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I don't know why you keep referring to the phenomenon as though it were an illusion based on observer dependency.

both clocks are indeed in the same reference frame as the observer

A caesium standard or caesium atomic clock is a primary frequency standard in which electronic transitions between the two hyperfine ground states of caesium-133 atoms are used to control the output frequency. The first caesium clock was built by Louis Essen in 1955 at the National Physical Laboratory in the UK.[1]

By definition, radiation produced by the transition between the two hyperfine ground states of caesium (in the absence of external influences such as the Earth's magnetic field) has a frequency of exactly 9,192,631,770 Hz. That value was chosen so that the caesium second equalled, to the limit of human measuring ability in 1960 when it was adopted, the existing standard ephemeris second based on the Earth's orbit around the Sun.

Remember that the caesium atom has been chosen because it's natural resonating frequency is equal to a second as defined by the movements of the earth around the sun,

then the E=hf transitions of the caesium atom are not fixed. E will increase or decrease as frequency increases or decreases.

In the NIST ground level relativity tests both clocks are held stationary with regards to each other, so kinetic energy cannot be responsible for the difference in frequency between the clocks... and logically speaking if the clock at 1 meter elevation were to zoom off horizontally at speed - adding the subsequent kinetic energy would further increase the frequency and the atomic clock would register a further increase in time, and not the decrease in rate of time as is observed.

[The De Broglie hypothesis holds that a particles energy is proportional to frequency, and momentum is calculated via velocity and mass. The fact that lights mass is calculated via kinetic energy is confusing, but as far as I am aware, a particles frequency is mass related, and it is a particles mass that is velocity related.

Ditch the notion of energy mass equivalence... and under this remit calculation of wavelength is time related and quantum can then be calculated as to a particles position and momentum simultaneously and without recourse to probability...

In a universe where we know that gravity has an effect on particles, and quantum is the world of particles, why is it that these equations you mention do not relate to each other?

Going back to the caesium atom, it's energy level and frequency increase in the weaker gravitational field.

All particles are in motion! When a particle is described as having a rest mass, all this means is that the particle is at rest relative to the earth's motion. ie: it is moving with the earth.

You say that the De Broglie frequency* of an atom is dependent on momentum. Momentum is calculated via mass and velocity. Frequency is calculated via energy... and e=mc2.{/quote]. As you wish. But if you put in the numbers, you will see that the deBroglie frequency of Cs133 is several orders of magnitude higher than the hyperfine transition frequency that drives the clocks. QuoteAre you saying that there is a distinction between how the energies that supposedly contribute to the mass of a particle, or atom, interact with gravity? no[quoote]You are saying that the clock frequency is a function of the electrons making up the structure of the atom. Breaking the atom down to its particle structure, the electron has energy, frequency, wavelength...and mass.

Are you saying that there is a distinction between how the energies that supposedly contribute to the mass of a particle, or atom, interact with gravity?

Why is the 'we don't know' aspect of physics irrelevant to a discussion that attempts to offer an answer to unknowns, or at least gives a 'reason for cause' for observables that may then be discussed?

If a photon gravitationally shifts in energy, any particle is gravitationally shifting in energy!

*(What is the difference between a De Broglie frequency of an atom, and the frequency of light? And if a De Broglie frequency differs from another type of frequency, what is this other type of frequency?)

just the fact that lights frequency reduces in a weaker gravitational field and a particle with mass, it's frequency increases in a weaker gravitational field.

While gravitational redshift refers to what is seen, gravitational time dilation refers to what is deduced to be "really" happening once observational effects are taken into account.

QuoteWhile gravitational redshift refers to what is seen, gravitational time dilation refers to what is deduced to be "really" happening once observational effects are taken into account.

OK so as was pointed out . Therefore in the case of the photon the energy equation becomes .If we take our wavelength as L (1 light second) then we can show that . This 1 hertz wave then shows the direct relationship to the Planck constant.

Whereby light having no mass has no KE.

Which led me to my post saying that it would be more terminologically correct to say that the energy of the hyperfine structure transition of the caesium atoms has gravitationally shifted in the weaker gravitational field for an increase in frequency.

I wonder what it is that is 'energy' related about frequency, that a rise or fall of frequency would cause light to have more or less energy?

Yes - we are on the same wavelength here! So our observer observing the reference frames of 22 clocks, placed at elevations from ground level, 1 meter in difference over 22 meters, will observe that all of the clocks are running at different frequencies relative to each other. The frequency of each clock will have increased relative to the clock below it.No kinetic energy involved here, just gravitational shifts to higher energy and frequency that any particle of mass will be subject to if placed in a weaker gravitational field. Edit: relative to a greater gravitational field.

Light travelling into a weaker gravitational field reduces in frequency...

h is a constant Alan. How can f define h, when h is defined via e, and f is defined via e, and then e is defined via e=hf? This is a circular route...

Planck noticing that there were bandwidths of increase in thermal energy that caused no change to the frequency of light, and that it took quantised leaps of an increase in energy to cause the frequency of light to change.

Using e=hf to calculate a gravitational shift in light, what is causing the e of this h?

Yes, gravitational redshift, blueshift of light...got it. Simple. Particles with mass gravitationally shift in the 'opposite' direction in the gravitational gradient, 'this' being my point!

E and f are experimental variables measured independently, and their ratio turns out to be a constant known as h.

In the mean time, I asked you: what the cause of h was when calculating gravitational shift...

You said:""In the case of the classic mossbauer photon, it's the quantum transition from a metastable state of the Fe57 nucleus to the ground state. The other well-known astronomical measurement is the spin-flip of the hydrogen electron in its ground state, emitting a 1420.405751786 MHz photon (the "21 cm line") ""You are describing effect, not cause.

This difference is what I'm trying to talk to you about.

If the light's frequency were to speed up, and the observer were experiencing time dilation, it seems like the effect would be exaggerated.

The book I read was called 'The Devil's Advocate' and the technique is called advocacy... Needless to say, I've still got a lot to learn (chuckle)...

Why does lights frequency increase in the slower rate of time, when the clock's frequency reduces in the slower rate of time?

The photon observed coming towards Earth from a weaker field, when seen as blue shifted will be further blue shifted as it gets closer. The blue shifted lights frequency 'increases' as the rate of time becomes slower.The clock's observed from Earth that are placed at stages of elevation getting closer to earth from a weaker gravitational field are all observed as running at increasingly slower rates of time the closer to earth they are placed. The clock's frequency 'reduces' as it's rate of time becomes slower.

Advocacy is about winning an argument. Physics is about finding out what happens in the universe. Aristotelians thought physics could proceed by disputation, but they were wrong every time. So nowadays we start with maximal observations and minimal assumptions, and we get stuff like flight, nuclear power, interesting astronomy, radar speed guns, and GPS.

Fiat lux.