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Technically relativistic mass is akin to the sum of all the energies.
Quote from: jeffreyH on 25/05/2016 11:02:11Technically relativistic mass is akin to the sum of all the energies. So - presumably if we take our caesium atomic clock and accelerate it up to relativistic speeds in a uniform gravitational field, the additional kinetic energy will increase the frequency of cycles? ...this cannot be correct because an increase in the frequency of cycles of a caesium atomic clock would of course register an 'increase' in the rate of the clocks time, and not the decrease in rate of time that is observed of an accelerated clock...I found this and thought it might interest you Jeff:http://web.mit.edu/lululiu/Public/pixx/not-pixx/photoelectric.pdf
A particle with mass's energy and frequency increases in a decreasing gravitational field.A massless photon's energy and frequency decreases in a decreasing gravitational field.
The question I asked concerning accelerating a caesium atomic clock to relativistic speeds in a uniform gravitational field, and if the resulting rise in kinetic energy would increase the frequency of cycles of the caesium atom, which of course would be incorrect, because this would register an increase in the rate of time and not the decrease in rate of time observed of an accelerated clock:
When two observers are in relative uniform motion and uninfluenced by any gravitational mass, the point of view of each will be that the other's (moving) clock is ticking at a slower rate than the local clock. The faster the relative velocity, the greater the magnitude of time dilation. This case is sometimes called special relativistic time dilation.
if the resulting rise in kinetic energy would increase the frequency of cycles of the caesium atom
Quote if the resulting rise in kinetic energy would increase the frequency of cycles of the caesium atomThat's a big "if" and has no foundation. Once the clock is moving at a constant speed, it has no idea that it is moving except in relation to another clock, so there's no reason why its atoms should behave any differently from when it was "stationary".
Huh? ...If a ceasium atomic clock registers a faster or slower rate of time, then it's energy and frequency are changing...
And... why would a gravitational field affect a photon given relativistic mass in a contrary direction to how it affects any other particle?
The only difference between the 2 scenarios apart from the photon having no mass is the fact of its velocity
A caesium atomic clocks frequency increases in a decreasing gravitational field relative to a clock at ground level. No kinetic energy involved when the 2 clocks are held stationary relative to each other. ie: 1 meter apart in elevation for instance.
Any particle with mass held 1 meter higher in elevation from another identical particle will therefore have a higher frequency than the lower particle...no?
You say a particle's kinetic energy increases as it falls to earth: looking at a caesium atom, if it is falling towards earth and its kinetic energy increases, it's mass increases with the additional energy via e=mc2 and its frequency will 'increase' as a result. An increase in the frequency of cycles of a caesium atom 'is' an 'increase' in the rate of time.
That's because of time-dilation effects. First, time appears to move slower near massive objects because the object's gravitational force bends space-time....