The BASICS of SPECIAL RELATIVITY THEORY Critical Review

Transcription

1 The BASICS of SPECIA REATIVITY THEORY Critical Review Nikolai Bouianov Toronto, Canada Keywords: Einstein, relativity Abstract: Critical review of the relativity basics.

2 My intent with this article was attempt to review Einstein s paper On the Electrodynamics of Moving Bodies on line by line basis. It appeared that I failed miserably. All I got was just the original Einstein s paper with just about ten percent of comments. Too much distractive rambling and a lot of erroneous math. I was ending with just a review of relativity basics, trying nevertheless to follow Einstein s paper. 1. Introduction I was always wondering by the fact how many research papers and articles it written on the subject, both positive and negative. Much less papers was written on the Archimedes principle of buoyancy, for example. To me it looks like the authors of such articles, even in support of Einstein are still have some doubts. As a matter of fact the validity of relativistic formulas usually is verified by testing some wellknown law of physics in relativistic case, usually against orentz transformation. Meanwhile the absurdity of the relativity basics becomes very clear just by attentively reading Einstein s paper. 2. Synchronicity Einstein once said, The secret to creativity is knowing how to hide your sources. And indeed such source is very well hidden in synchronization of two clocks. et s try to reveal the source The following Gedankenexperiment was appears in Einstein s paper: The body in the system A emits the light at the time t A measured in the system A The light reflected back in the system B at time t B measured in the system B The light coming back to the system A at the time t' A measured in the system A After some manipulation with the words one could find the following reasoning: In accordance with definition the two clocks synchronize if t B t A = t A t B (1) Even the brief look at the formula telling us that something is wrong here. Indeed, the synchronicity means the same rate of those two clocks. The term rate is very similar to the velocity. It is well known fact that velocity could not be measured using just one position of the body; at least two coordinates are required. In the formula (1) there are two time values for the system A, but only one for the system B. And our first impression is something wrong with the rates. Prior to further analyzing of the formula, I would like to point out the following. There is no such variable as time in the science of physics. There is always time interval in physic s formulas. It is always time measured from some event to the other event or our measurement. If some formula contains just t then such interval is defined implicitly by assumption that time in initial moment is equals to zero. Capacitor discharge formula for example contains time, but it is just interval passed from the beginning of discharge rather than some world time.

3 Taking a second look at the formula (1) one could see that it is not even a valid physics formula. et me explain using the following example. There are two persons boiling the eggs. The first one is living in New York, the other one in ondon. Both of them want their eggs to be boiled 8 minutes. So we could write that: t NY stop NY t start = t stop t start This is an example of valid formula. eft and right parts of the formula contain the values which belong to the same system and both parts have certain meaning such as time interval. et s do some math using formula above: t NY stop t stop NY = t start t start The formula is still correct from mathematical point of view, but where is the physics? Both left and right pars have absolutely no meaning. It not even a time shift between New York and ondon as we don t know which clock is ahead or behind of time. Moreover the values on the left and right side are mix of values from different systems. Take another look at the formula (1). It is exactly the formula we just derived for eggs. We are going to find some physics meaning of Einstein s formula by separation of variables which belong to different systems. Before making such separation we should take another small step. Since we have no idea what time means, we are going to replace time with time interval and introduce reference points or one could say time when clocks were started. So t A will be replaced by t A t 0A and где t B with t B t 0B. The formula (1) became: and (t B t 0B ) (t A t 0A ) = (t A t 0A ) (t B t 0B ) 2(t B t 0B ) = (t A t 0A ) + (t A t 0A ) And time in the system B, when light was reflected is simple averaging of emission and receiving times for the system A. What is the physical meaning of that? I don t know, the physics is precise science, it is not a statistic. Using new knowledge we just got, we could easily make almost any two clocks synchronous. et assume the clock rate in the system B is twice of the clock in the system A. ike two non-parallel lines should cross somewhere, any two clocks should show exactly same time once in a lifetime. et set this time to 7 o clock. You could also say that clock B was started when clock A shows 3.5 hours. When clock A shows 7 hours (after 3.5 hours), the clock in the system B will show 7 hours (the clock is twice as fast). Assume that light travel from system A to system B in one hour. The way back is also required one hour. We are emitting the light from system A exactly at 6 o clock. The light is reflected in system B when both clocks are show 7 o clock. The light is returning back to system A at 8 o clock. et s put our numbers in the Einstein s formula (1):

4 7 6 = 8 7 And according to the Einstein s definition, two clocks are synchronized! Right after formula (1) Einstein deduced that: In agreement with experience we further assume the quantity 2AB = c (2) t A t A to be a universal constant the velocity of light in empty space. It is essential to have time defined by means of stationary clocks in the stationary system, and the time now defined being appropriate to the stationary system we call it the time of the stationary system. Where this formula came from? Obviously it could not be deduced from formula (1). The formula (2) reflects the whole essence of relativity. It is saying the speed of light is not a constant, the speed of light is only constant for the round trip. 3. Causality Although the causality problems were not touched in the Einstein s paper, it is worth to take a brief look at. The relativistic theory telling us that if observer is travelling at the speed faster than light, then he would see effect precedes its cause. What is wrong with that? The events do not happened where the observer are, it s happened here, in my system. The observer is just receiving information about such events. et me bring you some example. Someone fell (I am taking the photo #1) and broke the leg (and I am taking photo #2). Now I am putting both photos to the envelopes and sending #1 by sea and #2 by air. Was causality broken when observer would receive photo #2 first? Why causality broken right away if I am using light mail for my messages? 4. orentz Transformation In this chapter I would like to discuss the orentz transformation. Not Einstein s transform, but rather orentz transformation which was developed before Einstein for the description of the body, moving through aether. The derivation of such transform is pretty straightforward and looks approximately like the following. et assume that the body moving with velocity of v, emit the light in the direction of its movement. The light beam is moving with the velocity of c. Then, according to classical mechanics the speed of light relative to non-moving observer will be c + v. According to the theory, on the other hand, the speed of

5 light should not exceed the value of c. The solution is simple let s multiply the classical result by the value of orentz factor: (c + v)γ = c This is it. Вот и все! And the orentz factor should be equals to: γ = c = 1 c+v 1+ v c (3) In the case of emitting the light in the direction opposite to the body s speed, we have: γ = 1 1 v c (4) If light is emitted at 90 degrees to the body s movement: γ = 1 1 v2 c 2 The formula could be easily extended for any emission angle. I was curious how the transformation of Einstein is connected to this old fashioned transformation. It seems like the propagation of light is aligned with the body s velocity, but transformation looks like it was emitted at 90 degrees. If you will take a closer look at Einstein s paper, it appears that his formulas were derived in completely different way. The Einstein s Gedankenexperiment was built like follows: We are emitting the light beam, which is travelling to the moving body, reflected and coming back. On his way to the rod the light is travelling with the speed of c+v and on the way back the light is travelling with the speed of c-v. It is not a joke. Exactly those values for the light speed could be found in the Einstein s paper. Then we are calculating the total time of travel: And average velocity will be equals to: T = c + v + c v = 2c c 2 v 2 V = 2 T = 1 с (c2 v 2 ) But we could not exceed the value of c, the multiplication by the orentz factor give us: and c = Vγ

6 γ = c V = c2 c 2 v 2 = 1 1 v2 c 2 ooks pretty much like Einstein s orentz factor, it is just a square root which is missing. The derived formula does not describe the movement of electron properly, while the square root does. The solution to the problem was simple split the above expression on two square roots. One is going to length contraction, the other one to time dilation. And the orentz factor for the velocity will be equals to one we just derived. Old orentz transforms are free of self-contradictions. The Einstein s transformation is selfcontradictive. Indeed, the speed of must be c+v on its way to reflector and c-v on its way back. Otherwise Einstein s formulas just could not be derived. All you got in this case will be formulas (3) and (4) of old fashion transforms. The reader could try to follow Einstein s in his derivation with the constant values of the light speed, i.e. replacing both c+v and c-v with c. Personally I doubt that anything could be deduced. We may state that: Einstein contradict himself about constancy of the light speed All Einstein s formulas were derived assuming two-way trip of the light. How such formulas could be applied to one-way movement? The following is another example of absurdity from Einstein s paper: applied to the axes of Y and Z it being borne in mind that light is always propagated along these axes, when viewed from the stationary system, with the velocity V 2 v 2 gives us Who was talking about light speed constancy? 5. ength Contraction and Ehrenfest Paradox The theory of relativity dealing with just one point, but not even any point. If you take a look at relativistic orentz transformation, you will noticed that the velocity of such point must be directed along X coordinate in the moving system and this X coordinate must be parallel to the X coordinate of our system. As a matter of fact the real life is more diverse that the theory and we could easily imagine the point which moving along Y coordinate. What should we do? The theory does not telling us anything about Y coordinate, it is one axis theory. Take a look how Einstein-orentz transformation was derived the velocity along X is necessary condition. According to orentz transformation Y does not contracts, but if we rotate imaginary coordinate system then contraction happened. Basically we should derive another transformation for the case of Y-velocity. We could always rotate the system of coordinate to make theory to be applicable for Y coordinate, but how should one calculate the system of two points? One of the points is moving along X and the

7 second one along X. If those points are not interacting then it is possible to calculate one of them, rotate the system, make second calculation and recalculate result to my coordinate system. What kind of theory is that? In case of gravitational interaction between points the relativity could not provide any answer at all. There are no other theory beside relativity which has such a big number of paradoxes associated with it. One of the paradoxes is Ehrenfest paradox. If solid disk is rotating with high speed, then circumference of that disk should contract according to relativity, while the radii is perpendicular to the movement and the contraction does not occur. The circumference not equals to 2πR anymore. One more time the theory does not telling us anything about the velocity change or contraction along Y coordinate, this theory was derived assuming Y velocity equals to zero! If you draw coordinate system associated with rotating disk, you could see that only two points are satisfied to initial condition of orentz transform derivation. For the rest of the disk the theory is not applicable. et s take a brief look on the modern length contraction derivation. The beginning and the end of the moving rod are considered to be a points and the distance between them is equals to the length of the rod. orentz transformation: t = γ(t + vx c 2 ) x = γ(x + vt ) y = y z = z Velocity v is X velocity. Hatched variables are related to the moving system. Then x 1 = γ(x 1 + vt ) x 2 = γ(x 2 + vt ) = x 2 x 1 = γ The orentz transformation is considered as a given by any textbooks. Einstein however could not use orentz transformation for length contraction derivation. The orentz transformation itself is the result of Einstein consideration. et s take a look (here A and B are the beginning end the end of the rod): et a ray of light depart from A at the time t A, let it be reflected at B at the time t B, and reach A again at the time t' A. Taking into consideration the principle of the constancy of the velocity of light we find that t B t A = r AB c v t A t B = r AB c + v where r AB denotes the length of the moving rod measured in the stationary system. Interesting, what is the constancy of light Einstein talking about. As one could see the light is travelling one way with the speed of c-v and back with the speed of c+v!

8 If we take a look back at 1, we could read: «...unless we establish by definition that the time required by light to travel from A to B equals the time it requires to travel from B to A...». Please take a look at two expression above. Two time intervals are definitely not equal. Moreover, if you replace c+v and c-v both with c, then no length contraction will ever happened. Almost every single page of Einstein paper is full of such contradiction. 6. Conclusion Enough said to have a strong doubts on the validity of relativistic formulas. Einstein s derivation of relativity formulas uses c+v and c-v values for the speed of light. All experiments performed for the support of relativity in fact could be used against it. References: [1] ON THE EECTRODYNAMICS OF MOVING BODIES. By A. EINSTEIN