Relativity Science Calculator - Gravitational Time Dilation and Red Shift .
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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 )

Gravitational Time Dilation

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: "Around-the-World Atomic Clocks: Observed Relativistic Time Gains", by J.C. Hafele and Richard E. Keating, Science - Vol. 177, July, 1972
[ note: for those who cannot view this page whole, see quicktime or flash movie ]

§ 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 .

Therefore,

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
1  "Red Shift In The Spectrum Of 40 Eridani B", by Daniel M. Popper, UCLA, 1954
2  "Gravitational Red-Shift In Nuclear Resonance", by R. V. Pound and G.A. Rebka, Jr., Lyman Laboratory of Physics, Harvard University, 1959, Physical Review Letters publisher, Volume 3, Number 9
3  "Apparent Weight of Photons", by R. V. Pound and G.A. Rebka, Jr., Lyman Laboratory of Physics, Harvard University, 1960, Physical Review Letters publisher, Volume 4, Number 7
4  "Effective Temperature, Radius, and Gravitational Redshift of Sirius B", by J. L. Greenstein et al., Hale Observatories, 1971, The Astronomical Journal publisher, 169: 563-566,
5  "On the Redshift of Sirius B", by J. L. Greenstein et al., Palomar Observatory, 1985, Royal Astronomical Society, Provided by the NASA Astrophysics Data System, 26: 279-288,
6  "Hubble Space Telescope Spectroscopy of the Balmer lines in Sirius B", by M.A. Barstow et al., 2005, Hubble Space Telescope observations obtained at the Space Telescope Science Institute, analysis by sundry universities and institutes

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 O2 7593.70 759.370 L Fe 3820.44 382.044
B band O2 6867.19 686.719 N Fe 3581.21 358.121
C (H-alpha) H 6562.81 656.281 P Ti+ 3361.12 336.112
a band O2 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
E2 Fe 5270.39 527.039 e Fe 4383.55 438.355
F (H-beta) H 4861.34 486.134 b1 Mg 5183.62 518.362
G Fe 4307.90 430.790 b2 Mg 5172.70 517.270
G Ca 4307.74 430.774 b3 Fe 5168.91 516.891
H Ca+ 3968.47 396.847 b4 Fe 5168.91 516.891
K Ca+ 3933.68 393.368 b4 Mg 5167.33 516.733
a 1 Angstrom = 1x10-10 meter = 0.1 nanometer
b 1 nanometer = 1x10-9 meter = 10.0 Angstrom

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 so-called 'gravity time' which is used in GPS engineering for submarines, cars, real estate developers, and so forth.

Clocks we know. But about so-called '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 so-called '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 space-time.

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:

1.  "Weighing The Non - Transiting Hot Jupiter tau Boo B", by F. Rodler, M. Lopez - Morales, and I. Ribas, June, 2012, Astrophysical Journal Letters publisher. This is the first  for a non-transiting planet and most impressive example using some of the equations already demonstrated here in this web page, especially and in particular , in determining a planet's mass by means of examining its light from a distance of 50 light - years away!! Amazing, simply amazing!

2. "The Theory of Relativity", 2nd edition, by R.K. Pathria, Distinguished Professor Emeritus University of Waterloo, Dover Publications, Inc.

3. "General Relativity and Gravitational Waves", by J. ( Joseph ) Weber, Professor of Physics, University of Maryland, 2004 Dover Edition of an unabridged republication in 1961 by Interscience Publishers, Inc., New York

4. "Introduction to Tensor Calculus, Relativity and Cosmology", by D. F. Lawden, Emeritus Professor, University of Aston in Birmingham, U.K., Dover Publications, Inc.

5. "Relativity: Modern Large - Scale Spacetime Structure of the Cosmos", Editor Moshe Carmeli, formerely of Ben Gurion University, Israel, World Scientific Publishing Co. Pte. Ltd.

6. "Feynman Lectures on Gravitation", by Richard P. Feynman, Fernando B. Morinigo, and William G. Wagner, Edited by Brian Hatfield, Forward by John Preskill and Kip S. Thorne, 1995, Addison - Wesley Publishing Co.

7.  "Experimental Tests of General Relativity", by John Mester, Stanford University, 2006

8.  "Time Dilation Near the Earth", Space Math, NASA

9.  "Gravitational redshift of galaxies in clusters as predicted by general relativity", by Radoslaw Wojtak, Steen H. Hansen & Jens Hjorth, Dark Cosmology Centre, Niels Bohr Institute, University of Copenhagen, September 29, 2011

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