## S.R. Defining Reciprocity

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### S.R. Defining Reciprocity

This is a continuation of my S.R. Defining the Present thread and my Relativity of Simultaneity thread which is currently locked in the Physics forum. For all the latest up to the minute news on the Theory of Relativity, stay tuned right here on the Personal Theories forum. But be warned, it's the wild west here and you need to be able to sift through the word salad to get to the truth. I'm just learning as I go along as well but I'm not very respectful of obstructive tactics.
ralfcis
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### Re: S.R. Defining Reciprocity

Too many lines are confusing on an STD so I will serialize the STD's. This one is a re-draw of the first STD depicting reciprocity in the Defining the Present thread:

This is both reciprocal perspectives of Alice and Bob at .6c
ralfcis
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### Re: S.R. Defining Reciprocity

Here is an equivalent STD with the reciprocity built right in without having to consider Alice or Bob as stationary. Earth is the stationary frame and their .33c relative velocity to earth adds up to .6c relative velocity to each other. Any conclusions drawn from this STD are valid for every other depiction of .6c between them. We'll break this down later.

ralfcis
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### Re: S.R. Defining Reciprocity

ralfcis » 24 Oct 2017, 16:29 wrote:Here is an equivalent STD with the reciprocity built right in without having to consider Alice or Bob as stationary.

Cool! This is a reincarnation of the Loedel spacetime diagram, which I have already referred you to before.

You could have saved yourself a lot of time by having checked it out at that time. ;)

BurtJordaan
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### Re: S.R. Defining Reciprocity

I didn't check it but I'm sure to take it where it's never been before.
ralfcis
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### Re: S.R. Defining Reciprocity

This is like chasing the elusive 'big foot'!
My intention is to ask you to reconsider the role of length contrction

A 1 unit rod passes a 1 unit rod at .6c, with no length contraction per your preference.
Measurement of a rod in any frame requires noting the location of the two ends simultaneously. When the far end of the A-rod crosses the B-rod, B measures the A-rod as 1.00/1.56 of the B-rod, which is a ratio of .64. Length contraction calculates (moving rod) r' = .8 r (static rod). Omitting lc for the B-rod, results in two orders of 1/gamma, i.e. too short!
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phyti
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### Re: S.R. Defining Reciprocity

This was already fully discussed on the RoS relativity of simultaneity thread oct 21 8:13am starting with this

x=x'/Y
t= Yt'
so c'=xY/(t/Y) = xY2/t
Y2= c2/(c2-v2)
Substituting v=c and we get c' does not equal c

I can only write stuff for you but I can't read it for you, you'll have to do that yourself.
ralfcis
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### Re: S.R. Defining Reciprocity

I am having so much trouble today with the conversion of M-std to E-std that I will just consider the simpler conversion from M-std to L-std before I tackle the other. (M is for Minkowski, E is for Epstein and L is for Loedel)

In this M-std I have added the Green hyperbolic line where t'=t=2 for any relative velocity, for every on-board clock. The times on on-board clocks can only be compared when the clocks are at 0 relative velocity and the reading has had time to propagate across their separation. If they are co-located both their relative velocity and separation are at an instantaneous zero even if they whiz past each other. The comparison between the two on-board clocks under these conditions is what relativity uses to establish permanent age difference between formerly moving clocks at a constant relative velocity. But wait, there's more.

I've added 2 blue lines to the M-std:

They represent Bob's line of present when he is considered stationary (flat) and when Alice considers him moving away from her (slanted). They consist of network clocks that are all sync'd to the same time. From both perspectives, when Alice's on-board clock is co-located with one of Bob's network clocks, those two clocks can be compared during a condition that is invalid for comparing the two on-board clocks which are neither co-located nor at rest.

Relativists have a problem with this because they consider the red lines (Alice's network clock) I'm adding as being a reciprocal condition to the blue lines thereby cancelling the validity of the blue network clock to Alice's on-board clock.

There are many problems with that argument:

1. Alice's network clock is not the same as Bob's so it can't invalidate Bob's reading. Nowhere does Bob's network clock share the same space and time as Alice's network clock.
2. When Bob's network clock is compared to Alice's on-board clock, it happens in a common present time. There is a delay between Alice's clock having the same reading as Bob's did so Alice's present can only be compared to a clock reading from Bob's past.
3. It's more practical to have a common clock network to many relatively moving frames than each moving frame having its own clock network.

Hence, why bother with a separate clock network for Alice. It in no way negates Bob's network clock reading of 2.5 for Alice's on-board clock reading of 2 by Alice having a network clock reading of 2.5 when Bob's on-board clock reading was 2. Different clocks at a different time and space are involved in the comparison.
ralfcis
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### Re: S.R. Defining Reciprocity

Here's how the Alice moving at .6c M-std slides over to form the Loedel std where Bob and Alice are both moving at .33c relative to earth.

The other half is where the Bob moving M-std slides over to form the same picture. The red line from Alice's network clock would have formed an X with the blue line but I do not feel it's important to include Alice's network clock as it somehow implies it negates the readings of Bob's network clock compared to Alice's on-board clock.

Similarly it should be easy to swap the t and t' axes to create an Epstein STD from a Minkowski but bad things are happening like the stationary frame's line of present is not horizontal and the moving frame's is. This then screws up the direction of time dilation where the stationary frame is dilating wrt the moving one.
ralfcis
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### Re: S.R. Defining Reciprocity

ralfcis » 26 Oct 2017, 17:14 wrote:The other half is where the Bob moving M-std slides over to form the same picture. The red line from Alice's network clock would have formed an X with the blue line but I do not feel it's important to include Alice's network clock as it somehow implies it negates the readings of Bob's network clock compared to Alice's on-board clock.

Yes, it does. The "somehow" is the mandatory reciprocity of values observed from the two frames, indicating that it is not aging that is observed, because each observes own propertime versus the others coordinate time.

Sweep them under the carpet and as you said later - "bad things happen". ;)

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### Re: S.R. Defining Reciprocity

Yes, it does. The "somehow" is the mandatory reciprocity of values observed from the two frames, indicating that it is not aging that is observed, because each observes own propertime versus the others coordinate time.

Ok I recognize this as a bonafide answer but unfortunately I don't know what it means. How can Akice's network clock be in the present with Bob's past on-board and present network clock? Although Alice's on-board clock and Bob's on-board clocks share the same time, they are separated so they don't really share the same present. Then to extrapolate that the two network clocks are therefore related to each other because they're related to 2 unrelated on-board clocks (who happen to share the same time reading) doesn't make sense to me.

because each observes own propertime versus the others coordinate time.

So the wording here is how relativity defines reciprocity whereas I defined it as getting the same network and on-board clock time dilations from either perspecive of a single participant. You're saying I must include the 2nd participant's perspectives to fully define reciprocity. But the 2nd participant's perspectives are not simultaneous with the first's so how can they be included in reciprocity?

Sweep them under the carpet and as you said later - "bad things happen". ;)

Are you saying the problems I'm finding with Epstein are unresolvable?
ralfcis
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### Re: S.R. Defining Reciprocity

ralfcis » 29 Oct 2017, 13:47 wrote:How can Akice's network clock be in the present with Bob's past on-board and present network clock? Although Alice's on-board clock and Bob's on-board clocks share the same time, they are separated so they don't really share the same present.

"The present" (as you use it) is a semantic term which has nothing to do with clocks, except in a very approximate way. Relativity uses the term 'simultaneity of events', with a very precise definition, which is also not dependent on clocks. It simply means that if events are observed as simultaneously, using the isotropy of the propagation of light (e.m. waves) in free space, by two or more observers that are stationary in the same inertial frame, then they are defined to be simultaneous for that inertial frame. Every different inertial frame has its own precise definition.

This principle can be employed to set clocks and determine distances and to make sense of observations. The imprecision of languages is the driving force behind most confusions and endless debates on forums. If you use your own definition, then we are not talking relativity and this discussion is futile.

So the wording here is how relativity defines reciprocity whereas I defined it as getting the same network and on-board clock time dilations from either perspecive of a single participant. You're saying I must include the 2nd participant's perspectives to fully define reciprocity. But the 2nd participant's perspectives are not simultaneous with the first's so how can they be included in reciprocity?

Likewise, "reciprocity" is also a loose semantic term with a somewhat different meaning in conversational language than in the precisely defined "reciprocal observations" of time dilation and Lorentz contraction between inertial reference frames (as embodied in the Lorentz transformations). I think you are using it in the loose sense. Please rethink you comment.

Are you saying the problems I'm finding with Epstein are unresolvable?

No, I'm not aware of problems with Epstein diagrams per se, just with your interpretations of them. Whatever diagram you use, nothing changes the underlying physics, which is precisely defined. They are just different 'crutches' to aid understanding. You tend to jump between them and sometimes loses the reader (and quite likely yourself). It is very tedious to work through your posts and point every error and/or misinterpretation.

BurtJordaan
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### Re: S.R. Defining Reciprocity

I cannot understand the definitions of your terms so I can't translate them into my terms which are the vernacular. Relativity hijacks English words, redefines them, then wonders why so few people understand relativity. For example "mass" means the opposite of what the english word means and contradicts itself in relativity by saying mass is both matter and energy (made up of massless particles). They can't even be bothered to use the correct term rest-massless. It's fine for relativists to speak their own language both in mathativity and Relenglish, but they should also be able to include the rest of us in an English conversation. Isn't that the real purpose of this forum or is it only for relativists to talk to each other. Maybe you could translate my terms into your language so I'd know what your terms mean. If not, I'll just continue in English and we'll have to go our separate ways.

English is flawed, that's why I use STD's which should be a common language to both of us but it isn't. It should even be a common language to anyone reading these posts if they went to high school but I really doubt anyone is even looking at the STD's. In my next post I'll go into some really painful detail of the math void between us in the STD's.

However, if you can't agree that a line of present is a straight line through space where all space points on that line have a common time, then we can't even have a math discussion. You're focusing on the hyperbolic line where the points share a common time but have different space values. You're defining that as some sort of simultaneity term because they all have the same age? So simultaneity also means something completely different than it does in English?
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### Re: S.R. Defining Reciprocity

Ralf, it seems to me that we continuously fail to communicate, so I'll rather not distract your efforts further. It also seems that you resolutely want to discover the essence of SR in your own way. Maybe that is the best for anyone, but it usually takes a long time, as you may have already discovered...

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### Re: S.R. Defining Reciprocity

I think I see the point where my understanding has diverged from relativity. I won't know for sure until I complete the STD analysis. Until then I'll use words to try to explain where the problem is. It's a very subtle difference in meaning and I know Jorrie isn't big on subtle; it's either relativity or it isn't and it would take too much trouble to rescue every misinterpretation of relativity. I'm sure just me stating that I misunderstood relativity is enough and he probably won't delve into the explanation of why. Even if he does, he'll probably say the explanation is still wrong. But I'm going to write it out anyway to maybe clear up any similar confusion that others may be experiencing.

P.S. Of course I'm going to blame relativity for creating the confusion, which is true but Jorrie won't like that perspective one bit.
ralfcis
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### Re: S.R. Defining Reciprocity

Here's where the problem begins:

I've shown this before, the graphical and mathematical difference between time dilation and length contraction.

Time dilation is the moving on-board clock slowing relative to the stationary network clock located at a distance from the stationary frame's on-board clock. All 3 clocks are in the same present moment even though the stationary on-board clock is separated from the stationary network clock and moving on-board clock. The stationary network clock and moving on-board clock are co-located so they automatically share the same present. The stationary clocks are sync'd and share the same present by virtue of the fact they're on the same line of present where all points through stationary space share the same time on that line. So by the transitive property, the moving on-board clock also shares the same present time as it's co-located stationary network clock. Relativity uses the term simultaneity but I don't know how that term translates into all 3 clocks sharing the same present time. I would assume all share the same clock time simultaneously once you compensate for the light delay between the stationary on-board clock and the other two.

The term "dilation" refers to the stationary perspective being able to "see" the moving on-board clock rate slowed relative to the stationary on-board clock even though both clocks tick at the same proper rate relative to their own frames. I don't know how relativity defines "see" but I assume it means when either the moving on-board clock is co-located with the stationary on-board clock or is co-located with the stationary network clock and the light delay back to the stationary on-board clock is compensated for.

Dilation allows a certain proper distance to be covered in less total moving on-board time (when compared to the total stationary time) while being balanced by length contraction to maintain the same relative velocity and speed of light from both perspectives. Since v=x/t, as t dilates from the stationary clocks' perspective of the moving on-board clock, x contracts from the moving frame's perspective of the stationary frame's distance to maintain the same ratio of v from both perspectives of each other.

Notice from the STD that length contraction is not the stationary perspective being able to "see" the moving frame's length pythagorically dilate relative to the stationary frame's length. But rather it's the stationary frame's ability to see its own length contract through the eyes of the moving frame looking at the stationary frame's length shrink with respect to the moving frame's length. See it's not like time dilation at all. It's more like double dilation which results in shrinkage.

Extrapolating on the same nomenclature for dilation and contraction, I have introduced 2 new terms: time contraction and length dilation. These are not in relativity but I will argue why they should be in order to clear up confusion.

Here's where the mistake makes its entrance. "Time contraction" which is Bob's stationary clock looking through the eyes of Alice's on-board clock looking back at Bob's on-board clock dilation wrt Alice's on-board clock, is not the same thing as the perspective from Alice being stationary and Bob moving. I know this is painfully confusing but maybe an analogy will help.

Alice is moving in a car past Bob who is parked. In her rear view mirror, it looks like Bob is moving away from her. It's as if Alice was stationary and Bob is moving but it's not like that at all because Alice is considered to be moving. If she stopped the car and Bob started moving, it would be something completely different than Alice moving and imagining Bob is receding from her.

"Time contraction" is Alice moving while seeing Bob is receding from her. Reciprocal time dilation is two separate perspectives. Alice moving and then Bob moving, each having their own separate time contraction of each other where, while moving they see the other recede from them. Reciprocity is not between time dilation and time contraction within 1 perspective but is the reciprocity of both time dilations and both time contractions from both perspectives.

I hope that cleared things up.
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### Re: S.R. Defining Reciprocity

Ok so here's where I think I stand so far:

What I thought was reciprocity, where Alice is moving and Bob sees her clock as dilating and she looks back at Bob and sees his clock dilating was actually relativity of simultaneity, the difference between Bob's on-board clock and Bob's time contracted clock (what Bob sees through the eyes of Alice's time dilated clock, dilated again).

What's different here is that only the stationary perspective has a network clock. When Alice is moving she is not dragging around her network clock to intersect with Bob's on-board clock from the past. She has no line of present when her perspective is the moving one. She does not see Bob's time dilated, Bob is the one who sees his own time contracted through Alice's dilated clock (which can also be thought of as a double dilation of his own on-board clock).

Of course, without confirmation from Jorrie that this is the correct interpretation, this could be one of many interpretations of the STD. But let's continue anyway.

Jorrie kept harping that unless Alice witnesses that Bob's network clock has been synchronized to his on-board clock, there is no way for Alice to trust his network clock reading when she intersects it at t'=2, t=2.5. I still disagree with that viewpoint and here's why:

Bob's network clock doesn't need to be sync'd in front of Alice because atomic clocks are universally accurate. When Bob establishes his network clock at 1.5 ly, he can remotely set that clock to his on-board clock via light signal taking into account the signal delay. He can make the remote clock send out a "certified sync'd" signal to all passing ships. When Alice starts her journey, she syncs her on-board clock to Bob's on-board clock because they are co-located at the start. When she intersects (co-locates with) Bob's network clock she sends a signal back to Bob with her time and the time she read off of Bob's network clock. There is no question that both are aware of the correct times but what happens in the reverse analysis when Bob is deemed to be moving?

The network clock switches over from Bob's to Alice's. It's a different clock comparison to a different clock and those times show Bob's on-board clock is dilating with respect to Alice's network clock. The way to resolve this reciprocity is to put both network clocks together on the same STD and prove the reciprocity is not simultaneous, that the two network clocks show reciprocity at different times. Hence one can always choose Bob's network clock and not be worried that reciprocity will invalidate time measurements made wrt to his network clock.
ralfcis
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### Re: S.R. Defining Reciprocity

Why not use one clock for each observer and simplify your explanation?

I know this is painfully confusing

I agree!
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### Re: S.R. Defining Reciprocity

ralfcis
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### Re: S.R. Defining Reciprocity

Why not use one clock for each observer and simplify your explanation?

I can see you don't accept the fact that two participants who started out together can relatively stop light years apart and relativity can still determine their permanent age difference without then reuniting as they do in the classic twin paradox. That's why you need the two on-board clocks plus a sync'd network clock. Show me how you would solve the above scenario with only the 2 on-board clocks.
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### Re: S.R. Defining Reciprocity

I'm not allowed to work on physics on the weekends but I have to write a quick note to myself on what's next:

I will draw an M-STD of reciprocity at .6c and then show observers at below .33c will see a different order of events than those above .33c but those at .33c will see Bob and Alice's on-board clocks simultaneously hit t=t'=2 and t=t'=2.75. This result proves from an outside observer's perspective, there's no way to establish who is aging potentially slower than the other. I need to explore whether using light signals between the two from each of their perspectives can establish an order of events between them. Relativity dictates I am doomed to fail because establishing a preferred frame contradicts the basic tenet that those engaged in constant motion cannot tell whether they are moving or stationary.
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### Re: S.R. Defining Reciprocity

ralfcis » November 3rd, 2017, 11:35 am wrote: Bob's network clock doesn't need to be sync'd in front of Alice because atomic clocks are universally accurate. When Bob establishes his network clock at 1.5 ly, he can remotely set that clock to his on-board clock via light signal taking into account the signal delay. He can make the remote clock send out a "certified sync'd" signal to all passing ships.

But surely Alice, after observing Bob's network and on-board clocks and allowing for the signal delay, will disagree that those two clocks are sync'd. However much Bob certifies that they are sync'd, they will not seem so to Alice, since she is in a different inertial frame.
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### Re: S.R. Defining Reciprocity

Alice has no direct observation of Bob;s om-board clock, only his network clock. Clocks can only be compared when co-located or separated and relatively stopped once the signal delay between them passes. Her on-board clock will differ from Bob's network clock but Bob's network clock will remain sync'd to Bob's on-board clock. Her on-board and bob's network clock difference has nothing to do with Bob's clocks unsyncing from each other.

If Bob had sent a signal to Alice from his on-board clock. Alice would eventualy be able to determine that at the point in question, when she intersected Bob's network clock, she will see his on-board clock was indeed sync'd to his network clock. If you want an STD to prove this I will provide one next week.
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### Re: S.R. Defining Reciprocity

I'm afraid I have to give up on understanding relativity. I've tried every mental gymnastic and complex explanation with wildly re-defined terms and it always falls apart. So I'm going to abandon all relativistic concepts.

1. There are only clocks and light signals. There are no lines of present, sync'd clocks, relativity of simultaneity or reciprocity.
2. There is a preferred frame and it's arbitrarily chosen as the one that has the network clock. As soon as you introduce a 2nd network clock then these parasitic concepts of reciprocity and simultaneity come into being.

Sorry if you felt I was getting somewhere, I got nowhere.
ralfcis
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### Re: S.R. Defining Reciprocity

ralfcis » Sat Nov 04, 2017 7:44 am wrote:Because you ask this question:

Why not use one clock for each observer and simplify your explanation?

I can see you don't accept the fact that two participants who started out together can relatively stop light years apart and relativity can still determine their permanent age difference without then reuniting as they do in the classic twin paradox. That's why you need the two on-board clocks plus a sync'd network clock. Show me how you would solve the above scenario with only the 2 on-board clocks.

Here's the synched signals with a slight refinement.
A and B are both moving relative to U at .3 and .6.
They send signals at the same local time .68, get a clock reading of 1.00, which returns at 1.47 local time. Each assigns the reading from the other at 1/2 round trip time (red), 1.08, per the SR convention. Each concludes the other clock is running slower. If we interchange A and B, the results are the same, since SR states the results depend on the difference in speed.
Notice the mathematical axis of simultaneity (red) is established using the same method as polling for a distant clock reading. The answer would be the same if A had a string of synched clocks along the x axis.
If A or B or both, changed velocity at the same local time, instantaneously, so each had the same velocity, they would be the same age, with equal clock rates.
While in relative motion, they each observe doppler effects, which do not determine aging.
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### Re: S.R. Defining Reciprocity

Hi phyti.
phyti » 06 Nov 2017, 18:12 wrote:They send signals at the same local time .68, get a clock reading of 1.00, which returns at 1.47 local time.

Good diagram, but it is slightly unclear what you mean by "local time". It is normally used for what you read on the face of a carried clock - and we specify which carrier. As you wrote it, it has nuances of a "universal time".

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### Re: S.R. Defining Reciprocity

BurtJordaan » Tue Nov 07, 2017 1:10 am wrote:Hi phyti.
phyti » 06 Nov 2017, 18:12 wrote:They send signals at the same local time .68, get a clock reading of 1.00, which returns at 1.47 local time.

Good diagram, but it is slightly unclear what you mean by "local time". It is normally used for what you read on the face of a carried clock - and we specify which carrier. As you wrote it, it has nuances of a "universal time".

There are a few terms I refuse to use, especially those considered politically correct. Proper time is high on my list, since it suggests impropriety, which has nothing to do with the subject. Einstein stated it simply as the time on the clock located near the observer, as opposed to a distant/remote clock.This carries the connotation of location.
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### Re: S.R. Defining Reciprocity

phyti » 07 Nov 2017, 19:01 wrote:There are a few terms I refuse to use, especially those considered politically correct. Proper time is high on my list, since it suggests impropriety, which has nothing to do with the subject. Einstein stated it simply as the time on the clock located near the observer, as opposed to a distant/remote clock. This carries the connotation of location.

Proper time is also not the subject and "political correctness" is not science.

That said, it seems that we have the same definition for "local time" just expressed in different words, provided that you mean "the clock [permanently] located near the observer", which is the same as "a carried clock".

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