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BilboBaggins2

## Main Question or Discussion Point

1. The

2. A clock in a gravitational field experiences time dilation and runs slower that one not in a gravitational field.

The clock’s rate is a function, not of the

3. The

These statements seem to contradict themselves:

(1) says that acceleration has no effect on a clock's rate.

(2) says that gravity slows a clock’s rate.

(3) says that acceleration and gravity are essentially the same … which means that an accelerated clock is essentially the same as a clock in a gravitational field … which means that an accelerated clock will be slowed.

But (1) states that a clock’s rate is not affected by its being accelerated!

I will be most grateful for an explanation and also for the name of any reference book which explains this in more detail. I have searched the web for answers but none seems to address the specific point.

I note there is no formula for the

(NB I completely understand that a moving clock runs slowly relative to a stationary observer due to its speed as given by the Special Relativity time dilation formula.)

__Clock Hypothesis__states that the rate of a clock does not depend on its acceleration but only on its instantaneous velocity. This has been experimentally verified at very high accelerations.2. A clock in a gravitational field experiences time dilation and runs slower that one not in a gravitational field.

The clock’s rate is a function, not of the

__gravitational acceleration__(m/sec^2); but of the__gravitational potential__, which is the work done to move the clock from infinity, where the field strength is effectively zero, to the clock’s location. This definition of gravitational potential works fine when the gravitational field is caused by a body like earth or the sun, where the field strength falls to zero at infinity.3. The

__Equivalence Principle__states that the local effects of motion in a curved spacetime (gravitation) are indistinguishable from those of an accelerated observer in flat spacetime, without exception.These statements seem to contradict themselves:

(1) says that acceleration has no effect on a clock's rate.

(2) says that gravity slows a clock’s rate.

(3) says that acceleration and gravity are essentially the same … which means that an accelerated clock is essentially the same as a clock in a gravitational field … which means that an accelerated clock will be slowed.

But (1) states that a clock’s rate is not affected by its being accelerated!

__Where, how and why am I going wrong?__**Question 1:**I will be most grateful for an explanation and also for the name of any reference book which explains this in more detail. I have searched the web for answers but none seems to address the specific point.

__If acceleration does affect a clock's rate what is the formula for it?__**Question 2:**I note there is no formula for the

__gravitational acceleration__affecting a clock's rate - only a formula for the__gravitational potential__affecting a clock's rate.(NB I completely understand that a moving clock runs slowly relative to a stationary observer due to its speed as given by the Special Relativity time dilation formula.)

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