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### Course: Physics archive>Unit 16

Lesson 3: Lorentz transformation

# Introduction to the Lorentz transformation

So we've got two coordinate systems from the perspectives of two observers. How can we convert spacetime coordinates between these? Enter the Lorentz transformation!

## Want to join the conversation?

• Did I miss something? I watched all the previous relativity videos, and I saw in "Angle of x-axis in Minkowski spacetime" that the two angles α must be identical, but where did we show the inverse tangent relationship (as Sal states at )?
• You're right, the video must have been left out somewhere, but we can get to the angle pretty easily by thinking about how the relative velocity of Sal's friend relates to the slope of ct'. Since her velocity is .5c, the slope of ct' is 2. We could graph it out and see that if her velocity was .25c, the slope of ct' would be 4; and if her velocity was .75c, the slope of ct' would be 1.333. Which makes sense because as she goes relatively faster and faster, the slope gets closer and closer to 1 (the slope of light).
So we can see that the slope of any ct' would be c/v.
Now because we know that slope is change in y/change in x we can use a little trigonometry to find the angle between ct and ct' (Draw a right triangle with with ct' as the hypotenuse and see for yourself!)
The tangent of an angle equals opposite side over adjacent side which for this triangle is change in x/change in y or v/c.
So tan α = v/c
Or α = tan^-1 (v/c)
• I think I find this really hard.
I started relativity by watching pop-sci videos and pop-sci books, which now makes it even more counter-intuitive for me.
Especially those thought experiments of the train and so, I seem to have the wrong information. I solved some of the problems with the thought experiments (the problems I had) and now it still hurts my brain
I wanna learn this interesting stuff but this is counter-intuitive to the fullest like so much crazy. I have no problem in accepting speed of light will be constant, since the electromagnetic field is stationary with respect to any observer and so on. But I find other stuff crazy and confusing.... Will I be able to do it?
Sorry I'm a bit demotivated cause of sleep deprivation but ah....
• Unfortunately this is counter intuitive and there is no way around it. Our intuition is mainly based on our every day experiences and they do not include any of these Relativistic effects. This is also a big issue with understanding quantum mechanics as well.

The only way to get past this is to keep at it.
• Can someone provide a proof or the derivation of the Lorentz factor? How was this factor discovered?
• can you guys do a series using the alternate coordinate system?
• Why are the coordinate transformations of space and time between uniformly moving ststems, -(where the grid lines are set up for each system such that the transformation equations of Lorentz Result, where the space and time mix inextricably and intimately in the new spacetime concept)- able to be,(and why are they), expressed in terms of the factor 1/{sqrt(v^2/c^2)}?
What does this factor represent which makes the transformation equations be what relations they are between the relative velocity of the reference frames , the speed of light c which is the same value in both frames and the space and time coordinates used in its calculation for each of the uniformly moving reference frames?
(1 vote)
• i have a question if lets say i am travelling at the speed of light in a rocket and ahead of me there is a wall since according to me time stops (by lorentz transformation) and so i will never hit the wall but according to some other rest frame who is watching both the wall and me will say that i collapsed into the wall and since both frames of reference are equally valid what will happen will i collapse or not please define in brief
(1 vote)
• First of all, you can't go the speed of light.
Second of all, in your reference frame, time is normal. You will see a wall coming toward you and then - wham.
• Isn't the Lorentz factor time dilation?
(1 vote)
• So can we say in other words that, conceptually, Minkowski graphs represent perceptual differences of events (based on frames of reference) of space and time due to the fixed speed of light? Where I am in my mind conceptually is that the "bending" of spacetime is viewed from an arbitrary frame of reference that takes into account all given frames. If this is correct, please help me understand the implications of the concepts.
(1 vote)
• can someone tell me how energy of light when noticed from a moving frame of reference with velocity v is E(1+v^2/2c^2)
(1 vote)
• So since the new pair of coordinate axes are not orthogonal to each other, this means that you can use express ct' in terms of x' and vice versa and hence there is a continuum of spacetime, they are not distinct of each other. Is this a mathematical way of realising the existence of spacetime?
I'm actually having difficulty understanding a non-orthogonal axes system....
(1 vote)