x ------- x
Update as of 07.06.2014

Hospoda, I am glad to inform you that more than a year has passed since the last comment to this post, I think that you are as excited about me as I am :)
Although each of the debating parties remained unconvinced, yet ... agree, it was interesting to argue;)
But ... time is ticking, and all of us, of course, are serious and busy people ... therefore, so as not to waste precious seconds in vain, I suggest you look at a 2 minute experiment that I recently invented.
And if, after viewing, you have any arguments in defense of the Theory of Relativity, then we can discuss a little.


x ------- x

In order to understand what this article is about, you need to have a clear head, free from stereotypes. Therefore, to begin with, I suggest you to invigorate your nervous system by solving one simple problem, which I invented 5 years ago to entertain my colleagues.

Warm-up task:

Inside the sphere there is a certain object that needs to be pulled out of it. The task is abstract, therefore you are not bound by the laws of physics and you can use any methods for solving, the condition is one - this object cannot pass through a sphere and the sphere cannot be destroyed.
Simplified:
There is a pebble inside the rubber ball, it must be pulled out, and the ball cannot be pierced with a knife, sawed with a chainsaw, etc.

I came up with 4 options for solving this problem (maybe you will find more):






I hope you were pleased to move the convolutions, well, now turn to the most interesting.

Paradox: "Time intervals"

Highlights in evidence:

1. In the Lorentz transformations used in the SRT there is no criterion, using which one can correctly calculate the chrono-velocity.

1.1. The crony rate is different for a different way of its CALCULATION for the same ISO.

1.2. Explaining the physical meaning of chronoscopic (for example, MEASUREMENT of chronospeed by d'Artagnan), to show that in reality (which SRT describes), it can be NOT that which is obtained in CALCULATIONS using Lorentz transformations.

1.3. To show that the Lorentz transformations without chrono-shift information cannot provide a correct calculation of the chronospeed.

Evidence:

Here are my reasons:
The purpose of this clause is to show what the logical / physical sense of chronospeed is.
The task is maximum - so that, after my logical description of the term “chronospeed”, you yourself came to the conclusion how to measure it.
The task is minimum - what would you agree that the method that I will give as an example of measuring / calculating time intervals is correct.

So, let's begin.
In order to understand the meaning of chronospeed, it is necessary to agree on a method for measuring the time between two events (time span).

We have two options:
1) Both events occur at the same point in space.
2) Events take place at different points in space.

The time intervals, we will measure the number of d'Artagnan squats, which they will have time to do between two events, as well as the usual hours. At first glance, it may seem that this is an unnecessary duplication, I agree, but as will be shown later, the introduction of d'Artagnan is crucial for UNDERSTANDING. That it will open your eyes.

1) Time span measurement procedure
When both events occur at the same point in space

- At the point where events take place are hours
- The clock is d'Artagnan
- At the time of the event1 on the clock t = 0, and d'Artagnan begins to squat, the number of squats is k = 0
- At the time of the event2 on the clock t = T, and d'Artagnan ceases to squat k = K
- RESULT: The measured time interval is equal to T in hours, and equal to K in d'Artagnan

2) Procedure for measuring time span
When events occur at different points in space

- At points of event1 and event2, watches 1 and 22 are placed with d'Artagnan (the clock is resting relative to each other)
- Watches P1 and P2 are synchronized by Einstein's method and then go forever synchronously (in ISO P1 / P2)
- At the moment of event1 at point1 on F1 t = 0, and d'Artagnan starts to squat k = 0
- At the time of the event2 at the point2 on the t2 t = T
- P2 sends a text message with this data (t = T) to d'Artagnan in P1, which still crouches. (what is sms is not important, it can be a certain signal or a carrier pigeon ... it doesn't matter, because it does not affect the measurement)
- Having received a text message d'Artagnan in P1 ceases to squat and looks in his journal. It turns out that when d'Artagnans crouch, they keep a squat log :). There are only two columns in this magazine - “Time” and “Number of squats that have already been performed.” It turns out that at time T, d'Artagnan in P1 managed to perform K squats.
- RESULT: the measured time interval is equal to T in hours, and equal to K in d'Artagnan.

Further…

Now we can measure the time intervals for two events at one point (1) and for two events at different points (2).

The PHYSICAL meaning of the measured time interval , we will consider, as the number of squats that D'Artagnan managed to perform between the event 1 and the event 2.
WHEN IT'S NOT IMPORTANT - in what way, 1m or 2m we measured the time interval, the number of squats will not change.

We will PROVE that the time interval measured in one ISO does not depend on the method of its measurement ((1) or (2)):
P1 / P2 - go synchronously, i.e. SIMULTANEOUSLY show the same indication t = T. Of course, regarding ISO P1 / P2.
Having remembered T on P2, we can ABSOLUTELY fairly claim that on P1 SIMULTANEOUSLY ie at the same moment t = T. Those. indications of a SYNCHRONOUS running clock do not depend on the distance between them (in one ISO). Those. in fact, we measured the time span in ISO P1 / P2, only with P1 clock, because the moment of completion of the measurement was made synchronously running clock P2, the readings of which are identically equal to the readings of P1 (in ISO P1 / P2).

Define the concept of "event duration":
The duration of an event AB is the time interval between event A and event B measured in one ISO.

Now you can enter the concept of chrono speed.
CHRONOSE (H) is a coefficient that shows how many times the DURATION of ONE and SAME events differs in different ISO.

The cron rate of ISO1 relative to ISO2 is the ratio of the time interval measured between event 1 and event2 in ISO1 to the time interval measured between THEMA event1 and event2 in ISO2.

For EXPERIMENTAL MEASUREMENT of chronospeed - it is enough to measure the duration of ONE and SAME events on the clock ch1 (T1) in ISO1 and the clock ch2 (T2) in ISO2.

H (u1, u2) = t1 / t2
H (u2, i1) = T2 / T1
Where
T1 - time span measured in ISO1
T2 - time interval measured in ISO2

EXAMPLE OF EXPERIMENT
Hafele - Keating (link to wiki, see below)
Calculate the chronospeed:

The event of the flight of the aircraft on the clock resting on the ground (P1) lasted 101min
The event of the flight of the aircraft on the clock in the plane (P2) lasted 100 minutes

H (P1, P2) = T1 / T2 = 101min / 100min
Those. for 101min by the hour P1, for the hour P2 has passed 100min

H (P2, P1) = T2 / T1 = 100min / 101min
Those. for 100 minutes by the hour P2, by the clock P1 has passed 101 minutes

This means that the chronoscope speed in the MOVING plane is less than the chronoscope speed on the ground.

Further…

BASED ON EXPERIMENTAL DATA
- the effect of slowing down time is due only to the speed of the object and does not depend on its acceleration. (shown on muons, see wiki link below)

Let us examine the symmetric example Pand5461,
crossing it with an example of senia

Then:
- Suppose we have 2 planets (fixed relative to each other) and relative to ISO1.

- Let there be a rocket1 flying past these planets (we will connect with it ISO2). First, past the first, then past the second. Moreover, the rocket flies at such a tremendous speed that from the point of view of ISO1, time in it practically does not move (on the clock in ISO2, 1 minute passed during the flight from the planet to the planet). But the distance between the planets is quite large. On the clock in ISO1, the ship flies 100 years.

- Let rocket2, identical to rocket1, rest on the second planet

- Event1: the nose of the rocket1 meets the nose of the rocket2
- Event2: the rocket's tail1 meets the rocket's tail2
- The time interval between event 1 and event 2 is called - "Touch"

As Pand5461 showed in its symmetric example,
( http://habrahabr.ru/post/151077/#comment_5870075 ),
When calculating with the help of Lorentz's transformations, the chronospeed ALWAYS turns out to be EQUAL.

Those. DURATION "Touch" for BOTH missiles: And the one that moves with great speed, and the one that rests on the planet - will be the same. Those. d'Artagnan in both rockets - sit down the same number of times!

But as we know:
THIS CONTRADICATES TO PHYSICAL REALITY.
- As time in a moving rocket1 can go slowly (it covered a huge distance in 1 minute on its internal clock - D'Artagnan crouched 10 times, and on the planets 100 years passed during this time - D'Artagnan crouched 10000 times).
- And while flying past a rocket2 resting on the planet, the time flow rate (chrono speed) in both rockets became equal, and all the physical processes there began to be performed at the same speed ???

PS
TEST QUESTIONS:
1) Do you agree that the proposed method of measuring the time intervals between two events does not contradict our physical reality?

2) Do you understand the PHYSICAL sense that I have put into the concept of “time span”? Do you agree that it does not contradict our physical reality?

3) You agree with my evidence - that the time interval measured in one ISO does not depend on the method of its measurement (1 or 2 hours)
- even if they do not agree, in the symmetric example, the time intervals are compared in the same way, so this does not affect the result

4) Do you agree
What does the considered symmetrical example of Pand5461, crossed with the example of senia, show the existence of a contradiction between SRT and physical reality (experimental data)?

---

Discussion:

1.1. The crony rate is different for a different way of its CALCULATION for the same ISO.

senia
"
Taki yes.
Which once again confirms its uselessness as a physical quantity.
"
- With this item like everyone agrees, albeit with sarcasm :)

1.2. Explaining the physical meaning of chronoscopic (for example, MEASUREMENT of chronospeed by d'Artagnan), to show that in reality (which SRT describes), it can be NOT that which is obtained in CALCULATIONS using Lorentz transformations.

senia
"
Stop!
This you can not prove without a real experiment.
"

- I rely on the following experiments:

( http://ru.wikipedia.org/wiki/Special_theory_relativity section: "Relativistic time dilation"). Those. on experiments that were carried out in reality. And on the conclusions reached by relativistic scientists:
- Atomic clocks flying on an airplane are behind the fixed atomic clocks.
- the effect of slowing down time is due only to the speed of the object and does not depend on its acceleration. (shown on muons)

1.3. To show that the Lorentz transformations without chrono-shift information cannot provide a correct calculation of the chronospeed.

senia
"
1. The correct calculation of “chronospeed” in SRT is not possible in principle - the term itself is not correct from the STO point of view.
2. What is the "correct" result?
"
- if the correct calculation of the “chronospeed” in the SRT is not possible, only because of the “incorrectness” of the term, then
you can rename “chronospeed” to “hz, what”, it makes no difference to me :) It is important that there are formulas by which you can calculate this “hz, that”, and they themselves are not contradictory, and that is equally important , there is an EXPERIMENTAL measurement method for this “hz that”, i.e. “Hz.chto” - has a physical meaning.
- if the correct calculation of the “chronospeed” in the SRT is not possible, for some other reason, the SRT is incorrect, not the term

- the correct result is when the result calculated by the formula corresponds to the result obtained experimentally in ALL cases.

All of these points, I have already DETAILED in the comments. You just have to read carefully, understand, and write your opinion on each item.
If we agree on them, then I will bring to the point 1.4.

TOTAL:
Clause 1 - I think that its meaning will be understood by ALL, only after discussion of all sub-items.

Clause 1.1. Everyone agrees with this
p.1.2. In the discussion ...
Clause 1.3. In the discussion ...

---

The Paradox: “The Watch d'Artagnan”

Well, you want to analytically - here you are, I’ll show you the cards :)

The first and most important observation is that it is impossible to refute the STO inside its framework. In order to show the existence of a contradiction, it is necessary to reach a qualitatively different “super-level” of consideration of the problem. It was not for nothing that I gave a warm-up task at the beginning of the article, because each of its solutions is such a qualitatively new approach to the problem, which cannot be solved in the standard framework. (in fact, I found 5 solutions, I really wanted to see if someone else would find 5e, although there might be even more of these solutions). But I digress, go to the paradox.

To begin with, it is necessary to define the concept of "time". We will give a more general formulation of this concept than that of Einstein, thereby going out from under the oppression of the SRT.
Time is the number of repetitions of some evenly repeating event.
After all, you see, you can measure time with anything and anything. For example, the length of a boa constrictor can be measured by parrots, and the waiting time of a tram at the bus stop can be measured by the number of skins from the seeds that we managed to click.

Now, we can make watches that do not obey the SRT.
If, for example, we consider hours as a flash of light, then the number of flashes of light from the moment the experiment started (mT = 0 at the 1st flash) will be an indication of our watches.

Further, we believe that our experiment should last mT = 10 flashes. Along the railroad tracks, after some equal distance from each other, we put 10 light bulbs with touch sensors (we believe that the sensor and the light bulb are at the same point). Under each light bulb we write its number, starting with 0, 1, 2 ... 9 - this is the scale of our watches + we put the 1st observer (cloned D'Artagnan).

We start the experiment:
The train moves evenly and rectilinearly along the railway track. It is located touch sensor, which closes the email. circuit when the sensor touches the light bulb on the platform and it turns on.
The task of d'Artagnan, who is in the train (let it be at the same point of the train as the touch sensor), with each flash of light to perform 1 squat, the same thing does the observer standing next to the light bulb that flashed on a fixed platform.

Further…
- The train pulls up to the first light bulb and it lights up, i.e. comes mT = mT '= 0 (1st flash)
D'Artagnan and the observer standing next to the light bulb SIMULTANEOUSLY, relative to any ISO, they begin to squat (since they are at the same point)



- The train pulls up to the 2nd light bulb and it lights up, i.e. comes mT = mT '= 1 (2nd flash)
To we see, our lamp clocks go SYNCHRONOUS.
D'Artagnan counts the flares and determines his time mT 'the observer determines the time mT on the scale (the number next to the light bulb, although the number can be coded for example with the color of the light bulb and then d'Artagnan will also determine the time on the scale, but this is not significant)

- ...

- The train pulls up to the 10th light bulb and it lights up, i.e. comes mT = mT '= 9 (10th flash)
The experiment ends



As we see:
1. Time passed in the train and on the platform for lamp hours mT = mT '= 9,
2. On the lamp clock D'Artagnan sat on the train 10 times and his clones next to the lights, also sat down 10 times, i.e. in total, they performed the same work.
3. Judging by the clock of Einstein (the Lorentz transformation), then the time in the train is less than on the platform t '<t. At the same time, d'Artagnan on the train and d'Artagnan on the platform (in total) are equally tired, but according to Einstein’s watch, the one that for some reason grew older less.

Question:
What then is the physical meaning of Einstein's “slow” time?

---

The arguments for and against (the dispute between two points of view):

Argument 1.

- Relativist:
Lorentz transformations can be obtained on the basis of a subset of the axioms of classical physics (CF). This fact reduces the proof of the consistency of STR to the proof of the consistency of CF.
( http://synset.com/ru/conversion_Lorenz )

- Doubting:
Yes, but at the same time, the 5th axiom was excluded from the 5th axioms of the KF: “If two events are simultaneous in one frame of reference, then they will be simultaneous in any other.” Because of the incompleteness of the remaining 4 axioms, the ALPHA constant appeared in the transformations. in the general case, it can have any value, but in our universe, it is> 0. The Lorentz transformations themselves do not define this constant (therefore, they are not contradictory). It is determined from the additional 5 postulates of theories.
From KF it follows that ALPHA = infinity, from HUNDRED ALPHA = speed of light. Those. The 5th postulate is implicitly introduced into the SRT: “If two events are simultaneous in one frame of reference, then they will NOT be simultaneous in any other moving relative to a given one.” and it CONTRADICATES to the 5th postulate of classical physics.
Conclusion: The Lorentz transformations themselves do not contradict the CF, the STR postulate contradicts it: ALPHA = speed of light, when in CF ALPHA = infinity.
So, the consistency of the SRT can not rely on the consistency of CF.

Argument 2.

- Relativist:
The most powerful argument in our dispute is that the results of SRT are confirmed by many experiments. And this theory is generally recognized in scientific circles.

- Doubting:
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Once the King came to the Sage and asked him a simple question: “How does the world work?”, To which, on reflection, he replied: “Everything is relative in the world, only the speed of light is constant, from the point of view of any observer it is always the same.” The king smiled and an argument broke out between them ...

Q: - That is, the principle of relativity is that all physical processes in inertial reference systems (ISO) for observers located in them are described in the same way?
M: - Yes, so far no sage has succeeded, being in a closed physical system, to determine whether this system is at rest or evenly moving.

K: - And why is the speed of light, from the point of view of any observer, always the same?
M: - This assumption was put forward by a very wise sage named Einstein in his special theory of relativity (STR). This theory is very authoritative, and the results of many experiments are close to the results that it predicts.

K: - So, if a uniformly moving train, outside of which a touch sensor is installed, passes and touches a searchlight resting on the ground, and they simultaneously turn on the light, then the light from the train headlights and from the searchlight will come at the same time to an observer who is on the train's path?
M: - Well ... no one conducted direct experiments (observers refuse to stand in the way of the train), mostly they drive light in a circle and receive indirect measurements, but in general, most wise men think that yes, the speed of light does not depend on the speed of the source.

K: - What kind of physical phenomena does SRT describe?
M: - Well, for example, time dilation.
If the observer's ISO1 moves relative to another's observer's ISO2, which is resting relative to him, then for a moving observer1 time passes more slowly, i.e. when he stops his watch will lag behind the watch of the rest of the observer2, and he himself will look younger.
M: - There is still a reduction in size.
The linear dimensions of the moving body relative to the “fixed” reference frame are reduced.
M: - There is still an effect which is called “Relativity of simultaneity”
If two spatially separated events (for example, flashes of light) occur simultaneously in a moving reference frame, they will not be simultaneous with respect to the “fixed” system. The relativity of simultaneity makes it impossible to synchronize clocks in various inertial reference systems in the whole space.

K: - But this is already interesting! But after all, the clock in one ISO can be synchronized?
M: Yes, the method of synchronization of such clocks was proposed by Einstein himself ...

"Well, well," the king said, thinking. “Einstein, I don’t look like a stupid guy, but we, too, don’t hang out at the same time. Tomorrow we will check the service station! I came to the conclusion that there is a contradiction in this theory. ”The sage grinned slyly:“ Thousands of clever men broke their spears about the SRT and no one managed to disprove it! ” “But after all they were not kings!”, The King answered at least slyly with a wink, and they laughed together.

On the same evening a royal decree came out:
“I command.
Build by tomorrow morning a train capable of moving in a vacuum evenly and straight with a speed equal to 2/3 of light. At the beginning of the train outside to install a touch sensor, which will be associated with a light bulb located inside. When the sensor is triggered, the light should turn on. Just put the same sensor and light bulb at the end of the train. In the middle of the train inside and outside put on the 1st photo sensor, which will record the arrival of rays of light from the beginning and end of the train.
To build a route (it is possible in space) from point X to point Y. In the middle of the route, through a distance equal to the length of the train, put two touch sensors, which, when touched with the corresponding sensor of the train start / end, will turn on fixed lights attached to them. ”

In the morning, the King accepted the work.
The space rocket train stood in the middle of a huge stadium and was aimed at heaven. All sensors and light bulbs were installed. On the case, covered with silver metallic, in the rays of the sun proudly gleamed the quality mark "Made in USSR". Gathered spectators, invited celebrities and idle onlookers waved red flags and chanted: “Above your head, pessimists!”. In general, everything was ready to start ...



The king approached the Sages aside and announced:
K: - Well, comrades, now we will start the train and see that the SRT has a contradiction!
M: - And how do we see this?
K: - It's all about bubbles ...
M: - In which bubbles ???
K: - In the green ... but now is not about that. Let me tell you about the course of the experiment.
M: -?!
K: - And so. The train will move evenly and straightforwardly along the paved track. Passing through the place where the fixed touch sensors are installed, it will touch them, and touch sensors will also work in the appropriate places of the train, so that those lights that are located inside the train and those that are stationary on the platform and correspond to the lights in the train ride.
From the point of view of an observer who is in a moving train, the light from the bulbs at the beginning and end of the train will come to the sensor located in the middle of the car - at the same time (since from his point of view the train is at rest and the distance from the beginning and end of the train to its middle is the same).
From the point of view of an observer resting relative to a moving train, the light from the beginning of the train will reach the sensor in the middle earlier than the light from the end of the train. This happens because the train is moving, and the light from the end of the train will have to catch up with the sensor moving away from it in the middle, i.e. he will have to overcome a greater distance than the light coming from the beginning of the meeting to the sensor.

K: - As you can see, there is a contradiction on the face - in the train moving ISO the sensor will detect the simultaneous arrival of the rays. And in the rest of the ISO, the same sensor will not detect the simultaneous arrival of rays!
M: (smiling indulgently) - You may not run the train, I will tell you why this happens. This is a well-known fact, which follows from the STR, is called - "the relativity of simultaneity." That is, according to Einstein's theory, the simultaneity of events at a distance is something relative, depending on the choice of reference system. Those. each frame of reference has its own time, which differs from that in another ISO, respectively, and the events in these ISOs will not be simultaneous.
At the same time, local simultaneity is preserved, in our example, the light bulb triggered from the sensor in the train's ISO at point x1 ', at time t1', will simultaneously light up in the platform's ISO, but correspondingly at point x1, and time t1.

K: (grinning) - That is, you are not embarrassed by the fact that there are essentially 2e universes with their time / space and a triggered / non-triggered sensor, one in the ISO train and the other in the ISO platform?
M: - No, in the framework of the SRT, it is quite natural, all events are determined with respect to any one ISO, regardless of the ISO, the event cannot be considered.

K: - So, my arguments did not convince you of the inconsistency of SRT?
M: - No
K: - Well, then let's wait ...
M: - What do we have to wait for?

The king, taking an oxygen cocktail from the banquet table, sat back in a chair more comfortably and, pulling a few sips from the tube, replied: "See."

About an hour passed , the audience had already started to get bored and throw beer cans at the stadium, some even managed to get into astronauts-machinists walking around there ... Suddenly, the stadium gates opened and a small truck headed for the train-rocket. His body was painted in a bright green color, on which translucent green bubbles were clearly visible, in the middle of which there was an inscription: “Green bubbles - wholesale and retail!”. From the car a few people carried the green box and dragged into the train-rocket ...

M: - What are these bubbles?
Q: - These are undercover agents, they work for the government ...
M: - And what have the agents?
Q: - I decided to take radical measures and give you my last argument ... The last argument of the king ... with which you will not disagree ...
M: (in a slightly startled voice) - Are they going to put us in prison for our views?
K: - No, no, of course ... You choose your own destiny.
M: - In what sense?
K: - I decided to dispel your confusion about the multitude of universes generated by ISO with its time and space.
K: - The agents you saw loaded a bomb onto the train and connected it to a sensor located in the middle of the train. The sensor is programmed to fire and activate a bomb only if it fixes the simultaneous arrival of two rays from the beginning and end of the train.
K: - Now we will start the train, but for now try to answer - will it reach the destination or will it explode on the way?
Q: - My faithful assistant, D'artanyan, is already at the point of arrival of the train, he will soon return and tell you if he has seen the train.
Hmm, but your choice is not great, there are only two options, and both of them contradict the SRT!
1. Regarding the ISO platform, the arrival of the rays to the sensor will not be simultaneous and the train will not explode.
2. Regarding the ISO of a moving train, the arrival of the rays to the sensor will be simultaneous and the train will explode.
If the train does not explode, then the ISO platform has an advantage (decisive influence on the sensor) over the ISO of a moving train, if it explodes the other way around. Those. In any case, some of the ISOs will not be equal, and this is a direct contradiction to the 1st postulate of SRT, which asserts that there are no ISO defined in the universe and all ISOs are equal.

By: - So the train will reach the destination ... or not? What report will D'artanyan return with?

Well, actually that's all. I hope you enjoyed this reading, and you answered the king's last question. Looking at the clock, I see that the end of the world has already come ... It would be symbolic to publish an article on February 21, 2012, after all, and the speed limit of this world is being questioned in it ... but at that time there was no normal design, and she had to go to the drafts ...

Now let's launch a rocket train and watch what happens in reality.
I am not as fast as the king’s retinue, it’s not realistic to create a rocket train in one night, it took several days ... This is where the source code (IDE C ++ Builder 2007) simulates the SRT universe and describes the ship’s motion using its equations. . Now I, like the once ancient mathematician, proving the Pythagorean theorem, can comment on the proof with just one word “Look!” ... although in the 21st century there will be three more relevant words: “Download, Launch and See!”.

Experiment 1.

In the program it is called “Simple Movement”, it does not set a goal to refute something. The task is to see how a simple rectilinear movement of a train looks in the STO universe, through the eyes of a fixed observer and an observer located in a train. It should be noted that in the computer model, colored rectangles around objects are simply for more visual visualization; in fact, objects are points in the middle of these rectangles.

As the main one, the fixed ISO K was chosen, relative to which the train is moving. Further, by converting the coordinates from one ISO to another, the points located in ISO K'associated with the train were calculated.
Here are the equations that were used to get the coordinates of the objects:

1. Point motion in a fixed ISO

x = x0 + v * t;

x - the current x coordinate of the point in the fixed ISO
x0 - the initial x coordinate of the point in the fixed ISO
v - point velocity in the fixed ISO
t is the current time for a point in a fixed ISO

Here t, changes with the step specified in the program, it yields x, corresponding to the given t.

2. Getting the coordinates in a moving ISO

Here
out_obj.v is calculated as Relativistic velocity addition
out_obj.t is calculated as the relativistic time interval that has passed since the beginning of the experiment
out_obj.x is calculated by the formula x '= x0' + v '* t'; according to the already calculated coordinates relative to the moving ISO

Full listing of the function for converting coordinates from K to K:

//---------------------------------------------------------------------------
//   abs -  x   t
// t_move_abs: x = x0 + v * t
//---------------------------------------------------------------------------
void __fastcall MMatPoint::MoveAbsFormula
(
	const double in_new_time	//  t  
)
{
	// x –  x  
	// x0 –  x  
	// v – 
	// t –    

	t = in_new_time;
	x = x0 + v * t;
}

2.  K’    K   m 

 ,          K   K’ 

  
(   ,     vv  mm):

//---------------------------------------------------------------------------
//      
//---------------------------------------------------------------------------
void __fastcall MMatPoint::TransformStoFormula
(
	const double in_move_v,		//      
	MMatPoint& out_obj			//      
)
{

	//   
	const double& m = in_move_v;
	double mm = m * m;
	double cc = g_light_c * g_light_c;

	try
	{
		// v' =   
		//     K ==> K'
		out_obj.v = (v - m) / (1 - (v * m)/cc);
	}
	catch(...){}

	try
	{
		// t' =  
		//     K ==> K'
		out_obj.t = t * sqrt(1 - (mm)/(cc));
	}
	catch(...){}

	try
	{
		//  x0' =  
		//     K ==> K'
		double x00 = (x0) / sqrt(1 - (mm)/(cc));

		//  x'       K'
		// x' = x0' + (v' * t')
		out_obj.x = x00 + out_obj.v * out_obj.t;
	}
	catch(...){}


	AnsiString dbg;
	dbg.printf("[%s (x=%0.2f, v=%0.2f, t=%0.2f)] ==> [%s (x=%0.2f, v=%0.2f, t=%0.2f)]",
		name, x, v, t, out_obj.name, out_obj.x, out_obj.v, out_obj.t);
	frmMain->m_Memo_Dbg->Lines->Add(dbg);
}

, …


. Ex1_t0.
t=0 ( ):

:
— = 30
v – (. A1, As, A2) = 20 (2/3c)
x – , (.. — A2, 2(240), As(120), A1(0))
t — = 0 (.. 0)

:
— = 30
v’ – (. A1’, As’, A2’) = 0
x’ – 2’(321.99), As’(161), A1’(0)
t’ — = 0 (.. 0)

[A2 (x=240.00, v=20.00, t=0.00)] ==> [A2' (x=321.99, v=0.00, t=0.00)]
[As (x=120.00, v=20.00, t=0.00)] ==> [As' (x=161.00, v=0.00, t=0.00)]
[A1 (x=0.00, v=20.00, t=0.00)] ==> [A1' (x=0.00, v=0.00, t=0.00)]

.. : K’ (A2’ — A1’) = 321.99, K (A2 — A1) = 240. .. , K’ K.


. Ex1_t10.
t — = 10 (.. 10)

[A2 (x=440.00, v=20.00, t=10.00)] ==> [A2' (x=321.99, v=0.00, t=7.45)]
[As (x=320.00, v=20.00, t=10.00)] ==> [As' (x=161.00, v=0.00, t=7.45)]
[A1 (x=200.00, v=20.00, t=10.00)] ==> [A1' (x=0.00, v=0.00, t=7.45)]

t (- ): K t=10, K’ t’=7.45. , K’ K, t’ 2,55 .

2.

: « ( — )»
. 1 : F1 F2 ( ) – . D1 ( ) – , , .

, , , (A1,A2; A1’,A2’) (F1,F2; F1’,F2’).


. Ex2_t0.
t=0: . A1-F1, A2-F2, A1’-F1’, A2’-F2’ , .. .

[D1 (x=120.00, v=20.00, t=0.00)] ==> [D1' (x=161.00, v=0.00, t=0.00)]
[A2 (x=240.00, v=20.00, t=0.00)] ==> [A2' (x=321.99, v=0.00, t=0.00)]
[As (x=120.00, v=20.00, t=0.00)] ==> [As' (x=161.00, v=0.00, t=0.00)]
[A1 (x=0.00, v=20.00, t=0.00)] ==> [A1' (x=0.00, v=0.00, t=0.00)]
[F2 (x=240.00, v=-30.00, t=0.00)] ==> [F2' (x=321.99, v=-30.00, t=0.00)]
[F1 (x=0.00, v=30.00, t=0.00)] ==> [F1' (x=0.00, v=30.00, t=0.00)]


. Ex2_t1.40.
t=1.40: . , K F1-D1 > F2-D2, K’ F1’-D1’ = F2’-D2’

[D1 (x=148.00, v=20.00, t=1.40)] ==> [D1' (x=161.00, v=0.00, t=1.04)]
[A2 (x=268.00, v=20.00, t=1.40)] ==> [A2' (x=321.99, v=0.00, t=1.04)]
[As (x=148.00, v=20.00, t=1.40)] ==> [As' (x=161.00, v=0.00, t=1.04)]
[A1 (x=28.00, v=20.00, t=1.40)] ==> [A1' (x=0.00, v=0.00, t=1.04)]
[F2 (x=198.00, v=-30.00, t=1.40)] ==> [F2' (x=290.69, v=-30.00, t=1.04)]
[F1 (x=42.00, v=30.00, t=1.40)] ==> [F1' (x=31.30, v=30.00, t=1.04)]


. Ex2_t2.40.
t2.40: , K, F2 D1 F2 – . , ! ’, , .

[D1 (x=168.00, v=20.00, t=2.40)] ==> [D1' (x=161.00, v=0.00, t=1.79)]
[A2 (x=288.00, v=20.00, t=2.40)] ==> [A2' (x=321.99, v=0.00, t=1.79)]
[As (x=168.00, v=20.00, t=2.40)] ==> [As' (x=161.00, v=0.00, t=1.79)]
[A1 (x=48.00, v=20.00, t=2.40)] ==> [A1' (x=0.00, v=0.00, t=1.79)]
[F2 (x=168.00, v=-30.00, t=2.40)] ==> [F2' (x=268.33, v=-30.00, t=1.79)]
[F1 (x=72.00, v=30.00, t=2.40)] ==> [F1' (x=53.67, v=30.00, t=1.79)]


. Ex2_t7.20.
t=7.20: , K’, F2’ D1’ F2’ – . , , … . ’, , .

[D1 (x=264.00, v=20.00, t=7.20)] ==> [D1' (x=161.00, v=0.00, t=5.37)]
[A2 (x=384.00, v=20.00, t=7.20)] ==> [A2' (x=321.99, v=0.00, t=5.37)]
[As (x=264.00, v=20.00, t=7.20)] ==> [As' (x=161.00, v=0.00, t=5.37)]
[A1 (x=144.00, v=20.00, t=7.20)] ==> [A1' (x=0.00, v=0.00, t=5.37)]
[F2 (x=24.00, v=-30.00, t=7.20)] ==> [F2' (x=161.00, v=-30.00, t=5.37)]
[F1 (x=216.00, v=30.00, t=7.20)] ==> [F1' (x=161.00, v=30.00, t=5.37)]


. Ex2_t12.
t=12.00: , , K, ( K’ ) F1 - D1.

[D1 (x=360.00, v=20.00, t=12.00)] ==> [D1' (x=161.00, v=0.00, t=8.94)]
[A2 (x=480.00, v=20.00, t=12.00)] ==> [A2' (x=321.99, v=0.00, t=8.94)]
[As (x=360.00, v=20.00, t=12.00)] ==> [As' (x=161.00, v=0.00, t=8.94)]
[A1 (x=240.00, v=20.00, t=12.00)] ==> [A1' (x=0.00, v=0.00, t=8.94)]
[F2 (x=-120.00, v=-30.00, t=12.00)] ==> [F2' (x=53.67, v=-30.00, t=8.94)]
[F1 (x=360.00, v=30.00, t=12.00)] ==> [F1' (x=268.33, v=30.00, t=8.94)]

:
’, ?

---

– .
. – – , . (), . . - , , , , – .

---

, v = 0,1;
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---

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(++Builder 2007) , exe Windows .
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