Relativity And Simple Algebra

[ralfcis]

I'm going to go on the PSX and ask 5 questions to see if I can convince them of my findings.

 

1. If length contraction is a product of relativity of simultaneity, why wouldn't time dilation be treated the same way?

2. If Einstein's clock sync method sync's clocks, is it possible to also use light signals to determine perspective time on sync'd clocks?

3. What is the difference between "slowed time" due to time dilation and the apparent slowed time of a receding clock reading due to the Doppler shift ratio (DSR)?

 

Hopefully the answers will lead to the conclusion that time dilation is not the result of moving clocks measuring slowed time. If they agree with that then relativity is dead. Then I'll ask the question 

 

4. Can perspective time just be considered a simple mathematical derivation of proper time?

5. Can proper time age difference be determined in real time and does it happen more gradually than an instantaneous lump sum?

 

Hopefully I don't get banned forever because the PSX is the only source of information left to me. Last time they dinged me heavily because the question I asked showed I didn't know the correct answer before I asked it.

Edited December 5, 2019 by ralfcis

[ralfcis]

Ok I've decided to take up Dale's challenge and edit this question down to the bare bones. This question has been answered to my satisfaction here The real meaning of time dilation  https://physics.stackexchange.com/questions/53232/the-real-meaning-of-time-dilation?noredirect=1&lq=1 but it does not address my specific question of how time dilation is caused by proper simultaneity. I'll explain what that is later.

 

We will use the muon example to explore this question and first put up a generic spacetime diagram generic muon example https://photos.app.goo.gl/Re8v5Suk9oY4q4Ed8 that is fairly close but has easier numbers than the real world version real world muon example https://photos.app.goo.gl/HCeLAxDapHGdmyLQ9

 

We have 3 axes in the generic diagram. The muon's time is the ct' axis, the earth's time is the ct axis and the distance the muon needs to traverse is the x axis. I'm leaving out the x'axis because that is nothing more than the perspective lines of simultaneity; horizontal blue for the earth and slanted thin red for the muon.

 

The green line is the proper simultaneity for the half speed perspective 

v_h=Yv/(Y+1) which is derived from the relativistic velocity combo formula.

 

Proper simultaneity does not change over distance because it is the underlying instantaneous causal present for all perspectives. It is the line whose 2 endpoints represent where the

 

(ct′)²=(ct)²−x² (also written as c²=v²+v_t² where velocity through time v_t=c/Y)

hyperbola intersects the two velocity lines.

 

Before I go into a numerical example, there are several main relationships between the axes.

v=x/ct This is 6/6.5 c in this example

Yv =x/ct' =6/2.5 =2.4

Y = ct/ct' = 6.5/2.5 = 2.6

vt=ct′/ct=c/Y = 1/2.6

 

The earth time coordinate where the green line of proper simultaneity is: t' = x/Yv =6/2.4 = 2.5 which is properly simultaneous to the muon t'.

 

The significance of red t' for the muon is where it starts its journey. For earth, blue t' is where it starts its stopwatch to time the muon. From the earth's perspective, the muon starts when the earth is -6.5 but the proper simultaneity prevents the earth from timing the muon until -2.5. Neither of their clocks is slower than the other, they tick at the same rate because within their own frames they are ticking at the rate of c through time. Every frame experiences this normal rate of how fast we go through time. This is like normal play speed on a DVD player where other velocities through time can be slow motion or fast forward. Normal play speed is c through time, don't confuse that with c through space.

 

What's happening here is a time trial for the muon but the perspective simultaneities are screwing up when to start the trial. We know both clocks are ticking at the same rate of c through time within their frames.We know that when they meet they can be legally set to the same time because the relative velocity was constant between them. We can have the muon send out a light signal when it starts and it will be received by earth at -.5. From that, the earth's perspective time of the muon's start is -6.5 because it took the light 6 to reach earth. But we know for all other conditions to be true, the earth timer had to start his stopwatch late (from his perspective) at

 

t'=x/Yv = 6/2.4 = 2.5.

 

This is how we can say the earth saw the muon take t=Yt' = 6.5 to traverse the 6 distance but the muon did it in 2.5 because it was travelling at Yv = x/t' = 2.4c while the earth perspective of the velocity was v=x/t = 6/6.5 = .92c.

 

There is no time dilation due to slowing of time, nor length contraction due to space shrinking, there is only velocity dilation where v' = Yv. The muon can cross vast distances in its own proper time because it traverses that distance at Yv =x/t'.

 

As a side note, relativity of simultaneity is not the same thing as a line of perspective simultaneity. RoS is about the hysteresis between perspective simultaneities which does not exist for proper simultaneity. So the relativity between the muon perspective simultaneity (t''=t'/Y) and earth perspective simultaneity (t=Yt') is Yt'-t'/Y = 6.5-.96 = 5.4 = vx/c² = 6/6.5 * 6 = 5.4.

 

P.S. You'll notice that the corresponding x coordinate for the earth's perspective of t'=x/Yv is the length contracted distance the muon crosses (x/Y = 6/2.6 = 2.3 from the muon's perspective) in its time (t'=2.5) which agrees with the popsci version of relativity.

Edited December 11, 2019 by ralfcis

[ralfcis]

Things are not going well on the PSX. No one has any idea what I'm talking about despite numerous edits of the question. I thought this was going to be a blockbuster. This spacetime diagram should be self-explanatory:

 

https://photos.app.goo.gl/M1zzbJLBoRD41kC4A

Edited December 8, 2019 by ralfcis

[ralfcis]

Ok, they were just playing some sort of moderator game to get me to focus on one question. The answer to my question was here:

The real meaning of time dilation.

In their own words, "It's not really clocks running at different rates, it's that different observers will disagree about the x and t spacing of the events."

 

What this means is I was right all along, time dilation is not a result of time slowing, it's a result of proper time relativity of simultaneity. As an analogy, it's not about a racer going down a track with his own slowed stopwatch and declaring he was going so fast down the track that he warped time and actually crossed it faster than the track timer said. This is the poppy cock that popsci, wiki article, comic book physicists are taught to believe and regurgitate. These scientologists unfortunately comprise 99% of physics forums.  What is mostly happening is the racer gets a huge head start by the relativity of simultaneity before the official start. The track time starts way late and he only has to go a little distance to the finish where the track time ends. What's also happening is the racer's velocity is Yv but is seen by the track as never going above the c speed limit. This trick allows him to cover the track in very little of his time while the track starts timing way after he already started. This is the correct interpretation of relativity. There is no such thing as time dilation due to time slowing or length contraction due to length physically contracting despite what your comic books say.

Edited December 9, 2019 by ralfcis

[ralfcis]

My post on the PSX is on-hold and I'm waiting for it to be understood, found correct or found incorrect. I can't continue asking subsequent questions if they leave it in limbo like this. 

[ralfcis]

Measuring the one way speed of light

 

 

While waiting for an answer to my previous question, I answered this question on the PSX.

My former mentor was obsessed with this question at first saying there's no way to prove the anisotropy of light (one-way vs reflected 2-way) until Don Lincoln responded to just slowly separate two sync'd atomic clocks and fire light from one to the other and measure the delay. The problem is moving clocks apart causes them to unsync but this is not a problem for a single clock that measures its own reflected beam. So moving them slowly apart introduces an error which can be accounted for using relativity.

 

Einstein's clock sync method uses light pulses to sync clocks and then you use those light sync'd clocks to measure the speed of light. The result is dependent on the assumption so it's a circular argument and is deemed untrustworthy.

 

In Einstein's day (1905) they didn't even yet know about atoms let alone atomic clocks so his clock sync method was all he had. Today we can depend on the universal accuracy of atomic clocks to free us from his method (which is ingrained into the derivation of the equations of relativity).

 

My solution is to move the clocks apart at a slow constant velocity and fire light from one to the other at a pre-agreed proper time on each clock without stopping. The light will meet where they started and you could use an inteferometer to measure any discrepancy in the one-way light speed due to imperfections in the test set up. When both clocks move at constant velocity, they both tick at the same proper time rate. It's a simultaneity (relative to their common starting point) that is independent of distance separation. If you stop the clocks, you invoke the twin paradox and a syncing problem between them.

Edited December 18, 2019 by ralfcis

[ralfcis]

What are the terms in relativity for age difference due to perspective time and proper time

 

I've edited this to get rid of any terms I may be misunderstanding.

 

I've been asking the same question for years and finally realize I haven't been clear on the question or on the terminology I've been using. I'm going to ask it as it pertains specifically to these examples:

 

spacetime diagram

 

Alice leaves Bob (deemed stationary) at .6c. When Bob's 10, Alice is 8 (blue line) whether she keeps going or turns around at the 3ly mark. Bob is 2 yrs older than Alice in either case from his perspective. If Alice re-unites with Bob she agrees with this age difference but if she kept going she'd say she's 8 and Bob's 6.4 from her perspective (red line).

 

From the half-speed perspective at 1/3 c (green line), Alice and Bob's ages remain the same so long as they remain at a constant relative velocity.

Is there a relativistic term for this such as "proper simultaneity"?

 

Constant relative velocity is guaranteed by a reciprocal Doppler Shift Ratio DSR so they will both age at the same rate and have no "proper age difference" while this is true (at .6c separating, DSR = 1/2 for both). It is not true during the 1st two Alice yrs after she turns around and the 4 Bob yrs before Bob receives a light signal (yellow line) that Alice has changed their relative velocity.

 

The half-speed green line perspective will then see Alice's proper time 2 yrs younger than Bob's after the time of relative velocity imbalance (ends when Alice = 6 and Bob = 8 and their DSR's both = 2). Alice will then remain constantly 2 yrs younger than Bob, year for year, from the half-speed perspective. This loss of 2 years occurs only during the time of velocity imbalance.

 

Is there a relativistic term for this duration? Is there a term for the difference in proper time between them such as "proper age difference"? Is there a mathematical model for how the proper age difference progresses during the velocity imbalance period? If not, I have one.

Edited December 23, 2019 by ralfcis

[ralfcis]

Does anyone here understand my question because no one on the PSX seems to. Twilight Zone. 

 

P.S. So the problem is we don't speak the same language and theirs looks insane to me. None of the terms that I use, that I've seen others use, match theirs. If I adopt theirs then I'll have to speak one language on regular forums and another on the PSX.

Edited December 23, 2019 by ralfcis

[ralfcis]

Since my banishment is imminent on the PSX, I'm storing my expanding details to the question of proper time being a better way of looking at things here before I lose access.

 

Day 1.

 

I guess I have 5 days to clarify and add details so I'll add them slowly. From Willo's comment I see it will be a difficult climb because how he defined terms was a complete shock to me. I've read 1 book and taken 1 on-line course and neither gave me his definitions. However, his revelation that the concepts I wanted terms for have no terms so reading further books would not give me the answers I seek.

 

I was going to ask a series of questions that would outline the advantages of using proper time and equations based on Yv to solve problems as opposed to reciprocal perspective time and the Lorentz transforms which are based on time dilation, length contraction and relativity of perspective simultaneity. The answers come out the same but the new math method seems so much more intuitive. The details will come out in various examples since this thread will be shut down anyway in 5 days. No point in asking more individual questions if they'll be shut down due to terminology but adding details to this question might make the concepts understandable and maybe I'll get the terminology I need.

 

Day 2.

 

Since none of my terminology seems to be correct, I'm going to define things in terms of mathematical concepts so it will get very basic at times. The first is relative velocity.

 

Unlike matter, waves have a fixed relative velocity to their mediums. Any attempt to force the wave to travel faster than this fixed relative velocity will result in the Doppler effect (so I have no idea what deSitter was trying to prove). The wave propagation velocity is dependent on the elasticity and inertia of the medium which is described by Hooke's law for mechanical waves (sound) through mechanical mediums and by Maxwell's equations for electromagnetic waves through electromagnetic mediums where the equivalent of inertia and elasticity is capacitance and inductance or permittivity and permeability.

 

Even though there is this difference between sound through air and a football through air, you can still have a relative velocity to both. If you run towards a football thrown at 5 mph relative to you and you run towards it at 5 mph, your total relative velocity to the football will be 10 mph. (A person watching from the sidelines will see your closing speed to the football as 10 mph but his relative velocity to both of you from the side will be near zero.)

 

The same math will be applicable to you running towards a sound wave. Your relative velocity will be the distance you travelled relative to the field in the time it took you to reach the sound or football plus their relative velocity to the field. The sound's relative velocity to the field is its relative velocity to its medium plus its medium's relative velocity to the field.

 

Light doesn't seem to work according to this formula. It is limited to c whether you're adding two velocities (w = (v+u)/(1+vu/c²)) or the two velocity components of light (c²=v²+v_t² where v_t =c/Y velocity through time.)(Incidentally those two equations can be combined into one

c²=((u+v)²+v_t²u_t²)/(1+vu/c²))).

 

So no matter how fast you move towards light, your relative velocity is always absorbed into c. But how is this possible as the classic way to calculate relative velocity is the distance you travelled in the time it took you to reach the light plus the light speed. The term (v+c) occurs in many derivations and not as just equal to c. So what's going on? If you move closer to the light, it's going to hit you sooner so your velocity must have some effect. The detailed math describing the Michelson Morley experiment (MMX) shows what's really going on. That detailed calculation will be next; first using perspective time and then using proper time to show how much clearer the concepts are.

Edited December 24, 2019 by ralfcis

[ralfcis]

Day 3.

This may be news to some but relativity never made the claim that plugging c into the velocity combo equation results in the conclusion that adding any velocity to c results in c. In fact plugging u=c into w=(v+u)/(1+vu/c²) results in v+c = v+c or plugging in w=c results in c=c, never v+c=c.

 

However I have managed to derive an equation that explains what's happening with (v+u) as u-> c : 

 

Y_u/Y_w=DSR_v

 

There's no room for infinities in physics and I've found coupling Y with DSR cancels out pesky infinities into finite limits. So as u-> c,  Y_u/Y_w approaches the finite value of DSR_v. Try some real world numbers like u= 40/41 c (Y_u= 41/9), v=3/5 c (DSR_v=1/2), w= 323/325 (Y_w= 325/36) So Y_u/Y_w = 164/325 =.466 and DSR_v = .5. The larger you choose u, the closer the ratio gets to .5 even though both Y_u and Y_w approach infinity. I can show the derivation for my equation.

 

Now that that's settled we can move on with how the MMX is solved using perspective time and then proper time.

Edited December 26, 2019 by ralfcis

[ralfcis]

P.S. I'm correcting past posts and I'm up to page 50 so far. The corrections are in red and some are quite important.

[ralfcis]

Day 4.

 

 

[Classic MMX/train/muon math] https://photos.app.goo.gl/MYbkUQeNk9PCtRt99

Here's the spacetime diagram of the MMX aka train in station aka muon example. It shows graphically where you get vx/c2, x, vt to plug into the Lorentz transforms. The problem is solved from the simultaneity of the train's perspective when light is "simultaneously" released from the back and front of the train. I'll go into more detail tomorrow. 

 

Day 5.

Ok seems like no one wants more detail. Here is how I solve the same example using only [proper simultaneity] https://photos.app.goo.gl/aEwLAJFuS3Pz1woe6. I am going into all this detail with the hope my descriptions can be joined to proper terminology. 

 

What's superior in using proper simultaneity is there is no need for Einstein's clock sync method. The train front hits the back of the platform and pink and yellow light signals are released in a proper simultaneity from which all perspective simultaneities can be derived. The lights are released in proper time which is only dependent on the universal accuracy of atomic clocks something Einstein did not have. 

 

 It also has the advantage that when the back of the train hits the platform  front, the platform and rear train clocks are co-located and read the same time as they should because only constant relative velocity was involved. 

 

Also, as I showed in my muon example (now closed) using this math technique, time dilation is not due to clocks in motion measuring slowed time but is due to relativity of simultaneity when the platform perspective calculates when the train's rear set off the yellow light signal and when the platform timer actually began timing much later. It's like a gun going off to start a race but the stopwatch is started much later. Time dilation is not about time slowing, it's about relativity of simultaneity.

 

It will be difficult to understand what I'm saying because of the language barrier I am trying to overcome. But if you dig into the math you'll see its beauty. Getting rid of perspective time allows one to see further using proper time simultaneity.

Edited December 29, 2019 by ralfcis

[ralfcis]

Day 6.

 

Just as the cause of time dilation and the muon results are caused by the relativity of simultaneity between the starting gun and the start of the stopwatch, so too is the measurement of relative velocity.

 

This next paragraph needs more work to be clear and correct. 

 

In my football example, the original separation between the thrower and the catcher is much greater than what is classically defined. The starting gun goes off for the catcher who starts 20 ft away at 5 ft/s but the throw at 5 ft/s comes much later at 10s after the start for a relativistic velocity result, of catcher to the football, of 5 ft/s instead of 10 ft/s in the classical definition where stopwatch is started simultaneously with gun.

 

This is apparent in the first STD using the train perspective. The pink light signal is cut short by the forward movement of the train rear to the light. If the train was stationary, that light signal would take a second to hit the back of the 1 ls long train but it only travels for .625s. The lengths of the pink and yellow signals are indeed affected by the train's movement even though they are both at c. But the train's relative velocity is not added to c because it starts at 1.5625 ls and the total time it takes to reach the light signal is .9375s. The light's flight time .625s so the relative velocity is 1.5625/(.9375+.625) =c. The train's velocity gets drowned out by its early start and its delayed timing. The magic is in the relativity of simultaneity, not in length contraction conspiring with time dilation to keep c constant from all perspectives as the popsci version of relativity teaches.

 

As you can see from the equations I've smattered on proper simultaneity STD, the Lorentz transforms no longer apply neither does Einstein's clock sync method. (I've added the two thin red lines of perspective simultaneity to make orientation between the two competing STD's easier.) The formula for Proper relativity of simultaneity is t'(1-Y) (where t'=x/Yv) whereas the formula for "moving" perspective simultaneity was vx/c². Painful for now to grasp why but further examples become very clear.

Edited December 31, 2019 by ralfcis

[ralfcis]

Well mystery solved why no one understands what I've been saying. It appears all the terms I've been using do not match the concepts I've been describing because those concepts have no terms and the terms I've been using pertain to other concepts. I now have to build an agreed upon glossary of terms and their definitions. For example, the accepted term for reciprocal time dilation is age difference and the accepted term, which apparently few use, for what I've been taught to call age difference is differential ageing. However, if I use the term differential ageing, people will assume I mean age difference because few know what differential ageing is. So I'm proposing the terms reciprocal and non-reciprocal or proper ageing due to relative velocity imbalance. Other terms that require agreement are half-speed, half-speed perspective simultaneity, proper simultaneity, partial non-reciprocal ageing and perspective simultaneity. I hope the glossary of terms won't extend beyond this. The concepts these terms will apply to currently have no agreed upon terms.

[ralfcis]

Here is my sarcastic retort to the PhD experts on the PSX:

 

Despite the fact it's been stated that this question needs both more details and more focus, it has indeed been understood and some answers have been provided so why is it getting closed? Just look at the wide variety of answers, from the answer is in books to the answer is not in books, to there is no term for this to there is a term for this, you just need to transpose the words age difference to differential ageing. They may look the same, but actually mean two different things.

 

They don't seem bright enough to understand sarcasm or their own field. All this experience has taught me is that relativity is in even more disarray than I  assumed. People have their own terms, can't agree on the concepts, can't use Algebra to resolve concepts and don't seem open-minded to new concepts. If they're such experts, it should be easy for them to identify problems in concepts using math but they won't go into the math at all. They even find numerical examples confusing? I can't tell them any of this because my best chance of getting any of the answers I need is that maybe someone there knows the answers. I need to vent though and here is the only place I can do it.

Edited January 2, 2020 by ralfcis

[ralfcis]

ANSWER to my question on the PSX:

 

I don't know how much time I have left before this question gets removed but we have come to a conclusion in the chat room that the answer is mathematical as there are no terms that fit my needs. So I will be presenting an answer in two parts. The first will be a mathematical explanation of the colloquial term "age difference" used here on the PSX. I will then mimic that explanation to mathematically describe the answer to the question I posted. It seems I'm not free to make up my own terms but I am free to make up my own variables. If you're going to shut me down, do it now before I put all this effort in or give me a deadline.

 

Ok, first is the STD for age difference as used here on the PSX.

 

https://photos.app.goo.gl/KtFcxp6xT4eF6DBp8

 

Now compare it to the STD for my description of proper age difference.

 

https://photos.app.goo.gl/somUntsEKgjWtyH79

 

The equation for age difference is the same in both

   t_ad=t−t′

but the equation for proper age difference is

 

t_pad=t′−x/Yv

 

The above formula is simplified to what happens during constant relative velocity. After the turnaround there is a period of relative velocity imbalance where 2 yrs are lost (pRoS_outbound + pRoS_inbound but more complicated than that) then a new relative velocity is established and the discrepancy in proper times is reflected on the ends of the green lines of simultaneity. The math that happens during the time of velocity imbalance will take many posts to describe.

 

Hence for the outbound leg t_pad = 0 and for the inbound leg (2 yrs after the turnaround) t_pad =2 for all t'.By choosing the half speed (1/3c is half of .6c) perspective's green lines of simultaneity, we eliminate the growth of t_ad that Alice's red lines of perspective simultaneity introduce. The formula for proper relativity of simultaneity removes the 2nd term from Alice's

 

RoS=(t_ad)+(t−t"−t_ad)

 

so that pRoS is simply = t_ad.

 

e.g. at t=1.25, t_ad = .25, RoS = .45 and the .2 remainder comes from the 2nd term. pRoS, on the other hand is just .25 which accummulates for every t'.

 

The formula

 

(ct′)²=(ct)²−x²

 

is also reduced to t'=x/Yv. Why is more clearly understood when you compare the Loedel STD which is two 1/3c velocity lines on either side of a 0c half speed line. This is how .6c relative velocity is drawn on a Loedel.

 

If you look in the lower right corner of the 2nd STD, you'll see how time dilation is not due to time slowing but due to the lag in time from when the starting gun goes off and the stopwatch starts timing the event. t' appears on both sides of the triangle but it's propped up on the right side by pRoS. pRoS represents the lag of when the purple stationary frame "sees" Alice start to when that purple frame starts timing her. So time dilation, just like length contraction, is a result of relativity of simultaneity; not time slowing or length actually contracting.

 

If you compare that to the same triangle in the 1st STD you should see problems with the classical approach. One side is still t' but the right side is t'/Y in duration which obscures the true meaning of time dilation. Also the assignment of t=0 on the right side is meaningless. It would still be meaningless if 0 appeared on both ends of Alice's 1st red line of simultaneity.

 

The time must be the same on both clocks at co-location because up to that point there has been no interruption in the constant relative velocity. A difference in clocks signifies that has happened and that error is avoided by properly setting t=0 on both sides of the triangle. This is only done using the proper green lines of simultaneity as shown in the 2nd STD.

 

There's a lot more to this but it'll only get more confusing for now (especially where I did not include green lines of proper simultaneity in the relative velocity imbalance zone). The answer to my original question was the variable t_pad and how it behaves mathematically. I'd prefer having an English term for it. I'm pretty sure it will be far easier closing this question than to try to understand the math I've presented.

Edited January 9, 2020 by ralfcis

[Vmedvil2]

So, whats the conclusion to all this ralfcis, this is now on page 71, what have you discovered?

Edited January 9, 2020 by VictorMedvil