Ralfativity 2.0

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Re: Ralfativity 2.0

Postby phyti on January 13th, 2018, 2:01 pm 

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.
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Re: Ralfativity 2.0

Postby ralfcis on January 13th, 2018, 4:23 pm 

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.

6c15.jpg


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.
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Re: Ralfativity 2.0

Postby ralfcis on January 13th, 2018, 5:30 pm 

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.
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Re: Ralfativity 2.0

Postby ralfcis on January 14th, 2018, 6:38 pm 

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

6c20.jpg


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.
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Re: Ralfativity 2.0

Postby phyti on January 16th, 2018, 1:08 pm 

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.
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Re: Ralfativity 2.0

Postby ralfcis on January 17th, 2018, 4:37 pm 

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.
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Re: Ralfativity 2.0

Postby ralfcis on January 17th, 2018, 10:43 pm 

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:

6c25.jpg


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:

6c30.jpg


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.

6c31jpg.jpg


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.
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Re: Ralfativity 2.0

Postby ralfcis on January 18th, 2018, 9:56 am 

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

6c32.jpg


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.
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