Jan Slowak

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  1. Jan Slowak

    Topic 4: Special Relativity - Lorentz transformations

    It is not a similar problem, but it is exactly the same problem with clearer explanations and pictures. I was going to help Ghideon move on. The sum of the two lengths for S' is vt' + ct' and it is the same length as x in S. We have two reference systems but we have only one reality!
  2. Jan Slowak

    Topic 4: Special Relativity - Lorentz transformations

    Another explanation for the same phenomenon. A reference system S' moves on the x-axis to the right at a constant speed v > 0. When S' passes the point P0, its clock is reset, t' = 0. At the same time, an event, a light signal, occurs in the point Px. Px is at a distance x from the point P0. While the light signal moves towards S', S' moves to the right. When the light signal reaches S', two distances occur on the x-axis. Distance [P0, S'] and distance [S', Px]. The length of these two distances is: Distance [P0, S'] = vt' Distance [S', Px] = ct' Then we have the following relationship: x = vt'+ ct'. Is this right?
  3. Jan Slowak

    Topic 4: Special Relativity - Lorentz transformations

    When I describe a physical phenomenon, make a mathematical model of it, presents my ideas, arguments, then I do not want to deviate from the main track. It's not possible! I present something, ask if I am right or wrong, then I want either an approval, Yes, or a No, but then you have to counter-argument. It should not be more difficult than that!
  4. Jan Slowak

    Topic 4: Special Relativity - Lorentz transformations

    This is no answer. If you answer NO, you must counter-argument.
  5. Jan Slowak

    Topic 4: Special Relativity - Lorentz transformations

    I analyze and talk about the derivation of LT. We don't have them yet! You cannot use them as counter-arguments. Please, do not send other pictures. We talk about my picture Fig. 4-05.
  6. Jan Slowak

    Topic 4: Special Relativity - Lorentz transformations

    Is there no one who wants to go through this thread and either confirm or argue against Fig. 4-05?
  7. Jan Slowak

    Topic 4: Special Relativity - Lorentz transformations

    This is not true! In the figure Fig. 4-03, we have processed and calculated the coordinates of the event in S. In the picture Fig. 4-04, we have processed and calculated the coordinates of the event in S'. I draw a new picture only with the components for S', see Fig. 4-05. This applies: during the same time t' as the light signal reaches S', the S' moves a distance vt'. S' knows that it moves at speed v > 0. S' registers the light signal at time t'. Then S' knows that it is from S at a distance equal to vt'. Is not it like that?
  8. Jan Slowak

    Topic 4: Special Relativity - Lorentz transformations

    I thought the same way as Bufofrog. We look at the picture Fig. 4-03. If we believe that t = 0 when the event occurred at point x, then t = x/c, time when S gets to know that the event occurred. Then E = (x, x/c). I would also like to point out that we cannot say much about the event unless you know the distance to it. Now we move on and also add the second reference system S' which moves to the right at constant speed v > 0. When the time is t = 0, t' = 0, both reference systems are located in the same point. Then, an event at distance x from the S-origo (S'-origo) occurs. See picture Fig. 4-04. What is special about S' is that while the light signal fails the distance x', S' moves the distance vt'. Am I right here?
  9. Jan Slowak

    Topic 4: Special Relativity - Lorentz transformations

    Maybe I was unclear. We look at Fig. 4-01. I am sure that x from E = (x, t) means the distance between the S-origo and the point on the x-axis where the event occurred, the point x. But what does t from E = (x, t) represent? What time do you mean here? We must also ask ourselves the question: How does S know that the event E has occurred?
  10. I really want to understand how Lorentz Transformations work! I refer to the picture Fig. 4-01: There we have an inertial reference system, S, that I depict with the axes x, y, x. In the future, we will only process the points on the x-axis, so in the next pictures I will draw only the x-axis. We regard this reference system as stationary, ie the distance between the reference system origin and the point where the event occurs is the same all the time. Then I would like help with defining what the coordinates x, t mean for S.
  11. Jan Slowak

    Special Relativity - SR - Time dilation

    I summarize once again my main idea in this thread: Special Relativity, SR: Lorentz Transformations, LT: LTx': x' = (x – vt)γ LTt': t' = (t – vx/c2)γ where γ = 1/(1-v2/c2)1/2 is called the Lorentz factor, LF. Time dilation, TD: t' = tγ In these two parts of SR there are two inertial reference systems S, S' and one event E = (x, t), E' = (x', t'). It is the same event with the different designation for S and S'. Now we follow the derivation of LT in [7] Modern Physics; Second edition; Randy Harris; Chapter 2; Special Relativity; 2008 You start with two linear equations: LEx': x' = Ax + Bt LEt': t' = Cx +Dt In the derivation of LT in [7], three special cases are used to determine the constants A, B, C, D. These three special cases SC1: x' = 0, x = vt SC2: x' = -vt', x = 0 SC3: x' = ct', x = ct are conditions that apply to LEx', LEt': Then: {LEx' and LEt' and SC1} and {LEx' and LEt' and SC2} and {LEx' and LEt' and SC3} → B = −Av, C = −A v/c2, D = A, A = γ → LTx': x' = (x – vt)γ LTt': t' = (t – vx/c2)γ If the derivation in [7] leads to LT and LT leads to the formula for time dilation then we must NOT have any contradiction during the verification of the derivation of LT. {LEx' and LEt' and SC1} is part of the derivation. Its verification LTt': t' = (t – vx/c2)γ SC1: x' = 0, x = vt → t' = (t-v(vt)/c2)γ → t' = t(1-v2/c2)γ → t'= t/γ must NOT lead to contradiction! But it does! This shows that the derivation of LT in [7] is not self-consistent!
  12. Jan Slowak

    Special Relativity - SR - Time dilation

    You write” The problem is that you swapped the frames” and ” In your LT derivation”: You forget that it is not my derivations of LT. So if you say I'm wrong, I'm right! In my work I show that the derivation of LT in [7] led to nonsense.
  13. Jan Slowak

    Special Relativity - SR - Time dilation

    LT and the formula for time dilation apply to all pairs of points ((x ', t'), (x, t)}, which verify the LT, of course. Do we have a different formula for time dilation for each point where you see a lamp blinking?
  14. Jan Slowak

    Special Relativity - SR - Time dilation

    I have never said that anyone should accept my conclusions in my work. In this thread, I show a mathematical evidence that LT is non-self-consistent. If you do not have counter-arguments, disproof, refrain from commenting. Mathematics is the queen of science! There is no mix of coordinate systems (frames) in this thread. It's about pure mathematics! You say I'll show something myself! In this thread, I show a mathematical evidence that LT is non-self-consistent.
  15. Jan Slowak

    Special Relativity - SR - Time dilation

    You just talk and talk.