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The caesium atom is affected by a higher gravity potential increasing its energy, and therefore the frequency of all of its particle constituents for an increase in frequency of its energy transitions.Light is affected by the higher gravity potential decreasing its energy and therefore it's frequency. This does not gel with the De Broglie wavelength concepts.

due to the difference in the gravity field gradient

a lower frequency in the weaker gravity field no matter redshifted or blue shifted...

Clock is on ground - it has a frequency. (electron cloud energy transition)Light is travelling away from Earth from ground - it has a frequency.Clock is raised to 1 meter away from Earth - it's frequency changes from what it was at ground level. This change is an 'increase' in frequency.

The light when at position 1 meter away from Earth - it's frequency has changed from what it was at ground level. This change is a 'decrease' in frequency.

I just do not get what about this you are not comprehending?

What I want to look at is why the 'invariant mass' of the clocks mechanism atom (and its particle constituents) are affected differently than the 'relativistic mass' of light by 'gravity potential energy'...

If we take a freeze frame of a path between the earth and the sun we can mark out positions along that path to produce what is called a configuration space. Each point can be labeled as an event in some field. If we then start running forward in time each point will evolve according to its position within the gravitational field. How will they evolve? It is only by thinking this problem through that things will become clear. Smolin spent years at a university. He is entitled to speculate.

Simply messing with time dilation won't give you an acceleration. If time is distorted by a gravitational field (and we know it is - we can measure it) then the effect will be the same at a given point for all small objects. But we observe a difference between an apple fixed to a tree (it doesn't move) and one in free fall (it accelerates). So you need to invoke length (to describe movement) and mass (because by observation, gravitational mass is exactly equal to inertial mass).I haven't stated that GR is the absolute theory of anything. It just happens to describe and predict the phenomena of time dilation, red shift, gravitational lensing and nuclear energy rather well.

A clock's atomic electron cloud energy transition is subject to gravity potential. It's frequency is 'increased' when placed 'in the weaker' gravity field. Light has a reduced frequency 'in the weaker' gravity field, no matter if it is redshifted away from a body of mass or blue-shifted towards a body of mass.