In my (so far) futile attempts to truly understand the mechanics of our beautiful universe, I can never get a satisfactory answer from astronomers, cosmologists, physicists, and other smart-guys about the nature of the"fabric of space."
I contend that if space can be bent, warped, folded, and otherwise manipulated, it must have mass. I differentiate this from the “Higgs Field” which, theoretically, gives particles their mass.
So, Cecil, I ask you: Does space have mass? If so, what would be the cubic dimensions of 1 gram of space?
AFAIR, “dark energy” is calculated to be around 0.6 joules per km^3. Thus the km^3 would have the mass of 0.6/c^2 kg or 6.676E-15 g.
So - from that, 1g of space has the volume of 149,790,293,588,975 km^3 - roughly 4 times the volume of our solar system (if we consider our solar system to be about 1 light year in diameter).
Seems on the high side. This site gives three estimates based on reasonable criteria, the largest of which is just under 2000 AU, or around 3% of a light-year.
I’ve thought of various possible answers to the question, but I think this is the mpost accurate picture IMO:
Firstly it’s not space that is curved in general relativty and other metric theories of gravitation, but spacetime. The term is usually the “fabric of spacetime”. In order to make metric theories of gravity work you can’t forget about the time dimension when considering curvature.
Obviously space is part of spacetime and so the effect of the curvature of spacetime is usually (but not always) that we can no longer think of space as being flat (mathematically speaking). The usual result is thoguh that space no longer has a well-defined geometry and where we do define a geometry over the whole of space (e.g. in the big bang theory) that is usually dependent on our frame of reference.
However I think it’s a non-sequiteur to say that because spacetime or space can be curved or warped in someway that it must have mass.Indeed in metric theories of gravitylike general relativity it is the presence of matter (in the boradest sense) that causes spacetime to be curved, when there is no matter present spacetime is flat (well there are arguably exceptions but I’llignore them).
The concept of the mass contained within a volume can be very tricky and arbitary in metric theories of gravity anyway, but I think it’s fair to see that in Einstein’s theory of relativity the mass contained in any volume of totally empty space (empty of any matter, empty of any fields, any gravitational waves, etc) is zero underr any reasonable definition of mass.
Oddly, that link has a picture of the Oort cloud, but doesn’t mention it in the text. The Oort cloud is thought to have a diameter of about 2 light-years, and is composed of objects which “belong” to the Sun gravitationally. That seems as fair as any other definition of the solar system.
I don’t accept the idea that because space(time) can be “bent, warped, folded, and otherwise manipulated, it must have mass” because it isn’t bent, folded etc. in the way mass is bent, folded etc. The cause of its bending & warping is gravity, and gravity is unique in that it is the only fundamental force still not linked to the other fundamental forces.
I believe there has to be a still undiscovered ‘property’ of spacetime thru which gravity affects it. Something akin to ‘subspace’ in Star Trek, which ironically is sort of a retelling of the antiquated idea of a luminiferous aether.
Either way it seems *more *likely to me that, whatever it is, it does not have mass.
It’s a bit complicated. Basically, ‘mass tells spacetime how to curve’, which yields to gravity – ‘spacetime telling mass how to move’. But, there are solutions to the Einstein equations in which there is no mass, but nevertheless, curvature. Also, the gravitational field carries energy, and generally, energy gravitates; but, the energy in the gravitational field is not a local quantity. There’s also the issue that it’s in principle possible for the graviton, the quantum of gravitational waves, to carry mass, but if it does, it must be extremely small to be in accordance with observation. Then, the vacuum, in quantum field theory, is not really empty, but filled with virtual particle creation and annihilation, which ought to yield a ‘cosmological constant’-like, repulsive gravitational contribution – but naive calculations on this basis yield a value to big by 120 orders of magnitude, the oft-quoted ‘worst prediction in physics’.
So, as I said, it’s complicated. The issue is basically, that in general relativity, it’s no longer as simple as ‘mass creates gravity’. The appropriate quantity is called stress-energy, and it takes into account energy- and momentum densities, energy- and momentum fluxes, pressure, and shear stress at some point in spacetime; the Einstein field equations then tell you the spacetime curvature generated by this stress-energy, from which you can then calculate the gravitational forces. The gravitational field certainly carries stress-energy; but, essentially because of the equivalence principle, that stress-energy can be made equal to zero at any one given point in spacetime – so it is not a local quantity. That means it can’t be lumped in together with the stress-energy of other fields, or of matter; nevertheless, you can define a quantity taking it into account.
So if you’re willing to accept ‘stress-energy’ as the appropriate generalization for ‘mass’, and are able to cope with the awkwardnesses introduced by defining a non-local stress-energy for the gravitational field, then I think the answer to your question is ‘yes’. But it can be a bit of a question of taste, really.
There’s yer problem. You’re jumping to a conclusion based upon a misunderstanding and then asking someone to calculate a result from that misunderstanding.
Yes, ‘empty’ space has mass. Mass defined as that which physically occupies three dimensional space.
Lawrence M. Krauss says, “If you removed all of the particles, all of the radiation, absolutely everything from space and all that remained was nothing that nothing would weigh something.”
What weighs something has mass.
“The word ‘ether’ has extremely negative connotations in theoretical physics because of its past association with opposition to relativity. This is unfortunate because, stripped of these connotations, it rather nicely captures the way most physicists actually think about the vacuum. . . . Relativity actually says nothing about the existence or nonexistence of matter pervading the universe, only that any such matter must have relativistic symmetry. […] It turns out that such matter exists. About the time relativity was becoming accepted, studies of radioactivity began showing that the empty vacuum of space had spectroscopic structure similar to that of ordinary quantum solids and fluids. Subsequent studies with large particle accelerators have now led us to understand that space is more like a piece of window glass than ideal Newtonian emptiness. It is filled with ‘stuff’ that is normally transparent but can be made visible by hitting it sufficiently hard to knock out a part. The modern concept of the vacuum of space, confirmed every day by experiment, is a relativistic ether. But we do not call it this because it is taboo.” - Robert B. Laughlin, Nobel Laureate in Physics, endowed chair in physics, Stanford University
Matter, a piece of window glass and ‘stuff’ have mass.
“The velocity of a wave is proportional to the square root of the elastic forces which cause [its] propagation, and inversely proportional to the mass of the aether moved by these forces.”
This is not a definition which is used in any field of science. You are, of course, free to define terms however you choose, but using different definitions from everyone else is an impediment, not an aid, to communication.
This, on the other hand, appears to be correct, given the best of our current understanding and a somewhat loose (but still precedented) definition of “weigh” or “mass”. Krauss is here referring to the same dark energy that Terr mentioned earlier in this thread.
One can still quibble about whether dark energy is a property of space itself, or merely a substance separate from space which is always found in it. Even absent dark energy, though, there are still some configurations of space which can be said to have mass: A black hole, for instance, is vacuum at every point in space (with the caveat that it also has a point that isn’t in space), but still has mass, and a gravitational wave has energy (albeit it’s difficult to say just where that energy is).
Welcome to the Dope, you are responding to a 2 year old thread. The OP hasn’t posted here since January of 2012. Interesting stuff, though. Also, something about the undead and physics.
eta: this post was (hopefully, quite obviously) not aimed at Chronos, who ninja’d my zombie. Damn ninjas.
‘Empty’ space has mass. Mass is defined as that which physically occupies three dimensional space.
The mass of ‘empty’ space is displaced by the particles of matter which exist in it and move through it.
“During the team’s dark-matter analysis, they noticed a ripple in the mysterious substance, somewhat like the ripples created in a pond from a stone plopping into the water.”
The ‘pond’ consists of the mass of ‘empty’ space. The analogy is two boats which pass by each other very closely. Their bow waves slosh back and forth and create a ripple in the water.
The ripple created when galaxy clusters collide is a displacement wave in the mass of ‘empty’ space.
The ripple created when galaxy clusters collide is a gravitational wave.
What ripples when galaxy clusters collide is the mass of ‘empty’ space.
‘Interpretation of quantum mechanics by the double solution theory - Louis de BROGLIE’
Page on Aflb
*“When in 1923-1924 I had my first ideas about Wave Mechanics I was looking for a truly concrete physical image, valid for all particles, of the wave and particle coexistence discovered by Albert Einstein in his “Theory of light quanta”. I had no doubt whatsoever about the physical reality of waves and particles.”
“any particle, even isolated, has to be imagined as in continuous “energetic contact” with a hidden medium”*
The hidden medium of de Broglie wave mechanics is the mass of ‘empty’ space. The “energetic contact” is the state of displacement of the mass of ‘empty’ space.
“For me, the particle, precisely located in space at every instant, forms on the v wave a small region of high energy concentration, which may be likened in a first approximation, to a moving singularity.”
A particle is a moving singularity which has an associated displacement wave in the mass of ‘empty’ space.
In a double slit experiment the particle travels a well defined path which takes it through one slit. The associated physical wave in the mass of ‘empty’ space passes through both. As the physical wave exits the slits it creates wave interference. As the particle exits a single slit the direction it travels is altered by the wave interference. This is the wave piloting the particle of de Broglie wave mechanics. Detecting the particle strongly exiting a single slit destroys the coherence between the particle and its associated wave in the mass of ‘empty’ space.
What ripples when galaxy clusters collide is what waves in a double slit experiment; the mass of ‘empty’ space.
Einstein’s gravitational wave is de Broglie’s pilot-wave. Both are waves in the mass of ‘empty’ space.
The mass of ‘empty’ space is what relates relativity and quantum mechanics.
I realized it was a two year old thread after I posted. I usually search the interwebs for “mass of empty space” for the past two weeks. However, I forgot the two weeks part and didn’t realize it until after I posted.
I was also confused as to who was responding to who.
Again, this statement is wrong: “Mass” is not defined that way, except possibly by you. To the rest of the scientific community, “mass” is defined as “that portion of the energy of a system which cannot be transformed away by a change to a different reference frame”.
“Since according to our present conceptions the elementary particles of matter are also, in their essence, nothing else than condensations of the electromagnetic field”
The electromagnetic field is a state of the aether.
Particles of matter are condensations of aether. Aether has mass.
‘DOES THE INERTIA OF A BODY DEPEND UPON ITS ENERGY-CONTENT?’ A. EINSTEIN
“If a body gives off the energy L in the form of radiation, its mass diminishes by L/c2.”
The mass of the body does diminish. However, the matter which no longer exists as part of the body has not vanished; it still exists, as aether. Matter evaporates into aether. As matter evaporates into aether it expands into neighboring places; which is energy. Mass is conserved.
When a nuclear bomb explodes matter evaporates into aether. The evaporation is energy. Mass is conserved.
It’s not; energy is conserved, but mass (which is a kind of energy) on its own isn’t. Nuclear processes are the prime example: in nuclear fusion, the resulting nucleus has a smaller mass than the sum of those that went into its creation, while in fission, it’s the other way round, with the daughter nuclei in sum being less massive than the one that broke apart. In both cases, the difference in mass is the energy released in the process, which is how we can use them to generate electricity (or blow things up).
They are very different things. For one, gravitational waves are defined in ordinary spacetime, while the de Broglie/Bohm pilot wave is defined on a much higher dimensional space, the ‘configuration space’ spanned by the parameters defining the configuration of a given system—for a system of N point particles, these are the 3N coordinates giving their positions, for example. Furthermore, they are mathematically quite different things: gravitational waves are solutions to the nonlinear Einstein equation, while the pilot wave is a solution of the linear Schrödinger equation. They can’t be said to be the same, or even similar, in any respect at all.