Ralfativity 2.0

[phyti]

Light is constant, so light lines are blue. A green line is an axis of simultaneity, and light gray is a measurement,
I don't see anything wrong with your graph with A moving at .6 relative to B, except round trip signals are required to measure distance. There is no feasible way to establish an astronomical coordinate system. As the example shows, each observers local clock is sufficient.

B sends at 1.25, receives a At=2.50 at 5.00.
(5.00+1.25)/2 = 3.13. B thinks the A clock rate is 2.50/3.13=.80.
A sends at 1.00, receives a Bt=2.00 at 4.00.
(4.00+1.00)/2 = 2.50. A thinks the B clock rate is 2.00/2.50=.80.
The perceptions are reciprocal and do not require symmetrical images.

[ralfcis]

How y'all doin because if you've been following along up til now, it's about to get complicated and very messy. I realized I had not explained how age difference unfurls year by year. I had only shown when the final answer could be known. It took me days of thinking but I've finally come up with an explanation of how age difference unfurls but it's really ugly. Here's the STD showing Alice leaving at .6c and either stopping or turning around.

We know if she keeps going at .6c, she and Bob will exhibit no age difference. I take this statement literally in that the aging difference is not indeterminate until a change in velocity is made, it is actually determined to be zero in all cases before a change in velocity and if no change in velocity is made. This means just because age difference seems to have the same values as time dilation, does not mean those values are being stored before the change in velocity is made. In our example, when Alice changes velocity, she does not age .25 years less than Bob for every year she travels. Even though Bob's t=5 and Alice's t'=4 at the moment she changes velocity does not mean she suddenly jumps from no age difference from Bob during the constant velocity to having aged 1 yr less than Bob at the transition point.

So we need to turn to the equivalent year I introduced in the last post. At .6c from Alice's perspective .8 Bob year is equivalent to 1 Alice year. So the line of present from Alice at t'=4 intersects Bob at t=3.2. 3.2/.8 = 4 equivalent years. The euivalent years are written in red on Bob's t-axis.

Up until the transition Bob has aged 4 euivalent years to Alice's 4 years. Bob is unaware Alice has stopped until he gets her message at t=8 and that he was not going at .6c relative to Alice since t=3..2. At t=8 he knows that he is suddenly at 0 relative velocity with Alice and her line of present is horizontal with his. He has to calculate her age difference value based on the instantaneous present as opposed to the time dilation value which is based on the delayed present.

So Bob whips out his graph paper and corrects his STD with a vertical line for Alice starting at t'=4. He sees his horizontal line of present intersects Alice at t'=7. Alice is not moving (v=0) so there is no relativity of simultaneity between them so their shared present is instantaneous no matter their distance separation. Since Bob and Alice now agree on a new relative velocity, all time after t=8 shows there is no more age difference accumulating but Alice has aged a year less than Bob between t'=4 and t'=7.

How does this 1 year accumulate over those 3 Alice years it took for the signal that a change in relative velocity has been made by Alice? You can't get the answer by superficially looking at the STD and seeing that Alice has always lagged Bob by 1 year. Again, that is time dilation, not age difference.

So where do you look on the STD to see age difference and ignore misleading time dilation. Well it's very complicated but I'll try to explain. We use the time Bob thinks Alice's clock says with Bob assuming Alice hasn't made a change in velocity. In fact, so far as Bob is concerned, she hasn't. We draw Alice's lines of present for every year past t'=4. We see Bob's equivalent aging every .8 yrs. But we know now that after the transition, .8 yrs for Bob equals .8 years for Alice. Bob can now see Alice was aging .2 yrs less per Alice year than he thought she was. At the end when Alice's line of present from t'=7.75 intersects Bob's line of present from t=8, we see that Alice has aged .25 years less for every year after the transition and the news reaches Bob. You can also see the same total on Bob's equivalent years where she loses .2 Bob years for every Bob equivalent year and there are 3.6 Bob equivalent years between t=3.2 and t=6.2 so the total number of years Alice ages less is .75.

But the answer of .75 must be wrong, the seemingly obvious answer is Alice has aged 1 year less than Bob so she must have aged .33 yrs less for every year during the transition delay. Nope, buried deep in the math of where Bob and Alice's final lines of present at t=8 and t'=7.75 intersect determines where the age difference stops accumulating. This is where I spent most of my time, I could not understand how aging .75 years less over 3 years works out to Alice having aged 1 yr less. If I've made a mistake I can't see it.

[ralfcis]

Sorry Phty I'm not interested in off-topic discussions. However, If you have a relativistic explanation of how age difference unfurls I'd love to see that (I know it doesn't exist). I'm not too comfortable with my explanation so I may need to do a few more examples.

[ralfcis]

Sad to say I've double checked my math from another angle and it's still the same. Here's the new StD..

When Bob gets his notification that Alice has changed their relative velocity at t'=4, he must go back and correct what he thought her age was. At t=8, Bob's 10 equivalent years were thought to match Alice's 10 yrs so there was no age difference between them. But meanwhile from t'=4, Alice was aging .2 yrs less than Bob thought for every equivalent Bob yr. So for 6 equivalent yrs, Alice would have been 1.2 yrs younger than Bob though. So 10-1.2 = 8.8. However, the message from Alice showed Any time past t=8 meant they had resyncd at a new relative velocity of 0 so no further age difference could accumulate. This means if Alice continued to lose .2 yrs for every equivalent yr between t'=4 and t'=7 that's .75 years Alice would have aged less in the 3.75 equivalent yrs in that interval. (She lost .2 in the 1st equivalent yr, .2 the next, .2 the next and .15 the last. his does not add up to the 1 yr Alice actually aged less than Bob because the time was cut off.

This mathematical phenomenon would only occur around changes down to low relative velocities. If you do the same calculation for how much less Alice ages than Bob when she turns around at .6c, You just convert the 1.6 years she aged less by multiplying by Y to get the correct answer that when Bob was 8, Alice had aged 2 yrs less than Bob.

[phyti]

Sorry Phty I'm not interested in off-topic discussions. However, If you have a relativistic explanation of how age difference unfurls I'd love to see that (I know it doesn't exist). I'm not too comfortable with my explanation so I may need to do a few more examples.

You're discussing aging, which requires a comparison of accumulated time for two clocks. My opinion, you're over thinking the problem.

In the gif, A moves at .6c relative to B. The reversal is a more realistic deceleration to avoid the 'time jump' in the popular explanations. The simplest method would be to draw light lines from the clock ticks in common time units of each to the other, and count them. B sent 10 ticks to A, while A sent 8 ticks to B. The gif uses 2 in the manner you use for each to monitor the other. Obviously there is diverging and converging paths, which provides doppler effects, which only provide a perceived clock rates.

A detects 2.3 ticks in a 4 ticks interval.
A detects 7.7 ticks in a 4 ticks interval.
A detects 10 ticks in an 8 ticks interval.
A sees the B clock run slow, then fast, even though its rate is constant!

B detects 4 ticks in a 7.7 ticks interval.
B detects 4 ticks in a 2.3 ticks interval.
B detects 8 ticks in a 10 ticks interval.
B sees the A clock run slow, then fast even though its rate is constant!

Both agree the A clock accumulated less time than the B clock.
How they appear to age before rejoining is irrelevant.

[ralfcis]

They do not have to rejoin just like they don't need to rejoin if Alice stops. The age difference is established when Bob gets the message from Alice of her new doppler ratio with Bob once she makes the change, that he has been going at .6c converging for the past 3 years. He can post process that info that 2 years earlier Alice was already 2 yrs younger than Bob. This was shown in a post here. I might need to alter this based on the info I got from my question on the physics forum.

[ralfcis]

Ok, there has been a break in the action here because I moved the question that stumped me into the physics forum and despite Jorrie's objections that relativity cannot provide me with the answer, I have found the answer anyway through ralfativity.

Here is the original question

"I'm looking for the math that shows if Alice stops for 3 years and she'll end up 1 yr younger than Bob at the end of those 3 years, how much younger is she for each of those 3 years."

Jorrie's answer before he locked the thread was:

"Bob is never present at the two events that concern Alice, so his aging is indeterminate for those two events. After 3 years of her stopping, Alice and Bob are still at two different events, but now they had time to exchange signals and could determine that they now share a mutual inertial frame and hence a shared definition of simultaneity. This, for the first time, allows a proper aging difference of 1 year to be established."

I'm afraid as you will see, ralfativity can now tally the per year age loss accumulation that relativity says is indeterminate

He goes on to say:

"Post-processing depends on arbitrary choice of reference frames and it is hence not a coordinate-independent result."

I've seen this a lot around the forum lately, " How can we determine reality if it's observer dependent." "If time dilation is reciprocal and dependent on perspective, how can we possibly determine age difference." Just choose a perspective and do the math. Here's an STD to show you what I mean:

This isn't a chart of the typical forum user's synaptic firings when trying to make a choice of which perspective to adopt, it's a STD of all the persectives available with their lines of present. We're going to choose Alice's perspective of Bob because Alice will be making the change in velocity and Bob won't have any idea of what's going on for 3 yrs after she makes that change. Alice sees's Bob's years time dilated so a .8 Bob yr form Alice's perspective is equivalent to 1 Alice year, Notice how this works if Alice keeps going:

Notice I've relabelled the Bob t-axis in Bob equivalent years. There is no age difference between Bob and Alice from Alice's perspective, when they are engaged in constant relative velocity.

The next STD is after he gets the message from Alice that she has stopped at t'=4. Bob had thought he had been engaged at .6c with Alice for his equivalent years from 4 until 10. Now he has to draw in blue that he was matching Alice's aging year for year after she stopped. Once he draws in his correct equivalent age, he can calculate how much of an age difference occurred year by year.

The red lines of present show what what Bob thought his age should have been but it gains .2 Bob years (.25 Alice years) for every equivalent year from 5 to 9. At equivalent yr 10, the .2 yrs Bob would have gained are cut off by the message from Alice who tells Bob that they are now engaged at 0 relative velocity and hence his line of present should go horizontal to match his. So the end result is Alice is 1 Alice yr behind Bob in the accumulation pattern of .2 Bob yrs gained from Bob equivalent years from 5 to 9 (Bob yrs 4 to 7.2).

I know, not easy to follow but it does prove, contrary to what relativity says, that you can plot age difference year by year. I should double check my result using the Alice turnaround example because this could have just been a fluke.

[ralfcis]

Ok here's the next example I promised adding to the credibility of this method. It's Alice returning at .6c. According to relativity, Alice should age Alice 2 yrs less than Bob when they re-unite. Ralfativity can make that prediction much earlier strictly based on when the signal reached Bob and Alice's line of present intersecting that point (the line from t'=5.5 and t=8). You can also see the half year by half year progression of the age difference tallying up to -1.6 which is equivalent to 2 Alice years. It all checks out

Relativity can't do this but there's nothing stopping relativity from adopting this relativistic math except that it contradicts the theory of relativity. I think I'll put all future examples in a separate thread. You will see age difference predicted for scenarios where there is no passing through 0 relative velocity. The theory of relativity cannot be tweaked to handle those scenarios at all.

[ralfcis]

Even though I got permanently banned from the physics forum, I am grateful to have asked the question that lead to my banishment. I was just not getting the right result for real time accumulation of age difference. I wanted to know if age difference was accumulating instantaneously, linearly as in 1/3 of a year over 3 yrs,or some other way. Turns out it was in a way I would have never guessed. I thought my theory was in grave peril but now I see things so clearly as I passed this last hurdle.

Here is a link to Brian Greene's on-line course from where I learned relativity 4 yrs ago:

https://www.youtube.com/playlist?list=P ... UgDLTwVbFc

Yeah I started communicating with Jorrie 10 yrs ago but I gave up for 6 yrs because I wasn't getting anywhere in finding the answer to my first question about the doppler effect and relativity so I gave up. In Greene's course I discovered that people eager to learn are people who are eager for acceptance. They just want to regurgitate scientific dogma for intellectual status and crank out the right answers for good marks. Science only advances with the right questions, not the right answers. Scientific consensus has always eventually proved to be wrong. Sorry Newton fans, Newton was clueless, that's why his "theory" is just a collection of laws, specific results under specific circumstances. Admiration for all the greats has always hindered science and now Einstein is in the way.

Whether my answers are right, and I know that they are, doesn't really matter as much as the questions that spawned them. The question that started it all rolling for me was how can Greene possibly say that past, present and future are all equally concurrent and just matters of perspective. Was this really an outcome of relativity, then I concluded either relativity or the world's chief scientainer on relativity was wrong. And if he was wrong, had relativity become a religion where you could pick and choose which scriptures you adhered to and which you could reject.

I see now where he went wrong. There are two presents; the instantaneous god's eye present we can't see, and the delayed information we can see of that present. That information allows us to see what the true present had been in the past or we can set up a flight plan for Alice and force the delayed present into the true present by setting up when in the future that info will be sent. This makes post processing and pre-processing equivalent and these are the past and future that could be made concurrent with whatever perspective of the present you were considering. This is the true interpretation of what Greene was misinterpreting.

Further to this point, Greene's concept of now slices was also gravely flawed. The now slices are the exact same thing as the length contracted x'-axis. The x'-axis is in the spacelike part of the Minkowski STD (outside the light cone as many of you like to say). There is no causality in this region because the speed of light info can't join two events. So when you draw a now slice from Alice to Bob, that is a line of instantaneous present that can only be made real through post or pre-prosessing. But there's no such thing as 2 presents in relativity so there's no way to explain what a now slice really means.

Jorrie's statement that it was silly to think post-processing could look into how age difference accumulates in real time would mean it's equally silly to be able to show how pre-processing actually shows how age difference accumulates in real time. I started this investigation in my Ralfativity 2.0 examples thread but there's a lot of eye opening physics in the description so I'm going to move that discussion here.

Even that math can be totally dismissed because, let's face it, anyone can read the final time difference between Bob and Alice when they relatively stop or re-unite without having any kind of fancy math describing what's happening. Knowing the age accumulation in real time has no effect on establishing the final age accumulation. However, that math is crucial in establishing age difference when they merely change relative velocity without stopping or re-uniting. Relativity says that's impossible which when proven possible here will be the end of relativity as a theory. That's what all this has been leading up to. Those whose intellectual goals are about social acceptance should read no further because change is traumatic for those who base their self-worth on that. Excuse me, I'm being beaten in the head with a frying pan right now.

[ralfcis]

Here is the STD Alice setting up with Bob when to send out a yellow light beam so it reaches her when t'=4.

This pre-processing can be done without length contraction because we know all Minkowski STD's at .6c must behave the same as the Loedel STD where Alice and Bob are leaving earth in opposite directions at .33c. The Loedel STD has light signals depicted of identical length but the minkowski has them of skewed length. That length must be unskewed by multiplying the time bob's travels through Alice's time frame by the doppler ratio. Essentially you get rid of length contraction by using a Minkowski STD using the perspective's time and Bob's proper space.

v'=Yv for Alice
c' = Y(c+v)

c' is what Bob sees his light signal crosses the 3ly to the rendezvous point at t'=4 from the time Bob has pre-agreed to send it which is t=2. Alice will already have a huge head start on that light signal. She will be 1.875ly away and will have already traveled 1.5 of her years. Alice will travel another 1.5 of her yrs to meet the light signal after it has traveled 3ly. So the speed of the light signal c' in Alice yrs/Bob's proper time is 2c but from both Alice's and Bob's perspectives in their own frames, the velocity is c.

In Alice's frame, Alice had a 1.5 Alice yr head start and then flew an additional 1.5 Alice years in 3ly proper distance so the light speed was c. Remember, no length contraction needed in this method.

In Bob's frame, the light traveled 3 ly in 3 of his years so again it was c. The trick comes in mixing the instantaneous time the light signal started, Bob's proper distance it traveled with the time in Alice yrs it took Alice to meet that light signal from that instantaneous starting point.

Alices's velocity in terms of Bob's proper distance and her time is 3ly/4 Alice years is .75c = v' =Yv = 1.25*.6c.
The formula for c' where the speed of light is going through Alice's time frame is not Yc as one would expect from Alice's formula. Here's how to derive the formula for c' = Y(c+v) (v is positive when Alice is separating and I haven't checked the formula for when they come together.)

Doppler ratio R=sqrt((c+v)/(c-v)) so R²=(c+v)/(c-v)
Y= c/sqrt((c+v)/(c-v)) so Y²=c²/((c+v)/(c-v))

With very little manipulation you get R=Y(c+v)/c

c'=Rc = Y(c+v) so c'=1.25(1.6) = 2c.

I learned this trick while struggling with conversion of Minkowski STD's into Epstein STD's. Both use the Doppler ratio for c' but Epstein had the messy complication that the slope of c was not fixed in both directions at a 45 degree angle. In the Minkowski, c is always 45 degrees but now each line has 2 times associated with it; the stationary frame side where R=1 and the moving frame side where R changes.

I'm basically getting rid of length contraction by mixing Bob's proper space with Alice's proper time. Nothing illegal about that.

[ralfcis]

Oops, messed up my sign. v separating is negative and the formula for c'=Y(c-v).

So, for example, v= -.6c because Alice is separating from Bob. Y = 1.25 so c' = 1.25(1.6) = 2c when you use Bob's space and Alice's time. All I need is just 1 relativist to accept this and betray their blind loyalty to length contraction or show the math is flawed. This is the point where relativity and ralfativity diverge yet I can't see where any rules of relativity have been broken.

[ralfcis]

I just noticed another way of pre-processing but also sending validating signals in real time of the flight plan:

Alice can pre-process when she wants Bob to send his signal to her by sending him a pink light signal when she reaches t'=1. The blue number on that pink signal says it will take .75 Bob years to reach Bob at t=2 and the red number on that pink signal means Alice will travel .6 of her years (.75/Y) in that time. Bob's blue horizontal line of present will join t=2 and t'=1.6. Alice's line of present from t'=2.5 will also join Bob's t=2. So Alice will travel 1.5 of her years from the time she sends the signal to Bob and then travel another 1.5 of her years for Bob's signal to reach her from t'=2.5. This is how she sees the light travel 3ly in 3 of her years to maintain c in her frame. Again, no need for length contraction which has always been the main point of contention between me and the relativists here. So prove me wrong and don't use how Star Trek uses length contraction to achieve warp speed as proof of your argument.

[ralfcis]

Ok for all you symmetry nuts out there here is the last STD in both Loedel and Minkowski forms explaining what is going on from both Bob`s and Alice`s perspectives. The two STD`s are identical from a relative velocity point of view but not identical when that relative velocity is also from an earth perspective (the cartesian coordinate background).

Alice`s perspective is between her parallel red lines of present. When t`=1, the start point when Alice sends her pink signal, Bob is instantaneously t=.8. The light takes .75 yrs to reach Bob at t=2 but Bob takes 1.2 of his years to get to the same point. On Alice`s t`-axis, she takes 1.5 of her years to age to a point (t`=2.5) that shares the same instantaneous present from her perspective as t=2 for Bob (the end of the pink light signal).

From Bob`s perspective, it`s a whole `nother story. His lines of present are the parallel blue lines. When t`=1, Bob`s present is at t=1.25 and he reaches the end of the pink light signal in .75yrs. His aging now matches how long the light takes to reach him whereas, from Alice`s perspective, it took Bob 1.2 yrs, much longer for the same light signal. For Alice, it only takes .6 of her yrs to be on the same line of present when the pink signal reaches Bob. From her perspective, it took 1.5 of her yrs to reach the same point.

So how is someone supposed to interpret what is really going on here

[ralfcis]

It looks to me, and I'm just spit-ballin here, that the valid numbers are the ones not separated from the perspective. So from Bob's perspective he takes .75 Bob yrs when the light from Alice takes .75 yrs to reach him. From Alice's perspective, she travels for 1.5 of her yrs from the time she sends the signal to Bob and he gets it. This would mean that from her perspective, the light must also take 1.5 yrs. Factoring in the Doppler ratio (or the factor Y(c-v)), the speed of light using Bob's space in Alice's time is 2c. The other numbers come from the two valid numbers divided by Y (.75/Y = .6 and 1.5/Y = 1.2).

So it all looks like it fits in with what I was saying except the blue and red numbers associated with the pink light signals from Alice to Bob should now be .75 and 1.5 indicating how many yrs the light signal takes in Bob's and Alice's time frame from Alice to Bob. The labeling of the yellow light signals from Bob to Alice was correct.

Here are the corrected STD's for the labeling of the pink and yellow light signals:

Yes this is hard for even me to follow but the point is the speed of light is c for all frame perspectives and I can use Earth's (not Bob's as I said before) square cartesian space per Alice's time for relative velocity and c' without needing length contraction.

[ralfcis]

I figured out what the math is telling me. When Alice sends her pink signal back to Bob, and you're using Earth's space and Alice's time, the pink signal from her perspective takes twice as long as the same signal from Bob's perspective. The velocity of Alice's signal from her perspective using Earth space and her time is therefore halved by the formula c'=Y(c+v) . This formula is the relativistic velocity combo law for Earth space/Alice time where c' can be treated as a velocity when added to v, the result cannot exceed c according to c=c'/Y - v.

For example c' for the pink signal from Alice's perspective is .5c. c'/Y = .4c. v = -.6c so the combined velocity .4 - - .6c is limited to c. Same thing applies to the yellow light signals from Alice's perspective using Earth space/Alice time. c'=2c. c'/Y = 1.6. x = .6c so 1.6-.6 is again c. c' is like a ball either thrown away from Alice as she's moving away from it or being thrown at Alice as she's moving away from it. Two more scenarios will come into play when Alice throws the ball and moves towards it or the ball is thrown at her as she moves towards it. This is a new way of looking at how a velocity relative to c is always c using c', Alice's perspective, her time and Earth's space.

The duration of the 1st half of Alice's journey after the pink light signal matches the duration of the pink light signal from her perspective. The duration of the 2nd half of her journey after the yellow light signal is triggered, matches her perspective of the duration of the yellow light signal.

[ralfcis]

So what else is the math whispering to me. Oh yeah, there's no such thing as moving or stationary perspectives, the only two perspectives are alice and bob. Their relative velocity can be oriented in any way within the light cone. Whether they're moving or stationary is irrelevant. The lines and endpoints will be the same in all orientations but only if you get rid of length contraction. So instead of expressing relativity of simultaneity as vx/c², I'm going to express it as tv²/c². I'll show you how this works on the STD:

So what is the real significance of the numbers on the t and t' axes? When Bob =2 he has a line of present to Alice =1.6 in accordance with the formula t=Yt'. Does this mean when Bob is 2 Alice is 1.6? Only from Bob's perspective. From Alice's perspective when Bob is 2, she's 2.5 as her line of present is the important one from her perspective. Bob's age is also 2.5 equivalent years according to the red Alice equivalent years on his t-axis. They are aging the same from Alice's perspective (and also from Bob's if you do that separate analysis).

You can further prove this is a correct age for Alice and Bob by having Bob send out a yellow light signal to Alice when the time on his clock is t=2 (Alice equivalent age of 2.5). The time the light takes to reach Alice is 3 Bob yrs factored by the doppler ratio at .6c to result in 1.5 Alice years. Indeed, from the instantaneous present she shared with Bob, his light signal traveled 1.5 Alice years and Alice herself traveled 1.5 Alice years to have that light signal intersect her at t'=4. This confirms that from Alice's perspective, she was not 1.6 when Bob was 2.

How do we correct this mistake? We use the relativity of simultaneity. We need this fudge factor because Alice was separated from Bob's perspective. The RoS from Alice's perspective is tY(v/c)²= .9. Add that to 1.6 and 1.6 is now corrected by the relativity of simultaneity to be 2.5 as it should be. People are more used to calculating RoS from Bob's perspective so for an example Alice at t'=1 shares a present with Bob at t=.8. RoS for Bob is t'Y(v/c)² = .45. Add this to t=.8 and t=.8 get's corrected to t=1.25.

No real need to ever consider RoS from either perspective so long as you know to read only the clock on a perspective's line of present that is closest to the perspective you're considering. (t'=1.6 should be ignored here, only t'=2.5 is valid.) So RoS has no real purpose in ralfativity because you don't need to calculate the true values, you can just read them off the STD. Length contraction also has no purpose as contracted length never comes into the calculation for age difference, the only result that really matters.

[ralfcis]

Ok so I guess there are no further questions about how to interpret STD's and we can move on to finish the example of how age difference unfurls in real time rather than through post-processing. I was hoping that relativists could have presented their counter-interpretation but I haven't ever seen one reasonably and simply presented so I can only assume one doesn't exist, it just has to be taken on faith.

[ralfcis]

We`re going to use the technique outlined in this thread to determine year by year age difference accumulation in real time. Alice stops at t`=4 and the only perspective considered will be Alice`s. The STD up until the transition shows no age difference has occurred,

We're going to erase those lines and add the yellow line from Bob that would have met Alice at t'=5 if she hadn't have stopped. This will form the baseline comparison of how Alice has aged differently because of the stop since there would have been no age difference if she kept going.

Alice bounces the pink light signal she sends to Bob at t'=1.25 and it forms Bob's yellow light signal that will meet Alice at t'=5. The speed of light is c from all perspectives but the time light takes to travel the Earth's network of distance milestones is affected by the timeframe it's traveling through in a similar way Alice's time is affected by Y. In this STD's depiction of the relative velocity, Bob's Y=1 and Alice's is Y=1.25. Light time is affected by a factor of Y(c-v) where v is negative if they're separating. The yellow light signal travels 3.75 Bob years which is 1.875 Alice years but the light will hit Alice in 1.5 Alice years if she stops.

The message from Bob is he and Alice were 3.125 Alice equivalent yrs at the start and subtracting the propagation delay of the yellow light signal should confirm that. For Alice not stopping (thick red line), 5-1.875=3.125. Correct! For Alice stopping (thick blue line), 4.5-1.5=3. So for the 1st half year after Alice stopped, she has aged .125 yrs less than the baseline of her not stopping. This real time difference is the same as was arrived at in the post-processing example but I suppose I'm going to have to prove the accumulated results agree with special relativity's final result which is the only result allowed in S.R. since it can't calculate incremental age difference. Aging and the universe are not digital so I can't see how S.R. can physically claim there can be no such thing as incremental age difference as I've proven here.

Length contraction is nothing more than measuring length with a clock and then being shocked that your length measurements contract because your clock is dilating. I've previously shown what length contraction looks like in an STD compared to time dilation'

Only 2 of the terms are used in relativity but the concepts are the same. Length contraction is Bob's perspective of Bob's space through Alice's perspective. What a tangled up mess of a concept. Instead I use the concept of Alice traveling Bob's space in her time which allows her to cross the universe at speed Yv from her perspective and not be limited by c. Only Bob's perspective of her speed is limited to c. I then allow her perspective of c to be altered by Y(c-v) just like her perspective of v is altered by Y. This is how I allow c to be constant in all frames and introduce relative c' to v' so it's no longer a mystery of how v relative to c is always c. V' relative to c' can be seen by light time changing relative to the timeframe it is traveling through. Oops i must go. I hope I can finish later.

[ralfcis]

There`s a mistake somewhere. My final tally came out Alice aged 1.05 yrs less than Bob instead of the correct answer 1 yr less than Bob. I don`t have time to find it right now.

[ralfcis]

Ok i worked it out and the explanation is complex but logical. It does shed light on why relativists think the age difference can only come out in a lump sum at the end of the spacetime path and you can't see it happen incrementally. It has to do with the fact that when Bob gets the news from Alice that she is actually 7 and not what Bob estimated she was on the assumption that they were still engaged at .6c relative velocity when they weren't, he simply has to cut off his calculations at 7. The 4th incremental change was .25 and a 5th was starting with only .05 yrs loss which was cut off by Bob getting the news from Alice that she is 7.

Here's the STD but I can see there is a simpler method for presenting these calculations. I just have to find it or go back to the post-processing method which was simpler to understand. Even if I wrote out how to interpret the STD, I doubt anyone would take the time to read that tedium.

The reason why relativity does not interpret this correctly is because it tries to say the swing in Alice's line of present at the transition point is where age difference occurs and it plays out indeterminately until Bob gets the news. I'm saying the the incremental aging is determinate and incremental but the reckoning occurs at the end not at the transition. Bob is convinced he is engaged at .6c constant relative motion until t=8, then he must simply recalculate the last incremental age difference that gets cut off because it never happened. The reality that Alice has been incrementally aging less all along is not affected by the end correction. Relativity never figured this out and simply couldn't know what the incremental age difference was because it made a wrong assumption. Relativists avoid this question because they simply never knew the answer. But believe me, this flaw snowballs into a whole bunch of questions relativity can't answer. It turns out having both participants having to either meet or stop is not necessary to establish age difference. I've had proof of this for over a year now and at the rate i'm going it will take another year to write it all out. Finally, though, I've got all my ducks in a line to fully support every detail of the proof.

[ralfcis]

Another mistake relativity makes is only considering age difference from Bob's perspective. Yes, Bob can't know the incremental age difference occurring during his blackout time between Alice's transition and him receiving the news. There is no info reaching him during this time. But Alice is fully aware the instant she makes the transition. She knows Bob will still calculate no age difference for 3 years and she uses his messages to her to see how much she's aging less incrementally. Again, closed minded assumptions from relativists has blinded them to the reality of incremental age difference. I think this may put in jeopardy their interpretation of the spacetime path as well. I don't know because they don't really share details of what their interpretations of relativity are except in a general Wiki article sense. Few specific questions are answered.

[ralfcis]

This is where relativity steers most people wrong, the twin paradox. I say steers because I don't see enough effort on relativity's part to steer people away from this common view. This is the Std of Alice leaving and returning to earth:

It looks obvious that when Alice reunites with Bob, she has aged 8 yrs and Bob has aged 10. It's easy to assume Alice has aged a quarter year less than Bob for every year she travelled. Just read the endpoints on Bob's yearly lines of present. The total for 8 yrs matches the final difference of 2 years. Please note this is a completely wrong analysis.

So then relativity throws in the reverse analysis where bob is moving and Alice is stationary. The story goes that Alice waits 4 yrs and takes off at .8824c which is .6c relative to Bob's .6c and catches up with Bob in 8 yrs. Here is the STD:

First thing they neglect to mention is that Alice does not take off from Earth, Earth has sailed away with Bob. Alice has taken off from empty space and it's a different space that measures length differently. Alice's trip is still 8 Alice years in total but the distance is no longer 6 Earth light years, it's 7.5 Alice light years. The distance markers are completely different.

Also, if you apply the faulty reasoning in the first analysis, Bob is aging a quarter year less than Alice every year she's stationary. So by the time she takes off, Bob is 1 yr younger. Alice has to make up 3 years so that she's 2 yrs younger younger than Bob when they reunite to show the reverse analysis works. So her higher velocity (that is still .6c relative to Bob) makes up that time by allowing her to age .75yrs less for each of the 4 years she travels catching up with Bob and the Earth. This reasoning is completely wrong even though it yields the correct final answer. But it breaks all the rules of relativity:

1. There is no age difference during constant relative motion.
2. The reverse analysis should yield identical results yet the faulty reasoning yields quite a different incremental aging process (which relativity does not recognize anyway).

I'll bet most people believe the faulty reasoning is correct and that's because relativity doesn't put in enough effort to steer people clear of this. I'm going to present the way ralfativity handles the reverse analysis and totally avoids false reasoning.

[ralfcis]

Anyone paying close enough attention to all this would say I had to invoke length contraction in the reverse analysis. So I came up with this STd to prove there is a ton of leeway on how you can mark your coordinates. I'll give you some time to reason out what this STD means and then I'll explain it later in detail. Basically it shows how length contraction can be absorbed into the time domain and how the Earth's proper distance markers can be put as the background cartesian coordinate reference frame. Alice can take off from this frame in 4 of her years and only travel 6 light years to catch up with Bob.

[ralfcis]

Before I go into explaining the details of the previous STD, it raises an important question, do we keep the same reference frame for the reverse analysis or do we adopt Alice's reference frame when we make her stationary? I doubt relativists will even see the point of this question. The answer I usually get is, do what Einstein tells you, he's been right for 113 yrs, that's all the explanation anyone needs.

Before I started defining the reference frame in terms of a network of proper distance milestone markers, I defined it in terms of a network of sync'd proper time clocks of whoever the stationary participant was deemed to be. But now I see this as no longer necessary. I can have the reference frame of Earth's proper distance markers whether Alice or Bob are deemed stationary and still get the same results. From a physical perspective, there is a difference between Bob being stationary with the Earth frame and then Bob at .6c with the Earth frame in the reverse analysis.

The blue time coordinates in the STD are the Earth reference frame with its network of proper distance milestones. The distance Alice or Bob travels is not length contracted wrt each other. Bob is moving at .6c relative to Earth so the red t' coordinates on his t'-axis are dilated by t=Yt' wrt the blue t coordinates. Alice's blue coordinates look like they're dilating wrt her red coordinates which indicates Earth is moving wrt her. This is a bit weird as Bob is moving wrt Earth and Earth is moving wrt Alice, the latter, not the former, would be consistent with relativity's reverse analysis. When the age difference comparison is made at the 6 ly mark, you compare Alice's blue coordinate to Bob's red one and multiply by Y (8-6.4)1.25 = 2. Alice is 2 Earth years younger than Bob.

[ralfcis]

Oh crap, I just noticed a mistake on the red numbers for Alice after t red=4. The t red=0 to 4 represents the timeframe where Alice is stationary and the earth frame is receding at .6c away from her. But then her speed relatively doubles to .8824c and the time numbers on her new velocity line did not correctly reflect this change. I'll correct shortly, maybe tonight.

[ralfcis]

Nope, no mistake but I am confused what Alice's red 12.5 and Bob's blue 10 mean. It seems to imply Alice is 2.5/Y = 2 years older than Bob. This means something but I don't know what yet.

[ralfcis]

Arrg I was wrong after all. Here is the corrected STD. The red 8 is compared to Bob's blue 10 and Alice remains 2 yrs younger.

[ralfcis]

I just want to do a quick check of all the v's and Yv's this STD represents. v=x/t, Yv=x/t'.

1. Let's start with Bob's v. His t-axis is the blue numbers which are re-written on his slanted line. So his x=6 when his t=10 so his v=.6c. Correct.

2. Now check Bob's Yv which are the red numbers written on his slanted line. The red numbers on the t-axis are irrelevant here. Yv for Bob = 1.25*.6c=.75c. His t'=red8 and his x=6ly. Yv=6/8 = .75. Correct.

3. For Alice, the blue t-axis represents the Earth frame moving away from her. The red t-axis is her proper time. So red t = Y blue t but only on the t-axis. So red t=4 = 1.25 (blue t=3.2) is correct.

4. The velocity of Alice's slanted line should be .8824c relative to the Earth timeframe so the blue t-axis is used. t=10-3.2=6.8 and x=6ly so v=6/6.8 = .8824. Correct.

5. Yv for v=.8824c relative to the Earth frame is 2.125*.8824c = 1.875c. The blue numbers on Alice's slanted line represent t'. So total t' for the slanted line is 6.4-3.2=3.2. x=6ly So Yv=6/3.2= 1.875. Correct.

6. The red numbers on Bob's slanted line are multiplied by Y = 1.25 to get the blue numbers on the t-axis. Similarly, the red numbers on Alice's slanted line (minus the offset of red 4) are multiplied by Y=2.125 and then added to the offset of 4 to arrive at the numbers on the red t-axis. So take the red 5 on the slanted line and subtract 4 which leaves 1. 1*2.125= 2.125. Add 4 and you get 6.125 on the red t-axis. Correct.

[ralfcis]

I can't post on the physics forum but here's a question that will test who really knows relativity in the "community". It's the classic handoff of clock info example where Alice leaves bob at .6c and charlie is approaching Bob from distant space at .6c. Where Alice crosses Charlie at 3ly, she hands off her clock info to Charlie so what does that clock info indicate when Charlie reaches Bob. Ignoring all the blah blah blah of spacetime path and clock sync problems that are just obstructionist smoke and mirrors to obscure the main point of this problem, you should get the answer that the info Charlie's clock carries indicates it has aged 2 yrs less than Bob's clock. Charlie and Alice have not broken constant relative velocity so they have aged the same as Bob. If Charlie had 2 clocks and only 1 was reset by Alice's passing, Charlie would have two atomic clocks with different readings on the same ship when he met Bob. Only 1 of the clocks in the same frame aged less.

To avoid all the usual smoke and mirrors, you can use the following STD.

Charlie is the red line and he has two clocks Only 1 is reset by Alice (the green line) when he crosses her path. We know when Charlie crosses Bob, One clock will indicate Charlie has aged 2 yrs less than Bob but what will the other indicate. I haven't worked it out yet but I will sometime in the future. The point will be, what if Alice had crossed at a velocity other than .6c meaning the crossing point was not at 0 relative velocity to Bob. Would this mean relativity would prohibit establishing an age difference because the 0v frame was not reached. I say no.

[ralfcis]

Oops I may have forgotten one very important point, when Charlie crosses Bob that is an instantaneous present with zero distance separation. Hence, even if Charlie did start at the same age as Bob in distant space and kept constant relative motion, age difference might come out at the crossover point due to the separation of bob and charlie at the start. Let's see what result the STD comes up with.