Frequency Shifting of Light

 

A great depiction of this physical phenomenon. Image courtesy of youstupidrelativist.com

 

MY EXPLANATION:

We have all heard of the doppler effect. If not, let me reiterate. Waves (light or sound) emitted by a moving object (a siren by an ambulance, for instance) will be shifted to a higher energy by the motion of the source (if, that is, it’s coming towards you). That is why you hear a higher pitch sound from an ambulance heading towards you. The same is true for light and is of huge importance to astronomy, since we can tell the relative motion of an object with respect to Earth by the light it gives off.

Well, Einstein showed us that effects we see due to an accelerated object look exactly the same as effects produced in a gravitational field. I am not going to cover the equivalence principle in depth, but will post a link to a quick explanation here. In my own words, it means this: in relativity, there is no difference between the physical effects experienced due to gravity, and the physical effects experienced when an object accelerates. A lot of the phenomena look the same.

Einstein showed us that the speed of light is constant in all reference frames. What does this mean? Well, to any observer the speed of light will always be measured at the same value (300,000,000 meters/second, or 186,000 miles/second). In order to climb out of a gravitational field (say, a GPS signal being sent to a satellite in orbit) light itself must expend energy. So let’s look at how this is accomplished (mathematically) for light.

A very handy, and useful equation, for light is:

c=f*λ

F in this case is the frequency of light, and λ is the wavelength. Frequency deals with how many cycles of the wave cross an area per time, and wavelength is the distance per cycle. The beauty of the equation above is that c is always the same number in vacuum (and not much smaller in air). If we know the frequency or the wavelength, we know the rest.

Einstein also told us that light is not just a wave, but a particle called photons. Before moving on, let me detail an equation that explains the energy of a photon:

Energy=h*f

H in the above equation is something called Planck’s constant (and is easily found in search engines, or physics book appendices). F, again, is the frequency of the photon. If energy is expended by a photon to climb out of the space-time depression (gravitational field) of a planet, then we will see this reflected in the equations. Since h is a constant in the energy equation, the only things that can change are E and f. Lower energy means a change in the frequency.

We can double check this with the knowledge that c must stay the same. So if the speed of light is the same, then the frequency will have changed. We call this red shifting, as the light has been shifted to the red (lower energy) end of the electromagnetic spectrum.


FREQUENCY SHIFTING OF LIGHT, IN A NUTSHELL!

A really handy way to think of frequency shifting is to think of a baseball being thrown from a moving vehicle. You may be familiar with this from basic physics courses, but I will reiterate the analogy.

Before release
The ball sits atop the truck, which is moving to the left at 3 meters/second. So the ball itself is moving 3 meters/second.

Now, the rider throws the ball with a speed of 6 meters/second (with respect to the truck) into the direction of motion. What happens? To a stationary observer, the ball is now moving 9 meters/second.

The ball has gained kinetic energy, more so than if the rider had thrown it at 6 m/s from a stand still.
The ball has gained kinetic energy, more so than if the rider had thrown it at 6 m/s from a stand still.

This works in the opposite way, as well. If the rider throws the ball behind them, against the truck’s direction of motion, it loses energy.

The ball, thrown against the direction of motion, loses speed. To the stationary observer, the ball is travelling 3 m/s.
The ball, thrown against the direction of motion, loses speed. To the stationary observer, the ball is travelling 3 m/s.

All of this is great, but what about light? Well, since it is understood that nothing can exceed light speed (300,000,000 meters, second), some interesting things happen. Photons travel at light speed, and no faster. Since any added energy can’t be put into speed, it has to go somewhere.

Remember the equation E=h*f. The only two varying quantities in this equation are the energy and frequency. When one changes, the other must! Below I will show a depiction of what is meant by frequency.

Image courtesy of rookshealthscience.com

Above we have a depiction of an electromagnetic wave, or light. The entire EM spectrum is considered light, just of different frequencies. I will use the words photon and light interchangeably, as it is understood that light behaves as both (depending how you are looking at it). The wavelength, as you see, is the distance between two waves. The frequency is a measure of how many times the wave (or light) crosses this imaginary axis that it propagates across. So, in the image, the frequency would be something like 4 (but normally, we have units of time as well, like 4 waves/second).

When a photon is emitted by a non-moving body, we have something like this:

The photon is emitted with a frequency depending on the process that produced it. Nothing too strange.
The photon is emitted with a frequency depending on the process that produced it. Nothing too strange.

But when the body that produces the photon is moving, interesting things happen:

The photon is compressed, so it’s frequency (number of times the EM field crosses the axis of propagation) is shortened. The added kinetic energy of the object is what increases the frequency. The same phenomenon for the ball works if the photon is emitted against the direction of motion. The energy loss is shown by a decrease in frequency.
The photon is compressed, so it’s frequency (number of times the EM field crosses the axis of propagation) is shortened. The added kinetic energy of the object is what increases the frequency. The same phenomenon for the ball works if the photon is emitted against the direction of motion. The energy loss is shown by a decrease in frequency.

What I have detailed here is commonly known as Doppler Shifting. You may know this effect from its manifestation with sound waves. It’s the same principle. Waves emitted in the direction of motion have a higher frequency, and waves emitted against have a lower frequency.

For modern astronomy, this phenomenon is very important. Astronomers can tell the direction of distant objects by the frequency shift of their emitted light. It is a way to help piece together the stellar neighborhood (and also works for distant galaxies).


A MORE REFINED TAKE:

We will need this diagram of the electromagnetic spectrum. Lower energy (more red) light is the lowest energy, and as we move to the right we increase the energy of the light. Image courtesy of www2.lbl.gov

The actual equation that tells us the expected frequency shift for a photon is shown below:

f=f0*(1+gh/c2)

The f here represents the frequency of the photon. The 0 subscript is the initial frequency of the photon. The g is Earth’s gravitational acceleration, the h is Planck’s constant again, and the c is the speed of light. So the only variable quantities in this equation are g and f (g can change if we deal with other gravitational sources, and depending on proximity to the Earth).

The Pound and Rebka Experiment took place in the 1960’s, and consisted of a light source at the top of a tower and a detector at the bottom. Comparing the mathematics to experiment, the researchers found a frequency shifted value that was within 1% of the expected value. Quite impressive! A dandy explanation of the experiment can be found here and here.


CURVED SPACE-TIME AFFECTS NOT ONLY LIGHT, BUT THE PERCEIVED FLOW OF TIME AS WELL!

Time Dilation