Relativity and Stationary Frames of Reference

“Relativity and Stationary Frames of Reference” seems like a contradiction to most scientists. A fundamental assumption in Einstein’s special theory of relativity is that all frames of reference are equally valid, and any observer can be considered to be a stationary observer.

Einstein’s assumption in the special theory of relativity, that all frames of reference are equally valid, is over-broad. For the mathematics of the special theory of relativity to work, a more narrow assumption would suffice. The only assumption that is necessary is that the speed of light is constant, regardless of the motion of the observer. It is not necessary to assume that other physical measurements are equally valid, regardless of the motion of the observer.

Narrowing the assumptions in Einstein’s special theory of relativity, it is now possible to consider the question: Is there such a thing as a stationary frame of reference, or could any observer consider himself to be a stationary frame of reference?

Let me give you the conclusion of the matter, and then I will explain the reasons for it: As soon as you assume that all frames of reference are equally valid, and any observer can consider himself to be a stationary frame of reference, then you end up with a mathematical contradiction in the special theory of relativity.

I am not the first one to bring this issue to light. As soon as relativity was published, scientists objected to the theory giving different examples preposterous conclusions from the special theory alone. When experiments demonstrated that light was bent by gravity, then the scientists were silenced. Many things in science are counter-intuitive, and it was thought that while it may not make complete sense, relativity must be true.

Mathematical contradictions still exist in the special theory when you assume that all frames of reference are equally valid. These contradictions are eliminated when you allow such a thing as a stationary frame of reference.

While I am suggesting that such a thing as a stationary frame of reference exists, it is very difficult to run experiments to determine what that stationary frame of reference is, or how fast we are moving through space with any degree of accuracy.

CNN posted an article – sorry, I do not have the link for it, where they stated that relativity was now under question, because measurements of time on satellites show that the earth is moving in space. This is to be expected when there is such a thing as a stationary frame of reference, but completely unexpected when you accept the assumption that all frames of reference are equally valid.

I have stated that there is a mathematical contradiction in special relativity when you assume that all frames of reference are equally valid. I can create a mathematical model which shows the contradiction, but that would be too lengthy and demanding for this forum. The mathematical model involves multiple observers moving relative to each other, and arriving at contradictory results, without changing their velocities. I would like to explain it with a story. Actually, the story is a take-off on one that was told shortly after relativity was published.

Two astronauts meet in space, perhaps away from any place where gravity would distort the results of their experiment. They synchronize their watches, and then speed away in opposite directions. Then they speed back and meet again. According to special relativity, each astronaut will think the other’s watch is slow. Even if they hold the watches side-by-side, they will remain in disagreement about the times on the watches.

As soon as you allow for a stationary frame of reference, the expected result becomes more rational.

What impact does this have on relativity? Actually, it is an adjustment to the theory. It does not demolish it. Relativity remains very accurate, even when you do not know what the stationary frame of reference might be. When we get a better idea of what the stationary frame of reference might be, then the most accurate calculations would take place by knowing that we are moving, and then taking our astronomical observations and determining how a stationary observer would see them.

General relativity is demanding enough, with the final conclusion of a rank three contravarient tensor equal to zero. The mathematics for relativity would become more complicated if we wished greater accuracy.

Many people believe that Einstein developed an entirely new mathematical model with the theory of relativity. This is not entirely true. Einstein relied on Newton’s equation, F=MA, in order to arrive at his most famous equation, of which e=m*(c squared) is a good approximation. I think we do not have accurate experiments on how Newton’s equation, F=MA, is affected by very high velocities, but this is a possible source of minor imperfections in the equation relating mass to energy.

If, indeed, Einstein’s equation relating mass to energy is extremely accurate (and I suppose it is), then you could get a measure of your own speed through space by determining how much energy you get when you convert matter into energy.

When a spaceship nears the speed of light, time slows down on the space ship, and it shrinks in the direction of motion, and the mass of the spaceship increases. There is one consolation, however. If the spaceship uses nuclear power, then the engines produce more energy as the ship goes faster. It is difficult to manage the additional energy. We will never have an opportunity to put these thoughts into a practical design anyway.

CNN posted an article – sorry, I do not have the link for it, where they stated that relativity was now under question...

Is this the article?

http://www.cnn.com/2002/TECH/space/0...ong/index.html

If so, it was discussed here earlier:

http://www.badastronomy.com/phpBB/vi...1412&forum=4&7

(added)
Ack! Where are my manners? Welcome to the BABB, Verlan.
_________________
<font color=000099>Never attribute to malice what can be adequately explained by ignorance or stupidity.</font>
Isaac Asimov

<font size=-1>[ This Message was edited by: Jim on 2002-10-02 16:25 ]</font>

Welcome to the BABB, Verlan! [img]/phpBB/images/smiles/icon_smile.gif[/img]

(Emphasis mine)

Your astronauts did, in fact, change their velocities.

There are no mathematical contradictions or paradoxes in Special Relativity (or General Relativity, for that matter), despite what you may have been told.

__________________
SeanF

"Ask to understand, but don't challenge unless you have the knowledge."--NEOWatcher

The contents of this post are ©2009 by SeanF and may not be copied or retransmitted in any form without the express written consent of SeanF

First, welcome to the BABB, Verlan.

SeanF is exactly right. The twin paradox has been discussed several times on this board. Our beloved Grapes has a nice write up on this.

For GR the problem gets much more complicated. Consider two astronauts orbiting a planet in opposite directions. Each is in a valid free-float frame (say that five times fast [img]/phpBB/images/smiles/icon_smile.gif[/img]) and each would observe the other as younger, right? But symmetry says that they should be the same age. Which is right? Symmetry is.

valid free-float flame
varid flee-float fame
valid fee-flot fam
vlalid free frot flab
valvid fee foot flem

No sweat [img]/phpBB/images/smiles/icon_smile.gif[/img] Now if I could just figure out what exactly it was that Einstien figured out before someone actually does prove him wronge.

A link for Special Relativity original paper can be found at

http://www.badastronomy.com/phpBB/vi...c=2289&forum=2

I don't think there's any contradiction in SR. As professor Einstein demonstrates, the constancy of speed of light necessarily leads to the conclusions of SR. The key is the concept of simultaneity. Frames of reference are necessary to explain the model.

A stationary frame is not necessary to either special relativity or general relativity, although there are theories of relativity--that have not been completely refuted--that do have preferred reference frames. I'm suspicious of any claim that there are mathematical inconsistencies in SR and GR, expecially without backup. This board may not be the appropriate place to display such a mathematical argument, but a link would certainly be appropriate.
I couldn't have said it better myself. [img]/phpBB/images/smiles/icon_smile.gif[/img]

Why, thank you, Grapes! [img]/phpBB/images/smiles/icon_wink.gif[/img]

(What? "Selective quoting?" What does that mean?)

__________________
SeanF

"Ask to understand, but don't challenge unless you have the knowledge."--NEOWatcher

The contents of this post are ©2009 by SeanF and may not be copied or retransmitted in any form without the express written consent of SeanF

There's a difference between an inertial frame of reference and just any frame of reference. In special relativity, the inertial frame of reference just keeps on going in a straight line because there are no gravitational effects allowed in SR, so you, an observer, can't change direction or speed without changing which inertial frame you're in.

In general relativity, I don't know how this whole thing works, but I would guess that the "moving in straight lines" is more precisely "moving along a geodesic". Maybe.

That's pretty much it. Any freely falling object moves along a geodesic. And in that reference frame (this sometimes called a free float frame), special relativity applies locally.

No, no. You're right again! Wow, twice in one thread. What are the odds?

Hey! That's an insult, isn't it? (How about that? Three times!) [img]/phpBB/images/smiles/icon_wink.gif[/img]

Although, I still haven't figured out whether this was an insult or not . . .

__________________
SeanF

"Ask to understand, but don't challenge unless you have the knowledge."--NEOWatcher

The contents of this post are ©2009 by SeanF and may not be copied or retransmitted in any form without the express written consent of SeanF

Dear Sean F Bad Fellow,

Thank you for your comment. I intended to cover to different situations. One involves no change in velocities, and the other involves changing velocities. It is true that when they speed away and speed back, they change their velocities.

I did not develop the model here where there are no changes in velocities. I just briefly mentioned that is the approach I took in the past to prove a point.

I could not find the link on CNN. A science article appeared on CNN suggesting that the speed of light might not be constant. I immediately replied to the article, stating that I felt the author took the position based on an incorrect interpretation of the Bible. The article immediately disappeared from CNN.

I thought you might be interested in my reply, but it certainly gets off the subject and addresses religious issues.

Anyway, here is a copy of the e-mail CNN sent to me, showing my response to their article:

C:HOTMAIL4

Verlan,

You make some extraordinary claims, and they require extraordinary evidence.

First, show us the "mathematical proof". Reproduce it as well as you can. There are plenty of us here that understand relativity and will happily entertain mathematics which will be far more convincing than any hand-waving or appellations to historically based inconsistencies.

Secondly, I have a question: do you know why relativity was developed? Have you explored the theory in its rigor and application? Have you considered the roots, that is the theory of electromagnetism and lorentzian relativity? Do you have any explanations for how to reconcile classical mechanics with classical electrodynamics other than through relativity? If so, are they mathematically rigorous? Are they explained in observations?

What are these "binary star" observations you speak of? What do they indicate? Can you give a citation?

Thanks.

<font size=-1>[ This Message was edited by: HUb' on 2002-10-11 08:45 ]</font>

JS Princeton and HUb',

I love your comments, and I thoroughly agree with the positions you have taken, with one minor exception:

HUb' stated "astrology {IMhO} assumes a nonvaring frame?" I do not believe in astrology, and, as far as I can tell, astrology has nothing to do with the subjects at hand.

I have prepared a more detailed answer. It is currently found at:

http://members.ispwest.com/vjk/RELATIV1.HTM

Sorry, Verlan, I don't think you have that right. Here's
how you really add relativistic velocities.

Your math error is actually a very common one. You assume that the squareroot of the sum of two squares is equal to the sum. It is not.

Another way you to write your formula for v_3 is as follows

v_3=sqrt(v_1^2+v-2^2-(v_1*v_2/c)^2)

If this is nonrelativistic v_1*v_2 much less than c^2, we get from your equation that

v_3=sqrt(v_1^2+v_2^2)

Which isn't true... in fact...

v_3=v_1+v_2

It's very clear why you are having a problem with negative versus positive velocities, which are the cases for which the above two equations are the most drastically different (since the square of a negative number is positive). Using your logic would lead us to believe that if point A and point C were travelling at the same velocity and we stuck a point B in between them travelling at a different velocity, we would measure a "relativistic" velocity that was equal to (roughly) twice the velocity of B instead of zero.

My recommendation to you is to look over the site I posted and derive the correct equation for v_3 from there. You will find that there is no paradox after all.

<font size=-1>[ This Message was edited by: JS Princeton on 2002-10-11 00:36 ]</font>

I don't see where he does that directly, but as you point out below, it is a consequence at non-relativistic velocities.
Huh? Does that work out? Hey, that's right. It follows right from his equation:

And, as you say, in order for that to be true, the right hand side would have to be also equal to v_1 + v_2

I think the basic error is his assumption that the dilations compound by multiplication. He assumes that if A sees B as twice as slow, and B sees C as twice as slow, then A will see C as four times as slow. That's obviously not true--just let C be the first observer A. A would see A as four times as slow?

<a name="20021011"> POST 20021011 aka gnuPLOT?
On 2002-10-11 08:25, GrapesOfWrath wrote: To: 6:06 A.M. HUb'
Can "NOT" control this 486/100 well enough to reply NOW.
when i CAN get back to the 386/20 i'll snip
the string and submit the question to GNUplot
my guess it will gag & I'll have to try to
translate it into gnuplot lexicon & syntax

v_3=sqrt(v_1^2+v-2^2-(v_1*v_2/c)^2)[/quote]
Huh? Does that work out? Hey, that's right. It follows right from his equation:
http://members.ispwest.com/vjk/RELATIV2.JPG
And, as you say, in order for that to be true, the right hand side would have to be also equal to v_1 + v_2
6:11 A.M. my 1st guess would be that ^ must change to **
I think the basic error is his assumption that the dilations compound by multiplication. He assumes that if A sees B as twice as slow, and B sees C as twice as slow, then A will see C as four times as slow. That's obviously not true--just let C be the first observer A. A would see A as four times as slow?
{my 0pollo_G for My delay in responce}

<a name="2-10-11.5CK"> POST 2-10-11.5CK aka 5clocks & nonvaring Frames
On 2002-10-11 09:02, HUb' wrote: To: 2-10-11 HUb' 6:21 A.M.

On 2002-10-11 08:25, GrapesOfWrath wrote: To: 6:06 A.M. HUb'

in my scheme {5 Clocks} {Earth orbits Sun / electrons ORBIT} etc
I 'poise there exist FIVE nonvariant frames
{Um a frame that holds each clock}
and astrology{ismS}{istS} would assume the D3 Clock 3 case
------------
anyway by this i dont mean that the interval of time
in any clock would be non variant
============
I think what i mean {though Shirly Not sure}
would be something along the lines of
{a circle has 360 degrees}
OR an ORBIT can be seen in such a way{FASHON}
as to appear closed
maybe expressing it in RADians would make it
more contempary?
ANYWAY 5 clocks = FIVE nonVariant Frames {whatevet that means}

<a name="2-10-11.C3"> POST 2-10-11.C3 aka d3C3 to D2c4
On 2002-10-11 09:20, HUb' wrote: To? 6:34 A.M.
<a name="2-10-11.5CK"> POST 2-10-11.5CK aka 5clocks & nonvaring Frames
iTS MY FURTHOR " BELIEF " that:
its physically possible
based upon personal experiences
to transport from a Clock3 Frame to Clock 4
and back {although its certainlyy not easy}
--------
and the Most noticable change
IS the physical concept of time || 2-10-13 maybe MENTAL concepts better
=======
whereby when transporting from C3 to C4
preceptions while in C4 of events ib C3 Slow
::::::
and "THEN" to transport back
time must catch up with you eventually
so there a period of time recompression
along with the regular faster intervals
SO its very violent as dV/dT's get excessive
???
so4me its the Angles for the most part that are the
ON Average non variant parts {but i think its on Avg. & can very tic to tick} Vairy Vary ? Variable?/?

<font size=-1>[ This Message was edited by: HUb' on 2002-10-13 11:11 ]</font>

<a name="20021011.11:51"> page 20021011.11:51 aka Mathemitica 4.2
386/20: 11:54 A.M. I dialed back in to pluck the string
to submit it to gnuplot , also to LIE & Quick Basic
results later.. anyway i found a discarded
MacWorld Nov 2002 mag and there may be a
relavent article there on page 45.
the article explains that ONLY
Mathematica 4.2 is Java capable
{not that i've Java nor plan to `ave `ER}
{it may well be something else i might skip}
---
in the article it discribes
FOUR DIFFEREN METHODS FOR GLOBAL OPTIMIZATION
4 RANDOM SEARCH
3 SIMULATED ANNEALING
2 NONLINEAR SIMPLEX ANGLORITHM
1 GENETIC PROGRAMMING
{being an ill_ogical negativFIST i list them in reverse order}

=== 4 Myself, i say oh,gee; you can get Color
output. thats nice especially for three or 4
different graphs
ftp://ftp.dartmouth.edu/pub/gnuplot
go there to download gnuplot (worth it even2day)
and try to search
http://www.macworld.com/2001/02/05/r...thematica.html

<a name="20021011.12:44"> page 20021011.12:44 aka Quick Results

1st I did try the string in gnuplot {parameter error
2 next i tried it in LIE {go nowhere "Quickly}
3 So I tried to load it directly in Quick basic .. got a v
-----------------------------------------
My guess: with my ill-Logical negativist
{UM randm search methode} I might get a
postable result next week }{after a mkt rally}
my approach will be VERY Slow now
and anyone who has the "script" in any of the
three above {any Script will be tried ]
---
in the article it discribes
FOUR DIFFEREN METHODS FOR GLOBAL OPTIMIZATION
4 RANDOM SEARCH
3 SIMULATED ANNEALING
2 NONLINEAR SIMPLEX ANGLORITHM
1 GENETIC PROGRAMMING
{being an ill_ogical negativFIST i list them in reverse order}




ftp://ftp.dartmouth.edu/pub/gnuplot
thats a FREE DownLoad but the site stalled ?
150 bucks is way to much
http://www.macworld.com/2001/02/05/r...thematica.html
and A grand & a half well try to leave a link annyway

<a name="20021012"> POST 20021012 aka A sea STORY
You are standing on the Main deck at the foot
of a vertical ladder that assends one level to the 01,
holding a cup full of coffee in each hand,
in realtively high seas. {thats the clue Hi C's}
and when the correct moment arrives
you climb the ladder without having to
hold on.
this is reported as a very true and
when the ASR-7 was still around
A verifiable tail.. attested to by
general "ayes" all around..
So yes its very reasonable to do so
WHEN THE TIME & conditions are right
------------------------------------------
I would say this about the act itself little
some have done it, others have not
=========================================
my point in this discussion a point removed
:::::::::::::::::::::::::::::::::::::::::::::
its my coontention, when doing this, that in
point of fact, {SOME} Human{s) can, relinquis hold
on the local referance frame {in this case}
(its the deck and the verticle ladder}
and transfers one{s} own stable eliment
{if that{s} what it might be called}
to a different (Larger, more generalized frame}
{the storm..at sea itself}
?????????????????????????????????
So its subtile. whatever here I refer to,
but its my conclusion .. that in fact some
MENTAL {call it dilusinal if you like}
SHIFT of reference {FRAME} Can & "DOES" take
place. and for those unable to do the shift, they
could not assend to the 01 without holding on
{TO THE LADDER} AS 4 MYSELF ? 2steps beyound
forget the foot prints on the ladder & just ASCEND { i mean lift a leg}{{ well? actually 2}}

<font size=-1>[ This Message was edited by: HUb' on 2002-10-13 11:18 ]</font>

Careful. You're 'bout in violation of the BOO 3.

I appreciate the comments by JS Princeton. He stated that I made a common math error, and I could not find such an error.

I would like to apologize to JS Princeton, because when I created my web site and made it available to bad astronomy, there was typographical error in some of the equations. I immediately corrected the errors, but before I could correct it, JS Princeton saw the web site and made his comments. The typographical errors did not affect my conclusions, and the corrections were made very rapidly, so I would be astonished if anyone else reviewed the web site with the typos.

I agree with GrapesOfWrath, Bad PhD, "I don't see where he does that directly, but as you point out below, it is a consequence at non-relativistic velocities." I cannot find where I made any math errors.

Back to JS Princeton Bad Intern. He establishes the point I am trying to make, rather than contradicting it.

The point in my mathematical exercise was NOT to find how to add velocities under relativity, but rather to show a mathematical contradiction.

When you want to prove that something is false in mathematics, you start first by assuming it is true. Then you work through the math and arrive at equations or results that cannot be true. When you do that, you have established that your original assumptions were wrong. This is a very common approach in mathematical proofs.

I used this approach, and I started with the assumption that all frames of reference are equally valid. I proceeded with the mathematics and arrived with an equation for adding velocities. I took the position that my equation for adding velocities was not correct, and therefore, the original assumption that all frames of reference are equally valid is not correct.

JS Princeton Bad Intern also took the position that my equation that for adding velocities is incorrect, which is exactly the point that I am trying to make.

I started by working with the effect that time has on multiple observers, and the assumption that all frames of reference are equally valid. The math developed into an equation for adding velocities, which both JS Princeton Bad Intern and I state is an incorrect conclusion.

JS Princeton Bad Intern gave an alternate equation for adding velocities, and I would like to compare my equation with his.

Both give relatively accurate results at velocities close to the speed of light. Both are correct when one of the velocities is zero. Both show the effects of relativity being realized only at higher velocities. My equation shows the effects of relativity being realized at much lower combined velocities than it should be realized, from an intuitive standpoint. From an intuitive standpoint, I would expect JS Princeton to be a more accurate depiction.

GrapesOfWrath Bad PhD also agrees with us, which helps prove my point, that my equation for adding velocities is incorrect.

GrapesOfWrath Bad PhD did a good job of articulating my assumption: "I think the basic error is his assumption that the dilations compound by multiplication. He assumes that if A sees B as twice as slow, and B sees C as twice as slow, then A will see C as four times as slow. That's obviously not true--just let C be the first observer A. A would see A as four times as slow?"

My assumption is that time dilations compound by multiplication. GrapesofWrath stated the assumption obviously is not true, but I do not follow the reasoning of GrapesofWrath.

<a name="2-10-23.4:59 A.M."> page 2-10-23.4:59 A.M. aka mATH hOUR
On 2002-10-23 07:16, Verlan J. Kliewer wrote: To? 5:00 A.M. PDT
yeeh? i still have a few TIMEX computers left
THEY DID HAVE a controls to switch from FAST to Slow & back
as i recall {earily 80? 20 years ago} the
difference between FAST & Slow
was the difference between PLOT & noPLOT
----------------------------------------
it was to long ago for me to REMember exactly
thoughi still have a book somewhere that could
explain the difference between the 2
====================================
4myself i'll just say now days i use this
faster 486/100 to READ {download} longer
.JPG's {not really very interested} etc
:::::::::::::::::::::::::::::::::::::::::
and i use the slower {more reliable 4me}
396/20 to update the OCT quakes page
YES; even thats old & borish
?????????????????????????????
so the question may as well be
Velocity (or in my terms) how quickly
{SLOWLY} IS THE mOON RECEEDING FROM EARTH
{um in centimeters per million orbits PLEASE}
(and of course the real Question)
how quickly does that rate change
send me the PLOT off your FAST computer
and as soon as I get one from MY Timex's
I'll send you? 1. No I've no intention in the next 20
years of even having to plug 1 in
//tilt\ As far as how fast Clock GPS15 slows :C.GPS11 wellyou know I don't get the data

OK, but you have to be very careful when you make additional assumptions--it could be those additional assumptions are wrong, not your original assumption.
Well, your final equation is obviously invalid, but your assumption that you can multiply relative velocities is in error.
[img]/phpBB/images/smiles/icon_smile.gif[/img] I'll try again, using X, Y, and Z. If X sees Y as twice as slow, and Y sees Z as twice as slow, then X will see Z as four times as slow. That's just a rephrase, right?

Now, let X=A, Y=B, and Z=A.

In special relativity, when A sees B as twice as slow, B also sees A as twice as slow. That does not mean, though, that A sees A as four times as slow.

<font size=-1>[Fixed quote BBcode]</font>

<font size=-1>[ This Message was edited by: GrapesOfWrath on 2002-10-23 08:49 ]</font>

I would like to clarify something. I do not have just one known assumption to arrive at an incorrect equation for adding velocities – I have two known assumptions.

One assumption is that all frames of reference are equally valid, that any frame of reference can be used as a stationary frame of reference.

Another assumption, pointed out by GrapesofWrath, is that time dilations compound by multiplication.

Maybe I do not understand GrapesofWrath’s statement correctly, “just let C be the first observer A. A would see A as four times as slow?”

I think GrapesofWrath takes the position that if there are two observers moving with respect to each other, then observer A would view B as having a time dilation, time slowing down. Observer B would then view A as having a time dilation also, time slowing down. When the assumption is made that time dilations multiply, then we would arrive at the illogical conclusion that observer A would then see its own frame of reference as being slower than its own frame of reference. Obviously, that does not make sense.

If I understand GrapesofWrath’s conclusion, he concludes that my original assumption, that time dilations compound by multiplication, can not be true, because of the contradiction.

The problem that I have with GrapesofWrath’s reasoning, if I have understood it correctly, is that he has a hidden assumption. He assumes that all frames of reference are equally valid, and that any frame of reference could be used as a stationary frame of reference. All contradictions vanish when the assumption is eliminated, when all time dilations are calculated with respect to the stationary frame of reference.

Such a hidden assumption is understandable, since it is deeply ingrained in our relativistic reasoning.

It seems to me that both assumptions, that all frames of reference are equally valid, and the assumption that time dilations compound by multiplication, cannot both be true.

Can anybody justify the assumption that all frames of reference are equally valid, and that any frame of reference can be used as a stationary frame of reference, without relying on the assumption that all frames of reference are equally valid? Do not bother trying to point to the many confirmations of the mathematics of relativity that we have observed. The same mathematical confirmations can be achieved without the assumption.

Do time dilations compound? If the answer is “no”, then I would suppose that would be devastating to relativity. We could address that issue if anybody should question it.

If, indeed, time dilations do compound, then what is the math behind it? Is it possible to construct the math for compounding time dilations so that it is both consistent with the assumption that all frames of reference are equally valid, and any frame of reference can be considered to be a stationary frame of reference, and be consistent with the mathematics of special relativity?

Correct me if I am wrong, but as far as I can tell, no matter how you calculate compounding time dilations, when you assume that all frames of reference are equally valid, and any frame of reference can be considered to be a stationary frame of reference, you will always arrive at the conclusion:

When two observers are involved, in the example given at the beginning of this segment, observer A will always arrive at the illogical conclusion that his time proceeds slower than his own time.

As far as I can tell, the only way to resolve this is to conclude that the assumption that all frames of reference are equally valid, that any frame of reference can be considered to be a stationary frame of reference, is incorrect and conflicts with the mathematics of special relativity.

HUb' Bad Master stated, "so the question may as well be Velocity (or in my terms) how quickly {SLOWLY} IS THE mOON RECEEDING FROM EARTH"

I will open a new topic about this.