Gravitational Waves: Questions from Josh on Mass & Space-Time

[joswitz]

hello,

I was reading a recent article about gravitational waves and I had a few questions... I actually have a lot of questions, but I digress. Let me first start with what I think I know to be right, and then move on to the questions about the subject.

-Time and space are connected. This connection is represented by a fabric in which the universe is contained.
Mass is believed to interact with this fabric. What we call gravity is the result of mass and space-time interacting.. I've seen the taut sheet and bowling ball demonstration.

Is it more accurate to view space-time as a 2-dimensional plane, or to see it as a 3-D field in which things reside in?

The article I read also talked about how gravity waves traveled at the speed of light. I was wondering why this would be true? Why would space-time ripple? Water ripples when a stone hit it, and a sheet will ripple when you move the bowling ball, but how do we know that space-time has this property as well?

Thanks!
Josh

 

[Nugatory]

Try to forget that you ever saw that analogy of a bowling ball on a rubber sheet - it's one of those things that science writers have been repeating without understanding for a century now. You'll find some better explanations of how curvature of spacetime (not space!) leads to gravitational effects in some older threads here - look especially for diagrams and a video from member @A.T.

Is it more accurate to view space-time as a 2-dimensional plane, or to see it as a 3-D field in which things reside in?

Neither. It's a four-dimensional continuum (the technical term is "manifold"). It's hard to visualize four dimensions, but it is possible to visualize many of the most interesting effects of relativity by working in two dimensions, one for space and one for time. Google for "spacetime diagram" and "worldline" for many examples. Or (as this is an I-level thread) give Taylor and Wheeler's book "Spacetime Physics" a try.

Why would space-time ripple? Water ripples when a stone hit it, and a sheet will ripple when you move the bowling ball, but how do we know that space-time has this property as well?

Water ripples: From what we know of the physics of liquids like water, we can derive equations that describe the behavior of the surface of a body of water when it is disturbed. Solve these equations (standard fare in the second or third semester of an undergraduate physics degree program) and one of the possible solutions will be waves propagating across the surface. Perform experiments such as tossing a stone into a pond, and we see waves matching the ones predicted by the equations... And that's how we know about water waves.
Gravity waves: The equations that describe the behavior of spacetime are the Einstein field equations of general relativity. Solve these and one of the solutions is waves rippling through spacetime. Perform experiments such as setting up the LIGO detector and we observe waves matching the ones predicted by the equations... And that's how we know about gravity waves.

This analogy is not historically accurate, of course. We knew about water waves for millenia before anyone ever found the equations that said they had to exist, while with gravity the equations came first and the observation followed. But the outcome, mathematical theory supported by observation, is the same.

 

[Ibix]

As to "how can spacetime ripple", how can it not? There is a difference in spacetime near a massive body compared to far away - various gravitational effects are stronger. If a mass moves around then you are nearer and further away from it, so those gravitational effects get stronger and weaker. If the strengthening and weakening propagates at a finite speed you get waves of stronger and weaker gravitational effect rippling outwards.

Reality is a bit more complex. For example, other considerations mean that any old movement won't do. However, orbiting masses will produce waves. But they need to be enormous masses moving at incredible speed to get any emissions that we can detect.

 

[joswitz]

As to "how can spacetime ripple", how can it not? There is a difference in spacetime near a massive body compared to far away - various gravitational effects are stronger. If a mass moves around then you are nearer and further away from it, so those gravitational effects get stronger and weaker. If the strengthening and weakening propagates at a finite speed you get waves of stronger and weaker gravitational effect rippling outwards.

Reality is a bit more complex. For example, other considerations mean that any old movement won't do. However, orbiting masses will produce waves. But they need to be enormous masses moving at incredible speed to get any emissions that we can detect.

I think my issue is picturing it as it is traditionally presented to those who really don't know much about the subject matter. When I think of a ripple, I think something like a wave that is traveling in the ocean, or a sound wave. Honestly its hard for me to explain what it is exactly that I see differently about things like water and air as compared to spacetime. Perhaps its because water/air have other properties that we can measure.. And its my understanding that spacetime is only measured due to its consequence(s).

So with that being said I can understand how we could feel/measure a gravity-wave. I just know so little about the subject, and it would behoove me to actually read up on it from scientific sources. I appreciate your guys responses and i'll check up on your suggestion @Nugatory .

josh