Jan Slowak

I wrote: In what way does the light signal follow the two reference systems? Two rockets = two reference systems. Note the following: - a light signal - one or more reference systems Each of these objects / phenomena is independent of each other. The light speed and its direction are independent of the source and the observer's movements!

I'll draw a picture. A light signal, a pulse, occurs on the x-axis and moves to the right with speed c. At the same time, two rockets start, one moves to the right with speed v and the other to the left with speed -v. In what way does the light signal follow the two reference systems?

I have never talked about quantum field theory!

Never! Never! The light speed and its direction are independent of the source and the observer's movements!

I have decided before to not continue to answer this thread because it was moved to Speculations and also other reasons. I only answer you because you are from Cluj-Napoca where I studied mathematics at the University of Babes-Bolyai in 1972-1977. I have analyzed the derivation of LT in [7]. But whatever you read about LT it says that reference systems S and S' move relative to each other at constant speed v. For example, if S' moves to the right with v, S moves to the left with -v.

We only talk about (x, t) and (x', t'). The image contains three axes for S and S' to see that it is a reference system i (x, y, z). The circle representing the wavefront is drawn in a plane but we only deal with the event, a point, where the circle crosses the x-axis. Hope this helps understand the picture. Then you should state the expression of the event's coordinates (x, t) for S and the event's coordinates (x', t') for S'. It would be good if you number pictures so that you can refer to them. One thing is not right in your last picture: There should be only the red circle, the wave front that occurs at the beginning of the thought experiment, then when the two reference systems coincide in the same point. The wave front does not follow any reference system!

This thread is closed by the moderator Phi for All, I refrain from processing it further.

We have two inertial reference systems S and S'. These move relative to each other at constant speed v. We say that S' moves to the right on our pictures. For the sake of simplicity, we treat a simplified case when the x-axis and the x'-axis coincide on the same line. Then we have an event that is considered by the two reference systems. We denote the event with E = (x, t) for S and E' = (x', t') for S'. Note that physically it is about the same event! The thought experiments dealt with in different derivations of LT begin with the moment when S and S' are in the same point. At this moment, the clocks in S and S' are synchronized. All this means that in the beginning we have E = (x, t) = (0, 0) E' = (x', t') = (0, 0) See the following image: Fig: t = 0, t' = 0 Do we agree on this? I'm talking about the derivation of LT from [7]. You refer to the link above which we can designate with eg [DLTf1P]. The picture you have drawn is not enough to see exactly what is happening and what relationships we have between the coordinates and what conditions you set on the equation system that is formed. One flash of light originating at the origin of two frames of reference moving relative to each other. (your words). I now draw a picture where we see how things stand out after the time t > 0, t' > 0. Note that the image is not drawn to scale. S and S' consider the event located on the wave front on the x-axis (x'-axis). See picture Fig. t > 0, t' > 0. Do we agree on this? If we agree then I would ask you to help me write down the values of x, t, x', t' and the relationships between them and the value of the distance between S and S'. So as this picture shows. Thanks!

It is only about the x-axis and the x'-axis that coincide with each other. [7] Modern Physics; Second edition; Randy Harris; Chapter 2; Special Relativity; 2008 I enclose pages 14-15 from [7]. You can draw a similar image as Fig. SC1 or Fig. SC2. Modern Physics Randy Harris 2008 pages 14-15-v1.pdf

In the derivation of LT in [7], three special cases are used to determine the constants A, B, C, D. SC1: SC1: LEx': x' = Ax + Bt LEt': t' = Cx + Dt SC1: x' = 0, x = vt → B = -Av SC2: SC2: LEx': x' = Ax + Bt LEt': t' = Cx + Dt SC2: x' = -vt', x = 0 → B = -Dv But I have not seen a figure describing SC3. Can anyone help me with such a figure? SC3: LEx': x' = Ax + Bt LEt': t' = Cx + Dt SC3: x' = ct', x = ct Thank you!

It wasn't me who started with such discussions. I mentioned several times that I only want to talk about mathematics, logic and physics. I felt insulted. I want to ask if this thread is closed.I would like to continue with other things. I have a few more things to discuss regarding the derivation of LT in [7]. Should I continue here or should I start a new thread?

You write: Why? Your logic is flawed. SC1, SC2, SC3 in the derivation of LT in [7] are three different problems, tre different physical phenomena, tre different thought experiments. They should NOT be combined in one and the same equation system! That's what is wrong. I suggest you think about this, talk to some other physicists and mathematicians. Think about what SC1 and SC2 are for something. And think properly what gives your right to put them in one and the same equation system. You do not have to be ironic in your answers. We should only talk about mathematics, logic and physics. No personal insults, thank you!

Please check my answer for swansont. Sorry, I missed a word. I should have written: We can discuss the derivation of LT in the link provided by swansont then. After we finish the derivation of LT in [7]. You write: We have shown you where you have gone wrong in your criticism of [7]. You haven't shown anything yet. Check my answers to swansont and Ghideon.

Please check my answer for Ghideon. Please try to familiarize yourself with my logic. The two SC from [7] can be compared to two problems that use the equation you specify y = mx + b. Problem 1: About cars. When setting conditions you get the following equation system: LEy: y = mx + b SC1: x = 0, y = 5 → b = 5 Problem 2: About aircraft. When setting conditions you get the following equation system: LEy: y = mx + b SC2: y = 0, x = 0; in this case, the line LEy goes through the origin of the coordinate system. → b = 0 These two problems have nothing in common!

I can repeat myself again. The derivation of LT in [7]: Special Case 1: we have the following equation systems: LEx': x' = Ax + Bt LEt': t' = Cx + Dt SC1: x' = 0, x = vt By replacing SC1 in LEx' we get a relationship between constants. The solution in this case is B = -Av. This solution, this relationship between constants, applies only to x' = 0! Special Case 2: we have the following equation systems: LEx': x' = Ax + Bt LEt': t' = Cx + Dt SC2: x' = -vt', x = 0 By replacing SC2 in LEx', LEt' we get a relationship between constants. The solution in this case is B = -Dv. This solution, this relationship between constants, applies only to x = 0! In [7] you combine these two solutions in one and get D = A. I want to draw the reader's attention to an important thing: Special Case 1 and Special Case 2 are two different problems, two different physical phenomena, two different thought experiments. They should NOT be combined. If you do so, the following applies: Special Case 1 give us B = -Av that applies only to x' = 0! Special Case 2 give us B = -Dv that applies only to x = 0! → D = A applies only to {x' = 0, x = 0} This is the case when the two reference systems are in the same point! Then no LT is needed.

I said at the beginning that in this section, I deal with the derivation of LT from [7]. We can discuss the derivation of LT in the link provided by swansont.

I cannot accept your counter-arguments by using words, by saying "it's not true"! Only mathematical arguments! Instead of words, you should use mathematical calculations. SC1 and SC2 are thought experiments! You said: ”I think you are the one who needs help from a competent mathematician.” I hoped that ScienceForum.net has the policy of NOT using personal defamation. It doesn't matter who we are (I don't know who you are, what education you have) we'll stick to the theme: The derivation of LT in [7] is not self-consistent! Please do not talk about anything else.

If you with Eqn 2.5 refer to page 15 in [7] then I say again: The result B = -Av which you get by solving the equation system LEx': x' = Ax + Bt LEt': t' = Cx + Dt SC1: x' = 0, x = vt applies only to x' = 0. The result B = -Dv which you get by solving the equation system LEx': x' = Ax + Bt LEt': t' = Cx + Dt SC2: x' = -vt', x = 0 applies only to x = 0. SC1 and SC2 are two independent experiments and you must NOT mix their results! Ask a professor of mathematics! You said After 115 years of mathematical development and experimentation. You are clearly wrong. This is no proof! See Cosmos - a short story; Stephen Hawking; page 15: "A physical theory is always provisional in the sense that it is merely a hypothesis: one can never prove it. However many times the experimental results are consistent with a particular theory, one can never be sure that the results next will contradict the theory. On the other hand, one can disprove a theory by finding only one that does not conform to the predictions of theory ”

Please do not deviate from the main theme: my analysis of the derivation of LT in [7]. Please check out Fig. 04: SC1 which has conditions x' = 0 gives the result B = -Av. This result applies to x' = 0! SC2 which has condition x = 0 gives the result B = -Dv. This result applies to x = 0! If you combine these two results in one, D = A, this result applies to {x'= 0 and x = 0}! Either you mathematically show that I am wrong or accept my results!

I think I am quite clear in what I write. It was not about some print errors, it is about fundamental issues. It is not a misprint or a mistake. It is about that in [7] and [3] one uses the mathematics in a wrong way! Please do not deviate from the main theme: my analysis of the derivation of LT in [7] which shows that LT is not self-consistent.

I do not know exactly how many different derivations of LT exist. I have analyzed in detail two in the following literature: [7] Modern Physics; Second edition; Randy Harris; Chapter 2; Special Relativity; 2008 [3] The special and general theory of relativity; Albert Einstein; The first part; About the special theory of relativity; 2006; swedish and recently I have read the suggested article on the link https://thecuriousastronomer.wordpress.com/2013/03/10/derivation-of-the-lorentz-transformations-from-first-principles/ I firmly claim that all three are not self-consistent (mathematically or logically or physically)!

I have explained at the beginning that I have analyzed the derivation of LT from [7] Modern Physics; Second edition; Randy Harris; Chapter 2; Special Relativity; 2008 You cannot refer to other letters, we must overcome this first. My motto: When studying a physical phenomenon, a mathematical model is developed to describ it. Such a model comprises built-in physical laws held together by mathematical tools. If the description of the physical phenomenon is correct, the mathematical model is also correct. After we have done a mathematical model and we work with it then only the math applies. In this part, we must respect mathematics to the fullest! --> One more time: Each special case has its scope: SC1 applies to {x' = 0} and SC2 applies to {x = 0} If you apply these two SC in the same equation system and get a result then the result applies in {x' = 0, x = 0}. SC1, SC2, SC3 are completely different thought experiments. If you apply them in the same equation system then the result applies in their common validity area!

Each special case has its scope: SC1 applies to {x' = 0} SC2 applies to {x = 0} If you apply these two SC in the same equation system and get a result then the result applies in {x' = 0, x = 0}. SC1, SC2, SC3 are completely different thought experiments. If you apply them in the same equation system then the result applies in their common validity area!

"No, that's not how boundary conditions work." I am sorry but to say a sentence is not a mathematical proof. I just prefer a proper mathematical evidence.

I enclose a document with my explanations and my evidence. LT are not self-consistent-eng.pdf