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## Main Question or Discussion Point

I have a light clock onboard a spacecraft moving past the earth parallel to an observer. The lightclock measures the time it takes for light waves to bounce between two mirriors. I have two sets of mirriors, one on the vertical axis perpendicular to the direction of travel and also a horizontal set, in line with the direction of travel.

c = 10 m/s (speed of light)

v = 6 m/s (velocity)

l = 4 m ( length between two mirrors)

Firstly I take a time measurement onboard the craft:

[itex]ts[/itex] = 2l/c = 0.8

Then from earth's reference frame I calculate the time by using the following two equations, for the vertical clock I use:

[itex]te[/itex] = [itex]\frac{ts}{√1-vv/cc}[/itex] (please excuse my writing vv/cc, I mean v

[itex]te[/itex] = 1 second

Then for the horizontal clock:

[itex]te[/itex] = [itex]\frac{2lc}{cc-vv}[/itex] (apologies again the bottom half should read c

[itex]te[/itex] = 1.25 seconds

.....clearly there is something wrong here, both clocks shold agree on the time.

So I apply the lorentz transformation to l in the horizontal clock:

[itex]Lo[/itex] = the proper length (the length between the mirrors in their rest frame)

[itex]L[/itex] = [itex]Lo[/itex]√1-v

and end up with a value of 3.2 for l in the horizontal clock....

so I go back to [itex]te[/itex] = [itex]\frac{2lc}{cc-vv}[/itex] (apologies again the bottom half should read c

this time with 3.2 as my value for l, and then I get:

[itex]te[/itex] = 1 second

This means the amount of distance the light covers between each set of mirrors is equal, so even though the length is contracted in one clock, the 'light distance' is equal, as it is in both the rest frame and the moving frame.

Now both clocks agree and i'm very happy :) .... I hope!

Does this adequately describe the mechanics and interplay involving the speed of light, length contraction and time dilation?

c = 10 m/s (speed of light)

v = 6 m/s (velocity)

l = 4 m ( length between two mirrors)

Firstly I take a time measurement onboard the craft:

[itex]ts[/itex] = 2l/c = 0.8

Then from earth's reference frame I calculate the time by using the following two equations, for the vertical clock I use:

[itex]te[/itex] = [itex]\frac{ts}{√1-vv/cc}[/itex] (please excuse my writing vv/cc, I mean v

^{2}/c^{2}however when I enter [sup[/sup] inside the fraction text it donsent seem to work :P im totally new to all this, trying to work it out as I go along, any help would be most kind)[itex]te[/itex] = 1 second

Then for the horizontal clock:

[itex]te[/itex] = [itex]\frac{2lc}{cc-vv}[/itex] (apologies again the bottom half should read c

^{2}-v^{2})[itex]te[/itex] = 1.25 seconds

.....clearly there is something wrong here, both clocks shold agree on the time.

So I apply the lorentz transformation to l in the horizontal clock:

[itex]Lo[/itex] = the proper length (the length between the mirrors in their rest frame)

[itex]L[/itex] = [itex]Lo[/itex]√1-v

^{2}/c^{2}and end up with a value of 3.2 for l in the horizontal clock....

so I go back to [itex]te[/itex] = [itex]\frac{2lc}{cc-vv}[/itex] (apologies again the bottom half should read c

^{2}-v^{2})this time with 3.2 as my value for l, and then I get:

[itex]te[/itex] = 1 second

This means the amount of distance the light covers between each set of mirrors is equal, so even though the length is contracted in one clock, the 'light distance' is equal, as it is in both the rest frame and the moving frame.

Now both clocks agree and i'm very happy :) .... I hope!

Does this adequately describe the mechanics and interplay involving the speed of light, length contraction and time dilation?