The following [tough] problem is for extra credit. I’ll treat it as an additional H‘N set. I will score it up to 2% of
your grade [it you get it right 1m%]. In clam I lambasted the formulation of Spec Rel for being too focused on light.
Here we‘ll re-derive the Lorentz Transformation without any mention of the speed of light. “We consider two inertial framesSandS'pm'ntioginthesamedirectionandwelettheoriginofS' movealongthesaxisofS [inthepoen'tive
zdirection 1. First write down a generic equation relating the mordinates [atr and t' to a and t] [2 points] 2. Hopefully your answer to the above has four unknowns. W'e can constrain them using the following relativity
postulates.
I .5" travels with velocity u with respect to S
I 3 travels with velocity —‘D with respect to 3"
I Time dilation [if any] looks the same from either frame Use these constraints to eliminate three of the four unknowns [6 points] 3. At this stage. one normally invokes the invarianee of the speed of light to constrain the last unknown. To check
your answer to the above, do this and confirm that you reproduoe the Lorentz transformation [2 points] 4. ifinstead of doing 3. show that we can always write the above in terms of a. Lorentz invariant velocity V2 = ope“ .
[T points] [Hint1 this is tough1 a good waj.r to do this is to show that you can change variables such that your
answer to 2. looks like a regular LT but with V2 playing the role of ca. Then use the group theory,r properties
you proved earlier this HW to show that this V2 has to be a oonstant] 5. We live in a world where V2 = c”, and siooe light is a massiess particle it travels at this speed. So light isn’t
special, its just that on } V3 :5 I]. Describe what would happen if i) V3 = cc. 13131-72 = i]. iii??? a: I}. [3 points]

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