0/0 and the speed of light

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0/0 and the speed of light

Postby batmanmg » Wed Oct 04, 2006 4:01 pm

so far what i've learned is that in any frame of reference light in a vacume travels at the same speed... C

the equation explaining relative motion is given as this

v<sub>xz</sub> = (v<sub>xy</sub>+v<sub>yz</sub>)/[1+(v<sub>xy</sub>v<sub>yz</sub>/c<sup>2</sup>)]

v = v<sub>xy</sub>
u = v<sub>yz</sub>
w = v<sub>xz</sub>

but what happens when you want to find velocity of light in a frame of reference moving at the speed of light?

v = c
u = c-h

where h is equal to zero, you end up with

w = (h/h)c or (0/0)c

What is the velocity of light relative to itself? Is it zero, or does it remain the speed of light?

If you have a car that is accelerating its speed closer and closer to the speed of light, the light comming from its headlights will continue moving away from it at the speed of light. But if you were to actualy reach the speed of light, would the light suddenly become motionless to you?
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Postby houserichichi » Wed Oct 04, 2006 5:10 pm

It's paradoxical because you're measuring as the frame of an observer. No observer can reach light speed but instead only have it as a limit. On the other hand, as velocity increases, external rulers get shrunk down further and further. When light speed is reached (there really is no such thing as "reaching" light speed since anything going that fast is and always has been travelling at that speed in the first place) the rulers have shrunk to size zero and, thus, travel an infinite distance in their own frame of reference. That is, a photon experiences no time. Since there's no distance at that speed then a photon also experiences no change in displacement. Quite literally, a photon never moves because there is nowhere for it to move and no time passes. Same token, a photon really has no frame of reference to begin with. If you perform Lorentzian transformations with the speed of light you get nonsense.
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Postby PWrong » Thu Oct 05, 2006 1:38 am

where h is equal to zero, you end up with

w = (h/h)c or (0/0)c

Take the limit as h -> 0, and you get c. You're allowed to do this.
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Postby batmanmg » Thu Oct 05, 2006 2:57 am

PWrong wrote:
where h is equal to zero, you end up with

w = (h/h)c or (0/0)c

Take the limit as h -> 0, and you get c. You're allowed to do this.


thats what i did when i ran through this scenario before, but after the entire dividing by zero thread i wanted to make sure it didn't do anything problematic.

also what about house's post.

houserichichi wrote:When light speed is reached ... the rulers have shrunk to size zero and, thus, travel an infinite distance in their own frame of reference.


doesn't time also shrink to 0? you'd get a (0/0) issue again for the velocity.

but either way... you say that it travels infinite distance. but that distance is measured by rulers of zero length. so its a 0 x infinity scenario... and really... i don't think that it its a size 0 i think that it is an infiently small size.. which gets you a (1/N) x N where N equals infinity... so one must wonder what the result is and why it is that result.
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