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DAC
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In the moving frame, relative to the stationary frame, if time is slowed and the speed of light isn't, why doesn't the light travel further in less elapsed time?
DAC said:In the moving frame, relative to the stationary frame, if time is slowed and the speed of light isn't, why doesn't the light travel further in less elapsed time?
The light clock is on the train as in the standard thought experiment.DaveC426913 said:You need to define your points of view. Where does the light travel? On the train? Next to the train?
Nugatory said:You always have to consider three effects:
- relativity of simultaneity
- time dilation
- length contraction
The way you've asked your question, you are only considering time dilation.
One good exercise is drawing a space-time diagram of the exact situation that you are considering with the paths of both observers, the light emission event, the light detection event, and the path of the light all shown. Do that, and you'll likely see how it all works consistently.
Another good exercise is to write down the the x and t coordinates of all the relevant events:
- emission event
- absorption event
- position of emitter at time of absorption according to train observer
- position of emitter at time of absorption according to platform observer
- position of receiver at time of emission according to train observer
- position of receiver at time of emission according to platform observer
in one or the other frame, and then use the Lorentz transforms (not the time dilation and length contraction formulas!) to transform into the other frame.
DAC said:The light clock-train thought experiment is about time dilation therefore so is my question. I don't have a physics background. Perhaps you could provide a simpler answer
i.e why doesn't light travel further in less elapsed time.
Why do you say "less elapsed time"? Time Dilation means it takes more elapsed Coordinate Time for the same amount of Proper Time. Sometimes we say the moving clock is ticking more slowly in the frame in which it is moving but that just means it takes longer for it to tick in the moving frame than it does in its rest frame.DAC said:The light clock-train thought experiment is about time dilation therefore so is my question. I don't have a physics background. Perhaps you could provide a simpler answer
i.e why doesn't light travel further in less elapsed time.
According to the second postulate of Special Relativity, light always travels at c according to the coordinates of any Inertial Reference Frame. It takes more Coordinate Time to travel a greater Coordinate Distance. Isn't this clear in the diagrams? Where do you see "less time elapsed"?DAC said:and if less time is elapsed, does the light travel further?
DAC said:Time passes more slowly in the moving frame. One second becomes o n e s e c o n d, therefore less time elapses. The light has more time to travel the longer mirror to mirror distance, whilst always traveling at c.
Let's make sure we agree on what this phrase means. It means: in the frame in which the clock is moving, the Proper Time of the clock passes more slowly than it does for the Coordinate Time of the frame, agreed?DAC said:Time passes more slowly in the moving frame.
Let's also make sure we agree on what this phrase means: It means one second of Proper Time for the moving clock gets stretched out to take more than one second of Coordinate Time and therefore less Proper Time elapses for the moving clock than Coordinate Time, agree?DAC said:One second becomes o n e s e c o n d, therefore less time elapses.
The light has more Coordinate Time to travel the longer mirror to mirror Coordinateror Distance, whilst always traveling at c according to he, agree?DAC said:The light has more time to travel the longer mirror to mirror distance, whilst always traveling at c.
The "Light clock on Train experiment" is a thought experiment that was first proposed by Albert Einstein in his theory of special relativity. It involves a clock composed of two mirrors and a light beam bouncing between them, and how the perceived passage of time changes when the clock is in motion relative to an observer.
According to the theory of special relativity, time appears to move slower for an observer on the train compared to an observer outside the train. This is because the speed of light is constant and the distance the light beam has to travel is longer for the observer on the train due to the train's motion.
Yes, the effects of time dilation in the light clock on a train experiment have been observed in real life through experiments using atomic clocks. These experiments have confirmed the validity of Einstein's theory of special relativity.
The perceived passage of time in the light clock on a train experiment can also be affected by the train's velocity, the distance between the mirrors, and the angle at which the light beam is reflected between the mirrors.
The light clock on a train experiment is a thought experiment that illustrates the concept of time dilation in Einstein's theory of special relativity. It helps to explain how time is relative and can change depending on an observer's frame of reference and the speed of the objects in motion.