Is the inertia of a massive object the result of gravity wave generation?

[DarkMattrHole]

TL;DR Summary

Is some inertia of an accelerated object the result of energy transfer to gravity wave?

Hi all. I just watched a great video on gravity wave 'telescopes'. So i have been wondering if any of my intuitive hunches are right about gravity waves.

Accelerated masses generate gravity waves that dissipate energy..
So let's say i turn my rocket ship engine on while sitting in deep space, and accelerate in a straight line at a comfortable one G -

A) does a small gravity wave begin outward at speed C at engines ON - a crest or pressure incline that sets the gravity field slightly away from zero (warp space-time), using some energy to do it, thereby resisting the ship from moving (draining the energy from the engines), as long as the acceleration persists? transferring the energy of the engines into the energy of the warp or wave in space-time emitted by the ship? Is any of that even close to what really happens? At any level at all?

How much of the energy put into throwing a baseball goes into the gravity field waves that result from accelerating it's mass? How do we know the percentage?

This could be wildly wrong, but I picture that as you constantly accelerate a mass (that is bends space-time), you twist space-time asymmetrically and compress it or stretch it one way or the other along the axis of accelerated velocity. This applied tension takes energy. For analogy, like twisting a guitar string and holding it twisted, a very long guitar string so when you twist and hold the string, the extra energy or rise in tension actually takes 'a while' to propagate down the wire, so it travels as a wave or ripple of extra tension. When your fingers run out of energy the twisting stops, like an engine turning off, the warp (wire) tension drops locally, and this drop travels down the wire, following after the earlier rise that propagated, and the result is a wave shape of some kind that propagates down the endless wire, or outward into space if you are in your spaceship. It would be great to know how far wrong this is and what the correct description is. sorry about the mixed analogies. Thanks for a great forum.

 

[Dale]

Accelerated masses generate gravity waves

This is not generally true. To generate gravitational waves you need to have a varying quadrupole moment. Linear acceleration of a single mass does not have that.

To get a quadrupole moment you need to have something like a pair of orbiting masses or a spinning barbell or stick.

 

[Ibix]

You can have situations where objects are not accelerating in any meaningful sense, but do emit gravitational waves (the ones we've detected fall into this class - stars and black holes are in free fall, not accelerating). You can have situations where objects are accelerating but do not emit gravitational waves (Kinnersley's photon rocket). You can have situations where objects are accelerating and do emit gravitational waves. As Dale notes, accelerating masses are not the source of gravitational waves - mass distributions with changing quadropole moments are. The point is that this may or may not be related to acceleration.

That said, if you are accelerating in such a way that you do emit gravitational waves then the energy carried by the waves comes from whatever's doing the accelerating. That energy is utterly negligible in all but the most extreme situations. For scale, the Earth-Sun system is predicted to emit gravitational radiation at around 100W, which isn't even close to being measurable. In terms of a baseball, we can barely measure its direct gravitational influence, let alone any gravitational waves it may or may not be emitting.

Changing topic, Ernst Mach did argue that the "absolute" nature of acceleration was somehow attributable to a relationship to the rest of the mass in the universe. Einstein was influenced by Mach's thinking, but my limited understanding is that the idea has never really been successful.

Finally, a note on intuitive guesses - intuition is effectively the voice of your experience. You can't have direct personal experience of gravitational waves, and if you don't know the maths of general relativity you don't have any theoretical experience either. To build up intuition, you will need to study the actual mathematical models (which can be done if you choose to put in the time). Unfortunately, YouTube videoes give a picture that is somewhere between "inaccurate but evocative" and "wildly wrong".

 

[timmdeeg]

Changing topic, Ernst Mach did argue that the "absolute" nature of acceleration was somehow attributable to a relationship to the rest of the mass in the universe. Einstein was influenced by Mach's thinking, but my limited understanding is that the idea has never really been successful.

As far as I remember Mach's principle is not consistent with Gödel's universe. And later Einstein has turned away from it.

 

[PeterDonis]

As far as I remember Mach's principle is not consistent with Gödel's universe.

That depends on what you think "Mach's Principle" means. At least some relativity physicists (John Wheeler, for example) said that GR is consistent with Mach's Principle, so any solution of the Einstein Field Equations, including the Godel universe, would be.

Ernst Mach did argue that the "absolute" nature of acceleration was somehow attributable to a relationship to the rest of the mass in the universe. Einstein was influenced by Mach's thinking, but my limited understanding is that the idea has never really been successful.

Again, that depends on what you think "Mach's Principle" means. In GR, the geometry of spacetime determines which states of motion are freely falling and which are not, so it determines which states of motion are "accelerated", and the distribution of stress-energy determines the spacetime geometry. So if Mach's Principle means "the distribution of stress-energy determines which states of motion are "accelerated", then GR is perfectly consistent with Mach's Principle. (This is basically the argument used by John Wheeler, who I referenced above.)

 

[Dale]

That depends on what you think "Mach's Principle" means.

This is the biggest problem with Mach's Principle. It is too "squishy".

If you define Mach's Principle in the way that Brans–Dicke did then it seems that the universe is not very Machian.

 

[DarkMattrHole]

Thanks all. Very helpful. So only varying quadrupole moment causes the waves. That includes spinning co-orbital bodies like colliding black holes, but not exclusive to them. Gravity waves account for tiny bit of energy

I found some equations. Also found some interesting comments on the physics stack exchange board that suggest that if two masses are oscillating in equal and opposite directions, like with a spring between them, then gravity waves (quadruple radiation) will be created. This makes sense to me. I imagine a redistribution after stellar collisions would give off a tiny gravity ripple or 'bang' of gravitational noise, something like that? Is this correct?

Regarding videos, there are some that do teach the math, and they are getting better all the time at presenting math. A lot of the confusion for some folks lies in the difference between what's 'going on' to create the world with its dimensions and rules, compared to the boggling complexity of formally stating even the simplest event within those dimensions and rules. Some folks never find out any of the simplicity in it for the complexity of math to describe it.
Here are the equations i found so far.
https://physics.stackexchange.com/q...-generated-by-a-time-varying-quadrupole-momen

 

[DarkMattrHole]

BTW - I can see wave creation is far stranger and more complicated than as depicted and animated in popular videos.

 

[vanhees71]

This is the biggest problem with Mach's Principle. It is too "squishy".

If you define Mach's Principle in the way that Brans–Dicke did then it seems that the universe is not very Machian.

I must admit, I've never understood Mach's principle in relation to relativistic physics. If I understand the pretty vague principle right it's the conjection that the inertia of an object is due to the presence of all other masses in the entire univers. For Mach simply related to the mass of objects since he was arguing within Newtonian physics and had no idea about the fact that inertia is related to all kinds of energy, momentum, and stress, which is one of the most important general results of relativistic physics in both the general and the special theory.

Within Newtonian physics this could make some sense, if one could find a clear mathematical description of it, making Newton's idea of "absolute space" (which in modern terms I'd formulate as the existence of inertial frames as a fundamental conjecture about the spacetime model) caused to some dynamical principle, i.e., some interaction at a distance, but I'm not aware of any clear mathematical description of such a model. That makes this idea, if feasible, a priori only applicable to non-relativistic physics or some action-at-a-distance non-local relativistic model, which however never has been properly formulated either in a convincing way (with the exception of Wheeler-Feynman absorber theory by eliminating the em. field from the dynamics of charged classical particles, but that has never worked when trying to quantize it).

If one looks at it from a modern perspective where the fundamental laws concerning matter are quantum, what comes closest to the dynamical explanation of inertia/mass is the relativistic QFT phenonmenon of "mass generation" ("mass without mass"). In the contemporary Standard Model we have two kinds of mass generation: The first is a perturbative one within electroweak theory (quantum flavor dynamics) and describes all masses via Yukawa couplings of the leptons to the Higgs field which provides also mass to 3 of the gauge bosons, describing W- and Z-bosons, via the Higgs-et-al mechanism.

The second is confinement of QCD. For everyday matter it's the far more important one (from the Higgs mechanism we get at most around 2% of the mass of the matter surrounding us).

All this for me has little to do with Mach's principle.