Relative velocity in S.R. for Dave

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Relative velocity in S.R. for Dave

Postby ralfcis on September 19th, 2017, 12:05 pm 

If you can understand relative velocity, you can understand special relativity. I've been staring at this sentence for two days now and don't know how to continue because the subject of relative velocity is so incredibly complex I don't know where to begin.

Ok I guess we'll start with the fact that separating two atomic clocks at a certain relative velocity will cause several different types of time difference between them:

1.apparent time differences during the relative motion:
a) time dilation (each clock slows w.r.t. the other by a factor of 1/Y)
b) relativity of simultaneity (the time difference between the non-dilated clock and what the non-dilated clock's dilated clock sees of the non-dilated clock). (For example at .8c the non-dilated clock is at 5 and its dilated clock is 3 and it sees the non-dilated clock at 1.8 so the RoS is 3.2) (RoS is like a bank of time that accumulates and gets cashed in at the end of a journey of separation or gets loaned at the beginning of a journey of clocks coming together and depletes during the journey.)
c) rate of time (a doppler effect where clocks appear to be going faster or slower than the dilated rate of time depending on velocity direction) (For example at .8c, every non-dilated year will take 3 dilated years to be seen in slow motion by the separating clocks and every 3 dilated years will take 1 non-dilated year to be seen in fast motion by clocks coming together.)

Don't worry, all this will become clear after extensive STD analysis.

2. permanent time difference after a relative stop in motion for a long enough time for data to propagate
a) The clock initiating the stop will eventually end up (takes light speed delay time for all data to be received) having aged less than the non-initiator by the dilated time at the stop.) (Again much STD work is needed to clarify this.)

3. permanent time difference after change in relative motion.
a) I've asked the question whether relativity recognizes that a full stop is not needed to establish a portion of permanent time difference but I never get an answer. Relativity is analog so any change in relative velocity will produce some permanent time difference, no digital full-stop is needed.

I will not be introducing the added complexity of Einstein's clock network synchronization or the debate between one-way and two-way speed of light. They are obstructionist barnacles that have attached themselves to the body of relativity making it difficult to see it in its purest form. I've seen the debates on these subjects go absolutely nowhere on this forum and usually end in the conclusion that "I guess we'll never know the whole truth."

Yeah, this isn't going well, no one will understand what I'm talking about so far. It gets even worse. For example, the relativistic velocity combination equation allows one to add velocities relative to a common stationary frame without the combined velocities exceeding the speed of light relative to that frame. (This is why any speed relative to c is c.) So there are differences relative to that frame between a .8c relative velocity between clocks where one is stationary and the other travels 4 light years (in 3 or 5 years depending on perspective) and .8c relative velocity made up of 2 clocks either separating or coming together at .5c.

I will also show how the journey from earth to a planet 4 ly away at .8c is identical to a round trip back to earth from the planet. I will also show how this is equivalent to 2 airplanes circumnavigating the earth through the poles and yielding no time difference relative to each other no matter what their combined relative velocity. I'll also show both Minkowski and Epstein STD analysis of each example and show what each one reveals.

Okay, let's begin, I promise minimal lines per STD this time.
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Re: Relative velocity in S.R. for Dave

Postby BurtJordaan on September 20th, 2017, 12:39 am 

An ambitious goal Ralf, so good luck with Dave. ;)

ralfcis » 19 Sep 2017, 18:05 wrote:3. permanent time difference after change in relative motion.
a) I've asked the question whether relativity recognizes that a full stop is not needed to establish a portion of permanent time difference but I never get an answer. Relativity is analog so any change in relative velocity will produce some permanent time difference, no digital full-stop is needed.

The trouble with such a question is that it hasn't got a simple answer. In cases where Alice does not stop, but just changes frame in a way that prevents her from passing Bob for the second time, you can only get an absolute answer after infinite time has elapsed - i.e. never. Then you are left with only a frame-dependent answer.

This does not mean one cannot stop the test and use relativity to calculate an answer from the perspective of any observer of your choice.
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Re: Relative velocity in S.R. for Dave

Postby phyti on October 16th, 2017, 1:56 pm 

ralfcis;
(from previous thread)
You make the problem unnecessarily complicated with additional clocks beyond the two required, and the mutual observations of A and B, which only provide clock rates and doppler effects. The issue is aging, i.e. accumulated time between separation and rejoining, which requires a clock comparison at each of those events.
No need of simultaneity and its associated 'time jumps'.
If A moves at .6c relative to B, 1/gamma=.8 and tA=.8tB.
For a closed course, the number of ticks is conserved,
If A receives 10 ticks from B, B receives 8 ticks from A.
This is the simplest case for two clocks moving along a closed course consisting of constant velocity segments. The difference in accumulated time depends on the speed profile for each segment. The obvious asymmetry of velocity change (which leads to the erroneous conclusion that acceleration is the cause) is only a feature of the setup and not a causal factor, since a velocity change could be applied to both clocks, and g is a function of v/c.
(Only half of the B signals are shown to avoid clutter.)
The time readings can be exchanged while passing at end points.
The 2 on the A path should be an 8!
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twin path aging.gif
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Re: Relative velocity in S.R. for Dave

Postby ralfcis on October 16th, 2017, 6:39 pm 

Thank you phyti for your post although it is in the wrong place as I'll be banned if I respond to it here. So you're saying it's certain that relativity uses 2 clocks and not 4 or 3 as is my latest determination. Hmm, Jorrie answered my repeated requests to the question of how many clocks relativity uses with as many as you like. Of course that's not an answer to the question, it's just an obstructionist tactic but you bringing it up here has made me decide to retire from having any further dialog with anyone on this forum. It's pointless and I'm too busy trudging my own way forward. I'll continue to write but ignore others posts. You should get your answers directly from Jorrie instead. Good luck with that.
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Re: Relative velocity in S.R. for Dave

Postby BurtJordaan on October 17th, 2017, 2:03 am 

phyti » 16 Oct 2017, 19:56 wrote:The issue is aging, i.e. accumulated time between separation and rejoining, which requires a clock comparison at each of those events.

I don't's think separation and rejoining is the issue that Ralf has - he struggles with the one-way scenario, where Alice has to 'stop' to be at rest in Bob's inertial frame again, before they can compare elapsed propertimes. Ralf thinks that you can just put a third clock, synchronized to Bob's at that point and without 'stopping', read off the instantaneous difference in aging between Alice and Bob on the fly. This is of course a coordinate dependent reading and has nothing to to with aging.

In order to observe absolute (propertime) differentials, one must of course bring Alice and Bob to rest in the same inertial frame, or they must fly past each other again. In both cases, they can do it with just their two clocks. The argument about the 4th clock came in when I tried to convince Ralf that what he does gives a relative, reciprocal aging measurement. One can put any number of sync'd clocks in each inertial frame, but without stopping or reversing for a second flyby, none will help him to observe a proper aging differential.
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Re: Relative velocity in S.R. for Dave

Postby BurtJordaan on October 17th, 2017, 3:25 am 

phyti » 16 Oct 2017, 19:56 wrote:The issue is aging, i.e. accumulated time between separation and rejoining, which requires a clock comparison at each of those events.

I don't think separation and rejoining is the issue that Ralf has - he struggles with the one-way scenario, where Alice has to 'stop' to be at rest in Bob's inertial frame again, before they can compare elapsed propertimes.[a] Ralf thinks that you can just put a third clock, synchronized to Bob's at that point and without 'stopping', she can read off the instantaneous difference in aging between Alice and Bob on the fly. This is of course a coordinate dependent reading that does not say anything about aging differential at that time.

In order to observe absolute (propertime) differentials, one must bring Alice and Bob to rest in the same inertial frame, or they must fly past each other again. In both cases, they can do it with just their own two clocks. The argument about the 4th clock came in when I tried to convince Ralf that what he does gives a relative, reciprocal aging measurement. One can put any number of sync'd clocks in each inertial frame, but without stopping or reversing for a second flyby, none will help him to observe a proper aging differential.

-=-

[a] Of course, Alice must stay "stopped" for long enough so that she and Bob can compare clocks by two-way light signals. This "stopped for long enough" also holds the key to aging differences - the spacetime paths of Alice and Bob was equivalent up to the "stop point", so no difference in aging happened. From that point onward, the difference in path lengths builds up to the constant value that is finally observed by the two-way signals as a proper time difference.
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Re: Relative velocity in S.R. for Dave

Postby ralfcis on October 17th, 2017, 6:35 am 

Ok I'll engage when I see something good and this is a clear explanation of our conflict.
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Re: Relative velocity in S.R. for Dave

Postby phyti on October 18th, 2017, 3:45 pm 

In the graphic previously posted, between the separation and rejoining, A and B agree the A clock ran slower based on signals received,8 to 10.The clocks do the accounting, no math required. The accumulated difference is established as they cross paths, and an exchange of info within a few seconds will not alter the results to any significant degree. If anyone objects to the instantaneous change for A, a 3rd anaut can complete the 2nd leg for A.
I've added a file that counters the acceleration argument.

.
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twin clocks3.pdf
(22.12 KiB) Downloaded 1 time
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Re: Relative velocity in S.R. for Dave

Postby BurtJordaan on October 18th, 2017, 4:40 pm 

OK, but as I said, the thread is about the one-way "paradox", not the standard "twin paradox" which you have described. There is no argument about the 'instant' acceleration that Ralf used, just that he has difficulty with how the "one-way" scenario is resolved.
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Re: Relative velocity in S.R. for Dave

Postby ralfcis on October 18th, 2017, 7:55 pm 

This thread is about helping Dave understand relative velocity and I will be continuing it in a few weeks.
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Re: Relative velocity in S.R. for Dave

Postby phyti on October 19th, 2017, 11:56 am 

Sorry for the interruption.
I wasn't aware of a 1-way paradox!
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Re: Relative velocity in S.R. for Dave

Postby BurtJordaan on October 20th, 2017, 2:37 am 

phyti » 19 Oct 2017, 17:56 wrote:Sorry for the interruption.
I wasn't aware of a 1-way paradox!

There isn't really one, just a name that I've given to Ralf's view that he expressed in the OP.

Ralf wrote:3. permanent time difference after change in relative motion.
a) I've asked the question whether relativity recognizes that a full stop is not needed to establish a portion of permanent time difference but I never get an answer. Relativity is analog so any change in relative velocity will produce some permanent time difference, no digital full-stop is needed.

The question is so open-ended, that it does not have one clear answer and it easily leads to erroneous, paradoxical conclusions. There are only two scenarios where a clear answer is possible (which have been discussed here and in many other threads), but there are a myriad of scenarios where a simple change in relative motion does not give a clear answer to the rhetorical question: "who has aged less?"

In the meantime, I think Dave_Oblad (for whom Ralf created this thread) is setting up home after a move and I don't see him around much. So you are welcome to help Ralf iron out in his thought processes, before Dave returns. ;)
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