## Ralfativity 3.0 The cause of age difference

This is not an everything goes forum, but rather a place to ask questions and request help for developing your ideas.

### Re: Ralfativity 3.0 The cause of age difference

In the above STD, the white lines angling slightly diagonally upward from the bottom to the top are, respectively, the world lines of (left to right) Bob, Alice, and some guy off the street. As you can see, these lines are instantaneously co-located in the permanent Now but permanently separated in the temporary eternal hereafter. Light signals are indicated by thick, weblike gray lines between the world lines because the lights weren’t working properly due to light-cone malfunction. The black stuff is where I forgot to do the math and I just put in the russet-gold blobs because they look kind of pretty. Anyway, it’s as clear as a bell now. When Bob is three years old in Alice’s frame, then Alice is nineteen years old in Bob’s frame unless some guy off the street is in constant relative motion with respect to gamma, who is at rest because he is lazy and has fallen asleep, and in that case, Bob is ten years old and Alice is dead.

The revised Homer transform is now given as =9/5c2(tœ-µ)/+∂ƒ∆= Notice that nowhere in this STD is any length contraction seen, unless Bob loses his boner for Alice, and in that case Viagra is prescribed.
davidm
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### Re: Ralfativity 3.0 The cause of age difference

I think you may be getting STD's finally.
ralfcis
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### Re: Ralfativity 3.0 The cause of age difference

Nice double entendre!
davidm
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### Re: Ralfativity 3.0 The cause of age difference

At last someone has made sense of a Jackson Pollock!

When I saw the Pollock, I wondered if it was a Poisson distribution. (attempting nerdy bilingual pun)

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### Re: Ralfativity 3.0 The cause of age difference

Funniest post ever.

But let's crunch some numbers here:

Because the speed of message delivery is irrelevant in the instantaneous present, a message that takes 4 yrs from one perspective and 12 from another, arrives simultaneously when both clocks read 9 proper time. Even if you depict Bob as the moving frame in the relativistic way and his message now takes 12 yrs to get to him, both he and Alice remain 9 in the instantaneous present when the message arrives.

They're also both 9 in the delayed present from the half speed perspective between them.

From Bob's perspective, they're both 5 in the delayed present if you take into account part of Alice's age is tied up in the distance she's away from Bob. 52=32+42.

From Alice's perspective, they're both 3 in the delayed present by the same formula: t2=t'2+x2.
32=1.82+2.42. (The distance she is away from Bob when her timeline says 1.8 is 2.4 ly from the STD).

Everything is consistent and checks out. This is a new way to define simultaneity from 3 different perspectives and 2 types of present.

What's also interesting is how the doppler shift ratio can normalize the length of the light lines. The doppler shift ratio is 1/3 at .8c and 1 at 0c. So the 12 yr long yellow line can be made equal to the 4 yr long pink line by multiplying it by 1/3. I don't yet see how this fits yet into simultaneity. The formula for doppler shift ratio is c/(Y(c-v)) where v is signed.
ralfcis
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### Re: Ralfativity 3.0 The cause of age difference

These new concepts open up solving problems relativity won't touch because they violate the rules of spacetime paths. For example:

Alice and Bob were born on 2 different planets 3 ly apart. They could tell by their mutual doppler shift that their relative velocity was 0c. They also sent light signals to each other to establish their ages before the start apart. To do this they only need to send 2 light signals to each other without any knowledge of their distance apart or how long the light signals took to propagate. They do know by the doppler shift what their relative velocity is and it doesn't need to be 0c but for this example it is. But remember, starting off with a relative velocity does not cause age difference, a change in velocity by one of the participants is required.

In this example they can determine that they start off at the same age at 0c. According to the formula t2=t'2+(x/c)2. They may look the same age but there is a hidden trap door for either one thinking of making a change in velocity. Their apparent ages can be affected by relative velocity to make t' smaller than t. What the velocity takes away from t', it stores into distance as x=c*sqrt(t2-t'2).

So if either Alice or Bob change velocity, that time locked away in their mutual separation will be permanently subtracted from the age of the initiator of the change. The other will not lose his time because he ended up traveling no distance.

That's right, time is stored as space. It's like time is a beaker of information and it gets poured into the beaker of space by velocity and gets stored and separated from the time beaker for both parties engaged in constant relative velocity. But the pouring doesn't become permanent until a change in velocity is made and the info that a change has been made reaches the other party. Once that happens, the non-initiators space beaker contents get poured back into his time beaker.

I'm not making this up, I'm just following what the math tells me.

Relativity has different rules. I don't believe relativity recognizes a start apart as a valid start to a spacetime path. Also, if Bob or Alice change direction that takes them further away from each other, relativity does not consider this a valid end to a spacetime path. Ralfativity doesn't use spacetime paths or even spacetime as space is invariant and separate from time (even though time can be stored as space).

PS Einstein made an assumption that the constancy of the speed of light from every perspective may necessitate both time dilation and length contraction. I'm proving this is not the only possible assumption and therefore not a valid conclusion, it's still only a hypothesis.
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### Re: Ralfativity in a nutshell

Ralfativity in a nutshell

1. The universe's structure and purpose is data processing.
2. Mathematics, particularly geometry, provides the rules for processing the data.
3. The data it processes is time. All events are timestamped.
4. The storage of that data is space. The more events timestamped, the more space is required to store them.
5. Gravity compresses the stored data to prevent space from expanding too rapidly.
6. Physical reality is the result of this data processing.
7. Energy is the physical manifestation of time and matter of gravity on space. Space is a substance with its own physical properties.
8. Data flow is limited by c. This causes causality.
9. Limited c also causes 2 realities or presents. We live in a c delayed present propagating from an instantaneous present we can only post-process from our delayed present vantage point.
10. Everything moves at a combined (velocity through time and velocity through space) rate of c.
11 .Time passes at the universal rate of c through time which is the normal rate of time flow for everyone stationary within a frame.
12. Those who move relative to you are in different frames. Relative velocity subtracts time rate from both perspectives of relative velocity and stores it into space as what we measure as distance.
13. The delay of c causes an information imbalance in relative velocity if one of the participants changes it. This imbalance causes the time stored as distance to be permanently removed from the time passage (age) of the initiator of the change relative to the other participant upon his reception of the change.
14. There is no length contraction, space is invariant, therefore there is no combined spacetime nor any need for it to explain constant c from all perspectives. If length contraction doesn't physically exist, then the physical results ascribed to it must have different explanations. However, space and time can be converted into one another just like matter and energy.
15. Time contraction has replaced length contraction for everything length contraction once explained. Time contraction is the time dilated perspective of another frame time dilated again through that frame's perspective of the original frame.
16. Time dilation, doppler shift ratio and age difference are not the same thing. For example, each leg of Alice's roundtrip at .6c has the same time dilation t=1.25t' but not the same doppler shift ratio (1/2 on outbound and 2 on inbound). A 2 on the inbound will look like the time rate of flow in the other frame is 2c and the outbound will show internal movement at half the normal time rate. This is caused by perspective and is not real. Age difference is only accumulated during the c delay time after a change in velocity during part of the inbound leg and not the outbound. It is not the sum of the time dilation.
17. There are now 3 types of simultaneity. The delayed simultaneity from each frame's perspective compensates the reciprocal time dilated readings with the aging that's stored in the distance between participants. The conversion formula is t2=t'2+(x/c)2.
18. There is now an instantaneous simultaneity independent from perspective where age lines connect the proper times within frames.
19. There is now a delayed simultaneity from the perspective of a common half speed frame between the two participants that gives the same results as the instantaneous simultaneity.
20. Ralfativity's method of determining age difference can calculate scenarios that relativity prohibits because of its spacetime path rules.
21. Ralfativity's method of determining age difference can calculate age difference before the end of a spacetime path.
22. Acceleration does not cause age difference nor does acceleration's equivalence to gravity from general relativity.
23. A pesky rule must be made to prevent multiple consecutive changes in velocity from being depicted on the same STD otherwise a scenario arises where the future can erase past established age difference. I believe the same rule applies to relativity.
24. The synchronized clock method in relativity has been replaced by distance markers in a pre-agreed reference frame and dependence on the universal accuracy of atomic clocks.
25. The Minkowski coordinate transform has been replaced by a simple coordinate rotation. So all the transform formulas in relativity have been changed.
26. Age difference can only be established upon co-location of information. Co-location of participants is irrelevant.
28. There is nothing special about the 0c relative velocity frame. It is a constant relative velocity inertial frame like any other. It has no magical properties except it makes the arithmetic simpler.
29. Ralfativity may not be able to define how age difference unfurls during the information imbalance but if you look at how relativity implies it, at least ralfativity is consistent that it's not dependent on perspective.
30. Velocity v is limited to c but v' (Yv) is not because v' uses mixed perspectives of dilated time and proper distance. v'=x/t'. v' is not subject to the rules of v because it's not v.
ralfcis
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### Re: Ralfativity 3.0 The cause of age difference

Dave I still think you're stuck on my claim that length contraction is irrelevant. Here's a video where Greene only uses length contraction and you're assuming this is the only way it can be done because that's the only way Greene is doing it. How'bout I show you doing the same calculation using only time dilation.

Let's calculate from our perspective how much time the muon needs to traverse 5.9km.

v=x/t
v=.994c which in km is .994 * 3*105 km/s

so t=1.98*10-5s from our perspective

The muon's time from the muon's perspective is 2.2*10-6s which is 9 times too short.

But how do you convert from t' to t? You multiply t' by Y which is 9.14 and you get 2.01*10-5s.

So from our perspective the muon only needs 1.98*-5s but it actually has, due to time dilation of his time from our perspective 0f 2.01*10-5s. Just barely more than enough to make the journey.

You can also solve the problem by using v'. v'=x/t' = 9.08c as Greene correctly calculated but completely missed the point that he was calculating v' and not v.

9.08c in km/s is 9.08*3*105 = 272 km/s = x/t' =x/2.2*10-5

Solving for x, the muon can traverse 5.99 km when all it needs to traverse is 5.9km so it does make it to earth.

Where do you see the necessity for length contraction? I hope you're not overpowered by numbers with exponents. Do you want me to replace them with decimal places?
Last edited by ralfcis on October 18th, 2018, 8:08 pm, edited 1 time in total.
ralfcis
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### Re: Ralfativity 3.0 The cause of age difference

I'm just bringing in this post from the physics forum for completeness. I'd like burtjordaan to verify please.

I'm seeing a lot of confusion about the terms reciprocal time dilation, permanent age difference (as shown in the twin paradox) and doppler shift ratio. If Jorrie could just verify the example and interpretation I give here as correct.

This is the STD of the clock handoff of Alice's clock information speeding away from earth at .6c (in red) to Charlie (in green) speeding toward earth at .5c. The pink signals are light signals Bob receives and the yellow are ones he transmits.

As long as constant relative velocity is maintained between participants, their clocks as seen from each others perspective are reciprocally dilating wrt one another but there is no permanent age difference occurring between them; they age at the same rate even though each one swears the other is aging slower than they.

So neither Alice or Charlie will show a permanent age difference with respect to Bob. The reason is Alice never closes her spacetime path with Bob and Charlie never starts it. There are rules in relativity in what constitutes valid starts and ends to spacetime paths. Even though Charlie and Bob co-locate, there is no age difference established between them. Even though Charlie has sync'd his clock to Alice's at the handoff and the reading on his clock says that Alice's clock reading has permanently aged 2 yrs less than Bob's when Charlie and Bob co-locate, Alice herself has not aged 2 yrs less than Bob. No acceleration has been involved in causing the age difference on Charlie's clock once co-located with Bob.

If Alice, Charlie and Bob had televised their entire trip and continually transmitted their tv signals out into space, Alice would see Bob's motion picture going at half speed slow motion. Bob would reciprocally see Alice moving in half speed slow motion. Bob would see Charlie going at 2x fast forward and Charlie would see Bob also moving at 2x fast forward normal rate of time. If c is the normal rate of time flow within a frame, Bob and Charlie would apparently see time flow in the others frame at 2c. This is an appearance as there can be no speed greater than c through either time or space.

This is the doppler shift ratio, not reciprocal time dilation. The reciprocal time dilation is .8 the time of earth's clock for both Charlie and Alice from Bob's perspective and also .8 of Charlie and Alice's clocks for Bob's clock from Charlie and Alice's perspectives.

Please confirm as I myself can't convince anyone of these facts.

P.S. Also a quick side question. Are multiple spacetime paths that feed each other in sequence allowed to be depicted on a single STD. I found when this happens, subsequent spacetime paths can erase a permanent age difference as if it never occurred.
ralfcis
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### Re: Ralfativity 3.0 The cause of age difference

Ralf, I'm definitely not willing to be dragged into this again, but yes, what you wrote is essentially correct. You are using some terms that may be misinterpreted, like "permanent age difference", which as you use it, is more precisely "the difference in elapsed proper time between two observers present at the same two events". The difference accrues when the two observers follow quantitatively different spacetime paths between the two events. "Absolute aging difference" would be a better popular contraction of the more precise definition, with "absolute" meaning 'coordinate choice independent'.

Note that this implies that the two observers must meet at least twice and directly compare identical clocks.

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### How to depict the Muon example in STD's

This is a great exercise to help people become less terrified of STD's.

The two axes of an STD are usually expressed in yrs and light years (c=1ly/yr) but they can also be expressed in nano seconds and ft as in c=1ft/ns. But what scales would we use to depict the numbers we have in our muon example?

1.x=5.9km
How many light yrs is 5.9km?
google 1 light year =9.461*1012 km and
x=.623*10-12ly

2. t=1.98*10-5s
what is the result for t in yrs?
t=.627*10-12yr

3. t'=2.2*10-6s
what is the result for t' in yrs?
t'=.069*10-12yr

4. t' converted to t =2.01*10-5s = .637*10-12yr

5. 5.99km = .633*10-12ly

So we can draw the std scales in nano yrs vs nano light years

The perspective is from the upper atmosphere to earth which can be deemed the stationary frames and the muon is moving at .994c. Notice the inverse slope can be either expressed as v =.623/.627 =.994c or v'=.623/.069=9.08c.

Here is another way to draw it using the earth perspective:

ralfcis
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### Re: Ralfativity 3.0 The cause of age difference

BurtJordaan Thanks Jorrie. Too bad I used up all my favors on the previous versions of ralfativity. My tenacity could be viewed as insane. 3.0 is finally correct and I wouldn't have gotten here without all your years of help. You taught me the correct way to interpret relativistic phenomena and I've incorporated them into ralfativity 3.0. Biv said he'd review it. I can't see any errors but it is significantly different from relativity and from ralfativity's previous versions as listed in my summary (which makes no sense unless the theory is read).
ralfcis
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### Re: Ralfativity 3.0 The cause of age difference

The off-topic banter was amusing but I had to trim most of it out, including mine. I hope members view such posts as ephemeral. DK if I can really comment on each of the 30 postulates. Some require a fairly lengthy examination of some unusual uses of terminology. For now, I must bow out.

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### Re: Ralfativity 3.0 The cause of age difference

I see posting the summary was a huge mistake because all the explanations are in the posts which you were going to read before the summary was posted. I shot myself in the foot. Now I have no possibility of an Eddington.
ralfcis
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### Re: Ralfativity 3.0 The cause of age difference

I think I need to clarify my position. The 30 postulates in my summary are not all postulates, some are possible conclusions arising from the postulates. I have no dispute with the facts of relativity but I do have a different explanation of the cause of those facts. Hence, I have a dispute with the theory of relativity (specifically on the cause of age difference from the twin paradox).

It's difficult to separate the conclusions from the assumptions which is important in avoiding circular arguments which relativity uses a lot. For example, length contraction is an assumption to explain the constancy of the speed of light. The speed of light is constant for all frames hence length contraction must be the only possible explanation of that. Hence, any other possible explanations must be false. That's the type of logic I'm up against.

I have also proved there is no need for length contraction to explain any of the facts of relativity. Therefore it is part of the theory and not part of the facts. It is an assumption but ralfativity has another assumption that also supports the facts of relativity. If it is not a fact of relativity then it cannot be used as a fact for other fields. The fact might arise out of those fields but that has nothing to do with it being a fact of relativity which I've shown it is not. Please prove otherwise.
ralfcis
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### Re: Ralfativity 3.0 The cause of age difference

There are no circular arguments in relativity.

Length contraction and time dilation are not "assumptions" of the constancy of c. Rather, they are entailments of it.
davidm
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### Re: Ralfativity 3.0 The cause of age difference

Whatever Dave, you never claim responsibility for your other erroneous statements so how can we even have an honest discussion?

Both the clock sync and length contraction theories are circular arguments. God created the universe and the universe exists therefore god exists. Same reasoning. Your mind is made up and you don't want to consider the counter arguments nor can you counter those counter arguments except by citing relativistic scripture.
ralfcis
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### Re: Ralfativity 3.0 The cause of age difference

It isn't the same reasoning, and I've made no erroneous statements.

If c is constant, as it is, then time dilation and length contraction, along with relative simultaneity, are entailed. That is not a circular statement.

But according to you, you have overturned all this, so why are you posting it here? Why don't you take it the broader scientific community?
davidm
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### Re: Ralfativity 3.0 The cause of age difference

"God created the universe" is not a fact, it's an assumption. That c is constant, is not an assumption, but a fact. And from this fact time dilation, length contraction and relative simultaneity automatically follow.

Anyway, I'm done with your BS. Have a good time!
davidm
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### Re: Ralfativity 3.0 The cause of age difference

Ok, since no one here can muster a mathematical counter argument supporting length contraction, I'm gonna have to do it for you. Here is an STD using the Minkowski frame moving at .6c. (red line time dilated). The numbered black line is the x'-axis which is length contracted. The stationary frame is in regular cartesian coordinates.

So within Bob's own perspective, he's not moving but he is aging. What is the velocity of light within his perspective. You draw a blue line from t=2 and the corresponding x=2 so the slope =1 which is c. So c is going at c from his perspective.

Alice is also not moving from her own perspective. Using her Minkowski coordinates, she also sees t'=2 and x'=2 so c is c within her frame.

Because Alice and Bob use the same line to depict c, this is supposed to depict that From Alice's perspective of c in Bob's frame, it's also c from her perspective and vice versa. In the Ralfski frame rotation there were be 2 lines for c. Alice would see Bob's c as much slower than hers and he would see hers as much faster than his.

So how do I get around this inconvenience of the depiction of c in order to get rid of the inconvenience of the depiction of length contraction?

Look closer at the compromise relativity makes. You'll notice that Bob's perspective of Alice at t'=2 shows light travels 4 Bob light yrs in 4 Bob yrs but Alice's perspective of Bob at t=2 shows light travels 2 Bob ly in 2 Bob yrs. Yes the slope of c is the same but light takes twice as long to travel twice as far from Bob's perspective of Alice than vice versa. Twice is significant because it is the doppler shift ratio at .6c.

Let's show what is really happens when Alice sends a yellow light signal in her own frame.

The time between the blue lines is 1 Bob yr. Alice's yellow light signal moves 1 Bob yr/ ly. Using a grid (3 black lines) that correlates to the light line, you see that grid intersects where the blue and yellow lines intersect but also intersects Alice's timeline unit spacing. Those 3 lines also intersect Bob's t-axis to show the doppler shift ratio of 2 between Bob's yrs and Alice's. The light grid lines tie Alice yrs to Bob yrs to the constancy of speed of light.

Let's see how this works for 8c:

Works the same since the doppler shift ratio is 3. The doppler shift ratio is used to normalize the depiction of the length of the light lines for every relative velocity and it allows the slope of c to remain 45o in all depictions without having c rotate with the coordinate rotation.

Is this clear to anyone? Could someone explain it back to me?

It's just way easier to understand that in Alice's frame her speed is v' =Yv=x/t' and that this doesn't violate v<c.

P.S. Another classic support of length contraction comes from the Michelson Morley experiment where the constancy of the speed of light is explained by the length contraction of one of the arms of the inferometer. This is just as validly explained using time dilation to compensate for the movement of the earth to keep c at c. Does anyone want me to go through that exercise?
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### Re: Ralfativity 3.0 The cause of age difference

Well look at this interesting piece of mathematical origami. It looks like the x'-axis in Minkowski's relativity can be made from Ralfski's coordinate rotation folded back on itself along the x-axis. Here's the proof for both .6c and .8c. So there goes any hope for anyone believing length contraction isn't a mathematical slight of hand of a simple coordinate rotation:

Is there anyone out there who can see this? This is the last piece of the puzzle I didn't understand the significance of and it turns out to be the stake through the heart of relativity. Relativity has been claiming only 1 c line for all frames when in fact it's been hiding its two c lines one on top of the other with the only clue being one was longer than the other. Counter arguments please, as if there are any.
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### Re: Ralfativity 3.0 The cause of age difference

Still crickets. Dave was right, it's time for me to move the dealership and peddle my wares elsewhere. What physics forum did Don Lincoln move to to get more eyes?
ralfcis
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### Re: Ralfativity 3.0 The cause of age difference

Oh crap, I made a mistake in my interpretation of the above STD. While I try to find a way to correct it, I would be very impressed if someone here could identify the mistake. It should be easy to spot for any one of the math geniuses here. I don't think that's even remotely possible.
ralfcis
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### Re: Ralfativity 3.0 The cause of age difference

ralfcis » October 22nd, 2018, 5:20 am wrote:Still crickets. Dave was right, it's time for me to move the dealership and peddle my wares elsewhere. What physics forum did Don Lincoln move to to get more eyes?

The admins and mods here have been predominantly life sciences and earth sciences with a couple of physics oriented folk like Jorrie and the late great Marshall. I wish we had more expertise, but these days you might do better at some place like...

https://www.physicsforums.com

I know a little physics (picked up along the way as a biology major, and from a bit of auditing in grad school), but my explorations have been more in GR than SR. But right now, Jorrie, and perhaps Faradave, are most likely to have a solid grasp on what you need to advance. And their interests are currently elsewhere. Good luck, wherever your journey takes you.

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### Re: Ralfativity 3.0 The cause of age difference

Is that where Lincoln went to because they won't even entertain personal theories. I was kicked off there years ago and permanently banned after a few minutes. I have no credentials and the discussions always degenerate into relativity 101 and assumptions that what I'm saying is due to ignorance and amateurism. Arguing with people is the only way I can get the kinks out and until I get all the kinks out, I can't play with the big boys yet. I'm worried I'm headed for a brick wall with the 4-vector math and tensors in GR. There is space contraction in GR, and since SR is a special case of GR, maybe length contraction and space contraction are related. If they are, that would be an insurmountable obstacle for me to get rid of it from SR unless I can get rid of it from GR also. I don't believe that's possible to do. My theory can survive that but it would lose a lot of its significance.

P.S. I wasn't aware of Marshall. Is he dead or did he also move on to a forum with more eyes?
Last edited by ralfcis on October 22nd, 2018, 6:49 pm, edited 4 times in total.
ralfcis
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### Re: Ralfativity 3.0 The cause of age difference

ralfcis » October 22nd, 2018, 4:17 pm wrote:... maybe length contraction and space contraction are related.

Edited to add: Did you mean that length contraction and time dilation are related? If so, yes.
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### Re: Ralfativity 3.0 The cause of age difference

See what I mean?
ralfcis
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### Re: Ralfativity 3.0 The cause of age difference

davidm
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### Re: Ralfativity 3.0 The cause of age difference

Ok problem solved and here are the STD's that explain the solution:

I'll supply the words tomorrow.
ralfcis
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### Re: Ralfativity 3.0 The cause of age difference

Ok here we go. This is going to be extremely painful to explain so let's start slowly with relativity's point of view.

Here is light speed from Bob's perspective. In relativity, there are no units for light but I'm going to introduce them anyway. From Bob's perspective, light travels one of his distance units (a Bob light year) in one of his time units (a Bob year).

Now we add Alice's Minkowski coordinate frame at 6c.

In relativity, Alice's coordinates are not square cartesian but rhombic Minkowski. At first glance it looks like both frames share the same light line. Alice's perspective of the light line in her frame is she travels one of her distance units (an Alice light year) in one of her time units (an Alice year). But hold on, Alice's perspective of the light line is it travels 2 Bob light years in one Alice year.

An Alice year from Bob's perspective is 1.25 Bob years. An Alice year is also .8 Bob yrs from Alice's perspective.

Which means from Bob's perspective of the speed of light through Alice's frame using Bob's units is 2 Bob ly/1.25 Bob yrs =1.6c.

Bob's perspective of the speed of light through Bob's frame using Bob's units is only 1 Bob ly/1 Bob yr = 1c.

Alice's perspective of the speed of light through Alice's frame using Alice units is 1 Alice ly/1 Alice yr = 1c.

Alice's perspective of the speed of light through Alice's frame using Bob units is 1.25 Bob ly/1.25 Bob yr = 1c.

Alice's perspective of the speed of light through Bob's frame using Bob units is 2 Bob ly/.8 Bob yr = 2.5c.

The permutations of perspective, mixed perspective and units go on and on. What's important here is if you consider each frame as independent, there is no confusion that each one sees his velocity through space is 0c, his velocity through time is 1c and the velocity of light through his space is 1c (light has no velocity through time, it's all through space). All the difficult interpretation happens when 1 frame tries to include another frame into his perspective of his own frame.

So now we're going to use ralfativity to clear things up. First, the formula for light units is:

c'=Rc where R is the doppler shift ratio (2 @.6c, 3 @.8c).

c' is the velocity of light Bob sees from his perspective through Alice's frame using her time units t' and Bob's space units x.

Here's an example:

In it Alice travels 3 Bob light years to some planet in 4 of her years. How long did it take light from her starting point on earth to reach the same planet from Bob's perspective through her frame using her units t' and Bob's space units x?

Bob's space units = 3 Bob ly purple line
Her time units in her frame = 1.5 Alice yrs green line
So c' in this mixed perspective = 2c

In ralfativity Alice travels at v' which is Yv which is x/t'. Bob's perspective of her is .75c and light being no different than any other velocity, he sees c at c' which is 2c. All this is because of the pre-agreed distance markers that were set up around earth's stationary reference frame.

There's a difference between reality and perspective in ralfativity, that distinction is not made in relativity. This is the reality Bob sees from his perspective:

When Alice reaches the planet, she has aged 4 yrs through time (which appears on her clock readout) and 1 year through space for a total ralfativistic age of 5. Bob has also aged 5 years in the instantaneous present when Alice touches the planet. Since it's his perspective and he hasn't moved, the clock readout on his clock is all age, none is lost to distance.

From Bob's relativistic perspective, light would take 3 Bob yrs to travel that distance (3 Bob ly) and Alice 5 Bob yrs at .6c. From Bob's ralfativistic perspective, light only takes 1.5 Alice years to travel 3 Bob ly and Alice 4 Alice years at .75 c. The distances inside Alice's ship are the same distances outside her ship. Space is invariant in ralfativity and v' and c' are not subject to the rules of v and c.

I figure it'll take about 20 re-reads before the questions stop about why my knobs max out at 10 and relativity's are set to 11. An intelligent question would be how ralfativity handles the train and the train station example if the train doesn't length contract from the station's perspective (and vice versa). Nessun dorma!
ralfcis
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