Understanding Time Dilation: Confusions and Questions Answered

[ritzmax72]

In the proof of time dilation. Below http://www.phys.unsw.edu.au/einsteinlight/jw/module4_time_dilation.htm
I have a doubt in symetry of time dilation.
If there's a big lcd screen digital clock in jasper's verandah(at rest wrt ground). And zoe is moving at speed close to c. Do he see that lcd digital clock's ticks of 1 second is longer than his own clock?

Also another question. How could jasper(rest) see the path of light? Do she really see hypotheneus path? Or its just hypothetical that light follow that path? How do we actually got to know light followed hypothetical path? By which instrument?

 

[Passionflower]

In the proof of time dilation. Below http://www.phys.unsw.edu.au/einsteinlight/jw/module4_time_dilation.htm
I have a doubt in symetry of time dilation.
If there's a big lcd screen digital clock in jasper's verandah(at rest wrt ground). And zoe is moving at speed close to c. Do he see that lcd digital clock's ticks of 1 second is longer than his own clock?

Also another question. How could jasper(rest) see the path of light? Do she really see hypotheneus path? Or its just hypothetical that light follow that path? How do we actually got to know light followed hypothetical path? By which instrument?

For transverse motion, as in the case you reference, what Zoe actually sees is that Jasper's clocks goes at a rate of:

$$\sqrt{1 - v^2}$$

So if for instance Zoe moves away with a relative speed of 0.6c she will see Jasper's clock tick 0.8 times the rate of his own clock.

For line of sight motion it is different, what Zoe actually sees or measures using his instruments is Jasper's clock divided by the line of sight Doppler shift which is:

$$\sqrt{ c+v \over c-v}$$

So if for instance Zoe moves away with a relative speed of 0.6c she will see Jasper's clock tick half the rate of his own clock. However if he wants to consider what is simultaneous using Einstein's clock synchronization he would have to conclude that Jasper's clock ticks 0.8 times his own clock.

For motion in an arbitrary direction Zoe will see Jasper's clock rate as:

$${ \sqrt{1 - v^2} \over 1+ v \cos \theta}$$

 

[yuiop]

In the proof of time dilation. Below http://www.phys.unsw.edu.au/einsteinlight/jw/module4_time_dilation.htm
I have a doubt in symetry of time dilation.
If there's a big lcd screen digital clock in jasper's verandah(at rest wrt ground). And zoe is moving at speed close to c. Do he see that lcd digital clock's ticks of 1 second is longer than his own clock?

Also another question. How could jasper(rest) see the path of light? Do she really see hypotheneus path? Or its just hypothetical that light follow that path? How do we actually got to know light followed hypothetical path? By which instrument?

You could use a bouncing ball rather than a photon and film the zig zag motion of the ball in Jaspers frame. The best way to do this would be to have a whole series of cameras mounted above the road and each camera takes a picture when the car is immediately below it and creating a film out of the sequence of pictures. The zig zag path is real in Jasper's frame. As for the LCD clock display, if this was mounted in Zoe's car then it would appear to be ticking slower than Jasper's clock, when observed by Jasper. If the LCD was on Jasper's verandah and was displaying Zoe's elapsed time, then this creates problems because of signal delays sending the time from Zoe's car to the LCD, so this is not a good idea.

P.S. Jasper is normally a "he" and Zoe is normally a "she". It is not clear whether you are talking about Jasper or Zoe when you say "Do he see that lcd digital clock's ticks of 1 second is longer than his own clock?".

 

[ritzmax72]

OH GENDER MISTAKE. NOT ACCQUAINTED with names.
I WAS TALKING ABT ZOE, "DOES(NOT DO) SHE SEE THE DIGI CLOCK TO TICK SLOW?" WAS THAT BECAUSE SHE PERCEIVE CHANGE IN DIGITS SLOWER THAN THEY ARE?? REASON; LIGHT WAVES TAKES ZIG ZAG PATH REACH HER EYES? IT THIS SO?

 

[ritzmax72]

@passionflower i didn't get ur reply's meaning. What zoe wud see is the clock in jasper's frame ticks at rate T=t/(1-v of zoe wrt jasper^2/c^2)^1/2
where t is zoe's own clock rate(duration of seconds, u can assume)
What is (1-v^2)^1/2 ?

 

[Passionflower]

Here is a graph showing what an observer actually sees or measures about a moving clock traveling at 0.6c.

At the top of the red curve you see a rate of 0.5 indicating a clock moving away from the line of sight. At the bottom of the red curve you see a rate of 2 indicating a clock approaching from the line of sight. At the extreme left and right of the red curve, which represents transverse movement, you can see that the clock rates are identical to the calculated time dilation based on the Lorentz factor (gamma).