(How) does the LIGO experiment falsify Newtonian gravity?

[EnumaElish]

Sorry for the amateurish setup that follows. Here's my thought experiment. Consider a 2-dimensional universe on the Cartesian plane. Earth is located at point (0,0). There is a binary system {A,B} oscillating around (1,1). To simplify, assume that the oscillation is 1-dimensional and occurs on the line segment between point p = (1 - ε/√2, 1 - ε/√2) and point p* = (1 + ε/√2, 1 + ε/√2). When A is at p, B is at p*. A approaches (1,1) from below and B approaches (1,1) from above. They cross at (1,1) and travel onward, A toward p* and B toward p. Because of Newton's inverse-square law, their tug is larger when the two bodies are separated at p and p* than when they both are at (1,1). From "earth," the distance to (1,1) is √2. Earth's distance to p is √2 - ε and its distance to p* is √2 + ε. For α ∈ [0,ε], the total tug on Earth is proportional to t(α) = 1/(√2 - α)^2 + 1/(√2 + α)^2. When A and B are at (1,1), α = 0 and t(0) = 1. When A and B are at p and p*, α = ε and t(ε) = 1/(√2 - ε)^2 + 1/(√2 + ε)^2, which exceeds 1 for all ε > 0. So under Newtonian physics the tug is not constant. Its strength rises and falls following a quadratic function. How do we know that what LIGO is measuring is not the ebb-and-flow of the Newtonian tug? Thanks.

 

[Paul Colby]

It would be interesting to work the numbers. As you see the "tug" falls off faster than $\frac{1}{R}$ because it's a near field effect. I think what you'd find is those black holes would have to be much much closer to us than is likely to get the level of effect seen. My guess is we would have noticed them by other means.

 

[PeterDonis]

How do we know that what LIGO is measuring is not the ebb-and-flow of the Newtonian tug?

First of all, I think you might be confusing the black hole merger that LIGO measured with binary pulsar systems, which are known to emit gravitational waves from indirect evidence but we have not directly detected the GWs they emit (they are considerably weaker than the ones LIGO detected). What you are describing is a basically constant "oscillation" as two objects mutually orbit each other. What LIGO measured was not a constant "oscillation" of two objects mutually orbiting each other, but a rapidly increasing oscillation (the two black holes spiraling into each other), then a quick burst (the holes merging), then a decreasing oscillation (the "ringdown" as the new, larger hole formed by the merger settled down into a stationary state).

Second, the ebb and flow of the Newtonian component of gravity would not cause the kind of oscillations that LIGO measured. Oscillations in the strength of Newtonian gravity would be longitudinal--you would expect objects to move towards the source, then away, then towards, then away, as the distance to the source decreased (making the Newtonian force stronger), then increased (making it weaker), then decreased, then increased, etc. But the oscillations observed by LIGO were transverse--the mirrors at the ends of the arms moved perpendicular to the direction of the incoming wave. Also, the two arms, going in perpendicular directions, did not oscillate in phase, but 180 degrees out of phase--heuristically, one arm was getting squeezed while the other was getting stretched, and vice versa. This kind of oscillation can only be explained by gravitational waves--i.e., by the particular prediction that GR makes for this scenario. There is no way to predict oscillations like this using Newtonian gravity, or using the Newtonian approximation in a GR framework. They are a new and different kind of effect.

 

[Paul Colby]

Also, the two arms, going in perpendicular directions, did not oscillate in phase, but 180 degrees out of phase--heuristically, one arm was getting squeezed while the other was getting stretched, and vice versa.

I agree that this is the effect due to gravitational waves, however, it's my understanding that the interferometer measures the relative length change between the two arms. Wouldn't the same experimental signal if only one arm moved?

 

[PeterDonis]

it's my understanding that the interferometer measures the relative length change between the two arms.

It measures the interference pattern at the detector, which basically corresponds to that (at least in the most commonly used coordinates--there are a lot of technical issues lurking here which are probably out of scope for this thread). See further comments below.

Wouldn't the same experimental signal if only one arm moved?

No. There would still be an interference pattern, but it would be different.

Also bear in mind that we have two LIGO detectors, whose arms are in different relative orientations (because they are at different places on the spherical Earth). We know the times of arrival of the signals at each detector, and the relative amplitudes and phases of the signals. Also, we have the waveforms--i.e., the variation in amplitude and frequency with time--from each detector. All of that data can be used to determine (at least approximately) the direction of the incoming wave and the transverse and longitudinal components of the arm oscillations, and their time variation. The data is consistent with the kind of transverse oscillation that is predicted for gravitational waves, and is not consistent with the kind of longitudinal oscillation you are describing.

 

[Nugatory]

It's worth noting that other observations have falsified Newtonian gravity as an alternative to GR, even long before we ever had the LIGO result. Thus, we would reject Newtonian gravity even if we could find a way of explaining the LIGO results in a way that agreed with it.

This recent thread has some more discussion on why we continue to seek experimental confirmation of all the predictions of GR.

 

[PeterDonis]

we would reject Newtonian gravity even if we could find a way of explaining the LIGO results in a way that agreed with it.

This is true if by "Newtonian gravity" we mean the theory of gravity that we had before we discovered GR; but the OP's question can actually be formulated in the context of GR, as something along the lines of "why can't the signal LIGO detected be due to longitudinal oscillations due to variations in the distance to the source?"

It is true, though, that if we restrict ourselves to the weak field, slow-motion limit of GR, which is the only context in which a "Newtonian" view of gravity makes sense as an approximation, we will predict waves of any kind that are so weak that we have no hope of ever detecting them, whatever their detailed nature. To get gravitational wave signals that have a chance of being detected, you have to have strong fields at the source, and such cases can't really be analyzed in the Newtonian terms the OP uses, except in a loose, heuristic sense, which is all I've really tried to do in this thread.

 

[Vanadium 50]

The Newtonian "ebb and flow" is 22 orders of magnitude weaker.

If you say, "Maybe the source is wrong, and the real source closer", it has to be much closer: like around Pluto. Such a massive object would have been noticed - indeed, the whole Solar System would orbit around it. If you make it smaller, it needs to be closer still. Earth-sized, it needs to be closer than Venus. Moon-sized, it needs to be closer than the moon.

Sorry, there's no way to get a Newtonian signal of the right magnitude.

 

[Paul Colby]

Sorry for the amateurish setup...

I spent a couple years looking at various alternatives to interferometers as a means of gravitational detection so I feel I have a more than passing knowledge of some of the issues involved. While the replies given are all well intended and in some limit accurate I feel they miss the experimental issues raised by quite a margin. For example how precise or accurate is the time of arrival of a noisy signal restricted to an audio frequency bandwidth? Enough to determine the direction and speed of propagation of the GW? The reason to ask this question is the very same one that motivates yours. How does the LIGO experiment falsify Newtonian gravity. It certainly does when taken with all the other facts that are known and one can simply accept this as fact and move on. Or one may use this as an opportunity to work the numbers behind the experiment and learn.

 

[PeterDonis]

how precise or accurate is the time of arrival of a noisy signal restricted to an audio frequency bandwidth? Enough to determine the direction and speed of propagation of the GW?

Have you read the published papers by the LIGO team? All of these questions are addressed there. Also there are several recent threads here on PF discussing these issues.

It certainly does when taken with all the other facts that are known and one can simply accept this as fact and move on.

Exactly. The LIGO experiment by itself was not intended to falsify Newtonian gravity; it was intended to confirm a specific prediction of GR, that gravitational waves exist and should be detectable from certain sources, of which the merger of two large black holes was one of the main possibilities.

Or one may use this as an opportunity to work the numbers behind the experiment and learn.

All of the numbers are in the published papers.

 

[EnumaElish]

Not to leave this stone unturned: what if they do not accurately have the [masses] of the objects involved? E. g. their true [masses] were orders of magnitude smaller than simulated or inferred?

 

[Vanadium 50]

But their masses are the same?

 

[PeterDonis]

what if they do not accurately have the size of the objects involved? E. g. their true sizes were orders of magnitude smaller than simulated or inferred?

By "size" do you mean mass?

 

[Nugatory]

Not to leave this stone unturned: what if they do not accurately have the size of the objects involved? E. g. their true sizes were orders of magnitude smaller than simulated or inferred?

The LIGO observations match the GR predictions for frequency and amplitude of the gravitational radiation produced by the collision of two black holes of a given mass. To get a falsification the GR prediction, we would need to determine the masses of the objects through some other means, and find that they do not match the mass as calculated with GR.

Unless and until that happens, we have an observation that can be explained in two ways:
1) GR predicted that we'd find something if we looked, we looked, and we found it.
2) GR predicted that we'd find something if we looked, we looked, and we found something that looked exactly like what GR predicted but is in fact something different. This something is the result of some currently unknown new physics that happens to cause objects of a given mass to radiate exactly the way that GR says objects with very different masses would radiate.

With neither evidence to the contrary nor any idea what this currently unknown new physics might be, #1 looks like the better explanation.

 

[EnumaElish]

By "size" do you mean mass?

Yes, I meant mass. I've edited the question.