Relativity And Simple Algebra

Moronium · March 25, 2019

Why don't you two lovebirds set up a booth somewhere else.

Carry on with your numerology exercise, Ralf. See ya in a year, eh?

ralfcis · March 25, 2019

Ok, back to the math.

We're going to derive a formula for the Doppler shift ratio (DSR) because that is what determines Alice's age difference during the time of relative velocity imbalance.

As you can see from the table below, the cDSR = v_htfor v>0 and cDSR = 1/v_htfor v<0 (velocities where Alice returns to Bob). You can verify what I'm saying by using relativity's formula for DSR.

So let's begin:

We use v_t = 2c²v_ht / (c² + v_ht²), v = 2c²v_h / (c² + v_h²) and v = v_h(v_t/c +1) derived earlier to get

2c²v_h / (c² + v_h²) = v_h (2cv_ht + c² + v_ht²) / (c² + v_ht²)

2c⁴+ 2c²v_ht²= 2c³v_ht + c⁴+ c²v_ht²+ 2cv_ht v_h² +c²v_h²+ v_h² v_ht²

v_h²= (2c⁴ + 2c²v_ht²- 2c³v_ht - c⁴- c²v_ht²) / (2cv_ht +c² + v_ht² )

v_h² = c²(c² + v_ht² -2cv_ht) / (c + v_ht)²

vh = c (c - v_ht) / (c + v_ht)

v_ht = c(c-v_h)/(c+v_h)

DSR = (c-v_h)/(c+v_h) where v_h is negative for v returning

Relativity uses DSR = sqrt ((1-v/c) / (1+v/c)) where v is negative for v returning

I just noticed the derivation would have been just 1 line had I started with relativity's formula. That was dumb. I can hear the 3 brain tremors nodding in unison pretending they understand.

Here's a bigger table of whole number velocity fractions if you want to play with values in the formulas.

v c Y v_h c v_t c v_ht c DSR t'

1 1 1 0 0 0

3280/3281 3281/81 40/41 81/3281 1/81 81

40/41 41/9 4/5 9/41 4/36 9

255/257 65/16 15/17 16/65 1/8 8

24/25 25/7 3/4 7/25 1/7 7

35/37 37/12 5/7 12/37 6/36 6

12/13 13/5 2/3 5/13 1/5 5

77/85 85/36 77/121 36/85 8/36 9/2

15/17 17/8 3/5 8/17 9/36 4

4/5 5/3 1/2 3/5 12/36 3

3/5 5/4 1/3 4/5 18/36 2

1/2 1.155 .268 .866 .577 1.73

8/17 17/15 1/4 15/17 3/5 5/3

5/13 13/12 1/5 12/13 24/36 3/2

1/3 1.06 .17 .943 .707 1.41

12/37 37/35 1/6 35/37 5/7 7/5

7/25 1/7 24/25 27/36 4/3

16/65 1/8 255/257 15/17 17/15

9/41 1/9 40/41 4/5

0 0 1 1

Here are fractional velocity numbers that don't fit in the above table very close to c so you can see what finite number infinity is approaching.

v c v_h c v_t c v_ht c DSR t'

21523360/21523361 21523360/21529922 6561/21523361 1/6561

All these whole number fractions are derived from the pattern recognition exercise I did earlier otherwise the calculations would have been too unwieldly and inexact.

Edited December 26, 2019 by ralfcis

Amplituhedron · March 25, 2019

So don't bother reading

Bingo!

ralfcis · March 25, 2019

And yet, here you are again unable to follow your own advice.

Edited March 25, 2019 by ralfcis

ralfcis · March 26, 2019

I deleted the last post because there's no need for the table again, the math in this post is too self-evident to require the use of numerical values to get a feeling for it.

I was exploring what happens when Alice returns to Bob at near -c, where does the time go that doesn't appear on her watch and why do the results for light returning at -c differ from matter returning at -c. This is all within the domain that relativity allows the calculation of proper age difference so I can directly compare my results with relativity's.

I had derived a formula for calculating age difference at the intersection between the returning velocity line and the line of perspective simultaneity originating from the time the light informs Bob that Alice had made a change in relative velocity between them. Now literal thinkers interpret this as a message from the pony express changing reality when reality actually changes because the speed of reality is the speed of information which is limited to the speed of light. With literal thinkers, the gears don't run too smoothly upstairs and I'm not actually referring to gears or stairs when I say that.

The formula is t' = X(v_h+c)/c (v_h is negative for v<0) where X is the distance separation between them at the transition point and t' is the time of velocity change on the watch of the person changing the velocity. It's basically the time and place for the velocity change using Bob's space and Alice's time. (In my theory, there is no difference between Bob's space and Alice's space as there's no such thing as length contraction but we'll humor relativity for now.) In order to get the age difference between them, just subtract Bob's age from the intersection point t' along the v_h line.

Alice's speed before she changes direction back to Bob is only really important to how far she's able to separate from Bob and how long it took for her to get to the transition point. No age difference occurs before the transition point as they age at the same rate in proper time. Their perspective ages are just illusion of perspective. Relativity believes their perspective ages are real by its definition of reality. The age difference rate only exists during the time it takes for the reality of the transition to reach Bob. In proper simultaneity, Bob will be t=4 at the transition but from his perspective simultaneity he will be t=5 at the transition and 8 when the light travels 3 ly to reach him. For a .6c return, Alice will be t'=4 at the transition and t'=6 when the v_h line of proper simultaneity intersects her's and Bob's velocity lines when the light signal reaches Bob at t=8. So she will have aged 2 yrs less than Bob which agrees with how relativity calculates age difference at the intersection of Bob's and Alice's velocity lines.

But there are other formulas which calculate how much time disappears from Alice's watch in order to arrive at that age difference. In relativity's case, the time that evaporates is due to Alice being able to travel faster through time due to her accelerated frame relative to Bob's constant velocity frame. I'm not familiar with the GR math that can put numbers to that. My simpler math indicates that Alice at .6c return is travelling at 2c through time during the 2 yr relative velocity imbalance period between her and Bob. So she ages a total of 4 yrs of which only 2 appear on her watch and 2 just evaporate. At .8c return, Alice is travelling at 3c through time during the 1.5 yr relative velocity imbalance period between her and Bob. So she ages a total of 4.5 yrs of which only 1.5 appear on her watch and 3 just evaporate.

The Doppler shift ratio is what determines her velocity through time rate during the velocity imbalance period and the reason for that is when she re-syncs with Bob, he has no way of knowing she has been going through time at a much faster rate than he has during the imbalance period. Even if he had been able to see her Doppler shift ratio in instantaneous proper time, he would see nothing abnormal in her perspective Doppler shift ratio. They would both have a value of 2c but the perspective one is just an illusion while the proper one is really happening and causing permanent age difference with neither having the ability to detect it.

The formula for DSR has been derived earlier as DSR = (c-v_h)/(c+v_h) where v_h is negative for v returning or feel free to use relativity's version DSR = sqrt ((1-v/c) / (1+v/c)) where v is negative for v returning but I don't like the extra calculation of square roots when simple arithmetic will do.

The formula for total Alice ageing both visible and invisible = t'(DSR) while the visible age = t'.

So the formula for lost, evaporated, invisible age is t'(DSR - 1).

You can enter various velocities from the table I provided earlier to make you more comfortable with the concept but the value I want to concentrate on is Alice's return at near -c. DSR works out to infinity and t' works out to 0. Now people who don't know math say 0 times infinity equals 0. Plug my table number that's very close to c and you'll find 0 times infinity equals 6 in this example. Let's expand the formula for invisible age to find out why.

t'(DSR - 1) = 3(c+v_h)(c-v_h)/(c+v_h) - 1)/c = 3( c-v_h -c -v_h)/c = -6v_h/c and v_h = -c so the answer is 6 yrs evaporates while 0 yrs appear on Alice's watch if she returns at near -c to Bob. She will start her journey back to him at 4 and end up still 4 while he is 8. She will not have aged infinite evaporated time while no time appeared on her clock but she will have only invisibly aged at 2c for each ly back to Bob for a total of 6 yrs evaporated from her watch which shows 0 time for her 3 ly trip.

If you remember the example with Alice choosing to go at +c from her transition point, 6 yrs were added to her clock. They did not evaporate from it. She ended up ageing 10 yrs while Bob aged 8 once the imbalance period was over.

So why doesn't light act this way (a valid question no relativist can answer). Relativists say light is born, travels the infinitely thin universe and then gets absorbed as soon as it was born. But that doesn't happen to Alice at near c. Her infinities resolve to finite numbers. But light sourced from Alice is quite different than the light signal from the transition point. When she's returning at near -c, she appears so blue shifted her sourced light frequency is infinity. When she's going away at + c, she appears so red shifted her frequency is 0 and undetectable as would be expected due to the Doppler effect. The reason the light signal she sent is not affected by the Doppler effect and appears at normal frequency is because there is no source pushing it and no receiver going towards it. The light signal is propagating relative to the electromagnetic medium of space and as the MMX proved, we can't have a relative velocity to that medium or to the light that propagates through it. We are material and the medium lacks material since it's a vacuum. We can only see our relative velocity to it through the Doppler effect. This is the reason all perspectives see the same constant for light, not some dreamed up concept that time dilates while space contracts and that's why a photon can travel the universe infinite times in zero of its time (it can't).

So what's the real answer? Well, since we can see light's frequency as it travels at c, we know time has not stopped from any perspective. Alice's sourced light frequency remains normal from her perspective but is effectively stopped from our perspective so we know time has stopped for her but it remains at the normal rate for light. This means the equation c² = v_t² + v²doesn't apply to light. It goes at c through time while it's going at c through space while Alice can only go at 0 through time while she's going at c through space from our perspective. This means the equation governing light must be 2c² = v_t² + v². No time evaporates from light's total time.

What does that mean, can light's ageing now be determined? Yes, and you can see it from Alice's time at near c. Going at +c away from Bob, no time evaporates from her clock and she ages 2 yrs for every light year her light signal travels back to Bob (which is 3ly). So she ages a total of 6 yrs. Returning at -c, all the 6 yrs evaporates from her clock but it does not evaporate from a light signal's clock. This means light ages 2 yrs for every light yr it travels not the ridiculous result relativity comes up with. In physics, there is no such thing as infinity that doesn't tend to a finite number. period. exclamation point.

But how can we prove this reasonable assertion in light of 114 yrs of completely crazy assertions from all the great minds? Muons. Muons age. Muons carry on-board atomic clocks as Muon half-life. You can detect their age change as their velocity through space approaches c. I'm saying straight up that as they approach c, they will age nearly 2 yrs for every light yr they travel. That age will be measurable when they recede from you but unfortunately it's invisible if they're coming at you. This will prove my math over relativity's math that comes up with an infinitely nonsensical answer.

Next up, how to model a black hole using relative velocity.

Ok, let the rabble's mindless heckling begin.

Edited December 20, 2019 by ralfcis

ralfcis · March 27, 2019

Damn, past 11, too late to start my next sesquipedalian apopheny. Tomorrow then.

Edited March 27, 2019 by ralfcis

ralfcis · March 31, 2019

I've been away on the black hole thread to see how my examples of Alice either returning or receding from Bob at near c could possibly seamlessly relate to Alice passing a black hole's event horizon thereby linking velocity's and gravity's effects on time as the same thing. But as it turns out, GR is not the only player in the black hole space and there are other effects to consider. So this post isolates relativity's effects from any others. We are going to estimate the effects on permanent age difference of Alice hitting the event horizon with her choosing to recede from Bob at near c after she separates from him at .6c. The transition to +c will be considered equivalent to Alice passing the event horizon. One important difference is that Alice can send a signal to Bob just before she transitions to +c at the 3 light year mark and it will get to him in 3 of his years. I think because of the contraction of space time around the event horizon, a signal from Alice will take longer to reach Bob and that will mess up my simplistic algebra. So we are going to assume there are no gravitational effects slowing the light back. If there are, then the age difference between Bob and Alice may be increased from what this example can calculate. So I've made things pretty simplified and idealized.

We saw in the 2nd example that Alice starts receding from Bob at .6c and transitions to +c away from him at the 3 ly mark. She will age 2 of her yrs for every year the light takes to get back to Bob. Bob will age 4 of his years. In proper time, the transition point happens when they are both 4. From Bob's perspective time, he is 5 when Alice is 4 at the transition. So he ends up 8 when the reality of her transition reaches him. She ages 2 yrs for every yr the light has taken to cross the 3 ly back to Bob. So at the moment it reaches him, she has aged a total of 6 yrs. She started the relative velocity imbalance when she was 4 and that imbalance time ends with her being 10 and Bob being 8. This is all in proper time. Since the velocity imbalance period is over, they will continue ageing at the same proper time rate and she will always remain 2 yrs older than Bob so long as no one makes any further velocity changes.

Now there is all kinds of debate on whether a black hole's event horizon can be modelled as a velocity transition to +c. But if it can, I have the math which shows that popular ideas of how a black hole's event horizon affects the age difference between Bob and Alice do not involve infinity. I've made the infinity cancel out of the formulas and what's left is a simple formula that is only based on the distance between the starting point and the event horizon.

Edited December 20, 2019 by ralfcis

ralfcis · April 2, 2019

This is later proved wrong so my proof that 2c² = v_t² + v² since v_t = v = c must also be wrong. I have to find where I went wrong.

The problem is Y_c (Y of c not to be confused with Yc (Y times c)) is infinity on its own but it is not infinity when it's multiplied by DSR. The two regulate each other to a finite value according to the equation Yu/Yw =DSR_v as will be explained later.

Based on the math I've presented so far, I can derive a formula for Y for light going at light speed. To derive Y for matter we use c² = v_t² + v².

Solving for v_t, we get v_t = c/Y

Plug that back in and we get c² = (c/Y)² + v².

Solving for Y we get Y = c/sqrt(c² - v²). No contradiction between the assumption and the result.

Now I said for light the formula changes to 2c² = v_t² + v² since v_t = v = c for light because we can see its frequency, time has not stopped for it.

Using the same derivation as above we get Y_c = c/sqrt(2c² - v²).

So the gamma for light is not infinity, the infinity resolves itself to Y_c =1.

This means that for light there is no reciprocal time dilation. Y is the same value as matter having a relative velocity of 0. Y_c =1 means you can't have a relative velocity to light because you can't have any reciprocal time dilation with light. This math is so complete and self-contained unlike relativistic math which has infinity in it that produces nonsensical results that the cult swallows hook, line and sinker without question.

Edited December 26, 2019 by ralfcis

ralfcis · April 5, 2019

Ok, I'm going to only concentrate on this thread until I'm finished. No more venturing out into the rest of the forum.

Moronium · April 5, 2019

Wise decision, Ralf. This thread is where you belong.

Now you can carry out your numerological "research" indefinitely without any interruptions from other posters.

fahrquad · April 6, 2019

ralfcis?

You are a total idiot, just like Moron.

But do carry on. It's amusing.

Welcome newbie!!! It is best to just let the two of them puff and posture like a couple of male Betta fish in adjoining bowls.

ralfcis · April 6, 2019

That's why I'm moving my bowl. I noticed the water's a little cloudy so I'm going over past posts to clarify them. So lucky this forum is the only one I've found that allows that.

ralfcis · April 11, 2019

I've been going over my old posts correcting mistakes here and there but I've realized I've been quite cloudy about my definition of v_t or velocity through time. v_t = c/Y so it's a property of time dilation and at a velocity through space v = .6c, v_t = .8c and the rate of time each observer "sees" of the other frame is slowed to 80% of their rate of time. This remains the same whether the two are separating or coming together at .6c. But if they broadcast their televised lives, they will actually see each others time slowed to 50% when separating and 200% when coming together at .6c due to the Doppler shift ratio.

So how is this possible, 2 different simultaneous views of the same clock reading? It's not, it's just more smoke and mirrors used by relativists to get you to believe in their magical powers. Time dilation can never be seen in the televised broadcast, it can only be calculated. Bob will never see that his clock says 5 and Alice's clock says 4 in the televised signal he receives. Her clock will say 2.5 because that is her time she broadcast to him delayed by 1.875 yrs it takes to reach Bob. Bob must calculate that Alice's signal took 1.875 yrs to reach him so he was 3.125 when Alice was 2.5 in his perspective present. This ratio gives Y = 1.25 which allows him to calculate he will be 5 and Alice 4 from his perspective. He won't get confirmation of that until he reaches 8.

So time dilation allows one to calculate Einstein's perspective time construct of what each clock said of the present time from one perspective. Unless you can see into the past, you will never witness time dilation on any two clocks no matter what relativists tell you.

But you will be able to witness the Doppler Shift Ratio (DSR) by comparing the two clock readings. Bob will actually see his clock say 5 and Alice's say 2.5. This isn't any kind of present time because Alice's signal is delayed from the past. But it does allow one to calculate what is the proper present time that they both share. I showed how to do this in past posts and the result is that Bob and Alice were both 2.5 in the causal present while in Bob's perspective present he was 3.125 when Alice was 2.5 and from Alice's perspective present she was 2.5 and Bob was 2.

Relativity does not recognize proper time causality as reality; the only reality, the only present is from your subjective perspective. In proper time, all clocks tick at the same rate within every frame in the universe. They do so even when there is a relative velocity imbalance when one changes the relative velocity. This does not mean there is a Newtonian universal absolute time. The clocks will lose proper time sync with each other during the relative velocity imbalance time which only lasts as long as it takes light to traverse the distance (which is invariant here but not in relativity) between the two participants. Even proper time is relative and not absolute. The only way to sync all clocks to the same time and not mess that up is if nothing changed its velocity or there was no gravity (which can be thought of as acceleration).

So in conclusion there are 2 different velocities through time because there are 2 different types of time. One, v_t is the time dilation in perspective time and the other is v_ht = c DSR which is responsible for age difference in causal time. I'm sure if you polled most relativists, they'd say age difference is a result of time dilation, not DSR and all would be completely wrong.

Edited December 20, 2019 by ralfcis

ralfcis · April 11, 2019

I've just realized writing the last post that a thermometer can measure time just as well as a clock. What's better about a thermometer is that it has an upper limit of temperature at c (which manifests as an infinite blue shift or a zero frequency red shift) and a lower limit of absolute zero. Both clocks and thermometers measure ticking. A clock counts regular orderly ticks whereas a thermometer measures average random molecular ticks of a substance. So if we measured the light frequency of a star at a distance from us and that star started to move towards us, we would get a doppler shift ratio. The time of relative velocity imbalance would be the time it took the light to traverse the distance between us at the moment we saw the star start to move. After that, a new relative velocity between us would be established and we could calculate from the DSR how much the star aged less than us once it changed its velocity.

Yes, you'd need to have followed what I've been saying in order to understand the last paragraph. But if you just accept it on face value for now, you'd understand how badly relativity fails in being unable to make this calculation because it doesn't have a valid spacetime path on which to base the calculation. I could use the same temperature method above to calculate the age difference of a star that started to move away from earth and relativity wouldn't even know where to begin. I feel so alone.

Moronium · April 11, 2019

I feel so alone.

You feel so alone because you have no idea about what anyone else ever said or did.

Cosmologists use the "temperature" of the CMB, and the doppler shifts creating apparent differences in that temperature to establish a standard for absolute time and absolute motion.

No one would try to say, as SR does, that because temperature can affect the rates at which physical processes occur (and even things like length, for example) "time" changes with every miniscule fluctuation in temperature.

Don't think I'm agreeing with the rest of your post just because I mention this, though.

Time dilation can never be seen in the televised broadcast, it can only be calculated.

You are correct that time dilation is never "seen" as relativists like to suggest, but is only calculated. Unfortunately, in SR those "calculations" are founded upon unsound premises. But, hey, the math still works out just fine. That said, doppler shift appearances have nothing to so with clock retardation (so-called "time dilation") to begin with.

I'll give you credit for one thing, Ralf. At least you are beginning to try to analyze concepts rather than just playing around with numbers willy-nilly.

This does not mean there is a Newtonian universal absolute time.

Who knows? Maybe one of these years you'll understand the concept of "Newtonian universal absolute time."

Who am I kidding? That aint never gunna happen.

Edited April 11, 2019 by Moronium

ralfcis · April 11, 2019

I've been playing milly-vanilly, not willy-nilly.

Moronium · April 11, 2019

I've been playing milly-vanilly, not willy-nilly.

OK. Fair enough.

Wasn't that the name of some bogus "music" group which faked all of its playing?

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