I want to tell you about a few interesting predictions of the general theory of relativity.
One of those has implication for effectively everyday life now.
It turns out that if certain things predicted by general theory of relativity are not taken
into account when a GPS system is designed that you might have on your smart phone it
won't work properly.
General theory of relativity is not something that is out there that is understood only
by a small group of highly trained cosmologists, but its implications are relevant now for
everyday life.
Let me discuss two of those.
So important results of the general theory of relativity.
I said that basically the essence of this theory is that it's geometrical in a way.
The way the gravity works is that a mass bends space and time because the two are intrinsically
coupled and then objects move in that curved space along the paths of shortest distance,
so called geodesics.
It turns out that the following two things are also predicted first so called gravitational
redshift.
What it is, is suppose that I have a body of mass "M" and let us have a source of blue
light next to it.
It emits photons or electromagnetic radiation at the wavelengths corresponding to the blue
light, but as these photons are moving away from the source of gravitational force they
are losing the energy.
Remember the energy of the photon is inversely proportional to the wavelength.
As the energy is reduced the wavelength grows.
After a while it will become a green and after awhile it will become red.
As the photon escapes the gravitational pull by mass M, it loses energy.
As a result the wavelength of light increases and that is because the photon energy is given
as a ratio of some universal constant which is the product of Planck's constant and the
speed of light.
You don't need to know all these details, so right here the constant over the wavelength.
As the photon moves away, it loses energy and as a result the wavelength increases.
As the energy is reduced, that means that it is equivalent to saying that the wavelength
increases.
What I've drawn here is of course exaggerated.
In principle, this exists even in the case of light that I shine from a flash light into
the sky.
As those photons escape the gravitational pull of the earth, their wavelength in principle
also increases for the same reason.
However, the mass of the earth is not that great compared to a neutron star or a black
hole -- a massive black hole.
That increase in wavelength resulting from the photon escaping the earth gravity is tiny,
but it's there.
People can actually measure it, but it's much more pronounced this increase in wavelength
from blue to red if the source is near a very massive object such as a dense neutron star
or a massive black hole.
Now this type of redshift is different from what we discussed in Astronomy1PO1.
The redshift caused by so called Doppler Effect which is the increase in wavelength when the
source of light is moving away from the observer.
This is totally different physical reason for the redshift.
As you will see as we start talking about the cosmology, there is a third type of redshift
so called cosmological redshift.
That has to do with constant expansion of the universe.
As the universe is expanding, imagine you have a surface of a balloon and you draw a
wavy line on the surface of the balloon.
As you put in more air, as the size of this three dimensional universe which is the surface
of the sphere increases what will happen to that wavy that you drew it will get stretched.
The wavelength, the distance between two successive crests or troughs, will be increasing as the
space is expanding.
That's yet another type of redshift but we'll talk about that one later.
Please do not confuse this gravitational redshift with the one caused by the Doppler effect.
The second prediction is that the stronger the force of gravity the slower the clocks
run.
This is, of course, quite general.
Again we have a body of mass M. It could be our earth.
It could be a star like sun.
It could be a neutron star or a black hole.
This could be even the horizon of a black hole, the boundary.
Say I have two clocks at different distances from this body.
The closer the object is to this body, the more curved the space is or the stronger the
force of gravity.
The force of gravity on this clock here is stronger than the force of gravity on the
one that is at the greater distance from the body of mass M.
Say that this clock here shows three o'clock, then this one that experiences a stronger
force of gravity would be actually late.
It would be showing 10 to 3.
Yet, initially, before they were brought near this mass, they were synchronized.
That is, they showed the same time.
The one that is experiencing stronger force of gravity runs slower.
As I mentioned these effects need to be taken into account when the clocks are put on satellites
that are part of the GPS system.
The relativistic effects both of special theory of relativity GPS stands for...How does it
work?
This is the earth and there are altogether 24 GPS satellites and they are at an altitude
of about 20,000 kilometers above the surface of the earth.
They move at a speed of 14,000 kilometers per hour.
They're distributed such that from any given point on earth, four are visible but usually
more.
Because they are at the altitude of 20,000 kilometers, they experience a smaller force
of gravity than at the surface of the earth.
I turns out -- when you do the calculation -- that the clocks on the satellites run by
45 microsecond faster than the clocks on the earth.
One microsecond is 10 to the -6 seconds.
This is effect of general relativity as we've just mentioned.
Now because the satellites are moving at fairly descent speed, 14,000 kilometers per hour,
the special theory of relativity tells us that the clocks because they're moving relative
to us with the speed, should run by seven seconds microseconds slower.
This is, of course, faster per day.
The mismatch is 45 microseconds per day, 7 microseconds slower.
This is prediction of special relativity.
The net time difference between the clock on the satellite and the ground clock is 45
minus 7.
They run 38 microseconds too fast.
You can say this is nothing.
45 times one millionth of a second the whole day that's nothing, but not so, the speed
of light is very fast.
The way this works is as follows.
The satellites are constantly sending signals and the signal contains the information when
the signal was sent according to the clock on the satellite.
The GPS receives that signal and knows the time when it arrived.
From the difference between the two times when the signal was emitted and when it was
received, we know how long it traveled.
We know the time.
We know the speed with which it was moving -- which is the speed of light -- and therefore
we can calculate the distance to that particular satellite.
If we know the distances of at least four satellites in three-dimensional space then
we can actually pin point the location of a person on the earth.
Is this time difference of 38 microseconds really important?
It is, because the speed of light is 300,000 kilometers per second or another way to view
it is one foot per nanosecond.
The speed of light is about one foot per nanosecond and one nanosecond is 10 to the -9 seconds.
We have, in one microsecond, thousand nanoseconds.
Then the distance that light travels in 38 microseconds is...I have 38 microseconds which
is 38,000 nanoseconds.
This is the same thing as 38 microseconds times one foot per nanosecond per day.
That is 38,000 feet per day and that is about 11 kilometers per day.
If you didn't take into account these relativistic effects, after one day your distances would
be wrong by 11 kilometers.
What was done was that actually the atomic clocks on the satellites were slowed down
so that there was no mismatch of 38 microseconds between the clocks on the satellites and the
ground clocks.
That's why the GPS can work.
You can use it on your smartphone or the GPS in the car to locate your position and the
direction of motion with great accuracy.
General relativity is something that has effect on our everyday lives at the present time
with the current technology.
This whole thing would not work...Can you imagine the air traffic if there was an error
of 10 kilometers per day in locating the planes?
It would be chaos out there.