Or, more accurately, kick it about 10^40 ways to Sunday.
If space has positive curvature, must it be a 3-sphere, or could it be a hyper-torus or some other shape ? Do 3-spheres have antipodeal points ? If yes, and yes, then what happens when gravity waves converge on the point antipodeal to a black hole merger?
What happens on a 2-sphere? Transverse wave on a sphere of liquid, what do the waves do when they meet ? I imagine the actual earth is irregular enough that there is no interesting convergence from a tsunami.
Having read a few things about the LIGO project and it’s devices I began to wonder if a gravitational wave detection system might not already be in place, on a larger scale.
Could the GPS satellite system, with it’s long base lines relative to each other, atomic clocks, on ground and on the satellites, be used as detectors?
The timings are constantly being tuned due to various sources of drift. Physical position and due to the very slight inaccuracies of the clocks, etc… Could data due to distortions of gravity waves be embedded in these drifts? In the numbers used to correct?
I don’t know if the data collected and relayed is fine and fast enough to find such minute and fast variations. But the distances between the satellites is much longer than the LIGO apparatus.
If the current capabilities are not there. Maybe they could devise and include them in GPS satellites that are going to be launched in the continuous replacement program.
Let’s not forget the communication possibilities… xkcd: Gravitational Waves
GPS wouldn’t be able to do it, but there are other “detectors already in place”: You can (in principle) detect extremely low-frequency gravitational waves through careful measurements of pulsar timing. It’s currently being pursued by a number of groups, but the big unknown is how common sources of such low-frequency waves would be.
Are gravitational waves the only means by which energy is released during an event like this?
I would imagine other forms of energy would be released, at the very least from whatever may go down on the accretion discs around the black holes.
I don’t think anybody knows yet. But everyone who had an all-sky astronomical instrument taking data on 2015/09/14 is now reviewing their data to see if they saw anything. IceCube has already announced that they did not see neutrinos.
I was thinking that multiple atomic clocks orbiting 20000 kilometers up, making a baseline of 40000+ between them would be able to detect time shift anomalies caused by gravity waves. The clocks are there. The satellite positions are known. I think it takes about 0.1 light second to go 40000 Kilometers. The problem with using the current system is probably that the clock data is not transmitted fast enough to catch the anomalies as they happen. And be able to compare them to other satellites that have not yet been affected by the wave’s time effects. There are likely many other technical reasons that the current system can’t do it. Due to being designed for another purpose. But it might not be too big a design addition to add the capabilities. Say an on board precise recorder of the clock data that is occasionally transmitted to base.
GPS satellites use radio wavelengths, not visible light, to communicate between the satellites, and the longer wavelength means less precision.
And a black hole merger will release negligble non-GW energy, but a neutron star or white dwarf merger (which LIGO should also be able to detect) would probably have an electromagnetic and neutrino component as well.
Even with satellites 46,000 km apart (20,000 km altitude in opposite directions), you need to measure the distance shift by 10^-14 meters to match the sensitivity of LIGO. That’s about 10 times the size of a proton.
I was struggling to try to understand this, since you can’t get anything “out” from beyond the event horizon (except in the exotic special case of Hawking radiation).
The only intuitive explanation I can come up with is that black holes spiraling in to each other at about half the speed of light, as these supposedly were, carry a tremendous amount of kinetic energy. When they collide, that energy is lost, and per E=mc[sup]2[/sup], it amounts to the equivalent of about three solar masses which was therefore lost in the combined mass.
Is this a correct or reasonable way of looking at it?
And if so, since nothing can actually escape a black hole, are gravity waves the sole manifestation of that energy? ETA: And the corollary to that – if gravity waves didn’t exist, WTF would anyone expect that the manifestation of the energy release of two black holes colliding could possibly be?
BTW, the New Yorker, as always, has a great backgrounder on the discovery.
Again, this isn’t true. You’re correct to note a contradiction between those two statements, which means that one of those statements is false, but the false statement is the one that says that you can’t get mass out from inside the event horizon. That does work out to be true for an isolated, non-spinning black hole, but it is not the case for a merger of two black holes, or for a spinning black hole.
Also, even if there were neutrinos, we wouldn’t necessarily expect to see them yet. The GW event was a billion light-years away. Neutrinos do not travel at c; they might be as much as one part per billion slower. It could be as much as a year after the observation to expect the neutrino pulse.
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.
I was curious about this and did a bit of Googling, and came across this pair of pages by Philip Gibbs and Luboš Motl:
http://blog.vixra.org/2010/08/06/energy-is-conserved/
http://motls.blogspot.com/2010/08/why-and-how-energy-is-not-conserved-in.html
As best I can tell, the argument goes something like this:
L: Energy is not conserved in GR, except approximately or in special situations.
P: Yes it is. You’re just ignoring the gravitational component. Include that and it’s always conserved exactly.
L: But if you do that, the answer is always exactly 0. It doesn’t tell you anything.
P: Sure it does, and so what? You can claim the same thing about Maxwell’s equations, and no one thinks they’re trivial.
L: It’s trivial because it doesn’t tell you anything beyond what you already know from GR.
Any thoughts on the subject? Is my summary a fair one? Does it really just come down to a personal definition of “trivial”?
I was thinking of other analogies and came to charge conservation, which as you know is also a consequence of Noether’s theorem. The total charge of the universe is almost certainly zero, or close to it, but that doesn’t seem like a trivial observation to me. Charge conservation is also a consequence of Maxwell’s equations, but it doesn’t seem fair to say charge conservation is trivial just because it doesn’t tell you anything that Maxwell didn’t.
And as an aside, and bringing the thread back to its title (if not the actual OP), the problem of localizing gravitational energy is especially problematic when it comes to the gravitational waves themselves. For a distant source, like we’re observing from Earth, and a correspondingly-weak wave, one can sweep the problem under the rug of higher-order terms which can be ignored, but in the strong-field case, you just can’t get around the fact that gravity is nonlinear, and gravitational energy itself gravitates.
I don’t mean a distance shift. The satellite positions are not known precisely enough for that. I propose that the gravity wave will affect the atomic clock in the satellite. That effect will then be seen in each other satellite but at different times due to their separations of up to 40000+ kilometers. However. The effect may be too small to be detectable. The temporal effect of being in a different gravitational level than the ground station clocks is detectable. But that is not a short term event. A gravity wave may not give a big enough difference in the clock to be detectable.
It is in some ways a matter of opinion, it really comes down to the question of how useful as a concept is the conservation of energy in general relativity. When the spacetime is static, global conservation of energy can be a useful statement of global time symmetry, when spacetime has certain asymptotic symmetries (such as when you assume the system is isolated), then it can be viewed as a useful statement of asymptotic time symmetry. Additionally when the spacetime is viewed as a perturbation of either of the above situations, then it can be seen as a useful statement of the perturbation from an approximate time symmetry.
The above situations cover a lot of physically interesting situations, so global conservation of energy in GR is never going to be a totally useless, but as a statement about a general spacetime which may not have the required time symmetries, even asymptotically or approximately, that is when it’s usefulness becomes highly questionable.
Double post
XKCD has a “What-If” about the energy transfer via neutrinos Lethal Neutrinos by the way.