## Thursday, September 13, 2012

### Q: If Light is Stretched/Compressed by a GW, Why Use Light Inside LIGO?

Wow!  It's been a while since I've posted...  After the start of a new semester (I have 150 students in the class I am teaching at LSU) and Hurricane Isaac (which shut LIGO Livingston down for almost a week, LSU for 3 days, and left me without power for a while), I am just getting my life back to a somewhat normal routine.  I love even the hectic parts of my life, but I've missed writing about gravitational waves here on Living LIGO!

Q: IF LIGHT IS STRETCHED/COMPRESSED BY A GRAVITATIONAL WAVE, WHY USE LIGHT INSIDE LIGO?

Today I am addressing a question that many professional physicists fully don't understand!  I wrote a little while ago about how light and gravitational waves will stretch out as the Universe expands (this is called redshift).  If an object is coming towards us, its light is compressed (and this is called blueshift).  Basically, if objects are moving, light and gravitational waves will experience a Doppler effectI have also written about how a passing gravitational wave will stretch and compress space in perpendicular directions.  When you put these two facts together, you come to the conclusion that the light inside the arms of LIGO is also be stretched and compressed by a gravitational wave.  So, how can we use this light to measure gravitational waves when the light itself is affected by the gravitational wave?

Like I suggested earlier, this is not obvious upon first inspection.  The apparent paradox arises from thinking of laser light as a ruler.  When you think of light, you usually think of it as a wave (which it is, but light is also a particle - however that isn't relevant to this discussion).  Waves have a wavelength -- the distance between each successive wave:

 Illustration of wavelength (represented by λ) measured from various parts of a wave. [Source: Wikipedia]

A passing gravitational wave will expand and compress space-time and the wavelength of the light we are using to measure gravitational waves is itself affected by the gravitational wave.  Since LIGO and detectors like it effectively measure the length of its arms and compares them to each other,  how can we rely on light to measure any length changes from a passing gravitational wave?

The solution begins to become clear when you start thinking of the laser light as a clock instead of a ruler.  When the light comes out of the laser, there is a fixed time between each crest of the wave (this is called the period of the wave).  Let's label each crest as 'tick' (like a clock).  Our laser (labeled 'Laser' in the image below) is very stable in that it produces a very consistent wavelength of 1064 nm (near-infrared light).  Because the speed of light is constant no matter how you measure it, that means that there are almost 282 trillion (2.817 x 1014) 'ticks' every second.  This light is then split into two equal parts (at the 'Beam Splitter' in the image below), one for each arm.

 Basic diagram of the LIGO detectors.

Since different things can happen to the light once it is in the arms, let's reference the beam splitter for making length measurements (i.e., let the beam splitter stay in the same place while the gravitational wave alternates squishing and stretching the arms).  A real gravitational wave will cause one arm to shorten and the other to lengthen.  This will also cause the laser wavelength in the shortened arm to decrease (blueshift) and the wavelength in the lengthened arm to increase (redshift).  But there is nothing in the detector that measures wavelength.  What it really measures is the shift in the arrival time of each 'tick' of the wavelength crests.  If the arms stay the same length (no gravitational wave), then the 'ticks' of the laser light come back to the beam splitter at the same time and produces destructive interference where we measure the light (labeled 'Photodetector' in the image above).  If a gravitational wave causes the length of the arms to change and shifts where the 'ticks' of the laser light occur, the two light beams will no longer return to the beam splitter at the same time.  It is this "out of sync" arrival time of the crests of the laser light that produces the interference patter we utilize to detect gravitational waves - we couldn't care less about the actual wavelength of the light (other than it was consistent going into the detector).

READ MORE FROM OTHER LIGO SCIENTISTS:

A wonderful, concise summary on why light can be used in gravitational wave detectors like LIGO has been published in American Scientist here.  The author, Peter Shawhan, is an associate professor at the University of Maryland, College Park.

There is also an article in the American Journal of Physics (vol. 65, issue 6, pp. 501-505) titled "If light waves are stretched by gravitational waves, how can we use light as a ruler to detect gravitational waves?"  This is a more technical article by Peter Saulson who is a professor at Syracuse University.