[alancalverd]

How do you define frequency? Then how do you measure it?

Do the emissions of a clock 'in' the top of tower frame of reference match the gravitational blue shift equation?

Do the emissions (gamma rays) of the Pound Rebka source emitted 'from' top of tower match the gravitational blue shift equation when arrived 'in' bottom of tower frame of reference?

Yes, yes. As you well know.

[Colin2B]

The experimenters measured each clock in the clock's own reference frame via a frequency counter that is part of the clocks mechanics, that sends the count via fibre optic cable to a computer for comparison.

There is no frequency counter in the clock mechanism, you must have misread something. Reread Alan's comment:

How do you define frequency? Then how do you measure it?

The frequency from the oscillator will contain some jitter so will be passed through a stabiliser and will be converted to a sqare wave to make comparison easier. It is this stabilised clock pulse which is used for comparison down the fibre - see my post #28.
The oscillator is free running, ie without any external clock reference, so if there were a frequency counter on board it would not return a value different from that which it would measure at the lower level. I explained in my simplified example why this is so.

[timey (OP)]

How do you define frequency? Then how do you measure it?

Do the emissions of a clock 'in' the top of tower frame of reference match the gravitational blue shift equation?

Do the emissions (gamma rays) of the Pound Rebka source emitted 'from' top of tower match the gravitational blue shift equation when arrived 'in' bottom of tower frame of reference?

Yes, yes. As you well know.

Frequency is defined as per how many cycles per standard second.
The standard second is defined as a 1 part duration of 86400 durations that make up the duration of 1 complete rotation of planet Earth.

(Edit: Colin the point is that whatever is counting the clock is doing so 'in' the clocks reference frame 'with' the clock, and that this info is being sent to computer by the cable.  The gathering of the information 'itself' is NOT reliant on a light pulse beacon travelling between the reference frames for observational comparison.)

So - the clock is following the gravitational blue shift equation for light emitted 'in' the top of tower frame of reference relative to the bottom of tower frame of reference.  We know the clock is emitting higher frequency photons 'in' the top of tower frame of reference... because a fibre optic cable is sending the information from the counter 'in' the clocks reference frame to the computer for comparison...

Let us hypothetically now observe the cesium atoms emissions emitted 'in' the top of tower frame of reference 'from' the bottom of tower frame of reference.
These light emissions must now travel to bottom of tower frame of reference to be observed, as do the gamma ray emissions from the Pound Rebka source.
We know that the frequency of the clocks emissions is already matching the blue shift equation as emitted 'in' top of tower frame of reference relative to the clock in the ground frame of reference - so after these higher frequency (relative to ground frame clock) photons emitted from the elevated clock reach the ground, what are the frequency of these photons ***now***  'in' the ground frame of reference?

[alancalverd]

Frequency is defined as per how many cycles per standard second.
The standard second is defined as a 1 part duration of 86400 durations that make up the duration of 1 complete rotation of planet Earth.

No!!!!!

One second is the time that elapses during 9,192,631,770 (9.192631770 x 10 9 ) cycles of the radiation produced by the transition between two levels of the cesium 133 atom.

So if you measure frequency by comparing a stable oscillator with a standard clock, you will get the same value anywhere if they are in the same reference frame, and a different value if they are in different reference frames. Which is exactly what we see when we launch GPS satellites.*

Whilst the cesium clock is the world legal standard, it isn't the most sensitive device for measuring small changes in spacetime: the aluminum ion clock runs at a much higher (optical rather than microwave) frequency so you get more cycles to compare in a given time, and it's more robust than a mossbauer rig. 

*interestingly, I understand that a circular orbit at around 9500 km gives an exact balance between GR and SR frequency shifts, so at some point in the launch the two clocks will resynchronise. You could even monitor progress on a Lissajous scope, but it's a horribly slow and complicated form of altimeter.

[Colin2B]

Colin the point is that whatever is counting the clock is doing so 'in' the clocks reference frame 'with' the clock, and that this info is being sent to computer by the cable. 

Nothing is doing the counting. Re read the article I quoted, what is referred to as the clock signal is the frequency output from the oscillators which can be compared directly without actually counting or measuring the frequency.
Consider the oscillator outputs as square waves, upper and lower, these pulses represent the 'ticking' of the Al ion:
 
      ___      ___      ___
     |.    |    |.   |    |.    |
  ---       ---       ---       ---

     ______         ______        ______
     |.        |.       |.        |       |.        |
  ---           ------           -------          ------
 
As you can see the upper frequency is higher than the lower. These can be fed via the fibre directly into a comparator which will give you the frequency difference using the lower frequency as a reference without having to measure either frequency. This will give you a fractional difference which is dimensionless and can be uses in the relativity formulae. Reread the detailed description in the science writeup and you will see that this is what they are doing.

Also, read Alan's post above it important to understand this.

[timey (OP)]

Why does the frequency of a  cesium atom define a standard second Alan?

The duration of a standard second is defined by historical time keeping based on a second being a division of the duration it takes for the planet to complete 1 full rotation of planet Earth.  There is nothing magical, nor special about the duration of a standard second, other than the fact that we measure the durations of all events against it.  Just so happens that the cesium atom resonates at a given frequency, when excited by a certain microwave frequency, that we can use to more precisely measure a period of a duration.  And the given frequency of the cesium 133 is the standard duration of a period by which a second second is standardised.

Your other commentary is interesting, but you do not answer the question relevant to the discussion...

The cesium atom does not operate at the same frequency at elevation, it has a higher frequency of cycles relative to the lower clock.  So no, you cannot say that the cesium atom is operating at the same frequency in all reference frames and only appears to have a higher frequency when observed from the lower frame, or visa versa.
NIST have recorded the frequency of the clocks in their own frames, 1 operating at the frequency we have set as standard, and the higher clock operating at an increased frequency that is said to be synonymous to a second that is shorter than the standard second.  The two states of the clock are ground state, and emitting photons state.  The atoms are thrown upwards through a microwave beam, are excited by this microwave beam, emit a photon in this excited state, and fall back to the bottom of the chamber.  The difference in gravity potential, ie: increase in gravity potential energy, is increasing the frequency of the elevated atoms emissions.  (note: A cesium atomic clock could be much more precise but for the fact of its own dimensions.  The chamber is 3 feet tall, and the microwave beam exciting the atoms could be more finely tuned except for the fact that the atoms experience time dilation effects within the elevations of the 3 foot chamber itself.  Hence the ion trap clock, which runs at a much higher frequency for more precision, but is not as reliable as the cesium atomic clock and must be used in tandem with the cesium atomic clock to be of any service.)

Never mind the length of second for mo.  Just looking at the increased frequency of the elevated cesium atom - the photons (cesium fountain) the clock is emitting at this elevation are of a higher frequency, relative to the lower clock... correct?

Colin - those signals are being sent from the clock to the computer for comparison.  There is NO reliance on an observation of a light pulse beacon from one reference frame to another to determine frequency.  When observing light that has been emitted 'in' 1 reference frame 'from' another, one can only view that light when it arrives in the observers frame, and this will be an observation of what the frequency of the light 'is' in the observers frame, not an observation of what frequency that light 'was' in the reference frame it was emitted from.
These are the only considerations at foot here.  Oscillators, counters, square waves, whatever - the fibre optic cable does not change the information of the clock sent from the clocks reference frame to the computer.

[nilak]

The cesium atom does not operate at the same frequency at elevation, it has a higher frequency of cycles relative to the lower clock.  So no, you cannot say that the cesium atom is operating at the same frequency in all reference frames and only appears to have a higher frequency when observed from the lower frame, or visa versa.

Suppose you are at ground floor. If you measure a piece of paper with a  stick you get 10 by 10 sticks for example. This means the paper is 10x10 in your reference frame. If you go higer at first floor, you measure the paper and you get 10x10 stick again. In your reference frame the paper still measures 10x10 sticks. You can even define a centimeter being the length of that stick. But you now, that, because of the gravity effect, the paper at the first floor is bigger. It is only when you compare the paper from a different reference frame you notice the difference. In the case if clocks the same thing happens. You define a second based on say 1G osciclations. No matter how fast is ticking you still say a second is 1G osciclations. Only when you compare the clocks from different frames of reference you realize their frequency was not the same.
Yes,  the difference in rates is real not an apparent, only it is impossible to detect an absolute value or even a change if everything arround is changing the same way.
A convincing  way to do the experiment is to leave the clocks count on their own for a longer period, then compare the results. But even if you measure realtime a tiny difference will always be measured  when sendig signals to the comparator.

These things happen because space is a dynamic real thing, like living inside a material witn regions of different built-in stress  . The space geometry is not homogeneous and also it changes with time hence we het curved spacetime geometry.

[alancalverd]

Why does the frequency of a  cesium atom define a standard second Alan?

for the same reason that King Edward II's arm defines the standard yard: because we say so!

The duration of a standard second is defined by historical time keeping based on a second being a division of the duration it takes for the planet to complete 1 full rotation of planet Earth.

In the words of Henry Ford, history is bunk. The earth does not keep precise time and is useless as a clock, even for agriculture (which is why we have leap years and leap seconds).

The cesium atom does not operate at the same frequency at elevation, it has a higher frequency of cycles relative to the lower clock.  So no, you cannot say that the cesium atom is operating at the same frequency in all reference frames and only appears to have a higher frequency when observed from the lower frame, or visa versa.

which is why I didn't say it.

NIST have recorded the frequency of the clocks in their own frames, 1 operating at the frequency we have set as standard, and the higher clock operating at an increased frequency that is said to be synonymous to a second that is shorter than the standard second.

nobody said that, because it isn't true. If you measure the frequency of a stable oscillator by comparison with a clock in the same reference frame, it will always be the same. If you compare it with a clock in a different frame, it will be different.   

Never mind the length of second for mo.  Just looking at the increased frequency of the elevated cesium atom - the photons (cesium fountain) the clock is emitting at this elevation are of a higher frequency, relative to the lower clock... correct?

It has been so for as long as anyone cares to remember. Why do you keep repeating it?

Colin - those signals are being sent from the clock to the computer for comparison.  There is NO reliance on an observation of a light pulse beacon from one reference frame to another to determine frequency.

Of copurse trhere is. How else can you measure or compare frequency?

  When observing light that has been emitted 'in' 1 reference frame 'from' another, one can only view that light when it arrives in the observers frame, and this will be an observation of what the frequency of the light 'is' in the observers frame, not an observation of what frequency that light 'was' in the reference frame it was emitted from.

Don't confuse the energy of the photons with the period between them. Not that it matters, because both are equally subject to GR shift.

[Colin2B]

The fibre optic cable does not change the information of the clock sent from the clocks reference frame to the computer.

Who said it does? Certainly not me.
I was merely pointing out that it is not necessary to have a frequency counter in order to measure a frequency difference.

It seems to me that you were saying that if the ion clocks at different heights contain frequency counters such that they measure the frequency in their respective frame, then the NIST experiment is flawed.
In this I agree with you, but not for the reasons you give, but for the simple fact that the experiment would have shown no difference between the frequencies of the clocks at different heights, nor the moving clocks.

Colin - those signals are being sent from the clock to the computer for comparison.  ........one can only view that light when it arrives in the observers frame, and this will be an observation of what the frequency of the light 'is' in the observers frame, not an observation of what frequency that light 'was' in the reference frame it was emitted from.

Ah, I see you still haven't worked out why the height of the computer is irrelevant (other than the fact that it has to be within the 75m fibre length). Read the article again and follow the methodology and it soon becomes obvious.
Hint: 100,000s of measurements were made of the tick rates with both clocks in the lower position. Bear in mind that they are not looking for absolute frequency measurements just δf/f₀, see equations 1, 2 and 3.
EDIT: just noticed that Alan has responded while I was typing this, he gives you additional hints in his last 2 comments - actually to be fair he's given it away!

Hence the ion trap clock, which runs at a much higher frequency for more precision, but is not as reliable as the cesium atomic clock and must be used in tandem with the cesium atomic clock to be of any service.

Not in this case. If you read the article you will see that in the Al clock they used logic ions of Be and Mg which not only give a very high Q factor but have better frequency uncertainties than Cs fountain.

Are you sure you've read this article?

[timey (OP)]

Alan - the only significance a standard second has in this discussion is that events are measured against it, including the frequency of anything.  No the planets rotation is not precisely regular.  The frequency of the cesium atom is more regular. Therefore modern science uses the cesium atom to measure this set duration of a period more precisely.  End of story!

When a cesium clock is running at the frequency of a standard second, the clock is being measured how?
Is it being measured via a method that counts the frequency of the cesium atom?
The answer to this question is yes.  The information is being transfered into square waves and sent to the computer...
How is the clock in elevation being measured?
Is it being measured via a method that counts the frequency of the cesium atom?
The answer to this question is yes.  The information is being transferred to square waves and sent to the computer...
The results of these measurements match the blue shift equation.

Now listen very carefully!
Taking just 1 cesium atom, at the same elevation as the clock, and exciting the atom to produce a photon that we are now going to observe 'from' the ground frame of reference, we must remember that unlike the readings from the clocks, the photon will only be observable 'in' the ground frame of reference 'when' it gets there...
This photon will have been blue shifted on its way to the ground frame of reference.
What frequency will it be?

Colin - I have not read that article you posted.  It is a PDF, and I cannot read them on this phone.  When the experiment hit the news, I read that the computer took readings from the moving clock at intervals.  I read that the upper clock and lower clock were connected to a computer.  I did not read how a light pulse is arriving at the computer having been gravitationally blue shifted, or Doppler shifted.

[timey (OP)]

If you think that I don't understand that your viewpoint is that in comparing the upper clock to the lower clock, the upper clock has more cycles per second than the lower clock, so in saying that a second is shorter in the upper frame, you are taking the stand that where there is a shorter second that the cesium atom is still operating at the same frequency of cycles that it will be operating at as per the lower clock, but in a shorter amount of time.

And in principal I am not disagreeing here.  If you shorten a standard second proportionally to the extra cycles of the higher frequency, the number of cycles per shorter second will be the same number of cycles per shorter second.  This being the exact equivalent of the amount of cycles the lower clock has per standard second...

I am of the understanding that physics is calculating an atom at elevation as emitting the same frequency of photon at elevation as it does on the ground.

I'm just taking the viewpoint that as far as calculating the universe goes, it is much more useful to view the situation as the cesium atom having a higher frequency in its elevated frame of reference held relative to the frequency a cesium atom has as per the standard second.

This being because light emitted from the atom at elevation is 'now' being calculated as emitted photons of a higher frequency, and this difference might well have a huge bearing on the interpretation of the Pound Rebka results.

[nilak]

You can define a second based on a cessium clock if that is the most accurate thing you have. Time we measure is not absolute, although I feel it is possible an absolute time to exist but its no way to define it. Speed of light (more precisely speed of causality which is equal to speed of light in vacuum) is absolute. You define its magnitude once and it stays like that forever everywhere.

How would you define a standard unit of time or second ?

[alancalverd]

Nobody is "calculating" anything about the frequency of the emitter. Whether it is a nuclear photon or a hyperfine spin-spin transition, all that matters is that the energy of the defining phenomenon is not dependent on gravitational potential (which is why we can't use a pendulum clock). If it was, then the energy would be orientation-dependent in a high-g field, and there is no evidence that it is (line broadening between the sun and Vega is a temperature and pressure phenomenon).

Since the initiating phenomenon is not  g-dependent, but the received frequency is, the explanation can only be that time is g-dependent.  This is convenient because it means we can predict the gravitational shift of all clocks, regardless of their mechanism (except pendulum clocks) as being exactly the same for any given gravitational potential. And to nobody's surprise (except for those who think the mechanism ought to be  g-dependent)  that's exactly what Pound & Rebka, NIST, GPS and everyone else finds by experiment, using mossbauer, rubidium, aluminum, cesium and mercury clocks, all with different initiating phenomena. 

[nilak]

 For cosmological purposes an absolute time theory can be thought. Time will be what we feel like it is. We have the intuition it is absolute. Defining time absolute will make speed of light variable. When studying twins paradox we will say one the time passed was the same for both. One of the twins will apear as younger and we will say, it is the consequence of the speed of light that slowed down in the rocket.
This theory will require a protocol in relation to GR. Energy wise we might get into more trubble.
Clocks we use now will not indicate time anymore. Time will have to be deduced.
 Timey, I think this is the time you are talking about.

Speed of light as constant has the advantage that it can apear as constant when measured using our clocks everywhere and can be thought as absolute also explains biological aging but it is in contradiction with our intuition, that is the drawback.

[Colin2B]

Colin - I have not read that article you posted.  It is a PDF, and I cannot read them on this phone.  When the experiment hit the news, I read that the computer took readings from the moving clock at intervals.  I read that the upper clock and lower clock were connected to a computer.  I did not read how a light pulse is arriving at the computer having been gravitationally blue shifted, or Doppler shifted.

I assumed your statement that you had read everything on the NIST experiment meant you have also read the Science article which was also on the NIST site at the time. Problem with press releases is they are not informative on detail and often take shortcuts in description because they cater for a wider audience. Most people would be confused by reference to blue or red shift (not Doppler) and those who aren't will easily work out that it doesn't matter. They will also use clock to describe the oscillator (as we all do) but to many people this includes a counter and display which isn't part of this 'clock' - even you assumed there was a frequency counter!

In my post I said you are not trying to measure actual frequencies, in fact it doesn't matter whether you are comparing relative to premoved or or just measuring, there is a height difference between measuring point and the measured frame which changes.
In the case of the moving clock the height didn't change so you wouldn't expect measured frequencies to differ unless due to motion.

PS There is no Doppler Shift because the upper clock had been moved to its new height when the second set of measurements were taken.

[timey (OP)]

Nobody is "calculating" anything about the frequency of the emitter. Whether it is a nuclear photon or a hyperfine spin-spin transition, all that matters is that the energy of the defining phenomenon is not dependent on gravitational potential (which is why we can't use a pendulum clock). If it was, then the energy would be orientation-dependent in a high-g field, and there is no evidence that it is (line broadening between the sun and Vega is a temperature and pressure phenomenon).

Since the initiating phenomenon is not  g-dependent, but the received frequency is, the explanation can only be that time is g-dependent.  This is convenient because it means we can predict the gravitational shift of all clocks, regardless of their mechanism (except pendulum clocks) as being exactly the same for any given gravitational potential. And to nobody's surprise (except for those who think the mechanism ought to be  g-dependent)  that's exactly what Pound & Rebka, NIST, GPS and everyone else finds by experiment, using mossbauer, rubidium, aluminum, cesium and mercury clocks, all with different initiating phenomena.

Yes - you are correct, nobody is calculating any of these atoms observed as increased in frequency at elevation, as being  increased in energy...

Why not?  All atoms will be increased in energy by the same proportionality and the equivalence principle is upheld.

A gamma ray emitted on the vertical Mossbauer experiment will be emitted at a higher frequency and energy at elevation than a gamma ray emitted on the ground.  It will be of the 'wrong' energy to be received by the receiver on the ground.  Add in a recoil motion, synonymous to the recoil motion that placing the atom in the crystal lattice has eliminated, or a forward motion (that according to NIST results will reduce the frequency of a clock), then the energy of the emitted photon will be reduced. (this would require one to view the kinetic energy, relativistic mass calculation of light alternatively)

By my reckoning, if one were to view events as so and make the correct calculations, that the value of how g is affecting the gravitational shift of light will be different, and very interesting... (and match with relativity results)

Nilak - I am reading your posts...  I don't have access to my own internet connection at mo, so am having to stay strictly on point with the purpose of the discussion.  I am not saying the speed of light is variable.  If the conversation takes the direction I intend, the subject will be being discussed presently.

Colin - I read everything available at the time, but that was 6 years ago.  My point is that an observation of light travelling through a gravitational change, and an atom emitting a photon at a different gravity potential are different.  Light can only be viewed 'in' the frame of observation, no matter where it comes from.  The clock emitting photons is being read by a computer.  The info travelling that fibre optic cable from the clock, does not 'change' on its way to the computer.

[nilak]

Nilak - I am reading your posts...  I don't have access to my own internet connection at mo, so am having to stay strictly on point with the purpose of the discussion.  I am not saying the speed of light is variable.  If the conversation takes the direction I intend, the subject will be being discussed presently.

Thanks,
   I don't think this is off topic. If you say, a clock cycle, like a rotation of a hand doesn't measure a second anywhere you place it, it means speed of light is variable. Speed of light is constant in the theory of GR. You can construct a theory where speed of light is not constant, no problem. It is a matter of preference, but clocks we have now, won't measure time anymore, they will measure the speed of light (defined as variable). You will need different clocks to measure time.

In GR the clocks we use measure time.  Clocks defined in GR are perfect. It is the definition of time. Perfect clocks don't exist in real life but still we have enough accuracy to test GR.

Time was already defined when we invented clocks (planetary clocks roughly measure the same time but they are not accurate).
We couldn't have defined time otherwise, because those were the clocks we had available and also, because when time was defined we didn't know, time we defined could change.

[timey (OP)]

No you are not off topic as such, just ahead of topic...

GR keeps the speed of light constant by rendering distance as variable...  It is actually possible to have a constant speed of light and keep distance constant in the face of an additional gravitational time dilation that runs counter directional to GR time dilation for reference frames of empty space in relation to M.  This rendering GR gravitational time dilation an m near M phenomenon...

But as said, this is well ahead of topic...  For the present we are looking at the frequency of atom's in elevation physically having a higher energy relative to atoms in a lower gravity potential, and emitting higher energy photons relative to the photons they would emit in a lower gravity potential.

P.S.  It is a documented fact that physics does not actually have a comprehensive theory of time.

[Colin2B]

Colin - I read everything available at the time, but that was 6 years ago. 

The Science article was 2010, 6 yrs ago. It triggered the press releases.

The info travelling that fibre optic cable from the clock, does not 'change' on its way to the computer.

Again I am not saying the fibre optic makes any changes to the info or light.

My point is that an observation of light travelling through a gravitational change, and an atom emitting a photon at a different gravity potential are different.  Light can only be viewed 'in' the frame of observation, no matter where it comes from.  The clock emitting photons is being read by a computer. 

I don't really understand what point you are making here, but the point I am making is that the height of the comparator/computer makes no difference to the result.
Just so we have common understanding (in no way trying to teach you relativity):
Both oscillators - we'll call them clocks - start at the same gravitational potential (GP).
The light from each enters a fibre optic at that GP and thus its frequency is as measured in that local time. The fibres are then routed to a comparator/computer which we will assume is at a different GP so the light exits the fibre at the local time at this height, this means that a measurement at this height will be different from one taken at the height of the clocks. If we wanted to measure the frequency at this height the computer would need its own atomic clock, but no worries one of the fibres carries light from the clock which will not move in height, so we can compare the two signals - which are still the same, but shifted.
So now we have a reference against which to measure the clock which is now moved in height relative to the computer, and the height it moves will define the change in GP and hence the change in frequency measured at the computer's height, and match the predictions of GR. Note, this change in GP is the same as between fixed clock and raised clock, so all is consistent.
Now, if you imagine varying the height of the computer you can see that the % difference in frequency will remain the same, so height of computer is irrelevant to these discussions.

[timey (OP)]

Colin - I do not understand why you think that I thought the gravity potential of the reference frame of the computer was relevant.  I gave indication that it was irrelevant posts ago when I stated the computer in another room entirely, at an unspecified, and possibly different height.

I thought you said the frequency of the clock was translated to square wave to be transmitted via the fibre optic cable...

The point I'm making:

The information of the square wave will not be changed by its transit to the computer via the cable.

Light emitted by the elevated clock, ***as seen from*** the lower clock, cannot be viewed by the lower frame ***until it gets there***, and ***will be changed*** in frequency during its transit from the upper frame to the lower frame.

Do you understand the difference?

Edit: I didn't mean that the info wasn't available 6 years ago - I read the info 6 years ago is what I meant.