# 2 Questions RE: LIGO Gravitational Waves

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1. Feb 22, 2016

### Cuboctonion

I have a couple of questions regarding the new detection of signals believed to be gravitational waves at LIGO

1. Two similar signals were detected at both facilities. Why does the Livingston signal appear to be weaker than the Hanford signal?

2. The signal in Livingston was reported to have been detected 7 milliseconds after the Hanford signal. How can this be possible if gravitational waves are supposed to travel at the speed of light? Is there just a margin of error involved, or does this imply that g. waves actually propagate at a different speed than predicted?

2. Feb 22, 2016

### Ibix

The detectors have different orientations, so their responses to gravitational waves from a particular direction are different. Think of a wooden bead on a straight wire as a water wave washes over it. If the wire is mounted vertically the bead will bob up and down. If it's mounted horizontally and perpendicular to the wave front it won't even twitch. Anything in between will respond by different amounts. This is analogous to what's happening with the LIGO detectors.

A signal propagating at the speed of light could produce a delay between 0 (if it travels perpendicular to the line between the detectors) and 10ms (if it travels parallel to the line between the detectors). I gather the observations put a hard upper limit of 1.7c on the speed of gravitational waves, and a lower limit below c. This is consistent with a velocity of c. Also there is no dispersion measured, which is difficult to explain unless they travel at c without dumping everything back to Maxwell. So, evidence, but not yet conclusive. More events and more detectors will improve the data in the future.

3. Feb 22, 2016

### BvU

Hello Cub8,

How far does light travel in 7 ms ?

4. Feb 22, 2016

### Cuboctonion

Ibix,
Thanks for your explanation. That actually makes a lot of sense the way you put it. I think I was originally thinking of it as being either perfectly vertical or horizontal without taking into account all of the possibilities in between!

One thing I still don't understand though.. You mention the figure 1.7c, and this is something I keep seeing, but you say that if the wave propagates at 1.7c it is still consistent with the velocity of c. (Also, that there could be a lower limit less than c)... If gravitational waves are expected to travel at c, how can it travel at 1.7 c and still be considered to be traveling at the speed of light? Or, in the same way, how could it go slower than c but still be considered to be consistent with the velocity of c? Also, how can anything be said to travel faster than c?

5. Feb 22, 2016

### Cuboctonion

Thank you BvU!

My quick estimation was about 1300 miles, compared to about 1860 miles from Hanford to Livingston (is that about right?), but mostly I was going off the figure of 1.7c I keep seeing for the idea that the supposed g. wave was not traveling at precisely the speed of light.

6. Feb 22, 2016

### BvU

The experimenters have a $\Delta t\over \Delta x$ with uncertainties. If the source is on the extension of line between the observatories you expect a big $\Delta t$, if it is on a perpendicular you expect zero.

7. Feb 22, 2016

### Ibix

I don't think anyone is expecting the speed to be anything other than c. But we don't like to assume and there has been the odd upset over the years.

This experiment is not telling us that the speed is 1.7c, only that it is not greater than 1.7c. The difference in arrival times is proportional to the extra distance the waves travelled to reach the second detector - that is, how much further from the event the second detector was. That extra distance could be anything up to 10 light milliseconds, the straight line distance beteeen the detectors, depending on the angle the waves came in at. The actual delay then puts an upper bound on the speed - in this case 10/7=1.4c. I'm working with rounded numbers and not accounting for errors at all, which is why I'm not getting the more conservative 1.7c. But that's basically where the limit comes from.