The Implications of Failure to Detect Gravitational Waves

[x(x-y)]

I was wondering what the implications of the failure of Einstein's original prediction of gravitational waves would be - how far would this invalidate the theory of general relativity? Several professors and researchers at the university I read physics at are heavily involved with international collaborations to detect gravitational waves, and so this lead to me to think of how "bad" it would be for current established physics if it turns out that they do not exist*.

 

I don't mind if you include mathematics and fairly advanced physics in your replies, as I am currently studying physics at degree level - so I should be able to handle some of the stuff you throw at this thread! Although, I realise that some "physics experts" here have PhDs in different fields of physics so obviously I can only handle so much!

 

 

 

 

* Indeed, I am aware that they are incredibly difficult to detect (or so it seems) and so even if we do not detect them within the next 100 years that doesn't necessarily mean that they don't exist.

[elfmotat]

I would find it incredibly difficult to believe that gravitational waves don't exist, because they're not only required by General Relativity (which has passed every experimental/observational test to date) but they're also required by much-less-complicated linear gravity theories such as Linearized GR and Gravitomagnetism - both of which are valid in the weak-field limit.

 

If you're familiar with electromagnetism and Maxwell's equations, the easiest way to see this is with Maxwell-esque GEM equations. If frame-dragging exists (which Gravity Probe B has confirmed to ~15% uncertainty) then these effects can be encapsulated in a "gravitomagnetic field" B_g. The gravitomagnetic field is produced by mass-current in the same way that in EM the magnetic field is produced by charge-current. The gravitomagnetic field along with the traditional Newtonian "gravitational field" (which we'll denote by E_g) have four Maxwell-esque equations which determine how the fields are produced:

 

[math]\nabla \cdot \mathbf{E}_\text{g} = -4 \pi G \rho[/math]

 

[math]\nabla \cdot \mathbf{B}_\text{g} = 0 [/math]

 

[math]\nabla \times \mathbf{E}_\text{g} = -\frac{\partial \mathbf{B}_\text{g} } {\partial t}[/math]

 

[math]\nabla \times \mathbf{B}_\text{g} = -\frac{4 \pi G}{c^2} \mathbf{J} + \frac{1}{c^2} \frac{\partial \mathbf{E}_\text{g}} {\partial t}[/math]

 

In a vacuum these reduce to:

 

[math]\nabla \cdot \mathbf{E}_\text{g} =0[/math]

 

[math]\nabla \cdot \mathbf{B}_\text{g} = 0 [/math]

 

[math]\nabla \times \mathbf{E}_\text{g} = -\frac{\partial \mathbf{B}_\text{g} } {\partial t}[/math]

 

[math]\nabla \times \mathbf{B}_\text{g} = \frac{1}{c^2} \frac{\partial \mathbf{E}_\text{g}} {\partial t}[/math]

 

Now you apply the same method for finding the differential equations for gravitational waves that you would to find the equations for EM waves (using the curl of the curl "trick"):

 

[math]\nabla^2 \mathbf{E}_\text{g}= \frac{1}{c^2} \frac{\partial^2 \mathbf{E}_\text{g}} {\partial t^2}[/math]

 

[math]\nabla^2 \mathbf{B}_\text{g}= \frac{1}{c^2} \frac{\partial^2 \mathbf{B}_\text{g}} {\partial t^2}[/math]

 

The solution to these equations are plane waves.

Edited February 8, 2013 by elfmotat

[elfmotat]

I should also point out that the GEM equations aren't Lorentz invariant because mass density and mass-current density (momentum density) don't form a Lorentz invariant vector because they are some of the components of a rank-2 tensor: the stress-energy tensor. This is where gravity and EM differ, because charge-density and current density form an invariant four-vector (rank-1 tensor): four current. Thus, Maxwell's equations are compatible with relativity while the GEM equations are not (though they do agree to a good approximation).

 

The "correct" form of linear gravity is Linearized GR, in which the metric is a perturbation of the flat Minkowski metric:

 

[math]g_{\mu \nu}=\eta_{\mu \nu}+h_{\mu \nu}[/math]

 

If we compute the Einstein Field Equations in terms of this metric and drop all higher order terms of h_uv (and impose a gauge condition), then we obtain the Linearized Field Equations:

 

[math]\square \bar{h}_{\mu \nu}=-\frac{16\pi G}{c^4}T_{\mu \nu }[/math]

 

where [math]\square=\left (\nabla^2-\frac{\partial^2 }{\partial t^2} \right )[/math] is the d'Alembert operator and [math]\bar{h}^{\mu \nu}=h^{\mu \nu}-\frac{1}{2}\eta^{\mu \nu} h^\sigma_{~\sigma }[/math].

 

These field equations are Lorentz invariant. We also see that if we set the stress-energy tensor to zero (a vacuum) then we obtain a wave equation:

 

[math]\square \bar{h}_{\mu \nu}=0[/math]

 

So a gravitational wave is really just oscillating perturbations in the metric. We can actually derive the GEM equations from the Linearized Field Equations by specifying a coordinate system and setting various components of "h" equal to scalar and vector potentials.

Edited February 8, 2013 by elfmotat

[ajb]

I too would find it hard to believe that gravitational waves do not exist. They seem inherent in GR and we do have indirect evidence for them.

 

One must not confuse lack of evidence as evidence they are lacking. Gravitational waves are going to be very hard to detect.

[imatfaal]

I too would find it hard to believe that gravitational waves do not exist. They seem inherent in GR and we do have indirect evidence for them.

 

One must not confuse lack of evidence as evidence they are lacking. Gravitational waves are going to be very hard to detect.

 

When you say indirect evidence do you refer to the fact that we would have to account in another way for the energy lost in the decaying orbit of binary pulsars. The precision with which the decaying orbit met the predictions if the system was producing gravitational waves of the expected amount was pretty good - and getting better. Or is there further experimental evidence in the last 20 years or so?

 

The Nobel Prize in Physics 1993

Russell A. Hulse, Joseph H. Taylor Jr.

[ajb]

When you say indirect evidence do you refer to the fact that we would have to account in another way for the energy lost in the decaying orbit of binary pulsars. The precision with which the decaying orbit met the predictions if the system was producing gravitational waves of the expected amount was pretty good - and getting better. Or is there further experimental evidence in the last 20 years or so?

As far as I know, binary pulsars provide the best strong field test of GR. I think the accuracy has improved over the last 20 years, but I do not know of any other good tests. There maybe other forms of evidence, but this is outside my area of expertise.

[x(x-y)]

Right, interesting, that's a lot of information to absorb - I'll try to crunch my way through those links and the information posted here when I have time.

[imatfaal]

Nobel lectures are normally worth reading/watching - as a layman it is about the best access I can get to the depth and breadth of the ideas and work that are judged worthy of a nobel. they are never that technical and often amusing and touching.

[altergnostic]

I have never been truly convinced of any gravity hypothesis, and as far as I am concerned, there has never been a single realistic model in history. We went from pulling force at a distance to matter curving the geometry of spacetime, which has great predictive power but still zero mechanics, it is purely abstract. We have come to conclude that nature may perhaps only be accessible through abstract models and should quit trying to visualize all interactions and causes, because we are not equiped to understand nature intuitively. I resist that approach and rather believe that it is our models that are not well equiped to explain nature, and cling on to the hope that we can change this someday.

 

I would not be too surprised if the waves are never detected (I still don't buy the higgs detection is the higgs boson - with the predicted properties of the particle - but let's wait and see).

 

I think it was Maxwell that propesed the dimensions mass are L^3/T^2, so the dimensions of gravity (L^3/MT^2) effectively cancel out and it becomes just a number.

 

A Miles Mathis (taken as a crank by a large portion of the scientific comunity) used this to express all force in terms of length and time and dispense with any idea of mass. "The idea of acceleration already includes the idea of impermeability" he said, since you need a boundary to determine acceleration (or the shape of a rigid body, for that matter). His idea was that gravity was a reestatement of mass which is a reestatement of inertia - they are all effects of a single property: expansion.

He proposed that all bodies expand at the same rate, so all proportions are kept constant.

He didn't like this idea and used it as a mathematical tool in the end (reversing all gravity vectors by the equivalence principle).

 

I don't think that this expansion has any material meaning, but the dimensions of mass may point us in a new direction indeed, one in which gravitational waves play no part, if they end up being falsified.

 

 

[elfmotat]

I have never been truly convinced of any gravity hypothesis, and as far as I am concerned, there has never been a single realistic model in history. We went from pulling force at a distance to matter curving the geometry of spacetime, which has great predictive power but still zero mechanics, it is purely abstract.

 

Any mathematical model is purely abstract. Even in our simplest physical model, Newtonian mechanics, forces are represented by vectors which live in an abstract vector space.

 

Objecting to a theory because it's abstract is rather absurd. As you said, our theories have great predictive power. That's the measure of a good theory, not whether or not it conforms to your naive intuitions.

 

We have come to conclude that nature may perhaps only be accessible through abstract models and should quit trying to visualize all interactions and causes, because we are not equiped to understand nature intuitively. I resist that approach and rather believe that it is our models that are not well equiped to explain nature, and cling on to the hope that we can change this someday.

 

That's a rather strange viewpoint. Our brains evolved to intuitively understand a slow, macroscopic world. That is where all of our intuition comes from. Why would you expect fast-moving things, very small things, very large things, etc., to conform to the way our brains evolved? When you learn about physics after ~1900, you have to train yourself to develop an intuition for the math because it's generally not possible to "picture" what's going on.

 

To quote Feynman:

 

"...and then there's the kind of thing which you don't understand. Meaning 'I don't believe it, it's crazy, it's the kind of thing I won't accept.'

I hope you'll come along with me and you'll have to accept it because it's the way nature works. If you want to know the way nature works, we looked at it, carefully, that's the way it works.

You don't like it? Go somewhere else!

To another universe! Where the rules are simpler, philosophically more pleasing, more psychologically easy. I can't help it! OK! If I'm going to tell you honestly what the world looks like to human beings who have struggled as hard as they can to understand it, I can only tell you what it looks like.

And I cannot make it any simpler, I'm not going to do this, I'm not going to simplify it, and I'm not going to fake it. I'm not going to tell you it's something like a ball bearing inside a spring, it isn't.

So I'm going to tell you what it really is like, and if you don't like it, that's too bad."

[md65536]

What does it even mean for gravity waves to not exist? Would that require that changes in a gravitational field are instantaneous? Wouldn't it require a whole bunch of new theories (scrapping all of GR and SR probably???) to model how that could even be possible?

[ajb]

What does it even mean for gravity waves to not exist? Would that require that changes in a gravitational field are instantaneous? Wouldn't it require a whole bunch of new theories (scrapping all of GR and SR probably???) to model how that could even be possible?

Gravitational waves come from considering small perturbations in the local geometry, some sensible assumptions and the Einstein field equations. If there are no gravitational waves then this would signal a serious problem with general relativity. It would mean that the classical regime of gravity is not described by GR, but this seems at odds with all our other evidence.

 

 

I am not sure if the lack of gravitational waves would necessarily imply instantaneous action of gravity, but for sure we would be confronted with the task of finding the correct description of gravity.

[fenrislupusgrey]

(missed you today Angela but I will wait.) gravity and it's effect are not just a function of mass. a more detailed "ah ha" is gained by looking at M-Theory, String and faults), Action at a Distance (spooky) and gradient variation/expression.... and just pondering the poor cat.

 

lol...

 

 

cool thread though.

Edited March 3, 2013 by fenrislupusgrey