inertial frames. The laws of physics do not hold with respect to non-inertial frames, as you apparently acknowledge here above, as according to the laws of physics according to SR clocks do not tick wildly, and there can be no superluminal speeds. In SR the kind of "accelerated frame" that you discuss is not suitable for physical inferences, as you nevertheless appear to do; the term is even misleading as it relates to an ensemble of an infinite number of Lorentz transformed inertial reference systems. Such a virtual "accelerated frame" does not even correspond to measurement results obtained with a real, extended physical system. But any of those inertial reference systems is suited for physical descriptions, without things like breaking the speed of light or the fictitious speeding up of far away clocks.

 

According to SR, the twin who turns around observes a Doppler effect due to his turnaround; no laws of physics are messed up, nor does any law of physics need to be messed up to understand the observation of the correct number of ticks of the stay-at-home's clock by the traveler.

Compare Langevin's description on p.51 of https://en.wikisource.org/wiki/Translation:The_Evolution_of_Space_and_Time

 

It's similar in classical mechanics. For example, on a fair there is a merry-go-round on which people may freely move. It can then happen that a guy looses contact and flies outward until crashing against the outer rim. Geometrically he observed coordinate acceleration relative to the merry-go-round, until hitting the outer rim (as a matter of fact it happened to me once, with one rib broken).

Suppose that this is discussed in a thread in which one desires to get better physical insight in how this should be interpreted according to classical mechanics.

In that thread someone states that whatever is measured is real, and in the merry-go-round space-time system, a force acts on the guy that accelerates him towards the rim. Would you not object, and clarify that in classical mechanics such a magical force is merely fictitious, due to pretending that the rotating platform is not rotating, but in rest? Or would you claim that textbooks are wrong as fictitious force should be called real force? Even that forces which originate from nothing that could be their cause, are not a hindrance for physical insight?

 

PS. One more illustration that I thought of, as in this discussion there was a comparison with using maps (e.g. #234 by Mordred).

Imagine the captain of an airplane using a series of country maps (Mercator) when flying around the world. His copilot remarks that coastlines change shape when they are flying over them. Really? Is that a good physical description to explain what is happening?

Correcting two glitches, sorry for noticing them too late:

- Michael -> Michel

-"fictitious speeding up of far away clocks" -> "fictitious speeding up of far away inertial clocks"

[Celeritas]

Tim88,

 

OK. Thanx for your review comments. I'll digest it carefully, before responding.

 

Best regards,

Celeritas

[VandD]

 

Red bold face mine. What you say here above strengthens my stated objection, but perhaps it was not sufficiently clear what I objected to for the sake of michael and robin.

 

I commented on the claim that "during periods of non-inertial relative motion, the twin A clock ticks faster than B's own clock within the B spacetime system", saying that it is not a valid physical description as it leads to messing with the laws of physics, even causality.

 

Apparently "the B spacetime system" referred to a reference system for physical measurements of the accelerating twin in which the twin is constantly in rest. If I misunderstood that, then my comment may have been misdirected; but from your above clarification I think that I correctly understood you.

 

In SR the laws of physics hold "in" (with respect to) inertial frames. The laws of physics do not hold with respect to non-inertial frames, as you apparently acknowledge here above, as according to the laws of physics according to SR clocks do not tick wildly, and there can be no superluminal speeds. In SR the kind of "accelerated frame" that you discuss is not suitable for physical inferences, as you nevertheless appear to do; the term is even misleading as it relates to an ensemble of an infinite number of Lorentz transformed inertial reference systems. Such a virtual "accelerated frame" does not even correspond to measurement results obtained with a real, extended physical system. But any of those inertial reference systems is suited for physical descriptions, without things like breaking the speed of light or the fictitious speeding up of far away clocks.

 

According to SR, the twin who turns around observes a Doppler effect due to his turnaround; no laws of physics are messed up, nor does any law of physics need to be messed up to understand the observation of the correct number of ticks of the stay-at-home's clock by the traveler.

Compare Langevin's description on p.51 of https://en.wikisource.org/wiki/Translation:The_Evolution_of_Space_and_Time

 

It's similar in classical mechanics. For example, on a fair there is a merry-go-round on which people may freely move. It can then happen that a guy looses contact and flies outward until crashing against the outer rim. Geometrically he observed coordinate acceleration relative to the merry-go-round, until hitting the outer rim (as a matter of fact it happened to me once, with one rib broken).

Suppose that this is discussed in a thread in which one desires to get better physical insight in how this should be interpreted according to classical mechanics.

In that thread someone states that whatever is measured is real, and in the merry-go-round space-time system, a force acts on the guy that accelerates him towards the rim. Would you not object, and clarify that in classical mechanics such a magical force is merely fictitious, due to pretending that the rotating platform is not rotating, but in rest? Or would you claim that textbooks are wrong as fictitious force should be called real force? Even that forces which originate from nothing that could be their cause, are not a hindrance for physical insight?

 

PS. One more illustration that I thought of, as in this discussion there was a comparison with using maps (e.g. #234 by Mordred).

Imagine the captain of an airplane using a series of country maps (Mercator) when flying around the world. His copilot remarks that coastlines change shape when they are flying over them. Really? Is that a good physical description to explain what is happening?

 

 

 

You forgot to tell us what the traveler's simultaneity lines read between the 2010.2 earth year and the 2013.8 earth.

(You refer to Langevin p51 but that's only the story of the light beams reaching the observers. That's not the issue. We are interested in what the traveler simultaneity lines read during turnaround.)

 

During outbound journey the traveler's simultaneity lines read a real physical earth clock. That clock has less time than the traveler's clock. Same story for the inbound journey. No discussion about that. (In case you doubt: put a set of cameras along a railway track, synchronise the shutter of all the camera's. The camera takes a picture of the passing moving clock an inch in front of the camera lens: a real physical clock with hands showing less time.)

 

Does -per traveler simultaneity lines- the earth clock time turns fictitious at 2010.3 and return being real at 2013.8? You must be joking.

Or do you consider ALL the earth clock readings per simultaneity lines fictitious? If a car drives fast enough I feel -during a split second-the shorther moving car touching between two fingers. Time dilation and length contraction are real. Fly at high speed to the moon and you will be there after 1 minute of your life because the distance to cover contracted. Nothing fictitious. And in earth simultaneity (3D space) the traveler aged only one minut of his life. Nothing fictitious.

 

PS.

It's possible the traveler's simultaneity lines during turnaround are not straight lines (if we don't use momentarily co-moving inertial frames during deceleration/acceleration), but that doesn't change the issue; they still read real earth clock times. and have to cover times between 2010.3 and 2013.8

Edited September 12, 2016 by VandD