Gravitational Time Dilation

[Widdekind]

Regarding Gravitational Time Dilation, according to N.D. Mermin (It's About Time, pg. 176),

In a uniform

Gravitational Field,

the lower clock runs slower than the upper one by precisely the factor

1 + g D / c

²

.

This has, seemingly, an intriguing Semi-Classical interpretation. For, let us see what "equivalent velocity" would produce the same Time Dilation factor:

[math]\gamma \equiv 1 + g \; D / c^{2}[/math]

Multiplying both sides by the Rest Energy of the Test Particle, w.h.t.:

[math]E_{0} + KE = \gamma \; m \; c^{2} = m \; c^{2} + m \; g \; D = E_{0} + \Delta U_{g}[/math]

Thus, the lower clock ticks slower by the same amount it would, if all of its additional GPE had been converted to KE (in flat space).

 

Yes?

 

 

Mod note: moved to its own thread

Edited July 22, 2009 by swansont
add mod note

[swansont]

Yes, the dilation terms are potentials, and it can either be kinematic or gravitational.