[time-nuts] FW: Pendulums & Atomic Clocks & Gravity

Dr Bruce Griffiths bruce.griffiths at xtra.co.nz
Tue May 29 01:17:39 EDT 2007


Neville Michie wrote:
>> Hi All,
>>     
> I am still having difficulty getting my head around the gravity point.
> Now I accept, in principle, that due to relativity  an intense  
> gravity field will slow a clock.
> My problem is visualising where you will find this field.
> At the centre of this planet gravity (from the planet) is zero. This  
> comes about by an elegant piece of
> calculus that shows that everywhere inside a hollow sphere the  
> gravity is zero. So a clock in the centre of Earth
> runs at the same rate as one on the surface? or does it run faster  
> because the one on the surface has the planetary gravity acting on it?
> I think that the one inside the Earth runs faster.
> But when you are between the Earth and Moon at a point where gravity  
> forces are neutral we should have the same rate as centre of planet?
> Now the way to measure gravity is to measure the force on a test  
> mass. If there is zero force there is zero gravity, except when you  
> are in orbit.
> This can be tested with 3 crossed gyroscopes that show your angular  
> velocity. If your angular velocity is negligible then the magnitude  
> of the gravity field is proportional to the force on a test mass.
> Unless you are in free fall accelerating towards a mass.
> I guess my question really is" can you know that you are in a zero  
> gravity field so your clock is running at the fastest rate?"
> Or is relativity relative. Does relativity only show up when there  
> are two frames of reference being compared, so there is no ultimate  
> reference frame with the fastest clock? Or can any clock have a  
> single relativity correction applied to it? How do you measure the  
> gravitational potential at any site? (ie the scalar quantity that  
> would be used to correct your clock).
> Has anyone got a clear answer?
> cheers, neville Michie
>   
Neville

You are somewhat astray its not the gravitational field but the change 
in gravitational potential that red or blue shifts an atomic clock as it 
is moved from one location to another.
The same gravitational potential difference can result for a small 
change in altitude in a strong gravitational field as a larger change in 
altitude in a smaller gravitational field.

Also the gravitational field within a spherical shell is only zero when 
the density distribution on the shell is spherically symmetric.
This is important in determining the gravitational field at the "centre" 
of a body that has mascons of different density to their surrounding 
matter they are embedded within.

A clock doesn't necessarily run fastest when the gravitational field is 
zero, it runs fastest when the gravitational potential is highest.
Locations of zero gravity and maximum gravitational potential do not 
necessarily coincide.

For example an atomic clock located at the centre of the Earth runs 
slower than one located on the surface (ignoring the effects of rotation).
However the gravitational field at the centre of the Earth is near zero 
whilst on the surface it is non zero.

Bruce




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