Energy carried by a gravitational wave

[Ale]

@Chronos

The relative strain is roughly equal to the reciprocal of the distance from the source, measured in terms of the radius of the black holes. That is, if you were only a few times the radius away, then your body would be stretched or compressed by a large fraction of your height. If you were 100 radii away, then a two-meter body would be stretched and compressed by about 2 cm, which would still be quite damaging. If you were 1000 radii away, then your body would be stretched and compressed by a couple of millimeters, which you might feel, but which wouldn’t be a big deal. At 10,000 times the radius, you’d be talking a stretch of a fifth of a millimeter, and good luck noticing that.

I find it curious that a massive release of energy such as this event would have a relatively minuscule effect.
A black hole with the mass of those involved in this have a radius of a few tens of kilometers at most, no? 10.000 times that is, give or take, the equivalent of the distance between the Earth and the Moon.
So, many times the energy output of the entire universe released as gravity waves, and if it would had happened around the Moon’s orbit* we wouldn’t had felt more than a hint of a shiver down here on Earth?

I’m baffled.

• Of course the other side effects of having a pair of massive Black Holes that close are ignored for simplicity, spherical chicken in a vacuum and all that…

[Chronos]

And all I can say to that is that yes, it is in fact mind-boggling. Back when I was still in research, I tried pretty hard to come up with some way by which that enormous amount of energy would couple with anything detectable, and every time, when I ran the math on it, just kept on coming up blank.

[leahcim]

Blog post that came through my twitter feed today:What would a gravitational wave sound like up close?

Basically at 1AU, gravitational waves would be audible. At 4000km, they would hurt your ears (although at that distance, there would probably be more immediate things available to hurt you). Presumably “enough distortion to fatally disrupt your biology just from gravitational waves” is closer than that.

[Hooleehootoo]

The author of that blog post calls an anti-tidal machine “magic[al]”. But see the work of Robert Forward. I believe a large version of this is used to protect the spacecraft studying the neutron star in Dragon’s Egg.

[EastUmpqua]

@Asympotically_fat

Easily-defined and universal global concepts of energy and conservation of energy don’t exist in general relativity. However taking advantages of certain properties, well-defined global energy and conservation of energy is usually assumed in astrophysical situations.

How it is defined is from the point of view of a set of very faraway observers, who can infer the total energy of a system from its gravitational field. They can also infer how much energy is carried away by gravitational radiation by the limit on how much energy can be transmitted to them by gravitational radiation. What is conserved is the inferred total energy of the system minus the energy carried away by gravitational radiation. By idealizing the system as being an isolated one and making the observers arbitrarily faraway, this gives us a well-defined and non-arbitrary concept of the conservation of energy.

Simply knowing the total energy of a system vs energy carried away from it doesn’t tell us much about the system though, so we might like to assign different portions of the total energy to different parts of the system. A big problem we run up against straight away is that gravitational energy in GR can never be truly described locally as free-falling observers never observe gravitational fields locally. Despite this problem we may still opt for quasi-local definitions of energy, but this quasi-local energy is more arbitrary and may depend more on the approach than the physics. Interestingly, though the total energy is always positive, some of the parts of the system may have negative quasi-local energy.

Numerical relativists when describing high-dynamical and relatively complex situations such as the merger of two black holes will utilize quasi-local definitions of energy. But it is difficult or even undesirable to interpret objectively in these situations exactly where the energy lost to gravitational radiation is coming from.

That said, it certainly ain’t wrong to say some comes from the kinetic energy of the BHs and some from the mass and this isn’t a problem as quasi-local energy “escaping from black holes” isn’t really a problem. Hawking radiation is a good comparison as the radiation and the energy it carries away is only a concrete concept for an observer faraway from the black hole.

What you haven’t taken into consideration is that c increases in extremely bent spactime (e.g. near the merger of two black holes), so some of the mass is ejected into less-bent spacetime and is traveling at >c. This ejected mass is unstable (moving FTL) and is converted directly to energy, in this case gravitational waves.

[Chronos]

And he also hasn’t taken into consideration that unicorns fart perfume, or that Sasquatch braids the Loch Ness Monster’s hair. And he has neglected to take into consideration all three of these facts for exactly the same reason.

[EastUmpqua]

My apologies for disrupting this thread, that was not my intention. I am new to this venue. But I still would ask someone to show me how we know c doesn’t increase in extremely bent spacetime. If a tenet to a theory said c did increase in bent spactime, what scientific observations could we make to prove or disprove it

[Chronos]

If a model said that c would vary in bent spacetime, then that right by itself would be enough to disprove it. Talking about c varying is like talking about discovering a new integer between 3 and 4. It literally doesn’t make sense. One is equal to one, and any model that says otherwise, in any conditions of spacetime, is absurd.

[EastUmpqua]

I wonder if Newtonian physicists said that to Einstein when he described time dilation.

[Chronos]

Completely different situation. Einstein didn’t say that one does not equal one; he said that two things previously thought to be equal weren’t.

In physics as we know it, c is an exact synonym for “1”. If you speak of c changing, you are either using the term “c” to mean something different than everyone else means (in which case you need to explain what you mean, and probably ought to use different terminology for that meaning for clarity), or you are saying that the value of 1 changes.

[EastUmpqua]

@Chronos

If a model said that c would vary in bent spacetime, then that right by itself would be enough to disprove it. Talking about c varying is like talking about discovering a new integer between 3 and 4. It literally doesn’t make sense. One is equal to one, and any model that says otherwise, in any conditions of spacetime, is absurd.

Perhaps there is a (as yet undiscovered) branch of mathematics that treats pi as an integer… Surly, we don’t know everything yet

[EastUmpqua]

@Chronos

Completely different situation. Einstein didn’t say that one does not equal one; he said that two things previously thought to be equal weren’t.

In physics as we know it, c is an exact synonym for “1”. If you speak of c changing, you are either using the term “c” to mean something different than everyone else means (in which case you need to explain what you mean, and probably ought to use different terminology for that meaning for clarity), or you are saying that the value of 1 changes.

I don’t understand what you mean by ‘c is an exact synonym for 1’. The units of c, distance x time, must be included for e=mc(2) to the get right units for energy. “1” doesn’t have units

[Dr.Strangelove]

c is just a conversion factor between distance and time. The only reason we have different units at all is history and practicality, though–in relativity, distance and time are on the same footing. If we use the same unit, then regardless of what we pick, it’s always 1, numerically: 1 meters/meter, or 1 seconds/second, etc.

[EastUmpqua]

Then how can e=mc(2) be used to calculate the amount of energy (kg)(m)2/(s)2 produced by a fusion reaction between two hydrogen atoms, if c=1? Energy doesn’t just equal mass, it equals mass times c(2). There seems to be a difference…

[Dr.Strangelove]

Energy does just equal mass. E=m (more accurately, E[sup]2[/sup] = m[sup]2[/sup] + p[sup]2[/sup]) is perfectly legitimate when we’ve removed the artificial distinction between space and time.

c as 299,792,458 m/s is no more physically meaningful than 5280 feet/mile or 16 oz/lb. They are just conversion factors equivalent to multiplying by 1.

[Dr.Strangelove]

Also, just look at the units of energy: the joule, for instance, is kg·m[sup]2[/sup]/s[sup]2[/sup]. Or, more generally, M·L[sup]2[/sup]/T[sup]2[/sup]. If length and time are measured the same way, then those units always cancel exactly. You’re just left with mass.

[Chronos]

Oh, and I finally got around to looking at that blog on hearing gravitational waves. He assumes that they would cause a pressure change in gases. Unfortunately, it doesn’t work that way (that was one of the dead ends I went down in trying to find a way to detect some of that prodigious energy). Gravitational waves stretch one way and compress in the other, in just such a way that volumes (and hence also density and pressure of a gas) remain constant. You might, however, be able to hear something from the wave acting directly on your eardrum. You might also get pressure effects if you’re in a room where one of the lengths is resonant but not the other two (ideally, one side of the room exactly equal to half the wavelength).

[leahcim]

@Chronos

You might, however, be able to hear something from the wave acting directly on your eardrum. You might also get pressure effects if you’re in a room where one of the lengths is resonant but not the other two (ideally, one side of the room exactly equal to half the wavelength).

Neat. It just reminded me of this thread because we were discussing at the start what you would “notice” and coming up with answers to “how close would you have to be to be killed”. This opens up the possibility of being merely annoyed, (or at least having a moment of “did you say something? No? Never mind then,”) but at a much larger distance.

[EastUmpqua]

@Chronos

Completely different situation. Einstein didn’t say that one does not equal one; he said that two things previously thought to be equal weren’t.

In physics as we know it, c is an exact synonym for “1”. If you speak of c changing, you are either using the term “c” to mean something different than everyone else means (in which case you need to explain what you mean, and probably ought to use different terminology for that meaning for clarity), or you are saying that the value of 1 changes.

I looked up natural units. In order for c to exactly equal “1” you must first assume that the speed of a locally-measured photon is always the same, even in extremely bent spacetime (e.g. the collision of two gigantic black holes). Since this assumption is part of the definition, how can it be used to prove that c is always invariant?

[Francis_Vaughan]

You need to go back further to understand what is being talked about.
You use the word “spacetime” but you need to understand what that actually is, before talking about its properties.

Spacetime comes from special relativity. Whilst there is a lot said about SR, the key point is really easy, if counter-intuitive. We exist within a four dimensional space. Not 3D and time advancing, but 4D, where one of the dimension is time. This make a huge difference, and it unifies our treatment of many things. The big change is that we discover that we are travelling though this 4D thing at a constant speed. No matter which direction we go in 4D, our speed is the same. If you stand still in the 3 spatial components we are rushing forward in the time dimension. If we move in any of the spatial dimensions the total speed in all 4 dimensions remains the same, and our speed in the time dimension reduces. That constant speed turns out to be the speed of causality. If you stand still you move at a speed of one second per second through time. If you measure the speed of a massless boson it turns out to be moving at the same speed, but entirely in the spatial dimensions, also at the speed of causality. In one second it travels the distance causality would move in a second. Once you know this, it is simple application of Pythagorus’ Theorem that allows you to calculate pretty much everything you need to know, and allows you to derive Einstein’s famous E = mc[sup]2[/sup]. It also makes no sense to talk about movement in spacetime as taking place at any speed other than a dimensionless 1. c = 1.

All that General Relativity did was to add acceleration to space. Famously - space tells mass how to move, mass tells space how to bend. Wrapped up in a partial differential equation that is all there is. You have GR.

But bending spacetime doesn’t change the nature of spacetime, in particular, it doesn’t change the intrinic property - that everything travels though it at a constant speed - 1. You can curve spacetime enough that the spatial dimensions are pointing in the same direction as time, and thus making it impossible to leave that area of curvature, but the speed you travel in spacetime doesn’t change. You still advance at 1.

To suggest that the intrinsic nature of spacetime changes if it is bent past a certain point would require radically new physics. And physics of an unpleasant kind - physics that adheres perfectly to our current understanding of GR in every respect, with very very high precision, but suddenly diverges from it in a capricious manner where we cannot measure it and have no way of understanding it. Science doesn’t really do this. Especially as it isn’t even clear what the idea even means.

The speed of light in a vacuum is a consequence of the speed of causality. Massless bosons travel at c, if they didn’t they would violate relativity. So too things with mass travel at less than c, many much less than c. And the conservation rule E[sup]2[/sup] = m[sup]2[/sup] + p[sup]2[/sup] tells us how.

When we fuse two hydrogen nuclei we take some of the binding energy (as visible in the residual strong force) that is holding the quarks together and release it. That binding energy was giving the nuclei their additional mass, and when it was no longer needed to hold a stable configuration of quarks in the new configuration, in the new nucleus, it was released. The energy was present as additional mass via E = mc[sup]2[/sup].