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## Physics library

### Course: Physics library>Unit 16

Lesson 3: Lorentz transformation

# Lorentz transformation derivation part 1

Using symmetry of frames of reference and the absolute velocity of the speed of light (regardless of frame of reference) to begin to solve for the Lorentz factor.

## Want to join the conversation?

• At what is the reason to suppose that the relationship between the Galilean transformation and the relativistic transformation is simply a scaling factor (gamma) rather than some more complex relationship? • At -- aren't you assuming too early that gamma(-v) = gamma(v)? If gamma were equal to say, 1/(1-v/c), for instance, then the scaling factor would, in fact, be different. • Could someone explain to me about the Galilean transformations? Thanks. • Newtonian physics codifies Galilean Transformations in its mechanics in velocities and implies that velocity depends on how you move even when you consider yourself inertial,for instance,if you're running at 1m/s and you were passed by a car whose velocity was 3m/s,then the way you view its movement is 2m/s because of its velocity 3m/s - 1m/s =2m/s. This is a brilliant analogy yet it's wrong,because it implies that at high speeds when you're stationary and you see a super vehicle moving at a half of speed of light and then he uses a laser pointing at the positive x direction,then it implies from there that the cosmic speed of light will be faster which would,in other words,imply that c is infinite and doesn't apply to e=mc^2 because it'd require an infinite amount of energy to support higgs mechanisms contribution to mass.

(I think I may make mistakes so uhm you can see few ideas on the internet that may help.)
• At 9.29 to 9.38 what does the line in the purple and later in the yellow mean and represent? I think it is the world line path of the photon shot out of Sallys flashlight relative to the S' system and it is not (but I am not sure about this) the path of the photon shot out of Sal flashlight relative to the S system . Is this true? • It could be the world line path of light from both Sal and Sally's flashlight, in both of their reference frames. This yields 4 possible scenarios!
Which of them had the flashlight does not matter because it was shone at t = 0, when their positions overlap anyways.
The reference frame does not matter because the path of light is the angle bisector between the two axels. This might be a better definition than that the path of light is at 45 degrees.
(1 vote)
• Why does the x-axis in the right graph not point in the second quadrant as well? • At , why is it x' = (x-vt), as opposed to x'=(x+vt)? • at why we assumed that the event which they're observing is a beam of light why won't it be another thing?and if it is another thing will the Lorentz factor be different?
(1 vote) • Why gamma is used as scaling factor over there?
(1 vote) • Yeah but, from both of our frames of reference, we see each other going to the "right" of us at velocity v, so why are we saying -v??
I mean, imagine that if you see me travelling towards your right, then from my frame you are travelling to the right.... same speed...
So right is positive. And thus the positive itself shifts as frame of reference changes!
Is it like a convention or so?
(1 vote) • "right and left" are only defined relative to which way you are facing, which is ignored here. A better (although still flawed) analogy would be compass directions. Eg, if we think of positive x as East and negative x as West, then v and -v go in opposite directions. if I am travelling at v relative to you, then I am moving "East", positive along the x axis from your point of view, and you are moving at -v, which is "West", negative along the x axis from my point of view.
(1 vote)
• I don't understand the difference between -v and v.
Wouldn't it only happen if we define one direction as positive and another as negative?
Shouldn't time dilation and length contraction be independent of the direction(we assume +ve)?
Besides ,assume if both Sal and his friend are looking towards and moving away from each other at C/2(in respective frames) ,shouldn't the relation between Sal's t and t' and his friends t and t' ,be the same due to symmetry?
(1 vote) 