Relativity Question

Ok, I have to admit that I had to look this up. So rather than spilling the beans, I'll say only that many of us have not just fathers, but also aunts... or uncles. Is that obtuse, or what?

Seems to be a right triangle to me fris.

Very good!!

It relates to the same phenomenom as the relative air speed velocity of an African versus a Eropean Swallow, That's all I'm saying.

Ahhh...an un-laden sparrow!

Speed of light!

The GPS satellites are quite high and quite slow moving - 12 hour orbits. Without looking up or calculating actual values, I can recall that the (lesser) gravitational time dilation at their altitude cause the GPS clocks to run faster than ground clocks. This difference more than offsets the (opposite) velocity time dilation on-board the satellites. Both effects are carefully calculated and implemented into the GPS timing system.

Jorrie is darn near spot on, I believe. Unfortunately, I, unlike him, had to look it up.

My obtuse reference to relatives was that one effect falls into the special relativity area, one falls into the general relativity.

Great question, which if it were not for the Web would have had me stumped.

Another way to look at this is: if you stick an 'earth-clock' on a tower at the North Pole, as high as the satellites, the satellite clocks would be recording less time than this high-ground clock - in agreement with the twin-paradox. You can read more about the twin paradox here.

The earths gravity is affecting the clock!

Hi !!

I wonder why no one is thinking about application of theory of reletivity in reverse. As mentioned in the above message when one of the twin brothers travels at a speed near to the speed of light and leaves the earth, his age and clock will slow down. Thus when he will return to earth he will be much younger to his twin brother. This is what is said ands explained many times to us earlier.

But I wonder, why the process of slowing the time and age will not be reversed when he return to the earth. For reaching to the earth heis speed has to be lowered, and as per theory of relativity his clock must run faster.Ageing process also shoud be faster.

In fact in both the cases i.e. Going away from earth at a high speed and returning to the earth at a lower speed, the effect should nullify. Isn't it ?

Any answer ?

V.S.Dave

Quote: "In fact in both the cases i.e. Going away from earth at a high speed and returning to the earth at a lower speed, the effect should nullify. Isn't it ?"

Not quite. The time dilation depends on the square of the speed and not on the direction of travel. Going away from Earth at high speed causes less time to elapse for the traveler. Returning at low speed will cause more time to lapse for the traveler, but not more than for the twin that stayed at home.

What I'm getting from all this discussion is that 'going FAST keeps us young!' ... *G*

This is another example that shows how using atomic decay to measure time needs to be checked against other time measurement techniques to better assure correct information.

Hi,

Yes, I believe Jorrie has it right. The velocity effect would slow the clock down, but the gravitational effect speeds it up much more.

What concerns me at the moment is the comment by halldavidl about atomic decay. While I certainly agree that any operational metrology reference needs to be backed up to check for failures (even GPS!) atomic clocks have nothing to do with atomic decay. I want to reinforce that even though atomic frequency standards (which is what they are) have the word "atomic" in them, they have nothing to do with atomic energy or weapons, which are involved with radioactive decay.

Atomic clocks put out frequencies (whose cycles are counted up to produce time) based on two principles: 1) atoms are in discrete energy levels, 2) energy is proportional to frequency. Atomic frequency standards work by locking a frequency to the energy of transistion between two atomic energy levels. None of the atoms involved with the standards are radioactive.

A little more detail on relativity: velocities in special relativity are generally relative to an inertial observer. The Earth's equator is moving at about 465 m/s (meters per second) relative to an inertial reference frame at Earth's center. GPS satellites are moving at about 4000 m/s relative to the center. So GPS satellite's are time dilated by about 7100 ns/d (nanoseconds per day), ie they would run slower, relative to a hypothetical clock at Earth's center. However the total effect due to gravity plus this effect is that GPS clocks run FASTER by about 38575 ns/d. Older satellites were set to run slower by this amount, the so-called "factory frequency offset."

While a nanosecond is one-billionth of a second, hence irrelevent to human experience, since GPS uses electromagnetic signals travelling at the speed of light to support navigation and timing, being off 1 ns means 30 cm or about 1 foot in position.

GPS has turned relativity from an exotic theory to an engineering necessity. In navigating with GPS we find our position in space and time. The space-time continuum is also an engineering reality.

A good reference for Relativity in GPS is:

http://relativity.livingreviews.org/Articles/lrr-2003-1/

For more info about atomic clocks, GPS, relativity, as well as some strange new physics like quantum computing, go to the NIST Time and Frequency Division web site:

http://tf.nist.gov/

Hi Marc, a very nice summary you gave.

In a way, the GPS system is also a test for the so-called 'one-way speed of light'. Measurement of the speed of light is usually a two-way effort, so that the same clock can be used for the 'start and finish lines'. GPS relies on perfect 'one-way isotropy' of light's speed - otherwise the accuracies we obtain are not possible.

Jorrie,

GPS is amazingly complex. All types of errors are required to be compensated for. These errors include subtle effects like the ionosphere refractive effects, the troposphere's delay for the signal, multipath signal reflection, and ephemeris errors to name a few. Even the Earth has annomolies that must be compesated for. As you know the polar circumfrance is different from the equitorial, the Earth's gravitational field is not uniform and there are external impacts such as solar wind, moon, and the Sun that all play a complicated role.

Quoting 'Hero': "GPS is amazingly complex. All types of errors are required to be compensated for."

Agreed. One can imagine how the non-uniform gravitational potential complicates the general relativity correction for time! Fortunately, by accurately tracking the spacecraft's orbit, one can deduce the non-uniformities pretty well.

Very nice first post, Marc!