Deriving Lorentz Transformation: Exploring vx/c^2

In summary, the Lorentz Transformation is a mathematical equation used to calculate the relationship between space and time for observers moving at constant velocities. It was developed by Hendrik Lorentz and is important for understanding the principles of special relativity and making predictions about physical phenomena. The vx/c^2 term in the equation represents the ratio of the moving object's velocity to the speed of light, and exploring its effects involves manipulating the equations. The Lorentz Transformation has various real-world applications in fields such as particle physics and technology like GPS systems.
  • #1
Jeno
17
0
Can i know how does the Lorentz transformation equations are derived?
x'=Y(x-vt)
y'=y
z'=z
t'=Y(t-vx/c^2)

Especially the equation for t', what is term vx/c^2 there implies?
thank you for answering me.
-Jeno-
 
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  • #4
Jeno said:
Can i know how does the Lorentz transformation equations are derived?
x'=Y(x-vt)
y'=y
z'=z
t'=Y(t-vx/c^2)

Especially the equation for t', what is term vx/c^2 there implies?
thank you for answering me.
-Jeno-
Well, you ask a lot here. It's a tall order, unless you desire a quick cheat sheet of sorts, with much assumed and/or omitted. Your question requires Sections 1 thru 3 of Einstein's 1905 OEMB paper, On the Electrodynamics of Moving Bodies. Section 3 is where the derivation takes place, whereby Einstein uses his kinematic model (thought experiment) of an emitter & reflector bouncing light back & forth.

The -vx/c^2 term is a temporal offset based upon distance x. Clocks in sync in the moving frame do not appear in sync per the stationary observing frame, however those moving clocks all tick at the same rate. If one clock reads 12am in some instant of your vantage, the other clock does not. It reads 12am at some other moment in your vantage, prior or later, even though the clocks are 12am AT ONCE per themselves. The delta time between like readouts (per you) depends opon the variable separation x, and the recorded velocity.

pess
 
  • #6
Hello,

Pete, there is something I would like to understand at the number (7) of your website :

[tex]v\gamma t' = v\gamma^2 t - \gamma^2 \beta^2 x = v\gamma^2 t - \gamma^2 vx/c^2[/tex]

Why does [itex]\beta^2 x = vx/c^2[/itex] if [itex]\beta^2 = v^2 / c^2[/itex]?

Isn't [itex]v\gamma t' = v\gamma^2 t - \gamma^2 v^2 x/c^2 = v\gamma^2 (t-vx/c^2 )[/itex] ?

Thanks
 
Last edited:
  • #7
Zeit said:
Hello,

Pete, there is something I would like to understand at the number (7) of your website :

vgamma t' = vgamma^2 t - gamma^2 beta^2 x = vgamma^2 t - gamma^2 vx/c^2

Why does beta^2 x = vx/c^2 if beta^2 = v^2 / c^2?

Isn't vgamma t' = vgamma^2 t - gamma^2 v^2 x/c^2 = vgamma^2 (t-vx/c^2 )?

Thanks
Infact, there is a mistake. It should be as you say. The last term shouldn't be gamma^2 vx/c^2 but, instead:
gamma^2 v^2x/c^2.
 
  • #8
Zeit said:
Hello,

Pete, there is something I would like to understand at the number (7) of your website :

[tex]v\gamma t' = v\gamma^2 t - \gamma^2 \beta^2 x = v\gamma^2 t - \gamma^2 vx/c^2[/tex]

Why does [itex]\beta^2 x = vx/c^2[/itex] if [itex]\beta^2 = v^2 / c^2[/itex]?

Isn't [itex]v\gamma t' = v\gamma^2 t - \gamma^2 v^2 x/c^2 = v\gamma^2 (t-vx/c^2 )[/itex] ?

Thanks
Its probably beccause I screwed up. :biggrin:

When I create these web pages I first do it with pen to paper. Then I transfer to an MS Word document so I can add equations etc. Then I take that and translated it into a web page. There's plenty of places to go wrong in this process. But thank you so much for pointing it out. I'll put this in my file of web pages to correct. Thanks again.

Best wishes

Pete
 
  • #9
No problem, I thank you for it, because I had been searching for this kind of webpage when I found this thread :biggrin:
 
  • #10
Zeit said:
No problem, I thank you for it, because I had been searching for this kind of webpage when I found this thread :biggrin:
Thanks. I got to tell you Zeit. Its a very good feeling when you've done an enormous amount of work and someone finds it of use. Thank you for letting me know. :approve:

Best wishes

Pete

ps - Feel free to e-mail me or PM me about anything whatsoever. Okay? :smile:
 
  • #11
Hello,

Thanks Pete for your proposal, I'll write you if I need to :-p

Good bye
 
  • #12
PETE, Please i want to know the similarities between lorenz and galilean transformation
 
  • #13
Richie,
How long are you willing to wait for a answer? Pete has not been active for nearly 3yrs.
I suggest you start your own thread.

Necroposting. Thread locked.
 

Related to Deriving Lorentz Transformation: Exploring vx/c^2

1. What is the Lorentz Transformation?

The Lorentz Transformation is a mathematical equation that describes the relationship between space and time in special relativity. It was developed by physicist Hendrik Lorentz and is used to calculate how measurements of space and time change for an observer moving at a constant velocity relative to another observer.

2. Why is it important to derive the Lorentz Transformation?

Deriving the Lorentz Transformation allows us to understand the underlying principles of special relativity and how measurements of space and time change for moving observers. It also helps us to make predictions and calculations for various physical phenomena, such as time dilation and length contraction.

3. What is vx/c^2 in the Lorentz Transformation?

vx/c^2 is the velocity of the moving observer relative to the stationary observer, divided by the speed of light squared. It represents the ratio of the velocity of the moving object to the maximum possible velocity in the universe, which is the speed of light.

4. How do we explore vx/c^2 in the Lorentz Transformation?

Exploring vx/c^2 involves manipulating the mathematical equations of the Lorentz Transformation to understand how the velocity of the moving observer affects the measurements of space and time. This can be done by plugging in different values for vx/c^2 and observing how it changes the resulting values for time dilation, length contraction, and other relativistic effects.

5. What are some real-world applications of the Lorentz Transformation?

The Lorentz Transformation has many applications in modern physics, including in the fields of particle physics, cosmology, and nuclear physics. It is also used in technologies such as GPS systems and particle accelerators. Understanding the Lorentz Transformation is essential for accurately describing and predicting the behavior of objects at high speeds and in extreme conditions.

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