# Relativity and simple algebra II

I'm still not certain what your "Doppler Shift ratio" is. You most often seem to write it like this:
DSRv=Yu/YwDSRv=Yu/YwDSR_v = Y_u/Y_w

but I don't know what the subscripts v, u and w refer to. It seems like there are three reference frames involved in that equation. Is that correct? If so, why do we need three frames to calculate a Doppler shift? Can't we just use the source and observer frames, if we want to do that?
w=v(+)u relativistic velocity combo equation

As u approaches c, w also approaches c. Y_u approaches infinity and so does Y_w but the ratios of these two infinities approaches DSR_v. I can provide the derivation of this equation but no one will read it or understand how it's possible. It's proof there are no infinities in physics that do not approach a finite value. This concept is very important but never used in SR which comes up with ridiculous theories that photons cross the universe in no time from their perspective while the math shows that's just not true. I have other equations for DSR which appears as a factor for many relativistic phenomena but is relatively unimportant in SR. I have not yet figured out the physical significance of its recurrence in so many unexpected places. More on this later.

Great once again you have proof of this phantom concept right? I mean you keep bringing it up over and over. When do you reveal your proof? Oh wait, I forgot, we agreed that SR can't work without length contraction. So when a theory is not borne out by experimental results, what happens to that theory?
If the theory is not borne out by experimental results, then we need to either modify it or throw it away and get a better theory.

Fortunately, all experimental results tend to confirm SR, so far.

James R said:
Epstein's axes are entirely different from a Minkowski diagram.
No they are exactly the same. They have the same labels. They describe identical equations. The axes are just swapped or in SR's case, the frame rotation is swapped.
That only shows me that you don't understand Epstein diagrams.

The radial rays on an Epstein diagram represent, essentially, the proper time axes of the objects involved. Relative speeds are represented by the angles between the rays. Where rays meet, the clocks in the different frames are mutually set to zero. Concentric circles on the diagrams represent circles of "equal proper time".

Behind the whole arrangement is what Epstein calls his central "myth" - that objects "travel through time" at a particular rate. The myth is convenient for certain calculations, but Epstein admits that it is a calculational device, rather than anything real.

On a Minkowski diagram, for instance, with axes x and ct (or x' and ct' or whatever), all light rays make an angle of 45 degrees to the x and t axes. That is not true in an Epstein diagram. Light rays emitted by a particular observer in an Epstein diagram travel at 90 degrees to the "ray" that represents that observer, because the 90 degree angle corresponds to the light moving at a relative velocity of c with respect to that observer.

As I previously advised, you probably should forget about Epstein diagrams, for now. They are not necessary, and they are obviously causing you some confusion.

Fortunately, all experimental results tend to confirm SR, so far.
There is no experimental result that proves length contraction as a physical phenomenon of space shrinking. Just rebut #172.

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in order for SR's explanation to be correct. This is a purely circular argument. The results bear out the hypothesis, therefore the hypothesis must have been correct all along and let's make sure of that by using the hypothesis for 116 years as if it's a genuine conclusion that now becomes fact.
Now you're sounding like you don't understand the scientific method.

We want to explain set of facts (or observations) F. So, we propose hypothesis H, which we think can account for facts F, and more besides. To test hypothesis H, we propose new experiments E, whose results are not known in advance. We use hypothesis H to make predictions P about what the results of E will be, if H is correct. We then conduct experiments E and compare the results R to the predictions P. If R and P all match, then we take that as evidence in support of the truth of H.

Over time, after lots of different Es have been done, hypothesis H may gain the status of a well-confirmed scientific theory T.

Nothing in this process is circular. We don't know in advance if R will match P, or not. If the results don't match the predictions of the hypothesis, then we need to modify the hypothesis and try again with new experiments, or else toss it out and go back to the drawing board to find a new hypothesis.

You should note, however, that even the most confirmed scientific theories (special relativity would certainly qualify as one of those) are never confirmed beyond all doubt. There is always the chance that some new experimental results will come to light that do not match the predictions of the theory. In that case, as scientists, we do what we do every time results don't confirm a hypothesis.

There complications, of course. Experiments inherently have sources of error in them - random and/or systematic. Most experiments do not provide us with absolute information, but information that comes with a quantified level of uncertainty. When results do not match a prediction (within the calculated limits of random experimental error), it is not necessarily the case that the hypothesis is wrong. Maybe something is wrong with the experiment, instead. This is why we usually do lots of experiments, rather than just one. In the case of SR, literally thousands of different experiments (maybe millions, depending on how you count them) have matched the predictions of SR. That's why we have high confidence that it is correct.

I can solve every example of relativity without once invoking length contraction.
No you can't.

There is no physical experiment that has been performed to verify its existence.
You may be correct when it comes to direct evidence for its existence. But when it comes to indirect evidence, there's a heap of it.

In terms of the formal theory itself, length contraction is a derived consequence of the postulates, as is the rest of the theory. You can't remove it from the theory while leaving the rest intact. If length contraction doesn't occur, then one or both of the postulates of special relativity must be false. So, which one is false? Or are both of them wrong? You tell me. You also need to then explain why all the experiments that have been done verify the theory, and have done so for 116 years now.

It even vanishes like a phantom effect once the velocity that creates it disappears.
It's like your man-at-a-distance example. Once he comes close, his thumbnail size disappears, like a "phantom effect". In both cases, this is because the effects being discussed have something to do with the observer, rather than the thing being observed.

Yet age difference from the twin paradox persists as a measurable result even after the velocity is gone.
There are many different ways to explain why that happens. It boils down to the effects of acceleration, which mean that one of the two clocks in the twin paradox spends part of its time in a non-inertial frame of reference.

Length contraction is the result of conflicting perspectives of simultaneity.
Yes.

Perspectives are illusions...
No. As you sit there in your chair reading this, your perspective is as real as mine.

No point in answering anything but #172. Where's your rebuttal? I'll continue with your backlog of questions in the meantime. Do you have any objections to my Md's and explanations on the train in the station example?

In fact, look up Raskar trillion fps photography that can photograph light in slow motion. Relativists say a photon crosses the length contracted universe in 0 time from its perspective (due to faulty math). So the shutter that sets the pulse width of the light being photographed should never open from the light's perspective and from our perspective, the light pulse should always be 0 wide. Yet when we open it for 1ms our time, the pulse is 1 ms wide even though it is travelling at c from our perspective so its pulse width should be zero from ours. We also see its velocity through space at c so its velocity through time should be zero yet we can see its frequency which is how fast its clock is moving.
You're introducing yet another new topic into this discussion. It would be easier if we could sort out one problem at a time, instead of trying to sort many things at once.

The main thing to say about your example here is that you're trying to appeal to how things might look from the "reference frame of a photon" or "the reference frame of a light beam". In fact, one of the motivating thoughts Einstein had, which led to his formulation of SR in the first place, is the thought that you can't ride along on a light beam. That is, a light beam has no "rest frame". Or, to put it in more stark terms, it is meaningless to talk about "the reference frame of the light".

What we can do is to consider how the world would look if we could travel very close to the speed of light. As $v\rightarrow c$, we find that $\gamma \rightarrow \infty$. In the rest frame of an observer travelling in the spaceship that is moving very close to the speed of light, "outside" distances in the direction of motion would approach zero, and "outside" clocks would appear to tick very very slowly compared to the spaceship clocks. That would mean that, from the point of view of an observer in the spaceship, the spaceship could cross any distance in a negligibly small amount of time, as measured by the spaceship clocks, as long as the spaceship was moving close enough to the speed of light.

A "pulse of light" probably consists of billions upon billions of individual photons. A pulse that is allowed through an aperture for 1 ms would have a length of 300 km from one end to the other in the "lab frame". It isn't really meaningful to ask a question like "From the point of view of a photon at the rear end of the pulse, how far away is a photon at the front end of the pulse", because that's assumes that we can ride along in the frame of a photon, which we can't. If the pulse was made up of tiny billiard balls travelling very close to, but not quite at, the speed of light, then we could ask that question. The answer would be that the distance in the "rear ball" frame could be very short, in that frame, and in the limit as $v\rightarrow c$, it would go to zero.

From a wave perspective, by the way, the frequency of a light wave is related to its speed and its wavelength by $f=c/\lambda$. We know how the frequency transforms for observers in different frames - just use the relativistic Doppler shift formula, with which you are familiar. But remember that the "frame of the light wave" is not a valid frame. You can't ride along on a light wave.

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Why would I care? Lorentz transforms only apply to the philosophy of SR.
As I said, if you want to toss out the Lorentz transformations, that's fine. But if you still want to do relativity - i.e. look at what observers in different states of motion measure - then you still need some transformation formulas, to allow us to predict measurements in a different frame when we already know then in one frame. The most basic transformations involve the transformation of the space and time coordinates between the two frames. I've already shown you Galileo's ones, and Einstein's. Are you saying you don't know what they are for your theory?

There is no x' in my math.
Then you're saying there's no way, in your theory, to compare the lengths of objects in different frames of reference.

Why do you then claim that length contraction doesn't exist in your theory?

If you can't compare lengths, how do you know there is no length contraction?

Show me one physical experimental result where I would need x' in order to arrive at the correct result.
Explain to me how muons can reach the ground before decaying, as in the muon experiment. Please do that (a) from the perspective (frame) of somebody standing on the ground, and (b) from somebody riding along beside one of the muons.

#172

This is a response to post #194:

I'm sure all of science would just love to get a hold of this magic thought experiment ruler you possess that spews out real experimental results.
All rulers spew out real experimental results.

Suppose I have a 30 cm (12 inch) ruler. I can sit here at my desk and measure the length of a book, say, using that ruler. Then, I can take that ruler, jump in my car and go for a ride at 100 km/hr along the freeway. While I do that, I can take the ruler and measure the length of the book again. It doesn't matter whether I sit at my desk or in my car: the ruler still works to measure lengths.

Now, I can also measure moving lengths with my ruler, in principle. For example, I can sit my laptop in my window and take a photo of a bird as it flies past. Then, I can pull out my trusty 12 inch ruler and measure the length of the bird on the photograph. If I'm really quick, I don't even need the photo. I can just mark off the two ends of the bird on my ruler at some instant as it is flying past the window.

I can do the same thing in my moving car. I can sit the laptop in front of the car window and photograph two trees beside the road, say. Then I can take my trusty ruler and measure the distance between the trees on the photograph. Or, if I'm really quick, I can just mark off where the trees are on my ruler as they go past the window, provided I mark them both at the same time.

I am mystified as to why you think any of these examples would be magical.

You can get hold of one of these magical ruler devices yourself, if you want one. They are available in lots of different stores. You can even order them online.

real clocks are those beside you or are light signals that contain clock messages or are calculated from a DSR which is delayed light signal info so they're not really real in your present time. I use proper time and don't need a perspective on Bob's clock to tell Alice what time it really is in her frame.
We agree that Bob and Alice can use clocks beside them to measure time in their respective frames. That is not in dispute.

You still refuse to read about the clock handoff scenario ...
Now you want to introduce yet another scenario. We can discuss your "clock handoff scenario" if you like. Please post the details and we can discuss it. It will make the discussion longer, of course, because we still haven't resolved a lot of issues from earlier scenarios. Up to you.

...and you don't understand that Alice and Bob can fly past or Alice can stop where Bob is and the determination of age difference is the same.
No. It won't be the same. If Alice stops, she must accelerate to slow down from speed v to speed zero in Bob's frame. That acceleration will affect the "age difference" - it will be different to the age difference if Alice just keeps flying past Bob's position at constant speed.

Alice coming to a stop where Bob is does not cause any age difference but a stop or a clock handoff at a distance would. It's because age difference results from an imbalance in relative velocity when a frame jump occurs at separation. This isn't an opinion, do the math or you can wait until I show you the math.
I'll wait until you show me the math.

The clocks must be co-located for all to agree on the permanent age diff. This is what the prophet decreed but my math completely shows it's false, light signals are enough to establish permanent age difference.
You'll have to provide a specific example that shows what you mean, I'm afraid.

permanent age difference has one definition in SR, not two. I'm not even sure what SR calls permanent age difference but when I ask this question on real physics forums, they are only familiar with the term "age difference" and have no term for the results in age difference when the two participants co-locate at the end of the twin paradox.
Human beings have a biological age. At any given time, a given human being has only one biological age. An "age difference" would be the difference in biological ages between two human beings, compared in some reference frame at a particular time.

I don't mind if you don't like the word "permanent" in "permanent age difference". The word "permanent" would only mean, presumably, that the age difference stays the same, in some frame, after some specified event.

No term at all because SR only sees proper time at co-location and does not recognize a permanent scar on proper time outside of co-location.
Proper time is always specific to a particular reference frame. There is no universal proper time, and therefore no scars on universal proper time.

But you'd need to consult with an expert to find this out for yourself.
You're advising me to talk to somebody else about your claims, your theory? Aren't you an expert on your own theory?

I get around this problem by using the Loedel perspective for a peek at proper time which is a universal god's-eye instantaneous present that SR doesn't recognize at the decree of the prophet.
You're mistaken if you believe that proper time is universal. It isn't. Proper time is just the time in some frame that is measured by a stationary clock in that frame. Different frames all have their own proper times.

All the disagreement stems from which subject are we going to discuss. You want to discuss SR and I want to discuss the topic of this thread which is relativity and algebra. You seem to treat them as the same topic and they are quite different.
I'm trying to help you to see where you're going wrong. To do that, I need to compare your erroneous results to the correct ones from SR.

Where your results agree with SR, there is no problem, other than possibly in matters of your incorrect interpretation about what the results are telling you.

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Looks like I've already answered page 4 so I'll move on to page 3.
It would be more useful to concentrate on moving forwards in the thread, rather than backwards. We've sorted out a lot of the issues of definitions etc. that came up early in the thread. Your choice, of course. But you'll probably end up just writing "AA" for a lot of things. There are better ways you could spend your time.

Time dilation does not cause permanent age difference in the twin paradox.
Then why does Alice end up with a biological age 2 years younger than Bob, with Alice's elapsed time being 8 years and Bob's elapsed time being 10 years? How is that not an age difference?

This is your, and most other people's, wrong assumption because it looks like the numbers are the same therefore they must be related. When Alice continues without velocity change, the numbers at Bob=10 and Alice=8 in time dilation match the same numbers as when Alice returns to Bob which are permanent age difference numbers. They are not related at all and this can't be accepted by close minded people who only see the same numbers.
Alice doesn't continue without velocity change in the twin paradox. She accelerates three times and ends up reuniting with Bob, so they can compare ages at the end of her trip.

I explain velocity change at a distance is the cause of permanent age difference and go through the math of how that works.
"Velocity change" is acceleration, by definition. We agree that accelerations are associated with time differences.

Until a velocity change or a frame jump happens, there is only the paradox or perspective illusion of reciprocal time dilation that is not due to time itself slowing but due to the relativity of simultaneity of when events are timed by the participants.
If you say so. Calling it a "perspective illusion" doesn't change anything that we can measure, so it's not very important.

Most people have been fed comic book pop sci versions of relativity which are dead wrong.
Luckily, you're not talking to those people here.

I've been fortunate to run into 3 truly and certifiably knowledgeable people on relativity in 10 yrs on forums which is why my views differ so wildly from those of pop sci and wikipedia.
Who were they?

When they spoke, I listened because they made sense not BS. Unfortunately people who actually know something have a rule of not engaging with questions that look outside of relativity.
It seems to me like you're looking for excuses to ignore the comments of anybody who is willing to examine your ideas. The argument would presumably go like this: you're willing to look at my "alternative" theory of relativity; therefore it follows you do not "actually know something", because if you did you wouldn't be interested; therefore I can write off anything you have to say about my ideas because you don't "actually know something".

Do you know how many nuts gravitate to physics forums and how difficult it is to separate the nuts from people who actually know math to back up their arguments?
Yes. For instance, I've been on this forum for 20 years now. How many nuts do you think I've seen who believe they have found a fatal flaw in the theory of relativity, or who believe they have a revolutionary new alternative that works better? The answer is: lots of nuts. The usual pattern is that these people get upset at the first hint of criticism of their new and revolutionary physics. Sooner or later, the discussion devolves into name calling and claims that nobody is qualified to examine the new revolutionary theory except for its promoter.

I just explained time dilation is not due to time slowing and then I explain time dilation is due to time not being counted from the observer's perspective due to relativity of simultaneity.
No. Time dilation is a separate effect to the relativity of simultaneity. The Lorentz factor $\gamma$ in the transformation equations ought to tell you that something more is going on with the time coordinates than a mere rotation. The coordinates are not just skewed, but also re-scaled between frames.

A clock handoff does not involve acceleration.
Okay, but so far you have not presented any clock handoff scenarios - just the twin paradox, which involves acceleration.

An instantaneous acceleration at the start or end causes no age difference at all. Maybe if you'd read you could understand why (hint, there's no distance separation involved).
That's fine for the twin paradox scenario.

Yes in the twin paradox PROPER time does slow during the period of relative velocity imbalance.
That's a meaningless statement. No observer's proper time ever slows. All observers always see their own clocks (which measure their respective proper times) as ticking the usual rate. It is only ever time in "other frames" which is observed to slow.

You won't see that explanation in any SR book...
Probably because it's meaningless.

...but if you're lucky you'll find out SR explains this using the Rindler metric which no one on a forum has ever heard of.
If you're talking about metrics, you're essentially talking about GR, not SR, although obviously there are a number of different metrics which are "flat".

If you think the Rindler metric is important enough to discuss, you ought to discuss it, rather than making wild guesses about who may or may not have heard of it.

In SR, time dilation is due to PERSPECTIVE time slowing which is not the same as PROPER time slowing.
That's a very muddled sort of statement. I can only repeat: all observers always see their own clocks (which measure their respective proper times) as ticking the usual rate. It is only ever time in "other frames" which is observed to slow.

You and I sort of agree on this, only you use bizarre "alternative" terminology to describe it. If you were more precise with your language, we wouldn't need to keep clarifying your meanings.

For example, what is "perspective time", exactly? Can you give a concise definition of the term "perspective time"? If all it means is "the time in some frame other than the 'rest' frame of the observer", then we're in agreement that "perspective time" slows. Of course, what is "proper time" in one frame will be "perspective time" in a different frame, and vice versa. It only confuses matters to speak as if there is a universal "proper time" common to all frames. That simply isn't true, which is why you won't find it in any reputable book on relativity.

However, SR is wrong, reciprocal time dilation is not time slowing at all as I've said over and over.
You can say it until your face turns red, but nothing in any of your calculations supports your claim that SR is wrong. On the contrary, you rely on the maths of SR every time you calculate a "proper time" or a "perspective time".

The answer is obtuse to you because you have never got enough information to form a correct opinion and you will never be given that information by the high priests of this religion.
You're losing credibility here, ralfcis.

SR is a scientific theory, not a religion. There is no "dogma" involved. The scientific method applies.

If you think SR is wrong, it is up to you to come up with some experiment or example where SR gets the "wrong" answer. Alternatively, you could try to attack it to show that the theory itself makes inconsistent predictions, or something - i.e. that it is logically or mathematically flawed in some way.

Good luck with both of those projects, because expert scientists have been trying to find flaws in relativity for 116 years now, and nobody has yet succeeded in demolishing or replacing the theory with something else.*

---
* Obviously, there are ongoing efforts to develop a quantum theory of gravity, but any such theory would incorporate GR is some kind of appropriate "classical limit".

There is no experimental result that proves length contraction as a physical phenomenon of space shrinking. Just rebut #172.
No point in answering anything but #172. Where's your rebuttal? I'll continue with your backlog of questions in the meantime. Do you have any objections to my Md's and explanations on the train in the station example?
I responded to post #172 in post #189.

Did you miss it?

Do you have any objections to my Md's and explanations on the train in the station example?
Yes.

I don't know why you couldn't respond to the scenario I put to you, and why you couldn't answer my questions about that scenario.

You tried instead to replace my scenario with a different one of your own making, and then you waved your hands and pretended that my questions were answered by your alternative scenario.

I'll probably get back to the train example later on.

That, by the way, would be a sort of "clock handoff" scenario, would it not?

I responded to post #172 in post #189.

Did you miss it?
Yes I did miss it and after reading it I'm just going to go ahead and continue answering your questions but since you're only interested in your own answers there's little point in going past that. Everyone is very comfortable in their "knowledge" so who am I to upset that. My quest is futile, always has been, always will be. I can only provide the information but it's up to others to take it or not.

#55

Are you saying that people in different frames of reference do not always agree on the value of the "DSR"? You seem to be saying that Alice can change the DSR, while it doesn't change for Bob, or something like that.
Yes during the relative velocity imbalance period Alice's change in velocity is delayed to Bob by c.
but I feel like I'm missing why it is useful.
Explains how Alice ages less than Bob after she changes her relative velocity and Bob is delayed in finding out.
You haven't specified which frame of reference you're using when you say "When Alice makes a change of velocity..."
Alice's frame
Alice's clocks to say when her velocity changes?
Alice's
Clearly, the clocks in different frames tick off time at different rates,
Clearly not in their own frames and SR is wrong that time dilation is a due to a difference in clock rates. Look at my Md for the real cause.
In particular, any two spatially-separated events cannot be simultaneous for both Alice and Bob.
The proper times on their clocks are proper time simultaneous from the Loedel perspective.
When you say "relativity velocity" here, which reference frame is measuring those relative velocities?
In constant velocity both agree on their singular relative velocity as confirmed from their DSR readings of the other participant. During the relative velocity imbalance period after a frame jump, their relative velocities do not agree causing a slowing of relative proper time in the change initiator.
It might be better, if you want to be specific, to talk about particular events in spacetime, because every observer agrees on which events happen; only the spacetime coordinates of events change between frames. As soon as you start talking about the velocity of something or somebody in a particular frame of reference at a particular time, it becomes difficult to translate that statement to some other frame, because the other frame obviously doesn't share the same notion of what is simultaneous, and it uses different clocks and rulers to measure velocities.
I have one frame and in it are velocity lines. I can switch frames by choosing a velocity line as the time axis of that frame but there's no point in that as the velocity line that I initially chose to define my frame is the one where the math is easiest to perform. It's not like SR that uses coordinates and translates those coordinates into the other frame's coordinates using Lorentz transforms. I have 1 frame, not two but any of the velocity lines can be that frame. I have no spacetime.
that doesn't raise any issues for me in terms of relativity, as far as I can tell.
In SR, relative velocity controls perspective time dilation. In my math, relative velocity controls the slopes of the Loedel lines of simultaneity which join proper times at their endpoints. In constant relative velocity, those proper times are the same. During the velocity imbalance period, they migrate. After that period, they remain permanently different by the proper time age difference between the two participants.
I don't really understand what you mean by "effects of any velocity ...".
Oops, the word change should have appeared after the word velocity.
Aren't you using the same definitions of "spacetime paths" as relativity?
I'm not but SR does use spacetime paths that must have co-located start and end points. I have a basic graphical unit that I can stitch together using light signals to make any of the spacetime paths SR uses but can't separate into sub-modules because that breaks the co-location rule of starts and ends. So I can calculate permanent age difference between the two for any spacetime path that doesn't start or end in co-location. eg SR can't calculate the age difference of a stop into the same frame at a distance even though light signals can be used to verify the age difference between the two even though other perspectives will see a different age difference from their perspective. Velocity changes between a stop and no change (0 permanent age difference) do not return but do have permanent age differences that SR can't calculate. Velocity changes that result in velocities greater than the constant relative velocity actually result in proper time speeding up for the initiator. Alice will end up permanently aging more than Bob if her velocity changes from .6c to .8c away from Bob according to my math but it is indeterminate using SR math because there is no valid clock co-location.
Only one frame can ever measure the "proper time" of an object - the one attached to the object, in which the object never moves (spatially).
Yes proper time is within each frame but the Loedel perspective allows us to see how proper time is joined between frames. The same proper times are joined in constant relative motion but outside of that, new correlations are made. Time slows or speeds up on the level of proper time, not perspective time as SR decrees.
I'm not seeing a flaw.
The flaw is the permanent age difference is obvious but SR is not allowed to recognize it due to its spacetime path co-location rule.
I don't understand what "infinite return time" means.
Alice's velocity line does not intersect Bob's in a stop they are parallel and never co-locate.
indicating, in effect, an unphysical infinite momentary acceleration.
Yes unphysical acceleration but it physically represents a clock handoff where Alice doesn't initiate a velocity change but her surrogate Charlie passes by her on the way back to Earth and she transmits her clock info to him. Charlie will then age two years less than Bob on his return journey to Bob but Alice will not experience any permanent age difference relative to Bob. This is the clock handoff scenario which you refuse to research and decide to apply the name to completely unrelated stuff. And once you do decide to look it up, will claim that you're the one who told me about it and I didn't understand it properly. Whatever.
While being the "explanation" for the "twin paradox" effect we see when Alice and Bob reunite, that turnaround doesn't affect any of the other reasoning we take away from the graphs.
Are you saying the turnaround at a distance is not the cause of permanent age difference? Are you then saying when Alice stops at co-location, that's the true cause of permanent age difference?

These questions are very good and show that Md's do not contain enough explanation on their own. They needed to be answered in greater detail.

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#57

a single observer can only ever be at a single position in space at a given time, where a reference frame is a system of coordinates that covers the whole of space and time.
A participant is a velocity line and any velocity line can be made a time axis of the frame without affecting the length unit spacing by adjusting the time unit spacing. But as I said, if I want to reassign a velocity line as the time axis of a frame without changing the diagram's time unit spacing, I have no choice but to alter the length unit spacing by a factor of x/Y in the main equation. For example if
$$(ct')^2 = (ct)^2 - x^2$$
where Bob's stationary frame velocity line forms the ct axis and I now want to set Alice's velocity line as the ct' axis of her frame without altering the spacing of her time units, I'm going to have to alter the spacing of her length units by changing the main equation to
$$(ct')^2 = (ct)^2 - (x/Y)^2$$
This is because her stationary cartesian grid has bigger squares than the cartesian grid of Bob's frame. This has nothing to do with actual length contraction (but it does algebraically construct Minkowski's x'-axis without needing to separately depict it). It primarily has to do with the depiction of each frame as stationary without altering the diagram. I've shown this before but have not explained why the main equation must be altered to accomplish this or the time unit size of the Md must be altered (I've shown this in the reverse Md depiction). In my math there is no need to change frames in this way because I don't use reverse diagram depictions.

Actually, the acceleration during the turnaround in the "twin paradox" scenario causes an effective "time gap" as the moving observer's notion of simultaneity shifts around due to her change of velocity.
That's SR where the line of Alice's perspective simultaneity swings from t=3.2 to t=6.8. I don't need her perspective simultaneity but I use the Loedel perspective simultaneity to join proper times and there is a gradual increase in the slope of the Loedel lines from the old relative velocity to the new one established by Alice's velocity change to Bob's delayed reaction to it. I don't have discontinuities in my Md's the way they're depicted in SR.
I also don't have the concept that Alice instantaneously swings from perceiving Bob's past (t=3.2) in her line of perspective present to perceiving Bob's future (t=6.8) in her line of present before it even happens to Bob leaving relativists like Greene to conclude past, present and future are illusions and all exist concurrently and can be accessed through different velocity perspectives. See Greene's two videos on this nonsense in the link I provided. I don't have this in my math because an event in proper time in one frame cannot be seen to happen first in an observing frame. There are no calculable glimpses into a future that has already existed since the beginning of time. Mathematically impossible except in SR which sets the illusion of perspective time as reality.
unless you're talking about a physical adjusting or resynchronisation of the clocks in one frame.
Yes, read up on it.
That would suggest that it is temporary, not permanent.
Permanent doesn't prohibit future changes which establish new permanence. You'll find there is no term in SR such as permanent age difference. The closest one is age difference and refers to the difference in time between the observing frame and the observed frame also known as non-permanent reciprocal time dilation. SR has no term for the proper time age difference at co-location after the twin paradox even if motion stops there.
I don't think so. I think the issue comes not from signalling delays, but from the change of reference frame during acceleration. If Alice turns around in her spaceship, then her "outgoing" frame (when she has velocity +v relative to Bob) is obviously different from her "return" frame (when she has velocity -v relative to Bob). At the turn around point, Alice must alter her frame from one to the other. In reality, she must pass through an infinity of frames in between as she does that (with velocities in the range from +v to -v). In the process, her notion of which spacetime events are simultaneous in her frame changes continuously.
Great. I assume you can show me the math (hint Rindler metric) that supports this notion. I've shown you my math and it's basic algebra. Acceleration plays no part in it but in slow turnarounds acceleration can be modelled as an average velocity. Certainly the frame jump is instantaneous in a clock handoff scenario which exists even if you close your eyes to it.
Relativity doesn't define "reality" or "perspective present", to my knowledge. Those are not terms I have seen in any standard text on relativity.
Correct. SR avoids this discussion like the plague because it avoids its failings by setting them as out of bound topics. Try asking an expert whether he agrees with perspective reality and he won't answer and he won't even know what proper time reality is because that doesn't exist in SR because it sounds too close to Newtonian universal time. It's SR's paranoia over anything that remotely suggests absolutism.
When you say relativity has no idea of "god's eye" perspective, isn't that exactly what a reference frame (extending through the whole of space and time) is?
No, a god's eye present is instantaneous across the frame. SR tries to simulate a god's eye present with Einstein's clock sync method setting all clocks to the same time across the frame but there is no way to instantaneously establish when an event happens first. So if we set the sun's time to be sync'd to our time, there's no concept of an instantaneous present where the sun is out and we're circling nothing for 8 minutes. SR says our subjective perspective that the sun is still there is more real than the sun isn't really there. That perspective present will invariably become perspectively real in 8 minutes but is not real before that because it's impossible to see that reality. There never was a god's eye present in your perspective present but there sure is a way to calculate what the god's eye present was in the past.
Talking about "changes" in the abstract risks leading to ambiguity.
I do assign Alice's time and Bob's space to events. That's my coordinate system which differs from SR.
I don't think the changes themselves propagate.
Really, so reality is not delayed. When the sun disappears, that's only a message, a note to you that the sun has disappeared and there's no sudden cold and darkness that comes with that information. Your understanding is shared by everyone I've ever met on a physics forum so I guess I must be wrong as majority rules in scientific consensus.
, you're going to need two - one for each of her two frames, before and after the turnaround.
SR does not allow breaking up the spacetime path into individual segments because a prior history affects the outcome. If you just present Alice's return, it looks identical to the muon experiment yet they both yield different results. The muon experiment does not involve permanent time difference because no velocity change has occurred so the clocks at co-location must share the same proper time.
In post #49, can I ask you what the green lines represent on your top graph? You say they are "Loedel perspective lines", but I don't know what that means.

They clearly aren't lines of simultaneity in Alice's reference frame. So what are they?

AA

Ok #58 is next.

#58
This is consistent with special relativity that says that when Alice and Bob are travelling at constant relative velocity, each sees the other's clocks (whatever they are) as running slower than their own, in this case by a factor of 2.
Reciprocal DSR is due to the delay of clock info and has nothing to do with time. A stationary clock face at a distance displays fixed delayed clock info but if that clock is moving at a distance, the clock info has a rate of delay, faster rate when they approach, slower rate when they recede. Reciprocal time dilation can't be seen, only calculated after the fact and it's a different rate than the DSR rate. . SR claims it's due to time itself actually slowing and its rate of slowing is independent of clock direction and clock info delay. Relativity of simultaneity explains it to me as the two clocks disagree on when start and stop times happen so the observing clock sets the start or stop time way before or way after the moving clock starts or stops its clock. This appears as time slowing when in reality both clock rates are the same normal clock rate of c through time.

She receives a signal from Bob at her t'=4, and then doesn't receive another signal from Bob until t'=4.5, half a year later.
No. Bob has a TV show of his life that he is continually broadcasting. He's got a clock in the background. Alice can compare what she sees on the face of that clock with what she sees on the face of her clock. This is their reciprocal DSR during constant velocity from which she calculates their constant relative velocity.
You're not being specific enough about reference frames and times.
Don't care. Alice sees a DSR of 2 from Bob and Bob continues to see a DSR of 1/2 from Alice until t=8 when his DSR from Alice switches over to 2 indicating their relative velocities are back in balance.
For Bob, for instance, as we can see from your graph, at time t=4.9 years, Alice's velocity is +0.6c according to Bob. At time t=5.1 years, Alice's velocity is -0.6c according to Bob. That information can be read easily from your graph.
Absolutely not.
The entire "imbalance period" you refer to happens, in effect, at the turnaround point in Alice's journey. At that point, her frame of reference has to change from one moving at +0.6c to -0.6c (in Bob's frame). All other parts of her journey are constant velocity, relative to Bob, so signals are sent and received at regular intervals during those parts of the journey.
Absolutely not. Please refer to what I'm actually saying without redacting words to fit your interpretation.
We could, for example, draw lines of simultaneity for Alice on your graph, and see the "time gap" in her idea of simultaneity at the turnaround point.
You could if you were reading a thread about SR instead of relativity and simple algebra.
Incidentally, you have drawn some green lines on your diagram, like the "Loedel lines" in your previous one. What are those? What do they tell us? They are not lines of simultaneity for Alice. If you think they are, you have made an error, because all Alice's lines of simultaneity in each "half" of her trip should be parallel to one another (she is travelling at constant speed in each half of her journey).
AA
Yes. That's the relativity of simultaneity. A standard, well-understood effect in special relativity. And we also have the signalling delays I talked about.
What context was that statement made? You're just agreeing with statements in which you recognize the words without recognizing the meaning.
I don't know what that is. It almost sounds like you believe this is some preferred frame of reference "underlying" Bob and Alice's perspectives. But special relativity has no preferred frames. I thought we agreed on that.

AA
Relativity has no problem with calculating "proper times".
SR calculates everything from perspective, Bob's perspective reality is his line of simultaneity with his perspective of Alice's proper time. SR is pretty boring if all it dealt with was proper times ticking in each frame without relating them to perspective time creating perspective reality. There is no such term as perspective reality in SR, it's implied but never openly discussed except when saying all perspectives are equally real.

yes
The confusion only comes when you aren't consistent - putting factors of c into some equations, while assuming c=1 in others.
If Alice is going at Yv from her clock she still must c going at c from her clock and that must involve a factor of c just like her factor of v is Y.
When v=0, gamma is 1. When v=c, gamma is infinite. I'd have to look back to find out how you're defining Y_t,
Similarly when v=c, v_t = o, Y_t=1 and Y= 00 (infinity) and when v=0. v_t=c, Y_t=00, and Y=1. The space and time equations are symmetrical.
Where are infinities cropping up?
I'll show you in future postings.
Can you please give me an example of where relativity would produce an infinite answer for any physical (i.e. measurable) quantity?
As u approaches c, w=u(+)v also approaches c and both Y_u and Y_w approach infinity but the ratio of Y_u/Y_w approaches the finite value of DSRv. The infinities of Y alsways cancel out in my equations but not in the equations I'll show you in SR.
Why do you say that it is impossible to pass "proper time information" in standard relativity?
As I've said many times, separated proper times are subject to other perspectives so SR has no universal proper time present because it is based on perspective reality.
The synchronisation of clocks in a single reference frame is something we assume has been done before we start using them for anything. The procedure is straightforward.

The relativity of simultaneity is a direct result of the Lorentz transformations. If you want to trace their origin back, it goes right back to the constancy of the speed of light in all frames and to the postulate of the constancy of the laws of physics in inertial frames. It has nothing to do with clock synchronisation, per se.
I don't want to go through this again because it has nothing to do with my math, this is SR math.
Two separated clocks that tick at the same rate can be used to define a "present"
No. We do not share the same present even though our clocks may be synchronized to the same time. Your present is delayed from my perspective and if you're moving relative to me your present is affected by both DSR and time dilation.
. As long as we're effectively at rest with respect to one another, we can agree on anything that is happening "now", no matter where it is happening, or how widely we're separated.
No. You drop a cup and tell me about that over the phone there is a delay in our present reality because c causes that delay. Einstein saw that problem and invented his clock sync method to create an artificial perspective present where everyone in a frame shares the same time from one end of a frame to the other. I hope this is the lat time i have to say this.

On to page 2, no page 9 or 8 maybe.