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## Physics library

### Course: Physics library>Unit 16

Lesson 3: Lorentz transformation

# Evaluating a Lorentz transformation

We'll consider an example of the Lorentz transformation with actual numbers, and analyze the results we get.

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• I'm finding it hard to word this, but I still have to try. What does it mean to say we observe anything? Is this a nonsense question or does physics have a definite answer to such a question? [I got thinking I guess a little too hard about the extreme cases here of beta = 0 and beta = 1.]
• Observation is data in any situation being recorded by an object foreign to the system. As jaketudan suggested, observation always changes the system.
• Using special reletivity, I was thinking about the time distortions when traveling at the speed of light, and since time is relative like light, I started thinking of how it would affect what you and others observe. For exgample, suppose you are traveling at the speed of light for 5 years in a round trip, and during that time, the uinverse to you seems to not move in time. Now your friend, who is not moving relative to you, sees your time stopped while you travel that distance. When you reach your friend, you stop, and meet your friend. What would happen, and would both realities exist, or would there be a minor paradox?
• This is called the twin paradox, but it is not really a paradox.
It seems like the situations of the twins are symmetrical, but they are not.
One twin experiences acceleration when he turns around to come back so that they can compare ages. Special relativity is for inertial reference frames, but only one twin stayed in the same, inertial frame the whole time, so this problem cannot be solved by simple application of special relativity.

We need to use a "more advanced" version of special relativity that accommodates acceleration, or use general relativity. When we do that, it will turn out that the one who was on the rocket will be younger when they are back together.
• Don't quite understand something, if ct is the value of how long it takes for light to go one meter, shouldn't we cal the points
(1m , 1 l*m) or light meter?
• c*t is measured in meters, but Sal misspeaks by calling the units "light meters." They're just meters.

I think what he meant to say is that 3x10^8 meters is a "light second" - the distance light goes in one second (in the same way that 9.46x10^15 meters is a "light year," because that's how far light goes in one year).
• when I try some values I get a negative number. what does that mean?
• As you said that for every 1 s in your frame of reference ,your friend travelling at a speed of C/2 ,has 0.58 s.
But , for her ,you too are travelling at a speed of C/2 ,so shouldn't for each 1 s of hers ,you would have 0.58 s too?
How does this play out?
• I want is Lorentz transformation is related to wormhole? As in Lorentz transformation the distance is contracted for fast moving observer,the same as in wormhole in which the space is contracted
(1 vote)
• Did anyone try calculating the Lorentz transformations for the velocity of bullet (at ) i did and my answer was that x' and ct' are 1.99 when x and ct are equal to 2

Could someone confirm this?
(1 vote)
• Why did Sal take the reciprocal of the square root of 0.75?
(1 vote)
• What if V goes above the speed of light C.
Will the lorentz factor be an infinite number?
(1 vote)
• IF (and it won't, but if) v were to exceed c, then you would have a negative number underneath the square root sign. This makes no sense and shows an algebraic reason v cannot exceed c. But, as v approaches c without exceeding it (which can happen), 1 - (v/c)^2 approaches zero and the lorentz factor approaches infinity.
(1 vote)
• So, as I understand it, the final values for x' and ct' should be a point on the graph with the tilted axes. Where exactly would this point be? It's hard for me to visualize it without more lines for this graph.
(1 vote)