1. Members,

Since James either cannot address this issue or chooses to dodge it let me clarify what we are looking at.

James R's continued arguement is very much like an affect we have all experienced.

That is a train whistle. As it approaches it sounds "Weeeee"
and as it passes and begins to receed it sounds "Oooooooooh."

The approaching sound has a higher pitch because as the train approaches each sound wave arrives sooner because the distance to travel is less than it would have been if the vehicle were sitting at rest relative to you.

When it receeds each sound wave now takes longer to reach you because distance is steadily increasing.

So the affect is to increase and decrease frequency or pitch from your frame of reference.

If you now count each sound wave using an on board counter.

Mark off an equal distance east and west of your location.

Have two trains with calibrated and synchronized whistles.

One train remains at rest and the other moves at 0.6c approaching from the east.

As the train passes the east marker it and the resting train begin to count sound waves and transmits a digital total count as it passes your location.

If the resting train transmits a count of 30,000 pulses. The traveling train will transmit a digital count of only 24,000 pulses.

The traveling train and resting train both reset their counters and as the traveling train receeds they both continue to count until the traveling train passes the west marker.

It then will transmit a digital total count of 24,000 counts and the resting train will have recorded 30,000 counts.

The synchronizaton is done any number of ways; including light signals and computing time delay of signals to and from respective frames with adjustments to the counts accordingly.

So the change in pitch to you is an "Illusion of motion" and did not affect the actual frequency of the whistle.

The "Perception" by observers that frequency is changing (speeding up and slowing down with vector of motion) and physical count results are two different issues.

In this example the wistle count represents time ticks.

The "Illusion of motion" of changing frequency does not have any bearing on the physical reality of time dilation of an accelerated frame.

It is equally important to note that while both the resting and traveling observer will experience the shift in frequency of respective whistles as they approach and pass, it is MORE important to understand that the digital information does not include reciprocity.

That is any prediction that both actually physcially tick slower is falsified. Because the traveling train is notified that the resting train had 30,000 counts to his 24,000 counts. So the view in SR is only valid physically for the traveling train which is what is supported by emeprical data.

The suggestion that the approaching clock increases tick rate to match a previous rest frame after having slowed due to having accelerated away is not supported since an inertial condition at turn around would create a new rest reference and the return flight is decreasing tick rate from that frame.

Clocks cannot and do not both physically increase and decrease tick rates simulatenously. They can "Appear" to do so but naot actually do so. The digital count of both frames is physical reality in both frames.

Sorry James R. Back to the drawing board.
nicely put MacM.

and pretty damn good for something Sciforums deems worthy of the cesspool....what an embarrassment....[for them ha]

2. Originally Posted by MacM
... you also used the term perpendicular. ...
Yes but ONLY when speaking of a velocity components, not the full velocities. I am sorry if I needlessly explained that last general case in words to you, under assumption you did not use the vector cross product.

I also illustrated it with the following "typed drawing":

|/

Two not co-linear velocities and one with greater speed - that is the most general case. You AFAIK have never commented on it but I guessed what would be your POV for it. Surely you understand from this drawing that the general case does not have the velocities perpendicular. Your post 93 "In such case they have a relative velocity composed of (A^2 + B^2)^0.5." is not useful for this general cases.

3. Originally Posted by MacM
...Holly cow the old simultaneity dodge. "What A or B or C thinks does not affect the emperical data" - Shssh....
No one is saying that it does, but you fail to realize that your set up only allows for the tick rates wrt to C's clocks to be measured. It is not possible for A to measure B's tick rate wrt to A's clocks.

You seem to assume that if they both are the same for C they are the same for ever one else also. The very fact, which you admit, that they are different for C and A (1000 vs. 800) shows that is not true or a safe assumption. You seem to want to have your "absolute physical tick" rates cake and eat it also when you need to measure time dilation. You can not have it both ways. Either tick rates do or do not depend on the frame that measures them.

I suspect that of the two alternatives I guessed in prior post, the second is more likely to be correct. Namely, that by A's clock, B clock is ticking too slow and also B did not travel as fast as A did the same distance (From marked start lines to C's location) as rapidly.

I.e. Both C & A agree that the other had the same relative speed but A does not agree that B had that speed too. If A & B by C's clocks and rulers were closing on C at 0.6c then A cannot see B wrt A traveling at 0.6c also. I do not like to say "see" but do so for clarity. For A to know by his clocks and rulers, A must measure B's speed not just assume it is what C measured or was reported to C by B.
Your scenario does not allow for this but you seem to falsely assume A would measure B's speed as it was measured by C.

Summary the accumulated ticks reported to C by A & B when they arrived at C, Na & Nb, were equal but A would measure that B's clock was slower and his velocity towards C was also slower than A's was so B accumulated ticks of a slower clock for longer period* to produce the same Nb.

I am not skilled enough with SR to run you thru the math showing this. I hope James or Pete can, but I am not sure it is even possible with the scenario you have set up.

Note this is not the old "simultaneous" BS as you also falsely assume.

---------
* With his slower speed, it took longer for B to go from start line to C. For C it took the same time for both A & B to travel this equal distance.

4. MacM:

Sometimes you forget that I'm in a different time zone. I do actually need to sleep from time to time, and I do actually have other things to do in life than to address your nonsense. You know, things like work, family, friends, etc.

But when you say it, you mean "In MacM reality, B is ticking ...", and there's no way to know whether, in MacM "illusion of motion" land the tick rate is the same or different.
Thank you. Thank you. Thank you. You have finally admitted yours is not some proven view better than my own. PLEASE MAKE NOTE EVERYBODY, I HAVE JUST BEEN VINDICATED BY JAMES R. He finally admits he cannot demonstrate his view is correct and mine is not.
Get with the program. All I said was that I don't know what your silly theory would or would not predict in any particular case. Since you don't know that yourself, it's hardly surprising.

You complain about Mac's useless theory where I simply state that given Bis ticks slower than C then C must tick faster than B and you want to have atissy fit and talk about "In C's frame". That is a perception issue and I have repeatedly stated the perception is not challenged.
You keep imagining that relativity makes some distinction between what you call "reality" and "illusion of motion". It does no such thing. And therefore, I do no such thing either. When I write "A sees B ..." I mean "In A's frame of reference, B really is ... , and the appearance supports that reality."

Get with it. Physical reality IS NOT a matter of observer perception.
Join you in your nuttiness? No thanks.

In B's frame, A's tick rate slows as it moves back to C's speed.
In C's frame, A's tick rate increases as it moves back to C's speed.
Show your work mathematically. Show the math to support C's view. c And I'll then show you your long standing error.
It's simple relativity that I taught you years ago.

The (final) speed of A relative to B is, let us say, 0.6c. The time dilation formula is:

$\Delta t = \frac{\Delta \tau}{\sqrt{1-(v/c)^2}}$

where $\Delta \tau$ is a proper time interval and $\Delta t$ is the time interval measured in a frame that does not measure proper time.

Here, A is moving, so A's clock measures proper time. If A ticks off a certain amount of time $\Delta \tau$, then in B's frame, the time recorded on B's clock will be longer, according to the formula. B therefore concludes that A's clock is running slow.

When A is stationary relative to C, v=0 and so $\Delta \tau = \Delta t$. This means that the time intervals recorded by A and C's clocks are the same - they tick at the same rate.

You still have not shown your work here and mathematically how you get C to think A is speeding up. Come on. close your arguekent that your view is superior. We are waiting. (Actually I'm waiting so I can cram it down your throat.)
Just to be clear, A starts off travelling at 0.6c relative to C. Then, in C's frame, A's velocity decreases to zero. For comparison, in B's frame, A's velocity starts at zero and then A's velocity increases to 0.6c relative to B.

In terms of tick rates or time intervals, the time dilation increases with increasing speed, so the difference in tick rates increases in B's frame and decreases in C's frame.

There's no mystery here. It's just a matter of understanding what a reference frame is - something you have never managed to grasp.

5. MacM:

Since James either cannot address this issue or chooses to dodge it...
Or has a life...

That is a train whistle. As it approaches it sounds "Weeeee"
and as it passes and begins to receed it sounds "Woooooo."

The approaching sound has a higher pitch because as the train approaches each sound wave arrives sooner because the distance to travel is less than it would have been if the vehicle were sitting at rest relative to you and sound arrived at a normal rate..
That is incorrect. In fact, the sound travels at the same speed through the air regardless of the train's speed. The increase in frequency is due to a "bunching up" of the sound waves due to the train's motion.

If you now count each sound wave using on board counters.

[snip]

So the change in pitch to you is an "Illusion of motion" and did not affect the actual frequency of the whistle.
No. The change in pitch in the Doppler effect is real for the person hearing it. And a digital frequency meter will confirm that it is not a mere matter of human perception, and certainly not any kind of "illusion".

This analogy is, in any case, utterly useless when you're discussing relativity, since sound waves have a preferred frame of reference - the frame of the medium (air) carrying the waves. The speed of sound relative to the train is different from the speed of sound relative to a person who is stationary on the track.

In comparison, the speed of light for a person on the track is the same as for a person on the train (assume, for simplicity, that the experiment is done in vacuum for light). Thus, the Doppler effect for light operates differently than the Doppler effect for sound.

The "Perception" by observers that frequency is changing (speeding up and slowing down with vector of motion) and physical count results are two different issues.
No, because frequency is the physical count of wave crests in a particular period of time.

The other problem with your example, of course, is that the Doppler effect for sound usually ignores time dilation, since this is assumed to be small for the kinds of speeds that trains travel (much less than the speed of light).

It is equally important to note that while both the resting and traveling observer will experience the shift in frequency of respective whistles as they approach and pass, it is MORE important to understand that the digital information does not include reciprocity.
Yes it does.

Take two trains with identical whistles. Have one of them (A) stationary on the track, and the other (B) moving at some speed. Both blow the whistles. An observer on train A hears B's whistle as having a higher pitch. AND an observer on train B hears A's whistle as having a higher pitch. In other words, BOTH observers hear the other's whistle as having a higher pitch than theirs - "reciprocity". In relativity, both observers observer the other's clock as ticking slower - "reciprocity".

Your example completely fails to show what you want it to show, apart from its many other flaws.

Clocks cannot and do not both physically increase and decrease tick rates simultaneously.
Correct, but nobody ever said they did.

Sorry James R. Back to the drawing board.
Yes. You have an awful lot of learning to do to make any progress.

6. Quantum Quack:

nicely put MacM.
Now read my response. I assume you'll be congratulating me even more.

Or are you just cheering on MacM because you think he's sticking it to the man?

and pretty damn good for something Sciforums deems worthy of the cesspool....what an embarrassment....[for them ha]
I've provisionally moved this thread back to Physics, on the basis that it may be instructive for some to see how real physicists deal with cranks.

7. Relegation to the cesspool is how real physicists deal with cranks.

8. Originally Posted by Billy T
Yes but ONLY when speaking of a velocity components, not the full velocities. I am sorry if I needlessly explained that last general case in words to you, under assumption you did not use the vector cross product.

I also illustrated it with the following "typed drawing":

|/

Two not co-linear velocities and one with greater speed - that is the most general case. You AFAIK have never commented on it but I guessed what would be your POV for it. Surely you understand from this drawing that the general case does not have the velocities perpendicular. Your post 93 "In such case they have a relative velocity composed of (A^2 + B^2)^0.5." is not useful for this general cases.
I do believe I went on to dsicsuss cases of co-moving non-parallel mnotion and that relative velocity between such clocks woudl not match emperical time dialtion.

That the correct time dilation can only be found if you compute actual motion to the "Common" rest frame for each and then take the differential dilations as the measured emperical dilation between the.

9. Originally Posted by Billy T
No one is saying that it does, but you fail to realize that your set up only allows for the tick rates wrt to C's clocks to be measured. It is not possible for A to measure B's tick rate wrt to A's clocks.
And some how that makes SR's predictions correct? Remember if a theory can't be tested it is falsified. Sure you want to stay with that conclusion that it is untestable?

Originally Posted by Billy T
You seem to assume that if they both are the same for C they are the same for ever one else also. The very fact, which you admit, that they are different for C and A (1000 vs. 800) shows that is not true or a safe assumption. You seem to want to have your "absolute physical tick" rates cake and eat it also when you need to measure time dilation. You can not have it both ways. Either tick rates do or do not depend on the frame that measures them.
They do not. Only the frame with actual velocity to the common rest frame is correct. The mere relative veloicty experienced by the resting frame has absolutely NO affect on any clock. It only generates the illusion that i.e. - the train frequency has increased. The train's frequency is what it is in it's own rest frame while moving inertial.

Originally Posted by Billy T
Your scenario does not allow for this but you seem to falsely assume A would measure B's speed as it was measured by C.
This hass absolutely nothing to do with what each clock measures while in motion. The emperical data is what it is as transmitted digitally between all clocks.

10. Originally Posted by James R
You know, things like work, family, friends, etc.
You actually have friends?

Just kidding James.

Originally Posted by James R
MacM:

Or has a life...

Get with the program. All I said was that I don't know what your silly theory would or would not predict in any particular case. Since you don't know that yourself, it's hardly surprising.
Your statement applies to SR or are you saying you can test and prove that the lab clock physically loses time compared to the accelerated particle? Not that it might just "appear" dilated as the change in the train's whistle?

Originally Posted by James R
You keep imagining that relativity makes some distinction between what you call "reality" and "illusion of motion". It does no such thing. And therefore, I do no such thing either. When I write "A sees B ..." I mean "In A's frame of reference, B really is ... , and the appearance supports that reality.
Absolutely false. I have never made any such assumption. Just the opposite. It is SR's failure to recognize that applying "Frame Switching" (who accelerted and hence has ACTUAL motion) to your calculations voids the relative veloicty arguement. The relative velocity experienced by the resting clocks has no affect and is not affected.

You continuously and repeatedly make false assertions about my views. You should attempt to at least follow what I have said and not just make up strawman objections.

Originally Posted by James R
Join you in your nuttiness? No thanks.
Another negative innuendo and invalid rebuttal.

Originally Posted by James R
That is incorrect. In fact, the sound travels at the same speed through the air regardless of the train's speed. The increase in frequency is due to a "bunching up" of the sound waves due to the train's motion.
See what I mean gang? I clearly stated that the shift in frequency was due to the changing distance waves had to travel conmpared to that of traveling waves when the train was at rest. (Hint James I said what you said. ) You can stop pretending to be teaching here now.

Originally Posted by James R
No. The change in pitch in the Doppler effect is real for the person hearing it. And a digital frequency meter will confirm that it is not a mere matter of human perception, and certainly not any kind of "illusion".
Never said the illusion was not "Apparent reality" to the resting observer. What I have shown is it is not the physical reality for the whistle. You are still wanting to talk about perceptions and not the physical reality.

Originally Posted by James R
This analogy is, in any case, utterly useless when you're discussing relativity, since sound waves have a preferred frame of reference - the frame of the medium (air) carrying the waves. The speed of sound relative to the train is different from the speed of sound relative to a person who is stationary on the track.
And as I have shown so does time dilation. The only emperically supported time dilation between clocks is to the preferred common rest frame.

Originally Posted by James R
In comparison, the speed of light for a person on the track is the same as for a person on the train (assume, for simplicity, that the experiment is done in vacuum for light). Thus, the Doppler effect for light operates differently than the Doppler effect for sound.
We are not talking about the apparent invariance of light but of emperically demonstrated time dilation between clocks. Even so the invariance may well (in fact much more likely) be just an illusion based on incomplete knowlefge of what we are looking at.

Originally Posted by James R
No, because frequency is the physical count of wave crests in a particular period of time.
Originally Posted by James R
The other problem with your example, of course, is that the Doppler effect for sound usually ignores time dilation, since this is assumed to be small for the kinds of speeds that trains travel (much less than the speed of light).
I certainly know that and I'm sure most here do as well. The analogy stands as a valid analogy of what you call time dilation vs actual time dilation.

Originally Posted by James R
Take two trains with identical whistles. Have one of them (A) stationary on the track, and the other (B) moving at some speed. Both blow the whistles. An observer on train A hears B's whistle as having a higher pitch. AND an observer on train B hears A's whistle as having a higher pitch. In other words, BOTH observers hear the other's whistle as having a higher pitch than theirs - "reciprocity". In relativity, both observers observer the other's clock as ticking slower - "reciprocity".
Right and:

1 - That is uncomfirmed emperically and is shear mathematical extrapolation without evidence.

2 - Ir is on the order of perception of motion between observers and does not have anything to do with the actual whistle frequency of the trains.

Originally Posted by James R
It's simple relativity that I taught you years ago.
Give me a break you haven't taught me anythign I didn't already know.

Originally Posted by James R
Your example completely fails to show what you want it to show.
QQ and I'm sure some others seem to disagree with your assessment.

Originally Posted by James R
There's no mystery here. It's just a matter of understanding what a reference frame is - something you have never managed to grasp.
Nice try Jmes but this post rings very hollow under the circumstances.

Originally Posted by James R
Yes. You have an awful lot of learning to do to make any progress.
Ditto for you. I had to educate you about GPS using a preferred frame the ECI and not relative velocity of the surface vs orbit.

There's no mystery here. It's just a matter of understanding what a reference frame is - something you have never managed to grasp.

11. Originally Posted by James R
Quantum Quack:

Now read my response. I assume you'll be congratulating me even more.

Or are you just cheering on MacM because you think he's sticking it to the man?

I've provisionally moved this thread back to Physics, on the basis that it may be instructive for some to see how real physicists deal with cranks.
Your posts unfortunately fail to actually address the issues raised and this is blatantely a false negative innuendo assuming I am a crank. I rather think I have raised some very valid issues which you find uncomfortable.

Your habit of posting things I said along with comments about my misunderstandings and your correcton are self-serving garbage.

Your repeated assertion that what observers see is reality is also growing rather old and thin since it is an unsupported (likely unsupportable) prediction. Which means relativity is falsified on first cause since it is not a valid theory if untestable.

12. Originally Posted by quadraphonics
Relegation to the cesspool is how real physicists deal with cranks.
You should first demonstrate that the poster is a crank. James R has been unable to do that. I rather doubt you have any emperical data to support his arguement for reciprocity either.

If you do then please post it or ( .....well you get the idea).

If it is untestable then it is falsified as a valid theory. Please show us data from the accelerated particle view that:

1 - It does see the lab clock dilated.

2 - That the percieved dilation means the lab clock actually lost time because the particle accelerated.

13. This thread isn't in the cesspool :\. What happeneddddd?

14. Originally Posted by MacM
You should first demonstrate that the poster is a crank.
You've presented a convincing demonstration of that point already, Mr. Spinning-Head-Avatar.

15. MacM:

Never said the illusion was not "Apparent reality" to the resting observer. What I have shown is it is not the physical reality for the whistle. You are still wanting to talk about perceptions and not the physical reality.
This analogy with the Doppler effect for sound is actually quite useful in working out what you think.

What you're saying is that a physical effect that can be measured by instruments that are not dependent on human perception, is only "apparent reality" and not real. You claim that the higher frequency of the train whistle heard by an observer on the track (or his frequency meter) is an "illusion of motion". But it isn't. If you rely on the supposedly illusory frequency to trigger off an alarm, say, or perform some other automated function, then it will work. And the alarm on the track won't trigger at the frequency of the whistle when it is at rest. So, there's no illusion involved.

You claim that what you have shown is "not physical reality for the whistle". That's a very interesting and revealing choice of words. You were very careful to include "for the whistle" there, weren't you? What your statement would say if you expressed it more explicitly is just this:

"The frequency shift of the whistle's sound is not heard in the whistle's rest frame."

But that's just a statement about one frame of reference. And nobody disputes that statement, either. What I, and all physicists, dispute is your claim that what is true in this one particular frame is true in ALL reference frames. As it happens, it is an empirical FACT that a frequency shift does occur in every frame other than the whistle's rest frame. And, importantly, the "perception" of whatever is measuring the frequency cannot be separated from the "reality" of what frequency is measured. In the track frame, the whistle's frequency really is different from its frequency in the rest frame.

Until we can sort out this major misunderstanding of yours, there's no point discussing Einstein's theory of relativity. So, from now on I propose we stick to discussing the classical Doppler effect until you are able to comprehend the reality of the frequency shift. Ok?

Take two trains with identical whistles. Have one of them (A) stationary on the track, and the other (B) moving at some speed. Both blow the whistles. An observer on train A hears B's whistle as having a higher pitch. AND an observer on train B hears A's whistle as having a higher pitch. In other words, BOTH observers hear the other's whistle as having a higher pitch than theirs - "reciprocity". In relativity, both observers observer the other's clock as ticking slower - "reciprocity".
Right and:

1 - That is uncomfirmed emperically and is shear mathematical extrapolation without evidence.
Rubbish. You can observe the Doppler effect for yourself very easily. Just go out on the street and listen to the engine sounds of cars as they go past you. You'll REALLY hear that frequency shift. Then, jump in your car and drive past a ringing bell or alarm or railway crossing. You'll REALLY hear the reciprocal frequency shift there, too.

If you don't believe me, and have never noticed the Doppler effect over the course of your life, then I'm sure plenty of other people here can confirm that it occurs and that they have empirically observed it themselves.

2 - Ir is on the order of perception of motion between observers and does not have anything to do with the actual whistle frequency of the trains.
Nonsense. A simple formula allows you to calculate the shift precisely, and it only depends on relative speeds, the speed of sound and, importantly, the known whistle frequency in some other frame.

I had to educate you about GPS using a preferred frame the ECI and not relative velocity of the surface vs orbit.
GPS doesn't use a preferred frame; it uses a few different frames for convenience, but they are not "preferred" in the sense you mean. I won't bother discussing GPS with you, since it is now apparent that you can't cope with the basic Galilean relativity of sound waves, let alone special relativity, let along general relativity.

16. Originally Posted by James R
Quantum Quack:

Now read my response. I assume you'll be congratulating me even more.

Or are you just cheering on MacM because you think he's sticking it to the man?

I've provisionally moved this thread back to Physics, on the basis that it may be instructive for some to see how real physicists deal with cranks.
You know JamesR I have always held the greatest respect for your opinions, scientific and other wise and still do.
You have macM by the proverbials on the issue of his sound analogy and admit I was too quick to offer support for it. As I see later you intend to make use of it... congrats... [ still doesn't deal with our misssing photon but congrats any ways...]

Now I would like to see an admission of error if appropriate on MacM's part so that I can congratulate him also on being so fair minded.

IMO it would be worth sticking just to the sound doppler effect issue until one of you guys has the balls to admit a mistake. Now I have rarely seen MacM back down and of course JamesR rarely makes a mistake to back down from...so this may prove rather interesting .

17. What you're saying is that a physical effect that can be measured by instruments that are not dependent on human perception, is only "apparent reality" and not real. You claim that the higher frequency of the train whistle heard by an observer on the track (or his frequency meter) is an "illusion of motion". But it isn't. If you rely on the supposedly illusory frequency to trigger off an alarm, say, or perform some other automated function, then it will work. And the alarm on the track won't trigger at the frequency of the whistle when it is at rest. So, there's no illusion involved.
what say yeh! MacM to above allegations...

18. Originally Posted by MacM
{post 108}...the correct time dilation can only be found if you compute actual motion to the "Common" rest frame for each and then take the differential dilations as the measured emperical dilation between the{m}.
Originally Posted by MacM
{post 109}... Remember if a theory can't be tested it is falsified. ...
I did not say SR cannot be tested. In post 103, said: “Your setup only allows for the tick rates wrt to C's clocks to be measured. It is not possible for A to measure B's tick rate wrt to A's clocks.” That does not “falsify SR,” just your set up is inadequate for such a measurement; however, I now extended your set up to show that the “MacM version of SR” contradicts itself, so it is false. (I apologize in advance for being careful, using defined symbolic terms, etc. to specify in detail everything, but you should read anyway and try to find a SPECIFIC point where I have not followed the procedures that your agreed to in post 93.)

To show that your POV is false, I need two clocks, A & B and two inertial frames C & E, which have respective motion at speed Vce along a common “X-axis” line. The origin of E, designated as E(0,0), is already far to the right of the origin of C and the separation between these origins is increasing. All motions I will use are along this same X-axis line. Before proceeding to my proof, either read blue text or skip it and refer back as needed.

]I expended some effort to clearly understand your version of SR and then summarize various cases. One was case (2b), which you quoted in your post 93 as follows:
“When there are two clocks, A & B, with constant relative velocity, both of which were once at rest in a frame, and they have no acceleration now wrt to that frame, then the Time Dilation, TD, of each is calculated ignoring the other as in (2a). This results in their respective “physical time dilations” PTDa & PTDb. If either were to have its time dilation correctly measured by observers, which are at rest wrt to the other, they would also measure the same PTDs. For example, if observers stationary wrt to clock A measure correctly the TDb they find DTb = PTDb.” {This is same as your first post quoted above, but more procisely stated in your terms and my math symbols.}

And you replied in post 93 with the single word: “correct.”
Just to remind others and you, if needed, case (2a) was a single clock now steadily moving wrt a frame that it was once at rest in earlier. We all agreed that such a steadily moving clock is ticking more slowing than other clocks that are stationary in that frame where the moving clock was once at rest and that conventional SR calculates the reduced tick rate, TD, correctly using its speed wrt that frame.)

Here is the current (also called “first”) situation:
Clock A is at rest at frame C’s Cartesian coordinate system origin, but B has steady speed along C’s negative X-axis equal to VBc . I.e. clock B is steadily crossing C’s “Y-axis” grid lines and clock A is stationary at C(0,0). Thus we all agree that it would seem correct to calculate the Time Dilations of clock B, TDb, compared to clock A’s tick rate via the standard SR equation using the speed VBc.

Here is what had happened a little earlier:
Both A & B were stationary at the origin of frame E, I.e. were at E(0,0), so were co-moving away from C(0,0) at speed Vce. (If you forgot what that is, see 2nd paragraph again.) Then both accelerated (in separate rockets, a & b) in the negative X direction (towards C’s origin) exactly the same until their C coordinates was very large and positive, for example the point C(100000, 0). At this point they are co-moving towards every more negative X locations with speeds wrt to C(0,0) of VAc = VBc or since identical, just Vc, which happens to be VBc as given just above in the “current situation,” I.e. Vc = VBc at this point. And of course, their common speed wrt to E(0,0) or Ve = Vc + Vce = VBc + Vce. At this point clock B stops accelerating and just forever coasts, but clock C begins to de-accelerate so that its speed is zero just as it reaches C(0,0), where it remains “forever.” I.e. this is how the “first situation” came to exist.

Now since both A & B started from rest together in frame E, we realize that the procedure (2b) (See blue text) must be used to compute their time dilations separately and then take the difference to find TDb, the Time Dilation of B wrt to the tick rate of clock A which is now stationary in frame C at C(0,0). I.e. we use the standard SR equation to calculate B’s actual “physical tick rate” with respect to the place where it was stationary with clock A, namely E(0,0) or their “common rest frame.”

To do this calculation for clock B, we use B’s speed wrt to that common rest frame. I.e. we use speed of VBe = Ve = VBc + Vce, from bold of prior paragraph. I will designate the results of this calculation, with VBe = Vce + Vce as PTDbe, the Physical Time Dilation of clock B wrt any of frame E’s stationary and synchronized clocks where clock B & A were once mutually at rest at E(0,0).

Likewise I use the std SR equation to calculate PTDae with the speed of clock A wrt to E(0,0) which is simply Vce as C is at C(0,0) forever now. Now in accordance with MacM’s agreed procedure, the Time Dilation of clock B wrt to the tick rate of Clock A, which is stationary at C(0,0) or “TDb” is just the difference in their Physical Time Dilations evaluated by std SR equations when their speeds wrt their “common rest frame” or in this case wrt E(0,0) is the speeds used in the calculations. I.e. TDb = PTDbe – PTDae. (This is a positive time dilation as PTDbe > PTDae since in either frame and certainly in frame E clock B is moving faster than clock A so has greater dilation.)

SUMMARY: Now two “MacM approved” but different methods have been used to calculate TDb. To distinguish them I will rename the one of the “first situation” one, which used speed VBc, TDb1 and call the other TDb2. TDb2 used two different speeds wrt to E(0,0), THEIR COMMON REST FRAME, to separately calculate the Physics Time Dilations of clocks, A & B and then subtracted these two PTDs to get TDb2.

The standard SR equations for PTDs are non-liner so it is highly unlikely that TDb1 = TDb2, but I suspect that for some particular choice of Vce, this is possible. I am too lazy to do all this numerically. (Perhaps Pete will – he sometimes, at least years ago, did enormous amounts of SR calculations.) I will just note that if by rare chance and the first Vce I selected did result in TDb1 =TDB2, then I would just select a different value for Vce. I.e. replace frame E in my story with frame F.

Also to further drive the stake thru MacM’s version of SR, I note that I have not yet told the entire history of clocks A & B. They were both once at mutual rest in frame F, side-by-side at F(0,0), before accelerating and then mutually coming to rest in frame E at E(0,0). Thus frame E is not the only “common rest frame.” It just happens to be their last one. As clocks A & B were NEVER at mutual rest in frame C, it is not a “common rest frame,” yet the calculation of TDb1 was done in accord with MacM’s agreed procedure and by far the simplest to do. (Also in accord with JamesR’s & Pete’s too.) In fact as MacM likes to point out, TDb1 is the one case for which there is “empirical validation” of the procedure in Earth based experiments . Also, there could have been a “common mutual rest” frame G before F, etc. for an infinite set of “MacM approved” and mutually conflicting TDb which use their speed wrt to a “common rest frame.”.

19. Originally Posted by Pete
Hi Mac,
“ Originally Posted by MacM
"A" & "B" will remain synchronized in any common frame not just the "C" frame. "

That is not what SR says.
Every time you assert that two clocks not in the same place are synchronized in all reference frames, you are demonstrating a misunderstanding of special relativity.
Hi Pete,
I jumped in here late, but did not MacM state that the clocks would remain synchronized in all "common" frames. I take this to mean if both decelerated symmetrically and arrived at a common velocity, then the clocks remain synchronized.

20. Originally Posted by MacM
Originally Posted by James R
"(h) If at the end of the process A ticks slower than D, but D ticks at the same rate as C, explain how D knew to speed up its clock when it was launched from A, whereas A knew to slow down its clock when launched from C. How do we tell the difference between A and D? "

Therein lies the great question. It is incumbent on us to seek that answer because clearly something is going on that we have no clue how that occurs, just as we have no clue how particle entanglement occurs.
This is what is oft referred to as the 'jackpot question'.

I will attempt a rational model to explain the James R transfers of knowledge in time dilating(+,-) clocks. The questions builds its own framework for discussion and while I as a practice I do not generally pass out kudos to James R, the question is remarkable, perhaps this will prove to be a bold move into the third millenium.

Consider that the answer does not necessarily need to be contained in SR theory, or non-SR theory, depending on your point of view. Instinctively, in the form of a mild epiphany, ‘the knowing’ factor has some characteristics of a ‘conservation law” more probably, or ‘maybe’ for the timid, in a form similar to the ‘conservation of angular momentum‘. The unobserved ‘forces’, and in fact the theoretically undesignated ‘forces’ that manage time dilation must be ’nonlocal’, in a JS Bell described form.

As long as we are reaching consider the multi-year trajectory trail of our solar system. Virtually all graphical and mathematical models I have seen are brute shorthand representations of the actual solar system motion. If the sun were the center axle of a tire and the planets are placed proportionately in their proper orbit, the fact of the sun’s motion provides a clue to the helical trajectory of each of the planets as modified by what is observed as tilted orbits, the whole enchilada is really a system of embedded helices with radii from the sun as is commonly understood.

When jumping from the earth surface we instinctively accept that the force of gravity brought us down to the surface. The conservation of angular momentum as I term is a stern master. Jumping upsets the equilibrium of the system and the nonlocal forces operate to maintain the balancing of angular momentum. We can ignore the instinct to apply yesterday’s angular momentum principles (amps). If our planet was a cylinder rotating around its center axis the example of ‘leaping and returning’ might make more sense when considering symmetry constraints.

We are this far so we might as well leave the sissy parachutes behind and jump for the hell of it.

http://www.metaresearch.org/cosmolog...of_gravity.asp

http://math.ucr.edu/home/baez/physic...rav_speed.html

http://www.metaresearch.org/media%20...G-Kopeikin.asp

These links discuss the general topic of the speed of gravity. The first link is a Tom Flandern paper which h makes the point that the speed of gravity is, for the timid, Vg > 10^10*c, the brave say it out loud the speed is infinite. The claim isn’t new as Flandern says the infinite speed of gravity was a known fact when studying at Yale in the 60s. If this, or either of the options presented here is the case we can discard the vector models of universal gravitational laws and conclude that forces between stellar objects suspected as originating gravitationally “just are”.

In the Einstein-Podowski-Rosen paper the measurement of the angular momentum of one of a twin set of photons has the effect of immediately determining the angular momentum of the other twin even though the other nonmeasured photon may be light years removed from the measured photon. The conclusion, or a conclusion is that the forces responsible to know when and what to do when one of the twin photons was measured are spatially insignificant and operate instantaneously.
t
Consider a play ground teeter-totter where the end points represent the angular momentum of the photons. Up and down whatever, grabbing one end (the measurement) immediately determines the other end. Assume the total angular momentum of the system was zero then the teeter-totter keeps a perfect accounting of the angular momentum. Mother Nature, so she told me, decided that twin photons should share angular momentum ‘vectors’ for reasons of efficiency and simplification of system properties.

As a youngster I stood on a rotating platform located in the Munich Science Museum. I, the distances of the weights from my centerline I was holding and the resultant angular velocity all required an unmonitored but strictly coordinated in a conservation mode the name of which I arbitrarily describe in words of angular velocity? There are, no doubts, a plethora of mathematical models that describe system in elegant mathematical prose but without the ’spooky’ nonlocal forces centers intrinsically embedded in the model, James R’s question doesn‘t get an appropriate scrutiny - I seriously advise against any knee jerk off the off the shelf mathematical or abject Ptolemaic insertion into the greater scientific psyche for the simple reason that the duh, ‘the insertion works, lets move on‘.

I personally am not enamored with the giants of the past but, having said this I must give deep credit to Isaac for his refusal to speculate the nature of the mechanism re inter-stellar gravitational motion. Action at a distance was a spooky proposition for him and while the universal gravitational force law seen as F = - GmM/x^2 does an admirable job of providing predictions for space/time determinations, there is nothing in the expression that even vaguely hints at force fields similar to what we generally accept as EM fields, or graviton exchanges or whatever.

This is mostly off the top the old head but who among you was aware that Charles Darwin almost titled his book, “Origin of the Species” as, “The Habits of Nature”. If any of the readers feel themselves immune, as a member of nature, from the habitual forces, nonlocal in nature, that drives us all, you had better take another look.

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