That's just repetition, not a rebuttal. There's nothing wrong with $$x'^{2} \,-\, (ct')^{2} \,=\, x^{2} \,-\, (ct)^{2}$$. Your application of it in the wrong context is your error, as I explained. When you misapply a theory, that's your fault. Not the theory's.
Three Experiments Challenging SRT
- Thread starter Masterov
- Start date
przyk has provided formulas but you haven't responded to them with any level of understanding. The problem here is you, not us. You just assert things without evidence as you just did when you claimed it's banned in Germany to disagree with relativity. You don't provide any evidence and you ignore the evidence I provide that show you're mistaken.
You are, you're just not using that word. You're claiming scientists know relativity is wrong, the LHC was a massive con job and there's a decree of silence for anything disagreeing with relativity. That is a conspiracy, whether you want to call it so or not.
I don't believe you.
You mean continuous parameters, not distributed. Parameters in non-linear dynamical systems regularly have continuous domains. The Lorenz attractor and the logistic map being examples known to anyone who has studied non-linear systems.
Do you deny the obvious.
Speak for yourself.
I try to call a spade a spade.
I do not care.
My book offers analytical methods of analysis (analytical and numerical analysis), the integro-differential essentially nonlinear (with hysteresis) equations in which there is no discrete parameters and space (which identified the problem) is continuous and non-limited.
Download monography (Russian language).
No.
Linearity is a special case of nonlinearity.
A linear function is a special case of approximation of the nonlinearity.
Not for any approximation of nonlinearity the solution can be written as a finite number of functions, whose properties are studied.
One method allows you to choose an approximation of the nonlinearity (in the class of parametric functions) for which the solution can be written as a finite number of known functions.
$$(ct')^{2} - x'^{2} = (ct)^{2} - x^{2}$$ - it is error.
Look again:
If speed of light is constant then: "time left" $$\neq$$ "time right"
Formula $$(ct')^{2} - x'^{2} = (ct)^{2} - x^{2}$$ provide two identical roots.
It is error.
No. Do you? Your equation does not have an invariant c.
For a ray travelling at the speed of light in the positive x direction, $$x \,=\, ct$$, which implies $$x^{2} \,-\, (ct)^{2} \,=\, 0$$.
So according to your equation, in a boosted frame:
$$
\begin{eqnarray}
(x' - vt')^{2} \,-\, (ct')^{2} &=& 0 \\
x' \,-\, vt' &=& \pm\, ct' \\
x' &=& (v \,\pm\, c) t' \,.
\end{eqnarray}
$$
\begin{eqnarray}
(x' - vt')^{2} \,-\, (ct')^{2} &=& 0 \\
x' \,-\, vt' &=& \pm\, ct' \\
x' &=& (v \,\pm\, c) t' \,.
\end{eqnarray}
$$
So according to your equation, the velocity of light transforms according to $$c' \,=\, v \,\pm\, c$$. Is that your idea of "invariant"?
My English is not good enough for to read it.
$$c' \,=\, v \,\pm\, c$$. Your equation predicts a varying c.
I provide equations, illustrate their application is supported by reality and Masterov fails to retort it while also complaining I don't provide any equations. Thanks Masterov, you make it so much easier when you're blatantly dishonest.
Here's another proof that your equation,
is wrong. When I was born, I was 0 years old and born 0 km from where I was born, so $$t \,=\, 0$$ and $$x \,=\, 0$$, and therefore:
Now, I'm 25 years old and I live about 756 km away from where I was born, and I'm sitting still, so $$t' \,=\, 25\,\mathrm{yr}$$, $$x' = 756\,\mathrm{km}$$, and $$v \,=\, 0$$. In the units I'm using, $$c \,\approx\, 9.46\,\cdot\,10^{12}\,\mathrm{km}/\mathrm{yr}$$. So:
Obviously here,
So your equation is wrong.
$$
(x' - v't)^{2} \,-\, (ct')^{2} \,=\, x^{2} \,-\, (ct)^{2} \,,
$$
(x' - v't)^{2} \,-\, (ct')^{2} \,=\, x^{2} \,-\, (ct)^{2} \,,
$$
is wrong. When I was born, I was 0 years old and born 0 km from where I was born, so $$t \,=\, 0$$ and $$x \,=\, 0$$, and therefore:
$$
x^{2} \,-\, (ct)^{2} \,=\, 0 \,.
$$
x^{2} \,-\, (ct)^{2} \,=\, 0 \,.
$$
Now, I'm 25 years old and I live about 756 km away from where I was born, and I'm sitting still, so $$t' \,=\, 25\,\mathrm{yr}$$, $$x' = 756\,\mathrm{km}$$, and $$v \,=\, 0$$. In the units I'm using, $$c \,\approx\, 9.46\,\cdot\,10^{12}\,\mathrm{km}/\mathrm{yr}$$. So:
$$
(x' - vt')^{2} \,-\, (ct')^{2} \,\approx\, - 5.60\,\cdot\,10^{28}\,\mathrm{km}^{2}/\mathrm{yr}^{2} \,.
$$
(x' - vt')^{2} \,-\, (ct')^{2} \,\approx\, - 5.60\,\cdot\,10^{28}\,\mathrm{km}^{2}/\mathrm{yr}^{2} \,.
$$
Obviously here,
$$
(x' - v't)^{2} \,-\, (ct')^{2} \,\neq\, x^{2} \,-\, (ct)^{2} \,.
$$
(x' - v't)^{2} \,-\, (ct')^{2} \,\neq\, x^{2} \,-\, (ct)^{2} \,.
$$
So your equation is wrong.
By the way, we still haven't seen a meaningful reply to [POST=2957966]this post[/POST] (which you largely ignored, despite it providing and linking to mathematics you asked for) or [POST=2958193]this post[/POST] (which explains the error you keep making with Minkowski's equation, and which you obviously ignored).
Something from one of your previous posts you might like to recall:
Something from one of your previous posts you might like to recall:
Unfortunately for you, you're wielding a double edged sword. If you keep making the same stupid mistakes, even when they're repeatedly explained to you, everyone on the internet gets to see that too. Just something you might like to consider before posting yet another of your knee-jerk replies.
Anyone who has access to a book on special relativity or the internet can check that your repeated assertion Lorentz transforms are based on $$x^{2} - (ct)^{2} = (x')^{2} - (ct')^{2} = 0$$ is false. You obviously haven't even bothered to find out what Lorentz transforms do and what impact they have. My posts illustrating their application to experimental data and their consistency with said data back up what przyk has been saying. You keep saying $$(x')^{2} - (ct')^{2} = 0$$ but that isn't a general result. The sign of $$x^{2} - (ct)^{2} $$ determines whether a location is time-like, space-like or null with respect to the origin. Setting it equal to zero is the third case. This is the causal structure of space-time in special relativity and a central concept. One you have failed to find out about and refuse to learn even when it's put in front of you.
Do you think if you lie enough time reality will bend to your desires? Do you think you're going to convince professional physicists, which przyk and I both are, you're worth listening to by lying about work we actually do?
Do you think if you lie enough time reality will bend to your desires? Do you think you're going to convince professional physicists, which przyk and I both are, you're worth listening to by lying about work we actually do?
You can derive the Lorentz factor from first principles using mirrors, reflected beams of light, and two observers.
All you need is Pythagoras and the assumption that the speed of light is the same for inertial observers.
You have one observer at say, A, the other at B and the mirror at C. A is stationary wrt "the ground", and B plus the mirror which is a distance h from B are stationary wrt each other.
B plus the mirror are comoving relative to A at constant velocity, v.
B emits light towards the mirror at time t, and sees it arrive back at t' so for B t' - t = 2h/c = t[sub]B[/sub]. During the same interval t' - t (from B's perspective), A sees B plus mirror move a distance vt[sub]A[/sub], say along A's x axis. But A also thinks the light travels a greater distance.
If you draw the diagram ('meh') and use Pythagoras, you get the factor 1/√(1 - v[sup]2[/sup]/c[sup]2[/sup]) between B's and A's measured times for the path length of a light pulse, where B is stationary wrt mirror and A isn't.
Thereby demonstrating how, for observers with relative velocities, time is also relative.
All you need is Pythagoras and the assumption that the speed of light is the same for inertial observers.
You have one observer at say, A, the other at B and the mirror at C. A is stationary wrt "the ground", and B plus the mirror which is a distance h from B are stationary wrt each other.
B plus the mirror are comoving relative to A at constant velocity, v.
B emits light towards the mirror at time t, and sees it arrive back at t' so for B t' - t = 2h/c = t[sub]B[/sub]. During the same interval t' - t (from B's perspective), A sees B plus mirror move a distance vt[sub]A[/sub], say along A's x axis. But A also thinks the light travels a greater distance.
If you draw the diagram ('meh') and use Pythagoras, you get the factor 1/√(1 - v[sup]2[/sup]/c[sup]2[/sup]) between B's and A's measured times for the path length of a light pulse, where B is stationary wrt mirror and A isn't.
Thereby demonstrating how, for observers with relative velocities, time is also relative.