Length Contraction: Light & Spaceships

Forestman
Messages
212
Reaction score
2
I understand the explanation for time dilation involving the light clock on the spaceship, or a train. But what is used to explain length contraction. Is there another example that is used involving a light beam and a spaceship.
 
Physics news on Phys.org
Forestman said:
I understand the explanation for time dilation involving the light clock on the spaceship, or a train. But what is used to explain length contraction. Is there another example that is used involving a light beam and a spaceship.

The first situation used a light clock oriented transverse (perpendicular) to the direction of relative motion to reveal time dilation.

Now, use a light clock oriented longitudinally (parallel) to the direction of relative motion... and require that one tick of this clock has the same duration as that of the first clock.

Look at my avatar.
 
Last edited:
Thanks robphy. I think I understand it now.
 
Well if you understand time dilation you are doing well, very well, indeed. I came across this recently and while I believe it's correct, it sure is interesting...anybody like to explain it?


In special relativity, the time dilation effect is reciprocal: as observed from the point of view of any two clocks which are in motion with respect to each other, it will be the other party's clock that is time dilated. (This presumes that the relative motion of both parties is uniform; that is, they do not accelerate with respect to one another during the course of the observations.)

In contrast, gravitational time dilation (as treated in general relativity) is not reciprocal: an observer at the top of a tower will observe that clocks at ground level tick slower, and observers on the ground will agree. Thus gravitational time dilation is agreed upon by all observers, independent of their altitude.

http://en.wikipedia.org/wiki/Time_dilation
 
OK, so this has bugged me for a while about the equivalence principle and the black hole information paradox. If black holes "evaporate" via Hawking radiation, then they cannot exist forever. So, from my external perspective, watching the person fall in, they slow down, freeze, and redshift to "nothing," but never cross the event horizon. Does the equivalence principle say my perspective is valid? If it does, is it possible that that person really never crossed the event horizon? The...
From $$0 = \delta(g^{\alpha\mu}g_{\mu\nu}) = g^{\alpha\mu} \delta g_{\mu\nu} + g_{\mu\nu} \delta g^{\alpha\mu}$$ we have $$g^{\alpha\mu} \delta g_{\mu\nu} = -g_{\mu\nu} \delta g^{\alpha\mu} \,\, . $$ Multiply both sides by ##g_{\alpha\beta}## to get $$\delta g_{\beta\nu} = -g_{\alpha\beta} g_{\mu\nu} \delta g^{\alpha\mu} \qquad(*)$$ (This is Dirac's eq. (26.9) in "GTR".) On the other hand, the variation ##\delta g^{\alpha\mu} = \bar{g}^{\alpha\mu} - g^{\alpha\mu}## should be a tensor...
Back
Top