Ok - the difference between a De Broglie frequency and other frequency is??? The ground state of an atom has an energy, and this energy is mass associated e=mc2. Momentum is calculated mv=p. So the De Broglie momentum symbol p already contains the ground state frequency of the atom within its value. Planck's constant h/p=wavelength, and then frequency can be established because frequency is inversely proportional to wavelength. The fact of the additional KE increasing the mass of the atom is a bit of a complication to these simple calculations...(adding gravity potential energy will also increase mass, but I will ignore this 'tiny' effect for the moment)

So - the NIST ground level relativity tests placed a clock on the ground, and a clock at 1 meter elevation. The clocks are in different reference frames, but the observer is in 1 reference frame containing both of the clocks and is observing both clocks. There is no KE involved as the reference frames of the clocks are stationary relative to each other and the observer.

Let's take this a stage further and place a clock at each meter of elevation for a distance of 22 meters (I'd say 22.5 meters as in Pound Rebka but I'm not liking the visual of a half clock, (chuckle)...)

Each clock's rate of time is linked to a computer read out that the observer on the ground is observing on a split screen. Each clock is in a different reference frame, but the observation of these different reference frames is remaining within 1 reference frame, this being that of the observer on the ground.

Each clock will consider that it is in its ground state transition energy and frequency, but the observer on the ground will observe that all of the clocks are registering a different frequency. At each meter of elevation, a clock has an increased frequency than the clock below it. In this situation it must be the added energy of gravity potential that has increased the frequency of the atom.

Now let's say that we repeat this exact scenario 'somehow', and measure the frequency of atoms that have more or less ground state energy at ground level, and then measure them at elevations of a meter apart... Adding gravity potential will increase the energy, and therefore the frequency of those atoms ground state at elevation in the same way that the caesium atom's frequency is increased at elevation. But this increase in frequency that atoms of different ground state energies from a caesium atom will experience is proportional to their rest mass, and not proportional to the increase in frequency that the caesium atom increases by at the same elevation.

Therefore the possibility that the caesium atomic clock is only measuring an increase in the rate of time for its own self is a valid and logical train of thought, and investigation.

If the rate of time for a caesium atom increases with additional energy, and we can say that all atoms rates of time increase with additional energy, then the concept of a gravity well slowing the rate of time is illogical.

Looking at how light of 'any' frequency decreases in the weaker gravitational field, and by ignoring KE, one can then go on to consider that the photon has 0 energy ground state, and that the energy that the light has has been given to it by the energy of the interaction that caused it to be emitted. This energy then becomes gravitationally shifted as light moves through a gravitational gradient, but take note - light's energy is shifted in the opposite direction within a gravitational gradient than an atom's is.

Logically speaking, and in keeping with the logic of current time dilation considerations, there exists the possibility that there is an inverted time dilation phenomenon that has been overlooked.

Returning to the question of KE, if KE is added a frequency must increase and this is not in keeping with the behaviour exhibited by the caesium atom clock when it experiences a increase in its rate of time due to an energy increase, and observation of a caesium atomic clock's rate of time when in motion is that it's frequency is reduced relative to the stationary clock.

Logically speaking there may be another way to add up the energies that account for frequency. Obviously we have e=mc2 + gravity potential. If we add KE the rate of time increases, if we subtract it, hmmm, well I'm no mathematician, but KE amounts to quite a lot of energy... Can we consider that the gravitational field itself has a non zero energy that must be added (looking at light) and that we can then subtract KE from the sum total of e=mc2 + gravity potential + non zero energy of g-field, for a slowing of time? Whereby light having no mass has no KE... It's energy is shifted by the gravity field and it's subsequent wavelength is time related. Take the energy and frequency of a light wave at ground level, earth...run that light wave through a gravitational gradient, and remembering that the caesium atom frequency at ground level is the definition of the second that frequency is measured by, any difference in frequency observed of a different reference frame, can indicate a change in that reference frames rate of time.

This system places the rate of time running faster for gravity wells and slower out in space, which is reflected in the reduction of the frequency of light in space, and the increase in frequency of the caesium atom, or any other atom at elevation, with the addition of gravity potential as we observe...

Ultimately suggesting that the phenomenon of time itself is energy related, and leading me back to Jeff's equation:

OK so as was pointed out [tex]\rho\,=\,\frac{h}{\lambda}[/tex]. Therefore in the case of the photon the energy equation becomes [tex]E\,=\,\frac{\rho{c^2}}{\lambda\nu}[/tex].

If we take our wavelength as L (1 light second) then we can show that [tex]E\,=\,\rho{c}\,=\,\frac{hc}{L}\,=\,\frac{h}{t}[/tex]. This 1 hertz wave then shows the direct relationship to the Planck constant.