Re: Relativity?
Posted: Mon Oct 30, 2017 1:14 am
Imagine a train and an embankment. The train is rushing past the embankment.
There is a kid on the train who rolls a marble. There is another kid on the embankment who rolls a marble.
This is a thought experiment, so it’s perfectly OK to imagine that the kid on the train and on the embankment roll their marbles at an identical rate of speed. In practice, this would be almost impossible to achieve except by dumb luck, but it’s OK for a thought experiment in order to illustrate a principle.
But even though the kid on the train and the kid on the ground have rolled their marbles at the same velocity, they are not ACTUALLY the same velocity. This is because, if both kids roll their marbles at one foot per second, the marble of the kid on the train will ADD the velocity of the train to the velocity of his marble. Hence, his marble will TRAVEL FASTER THAN the marble of the kid on the ground, even though both will measure, in their respective frames, the marble moving at one foot per second (the train must be an inertial frame — in constant uniform motion.)
In other words, the velocity of the marbles vary across frames. This is in conformance with the law of addition of velocities, or Galilean additivity.
Now, instead of a photon clock, we are going to build a marble clock. It works the same way as a photon clock, except that a marble, not a photon, goes down to the bottom and bounces back to the top. A round trip counts one second.
The marble clocks are synchronized in the ground frame. Each ticks off a second with military precision.
We put one marble clock on the moving train and leave the other on the ground. Will they remain synchronized?
Yes! Observe that on the train, the marble in the marble clock has a longer path to travel, to hit the bottom of the clock and return to the top, in order to tick off one second. It has a longer path to travel, because the bottom and tops of the clock are moving targets, unlike the marble clock in the stationary frame.
BUT, the marble in the moving train PICKS UP THE SPEED OF THE TRAIN! Because it does, the marble clock in the train and the marble clock on the ground remain in perfect synchrony — each agreeing on what constitutes one second.
Although the marble on the moving train has a longer distance to traverse than the marble in the ground frame, IT IS MOVING MORE QUICKLY.
THAT IS WHAT LIGHT DOES NOT DO.
Unlike the marble, the photon WILL NOT ADD THE SPEED OF THE MOVING FRAME. Thus, in addition to traversing a longer path than the photon in a photon clock on the ground frame, it will, from the point of view of the rest frame, take a longer time to trace that path.
Conclusion: a marble clock on a moving frame and a marble clock in the ground frame remain in synch.
But a photon clock on a moving frame and a photon clock on the ground frame do NOT remain in synch. The moving-frame clock ticks slower.
The marble clocks tick the same because of the variability of the speed of the marbles.
The photon clocks tick differently because of the invariability of the speed of photons!
There is a kid on the train who rolls a marble. There is another kid on the embankment who rolls a marble.
This is a thought experiment, so it’s perfectly OK to imagine that the kid on the train and on the embankment roll their marbles at an identical rate of speed. In practice, this would be almost impossible to achieve except by dumb luck, but it’s OK for a thought experiment in order to illustrate a principle.
But even though the kid on the train and the kid on the ground have rolled their marbles at the same velocity, they are not ACTUALLY the same velocity. This is because, if both kids roll their marbles at one foot per second, the marble of the kid on the train will ADD the velocity of the train to the velocity of his marble. Hence, his marble will TRAVEL FASTER THAN the marble of the kid on the ground, even though both will measure, in their respective frames, the marble moving at one foot per second (the train must be an inertial frame — in constant uniform motion.)
In other words, the velocity of the marbles vary across frames. This is in conformance with the law of addition of velocities, or Galilean additivity.
Now, instead of a photon clock, we are going to build a marble clock. It works the same way as a photon clock, except that a marble, not a photon, goes down to the bottom and bounces back to the top. A round trip counts one second.
The marble clocks are synchronized in the ground frame. Each ticks off a second with military precision.
We put one marble clock on the moving train and leave the other on the ground. Will they remain synchronized?
Yes! Observe that on the train, the marble in the marble clock has a longer path to travel, to hit the bottom of the clock and return to the top, in order to tick off one second. It has a longer path to travel, because the bottom and tops of the clock are moving targets, unlike the marble clock in the stationary frame.
BUT, the marble in the moving train PICKS UP THE SPEED OF THE TRAIN! Because it does, the marble clock in the train and the marble clock on the ground remain in perfect synchrony — each agreeing on what constitutes one second.
Although the marble on the moving train has a longer distance to traverse than the marble in the ground frame, IT IS MOVING MORE QUICKLY.
THAT IS WHAT LIGHT DOES NOT DO.
Unlike the marble, the photon WILL NOT ADD THE SPEED OF THE MOVING FRAME. Thus, in addition to traversing a longer path than the photon in a photon clock on the ground frame, it will, from the point of view of the rest frame, take a longer time to trace that path.
Conclusion: a marble clock on a moving frame and a marble clock in the ground frame remain in synch.
But a photon clock on a moving frame and a photon clock on the ground frame do NOT remain in synch. The moving-frame clock ticks slower.
The marble clocks tick the same because of the variability of the speed of the marbles.
The photon clocks tick differently because of the invariability of the speed of photons!