[timey (OP)]

I would have thought the direction would be obvious in the g-field due to accelerative and decelerative aspects.

Cannonball falling down towards trampoline: a is increasing, v is increasing, p is increasing, kinetic energy is increasing, potential energy is decreasing.
Cannonball bounces off trampoline upwards at v: a is decreasing, v is decreasing, p is decreasing, kinetic energy is decreasing, potential energy is increasing.

Add kinetic energy to upward bound cannonball converted into the form of acceleration: a increases, v increases, p increases...
Potential energy is also increasing with increasing h from M, so does the added kinetic energy, (minus energy conversion losses to acceleration), have to ,is it match(?), or outweigh(?) potential energy in order that a, v and p do not arrive at 0?

...And, If the trampolines were (impossibly) identical: then because the fact of the potential energy gained at height by the both the cannonballs will be equally proportional for the differing mass value of both cannonballs to the conversion of potential energy to kinetic energy then converted into 'bounce' energy for both mass values, changing the direction of both cannonballs from downwards to upwards, the 100kg cannonball will come to rest on it's trampoline at the same moment in time as the 10kg cannonball - (of equal spatial dimensions to 100kg cannonball, to equalise air drag) - will come to rest on it's trampoline, if both cannonballs had been dropped into free fall onto their trampolines at the same moment in time.

So - Here can we observe that energy for m at h from M is not observer dependent?  It cannot be observer dependent because it has observed physical consequences.
Therefore the observed frequency of a caesium atomic clock's caesium atoms at h from m, or in relative motion, will have a frequency associated energy, and neither this energy, nor the observed frequency, can be considered to be observer dependent.

[alancalverd]

So - Here can we observe that energy for m at h from M is not observer dependent?  It cannot be observer dependent because it has observed physical consequences.
Therefore the observed frequency of a caesium atomic clock's caesium atoms at h from m, or in relative motion, will have a frequency associated energy, and neither this energy, nor the observed frequency, can be considered to be observer dependent.

Poppycock, as you well know.

Potential energy = mgh. h measured from where? If you drop your cannonball from 100 ft, it will be passing an observer at 50 ft rather more slowly than it hits the ground at 0 ft. Kinetic energy = mv²/2. So the kinetic energy seen by an observer depends on the altitude of the observer relative to the starting point of the canonball.  Which is exactly what Pound-Rebka and countless others have discovered.

[timey (OP)]

0h - so now you admit that the observer at 50 feet will actually observe the ball to be travelling more slowly at 50 feet, a fact that will also be noticed by the observer on the ground, as acceleration is noticeable, but you refuse to agree that the caesium atomic clock's energy at h from m is causing the higher frequency that is observed by the observer on the ground?

If the cannonball has more potential energy at h from M, then so will the caesium atom.

The Pound Rebka uses a photon, a photon cannot be observed until it reaches an observer.
Fortunately this is not the case with falling cannonballs, falling coconuts, or caesium atomic clock's held at rest to the g-field at a higher gravity potential.

[alancalverd]

0h - so now you admit that the observer at 50 feet will actually observe the ball to be travelling more slowly at 50 feet, a fact that will also be noticed by the observer on the ground, as acceleration is noticeable, but you refuse to agree that the caesium atomic clock's energy at h from m is causing the higher frequency that is observed by the observer on the ground?

If the cannonball has more potential energy at h from M, then so will the caesium atom.
.

It's exactly the same phenomenon, with the same result. Potential energy becomes kinetic energy. In the case of a mesoscopic object, it goes faster as it falls down a potential well. In the case of a photon, its frequency increases.  The difference is that an observer on the ground has no way of knowing anything about the photon until it arrives, but so what? What's your problem?

[timey (OP)]

The caesium atomic clock at h from M, held at rest with respect to the g-field, isn't experiencing a conversion of potential energy to kinetic energy.

Yes - the frequency of the photon increases as it falls into a gravity well, but the frequency of the caesium atomic clock is observed of a higher frequency if you place it at h to M in the gravity well, and is of lower frequencies at lower h's from M.

One cannot observe what the frequency of an emitted photon is at h from M unless one is at h from M with the photon being emitted.  But one can know what the frequency of the caesium atomic clock is at h from M, because the clock is recording that frequency 'at' h from M.
(Where that frequency recorded at h from M is 'then held relative' to the frequency of a clock at ground level, this being 9,192,631,770Htz)

The point isn't that one cannot know anything about a photon until it arrives.  The point is that one can know something about the clock held at rest with respect to the g-field at h from M.

But... and this is my problem Alan - physics will tell me that I can observe the caesium atomic clock on the ground at a frequency of 9,192,631,770Htz, and that when placing the atomic clock at rest with respect to the gravity field at 1 metre h from M, will then observe the clock to have a higher frequency.
But if I place myself at 1 metre h from M with the clock, that I will then observe the clock as having the frequency of 9,192,631,770Htz, and therefore that this change in frequency that I observed of the clock when I was 1 metre below is observer dependent.

If I were to observe a photon being emitted 1 metre below me, I would observe this photon as having been redshifted from its emitted frequency, suggesting that if I placed myself with the emitter that is 1 metre below, I would observe the emitted photon as being of a higher frequency than I did when I was placed 1 metre above the photon emitter.
If I were to observe a photon being emitted 1 metre above me, I would observe this photon as having been blue shifted from its emitted frequency, suggesting that if I placed myself with the emitter 1 metre above me, that I would observe the emitted photon to be of a lower frequency than I did when I was placed 1 metre below the photon emitter.

But according to physics, no matter what potential, or what relative motion the atomic clock is experiencing - when I am with this clock it will always register as having the frequency of 9,192,631,770Htz.
And physics will tell me thus that the observed frequency of the clock when I am not with it is observer dependent.

This structure is not compatible to the notion that a person will age in keeping with their time dilated clock...
If the frequency is always 9,192,631,770Htz - no matter what potential, or what relative motion - then a person ageing in keeping with their time dilated clock will age no faster, or no slower than anyone in any other potential, or relative motion...
Unless of course one considers that the persons atoms are affected as the clock is, and that all atoms are changed in frequency at differing potentials (as per light in the gravity potential but contra directionally with respect to the gravity potential).  And also that all atoms will be changed in frequency in relative motion.
In which case when measuring the frequency of 'my' clock as per the time registered on 'my' clock, I will always observe 'my' clock to have a frequency of 9,192,631,770Htz no matter the gravity potential I am located in, or the relative motion that I am moving at.

However - this would mean that the frequency of the clock 'is' observer dependent from the viewpoint of an observer 'with' the clock, and that the observer at a differing potential, or in relative motion to the observation, i.e: 'not' with the clock, is not observing an observer dependent phenomenon, but is observing an 'actual phenomenon' that 'does' occur for the observed clock which 'is' indeed of a different frequency in the differing gravity potential, or in relative motion to the observer.

If light 'is' of a differing frequency in the differing gravity potential, then physics cannot state that the atom's frequency will be of the same frequency in the differing gravity potential, and that any change to this frequency as observed by the observer in a differing gravity potential to the clock are only observer dependent.
But physics can state that light is of a different frequencies in the gravity potential, and that we can only see light when it arrives at our location.
And physics *'could'* state that an observation of an atomic clock in one's own location will always be observed to be 9,192,631,770Htz when measured via the time the clock is running at in one's own location.
...And the problem would thus
be solved.

[alancalverd]

The caesium atomic clock at h from M, held at rest with respect to the g-field, isn't experiencing a conversion of potential energy to kinetic energy.

But the falling photon is. That's all there is to it. No problem.

[timey (OP)]

...and why is that related to the clock held at rest with respect to the g-field at h from M?

[alancalverd]

The elevated clock runs faster as seen from the ground. The photon emitted from an elevated source has a higher frequency as seen from the ground. Same phenomenon, same effect. No problem, no conundrum, just general relativity at work.

[jeffreyH]

If you are at a lower elevation you would calculate that individual photons are emitted at a faster rate at a higher elevation. This is just the effect of the differing rates of time at different gravitational potentials. It is the consequence of time dilation.


Near the event horizon of a black hole the rate of emission is so low  that it may be indistinguishable from no emissions at all.

[timey (OP)]

You and Jeff both are quoting relativity without thinking about how you are calculating it, and are relying on time being faster at h from M to back up your conclusion.
...And your answers do not describe a person ageing in keeping with their time dilated clock that is in relative motion at-all, not physically or logically, and do not give physical description of why a body ages faster in the higher gravity potential.

A photon is converting potential energy into kinetic energy and its frequency increases...
The clock is being held at rest with respect to the g-field at h from M.
It has gained potential energy - as described of the cannonballs on the trampoline - but it has not converted this potential energy into kinetic energy.
If the cannonballs on the trampolines are converting potential energy into kinetic energy, firstly:
You have told me that potential energy is added or subtracted negatively, and kinetic energy is added or subtracted positively, so how can -energy be converted into + energy as you have said here:

quote Alan:

It's exactly the same phenomenon, with the same result. Potential energy becomes kinetic energy. In the case of a mesoscopic object, it goes faster as it falls down a potential well. In the case of a photon, its frequency increases.

Edit: ...and where you say that the mesoscopic object is falling faster, while in reply to my saying that the 100kg cannonball is robbed of more of its energy at touch down on the trampoline than the 10kg cannonball you say this:

Obviously, but it started out with more

By rights what you suggest would ensure that the 100kg cannonball accelerates faster in free fall than the 10kg cannonball, and we know it doesn't...

The only means of describing the 2 differing mass value cannonballs bouncing to the same height when dropped from free fall onto their trampolines is to state that the 100kg cannonball has picked up more potential energy at h from M than the 10kg cannonball, to then convert into more kinetic energy than the 10kg ball will.  Hence the 100kg cannonball making a deeper dent in the trampoline when it bounces.

Apart from the fact of converting a negative aspect directly into a positive aspect, where mathematically speaking to arrive at a figure that isn't 0, potential energy must be being converted into a greater number/or value of kinetic energy units per potential energy units...
...secondly:

If the clock only has more energy on an observer dependent basis, then how come we can observe the physical consequences of the 2 cannonball converting potential energy into kinetic energy so that both the 10kg cannonball and the 100kg cannonball bounce off the trampolines to the same height?

If potential energy at h from M is only observer dependent, there would be no physical consequences such as observed of the differing values of cannonball mass's bouncing to the same height.

Furthermore, if light's frequency at h from M can be calculated, rather than observed, then why are you ignoring the calculation that states that the clock will be observed to have a higher potential energy at h from M?
If the clock has not converted that potential energy into kinetic energy, which it cannot because it is at rest with respect to the g-field, it will still have that potential energy at h from M...

[alancalverd]

I haven't calculated anything regarding time and frequency, just observed it - or, to be strictly true, quoted other people's reliable observations.

If your calculation doesn't match the observation, it's wrong. This is science, not economics. 

By rights what you suggest would ensure that the 100kg cannonball accelerates faster in free fall than the 10kg cannonball, and we know it doesn't..

nonsense. There are no "rights", only the universal law of gravitation and Newton's laws, which are mathematical summaries of the observation that all bodies accelerate at the same rate in a gravitational field. Since potential energy = mgh, the object with more m will have more pe. And since ke = mv²/2, the object with more m will have more ke. But as ke gained = pe lost, v will be the same at any point for any object dropped from the same height because m appears on both sides of the equation.  And thus it is.

The interesting question is why? 

As for elevated clocks, an observer next to the clock will see that it is keeping perfect time regardless of its gravitational potential. The problem lies with the clock at a lower gp, which appears to be running slower.

[timey (OP)]

Why do you say that a clock having a differing time is a problem!

GR clearly marks out that time runs at differing rates at differing gravity potentials, SR uses motion related time dilation in its maths, and the equivalence principle is quite clear that an observer with the clock will observe its frequency to be 9,192,631,770Htz, i.e ticking normally.

I certainly don't have a problem with a clock running fast or slow.  What I am looking at is 'why'.

I have not made any calculation.  I don't need to.
Clearly the clock held at rest with respect to the g-field at h from M will have more gravity potential energy than another clock held at rest wth respect to the g-field at a lesser h from M will have...

Yet physics states the frequency of the clock observed in the other gravity potential as observer dependent, and that if one places oneself with the clock in the other gravity potential that this observation disappears like some sort of mirage and the clock in the other gravity potential is ticking normally.

All I am saying Alan is that if one considers that when one is in a higher gravity potential with the clock held at rest with respect to the g-field at h from M, that all mass has more gravity potential energy at that h from M compared to mass located at a lower gravity potential, and therefore a higher frequency, and that if one measures the frequency of the elevated clock via the tick rate of the elevated clock, rather than the tick rate of the clock on the ground, then the elevated clock will have a frequency of 9,192,631,770Htz instead of the slightly higher frequency observed of the elevated clock from the ground, where the ground clock is now observed from the higher gravity potential as ticking slower.
But the clock on the ground measured via the tick rate of the clock on the ground will also have a frequency of 9,192,631,770Htz.

Therefore the tick rates of a clock observed of another gravity potential are really ticking faster or slower, and the frequency and the energy observations of the clock in the differing gravity potential to one's own location are not observer dependent, but are really occurring.
Then it is the observation of one's own clock that is observer dependent, because when measuring one's own clock, one is doing so by the tick rate of the clock one is with, and the mass of one's body also has the potential energy of the potential one is located in and will age in keeping with their time dilated clock, thus giving 'physical cause' for aging in keeping with a time dilated clock.
Then we can go on to look at SR motion related time dilation as being kinetic energy related.

[alancalverd]

Too much faith. What do you mean by "really" ticking faster or slower?

The essence of science is absolute honesty and humility. There are no special places in the universe. All you can say is "From where I'm standing, the other clock appears to be running slow", and the other guy says "and yours appears to be running fast". If we know the clocks are identical, we can deduce that they are at different gravitational potentials.

Why is it a problem? Because if you don't know the magnitude of the offset, your satnav won't work and you will misidentify the spectrum of a distant star.  Fortunately we can calculate GR and SR corrections for nearby phenomena, and we can recognise spectral patterns from which we can deduce the mass or speed of distant objects.

Not a good idea to try to deduce time dilation from kinetic energy because ke is specific to each object (being a function of m) whereas time dilation is the same for all objects at a given speed or potential, so why mess about multiplying by m and then dividing by it? 

[timey (OP)]

I mean that the clocks are really ticking at different rates in differing gravity potentials, and that clocks are really ticking at different rates in relative motion.

There is no special place in the universe, but there are differing places in the universe.

And having deduced that your clock and my clock are identical, and that we both see each other's clock as ticking at a different rate to our own, we can with all honesty and humility ask why, and then try and figure it out.

No - what we have is a system of two sets of mathematics, namely GR and SR, which are the best we can do so far to attach physical meaning to cosmological observation.

Free fall and escape velocity is also the same for all m at any given potential...
Acceleration is calculated as per F=ma, and speed is a byproduct of acceleration.
The cannonballs bouncing on their trampolines are reliant on an m calculation, but result via proportionality to a physically equal result.
Why would time dilation be any different?

If the 100kg cannonball dropped into free fall has more potential energy to start with than the 10kg cannonball, then all that is occurring is a proportional conversion of gravity potential energy into kinetic energy per mass unit.  The cannonballs accelerate in free fall at the same rate, and they bounce off trampoline to same height.

The same can be said of adding a non-gravity related accelerative force to m.
F=ma where in racing terms if an engine has a certain Force, then reducing m will increase a, and adding m will reduce a...
Add m without reducing a and F increases.  Reduce a without reducing m and F decreases.
It's a proportional relationship reliant on an m calculation, but F in relation to m and the resulting a are equal per unit of mass.
Again - why would a time dilation calculation reliant on F in relation to m and a be any different?

[alancalverd]

We know why. It's all in GR and SR. They are based only on the observation that the speed of light is constant for all observers. Maxwell explains why this is so. 

We don't "deduce" that our clocks are identical: we do experiments with identical clocks and find that the predictions of GR and SR are correct.

Dunno what you mean by "physical meaning". We make observations, we interpret them, we make explanatory and predictive hypotheses, we test them with more observations. There is no "meaning", just nature doing its thing. 

[timey (OP)]

No - its not all in GR and SR.  Relativity does not describe all the observations of the universe.  And in addition to not describing all the observations of the universe, in describing the observations it can describe by the mathematical means it employs, not only do these mathematical means not give any physical cause and effect for gravitational acceleration or time dilation, relativity is also reliant on dark energy and dark matter otherwise it is not a valid theory.

Again I repeat - Maxwell describes why the speed of light is the speed of light, but Maxwell could not unite his mathematics with gravity.

Yes - GR and SR predictions have been experimentally verified, but the physical cause for these predictions is still lacking.

Meaning - sorry wrong word... Relativity 'interprets' observation, and on the basis that one remain within the bounds of experimentally validated interpretation, one may make alternative interpretations for 'further' description, and this does not negate the possibility of re-interpretation of observation concerning the deductions made on the basis of experimentally unverified interpretations, nor attributing physical cause where non has so far been attributed.

It's called progressive thinking, and that's just a human mind doing its thing.

[timey (OP)]

As with F=ma, the speed-distance-time formula is also a proportional relationship...

Where:
If one holds the period of time traveled in as constant and increases speed, distance travelled is greater.
If one holds distance travelled as constant and increases speed, the period of time travelling in is lesser.
So here we see that:
When rendering speed as a variable, one is holding time periods (length of second) and distance lengths (value of a metre) as being constant

But to say...
If one renders distance length (value of metre) as a variable, that one can hold time periods (length of seconds) and speed both as constants.
...this is not physically possible.
Therefore we say that:
If one renders distance lengths (value of metre) and time periods (length of seconds) as variable, one may hold speed as a constant. (SR)

But it 'is' physically possible to say:
If one holds time periods (length of seconds) as variable, one can hold distance lengths (value of metre) and speed both as constant.

And then by applying this last remit to observation to attribute possible cause and effect becomes very interesting Alan.  Very interesting indeed!

[alancalverd]

If you say so.

[timey (OP)]

Been saying so here for about for 2 years now Alan.
Surprises me that you haven't noticed...

[timey (OP)]

So when a physicist observes that my clock is running slower than his clock, and I observe that his clock is running faster than mine, and he tells me that we can deduce that we are in differing gravity potentials - does this mean that we are experiencing differing amounts of gravity potential energy?