[jeffreyH]

Timey have a look at state space representation. It is something that could be useful to you. Don't be put off by the fancy sounding name.
https://en.m.wikipedia.org/wiki/State-space_representation

[timey]

This is why mathematical frameworks such as GR and Quantum are of import.  Both are speculations that have been tested by experiment to be relevant.  Any further speculation as to how GR and Quantum may be unified would also have to be tested by experiment.  Note that speculation comes before experiment.  On the basis that GR has passed every test so far, we can use the premise of GR with some degree of confidence in order to further speculate.  It is by using the premise of GR that I have further speculated.

Theory is more often driven by observation than by speculation. When scientists do speculate it is from a position of knowledge of theoretical frameworks. The what ifs are informed.

My what ifs 'are' informed and are posed from a position of knowledge of theoretical frameworks.

Timey have a look at state space representation. It is something that could be useful to you. Don't be put off by the fancy sounding name.
https://en.m.wikipedia.org/wiki/State-space_representation

Thanks for the link.  A fancy name does not put me off, but the maths enclosed are quite 'rich'.  Can you explain why you believe this to be of import to me for the process of making a consideration concerning particles of mass being attributed gravity potential energy as to their position in a gravity field?

[jeffreyH]

Look under non linear systems. The pendulum is a gravitationally influenced system. It involves change in elevation and gravitational potential. Depending upon the length of the pendulum there could be marked differences in time dilation along the path of motion. Here you have SR meets GR.

[timey]

:Quora
The time perod for simple pendulum is inversely proportional to the square root of acceleration due to gravity.
Time period=2×pie×(l/g)^0.5
And acceleration due to gravity is inversely related to square of the distance from the center of the earth.
g=GM/r^2
Thus, higher the altitude, lesser the acceleration due to gravity, and greater the time period. And it will lose time.

I don't really think that increasing or decreasing the length of a pendulum has anything to do with time dilation.  The pendulum clock will 'lose time' at elevation which means it is running slow.  This is in contradiction to the GR remit of a clock running faster at elevation.

I think that if we want to look at GR meets SR, then, as I have previously suggested, we should look at the Shapiro effect testing of GR being consistent with SR.

[jeffreyH]

:Quora
The time perod for simple pendulum is inversely proportional to the square root of acceleration due to gravity.
Time period=2×pie×(l/g)^0.5
And acceleration due to gravity is inversely related to square of the distance from the center of the earth.
g=GM/r^2
Thus, higher the altitude, lesser the acceleration due to gravity, and greater the time period. And it will lose time.

I don't really think that increasing or decreasing the length of a pendulum has anything to do with time dilation.  The pendulum clock will 'lose time' at elevation which means it is running slow.  This is in contradiction to the GR remit of a clock running faster at elevation.

I think that if we want to look at GR meets SR, then, as I have previously suggested, we should look at the Shapiro effect testing of GR being consistent with SR.

The inputs for the above could equally well be objects falling in a gravitational or alternatively being supported against gravity.

[timey]

I'm quite sure these were pertinent consideration over 100 years ago, but since Einstein and other's too numerous to mention have done all the hard work for us?  For instance, I don't read about modern experiments testing GR and SR via the simple pendulum.  But I do read about experiments testing GR via the Shapiro effect, and I do read about even more modern experiments testing both GR and SR via atomic clocks.

Since the Shapiro testing of GR is consistent with SR, if one was interested in making comparison...this is an obvious avenue for investigation.

[alancalverd]

The period of a pendulum depends on the local value of g, so it won't work in deep space, free fall or orbit, where g = 0.

[timey]

The period of a pendulum depends on the local value of g, so it won't work in deep space, free fall or orbit, where g = 0.

I think you need to take this onboard...

http://www.yalescientific.org/2010/10/mythbusters-does-zero-gravity-exist-in-space/

But yes - a pendulum would not work in free fall, or orbital free fall.  A pendulum that is in deep space, but not in freefall, will hypothetically swing very slowly indeed to the tune of the nearest g-field.

(Btw Alan - I was lucky enough to catch a glimpse of the Red Arrows flying by in formation today.  Wonderful sight indeed!  Made me think of you...) 

[jeffreyH]

The period of a pendulum depends on the local value of g, so it won't work in deep space, free fall or orbit, where g = 0.

So you've never heard of the deep space pendulum trick?

[alancalverd]

What I think it is important to realise is that any photon that is emitted by the clock in the higher potential has been blueshifted by the time it is observed in the lower potential.  If you minus the magnitude of the blueshift then the clock isn't ticking faster.  General relativity states that the clock is indeed ticking faster.

Very unscientific. What we observe is blue shift, and we observe it to be dependent on gravitational potential difference. Those are the experimental facts. GR is a mathematical model of those facts. It can't "state" anything, but it can and does provide a consistent and accurate prediction "as if" spacetime is  warped by gravitation.

[timey]

Very unscientific

Cheers!

What we observe is blue shift, and we observe it to be dependent on gravitational potential difference

Could you scientifically tell me from which frame we observe the blueshift from?  This being my point.  Let me answer that for you.  It will be 'from' the lower potential.

Those are the experimental facts

Where the fact is that one will not observe the clock to be emitting blueshifted photons when one is in the higher potential 'with' the faster ticking clock, and the fact is that the mathematical framework of GR predicts that the clock in the higher potential 'is' ticking faster.

The mathematical framework of GR also predicts that the photon emitted by the clock in the higher potential will be gravitationally blue shifted 'by' its change of position 'from' the higher potential 'to' the lower potential, the lower potential being the 'only' frame that one will observe this blueshift from.

So - scientifically speaking Alan, since the mechanism of the clock is reliant upon frequency, and it can only tick faster if the frequency is increased from 9,192,631,770 Hz, can you please explain exactly what frequency of photon is being emitted by the clock in the higher potential?

[jeffreyH]

Ah groundhog day!

[timey]

Ah groundhog day!

Ah yes - An astounding display of scientific expertise there Jeff!  I'm nominating you for best physics moderator of the year award.     

[yor_on]

I don't know Ken.

I'll cite this though.

"Remember that the intensity of an electromagnetic wave is defined as the wave’s power per unit area. Predictions based on the wave model of light include:

• Light (that is, electromagnetic waves) of any intensity should cause electrons to be emitted. If the intensity is low, it will just take longer for the metal to absorb enough energy to free an electron.

• The frequency of the electromagnetic waves should not really matter. The key factor governing electron emission should be the intensity of the light.

• Increasing intensity means more energy per unit time is incident on a given area, and thus we might expect both more electrons to  be emitted and that the emitted electrons would have more kinetic energy.

Amazingly, despite a century of success in explaining many experiments, the predictions of the wave model of light are completely at odds with experimental observations. "

What Planck introduced he himself thought of as a firstly 'mathematical trick'. It was Einstein that put it into context when he used Planck's formula for the spectrum of a black body to introduce the idea of 'photons', finite quanta instead of a wave. No longer a wave but quanta of energy interacting with electrons in that 'black body'.