11.1 The Mathematics of Slow Time

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Sami Al-Suwailem

There are actually two right-triangles in this lecture: (1) One in which the hypoteuse = D and the opposite = L (but the adjacent is not specified). (2) One in which the hypotenuse = c, the adjacent = c.cos(theta), and the opposite = c.sin(theta). Prof. Greene shifts from the first triangle to the second then back to the first without making these shifts clear. Not only this is confusing, it also involves additional steps of derivation that could have been avoided if there were only one triangle. Other writers show the derivation of gamma from only one triangle using only Pythagoras theorem.

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javier rodriguez de rivera

Just to note that always what happens is that WE SEE that other clock is faster or slower than ours, but not that the clock is faster or slower, not that the time goes slower or faster, only that we see one clock different form the other. Since there is not fix and unique reference system it can not be affirm that one clock is faster or slower or the time is faster or slower, only that we measure it differently. The light does not take an horizontal speed when the box move, we SEE that trajectory because our relative movement. Since there is not an absolute space we can not affirm that the light have this or that trajectory, only that in relation to us we measure that trajectoy in our reference.
I know this is implicity in the explanation.

Timothy Connally

If we consider the case where v=c, then cos theta is c/c. This is 1. Then we know that theta must be 0 degrees. It seems that light itself travels parallel to the direction of its motion and thus its own clock never ticks. I may be taking a leap of logic here. It seems to me a particle of light cannot experience time. From light’s own perspective, it seems its source and destination must be the same with no time or distance between (in direction of source to destination from our perspective.). Is it reasonable to imagine time and (a dimension of) space reducing to zero at the speed of light?

Istvan Joba

@Timothy, yes, that's my understanding as well.
At light speed both the rate of passage of time reaches zero (time dilation) and the length of space is also shortened to zero (length contraction). This also means anything with mass (requiring space to hold that mass) can never reach light speed as it cannot fit in zero space.

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