Gravity Waves: Measure Spacetime Stretch with a Ruler

[Albertgauss]

Hi all,

On the website of gravity waves by PhD comics:



At minute 1 and 5 seconds to minute 1 minute 20 secs.

"Now if the spacetime between you and me stretched or compressed, we wouldn't notice it if we had made marks on our metaphorical sheet...because these marks would also get stretched."

Does this mean only for trying to measure the stretch of spacetime with a ruler?

I understand that gravity waves are incredibly weak, but if the stretching was significant, things would certainly spread out as I would perceive them, it seems, and I would at least notice that objects formerly close to me are now farther away? Is this correct?

 

[PeterDonis]

I understand that gravity waves are incredibly weak, but if the stretching was significant, things would certainly spread out as I would perceive them, it seems, and I would at least notice that objects formerly close to me are now farther away?

It depends on how you measure the distance. If you measure it with a ruler, the ruler would (at least to a first approximation) stretch with the wave. But only to a first approximation, because the ruler has internal forces between its atoms, which would resist the stretching. To make a detailed prediction of how the ruler would respond, you would have to know the details of the internal forces, which are very difficult to calculate.

The LIGO detector, which has been in the news because of its detection of gravitational waves (btw, the term "gravity waves" refers to a different phenomenon, one which has nothing to do with GR), uses a different principle: it has laser beams traveling back and forth along two arms. Stretching or squeezing of the arms due to a passing gravitational wave causes the round-trip travel times of the laser beams to vary, providing a measure of distance (lengths of the arms) that doesn't involve difficult to model properties of materials like a ruler does. (At least, this is how it looks in the most commonly used coordinates; since this is relativity, "length" and "time" are coordinate dependent, so one has to be careful when describing what is on.)

 

[pervect]

Hi all,

On the website of gravity waves by PhD comics:



At minute 1 and 5 seconds to minute 1 minute 20 secs.

"Now if the spacetime between you and me stretched or compressed, we wouldn't notice it if we had made marks on our metaphorical sheet...because these marks would also get stretched."

Does this mean only for trying to measure the stretch of spacetime with a ruler?

I understand that gravity waves are incredibly weak, but if the stretching was significant, things would certainly spread out as I would perceive them, it seems, and I would at least notice that objects formerly close to me are now farther away? Is this correct?

For a slow space-time stretch, a ruler will measure the same thing that the lasers Ligo uses. You could create "marks" by putting rocks way out in empty space far away from any mass, and use rulers to measure the distance between the rocks. The GW's would make the rocks move relative to the ruler, except at the midpoint of the ruler. So, the further away the freely-floating masses were from the center of the ruler, the more the masses would move relative to the ruler. Here on Earth, you'd need to hang the rocks from strings to counter gravity (rather than having them float weightlessly). You'd also need to carefully isolate these masses from vibrations and external influences of all sorts, and use extremely precise rulers. This is essentially how Ligo works, with the lasers acting essentially as very precise rulers.

A perfect ruler is a rather abstract concept that doesn't actually exist. Properly implemented, laser beams are an excellent approximation to a good ruler, even though they are not perfect. They are so good that they are essentially the basis for the SI definition of the meter, which is : http://physics.nist.gov/cuu/Units/meter.html
"The meter is the length of the path traveled by light in vacuum during a time interval of 1/299 792 458 of a second."

 

[PeterDonis]

For a slow space-time stretch, a ruler will measure the same thing that the lasers Ligo uses.

"Slow" here meaning "slow enough that the stress induced in the ruler does not have any measurable effect on its length". But this also implicitly assumes that the stretching is periodic (stretch, then squeeze, then stretch, then squeeze), which is true of a gravitational wave, and of small amplitude, which is true of a gravitational wave as long as the ruler is not too close to the source.