[alancalverd]

"Faster" compared with what? (Hint - the one on the ground!) And I don't think NIST uses the term "frequency of cycles", just "frequency". 

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]

The cesium atom determines the frequency of the microwave source.

 

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.

The difference betwen definition and calibration is significant to professional nitpickers like standards physicists.

[timey]

Be that as it may Alan, the only part of the process that I am concerned with is the frequency of the elevated clock being greater than the clock that is on the on the ground in the stronger gravitational field.

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, not because it is the definition of the phenomenon of time itself.  It is only a measurement.

The frequency of the caesium atom increases in the weaker gravitational field due to the addition of gravity potential?

[alancalverd]

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,

Only if you believe that  9,192,631,770 = 1, and I think you may be alone in that belief.

Those who know a bit more would say that cesium is chosen because 9 GHz microwaves are easy to generate and manipulate, and the cesium ground state hyperfine transition is very stable and easy to identify within the cesium absorption spectrum. The magic number was chosen as the best estimate of the length of an astronomical ephemeris second in terms of the frequency of a cesium clock, and from that moment on, the clock defined the second and all astronomical measurements became secondary measures.   

Not a good idea to talk about the "frequency of the cesium atom" lest deBroglie fans think you  mean the deBroglie frequency of the atom, which depends on its kinetic energy. The hyperfine splitting energy doesn't.

As the energy (and hence frequency: E=hf) of the cesium clock transition is fixed, the phenomenon of one clock running fast or slow compared with another is due to the relativistic gravitational and/or motion dilation of time between observers.   

[timey]

I very rarely believe anything these days.  Belief is illogical.  I have read that a caesium atoms transitions at the frequency of 9,192,631,770 Hz defines the length of 1 standard second, and have yet found no evidence to suggest anything otherwise.

If the frequency of the atoms of the elevated clock is greater than the frequency of the atoms of the clock at ground level, 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.

[alancalverd]

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

That's the difference between classical mechanics and quantum mechanics + relativity. QM sensibly says E is fixed because the atom has no idea where it is, and the electrostatic forces inside an atom are much larger than any possible perturbation. Relativity says time is compressed or expanded by gravitation. Common sense says the observer next to the clock doesn't see any change, because he has no other reference. Calculation says an observer at a different gravitational potential will see a difference between the clocks. Experiment says that is exactly what happens. 

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.

"Ground level" is not "1 meter above ground". Even a cheap GPS like the £200 gadget in my tatty old Cessna can tell the difference, thanks to gravitational time dilation. Relative velocity time dilation is not the same phenomenon as gravitational dilation, as you know (we've discussed this before). Other experiments have shown (indeed you have quoted them) that relative motion slows time, exactly as predicted.

It's interesting to calculate both effects for an orbiting astronaut (low earth orbit, speed dominates, received frequency decreases) and a GPS satellite (high orbit, gravitational shift dominates, frequency increases). There will be some orbital distance at which the effects cancel and a "space clock" keeps time with a "ground clock" - just like your favorite Pound-Rebka experiment!

[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.

Not quite true, but wholly irrelevant. Maybe next time! But you will confuse yourself less by sticking to the usual terminology: the frequency of a cesium clock (9 gigahertz microwaves, lower than optical)  is not the deBroglie frequency of a cesium atom (way up with cosmic gamma radiation) 

[timey]

The difference between quantum and relativity, and the fact they cannot be reconciled with each other is exactly the region I'm interested in...

Nope ground level is not 1 meter above ground!!!  NIST used 2 clocks, one on the ground (sea level presumably) and one at 1 meter elevation...  If the clock elevated at 1 meter zoomed off horizontally at speed was the consideration...  (I could have zoomed the ground level clock off at speed, but it wouldn't have made for such a good working visualisation due to drag factor. ...)

Yes, I am aware that my description of frequency being mass related and mass being velocity related is "not quite true"... this being because e=mc2...

Edit:  The lower microwave region kicks the energy and therefore the frequency of the caesium atom up an energy level.  (Quantum). At elevation the frequency of the atom increases (gravity potential, Relativity).   The energy level of the atom increases the frequency and the wavelength gets shorter (De Broglie hypothesis)

I can see the possibility that an increase in frequency can be associated with an increase in the rate of time (caesium atom behaviour at increased frequency in a weaker gravitational field) and that a lower frequency such as experienced by light in a weaker gravitational field can be indicative of a decrease in the rate of time.

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...

[alancalverd]

Difficut to know where to begin to lead you out of this snowdrift of pseudoscience, so let's ignore the stuff about cesium atoms (why not? you have ignored what I told you!) and start with 

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...

You will know from your wide and deep reading on the subject, or even Wikipedia, that mass-energy equivalence does not enter into derivation of, or the equation for, gravitational redshift, nor relative velocity shift. Nor does probablity or quantum mechanics. Relativistic shifts and time dilation are purely classical, continuum, deterministic phenomena.

Keep it simple. In general, truth is found through simplicity.

[timey]

I'm not ignoring what you have told me...  What I am doing is employing a technique that solicitors use when cross examining witnesses.  I read a book on it.  One leads the discussion to the area one wishes to illuminate.  I forget what the technique is called, I'm out at mo, but will look at the book when I get back later and tell you.

I have read extensively on all of the things that you have 'told me'.  I might not know how to manipulate mathematics but I do have a good understanding of current physics and  therefore please understand that when I make deviations from current physics I do so purposefully.

You seem to be unconcerned that physics is divided into 2 working hypothesis that cannot be reconciled with each other.  I observe a universe that is working as a whole.  The reason I observe this is because the universe does work as a whole, therefore there must be a 'bridge' between quantum and the observed effects of gravitational shift and energy change that are currently Relativity.  It is the goal of theoretical physicists worldwide to reconcile these theories with each other, and it is widely accepted among these physicists that in order to do so, alternatives must be considered.

Perhaps you are confusing the consideration of alternatives to be a 'snowdrift of pseudoscience'?  Or perhaps there is no confusion and you could then rename your board of New Theories as such, instead of 'New Theories'?

Keep it simple:  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.  Are you measuring what the rate of time is for that location of weaker gravity field, or are you merely measuring what the rate of time is for the caesium atom via the gravitational shift of an increase in energy, and therefore an increase in frequency, it has suffered in the weaker gravitational field?

[alancalverd]

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?

The only equations I have mentioned, of gravitational and velocity shift, are very closely related to each other. Neither has any implied or observed quantum implications as they are both continuum phenomena. Hence no need for a bridge of any sort. 

"Quantum is the world of particles" is journalism or philosophy, not physics.

There is a legitimate question as to why gravitation is not quantised, and the answer is that we don't know, or the quanta are very small, but the question is irrelevant to the present discussion.

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

beware of snow. The potential energy of an atom increases as it moves up the gravitational well. The deBroglie frequency of an atom depends on its momentum, which can be any value you like, or zero if it isn't moving. Neither has anything to do with the clock frequency, which is a function of the electronic structure of the atom, not its environment or relative speed. That's why we use cesium clocks, hydrogen spectra, mossbauer photons and the like, to investigate relativistic frequency shifts. 

[timey]

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.

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?

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.

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?)

[alancalverd]

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.

Alas, this planet is of no cosmic significance. Pmb prefers the term "proper mass", but I think the term "invariant mass" is more descriptive. It's the bit that doesn't depend on speed.   

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.

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?

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.

Yep. And it's only the quantised energy that matters here.

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?

because in this instance, the cause is known.

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

True, but irrelevant.

*(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?)

I'll leave you to calculate or look up the numbers. Hint: the answer is "enormous"!

[timey]

Why is the fact of an electron gravitationally shifting irrelevant, if the electron's quantised energy transition is shifting the frequency of the clock in the weaker gravitational field?

I did not mean the 'value' of the supposed difference between a De-Broglie frequency of a particle with mass and the frequency of light, 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.

You also implied that a De Broglie frequency differs from frequency of another kind.  I wanted to know what this other frequency related to, if it is not associated with the energy of the particle, as the De Broglie frequency is...

[jeffreyH (OP)]

https://en.m.wikipedia.org/wiki/Hyperfine_structure

[timey]

So instead of saying that it is the caesium atom's energy, or the electron's energy that has been gravitationally shifted in the weaker gravitational field for an increase in frequency, 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?

[alancalverd]

No. As far as the observer in the weaker field is concerned. there has been no change in anything.

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.

If you keep repeating this you may convince yourself, but nobody else. One more time: the frequency of electromagnetic radiation as seen by an observer in a weaker gravitational field is lower than that seen by an observer at the source.

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.

Now what do you mean by the frequency of a particle?

[timey]

Yes it is well documented that observers in differing reference frames will observe their clock to be the correct time.  This is the premiss of the equivalence principle, whereby any reference frame is the equivalent to any other reference frame, and it is the 'other' reference frame that will appear to the observer to be running slow or fast.

But... can we please leave the observer out of the picture and consider all 'appearances' of other reference frames as being a) occurring as an observer independent phenomenon, and b) as being relative to the standard second?

The De Broglie hypothesis states wavelengths for particles with mass.  A wavelength comes inherent with a frequency, and this frequency is energy related.  More energy = higher frequency = shorter wavelength.

Whether anybody observes it or not, lights frequency decreases in a weaker gravitational field.  Whether anyone observes it or not, a particle with mass's frequency increases in a weaker gravitational field... I can say this once, or a thousand times, and it will still be an observed fact of physics...

Quote
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.

Interesting turn of phrase that... (chuckle)

[alancalverd]

Perhaps, when you say "a particle with mass's frequency" you mean "deBroglie frequency". In that case (and it would be so much easier if you used the same words as everyone else) your conundrum is easily explained.

deBroglie frequency f= E/h. As a particle falls from a high gravitational potential, its kinetic energy increases so f increases. I think the confusion arises from the fact that a high gravitational potential means a low gravitational field.

You can't leave the observer out of relativistic matters, by definition: "relative" means that there must be two reference points. The power of relativity is in the realisation that in the absence of a universal reference frame there must be reciprocity between observers, but a convergent gravitational field provides an asymmetric reference.

As far as the standard second is concerned, the hyperfine transition that defines it is the energy difference between the spin + and spin - states of the outer electron in the Cs133 atom with reference to the nuclear spin. The difference is independent of gravitational field because "+" and "-" are only defined with respect to the nuclear spin, which is randomly oriented in a gas. Therefore the frequency is fixed for a stationary local observer but may appear different to an observer who is moving (Doppler shift) or at a different gravitational potential (gravitational red shift). We can set the D shift to zero by not moving. Now we observe an asymmetric G shift but we know that the originating phenomenon is unaffected by gravitation, so we say that time is compressed by gravitation. 

[timey]

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 . 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.

[jeffreyH (OP)]

 [] Don't blame me.

[timey]

Of course not Jeff,  I am completely to blame for my own ideas, it is your equation, as I stated in my first post here, that has interested me...

...and it is your equation that is to blame for my participation in your thread with my alternative take on observation in relation to the relationship you potentially outline between Planck's h constant and hertz.