Question about cause of gravitational waves

[TheMohawkNinja]

Hello,

I've been doing some research on gravitational waves since their discovery, and I found that all of the places I looked were missing an important piece of information, that is: What is the mechanism by which angular momentum is being conserved.

All of places that I've searched will effectively just say "the black holes orbits decrease because conservation of angular momentum, and that mass is converted to energy and propagated as the waves". But they don't explain why the mass is being lost to begin with, just that it conforms with a law of physics.

To explain what I am getting at with an analogy: When a baseball is hit with a bat, some of the energy in the system is lost because there is a batter holding the bat, and the battery is in contact with the ground, so the kinetic energy of the ball impacting the bat is partially lost to the ground beneath it. As a result of all of this, the overall amount of energy is conserved. In the context of the black hole merger, I understand that when the "bat" and the "ball" (i.e. the two black holes) merge, some energy is lost to the "ground beneath" (i.e. space), as that conforms with the law of conservation of angular momentum, but while I understand that the bat and the ball lose energy in the analogy due to the bat being connected to the ground, and therefore some of the kinetic energy will propagate through the batter and into the ground, I don't understand why the two black holes have to dump energy.

Understand what I'm getting at?

 

[Jeff Rosenbury]

In your bat example, energy is not lost to the ground (mostly, anyway). Energy is lost to the inelastic bat and ball. This shows up as a slight heating of the bat and ball.

What is lost to the ground is momentum, both linear and angular. The ball will change direction (linear) and usually change spin (angular).

The conservation laws of energy, momentum, and angular momentum come from our observations. These include thousands of experiments through the years, none of which were seriously contradictory. (I'm sure some bad data exists somewhere, but no scientists take it seriously.) These include the recent discovery of gravity waves which likely wouldn't exist without the conservation of angular momentum. What I mean here is that it's hard to imagine a model without conservation which would give the observed results. So the observation, in addition to its other merits is also a trivial confirmation of the conservation of angular momentum. (By "trivial" I mean no one seriously doubted the conservation.)

 

[TheMohawkNinja]

In your bat example, energy is not lost to the ground (mostly, anyway). Energy is lost to the inelastic bat and ball. This shows up as a slight heating of the bat and ball.

What is lost to the ground is momentum, both linear and angular. The ball will change direction (linear) and usually change spin (angular).

The conservation laws of energy, momentum, and angular momentum come from our observations. These include thousands of experiments through the years, none of which were seriously contradictory. (I'm sure some bad data exists somewhere, but no one takes it seriously.) These include the recent discovery of gravity waves which likely wouldn't exist without the conservation of angular momentum. What I mean here is that it's hard to imagine a model without conservation which would give the observed results. So the observation, in addition to its other merits is also a trivial confirmation of the conservation of angular momentum. (By "trivial" I mean no one seriously doubted the conservation.)

I understand that the laws are derived from the observations, but since they have been shown so many times to be true, unless we do find good reason to think otherwise, we can just treat the laws as axioms, and therefore (for all intents and purposes) refer to them as laws that define the universe?

 

[Jeff Rosenbury]

I understand that the laws are derived from the observations, but since they have been shown so many times to be true, unless we do find good reason to think otherwise, we can just treat the laws as axioms, and therefore (for all intents and purposes) refer to them as laws that define the universe?

In science Laws are not axiomatic. Laws are changeable as our understanding advances. Science changes as we refine our understanding. Axioms are for math; dogmas are for faith; and laws are for governance. The scientific term "law" is a mistake of history. It's meaning has little relation to hard and fast rules.

A better way to think of the laws of science is that they form a model of how the universe exists. The model looks like the universe, sort of. The model promoted by this website is the standard model and it's the best estimate the scientific community has found to date. But I don't know of anyone who thinks it's 100% correct. Still, it's better than the model we had 100 years ago, or last month before the discovery of gravity wave for that matter. (Gravity waves seem to support the standard model from what I've read, though I'm no expert.)

Whether there can even be a model that is 100% true to the universe is (I think) an open question in the philosophy of science.

Above all science is a process. (Unless it's your paycheck of course. Feeding the little ones is pretty important too.)

 

[Chronos]

Even in the bat and ball example, that the aggregate energy of the bat and ball system is a conserved quantity according to GR and the law of conservation of energy. The system converts a small fraction of its mass and kinetic energy to sound waves as a consequence of the collision. The same thing happens when black holes 'collide' except an equivalent fraction of mass and kinetic energy is converted to gravity waves. Scientists measured the amount of gravitational energy detected by LIGO and found it to agree with the predictions of general relativity.

 

[alw34]

Still, it's better than the model we had 100 years ago, or last month before the discovery of gravity wave for that matter. (Gravity waves seem to support the standard model from what I've read, though I'm no expert.)

Gravity is not part [yet] of the standard model of particle physics. It's a glued together hodge podge of different theories coupled with observational inputs, such as the mass of the electron with theories of the electromagnetic, strong and weak nuclear forces. It seems the weak and electromagnetic forces have been 'unfiied' in an overarching mathematical formalism,'electro-weak theory, but not yet for the rest. Gravity remains especially unique.

 

[alw34]

What is the mechanism by which angular momentum is being conserved.

"the black holes orbits decrease because conservation of angular momentum, and that mass is converted to energy and propagated as the waves"

Well, until the black holes actually 'collide', I 'm not sure either of the 'masses' decreases. Could be.

In any case, as massive objects orbit each other, say neutron stars or black holes as examples, or Earth around the sun, they disturb the space-time around them. Those ripples in space time require energy to generate and carry off energy in the form of gravitational waves. Sound, conduction and convection require a medium, and there is little in space, but gravitational waves and any heat radiation require no such medium and so they surely carry energy away.

PS: "masses decrease"...I'm not talking about accretion disks being swallowed nor the accretion discs colliding and then being swallowed...obviously that generates all sorts of additional energy.

 

[Jeff Rosenbury]

Gravity is not part [yet] of the standard model of particle physics. It's a glued together hodge podge of different theories coupled with observational inputs, such as the mass of the electron with theories of the electromagnetic, strong and weak nuclear forces. It seems the weak and electromagnetic forces have been 'unfiied' in an overarching mathematical formalism,'electro-weak theory, but not yet for the rest. Gravity remains especially unique.

Of course I meant the standard model in the broader sense of scientific consensus. There are plenty of websites for alternative theories (moon = green cheese or whatnot). My understanding is that this isn't one of them. So discussions on general relativity are allowed while discussions on my new perpetual motion device are not.

 

[Drakkith]

What is the mechanism by which angular momentum is being conserved.

Imagine two hard billiard balls undergo a collision in outer space. Here linear momentum is conserved. P_1a + P_2a = P_1b +P_2b, where P1 and P2 are the momenta of each ball, or mv, mass times velocity.
By what mechanism is linear momentum conserved here? The answer is that the mechanism is the forces by which the two billiard balls interact via (mostly the EM force). If we were to look at the repulsive forces, velocities, and accelerations during the collision process and do all sorts of complicated math we would find that the momentum is conserved.

For inspiraling black holes, the mechanism is their interaction with spacetime itself. As an analogy, consider the fact that a charged particle undergoing acceleration will interact with the EM field to produce radiation. But this interaction goes both ways. The field interacts with the electron and has the effect of robbing the electron of momentum. If the acceleration is directed radially, such as an electron orbiting a positively charged particle, this leads to an in-spiral until the electron impacts the positive charge (we're ignoring quantum physics and assuming classical behavior). The electron will radiate away energy and momentum during the entire in-spiraling process. If we were to again analyze this situation using complicated and tedious math, and taking into account the EM field and radiation, we would find that the angular momentum lost by the electron during its in-spiral was actually gained by the EM field as EM radiation.

Orbiting objects radiate gravitational radiation through an interaction with spacetime in an analogous manner to how charged particles radiate EM radiation through an interaction with the EM field.

Well, until the black holes actually 'collide', I 'm not sure either of the 'masses' decreases. Could be.

That's right. The mass of the system as a whole would decrease, not the mass of each individual black hole. One caveat here is that black holes are not physical objects in the sense that they don't have discrete, physical surfaces. The event horizon is not a solid barrier and the two black holes are free to merge together. This merger results in a 'ringdown' where the new event horizon settles down into equilibrium by, again, radiating away energy and momentum in the form of gravitational radiation.

The net result of all this is that a significant portion of the total mass of the system is lost as gravitational radiation.