Ralfativity Pt 5: The Cause of Age Difference

P.S. Interesting to note that the slope of the orange lines of instantaneous present of .2 indicates Bob and Alice travel with a hidden intermediate relative velocity of 5/13 c during the delay of info period.

Here is an STD that explains all the misconceptions people have about relativity:

It is a stationary depiction (not to be confused with a stationary perspective) of Bob waiting 4 years before he takes off to catch Alice at .8824c relative to earth (which is .6c relative to Alice). Since Bob is the one who changed the relative velocity between them, he will be the one who ages 2 yrs less than Alice.

Nearly all people confuse this STD with the following one (taken right from Jorrie's book, Relativity 4 Engineers):

Even though I've highlighted the differences between the two STD's, there's no way a relativist will be able to see them. The top one is Bob taking off from earth to meet Alice and causing age difference. The bottom one is the stationary depiction of Alice taking off from an empty patch of space to meet Bob. It is supposedly the reverse analysis where Bob is now the moving perspective and Alice is the stationary. I've debunked all this nonsense in pt 3 but it gets even worse if you look closer at how the age difference unfurls. (Most relativists are also blind to the difference between reciprocal time dilation and permanent age difference and there's just no way, I've found, to get them to understand.)

In the bottom STD, it looks like since Bob is "moving", he is ageing less than Alice for the first 4 years. Then Alice's catch up speed allows her to re-establish that the two depictions of Bob stationary and then Alice as stationary are equivalent because Alice ends up 2 yrs younger than Bob.

But they are not equivalent at all if you confuse reciprocal time dilation with age difference (no one is ageing less than the other during the reciprocal time dilation of constant relative velocity). With Bob stationary it looks like Alice moving is always ageing less than Bob but with Alice stationary, Bob looks to be ageing less than Alice at first.

This contradiction is due to relativity's sloppy definition of terms (like time dilation, ageing, present, reality, perspective, depiction, time) and then trying to cover up that sloppiness by saying you are forbidden from trying to determine how age difference unfurls, only the end result counts. Relativity tries to cover up that changing perspective doesn't yield the same age difference results during progression. A theory is falsifiable not only by the things it predicts wrong but also by the things it cannot predict right. How age difference progresses is what relativity can't predict right.

Here is the STD for .6c with its half velocity of .33c and the purple lines of instantaneous present between Bob and Alice showing they are the same age on their proper time on-board clocks. The green .33c half velocity lines of simultaneity share the same slope as the purple lines and depict that, from this .33c perspective, Alice and Bob age the same. This delayed perspective affords a window into the hidden instantaneous present.

Also on this STD are the blue lines of simultaneity from Bob's perspective and the red ones from Alice's perspective. All this STD shows are 4 types of lines of simultaneity between 2 frames depicted in a Minkowski format at a single relative velocity of .6c.

But what would we get if we plotted an STD of the instantaneous simultaneity at t=1 and t=2 for all constant relative velocities. The instantaneous present lines of simultaneity would plot out the hyperbolic lines of relativity's time-like interval. The light-like interval, the line c, is made up of separate overlapping lines, all of the same slope, for each relative velocity. More on this later.

So there are many versions of instantaneous present depending on relative velocity. Therefore this instantaneous present is not the same thing as the Newtonian universal present.

The following STD is redrawn from the top of this thread to show how age progresses after the time a change in relative velocity is made. At t'=4, Alice returns to Bob at .8c. The lines of instantaneous present get pretty deformed. No lines of perspective simultaneity are drawn because they are irrelevant to the progression of age difference. It all happens in the unseen instantaneous present (which relativity doesn't recognize).

The change Alice makes at t'=4 doesn't reach Bob until t=8. So up until that time, Bob's purple lines of instantaneous present remain fixed on Alice's initial relative velocity of .6c. Bob thinks Alice is still ageing at the same rate as he is.

But Alice, in the instantaneous present is ageing less than Bob. So she draws new light green lines of present between her time at her new speed and the time she would have been seeing at her old speed. The time difference between the old instantaneous present and the new, will allow Bob to see how much less Alice aged for every Bob year until he's informed of her velocity change at t=8.

From the blue bars which represent the age difference, we can see Alice aged .625 yrs less per Bob year. Bob can redraw his old purple lines to the new brown lines correlating his proper time to Alice's proper time in the new instantaneous present. In constant relative velocity, the times will read the same but during age difference propagation, the times reflect the difference between their ageing.

At t=8, Alice will have lost a total of 2.5 Bob years so she will only be 5.5 Alice years at the instant Bob is notified of her relative velocity change. From that point on, Alice will remain 2.5 yrs less than Bob because after t=8, a new constant relative velocity of .8c approaching (the former one was .6c separating) has been established and no more age difference can accumulate.

Although the role of Bob or Alice's perspective simultaneity is irrelevant, the half speed perspective simultaneity is very useful for establishing the slopes of the instantaneous present lines. The green .33c perspective simultaneity has the same slope as the .6c instantaneous simultaneity. The aubergine .5c perspective simultaneity has the same slope as the .8c instantaneous simultaneity. The light green 5/13 c (which is the half speed between .6c and .8c) perspective simultaneity has the same slope as the instantaneous simultaneity between Alice at .6c and Alice at .8c.

The only way to see the pattern of this method is for me to do a lot of examples. There will be examples and results that relativity can't solve.

Here is an STD depicting how age difference unfurls for Alice making a slew of velocity changes after she has travelled 3ly at .6c. The method on how I arrived at this STD is not exactly the one I outlined above which needs a more in depth explanation and some corrections.

The important thing to note is how the final age difference can be established when the info reaches Bob, not when Bob and Alice re-unite. So ralfativity can predict it earlier than relativity can simply because there is no further age difference once Bob re-establishes a new relative velocity with Alice. The age difference result is where the half speed line of simultaneity from t=8 intersects the return velocity line. So, for example, The half speed line for .8c is .5c and its line of simultaneity (which has the same slope as the instantaneous line of simultaneity) intersects the .8c line at t'=5.5. So Alice has aged, in a smooth progression of -.625yrs/bob yr, 2.5 yrs less than Bob when he receives the info of her velocity change.

The other important thing to note is the STD makes predictions of age difference even if Alice slows down and doesn't come to a full stop which relativity says is impossible. This area is between Alice v=0 and v=.6c separating. The two velocities at .198c and 5/13 c separating where Alice will have aged .7 and .4 years respectively less than Bob when the news of Alice's change reaches him. Again, once the news of the change reaches Bob there will be no further accumulation of age difference because Bob has resync'd himself to the new constant relative velocity between him and Alice. This is what relativity truly says, not the stuff you've been hearing for the last 113 yrs.

The STD can be extended to take into account if Alice accelerates away from Bob and I'd have to do the calculations to verify what happens. There is nothing stopping the extension of the hyperbolas into this region.

Relativity is just pure mathematics and all the misinterpretations of it are due to ignoring what the math is saying and listening to what people are saying and I'm laying all the math out into the open so you can make your own decisions.

Ok the derivation of these age difference progression hyperbolas is just a tad more complex than I had initially explained. Instead of showing you the STD which is hard to read on this forum,

I'm just going into the algebraic derivation. The top hyperbola is easy to figure out because its points are formed by the intersections of the half speed lines of simultaneity with the velocity lines as described in the previous post. Now you want to calculate the age difference between what Bob thought Alice was at t=8 = t', and what he found out her age was when the news reached him at t=8 from t'=4. Bob is in the imbalanced relative velocity zone for 4 yrs. So you draw a horizontal blue line through t'=8 and you get the following values:

Alice returning at .9756c , she ages 2.4 yrs total less than Bob at .6yrs per bob yr.

Alice returning at .8824c , she ages 2.45 yrs total less than Bob at .61yrs per bob yr.

Alice returning at .8c , she ages 2.5 yrs total less than Bob at .62yrs per bob yr.

Alice returning at .6c , she ages 2.5 yrs total less than Bob at .62yrs per bob yr.

Alice returning at .3846c , she ages 2.4 yrs total less than Bob at .6yrs per bob yr.

Alice returning at .2c , she ages 2.25 yrs total less than Bob at .56yrs per bob yr.

Alice stopping , she ages 2 yrs total less than Bob at .5yrs per bob yr.

Alice leaving at .2c , she ages 1.6 yrs total less than Bob at .4yrs per bob yr.

Alice leaving at .3846c , she ages 1.1 yrs total less than Bob at .27yrs per bob yr.

Alice leaving at .6c , she ages 0 yrs total less than Bob at 0yrs per bob yr.

Alice leaving at .8c , haven't calculated it yet, I need more room on the STD. It'd be interesting if it turns out Bob will have aged less than Alice if her velocity change is an increase in separation speed.

I have refined the methodology of defining age difference mathematically.

First a definition of terms and numbers we'll be using:

Examples of "half speed" or "half" the relativistic velocity combination are:

.6c relative velocity is the relativistic velocity combination of two frames at .33c.
.8c relative velocity is the relativistic velocity combination of two frames at .5c.
.8824c relative velocity is the relativistic velocity combination of two frames at .6c.
.9756c relative velocity is the relativistic velocity combination of two frames at .8c.
.3846c. relative velocity is the relativistic velocity combination of two frames at .2c.
.2c relative velocity is the relativistic velocity combination of two frames at .1c.

The slopes of the lines of simultaneity x/t for each of these half speeds is the inverse of the slope of their velocity lines x/t so:

.33c half speed slope of simultaneity line is 3.
.5c half speed slope of simultaneity line is 2.
.6c half speed slope of simultaneity line is 5/3.
.8c half speed slope of simultaneity line is 5/4.
.2c half speed slope of simultaneity line is 5.
.1c half speed slope of simultaneity line is 10.

What's interesting to note is that the slope of the half speed perspective's lines of simultaneity intersect the same numerical values of proper times on the full relative velocity lines as shown in this spacetime diagram (STD):

The thin red line is .6c relative velocity depicted in a Minkowski STD. Alice red is depicted as moving and Bob blue is depicted as stationary when actually both are moving at .6c relative to each other. The horizontal blue lines are Bob's lines of simultaneity from his perspective and the thick red lines are Alice's lines of simultaneity from her perspective.

The thin green line is the half speed (.33c) of .6c. The slanted green lines are the half speed lines of simultaneity which happen to intersect Bob and Alice's proper on-board times. This gives us an indication that, from the half speed perspective, Alice and Bob are ageing at the same rate simultaneously. In fact relativity dictates that any constant relative velocity between two frames yields no age difference between the two participants Bob and Alice. Age difference being a permanent phenomenon is not the same thing as reciprocal time dilation which is due to perspective.

Now let's say Alice stops at the 3 ly mark. She sends a light signal to Bob informing him she has stopped. During the 3 yrs it takes for the light signal to reach Bob, his relative velocity to Alice remains at .6c and her relative velocity to Bob has changed to 0c. This imbalance in relative velocity is verified by the Doppler shift ratio between them. Alice sees a Doppler shift ratio of R=1 and Bob sees R=1/2 which correspond to v=0 and v=.6c respectively.

Upon receiving the news, Bob will be able to calculate Alice has permanently aged 1 yr less than Bob even though they never re-unite. They are separated by distance and separation has a time value associated with it just by the very fact it takes time to traverse a distance. (There is a mathematical formula for converting separation into a time value but I won't discuss it here.)

So let's calculate the age differences for various velocities for when Bob and Alice re-unite or co-locate in an instantaneous present (effects of the delay of the speed of light will be negligible between them). I know, I know, when do I get to the puzzle? I'm still laying the groundwork and setting up the parameters.

If you draw the STD, which I will show later, you get the following results for age difference due to co-location:

At .6c return, Alice's v line intersects Bob's at t=10 and t'=8 so the age diff is 2 yrs less for Alice.
At .8c return, Alice's v line intersects Bob's at t=8.75 and t'=6.25 so the age diff is 2.5 yrs less for Alice.
At .8824c return, Alice's v line intersects Bob's at t=8.4 and t'=5.6 so the age diff is 2.8 yrs less for Alice.
At .9756c return, Alice's v line intersects Bob's at t=8.075 and t'=4.675 so the age diff is 3.4 yrs less for Alice.

This method makes it very hard graphically to establish where the .3846c and .2c return velocities would intersect with Bob to establish their age difference. Well let's just use the way Alice establishes her age difference when she stops and can't co-locate with Bob, with the info contained in her light signal. It turns out this method employs where the half speed lines of simultaneity (green) intersect Alice's return velocity lines (red).

The green lines of simultaneity are labelled with their corresponding half speed velocities which of course have corresponding relative velocities between Bob and Alice.

.9756c (half speed .8c) has a simultaneity line slope of 5/4 and intersects the red v line at t'=4.6. 8-4.6=3.4
.8824c (half speed .6c) has a simultaneity line slope of 5/3 and intersects the red v line at t'=5.2. 8-5.2=2.8
.8c (half speed .5c) has a simultaneity line slope of 2/1 and intersects the red v line at t'=5.5. 8-5.5=2.5
.6c (half speed .33c) has a simultaneity line slope of 3/1 and intersects the red v line at t'=6. 8-6=2
.3846c (half speed .2c) has a simultaneity line slope of 5/1 and intersects the red v line at t'=6.4. 8-6.4=1.6
.2c (half speed .1c) has a simultaneity line slope of 10 and intersects the red v line at t'=6.7. 8-6.7=1.3

There's 1 more line of simultaneity to consider, but it's not for a returning velocity or even a stopped one, it's a separating velocity where Alice does not make a velocity change.

.6c (half speed .33c) has a simultaneity line slope of 3/1 and intersects the red v line at t'=8. 8-8=0 age difference.

So we see we got all the right answers plus 3 more right answers. But we can get so many more using this method. There are areas of this graph that seem incomplete. What happens if Alice just slows down a little when she makes her velocity change. What happens to the age difference if she speeds up? These questions are mathematically solvable, but does relativity allow them to be solvable? That's the puzzle.

Here's the STD with velocities where Alice slows down and doesn't stop or return.

We can see that separating velocities also yield results for age difference:

.2c (half speed .1c) has a simultaneity line slope of 10/1 and intersects the red v line at t'=7.3. 8-7.3=.7
.3846c (half speed .2c) has a simultaneity line slope of 5/1 and intersects the red v line at t'=7.6. 8-7.6=.4

Would anyone believe this nice clean hyperbolic line joining the points of intersection is some meaningless coincidence? If this method yields final age difference results, can it predict age difference results as they unfurl for each year Bob ages? (The answer is yes mathematically but what does relativity have to say about it? What happens if you extend the hyperbola to separating velocities of greater than .6c? Is that allowed under relativity? Here's the STD:

So if Alice accelerates to .8c away from Bob she will turn out 8-8.6=.6 yrs older than Bob.
And if Alice accelerates to .8824c away from Bob she will turn out 8-9=1 yr older than Bob at the time he gets her message that she is accelerating away.

It seems counter-intuitive that Alice is ageing faster than Bob yet is still covering vast distances in very little of her time. She has only aged faster than Bob for 4 Bob years but the rest of the time is ageing at the same rate as Bob while still travelling the common invariant space at Yv.

Does anyone have a problem with this because if you follow the current interpretation of relativity, you should.

Here is the STD showing the smooth progression of age difference between Bob and Alice for every Bob year in the transition period between constant relative velocities. The derivation of this STD uses the same relativistic tools outlined above. How would the classical relativistic method for determining age difference be able to achieve the same results? I'm just using 2 simple relativistic rules:

1. Age difference can't occur during constant relative motion which can be determined by matching rx and tx doppler shift ratios of broadcast clock readings. This leaves a window of time where age difference can occur. Bob and Alice do not continue ageing differently after that window is closed.

2. Since 1 is true, the window is not closed by co-location of the participants but by reception of delayed information about the change in relative velocity. The co-location of participants occurs outside the window of ageing difference so it irrelevant and only confirms the total age difference that had been established earlier.

Here's the total STD which includes Alice accelerating away from Bob at .8c and .8824c

I just discovered that on these diagrams you can click to enlarge. Sorry, I don't understand software or scripting commands to understand why.

You'll be forever known here as Ralphie, the guy with all the STD's....

I've been working on some monsters today. Too bad no one knows what they mean.