Dear Friends,
let me offer you a short version of my Lecture that will be, I hope, useful for current discussion on that matter.

The special role of time in Nature and Twins Paradox.
(Amendment to the Lectures on SRT)

Formulation of Twins' Problem.


This famous paradox is used so many times in the discussions on sense of SRT, that it deserves to be discussed in a special Lecture in straight and non-ambiguous manner.

The Twins Paradox (TP) was appeared just after Einstein's 1905 article "On the electrodynamics of moving bodies" and its formulation is the following.

Let's consider two twin-brothers; one (brother #2) is launched to be caring away with a speedy rocket and another one (brother #1) is staying on the Earth. After the rocket will return on the Earth what ages the brothers will be?

Assuming that the rocket was moving mostly with the constant speed V (except the three short enough periods of time when the initial acceleration, the turn back and final deceleration were accomplished) we can apply the Lorentz time-delay formula

T2 = T1 square root(1-v^2) (*)

where the velocity of the inertial movement of rocket, v, is measured in the units of c - the speed of light in vacuum, i. e. v = V/c..

As one can see, at return to home the age of brother #2 will be changed on the period of time T2, although the age of brother #1 will be changed on the period of time T1 > T2. Therefore, we come to the conclusion, that the moving brother is aging slower then rested one.

Because our assistant in this consideration - the brother #2 - was not the unique contents of rocket, we, thinking about measurements of the passing time that are possible in rocket, very soon will come to the general conclusion that:

The all processes in the moving reference frame becoming slow down, i. e. the physical time in the moving reference frame is passing slower than in the rested one.

Such a conclusion was very unexpected in earlier XX, but now we know that this is an essence of the Lorentz dilation of time. And there is no paradox jet.

Many of physical characteristics are changing in regard to moving observer. A long before Einstein we knew that momentum, kinetic energy, electrical field and some other physical properties are changing in regard to moving reference frame. Nobody would say: "Look, what a paradox - the resting on Earth brother says that the kinetic energy of ball, the moving brother keeps in his packet, is none zero!" Or "Look, he also says that there is some magnetic field around this charged ball, that the moving brother keeps in his hands!" Everybody knew that resting brother is right and there was no paradox. The Einstein's discovery, that not only those classic properties, but also such things as length, masses, volumes, angles, forces, etc, that before Einstein were counted as unchangeable absolute quantities, also are changing in the inertial moving reference frame, was very unexpected and exciting, but there was no paradox. It was the new Physics - Physics of Special Relativity Theory (SRT). The only Physics we new today...

Of course, SRT was an intellectual shock for the majority of people. But it was not a unique one in our history: the same shocking was the Galilee's discovery of the law of inertia - that really free body moves with a constant velocity. This discovery had eliminated the Aristotle's paradigm that reason of velocity is the force: no force - no constant velocity. And this discovery had eliminated Aristotlean Physics and opened the door to the new - Newtonian - Physics. The same cultural shock humanity had experienced after Copernicus' discovery of the Helio-centric system. This discovery had eliminated the Ptolomeian paradigm - that center of World is the Earth - and opened the door to the new - Copernicus model of the Solar system. All such shocks were occurred because in all such cases Science was crashing the Common sense - "What I see and feel - so it is in Nature, no matter what causal relations are staying behind that and because of that".
[By the way, in spite of fact, that every textbook on Logic names the Common sense as one of most often and usual logical mistaken approaches, it still is a beloved manner and word for ... politicians. Do you know why? Because the majority of us still lives and votes following the Common sense. As we live, so we vote...]


Appearence of Paradox.


The paradox appears as soon as we will try to apply the Principle of Relativity of Motions to the problem of our twin-brothers.

Indeed, the moving brother #2 can describe situation in the same way: he is resting, but his brother #1 on Earth is moving (together with whole Earth) in opposite direction with the same velocity. So, the formula for his time-delay should be the following

T1 = T2 square root(1-v^2)

Therefore, he and everything on Earth should be aging slower. When they will meet again on Earth he will be much older than his brother on Earth will.

And there appears the famous Twins Paradox: "Which one of these two twin-brothers really will be younger at their meeting on the Earth again?"

And let us repeat: the paradox is not in the time-delay effect, but in the seeming impossibility to decide, which of brothers will be younger.

Irrelevance of acceleration.


Before we will analyze TP let us consider some the most popular "resolutions" of it, still widely spread in the literature.

1. The philological "resolution": "Twins Paradox can be explained only in the frames of GRT". Let us recall that TP has nothing to do with General Relativity, it is "a child" of Special Relativity Theory. Of course, the actual resolution of TP may be lying somewhere "outside" SRT, but a simple consternation of that possibility without evident presentation of any proof sounds as an attempt to avoid of any resolution, at all.

2. The most popular "resolution": "On of twins evidently experienced the accelerations; therefore he can not be considered as an inertial reference frame and Principle of Relativity and Lorentz transformations are not applicable to him. He, and namely he will be aging slower than the first twin, remaining on the Earth".

This "resolution" of Twins Paradox is simply logically wrong one. To recognize this fact, let us consider motion of rocket more detailed. Whole journey of rocket consist of five consecutive parts (segments, intervals):

A. Initial acceleration till velocity V; let it takes time ta.
B. Inertial motion from Earth with velocity V; let it takes time tb.
C. Turn back (turn velocity from value V to value -V); let it takes time tc.
D. Inertial motion with velocity -V back to Earth; let it takes time td.
E. Final deceleration till zero velocity; let it takes time te.

As one understands, parts A. C and E could be the same, no matter how long times tb and td are. In other words, no matter how long time racket will be kept moving inertial, the parts of accelerations and decelerations can take the same times (at all the same given means of energy, engines, supply, etc).

But the time-delay we are calculating by the Lorentz formula concerns only to the inertial motion. And this time dilation absolutely no-how is connected with past or future of the currently inertial moving body. In SRT the history of motion of the reference frame has nothing to do with description of the current physical events in this reference frame (at least, for the closed systems of the material points). Any dependence of description of any closed physical system upon dynamical history of the currently inertial reference frame would be a direct violation of Principle of Relativity.

Therefore, if we will chose (tb + td) >> (ta + tc + te) whole time-delay will be practically accumulated in the regime of the inertial motions (forward from and backward to Earth).

Moreover, the same parts A, C and E can correspond to the absolutely different tb + td , so that, even if these parts are compensating one duration of tb + td at one choice of it, they can not compensate the another duration of tb + td at another choice of it.

This is why non-inertial parts of rocket's journey does not play any role in the formulation of the Twins Paradox, no matter is acceleration equivalent to gravity, or is not.


Irreducibility of time's dilation.


One of my fellows told me that due to the existence of the Twins Paradox the Mother Nature does "the intellectual abuse" to us. I guess, it is indeed so...

Let us now start our analysis of this dramatic situation with Twins paradox.

The first of all let us emphasize absolutely unique meaning of the Lorentz transformation of the periods of time. Although in the sense of instant values of velocity of motion, v, we have the following very similar formulas like

- time periods
T2 = T1 square root(1-v^2) (*)
- masses
m2 = m1 /square root(1-v^2) (1)
- lengths
L2 = L1 square root(1-v^2) (2)
- volumes
V2 = V1square root(1-v^2) (3)
- momentum
P2 = (P1 - v E1/c2) /square root(1-v^2) (4)
- kinetic energy
E2 = (E1 - vP1) /square root(1-v^2) (5),

etc., etc; all formulas (1) - (5) have absolutely different sense than (*) does.

Indeed, as soon the velocity of moving reference frame #2 in respect to the reference frame #1 will decrease to zero, i. e. the reference frame #2 will became coinciding with the reference frame #1, as all relativistic differences in masses, lengths, volumes, momentum and kinetic energy will disappear, but the time dilation, accumulated due to (*), will remain forever.

In other words, any moving system, being decelerated to coincide with rested one, loses all discrepancies in physical characteristics it had at motion except time-delay. This is why we have Twins Paradox and do not have any paradox with mass, lengths, volumes, momentum, kinetic energy - both brothers will have all them the same at meeting on the Earth again.
As I have emphasized in clause 1 of present analysis, the time, in contrast with any other Lorentz-non-invariant value, has a unique property: it accumulates all Lorentz-delays during the motion and conserves it forever.

All others values in Nature will lose all relativistic differences they had between moving and resting systems as soon as the velocity of moving reference frame (RF) #2 will decrease to zero and RF #2 will decelerate to became coinciding with a rested RF #1. But the time delay, described by
T2 = T1 square root(1-v^2) at duration of any period of non-zero v, will be accumulated and will be conserved forever.

[Let us recall that in formula (*) v is velocity of RF #2 in regard to RF #1 measured in units c - the speed of light in vacuum]

I will call this feature of time as "the Time Dilation Irreversibility", or TDI. As one should understand, TDI exist only because natural property of time, and not because of specific form of Lorentz-transformation: any relation like T2 = kT1 will lead to the same conclusion.

To illustrate TDI with ultimate clarity let us assume that brother #2 turns on his clocks at the end of each part of acceleration and/or deceleration and turns it off at the start of each part of acceleration and/or deceleration. So that the readings of clocks remain the same (clocks simply do not work) during any period of non-inertial part of motion of rocket and in contrary - clocks are working during each period of the inertial motion of rocket. It is obvious that the final readings of such clocks will accumulate real duration of the parts of inertial motion of the considered rocket. And they will show this duration forever, even after the rocket will return on Earth.

If (tb + td) >> (ta + tc + te) this readings will be exactly the duration of time 2T2 we are comparing with 2T1. And namely their ratio T2/T1 will be equal to square root(1-v^2) we are talking about.

Let us talk about namely this accumulated duration for both brothers in contents of the Twin Paradox. Let us keep in mind the fact that the history of motion of the reference frame has nothing to do with description of the current physical events in this reference frame. Then we will evidently see that there is no place for the most often "resolution" as "Lorentz transformations are not applicable to the non-inertial reference frames". Then everything in our formulation of the Twins' Problem in SRT will be absolutely correct and we will come to the Twins Paradox.


The generality of Time Dilation.


The assertion that "Lorentz time dilation phenomenon is not applicable to the non-inertial reference frames" is wrong in general. Indeed, let us consider evidently non-inertial motion of some material body with velocity v(t) essentially depending upon time. Of course, the Lorentz formula for time dilation (*) is not applicable to the finite segments of time in this case. But one should be sure that this formula definitely is applicable to the infinitesimal intervals dT1 and dT2, for which one can write down:

dT2 = dT1 square root(1-v^2) (6)

Therefore, for entire non-inertial motion between moments To and T (measured in the rested - laboratory - reference frame, where we measure T1) one will have the following value of the total time dilation:
. tillT
Integral {square root(1-v^2)}dt = T2 (7)
.fromTo

It is true that the motion during any infinitesimal period of time is physically undistinguishable from the inertial motion with velocity that is equal to the value of the instant velocity at real motion. Ultimate proof of this conclusion one can find if he/she will recall the Principle of Quantification of Interactions: any interaction consist of acts of quanta exchange, between which the interacting bodies are moving by inertia.

If one will notice that T2 in (7) is Lorentz-invariant quantity ( square root(1-v^2)dt is the proper time interval and it is the Lorentz- invariant variable), he/she will come to the conclusion that we are talking about quantities that are the same in any other inertial reference frame.

Therefore, the Lorentz time dilation is a common Lorentz-invariant effect and is applicable to any motion of the material bodies. Formula (7) represents the quantitative measure of it. This formula evidently shows that the time dilation is accumulated during whole time of motion. And the Twins Paradox appears when we connect this effect with the Principle of Relativity of Motions.


The origins of the Twins Paradox.


Therefore, the Twins Paradox appears only because of and only due to three independent factors acting together:

- The existence of time dilation;
- The time dilation's irreversibility;
- The Principle of Relativity of Motions.

And TP would be in any theory with time-delay no matter what causes this time dilation - whether velocity of motion, or strong gravitational field, or replacement in other places, or something else...

Looking on these three factors, one can come to the following conclusion:

"To avoid TP we have to sacrifice one of three:

- the existence of time dilation,
- the irreversibility of time dilation, or
- the Principle of Relativity of Motions".

Does one feel the seriousness of problem of existence of the Twins Paradox for whole contemporary Physics?


Role of Paradoxes in Science.


To emphasize this critical situation, let me remind you one more time the role of real paradox in any theory.

Paradox never proves or disproves any theory. Moreover, there exist so called the Geodel's theorem, which states that in any particular formal theory one can find a true assertion overcoming all what can be proven in the frames of that theory. As you understand, each such finding will sound as a paradox of that theory.

Bertrand Paradox did not make the Sets Theory wrong, Zehno Paradox did not make the ancient kinematics wrong, so the Twins Paradox does not make Lorentz transformations wrong (without Principle of Relativity there is no need to know any transformations between two relatively moving references frames, at all). Paradox always was indicator of necessity (or possibility) of the more general theory, or more general interpretation of old theory, etc. Many paradoxes with a time were resolved due to development of theories that gave birth to them.

Science holds the Lorentz transformations because whole contemporary Physics with all its achievements in the area of energies comparable with a rest energy of body is based on this transformation. And that is a lot, and this means a lot... To force us to reject this transformation one has to

- Bring on light very, very important facts of Nature that absolutely unavoidable shown that Lorentz invariance is wrong or

- Construct a new theory, which explains the all achievements of old one and predicts really measurable differences in a serious set of a new effects and phenomena.
Everyone, who decide to move on that way should remember one very practical statement of Dirac: "Any finite set of facts of Nature can be explained by the infinite set of wrong theories"... At least, it will help to some of us be more careful at their unreasonable rejection of the traditional Scientific theories... In other hand, the Twins Paradox indeed remains some kind of abuse of our intellectual ability...

I am absolutely sure that resolution of Twins Paradox will lead us to totally new level of understanding of Nature...

.. the Twins Paradox indeed remains some kind of abuse of our intellectual ability...

I am absolutely sure that resolution of Twins Paradox will lead us to totally new level of understanding of Nature...
Y'lost me about four 5ths of the way through it. But why all the malarkey?? The Twin Paradox is resolved with straightforward SRT Lorentz Transform a LOT more simply and consicesly at
my Twin Paradox w/o Accel (http://sysmatrix.net/~kavs/kjs/addend4.html)
.. and it doesn't even "lead us to totally new level of understanding of Nature." It's just the standard level of understanding.

But there IS something hard to fathom about the One-way Twin Paradox. Maybe I'll post about it.

..there IS something hard to fathom about the One-way Twin Paradox.
You're a space ship seemingly stock still out in deep space. You set up an experiment: a projectile is shot out of a cannon and proceeds coasting down a long tube. The projectile has an onboard atomic clock. Soon after the blast is dissipated and the initial acceleration phase ends, the projectile's motion triggers a switch on an adjacent clock, one that is stationary to the ship itself. At this occurance, the lab clock is synchronized with the projectile's clock reading. After that the projectile coasts frictionlessly until it runs into a really overstuffed cushion at the tube's end and decelerates to a halt. Now the clocks can be compared in the same frame.

It is discovered that the projectile aged the less. Why? Because folks in the lab saw it move! Well why didn't the projectile "see" the lab clock move and suffer time dilation, hmmm? Answer: it did. But when it felt that G-force at the end, an additional time flow distortion entered into the reckoning, one that ascribes sped up time to the receding lab clock, in just such precise degree as to toally compensate for the time dilation that must be ascribed as well. But this additional distortion isn't even a factor in the lab's native frame. They don't feel the G-force, and hence they are computationally detached from its implications.

The two-way Twin Paradox is just a continuation of the one way, except that the projectile's deceleration phase is against a springboard, and it is propelled back again. [Again, a trigger while still coasting demarks the end of its return leg.] The direction of acceleration is the same as before, just twice as long. The clock discrepancy should wind up being double what was seen in the one-way test, assuming perfect elastic collision of course and a return speed equal to the former.

Yuriy,

Nobody cares about YOUR lectures. Look around you could throw a bowling ball through here. Go back to Physlink where your lectures were equally resisted.

Yuriy,

Your presentation contains a number of errors. For a start, I will point out one.

This "solution" of Twins Paradox is simply logically wrong one. To recognize this fact, let us consider motion of rocket more detailed. Whole journey of rocket consist of five consecutive parts (segments, intervals):

A. Initial acceleration till velocity V; let it takes time ta.
B. Inertial motion from Earth with velocity V; let it takes time tb.
C. Turn back (turn velocity from value V to value -V); let it takes time tc.
D. Inertial motion with velocity -V back to Earth; let it takes time td.
E. Final deceleration till zero velocity; let it takes time te.

As one understands, parts A. C and E could be the same, no matter how long times tb and td are. In other words, no matter how long time racket will be kept moving inertial, the parts of accelerations and decelerations can take the same times (at all the same given means of energy, engines, supply, etc).

But the time-delay we are calculating by the Lorentz formula concerns only to the inertial motion. And this time dilation absolutely no-how is connected with past or future of the currently inertial moving body. In SRT the history of motion of the reference frame has nothing to do with description of the current physical events in this reference frame (at least, for the closed systems of the material points). Any dependence of description of any closed physical system upon dynamical history of the currently inertial reference frame would be a direct violation of Principle of Relativity.

Therefore, if we will chose (tb + td) >> (ta + tc + te) whole time-delay will be practically accumulated in the regime of the inertial motions (forward from and backward to Earth).

This is only true for the Earth frame. It is not true in the spaceship frame.

Any explanations, please, ... what "this" and what "it"?

Let me finished discussion with MacM by this clear and plain application of SRT. I hope, young readers will find there a lot new thoughts...

The practical usage of the Lorentz transformations.

(Amendment to the Lectures on SRT)

What are the Lorentz Transformations?

Let us start with reminder of the sense of the Lorentz transformations (LT).

1. First of all let us recall that LT are describing relations between coordinates and times of events in two inertial reference frames (IRF).

2. Any event is happened somewhere and sometime, i.e. any event can be characterized by 3 space coordinates x, y, z and time t. Therefore, each event can be characterized by its space-time 4D-coordinates (x, y, z, t). If something occurring requires for its description more than one 3D-space point and/or more than 1time point, it is not an event but some complex phenomenon consisting of many events. In that case we should apply LT separately to each event this phenomenon consist of.

3. The Lorentz transformations are the following:

y’= y; z’ = z ; x’ = (x - u t )/[1- (u^2/c^2)]^1/2 ;
t’ = (t – ux/c^2)/[1- (u^2/c^2)]^1/2 …(*)

where a^n means “ a in power n”.

The Lorentz transformations (*) are describing relations between instant coordinates and moment of time of some event observed in two inertial reference frames (IRF): "the rested one"- the LabIRF (x, y, z, t) - and "the moving one"- the MovIRF (x’, y’, z’, t’) - which is moving forward along axis X of LabIRF with some constant velocity u in respect to,LabIRF and keeps the parallel orientation of two other coordinate axes to Y and Z.
So, there talk goes about events and only events. Each event is characterized with moment of time t, when that event has happened, and with coordinates (x, y ,z) of point in Space, where that event has happened, i. e. by set of four variables (x, y, z, t). Namely these four variables, measured in two different inertial reference frames, are connected by the LT.

Very important notice: LT in form (*) are written for IRF that are synchronized in the beginning. It means that the special event (0, 0, 0, 0) has the same coordinates in both considered IRF. In other words, we are talking about IRF that put their clocks on 0 when they were coinciding with each other.
For another manner of synchronization LT will have another form.

As one can see, LT are one-parametric transformations, LT = LT[u], and this parameter is the velocity u of motion of one inertial reference frame relatively another one.

As one can see form a group - the Lorentz group - in regard of some specific law of addition of velocities. This law of addition can be easily found due to linearity of LT. Indeed, let us differentiate (*). For the infinitesimal quantities it gives:

dy’= dy; dz’ = dz ;
dx’ = (dx - u dt )/[1- (u^2/c^2)]^1/2 ;
dt’ = (dt – udx/c^2)/[1- (u^2/c^2)]^1/2 …(1)

But dx/dt = Vx and dy/dt = Vy and dz/dt = Vz just are the components
(Vx, Vy, Vz) of velocity V in LabIRF. Accordingly, dx'/dt' = V'x, dy’/dt’ = V’y and dz'/dt' = V’z just are the components (V’x, V’y, V’z) of velocity V’ in MovIRF. Therefore, from (1) it follows:

V’y = (dt/dt') Vy; V’z = (dt/dt’) V’z;
V’x = (dt/dt')(Vx - u )/[1- (u^2/c^2)]^1/2 ;
(dt’/dt) = (1 – uVx/c^2)/[1- (u^2/c^2)]^1/2 ……………………….(2)

or

V’y = [1- (u^2/c^2)]^1/2 * Vy/(1 – uVx/c^2)
V’z = [1- (u^2/c^2)]^1/2 * Vz/(1 – uVx/c^2)
V'x = (Vx - u)/(1 - uVx/c^2) ………….………………………..…(3)

This is the famous Einstein's law of addition of velocities.

As one can see, no one inertial observer can see velocity more than c caused by the motion of this observer for any material body in the Nature. Indeed, if Vx < c, then V'x < c too no matter how fast the observer moves, i. e. now big u is. Particularly, if Vx = c, then V' = c, no matter what value u has. This just expresses the Einstein's Principle of Absoluteness of the speed of light in vacuum.

As one can see, the Einstein's law of addition of velocities is a genuine result of the Lorentz transformation.

Often one can hear assertions like that: "The Lorentz transformations do not prohibit the existence of bodies moving with speed more than speed of light in vacuum". This is not true - Lorentz transformations do prohibit motion of bodies with speed more than c. Indeed, let us assume that some body has a speed v>c in regard of some inertial reference frame. In the second inertial reference frame, moving relatively the first one with velocity u < c in the same direction as v, this body will have a velocity:

v' = (v - u) /(1 - uv/c^2)

Let us now look on that body from the particular inertial reference frame moving with velocity u equal to c^2/v < c (because we assume that v>c). Then we will have v' = infinity, what makes situation being a physically absurd one: this body has to be out of Universe in any moment of time! Therefore, the Lorentz transformations do prohibit the existence in our Universe of bodies moving with speed more than speed of light in vacuum.

Let us now directly show that the Lorentz transformations are forming a group in regard to law (3). For that let us consider some event A in three inertial reference frames: IRF-O, where we have (x, y, z, t), IRF-O’, where we have (x’, y’, z’, t') and IRF-O", where we have (x”, y”, z”,t").
Then we will have:

LT[u]- RF-O' through RF-O:
y’ = y, z’ = z; x’ = (x - u t )/g[u]; t’ = (t - ux/c^2)/g[u]…………….(4)

LT[w]- RF-O" through RF-O:
y” = y, z" = z; x" = (x - w t )/g[w]; t" = (t - wx/c^2)/g[w]………..(5)

LT[v]- RF-O" through RF-O:
y” = y’, z" = z’; x" = (x' - v t' )/g[v]………………(6)

To have LT[w] = LT[v] * LT[u] we should substitute (4) in (6). The result should coincide with (5). Doing that, one will get the following

y” = y, z" = z ;
x" = x [1 - (uv/c^2)]/(g[u]g[v]) - t (u - v)/(g[u]g[v])………….(7)
t" = t [1 - (uv/c^2)]/(g[u]g[v]) – x*(u - v)/(g[u]g[v]*c^2)

Comparing that with (5), one can find that there should be true the following equations:

1/g[w] = [1 - (uv/c^2)]/(g[u]g[v]) and w/g[w]= (u - v)/(g[u]g[v]*c^2)

with g[s] = [1 – s^2/c^2]^1/2

This system easily can be solved and the answer is:

w = (u-v)/(1 - uv/c^2), i.e. exactly the low (*).

Mentioning that LT[0] = 1, we can conclude that we have proven that
the Lorentz transformations form the group in regard to Einstein's law of addition of velocities.

Of course, all results of SRT have to transit to the appropriate results of the Newtonian Mechanics if all figured velocities, except c, are much less than c. This transit formally is c -->infinity at limited values of all other velocities.
There are many invariants of the Lorentz transformations - the constructions that do not change at any Lorentz transformations. The simplest of them is so-called infinitesimal Minkowski interval:

ds = [c^2*dt^2 – dx^2 - dy^2 - dz^2]^1/2 ………………… (8)

One can easily prove that it stays the same in the any inertial reference frame. But the interval is not the only Lorentz-invariant. For example, the elementary 4D-volume also is Lorentz-invariant.

How LabIRF-observer describes the Reality.

Let us consider two events having in LabIRF the following 4D-points:
Event A = (Xa, Ya, Za, Ta) and Event B = (Xb, Yb, Zb, Tb). The LabIRF-observer will say that those events are occurring with time delay T = |Tb-Ta|. Being asked to predict what will see MovIRF-observer, LabIRF-observer will answer: According to LT MovIRF-observer will see 4D-coordinates

Ya’=Ya; Z’a = Za;
Xa’ = (Xa - uTa)/[1- (u^2/c^2)]^1/2 ;
T’a = (Ta – uXa/c^2)/[1- (u^2/c^2)]^1/2 …(9)

and

Yb’=Yb; Zb’ = Zb;
Xb’ = (Xb - uTb)/[1- (u^2/c^2)]^1/2 ;
T’b = (Tb – uXb/c^2)/[1- (u^2/c^2)]^1/2 …(10)

respectively.

Therefore, LabIRF-observer will predict that MovIRF-observer will see events A and B with 4D-coordinates as they are given by (9) and (10).
Particularly, MovIRF-observer will see two events happened for the LabIRF-observer in the same 3D-point (Xa=Xb) one after another with time delay T = |Tb-Ta| as events that are happening in the different 3D-points with time delay between them equal to

T’ = |T’b-T’a| = T/[1- (u^2/c^2)]^1/2 ………………….…(11)

Please, pay attention: [1- (u^2/c^2)]^1/2 stays in the denominator! [This is a point that MacM and similar guys never have aprechanded].

Therefore, Lab IRF-observer will say : «MovIRF-observer sees all time-intervals between events in my RF longer than I see them ».

How LabIRF-observers sees events A’ and B’ that are happened in MovIRF with time delay T’ = |Tb’-Ta’| one after another?

Let us consider two events having in MovIRF the following 4D-points:
Event A’ = (X’a, Y’a, Z’a, T’a) and Event B’ = (X’b, Y’b, Z’b, T’b).
The LabIRF-observer will say that those events in some 4D-points (Xa, Ya, Za, Ta) and (Xb, Yb, Zb, Tb), respectively.
To find these points we should solve equations (9) and (10) in respect to (Xa, Ya, Za, Ta) and (Xb, Yb, Zb, Tb).
After we will do that we will find:

Ya=Y’a; Za = Z’a;
Xa = (X’a + uT’a)/[1- (u^2/c^2)]^1/2 ;
Ta = (T’a + uX’a/c^2)/[1- (u^2/c^2)]^1/2 …(12)

and

Yb=Y’b; Zb = Z’b;
Xb = (X’b + uT’b)/[1- (u^2/c^2)]^1/2 ;
Tb = (T’b + uX’b/c^2)/[1- (u^2/c^2)]^1/2 …(13)

respectively. It is so called Reverse LT.

Therefore, LabIRF-observer will see events A’ and B’ with 4D-coordinates as they are given by (12) and (13).

Particularly, LabIRF-observer will see two events happened for the MovIRF-observer in the same 3D-point (X’a=X’b) one after another with time delay
T’ = |T’b-T’a| as events that are happening in the different 3D-points with time delay between them equal to

T = |Tb-Ta| = T’/[1- (u^2/c^2)]^1/2 ………………….…(14)

Please, pay attention: [1- (u^2/c^2)]^1/2 stays in the denominator!

Therefore, Lab IRF-observer will say : «In MovIRF all time-intervals between events are shorter than I see them ».

Let us now compare two results: (11) and (14):

T = T ’* [1- (u^2/c^2)]^1/2 ……………….……...(11)……T < T ’

and

T ’ = T * [1- (u^2/c^2)]^1/2 …………………..…(14)……T >T ’

And here we have no contradictions or paradox: those formulas are concern absolutely different events: (11) – case two events in the same 3D-point of LabIRF and (14)- case two events in the same 3D-point of MovIRF. The readings of Clocks are just such kind of events! Therefore, the proven results show that:

- The MovIRF-observer sees clocks of LabIRF running slower than his own clocks do.

- The LabIRF-observer sees clocks of MovIRF running slower than his own clocks do.

This is the World of SRT and there is no paradox, no mistakes, or misinterpretation of the Nature. It is simply the features of our World!

Let me finished discussion with MacM by this clear and plain application of SRT. I hope, young readers will find there a lot new thoughts...

The practical usage of the Lorentz transformations.

(Amendment to the Lectures on SRT)

What are the Lorentz Transformations?

Let us start with reminder of the sense of the Lorentz transformations (LT).
1. First of all let us recall that LT are describing relations between coordinates and times of events in two inertial reference frames (IRF).
2. Any event is happened somewhere and sometime, i.e. any event can be characterized by 3 space coordinates x, y, z and time t. Therefore, each event can be characterized by its space-time 4D-coordinates (x, y, z, t). If something occurring requires for its description more than one 3D-space point and/or more than 1time point, it is not an event but some complex phenomenon consisting of many events. In that case we should apply LT separately to each event this phenomenon consist of.
3. The Lorentz transformations are the following:
y’= y; z’ = z ; x’ = (x - u t )/[1- (u^2/c^2)]^1/2 ; t’ = (t – ux/c^2)/[1- (u^2/c^2)]^1/2 …(*)
where a^n means “ a in power n”.
The Lorentz transformations (*) are describing relations between instant coordinates and moment of time of some event observed in two inertial reference frames (IRF): "the rested one"- the LabIRF (x, y, z, t) - and "the moving one"- the MovIRF (x’, y’, z’, t’) - which is moving forward along axis X of LabIRF with some constant velocity u in respect to,LabIRF and keeps the parallel orientation of two other coordinate axes to Y and Z.
So, there talk goes about events and only events. Each event is characterized with moment of time t, when that event has happened, and with coordinates (x, y ,z) of point in Space, where that event has happened, i. e. by set of four variables (x, y, z, t). Namely these four variables, measured in two different inertial reference frames, are connected by the LT.
Very important notice: LT in form (*) are written for IRF that are synchronized in the beginning. It means that the special event (0, 0, 0, 0) has the same coordinates in both considered IRF. In other words, we are talking about IRF that put their clocks on 0 when they were coinciding with each other. For another manner of synchronization LT will have another form.
As one can see, LT are one-parametric transformations, LT = LT[u], and this parameter is the velocity u of motion of one inertial reference frame relatively another one.
As one can see form a group - the Lorentz group - in regard of some specific law of addition of velocities. This law of addition can be easily found due to linearity of LT. Indeed, let us differentiate (*). For the infinitesimal quantities it gives:
dy’= dy; dz’ = dz ;
dx’ = (dx - u dt )/[1- (u^2/c^2)]^1/2 ;
dt’ = (dt – udx/c^2)/[1- (u^2/c^2)]^1/2 …(1)
But dx/dt = Vx and dy/dt = Vy and dz/dt = Vz just are the components (Vx, Vy, Vz) of velocity V in LabIRF. Accordingly, dx'/dt' = V'x, dy’/dt’ = V’y and dz'/dt' = V’z just are the components (V’x, V’y, V’z) of velocity V’ in MovIRF. Therefore, from (1) it follows:
V’y = (dt/dt') Vy; V’z = (dt/dt’) V’z;
V’x = (dt/dt')(V’x - u )/[1- (u^2/c^2)]^1/2 ;
(dt’/dt) = (1 – uVx/c^2)/[1- (u^2/c^2)]^1/2 ……………………….(2)
or
V’y = [1- (u^2/c^2)]^1/2 * Vy/(1 – uVx/c^2)
V’z = [1- (u^2/c^2)]^1/2 * Vz/(1 – uVx/c^2)
V'x = (Vx - u)/(1 - uVx/c2) ………….………………………..…(3)
This is the famous Einstein's law of addition of velocities.
As one can see, no one inertial observer can see velocity more than c caused by the motion of this observer for any material body in the Nature. Indeed, if Vx < c, then V'x < c too no matter how fast the observer moves, i. e. now big u is. Particularly, if Vx = c, then V' = c, no matter what value u has. This just expresses the Einstein's Principle of Absoluteness of the speed of light in vacuum.
As one can see, the Einstein's law of addition of velocities is a genuine result of the Lorentz transformation.
Often one can hear assertions like that: "The Lorentz transformations do not prohibit the existence of bodies moving with speed more than speed of light in vacuum". This is not truth - Lorentz transformations do prohibit motion of bodies with speed more than c. Indeed, let us assume that some body has a speed v>c in regard of some inertial reference frame. In the second inertial reference frame, moving relatively the first one with velocity u < c in the same direction as v, this body will have a velocity:
v' = (v - u) /(1 - uv/c2)
Let us now look on that body from the particular inertial reference frame moving with velocity u equal to c2/v < c (because we assume that v>c). Then we will have v' = infinity, what makes situation being a physically absurd one: this body has to be out of Universe in any moment of time! Therefore, the Lorentz transformations do prohibit the existence in our Universe of bodies moving with speed more than speed of light in vacuum.
Let us now directly show that the Lorentz transformations are forming a group in regard to law (3). For that let us consider some event A in three inertial reference frames: IRF-O, where we have (x, y, z, t), IRF-O’, where we have (x’, y’, z’, t') and IRF-O", where we have (x”, y”, z”,t"). Then we will have:
LT[u]- RF-O' through RF-O:
y’ = y, z’ = z; x’ = (x - u t )/g[u]; t’ = (t - ux/c^2)/g[u]…………….(4)
LT[w]- RF-O" through RF-O:
y” = y, z" = z; x" = (x - w t )/g[w]; t" = (t - wx/c^2)/g[w]………..(5)
LT[v]- RF-O" through RF-O:
y” = y’, z" = z’; x" = (x' - v t' )/g[v]………………(6)
To have LT[w] = LT[v] * LT[u] we should substitute (4) in (6). The result should coincide with (5). Doing that, one will get the following
y” = y, z" = z ;
x" = x [1 - (uv/c^2)]/(g[u]g[v]) - t (u - v)/(g[u]g[v])………….(7)
t" = t [1 - (uv/c^2)]/(g[u]g[v]) – x*(u - v)/(g[u]g[v]*c^2)
Comparing that with (5), one can find that there should be true the following equations:
1/g[w] = [1 - (uv/c^2)]/(g[u]g[v]) and w/g[w]= (u - v)/(g[u]g[v]*c^2)
with g[s] = [1 – s^2/c^2]^1/2
This system easily can be solved and the answer is:
w = (u-v)/(1 - uv/c^2), i.e. exactly the low (*).
Mentioning that LT[0] = 1, we can conclude that we have proven that
the Lorentz transformations form the group in regard to Einstein's law of addition of velocities.
Of course, all results of SRT have to transit to the appropriate results of the Newtonian Mechanics if all figured velocities, except c, are much less than c. This transit formally is c -->infinity at limited values of all other velocities.
There are many invariants of the Lorentz transformations - the constructions that do not change at any Lorentz transformations. The simplest of them is so-called infinitesimal Minkowski interval:
ds = [c^2*dt^2 – dx^2 - dy^2 - dz^2]^1/2 ………………… (8)
One can easily prove that it stays the same in the any inertial reference frame. But the interval is not the only Lorentz-invariant. For example, the elementary 4D-volume also is Lorentz-invariant.

How LabIRF-observer describes the Reality.

Let us consider two events having in LabIRF the following 4D-points:
Event A = (Xa, Ya, Za, Ta) and Event B = (Xb, Yb, Zb, Tb). The LabIRF-observer will say that those events are occurring with time delay T = |Tb-Ta|. Being asked to predict what will see MovIRF-observer, LabIRF-observer will answer: According to LT MovIRF-observer will see 4D-coordinates
Ya’=Ya; Z’a = Za;
Xa’ = (Xa - uTa)/[1- (u^2/c^2)]^1/2 ;
T’a = (Ta – uXa/c^2)/[1- (u^2/c^2)]^1/2 …(9)
and
Yb’=Yb; Zb’ = Zb;
Xb’ = (Xb - uTb)/[1- (u^2/c^2)]^1/2 ;
T’b = (Tb – uXb/c^2)/[1- (u^2/c^2)]^1/2 …(10)
respectively.
Therefore, LabIRF-observer will predict that MovIRF-observer will see events A and B with 4D-coordinates as they are given by (9) and (10).
Particularly, MovIRF-observer will see two events happened for the LabIRF-observer in the same 3D-point (Xa=Xb) one after another with time delay T = |Tb-Ta| as events that are happening in the different 3D-points with time delay between them equal to
T’ = |T’b-T’a| = T/[1- (u^2/c^2)]^1/2 ………………….…(11)
Please, pay attention: [1- (u^2/c^2)]^1/2 stays in the denominator! [This is a point that MacM and similar guys never have aprechanded].
Therefore, Lab IRF-observer will say : «MovIRF-observer sees all time-intervals between events in my RF longer than I see them ».
How LabIRF-observers sees events A’ and B’ that are happened in MovIRF with time delay T’ = |Tb’-Ta’| one after another?
Let us consider two events having in MovIRF the following 4D-points:
Event A’ = (X’a, Y’a, Z’a, T’a) and Event B’ = (X’b, Y’b, Z’b, T’b). The LabIRF-observer will say that those events in some 4D-points (Xa, Ya, Za, Ta) and (Xb, Yb, Zb, Tb), respectively. To find these points we should solve equations (9) and (10) in respect to (Xa, Ya, Za, Ta) and (Xb, Yb, Zb, Tb).
After we will do that we will find:
Ya=Y’a; Za = Z’a;
Xa = (X’a - uT’a)/[1- (u^2/c^2)]^1/2 ;
Ta = (T’a + uX’a/c^2)/[1- (u^2/c^2)]^1/2 …(12)
and
Yb=Y’b; Zb = Z’b;
Xb = (X’b - uT’b)/[1- (u^2/c^2)]^1/2 ;
Tb = (T’b + uX’b/c^2)/[1- (u^2/c^2)]^1/2 …(13)
respectively. It is so called Reverse LT.
Therefore, LabIRF-observer will see events A’ and B’ with 4D-coordinates as they are given by (12) and (13).
Particularly, LabIRF-observer will see two events happened for the MovIRF-observer in the same 3D-point (X’a=X’b) one after another with time delay
T’ = |T’b-T’a| as events that are happening in the different 3D-points with time delay between them equal to
T = |Tb-Ta| = T’/[1- (u^2/c^2)]^1/2 ………………….…(14)
Please, pay attention: [1- (u^2/c^2)]^1/2 stays in the denominator!
Therefore, Lab IRF-observer will say : «In MovIRF all time-intervals between events in are shorter than I see them ».
Let us now compare two results: (11) and (14):
T = T ’* [1- (u^2/c^2)]^1/2 ……………….……...(11)……T < T ’
and
T ’ = T * [1- (u^2/c^2)]^1/2 …………………..…(14)……T >T ’
And here we have no contradictions or paradox: those formulas are concern absolutely different events: (11) – case two events in the same 3D-point of LabIRF and (14)- case two events in the same 3D-point of MovIRF. The readings of Clocks are just such kind of events! Therefore, the proven results show that:
- The MovIRF-observer sees clocks of LabIRF running slower than his own clocks do.
- The LabIRF-observer sees clocks of MovIRF running slower than his own clocks do.
This is the World of SRT and there is no paradox, no mistakes, or misinterpretation of the Nature. It is simply the features of our World!

READERS:

Let me make it abundantly clear. Yuriy and I are not having a discussion.

Yuriy is talking to himself as always. Typical of his posts are these long winded FIAT declarations reciting text books.

I have no interest in such a discussion. He is incapable of discussing anything. He likes to dictate and claim he knows it all. "This is the way it is, the books says so".

Not a very interesting fellow I am afraid. And a damn boring teacher and absolutely full of conceit. I for one will ignore his post other than to correct any feloneous statements he may make. Which he has made in the past and I corrected him by posting other physicists comments about his position. Which is why he is bent on pretending to correct me.

Anybody can read a book. Very few (including Yuriy) can think on their own and discuss anything not previously dictated for them.

Let me make it abundantly clear. Yuriy and I are not having a discussion.

Yuriy is talking to himself as always.Wow, sounds like the UniKEF thread.

Wow, sounds like the UniKEF thread.

:D Cute even for you Persol.

To MacM
Hey, the smart one....
I insist that this part:
"Often one can hear assertions like that: "The Lorentz transformations do not prohibit the existence of bodies moving with speed more than speed of light in vacuum". This is not true - Lorentz transformations do prohibit motion of bodies with speed more than c. Indeed, let us assume that some body has a speed v>c in regard of some inertial reference frame. In the second inertial reference frame, moving relatively the first one with velocity u < c in the same direction as v, this body will have a velocity:

v' = (v - u) /(1 - uv/c^2)

Let us now look on that body from the particular inertial reference frame moving with velocity u equal to c^2/v < c (because we assume that v>c). Then we will have v' = infinity, what makes situation being a physically absurd one: this body has to be out of Universe in any moment of time! Therefore, the Lorentz transformations do prohibit the existence in our Universe of bodies moving with speed more than speed of light in vacuum"
I created for the first time in history of Physics - you will not find that simple argument against super-c motion anywhere else. So, sometimes I can think, do I?

To MacM
Hey, the smart one....
I insist that this part:
"Often one can hear assertions like that: "The Lorentz transformations do not prohibit the existence of bodies moving with speed more than speed of light in vacuum". This is not truth - Lorentz transformations do prohibit motion of bodies with speed more than c. Indeed, let us assume that some body has a speed v>c in regard of some inertial reference frame. In the second inertial reference frame, moving relatively the first one with velocity u < c in the same direction as v, this body will have a velocity:

v' = (v - u) /(1 - uv/c^2)

Let us now look on that body from the particular inertial reference frame moving with velocity u equal to c^2/v < c (because we assume that v>c). Then we will have v' = infinity, what makes situation being a physically absurd one: this body has to be out of Universe in any moment of time! Therefore, the Lorentz transformations do prohibit the existence in our Universe of bodies moving with speed more than speed of light in vacuum"
I created for the first time in history of Physics - you will not find that simple argument against super-c motion anywhere. So, sometimes I can think, do I?

Outright babble and self congratulations. You are doing nothing but citing relavistic formulas. Sometime you might need to read up on the number of unexplianed FTL items actually observed in the universe. Before you pop off about how that is explained I am very familiar with about 6 - 8 different soultions to such observations. Collectively all such explanation have not explained the observations.

The biggest problem you have is you cannot and will not think outside the text book. How do you expect to ever discover anything if you do not look beyond the current theory?

The biggest problem yo have is you cannot and will not think outside the text book. How do you expect to ever discover anything if you do not look beyond the current theory?

Like inventing UniKEF? Heheheheheheh :D

MacM, you have said: “The biggest problem yo have is you cannot and will not think outside the text book. How do you expect to ever discover anything if you do not look beyond the current theory?”.
I’m not expecting, and never was, discover beyond the current theory – I did and continue to do that - discovering beyond, but in agreenet with, current theory. Do you now why? Because it is my profession.
And that is why I see what a BS you are trying to spread around in Internet….

MacM, you have said: “The biggest problem yo have is you cannot and will not think outside the text book. How do you expect to ever discover anything if you do not look beyond the current theory?”.
I’m not expecting and never was – I did and continue to do that. Do you now why? Because it is my profession.
And that is why I see what a BS you are trying to spread around in Internet….

Funny. You have yet to do anything but recite text books. When will you ever learn that quoting Relativity does not and will not ever prove Relativity.?

Before you make comment about others views you should understand those views and be able to actually show error in such views and not simply withdraw into the text book and claim because "This or that theory says so".

Suppose you try to explain Relativity Time Dilation as being real when it can be shown that it is impossible? You are comfortable at accepting the impossible as merely counter intuitive? That makes you a fool not knowledgable, free thinking or intelligent.

It may be your profession but you are clearly entrenched in your views and have no possibility of new discovery.

Before you make comment about others views you should understand those views and be able to actually show error in such views*Persol looks at MacM and clears his throat*
When will you ever learn that quoting Relativity does not and will not ever prove Relativity.?The issue here isn't one of proving relativity. It's showing that your attempted disproof isn't disproving relativity, but what you think relativity says.

*Persol looks at MacM and clears his throat*
The issue here isn't one of proving relativity. It's showing that your attempted disproof isn't disproving relativity, but what you think relativity says.

Unfortunately you have failed at that mission. Re-read the the test. Clean your glasses and actually think about what is written without making the false assumption at the outset that I am wrong.

1 - You will either be forced to agree or,

2 - Show complete incompetence to follow physical logic of what is and is not possible or,

3 - Continue to flap your gums and making senseless noise which has no bearing on the issue or has a modicum of truth.

Dear Friends,
Let me add to this thread one more addition to my Lectures on SRT. I think it will be useful for population of this Forum.

“There is no intuitive SRT”
(Addition to the Lectures on SRT)


The Special Relativity theory was, I guess, the first physical theory that has explained the Nature in terms and notions that are lying beyond intuitive human imagination. Not because it was operating with some unusual or far of elementary Math, but because SRT from the its very beginning was considering and challenging the most fundamental notions and perceptions on the base of Nature’s behavior on the level unreachable for the human perceptive organs. Humanity had met same situation before - some discoveries before SRT also dealt with things that were not reachable for human’s perception organs for instance the electromagnetic waves. But it was the first time when we had no possibility to create devices that would help us directly investigate phenomena we are talking about. Whole our conventional World around us was out of limit when the essential challenge of SRT was possible. It was paradoxical situation – totally destroying our cozy Newtonian paradigm about time and space around us and in the entire World, SRT did not gave us a single possibility to check it out in our Laboratories! And only many years after SRT was established we get some possibilities to challenge it in Laboratories. (The earlier direct challenge was the Kaufman’s experiment with beam of electrons, when he confirmed the Einstein’s formula for mass’s dependence on body’s velocity). But SRT was talking about so familiar things as time and space! Of course, every intellectual got intriguing and was talking about SRT a lot… And ideas, which SRT was promoting about natural features of those super-familiar things, as time and space – was so shocking, so unusual that SRT generated more its very own “enemies” than “friends”.

Whole my experience shows me that there are much more fundamental circumstances of such widely spread rejection of SRT by conventional – classic – human brain, than it might be seen at the first look on that problem. Let me tell you about some of them.

1. Many people are sure that SRT, at least – in its basic version, can be apprehended and understood by anyone who knows elementary Algebra. This is the first Illusion.
Indeed, the basics of SRT can be obtained and narrated due to elementary Algebra. But to understand what this elementary Algebra had delivered, one should know and be familiar with much more Math. First of all, he/she should be familiar with Theory of Transformations, to be able to recognize what means the fact that Lorentz transformations form the group.
Many people known and understand Lorentz transformation in right way; many of them knew or have heard that they are forming a group – so called Lorentz special group. But they do not understand what it means. Many of such people are spending their time and intellect to create some “clever” system (mostly imaginary, but often even construct such devices) of inertial observers, which would be able to challenge SRT and prove that Lorentz transformations are wrong … because some events for those observers will appear and look differently, not as those transformations predict. Of course, all such guys are agreed that all events in Nature should appear and look the same in any reference frame (the major Principle of Relativity – the only base of any scientific understanding of Universe). And they are trying to prove that for their system of device the Lorentz transformations give something else. Like that: "The results of some events for observers A, B and C should be a, b and c, but LT give another results - a’, b’ and c’, respectively" or visa versa. For instance, "in result of same events the clocks of observers A, B and C should read a, b and c, but LT give different values of readings for those observers".The problem of those people is that they do not realized what means the fact that LT forms a group. Who knows the Theory of Transformations, is sure that IF SOME TRANSFORMATIONS OF THE COORDINATES AND TIME IN SOME SET OF THE REFERENCE FRAMES FORMS A GROUP, IT MEANS THAT THE RESULTS OF ANY EVENTS IN NATURE WILL BE THE SAME FOR ANY OF OBSERVERS IN ANY OF SUCH REFERENCE FRAMES. This is a well proven by pure Math the basic theorem of the Theory of Group. And anybody easily can prove (due to elementary Algebra) that LT indeed form a group (you can see it, for instance, in [1] -“The Scientific Notes”, vol. #6 on my web site www.minescience.com (http://www.minescience.com)).
This is why professionals do not even listen to anyone who says that he created some clever system of the inertial reference frames where results caused by the some particular events look differently.

If inertial observer A says ”I read my clock (or length, or mass, or some another characteristic) as Aa and B’s clock as Ba” and if inertial observer B says ”I read my clock (or length, or mass, or some another characteristic) as Bb and A’s clock as Ab”, then any another inertial observer will confirm those measurements. He will say: “I also see that observer A reads his clock as Aa, B’s clock as Ba and that observer B reads his clock as Bb, A’s clock as Ab”. All what we need to do is to make sure that all these statements are reflecting the right applications of the Lorentz transformation to the each of these clocks.

And namely that fact of confirmation by any other inertial observer is what gives us a right to say “Those measurements are the Reality”, no matter how unusual and unexpected by our classic mentality it looks and sounds.

More over, this Reality brings us to some paradox – the Twins Paradox – that can be considered as an assaulting of our intellectuality. But that is Reality and we should learn to live with it…

2. Let us consider one more example, which disproves opinion that without knowing of basics of whole Math there is a possibility of a deep understanding of SRT.
Indeed, let us consider one more circumstance in SRT, which was troubling Einstein whole his life. …

(Further text did not concern to the topics discussed on our Forum, so I will not touch that yet)

Dear Friends,
let me offer you a short version of my Lecture that will be, I hope, useful for current discussion on that matter.

The special role of time in Nature and Twins Paradox.
(Amendment to the Lectures on SRT)

.

Irrelevance of acceleration.


Before we will analyze TP let us consider some the most popular "resolutions" of it, still widely spread in the literature.

1. The philological "resolution": "Twins Paradox can be explained only in the frames of GRT". Let us recall that TP has nothing to do with General Relativity, it is "a child" of Special Relativity Theory. Of course, the actual resolution of TP may be lying somewhere "outside" SRT, but a simple consternation of that possibility without evident presentation of any proof sounds as an attempt to avoid of any resolution, at all.

2. The most popular "resolution": "On of twins evidently experienced the accelerations; therefore he can not be considered as an inertial reference frame and Principle of Relativity and Lorentz transformations are not applicable to him. He, and namely he will be aging slower than the first twin, remaining on the Earth".

This "resolution" of Twins Paradox is simply logically wrong one. To recognize this fact, let us consider motion of rocket more detailed. Whole journey of rocket consist of five consecutive parts (segments, intervals):

A. Initial acceleration till velocity V; let it takes time ta.
B. Inertial motion from Earth with velocity V; let it takes time tb.
C. Turn back (turn velocity from value V to value -V); let it takes time tc.
D. Inertial motion with velocity -V back to Earth; let it takes time td.
E. Final deceleration till zero velocity; let it takes time te.

As one understands, parts A. C and E could be the same, no matter how long times tb and td are. In other words, no matter how long time racket will be kept moving inertial, the parts of accelerations and decelerations can take the same times (at all the same given means of energy, engines, supply, etc).

But the time-delay we are calculating by the Lorentz formula concerns only to the inertial motion. And this time dilation absolutely no-how is connected with past or future of the currently inertial moving body. In SRT the history of motion of the reference frame has nothing to do with description of the current physical events in this reference frame (at least, for the closed systems of the material points). Any dependence of description of any closed physical system upon dynamical history of the currently inertial reference frame would be a direct violation of Principle of Relativity.

Therefore, if we will chose (tb + td) >> (ta + tc + te) whole time-delay will be practically accumulated in the regime of the inertial motions (forward from and backward to Earth).

Moreover, the same parts A, C and E can correspond to the absolutely different tb + td , so that, even if these parts are compensating one duration of tb + td at one choice of it, they can not compensate the another duration of tb + td at another choice of it.

This is why non-inertial parts of rocket's journey does not play any role in the formulation of the Twins Paradox, no matter is acceleration equivalent to gravity, or is not.



You are telling us that acceleration on an organic entity has no physiological effect regarding the aging process as described in special relativity theory. You certainly sound convincing, or convinced of your position, Feynman on the other hand, says that acceleration is the "answer" to the resolution of the twin paradox, acceleration is everything. If we decide on reputation, who wins the debate?

I have been observing these debates with a differing intensity of interest and understanding, but this post seems to pull out some of the stops of hesitation.

I cannot resolve in my mind any agreement with your thesis here for a least one absolute reason. When we accelerate matter in linear accelerators, for instance, drastic changes of form mand substance are observed during the process. The energy state of the organism, or entity increases, the energy state changes. Put an organic entity through that same process and you will always have the possibility of definitely affecting the longevity of the organism. In the extreme case, extreme for the orgamism, not for the rate of accelration, the organism can be splattered flatter than a pancake. Consider all the accelerations felt by high speed jet pilotss and crews undergoing extended accelerations of 10 g'e and more, Very definte physicological changes are noticed. You are aware of this I am positive.

Accelerating any object to a higher velocity has more, I opine the only affect on the organism and the cruise at uniform motion is meanining less, some were around zero affect. Remeber the law of inertia that they deprogrammed you from undersatnding that by itself, to the phyisiological effect on the organism ,when affected by an external force?. Many promoting SR are fond of telling us tha the "brain functions" will slow proportionately to the extent that the moving observer will not be able to tell the difference between his thinking at extended velocity from that at relative velocity near zero. This, the extension of life at high speeds, is the biggest sham of all and is offered without the slightest scintilla of expeimenta; proof. But SR promters don't need proof, do they? They all have formulae to pull out of their ditty bag.

You and I both know that SR is constructed from postualtes and assumptions regarding the measurment of the speed of light anad the "failure of Galilean transformations" to adequately handle Maxwell's equations, which have their own share of postulational constructs. You are no doubt an expert on relativity, which no one can deny you, but your egostistical assumption that SR is a structure describing reality, truth etc is as bogus a scam as any smiling street corner three card monte dealer has ever practiced, as bogus as any that has ever been seen stuttering some singing self-seving sonorous songs of serious scientist, shiit, bull-shiiit.

We are constantly bombarded with the claim that the mathematics of science takes us out of the sphere of voodoo and speculation when every professor of SR makes the point that one has to discard the intuitive, the learned, the rational, the observed and accept the skewed intellectual sm of SR. You can have it Yuriy, all of it for all iI care, just don't ever go to Jamaica and give your anti-voodo SR lectures there because some of the locals just might conduct a lttlle ceremony some evening and you might find yourself waking up up the next morning with a bad case of leprosy and a decapitated chicken's head on your front doorstep, or maybe you simply wont wake up.

I know the mantra: the thousands of experiments supporting SR, which boils down to millions of claims of scientific superiority, la di da, which amounts only to "truth through volume".

I have a scientific observation I must share with you and your SR industry: Its all bullshit. Acceleration is the only force organic entities experience, and lies of course, and truth.

Geistkiesel

"The enemies of truth. Convictions are more dangerouis enemies of truth than lies" FN

Hi, Mac M.

Why dont you do us all a favour, and stop replying to yuref. It's the only way to slow him down. It is exedingly boring for those of us who like to read all of the post to strugle through all that verbiage.
Perhaps you and I have'nt always agreed in the past, but at least we have had a few intelligent discussions of a reasonable short duration.

REGARDS APOLO

“You are telling us that acceleration on an organic entity has no physiological effect regarding the aging process as described in special relativity theory. You certainly sound convincing, or convinced of your position, Feynman on the other hand, says that acceleration is the "answer" to the resolution of the twin paradox, acceleration is everything. If we decide on reputation, who wins the debate?”
Where from you got that I even touched issue of biological effects of acceleration? Do you read my posts, at all? Or you are fantasize on what you want hear from me?
In clause “Irrelevance of acceleration” I gave readers an argument, a purely kinematical argument that acceleration can not explain any compensation of age delay at inertial parts of motion. That is it, nothing else. If it is so, then appealing to acceleration of one brother we do not explain why his conclusion about age delay of his twin on Earth becomes invalid. And I do not recall any Feynman’s resolution of this Paradox. Do you?

Hi, Mac M.

Why dont you do us all a favour, and stop replying to yuref. It's the only way to slow him down. It is exedingly boring for those of us who like to read all of the post to strugle through all that verbiage.
Perhaps you and I have'nt always agreed in the past, but at least we have had a few intelligent discussions of a reasonable short duration.

REGARDS APOLO

I, on the other hand, found Yuriy's lecture quite fascinating. Thanks, Yuriy.
I am sure others agree me also, opinions are like asxxxxxx, everyone has one.

Hi, Mac M.

Why dont you do us all a favour, and stop replying to yuref. It's the only way to slow him down. It is exedingly boring for those of us who like to read all of the post to strugle through all that verbiage.
Perhaps you and I have'nt always agreed in the past, but at least we have had a few intelligent discussions of a reasonable short duration.

REGARDS APOLO

Perhaps you are right. It seems several here have identified his BS as just BS. But it is difficult to ignore when he enters my name into other threads and or enters discussions and goes completely off topic.

But I am working on bringing him down to size. Hopefully you will have noted that I have withdrawn from (5) threads already to cut back on such garbage.

2Inquisitive,

I admit that Yuriy writes lengthy explanations and generally adheres to reciting the mainstream ideas. If that is your interest then I have no objection to that but I do object to his conduct on this board of attacking personalities rather than addressing issues.

His lectures are not of interest to me. But that is personal preference. I prefer to look deeper than the sugar coating they place on irrational thought.

See above post. Just what we need. Long winded, poorely written, hardly readable essays and lectures selected by an egotist.