Special Relativity - SR - Time dilation

[Ghideon]

1 hour ago, Jan Slowak said:

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!

You still have to apply the mathematics under valid conditions and in context where that mathematical model is applicable.

1 hour ago, Jan Slowak said:

There is no mix of coordinate systems (frames) in this thread.
It's about pure mathematics!

Until you clarify the confusing use of time dilation vs Lorentz transformation this thread is exactly about mix of frames of reference.

Do you mind if I post a diagram to highlight what I find confusing? Or is that not allowed according to your rules?

 

[beecee]

12 hours ago, Jan Slowak said:

I have written and submitted a lot of articles to physics magazines. But they are negative in the same way that you are on this forum.

Their answer is the same
Thank you for your submission to … . We have assessed your manuscript and have considered its suitability for the journal very carefully. We regret to inform you that your article will not be considered for review as it does not meet our strict publication criteria.

The quality and presentation of any research published in ... must be of the highest standard. Submissions should clearly demonstrate scientific rigour, extensive literature research and a careful assessment of the validity of any conclusions presented in the manuscript. Your manuscript does not meet these key publication criteria and we are unable to consider it further.
We are grateful for your interest in … .
Yours sincerely..

Perhaps you need to listen to the professionals instead of sticking your fingers in your ears and shouting Lalalala! 

4 hours ago, Jan Slowak said:

Mathematics is the queen of science!

And it appears as the experts have shown, that your mathematics is wrong...sad!!!

[Ghideon]

On 6/8/2019 at 12:31 PM, Jan Slowak said:

You just talk and talk. You dare not take hold of my concrete questions. Come with a mathematical counter-proof regarding t '= tγ (t' = t/γ).

(1): [math]t'= \gamma (t- \frac{vx}{c^{2} } )[/math]

(2): [math]t_{2}'-t_{1}'= \gamma (t_{2}- \frac{vx_{2}}{c^{2} } )-\gamma (t_{1}- \frac{vx_{1}}{c^{2} } )[/math]

(3): [math]t_{2}'-t_{1}'=\gamma ((t_{2}- \frac{vx_{2}}{c^{2} } )- (t_{1}- \frac{vx_{1}}{c^{2} } ))=[/math]

(4): [math]\gamma ((t_{2}-t_{1})-( \frac{vx_{2}}{c^{2} } )- (- \frac{vx_{1}}{c^{2} } ))=\gamma ((t_{2}-t_{1})-( \frac{vx_{2}}{c^{2} } - \frac{vx_{1}}{c^{2} } ))=[/math]

(5): [math]\gamma (\Delta t- \Delta x\frac{v}{c^{2}}) [/math] where

[math]\Delta t'=t_{2}'-t_{1}' [/math]
[math]\Delta t=t_{2}-t_{1} [/math]
[math]\Delta x=x_{2}-x_{1} [/math]

(6): [math]\Delta x=0 \Longrightarrow \gamma (\Delta t- \Delta x\frac{v}{c^{2}}) =\gamma (\Delta t-0)=\gamma \Delta t[/math] 

 

Explanations of the equations, their implications and conclusions:

(1): Common form of the Lorentz transformation, parametrized by the real constant representing a velocity confined to the x-direction. Only displaying time coordinate. 

(2): Lorentz transformation of the interval between two events separated by some distance in x-direction and separated by some time.

(3), (4), (5): Rearrange and use delta

(6): Apply the Lorentz Transformation* for the interval (5) for delta x=0 (Time dilation**) results in the correct formula for time dilation.
Conclusion: Since Lorentz transformation and time dilation are related but have different definitions the mathematical formulas are derived differently and looks different. Using the correct notation, provided by @Strange in the first response, also highlights this. Equations (1) and (6) are not the same and by definition not meant to be, but (1) can be used to derive (6).

Therefore the following statement about derivation of Lorentz transform is incorrect unless clarification about the use of  Lorentz Transformation and Time dilation is clarified by OP:

On 6/7/2019 at 7:36 PM, Jan Slowak said:

My comment: In the derivation of LT in [7] is used LEx ', LEt', SC1, SC2, SC3 and as a result you get time dilation t' = tγ.
But the verification of the derivation, LTt' with SC1 gives us t'= t/γ.

This shows that the derivation of LT in [7] is not self-consistent! 

 

 

Here is my own take at stating the differences***

Lorentz transform: the calculation of the coordinates  (x’,y’,z’,t’) of an event in one frame of reference given the coordinates (x,y,z,t) of the same event in another inertial frame. The two frames of reference are moving with the relative constant velocity v.

Time dilation: Calculation of the time interval between two events in a frame of reference S’ when the two events are taking place at the same point (x,y,z) in space but separated in time (t1, t2) in another frame of reference S.

*) https://en.wikipedia.org/wiki/Lorentz_transformation#Coordinate_transformation

**) https://en.wikipedia.org/wiki/Time_dilation#Velocity_time_dilation

***) I try to use my own words as an exercise in SR; corrections welcome.

Edited June 9, 2019 by Ghideon
simplified equation, added definitions of deltas, format, added citation

[beecee]

On 6/8/2019 at 3:36 AM, Jan Slowak said:

 This is one of the reasons I said that SR is nonsense.
I regret that everyone is upset by my conclusion but I have a lot more aspects of SR that I have analyzed in detail and everyone shows the same thing.

Or possibly you misunderstand. Because obviously SR is not nonsense and has been experimentally and observationally validated many times.

[Strange]

On 6/7/2019 at 6:36 PM, Jan Slowak said:

I regret that everyone is upset by my conclusion 

It is not your conclusion that I have a problem with, it is your refusal to discuss the explanations of your errors. 

[DanMP]

On 6/7/2019 at 8:36 PM, Jan Slowak said:

[7] Modern Physics; Second edition; Randy Harris; Chapter 2; Special Relativity; 2008
In the derivation of LT in [7], three special cases are used to determine the constants A, B, C, D.

The result of this derivation gives the following: B = −Av, C = −Av/c², D = A, A = γ. If you replace these values in
LEx': x' = Ax + Bt
LEt': t' = Cx +Dt
you get
LTx': x' = (x – vt)γ
LTt': t' = (t – vx/c²)γ
It is these two equations that are LT.

But during the derivation, the combination LEt', SC1 is not used. Therefore, we make a verification of a solution (as one should always do).
We calculate LTt' in SC1:
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

The above shows (correctly) that for "SC1: x' = 0, x = vt", when the primed clock (consider it a light clock) is in the origin of the S' frame (x'=0), moving with the speed v away from the origin of the S frame (x=vt), Lorentz transformations yield: t'= t/γ  (where t' and t are in fact  Δt' and Δt,  time intervals from the moment t₁'=t₁=0 when x₁'=x₁=0).

 

On the other hand

On 6/6/2019 at 5:05 PM, Jan Slowak said:

this relationship:
t' = tγ

taken from:

On 6/6/2019 at 5:05 PM, Jan Slowak said:

Check for example https://en.wikipedia.org/wiki/Time_dilation

(more precisely https://en.wikipedia.org/wiki/Time_dilation#Velocity_time_dilation)

is valid for x=0, not for x'=0 as in "SC1" (where x' and x are in fact  Δx' and Δx), so t and t' are swapped ... This is the origin of the "error". In fact Lorentz transformations are correct, as we all know.

Edited June 11, 2019 by DanMP

[swansont]

52 minutes ago, DanMP said:

The above shows (correctly) that for "SC1: x' = 0, x = vt", when the primed clock (consider it a light clock) is in the origin of the S' frame (x'=0), moving with the speed v away from the origin of the S frame (x=vt), Lorentz transformations yield: t'= t/γ  (where t' and t are in fact  Δt' and Δt,  time intervals from the moment t₁'=t₁=0 when x₁'=x₁=0).

 

On the other hand

taken from:

(more precisely https://en.wikipedia.org/wiki/Time_dilation#Velocity_time_dilation)

is valid for x=0, not for x'=0 as in "SC1" (where x' and x are in fact  Δx' and Δx), so t and t' are swapped ... This is the origin of the "error". In fact Lorentz transformations are correct, as we all know.

IOW, the analysis improperly swapped frames of reference, despite the claim to the contrary.

[Jan Slowak]

2 hours ago, DanMP said:

The above shows (correctly) that for "SC1: x' = 0, x = vt", when the primed clock (consider it a light clock) is in the origin of the S' frame (x'=0), moving with the speed v away from the origin of the S frame (x=vt), Lorentz transformations yield: t'= t/γ  (where t' and t are in fact  Δt' and Δt,  time intervals from the moment t₁'=t₁=0 when x₁'=x₁=0).

  

On the other hand

taken from:

(more precisely https://en.wikipedia.org/wiki/Time_dilation#Velocity_time_dilation)

is valid for x=0, not for x'=0 as in "SC1" (where x' and x are in fact  Δx' and Δx), so t and t' are swapped ... This is the origin of the "error". In fact Lorentz transformations are correct, as we all know.

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?

 

[Ghideon]

2 hours ago, Jan Slowak said:

Do we have a different formula for time dilation for each point where you see a lamp blinking?

No.
You can check the math in https://www.scienceforums.net/topic/119174-special-relativity-sr-time-dilation/?do=findComment&comment=1106227

 

Edited June 11, 2019 by Ghideon
link missing

[DanMP]

18 hours ago, Jan Slowak said:

Do we have a different formula for time dilation for each point where you see a lamp blinking?

The formula is the same. The problem is that you swapped the frames. Time dilation is usually calculated for a clock (it doesn't matter if it is a light clock as in your link or any other clock) and from a reference frame. In your LT derivation the clock was static in the origin of S' (the condition was x'=0), while in the geometric calculation  the clock was static in S frame (the initial x' was different than the final x', while x was 0 all the time). So, in order to compare the results, you have to keep the same scenario/notations and to swap t' with t in one of the calculations.

Edited June 12, 2019 by DanMP

[Jan Slowak]

7 hours ago, DanMP said:

The formula is the same. The problem is that you swapped the frames. Time dilation is usually calculated for a clock (it doesn't matter if it is a light clock as in your link or any other clock) and from a reference frame. In your LT derivation the clock was static in the origin of S' (the condition was x'=0), while in the geometric calculation  the clock was static in S frame (the initial x' was different than the final x', while x was 0 all the time). So, in order to compare the results, you have to keep the same scenario/notations and to swap t' with t in one of the calculations.

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.

 

[swansont]

12 minutes ago, Jan Slowak said:

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.

 

The derivation is fine. The frame-swapping happened in the (incorrect) application of the equations.

[Ghideon]

24 minutes ago, Jan Slowak said:

In my work I show that the derivation of LT in [7] led to nonsense.

In my work* I have shown that you are incorrect. @DanMP as well has provided mathematical arguments as you requested. How about you supply some analysis of the math you requested, instead repeating the incorrect claims?
I suggest you try to provide some answers to my posts, as described in the rules for speculations section.

 

*) at least until you provide clarifying details; https://www.scienceforums.net/topic/119174-special-relativity-sr-time-dilation/?do=findComment&comment=1106227

[DanMP]

18 hours ago, Jan Slowak said:

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.

Ok   what you did wrong was not the actual swapping, but the fact that you didn't notice that the notations were different. In your LT calculation (not derivation, sorry) S' was moving to the right, while in the geometrical calculation, S was moving to the right, as you can understand from the picture and its caption:

Quote

Left: Observer at rest measures time 2L/c between co-local events of light signal generation at A and arrival at A.
Right: Events according to an observer moving to the left of the setup: bottom mirror A when signal is generated at time t'=0, top mirror B when signal gets reflected at time t'=D/c, bottom mirror A when signal returns at time t'=2D/c

 

As I wrote above, in order to compare the results, you have to keep the same scenario/notations, because (unfortunately) the notations are not the same everywhere, as you may see also in other 2 examples/derivations:

https://www.amnh.org/learn/pd/physical_science/week3/time_dilation.html

https://phys.libretexts.org/Bookshelves/University_Physics/Book%3A_University_Physics_(OpenStax)/Map%3A_University_Physics_III_-_Optics_and_Modern_Physics_(OpenStax)/5%3A__Relativity/5.3%3A_Time_Dilation

 

Edited June 13, 2019 by DanMP

[Jan Slowak]

On 6/13/2019 at 3:50 PM, DanMP said:

Ok   what you did wrong was not the actual swapping, but the fact that you didn't notice that the notations were different. In your LT calculation (not derivation, sorry) S' was moving to the right, while in the geometrical calculation, S was moving to the right, as you can understand from the picture and its caption:

 

As I wrote above, in order to compare the results, you have to keep the same scenario/notations, because (unfortunately) the notations are not the same everywhere, as you may see also in other 2 examples/derivations:

https://www.amnh.org/learn/pd/physical_science/week3/time_dilation.html

https://phys.libretexts.org/Bookshelves/University_Physics/Book%3A_University_Physics_(OpenStax)/Map%3A_University_Physics_III_-_Optics_and_Modern_Physics_(OpenStax)/5%3A__Relativity/5.3%3A_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!

[swansont]

Instead of reposting, I will simply call your attention to all o the objections people have made, and you have ignored. Repeating yourself will not make them disappear.

[Phi for All]

1 hour ago, Jan Slowak said:

I summarize once again my main idea in this thread:

!

Moderator Note

This isn't working for ANYBODY! Your summaries are WRONG, people have told you why, but you ignore what they're saying. You claim a theory is wrong when it's used EVERY DAY in modern science.

YOU. ARE. MISTAKEN.

You keep making the same mistakes, so I'm going to recommend that you stop re-posting your obvious nonsense and READ THE REPLIES. You're wrong about this, and you're being stubborn in the face of so many people who understand the science. If you can't bother to fix your ignorance in this regard, there is NOTHING discussion can do for you. You need to overcome this mental block that makes you think SR is wrong just because you don't understand it.

I'm closing this thread and I'm going to recommend that you look through some of the other threads in Speculations where people didn't understand Relativity. Perhaps you can learn from them, since you can't learn from experts. Don't open any more threads about this until you've done some rigorous study!