Simple lorentz trans. question

  • Thread starter Thread starter Ja4Coltrane
  • Start date Start date
  • Tags Tags
    Lorentz
Ja4Coltrane
Messages
224
Reaction score
0
I have been trying to derive the equation for relative velocity for a while and have had no success. I don't know, perhaps I am slightly misunderstanding SR or something. Does anyone have suggestions for understanding the derivation?
 
Physics news on Phys.org
Ja4Coltrane said:
I have been trying to derive the equation for relative velocity for a while and have had no success. I don't know, perhaps I am slightly misunderstanding SR or something. Does anyone have suggestions for understanding the derivation?
You mean, derive it from the Lorentz transformation? Just take an object with velocity v in one frame, find the coordinates of two events on its worldline (to make it simple the first could be the origin, the second could be the event x=vT, t=T), then find the coordinates of the same two events in another frame moving along the same axis of the first frame's coordinate system, and find (change in position)/(change in time) for the events in the second frame.
 
velocity transformations

Ja4Coltrane said:
I have been trying to derive the equation for relative velocity for a while and have had no success. I don't know, perhaps I am slightly misunderstanding SR or something. Does anyone have suggestions for understanding the derivation?

If you intend to derive it without using the Lorentz transformation have a look at
W.N. Mathews Jr. "Relativistic velocity and accelereation transformation from thought experiments," Am.J.Phys. 73 45 (2005)
I will send you a simpler approach to the same problem
 
velocity transformations

Ja4Coltrane said:
I have been trying to derive the equation for relative velocity for a while and have had no success. I don't know, perhaps I am slightly misunderstanding SR or something. Does anyone have suggestions for understanding the derivation?

If you intend to derive it without using the Lorentz transformation have a look at
W.N. Mathews Jr. "Relativistic velocity and acceleration transformation from thought experiments," Am.J.Phys. 73 45 (2005)
I will send you a simpler approach to the same problem
 
Ja4Coltrane said:
I have been trying to derive the equation for relative velocity for a while and have had no success. I don't know, perhaps I am slightly misunderstanding SR or something. Does anyone have suggestions for understanding the derivation?
There is a derivation on my website at

http://www.geocities.com/physics_world/sr/velocity_trans.htm

If you have any questions about this derivation then please ask.

Good luck

Pete
 
Using the Lorentz Transformations, one has compose two boost transformations.
The following links will start you off on various methods... but you'll have to finish the calculation.

In matrix form, you multiply two boost matrices, then identify the terms as if it were a single boost [possibly with rotation]. Follow the links, https://www.physicsforums.com/showthread.php?t=121285

Alternatively, one can use vector methods
https://www.physicsforums.com/showthread.php?p=961307#post961307

The k-calculus method is extremely efficient.
https://www.physicsforums.com/showthread.php?t=113915

I'm not a big fan of the usual derivation with infinitesimals.

In the end, for composition in "the same direction", you'll end up with a simple hyperbolic trig identity for tanh.

Which method are you using?
 
Last edited:

Thread 'Describing the Big Bang'

I started reading a National Geographic article related to the Big Bang. It starts these statements: Gazing up at the stars at night, it’s easy to imagine that space goes on forever. But cosmologists know that the universe actually has limits. First, their best models indicate that space and time had a beginning, a subatomic point called a singularity. This point of intense heat and density rapidly ballooned outward. My first reaction was that this is a layman's approximation to...
View full post »
Thread 'Dirac's integral for the energy-momentum of the gravitational field'

Thread 'Dirac's integral for the energy-momentum of the gravitational field'

See Dirac's brief treatment of the energy-momentum pseudo-tensor in the attached picture. Dirac is presumably integrating eq. (31.2) over the 4D "hypercylinder" defined by ##T_1 \le x^0 \le T_2## and ##\mathbf{|x|} \le R##, where ##R## is sufficiently large to include all the matter-energy fields in the system. Then \begin{align} 0 &= \int_V \left[ ({t_\mu}^\nu + T_\mu^\nu)\sqrt{-g}\, \right]_{,\nu} d^4 x = \int_{\partial V} ({t_\mu}^\nu + T_\mu^\nu)\sqrt{-g} \, dS_\nu \nonumber\\ &= \left(...
View full post »

Thread 'A sufficient condition for integrability of equation ##\nabla g=0##'

In Philippe G. Ciarlet's book 'An introduction to differential geometry', He gives the integrability conditions of the differential equations like this: $$ \partial_{i} F_{lj}=L^p_{ij} F_{lp},\,\,\,F_{ij}(x_0)=F^0_{ij}. $$ The integrability conditions for the existence of a global solution ##F_{lj}## is: $$ R^i_{jkl}\equiv\partial_k L^i_{jl}-\partial_l L^i_{jk}+L^h_{jl} L^i_{hk}-L^h_{jk} L^i_{hl}=0 $$ Then from the equation: $$\nabla_b e_a= \Gamma^c_{ab} e_c$$ Using cartesian basis ## e_I...
View full post »

Similar threads

I Lorentz Transformation: Premises + Derivation
Replies
5
Views
2K
I Links between the Lorentz equations and SR/GR
Replies
17
Views
2K
I Coord Transform in de Sitter Space: Phys Significance &Linearity?
Replies
5
Views
2K
I Is There Experimental Evidence That Contradicts Time Contraction Predictions?
Replies
5
Views
2K
B Calculating Time taken to reach speed with Time Dilation
Replies
18
Views
1K
I Special relativity vs Lorentz invariance
Replies
29
Views
3K
I A Hidden Zero in Einstein's Simple Derivation
Replies
22
Views
2K
B Deriving Lorentz Factor: An Analysis of Jimmy360's Method
Replies
4
Views
2K
I Can we choose different functional forms for Lorentz transformation?
Replies
10
Views
1K
I Explore Spacetimes, Metrics & Symmetries in Relativity Theory
Replies
7
Views
2K

Hot Threads

Recent Insights

Back
Top