Einstein's Gravitational Time Dilation and Spectral Red  Shift
"Not everything that counts can be counted, and not everything that can be counted counts"  Albert Einstein ( 1879  1955 ) ( Sign hanging in Einstein's office at Princeton )
"When you can measure what you are speaking about and express it in numbers, you know something about it"  Lord Kelvin ( 1824  1907 )
Question: Is Time Dilation Actual Physical Reality or Merely Mathematical Sophistry?
The October 1971 Joe Hafele and Richard Keating Famous Experiment Using Four Cesium  Beam Atomic Clocks
testing general and special relativity time dilation on a British Airways Boeing aircraft
movie source: PBS's NOVA Science  "Time Dilation Experiment, October 1971"
source: J. C. Hafele and R.E. Keating, Science 177: 166  68 &168  70 ( 1972 )
Read: "Performance and Results of Portable Clocks in Aircraft", by J.C. Hafele
Also: "AroundtheWorld Atomic Clocks: Observed Relativistic Time Gains", by J.C. Hafele and Richard E. Keating, Science  Vol. 177, July, 1972
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§ Conclusion: Given different gravitational energy potentials located at different spacetime points, there are correspondingly different proper time intervals whose time dilation is still given by
Gravitational Red  Shift of Spectral lines
( gravity can change light’s frequency )
The Ever Expanding Cosmos is Red  Shifted
Calculating the Gravitational Einstein Red  Shift Originating from the Sun
Going back to
we shall completely neglect the Earth's gravitational field potential at its surface and simply look at the light emitted from the Sun's surface with frequency ( which is the same standard laboratory frequency created on Earth ) and therefore observed incoming onto the surface of the Earth having frequency .
and finally
Time  Dilation Experiments  

Experiment  Observed Object  Measured Red  Shift ( Fractional Frequency Shift ) 
Equivalent Red  Shifted Velocity ( effective velocity ) 

Daniel M. Popper ( 1954 ) ^{[1]} Dept. of Astronomy, UCLA 
red  shifted H  lines on 40 Eridani B 
7.0 x 10^{5}  20.99 km/sec  
Pound  Rebka ( 1959, 1960 ) ^{[2, 3]} Harvard 
red  shifted   2.5 x 10^{15} ( 1/2 of 5.13 x 10^{15} ) 
 7.5 x 10^{10} km/sec  
Jesse L. Greenstein et al. ( 1971, 1985 ) ^{[4, 5]} Hale Observatories, 1971 Mt. Palomar Observatory, 1985 
red  shifted H  lines on white dwarf Sirius B 
2.968 x 10^{ 4}  89.0 km/sec  
M.A. Barstow et al. ( 2005 ) ^{[6]} Hubble Space Telescope 
red  shift of the Balmer lines on white dwarf Sirius B 
2.68 x 10^{ 4}  80.42 km/sec  
Using Relativistic Red  Shift to Determine Velocity and Time
Some Astronomical Spectral Lines ( Fraunhofer lines )  

Line Designation  Due to element  Wavelength ( Å )^{[a]} 
Wavelength ( nm )^{[b]} 
Line Designation  Due to element  Wavelength ( Å) ^{[a]} 
Wavelength ( nm )^{[b]} 
A band  O_{2}  7593.70  759.370  L  Fe  3820.44  382.044 
B band  O_{2}  6867.19  686.719  N  Fe  3581.21  358.121 
C (Halpha)  H  6562.81  656.281  P  Ti^{+}  3361.12  336.112 
a band  O_{2}  6276.61  627.661  T  Fe  3021.08  302.108 
D1  Na  5895.92  589.592  t  Ni  2994.44  299.444 
D2  Na  5889.95  588.995  e  Hg  5460.73  546.073 
E_{2}  Fe  5270.39  527.039  e  Fe  4383.55  438.355 
F (Hbeta)  H  4861.34  486.134  b_{1}  Mg  5183.62  518.362 
G  Fe  4307.90  430.790  b_{2}  Mg  5172.70  517.270 
G  Ca  4307.74  430.774  b_{3}  Fe  5168.91  516.891 
H  Ca^{+}  3968.47  396.847  b_{4}  Fe  5168.91  516.891 
K  Ca^{+}  3933.68  393.368  b_{4}  Mg  5167.33  516.733 

For example, Andromeda X [ satellite galaxy of Andromeda ( M31 ) ] has been determined to lie at a distance of 2.9 M ly from the center of earth's solar system which would naturally be the sun where the entire Andromeda galaxy system is approaching Milky Way at a velocity of 300 km/sec. Two of the most prominent spectral lines are the H and K for ionized calcium. Choosing spectral K where its rest frequency is inverse to its rest wavelength provides the following:
We have = 393.368 nm for the observed lab rest  wavelength for spectral K. Let's say, hypothetically, that for this approaching Andromeda X satellite galaxy = 390.018 nm, the observed shorter wavelength by means of astronomical spectroscopy for element Ca^{+}. Therefore for "line of sight" relative motion [ see: Astronomical Doppler: Relativistic Red  Shift ],
Summary: Starry Night Reveals A Canopy of Clocks
( 'gravity time' or General Relativity time as opposed to Special Relativity time )
note: time is the measurement of the relative motion of bodies  Relativity Science Calculator
The previous mathematical explanations give a deeper understanding for 'time', whatever that is, and 'clocks' to show what sort of equation is involved in determining socalled 'gravity time' which is used in GPS engineering for submarines, cars, real estate developers, and so forth.
Clocks we know. But about socalled 'time', we’re not so sure are we?
Here’s the best page for Special Relativity 'time': http://www.relativitycalculator.com/doppler_sound_light.shtml
Then once you comprehend Special Relativity 'time' employing distances away from the observer’s eye traveling at some velocity, then all there’s left to understand is when there's an enveloping field of gravity where gravity slows down clocks and human metabolisms. Take away a field of gravity, things such as clocks and human movement simply speed up. And different amounts of 'gravity intensities' will in turn effect accordingly different rates of progression for the hands of a clock to be exceedingly simplistic.
And, in a nutshell, the equation for enveloping gravity as it directly affects socalled 'time' is simply:
where c = speed ( not velocity! ) of light in a pure vacuum; G is a universal constant first set forth by Newton and later whose numerical value was actually discovered by Englishman Henry Cavendish in 1797; M is the mass creating the gravity field; and r is the distance into the portion of the enveloping gravity field ( could be more or less intense gravity ) to a specific point in spacetime.
Now the on top of the fraction is 'proper time' or "wrist watch time" attached to yourself. And is coordinate time of some clock at some distance traveling away from you as what would reside at a star. Therefore when you look up at a starry night, what you’re actually seeing is a canopy of clocks. Yes!! Each "ticking away" ( frequency emanations ) at a different rate depending on their position and velocity away or coming towards you. That’s why first go to: http://www.relativitycalculator.com/doppler_sound_light.shtml!
All of this is really very philosophical. Not just mechanical, formulaic physics or cold, austere mathematics. Rather: Philosophical!! Thank you Einstein!!
§ References:
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