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randyu
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If A travels at .99c in his negative coordinate direction then his length expands and time increases observed by B moving at v=.6, the opposite of normally discussed situations. How is this explained?
In an Inertial Reference Frame in which A is traveling at -0.99c and B is traveling at 0.6c, gamma for A is just over 7 and gamma for B is 1.25. These are the factors that the time on their respective clocks is dilated and the reciprocal of those factors are their amount of length contraction along the direction of motion. That's as good an explanation as I can provide but it doesn't seem to coincide with what you are suggesting since it is not the opposite of normally discussed situations.randyu said:If A travels at .99c in his negative coordinate direction then his length expands and time increases observed by B moving at v=.6, the opposite of normally discussed situations. How is this explained?
Thanks George,ghwellsjr said:it doesn't seem to coincide with what you are suggesting since it is not the opposite of normally discussed situations.
Let me start by giving you a helpful hint: instead of using the letter "Y" to represent gamma, if you hit the "Go Advanced" button below the place where you compose your response, it will take you to a new page that has some "Quick Symbols" off to the right where you can click on "γ" to insert it into your response. Just make sure you unhighlight it or it will disappear. It's not a very good looking gamma but at least it has its own symbol.randyu said:Thanks George,
I was thinking something like standard setup, t'=x=x'=0 @ t=0
then let x=-1 @ t=1
t'=Y(t-vx/c2)
t' = 1.25 (1 - 0.6 (-1)/1²) = 2
therefore, Δt'=2
a doubling of time intervals
That's correct, but it's not dealing with the time dilation of a physical clock at rest in either the x,t frame or the x',t' frame, since Δx is not zero and neither is Δx'. The time dilation equation Δt' = γΔt is intended to answer the question "if you have a clock that elapses a time Δt between two events on its worldline (so Δt is both the clock's proper time and the coordinate time in the frame where the clock is at rest, meaning Δx=0 in that frame), then what is the time Δt' between those same two events in the frame where the clock is moving at speed v?"randyu said:Thanks George, humm... I'll need to think about those.
To clarify, in my setup frame x' is moving at +.6c, v=+.6c
the clock in x is moving to the left at -.99c
then @ t=1, x=-.99
Δt'= γ(Δt-vx/c2)
Δt' = 1.25 (1 - 0.6 (-.99)/1²) = 1.9925 ≈ 2
still wrong I guess but why?
Time expansion/contraction is a phenomenon in which time appears to move at different speeds for different observers. This is due to the theory of relativity, which states that time is relative and can be affected by factors such as speed and gravity.
Time expansion/contraction occurs due to the effects of special relativity and general relativity. In special relativity, time dilation occurs when an object moves at high speeds, causing time to appear to slow down for that object. In general relativity, time dilation can also occur due to the effects of gravity, with time appearing to run slower in areas with stronger gravitational fields.
Yes, time expansion/contraction has been observed in experiments and in everyday life. For example, atomic clocks on satellites have been found to run slightly faster than clocks on Earth due to their higher speeds. Additionally, astronauts who have spent extended periods of time in space have been found to age slightly slower than their counterparts on Earth.
In most cases, time expansion/contraction has a very small effect on our daily lives and is not noticeable. However, it is important to take into account when dealing with extremely precise measurements, such as in GPS systems or when conducting experiments involving high speeds or strong gravitational fields.
No, time expansion/contraction is a fundamental aspect of the theory of relativity and cannot be reversed. However, it is possible for time to appear to move at different speeds for different observers, depending on their relative speeds and positions.