It looks like you’re right. From this site the spave between the two observers must be flat to have paradoxes caused by FTL communication.
Toadspittle: I believe that the expansion of space is operating on all scales equally. Thats why more distant galaxies look they’re moving away from us more quickly - simply because there is more space between us which is all expanding equally. Its happening too slowly for us to detect it on the scale of our solar system.
We don’t know what scale or what form dark matter appears to operate on. Basically the universe is slowing its expansion far more quickly than we would expect given the amount of matter we can see. What is causing this whether its dark matter or something else we don’t know.
I’ve posted “what if” questions re physics and cosmology before; I love this stuff.
What I find remarkable, and (we’re all friends here, right?) very gratifying is that some of these made-up “what-if’s” of mine can actually chug along for a ways before being shot down. (Huh; mixed metaphor.)
I was unaware that some contemporary physical thinkers really are considering both my “ideas” as an alternative to the “dark matter” hypothesis. I’ve never heard of “MOND” in my life, nor Dirac’s “large number hypothesis” (sounds mucho fun). But even if my notions are losers, they’re not, at least, obviously so from the start.
Sentient Meat or somebody: about that average-distance thing…I get the general idea, but…what’s the actual formula?..you know, radius times this divided by that squared, and so on. It seems relevant in determining how far back in time we are “seeing”.
The casualness of my tone is not meant to characterize the significance of these topics, by the way.
Selecting the centre of a disc whose edge is at radius R, we want the radius r for which the area of the disc past that radius (ie the area of the flat anulus of outer radius R and inner radius r) is exactly equal to the area of the inner disc.
the area of the outer ring is
[symbol]p[/symbol]R^2 - [symbol]p[/symbol]r^2
the area of the inner ring is
[symbol]p[/symbol]r^2
So the value of r for which the two are equal is gained by equating these two:
[symbol]p[/symbol]R^2 - [symbol]p[/symbol]r^2 = [symbol]p[/symbol]r^2
Or, [symbol]p[/symbol]R^2 = 2[symbol]p[/symbol]r^2
Rearrange and cancel: r=R/(root 2),
ie. the average distance from the centre of the disc is R divided by root 2.
It is my understanding that currently, energy is assumed to not generate gravity. Has any scientist taken into account the gravity that would be induced by energy currently floating around in space? I mean, after 20 odd billion years of radiation, there’s probably quite a bit out there. Then again, perhaps I’m just pissing in the wind.
It’s my understanding (and I could be pathetically wrong) that energy was explicitly assumed to exert gravitational forces in exactly the same way as if it were mass. I thought that was the whole point of E=mc^2; energy is mass, and mass is energy, and what holds for one holds for the other. This is what allows light particles to be affected by the gravity of large bodies, eg, the sun.
Along the same vein, you seemed to imply that we would have more energy out there now than we would’ve 20 billion years ago, which isn’t really correct. The amount of mass-energy that we have now hasn’t changed a bit since the dawn of (space-?)time. Some of that mass has been “converted” into energy, but this doesn’t mean there’s more stuff out there affecting gravity now than there was before.
Scott Dickerson:
My knowledge of General Relativity is pretty minor, but I’d always thought that the whole point was the gravity didn’t behave according to a strict distance-squared rule. It’s close, and as you get farther away it’s undetectably close, but it’s not precise. The main places where it differs from the -square rule are near superdense bodies, like black holes. When you get really close to really dense things, space-time does all manner of weird-ass contortionist things, and Newtonian rules no longer apply, just as things like F=ma and velocity addition fall apart at linear velocities near c.
So your idea holds merit. In fact, it holds such merit that Einstein beat you to it by 100 years.
And of course, if I’m completely full of it, I would love to be corrected.
Jeff
Your equation is for the average distance from the center of a circle to an arbitrary point on the circle. I interpreted his question to mean the average distance between two arbitrary points in the circle. If that’s the case, the result I got was:
sqrt(r^2 + (R^2)/2), where R is the radius of the circle, and r is the distance from the center of the circle to the arbitrary point in question
When the arbitrary point happens to be the center of the circle, then my equation simplifies into yours.
If what Scott was asking for was, in fact, what Sentient already posted, then I apologize for the waste of bandwidth.
Jeff
Yes, that’s what I think too, but I’ve often heard otherwise. Crazy physicists.
Well, some percentage of mass that was intially present when the big bang went boom is currently twiddling around space in the form of photons. Since most of them aren’t hitting us, we can’t see them, but we can feel their gravitational effects (assuming we’re right in that they have an effect). If enough energy is present in such fashion, that would nicely account for the discrepancies currently associated with dark matter, without having to stoop to invisible spacedust or a mutating G.
Ah, yes. Very good point. Not so much the creation of “new” energy as just a very wide dispersal of what there already was, and in such form as to be very difficult to measure.
I wonder, though, isn’t all of that accounted for by the 3K background radiation we see in all directions? Doesn’t that represent all of the photons and space dust and whatnot that’s leftover from the Big Bang, and past generations of stars, and such?
Crap, my mind isn’t used to all this… thinking… Better feed it some more 80’s pop rock before I get a migraine.
Jeff
We are able to tell exactly how much background radiation left over from the big bang there is in the universe as it must be the same in all places, so that could not account for the missing mass. Dark mass is made up of two components baryonic and non-baryonic. The baryonic componet is just bascially star debris etc., however this can’t account for all the dark mass so you have the non-bayronic dark mass which is the bone of contention here. The best theory for this is made up of massive but weakly interacting particles (not photons, as they are not dark or massive) left over from the big bang.
Dark energy is what’s being postulated to explain the apparent acceleration of the expansion of the universe. The latter is a relatively recent discovery and so post-dates most of the speculation over dark matter.
More specifically, ordinary matter has the property that as space expands the matter spreads out and so becomes less dense on average. Since mass and energy densities are related (via E=mc[sup]2[/sup]), this means that the density of the energy from ordinary matter falls as the universe expand. Now the simplest way of explaining the accelerating expansion would be by having a cosmological constant. But you can think of that as coming about by space being filled with a funny form of energy. Rather than having its density fall as the universe expands, it stays the same. In other words, the more space you have, the more of this dark energy you have. This seems a little strange compared to the energy associated with everyday matter, but it’s a bit less strange in quantum field theory.
What seems to have happened is that the early universe was dominated by the energy density from ordinary stuff (including dark matter). But as the density of that fell, it more recently became less important overall than the energy density from dark energy. At which point the acceleration kicked in.
Currently, nobody has much of a firm grasp on dark energy beyond this. Of course, with two unknown phenomena out there, it’s tempting to suspect that they’re related, but it’s still early days.
Further to MC’s comment about the photons from the Big Bang being rather well accounted for, the number of photons out there (technically, the photon density) is actually probably the single most secure fact in cosmology. It’s easily deduced from the temperature of the background radiation and that’s now extraordinarily well measured. Turns out that there are about half a million photons per litre.
Dear Masters of the universe, I know I haven’t really got any say in the matter, but can you fix it so that the Dark energy hypothesis is ever so slightly wrong?
I understand it could make the creation of E-R wormholes a little easier if there is bucket loads of dark energy lying around, which means that humanity might be able to colonise the Virgo Supercluster after all, which is nice, but
the downside seems to be
that the universe repels itself into tiny little bits in just under 20 billions of years.
I meant- look here. There will still be billions of red dwarfs merrily fusing away at that date…I was hoping to put civilisations around all those stars.
thanks, eburacum
I wasn’t aware that in the General-Relativistic view, what happens to gravitation around a largish mass is to be viewed as a modification of the exponent of attenuation re the gravitational field.
I thought the idea was that the generic formula really does hold, BUT you have to take into account that the distance factor (the space over which it holds) is not what we presume “from the outside,” but involves a degree of curvature-- ie, “more distance” packed into the same perimeter. No?
SentientMeat and ElJeffe–
We’re gettin’ there. I’m asking this:
Given a disk of radius R, and one point P selected at random lying within said disk, how does one calculate the AVERAGE DISTANCE between P and all the other points lying within the disk? (I think this is like treating P as the origin of an infinite number of radial line segments, each one of which ends on one point on the circumference of the circle; finding the midpoint of each such quasi-radius; and then somehow determining the average distance to all those midpoints. Mm?)
It took me two months to figure out how to collimate my new telescope. This thread gives me a headache.
Still, though, I have a question. Is dark matter referring to simple dust that doesn’t happen to be illuminated, as Sam Stone would suggest? It seems to me the existence of non-illuminated dust is pretty old hat; the Horsehead Nebula or Coal Sack Nebula, for instance, or the dust lanes you can plainly see in any galaxy including our own.
RickJay, the dark mass does include the hadronic (and necessary leptonic) particles that make up space dust. However this cannot account for all of the dark mass. So what we are talking about is probably completly undiscovered WIMP(s) (Weakly-Interacting Massive Particle(s)), though neutrinos have been put forward as a candidate for dark matter too.
This isn’t much of a debate, but, I recently read a book on the subject… and wouldn’t you know, it’s available for a free read online via the National Academies Press site.
Check it out: http://books.nap.edu/books/0309084075/html/index.html
