They fall off as the distance, yes, but you don’t seem to grasp either how much more powerful a binary system’s waves are than the Sun-Jupiter system, nor how extremely tiny even these are. We’re talking about measuring a change of the width of an atom over 4km.
Besides which, there’s the signal-to-noise problem you’re discounting. It’s not just “can we detect them?”, but “how can we be sure that’s what we’re detecting?”
Sure, but if you’re talking about a gravitationally bound system it seems kind of silly to ignore the higher-order terms in the gravitational field. Similarly as a two-body problem I guess if Earth and Moon collided they would have to bounce off each other, but that seems silly too.
There is a question of the thermodynamic equilibrium point (also related to David Simmons’ question)–if orbiting bodies are constantly pumping energy into gravitational radiation, where does all this energy go? Do we end up with a very hot gravitational field and very low-temperature matter? The short answer is that they ought to reach a thermodynamic equilibrium. This is complicated, though, by the expansion of the universe, which redshifts radiation and hence reduces its energy more quickly than it cools matter. In an expanding universe I would expect to see more energy pumped into the gravitational field than extracted back out to matter motion, on average.
This is analogous to the case of electromagnetic radiation, much of which in fact has not been absorbed by dust. The EM decoupling time z~1000 was the last time when matter and electromagnetic radiation were in overall thermodynamic equilibrium. Since that time, cosmological redshifts have cooled the EM field to the 2.725K we see today. --In particular, we see it today; the cosmic microwave background radiation we measure is electromagnetic radiation that hasn’t scattered appreciably since decoupling, ~13 billion years ago.
So where does cosmically redshifted energy go? I don’t know. Conservation of energy is a local principle, and is as far as I know is not generally thought to apply cosmologically in an expanding universe. Note that the early universe is thought to have been radiation-dominated–that is, having far more energy in radiation than in matter, and hence having a stress-energy tensor approximately that of pure radiation–but soon transitioned to a matter-dominated universe, because of this redshifting. (It may have recently transitioned to an accelerating dark-energy-dominated universe.)
As for observability of gravitational radiation, it’s true (as Mathochist says) that we haven’t yet “directly” observed gravitational waves. “Direct” observation, in this case, means observing strains in the spacetime curvature of order (IIRC) one part in 10[sup]21[/sup] which can arise as a result of the final stages of decay of orbits of compact massive objects (primarily neutron stars and black holes) sufficiently close to us, and comparing the signal to those expected for theoretical (usually large finite-element simulation) results for those collisions. Even these “strong” signals are so tiny that noise is an enormous problem. LIGO, for example, is trying to measure optical-path-length differences, over its kilometer-scale interferometer, of order 10[sup]-18[/sup]m --not just smaller than an atom, but smaller than an atomic nucleus.
Oops, forgot the last paragraph:
But though nobody’s directly observed energy loss to gravitational radiation, the Hulse-Taylor binary pulsar has shown a frequency shift which is consistent with this energy loss. (This system is still far from the final collision, so measurements require high precision–fortunately provided by the pulsar’s excellent clock–and only provide weak constraints on the form of the post-Newtonian gravitational theory. But they are consistent with general relativity, so far.)
Oh, I know all that. However an effect that is too small to detect or one that is so small that it is below your measuring system noise is difficult to separate from no effect at all.
Detection efforst are now underway. Let’s see what they come up with.
And I don’t see why a bleck hole, per se, should swallow the universe unless the object from which it formed would also have had the gravity to attract the universe to it despite the general expansion.
Well, I guess it depends what you call a “physical object” – of course the motion involved can be at the microscopic level, as in your example of the sun heating an object.
Well, masses have to move in a certain way to produce gravitational waves. So the waves take energy out of the system (which goes into the waves themselves), and the motion of the system changes as a result. E.g., if two stars are orbiting each other, they produce gravitational waves, which carry energy out of the system. Thus, the stars should slowly spiral towards each other. (This has been observed. In fact, the discovery of such a binary system earned the 1993 Nobel Prize in physics.)
But your talk of the objects having “radiated their gravity away” gave me the impression you thought eventually they would stop exerting gravity on each other at all. That’s not right. If the objects are moving in such a way that they produce gravity waves, that motion gradually goes away as energy is lost. But they will continue to exert gravitational force on each other indefinitely – as I said, gravity does not require a power source.
By the way, I realize the comparison of gravitational waves to God was a bit of a joke, but still, it’s worth noting that (1) there is very strong physical evidence for the existence of gravitational waves (e.g., the aforementioned changes in the orbits of binary pulsars), and (2) as you mention, there are current experiments underway to directly detect gravitational waves.
Just because the technology has in the past not been good enough for direct detection doesn’t mean this is something people are “taking on faith” – and it’s obviously a far cry from claims that are not scientifically testable even in principle.
OK, then, would it make you happier if I said that the gravitational force 150,000,000 km away from a hypothetical spherically-symmetric star is exactly the same as the gravitational force 150,000,000 km away from a non-rotating black hole? The Sun is, in fact, ever so slightly different from a Schwartzschild source, but that’s because the Sun is messy, not because of any black hole weirdness.
Correct. A black hole won’t eat anything that wouldn’t be eaten by a “normal” object of that mass, either. If anything, it’ll eat less, because it’s a smaller target.
And bleck holes don’t eat anything… They just hold their nose, shut their mouths, and say “bleck” whenever you offer them any food :D.
Hmmm. Will dust particles absorb much EM radiation that has a wavelength much, much bigger than the dust? The background radiation is in the microwave region having a wavelength in the meters, isn’t it?
I think I pulled a Double Dubrovsy. I not only misspelled “black” but I think I misspelled the misspelling. Shouldn’t it be “blech”?
Dust preferentially absorbs higher frequencies, so it is more important at optical bands. The CMBR is primarily at millimeter wavelengths.
No, it would not make me happier. The mass of a star is obviously spread out more widely than the mass of a black hole. Wouldn’t this make a slight difference at some distances?
Anyway, my main point is that there is a flaw in your reasoning. Your mathematical model is ignoring elements that may make a difference in the long run.
Not as long as you stay outside of the star. For a static spherically-symmetric mass distribution, the vacuum solution (i.e., outside of the star) depends only on the distance from the center and on the mass (and charge) at smaller radii. The spacetime outside of a spherically-symmetric object looks exactly the same, in general relativity, whether it’s a star or a black hole.
(A similar result holds in Newtonian gravity.)
In fact, all of the equations of classical mechanics strictly apply to point masses. From a point outside uniform symetrical body it acts like a point mass at its center of mass.
That’s a rough description and there are various limitations on applicability of the principle but for most purposes it is more than satisfactory.
True, with the caveat that star’s aren’t perfectly spherically symmetric. There is an ever-so-slight correction to the gravitational field due to the fact that it’s slightly squashed at the poles; but this correction is tiny (at Mercury’s orbit, it changes the field by about one part in a hundred billion) and, as you noted, doesn’t particularly have anything to do with the matter being “spread out.”
But, but, but … I though one of Einstein’s fundamental assumptions was that the physics is the same everywhere.
Of course, there is the question of where the energy in red shifted light went. I started by saying this is too deep for me. Maybe I’ll go back to that position.
David, you’ve probably already read this, but if not you might find John Baez’ Physics FAQ, Is Energy Conserved in General Relativity?’ interesting.
http://math.ucr.edu/home/baez/physics/Relativity/GR/energy_gr.html
Conservation of energy is a local principle, and that local principle holds everywhere. There is a difference between a local principle which holds everywhere, and a global principle.
Allow me to explain. Suppose you have a small box. You can accurately measure how much total energy is inside the box at all times, and you can also measure how much energy passes through the walls of the box, and in which direction. That energy can be in any form whatsoever, but you’ll measure it all. The principle of conservation of energy says that the change in the total amount of energy inside the box is exactly equal to the total amount of energy which passes through the walls of the box. So if the box contains ten Joules, and you see five more Joules go in through the walls, the box will then contain fifteen Joules.
The problem is that this only works for small boxes (or more precisely, it works in the limit where the size of the box goes to zero). This is what we mean when we say it’s a local property. For a single small box, the expansion of the Universe is irrelevant. But if you had a very large box (large compared to the characteristic scale of the Universe), the expansion of the Universe would be relevant, and you’d see the amount of energy in the box changing without energy passing through the walls. This happens even though the large box is made up of many smaller boxes, in each of which energy is being conserved.
By “local” I didn’t mean that it only applies around us, just that it only applies in small neighborhoods of wherever you happen to be looking. (Baez’ article, linked by Ring, says it much better than I could.)
I get a glimmer of the idea although I got off the mathematical train a few stops before tensors.
Even in ordinary thermodynamics I’ve always considered entropy as a sort of bookkeeping quantity that preserves conservation of energy. I don’t see much practical difference between energy disappearing and energy becoming unavailable.
Well I don’t know if I can agree with that statement David. In Classical Mechanics (Per that sadist Goldstein) conservation of energy certainly holds, but there’s no way it can hold without taking into account unavailable energy.
Oh absolutely. It’s sort of like double entry bookkeeping and it allows a thorough accounting of the total energy in a system.
It there is such a thing as a heat death in store for the universe there will be plenty of energy around in fact all that the universe started with (minus that which condensed out to matter), but none of it will be available as everything will be at the same temperature. I think it takes a pretty strong magnifying glass to detect a practical difference between that and not having any anergy at all.