Physics: Your scenario does NOT display "time dilation", it demonstrates a different geometrical phenomenon: different timelike paths through spacetime can have different elapsed proper times. Every clock ALWAYS ticks at its usual rate, regardless of where it might be located or how it might be moved [#]. If you want to compare a moving or distant clock to a clock nearby, you must use SIGNALS from the other clock to this one, and you must consider how those SIGNALS are affected (by the motion or distance) -- do that and you find the ENTIRE effect is due to the way those SIGNALS are measured, leaving "no room" for the clocks to tick at different rates.

[#] That is \integral d\tau, when integrated along the path of the clock between successive ticks, ALWAYS remains the same, regardless of the path or the geometry of the manifold along the path. Here \tau is the clock's proper time.

The fact that clocks A and B experience different elapsed proper times along their different paths through spacetime is no more remarkable than the fact that for triangle UVW the paths UV and UWV have different lengths. Indeed if your "tool" used instantaneous accelerations and inertial motion between them, your scenario is just a triangle in spacetime, with clock a traveling UV and clock B traveling UWV (U is when they separate, V is when they rejoin, and W is a turn-aound in clock B's path that enables it to come back to clock A).

>	To describe this phemomena (experiment) IMO the wording APPEAR is wrong.

Yes. Say "is measured (in the appropriate inertial frame)" instead. This is not mere appearance, and this effect can and does have real physical consequences (e.g. pion beam lines that are a kilometer long -- in the lab it takes the pions 3.3 microseconds to traverse the beamline, but the pions experience elapsed proper times considerably less than their 26 nanosecond lifetime). There are other, more direct experimental implementations of the "twin paradox"....

Tom Roberts

10 Galilean transformation equations and Robert B. Winn

11 Galilean transformation equations and Robert B. Winn

Cannot they both change frames? Does not any change in speed implies a change in frame? Anyway what has changing frames to do with this experiment? IMO the most important issue is (in case 2) that clock B must change its speed (direction of speed)

> > >

You ASSUME that it was running slower in transit, but there is another explanation, one that doesn't run into a paradox (i.e., while B was in transit, he saw A's clock running slower).

> >	I do not see any paradox. This is a physical experiment and it requires a physical explanation.

>	And there is one: one that does not require either clock to actually be running slower.

I do not understand how this explanation explains the outcome of the experiment i.e. that when the two clocks meet their readings are different.

> >	While B is in transit it is "difficult" to see A's clock The same for A to see B's clock. Ofcourse each can transmit at regular intervals a timing system.

>	Sure. Not really so difficult after all. Of course, Doppler effects and time delays would have to be taken into account.

> > > >

To describe this phemomena (experiment) IMO the wording APPEAR is wrong.

> > >

Nope. What is wrong is claiming that clocks in motion actually run slower. The first problem is, What do you mean by "in motion"? B can justifiably claim that HE is stationary and A is in motion

> >	That is "correct" before they meet again.

>	Which can't happen unless one of them changes frames.

If you mean unless at least one changes its speed. In this experiment clock B has at least change its speed twice.

> > >

(which is why A's clock APPEARS to run slower to B).

> >	And vice versa. The wording APPEARS is tricky when they are in transit. IMO after they meet the word APPEAR can not be used any more.

>	They will be reading different times, but you still can't assume either of them was "running slow." As Paparios says, it's a geometric projection effect.

Why can not I say that one clock is running slower as the other (while moving)? Such an description is in accordance with the final observation i.e. that the readings are different.

IMO the only lesson learned from this experiment that when you want to understand the laws of nature you should not use clocks which move relatif to each other and if you do then you should adjust the readings of each clock.

Nicolaas Vroom

12 Galilean transformation equations and Robert B. Winn

Sure, but then one cannot say anything definite without describing exactly how each did so. You would also have to define another frame that remained inertial. Why would you try to insert such complications into a simple statement?

>	Does not any change in speed implies a change in frame?

Yes (we're discussing SR here).

>	Anyway what has changing frames to do with this experiment?

It should be obvious that A and B cannot get back together without doing so, and THAT is the crux of the matter (look at a Minkowski diagram of the situation).

>	IMO the most important issue is (in case 2) that clock B must change its speed (direction of speed)

THAT changes frames.

> > > >

You ASSUME that it was running slower in transit, but there is another explanation, one that doesn't run into a paradox (i.e., while B was in transit, he saw A's clock running slower).

> > >

I do not see any paradox. This is a physical experiment and it requires a physical explanation.

> >	And there is one: one that does not require either clock to actually be running slower.

>	I do not understand how this explanation explains the outcome of the experiment i.e. that when the two clocks meet their readings are different.

Look at a Minkowski diagram: the paths have different lengths.

> > >

While B is in transit it is "difficult" to see A's clock The same for A to see B's clock. Ofcourse each can transmit at regular intervals a timing system.

> >	Sure. Not really so difficult after all. Of course, Doppler effects and time delays would have to be taken into account.

> > > > >

To describe this phemomena (experiment) IMO the wording APPEAR is wrong.

> > > >

Nope. What is wrong is claiming that clocks in motion actually run slower. The first problem is, What do you mean by "in motion"? B can justifiably claim that HE is stationary and A is in motion

> > >

That is "correct" before they meet again.

> >	Which can't happen unless one of them changes frames.

>	If you mean unless at least one changes its speed. In this experiment clock B has at least change its speed twice.

Exactly!

> > > >

(which is why A's clock APPEARS to run slower to B).

> > >

And vice versa. The wording APPEARS is tricky when they are in transit. IMO after they meet the word APPEAR can not be used any more.

> >	They will be reading different times, but you still can't assume either of them was "running slow." As Paparios says, it's a geometric projection effect.

>	Why can not I say that one clock is running slower as the other (while moving)?

Because you cannot ascertain WHICH clock is "moving." Speed is purely relative.

>	Such an description is in accordance with the final observation i.e. that the readings are different.

But it's not in accordance with what actually happens. Remember? Which clock ends up behind the other depends upon who changed frames.

>	IMO the only lesson learned from this experiment that when you want to understand the laws of nature you should not use clocks which move relative to each other and if you do then you should adjust the readings of each clock. Nicolaas Vroom

Sounds like you are reinventing the first postulate (PoR) here.

13 Galilean transformation equations and Robert B. Winn

Anyway I assume that you agree with the possible outcome of such an experiment. A better word for tool is maybe actor.

> >	That means during the time that clock B travelled (away and back) clock B did run slower than clock A.

>	No. The problem is as much in your wording as in your physics, but BOTH are wrong. Wording: When you say "that clock runs slow", you mention ONLY the clock, and thus cannot impose some OTHER reference, all you can use is the clock ITSELF.

I write on purpose that clock B runs slower than clock A. That means I compare the condition of two clocks based on its final outcome.

>	And the clock just ticks along at its usual rate.

No. Based on the final observations at least one does not.

>	Indeed put a frequency standard right next to it, co-moving with it, and it will show that the clock DOES tick at its usual rate. So moving clocks DO NOT RUN SLOW.

When you put an other frequency standard A' near clock A and one B' near B (co moving with B) the pairs A',A and B',B each pair will show the same result but disagree which each other: the pair B',B will run behind.

>	This was not fully understood until after 1916 when GR was published. Even today, elementary or popular writings often take that shortcut to avoid the lengthy and complicated explanation I give here.

I do not understand what GR has to do with this.

>

One can say "Measured in the inertial frame of clock A, clock B did tick more slowly than clock A". But you didn't say that. Remember there is no "absolute" frame, and if you make a measurement in some frame, you MUST mention the frame used. It seems you are implicitly assuming a measurement in the frame of clock A, but you did NOT mention that.

The frame I use is a table which initialy and finaly contains two clocks: A and B.

>

Physics: Your scenario does NOT display "time dilation", it demonstrates a different geometrical phenomenon: different timelike paths through spacetime can have different elapsed proper times. Every clock ALWAYS ticks at its usual rate, regardless of where it might be located or how it might be moved [#]. If you want to compare a moving or distant clock to a clock nearby, you must use SIGNALS from the other clock to this one, and you must consider how those SIGNALS are affected (by the motion or distance) -- do that and you find the ENTIRE effect is due to the way those SIGNALS are measured, leaving "no room" for the clocks to tick at different rates.

IMO the physical explanation that at the end of the experiment the two clocks show a different reading is only because the two clocks experience different accelerations. These different accelerations influence the internal operation of each clock differently. IMO when you move a clock which operation is based on light signals which the speed of light (a little less) it does (almost) not tick at all. (comparing equal distances)

>	There are other, more direct experimental implementations of the "twin paradox"....

I do not understand why you call this a paradox. If my clock A shows 10 ticks and the moving clock B shows 6 ticks when the moving clock returns you know there is a time keeping problem. When the moving clock B shows 3 ticks at furthest distance and this distance is known (in straight line and B's speed is constant) then IMO it only makes sense to use my 10 ticks in order to calculate B's average speed. (because the clock B is running slow)

Nicolaas Vroom.

14 Galilean transformation equations and Robert B. Winn

The equations that describe what you describe are the equations that scientists threw away in 1887, the Galilean transformation equations.

x'=x-vt
y'=y
z'=z
t'=t

15 Galilean transformation equations and Robert B. Winn

So go ahead and explain what you mean by this changing of frames. As far as I can tell, a clock in S' never leaves S'.

>

> > >

(which is why A's clock APPEARS to run slower to B).

> >	And vice versa. The wording APPEARS is tricky when they are in transit. IMO after they meet the word APPEAR can not be used any more. Nicolaas Vroom.

>	They will be reading different times, but you still can't assume either of them was "running slow." As Paparios says, it's a geometric projection effect.

Geometric projection effect. That sounds kind of complicated. Could we say that one frame of reference just has fewer transitions of a cesium atom?

16 Galilean transformation equations and Robert B. Winn

Well, that all sounds very technical, but if you are going to define a second as a certain number of transitions of a cesium atom, then you still come up with the fact that one cesium atom has slower transitions than another cesium atom. I think Galileo had a better definition of a second than scientists of today have.

17 Galilean transformation equations and Robert B. Winn

The definition of a frame of reference appears to me to need to be clarified. Einstein appeared to understand it better. He said there was a frame of reference of a stationary clock called S and a frame of reference of a moving clock called S'. If the moving clock slows down and stops moving relative to S, it still has its own frame of reference S'. The only thing we can say with regard to S and S' is that neither is moving relative to the other. There is no change of frames of reference.

18 Galilean transformation equations and Robert B. Winn

Scientists did not "throw them away", it's just that we now recognize they are only an approximation to a MUCH better theory that uses Lorentz transforms between (locally) inertial frames.

And that recognition did not happen in 1887, more like the decade or two after 1905 -- it was a process, not a single event; it started with Einstein's 1905 paper. Note the key point of that paper is not his postulates, it is his approach: recognizing the importance of symmetries in physics.

Tom Roberts

19 Galilean transformation equations and Robert B. Winn

But that is NOT what happens. Clock B just travels a different path between the endpoints than clock A, and the paths have different elapsed proper times.

Two cars drive from Chicago to New York, one directly and one via New Orleans. Their odometers display different distances. Do you seriously think the calibrations of their odometers are different? -- Of course not, they merely traveled different distances between the endpoints. The twin scenario, and yours, are EXACTLY the same, except in a space-time plane. It's also true that for the cars we have a clear an obvious "frame" to use, that of the earth; for the clock scenarios there is no such ready-made and obvious frame of reference.

Comparing the two clocks' values at the endpoints is NOT sufficient to conclude their tick rates are different. You MUST also account for their different paths, and when you do, you find it accounts for 100% of the difference, leaving "no room" for them to tick at different rates.

After all, this has been done, several times in several ways.

>	That means I compare the condition of two clocks based on its final outcome.

OK. But the ONLY conclusions you can make from that are those supported by the measurements you made. You did NOT measure their tick rates, and thus cannot make any statements about their tick rates.

>>	And the clock just ticks along at its usual rate.

>	No. Based on the final observations at least one does not.

Not true. See above.

You did NOT compare rates, and thus cannot make any statement about their rates.

I, on the other hand, can extend your scenario to include frequency standards co-located and co-moving with each clock. They MEASURE each clock to always tick at its usual rate.

>>	This was not fully understood until after 1916 when GR was published. Even today, elementary or popular writings often take that shortcut to avoid the lengthy and complicated explanation I give here.

>	I do not understand what GR has to do with this.

It taught physicists that the integral of proper time is the relevant quantity.

>>

Physics: Your scenario does NOT display "time dilation", it demonstrates a different geometrical phenomenon: different timelike paths through spacetime can have different elapsed proper times. Every clock ALWAYS ticks at its usual rate, regardless of where it might be located or how it might be moved [#]. If you want to compare a moving or distant clock to a clock nearby, you must use SIGNALS from the other clock to this one, and you must consider how those SIGNALS are affected (by the motion or distance) -- do that and you find the ENTIRE effect is due to the way those SIGNALS are measured, leaving "no room" for the clocks to tick at different rates.

>	IMO the physical explanation that at the end of the experiment the two clocks show a different reading is only because the two clocks experience different accelerations. These different accelerations influence the internal operation of each clock differently.

Not in SR or GR. In both of them, it is the different PATH that matters, not the different accelerations. Of course in SR one needs accelerations to make the paths different. But in GR one does not. For all cases, it is the PATH LENGTH (integral of proper time) that matters.

>>	There are other, more direct experimental implementations of the "twin paradox"....

>	I do not understand why you call this a paradox.

Because that is its name.

"Paradox" has two meanings, and the relevant one is "a SEEMING contradiction that upon analysis proves to be fully consistent".

>	If my clock A shows 10 ticks and the moving clock B shows 6 ticks when the moving clock returns you know there is a time keeping problem.

Not "problem", but "difference". After all, this is completely unavoidable: different paths can have different lengths, and for a timelike path that length is elapsed proper time.

Tom Roberts

20 Galilean transformation equations and Robert B. Winn

>>	Tom Roberts

>

So, in other words, you are saying that if you step on the accelerator of your car, your car gets shorter. Here is the problem you have. If you use the correct equations for relativity, they show that if one clock ticks ten times and the other only ticks six, then according to the time of the slower clock, the car is not getting shorter, it is going faster. The equations show the exact relationship.

Totally nonsense. It reveals you have no idea what is going on in Physics.

21 Galilean transformation equations and Robert B. Winn

The problem with the Galilean transformations is not that they are total nonsense. They are a perfectly legitimate set of coordinate transformations. However, they do not exactly describe the relationship between relatively moving systems of inertial coordinates (meaning coordinate systems in which Newton's equations of mechanics hold good to the first approximation).

Remember, Maxwell's equations (1865) already showed that objects (whose size and shape is governed by electromagnetic forces) contract by a factor of sqrt(1 - (v/c)^2) when moving with speed v, and this has been confirmed experimentally. Any viable theory of relativity must account for this.

22 Galilean transformation equations and Robert B. Winn

No, you DON'T "have" to go by what Saint Albert said. It's just that you WANT to do that because your mind is hermetically sealed and refuses to accept new data.

>	not by what one of his disciples says a hundred and some years later.

Why not? If an aged idea is more valuable than a new one, why not accept phlogiston or the existence of only four elements (earth, air, fire and water)?

>	Einstein said that the clock in S' was slower.

Yes, he did. He was wrong. That means YOU are wrong, too. He had an excuse because he lived a century ago. YOU don't have that excuse.

>	That is what the equation indicates.

Is it? What qualifies you to assert that? The LT relates time on clocks that are not co-located. If they aren't co-located, how do you know your measurement is accurate? The fact is that you don't. Furthermore, the LT predicts that the clock in S' will measure the clock in S as the slower clock, so your assertion that the clock in S' is actually running slower is completely irrational.

>	To get a faster clock you have to use General Relativity.

Trying to insert GR into an argument about SR is pettifogging.

>	Nothing refutes the Galilean transformation equations.

Completely false and baseless assertion.

>	[Regurgitated falsehoods deleted]