PaulS1950 said:Here is a question:
Is the "density" of space lower where it is expanding?
Ikon Rahu said:I am curious about the expanding universe - that is, that the space itself is expanding. Why can't we notice the effects of an expanding universe here in our own solar system? Why doesn't space expand here around us? Wouldn't this result in more space between our molecules and so on until we would see more space between the objects in our local environement?
Mark M said:Because of gravity. Even gravity, the weakest force, is able to negate the effect of expansion inside of the galaxies. Dark energy does, however, have very tiny effect - but it's like an ant trying to move a bulldozer.
phinds said:I agree w/ your analogy but not its conclusion. If an ant pushes on a bulldozer, it's not the case that the ant has a little tiny effect, it is the case that the ant has absolutely no effect at all because it cannot to any extent overcome the forces holding the bulldozer in place.
phinds said:I agree w/ your analogy but not its conclusion. If an ant pushes on a bulldozer, it's not the case that the ant has a little tiny effect, it is the case that the ant has absolutely no effect at all because it cannot to any extent overcome the forces holding the bulldozer in place.
Drakkith said:I remember a thread about this. Did we ever come to a conclusion? I thought the expansion increased the distance between objects ever so slightly but doesn't keep increasing it. You can think of it as a very slight reduction in the force holding objects together. IE the distance between the Earth and the Sun is increased by like 0.1 mm due to expansion, but it doesn't keep increasing. (Ignoring acceleration of the expansion)
Chronos said:The best guess I heard on solar system effects is around 40 meters on Earth orbit over the last 4.5 billion years, but, that is somewhat less than the effect of radiative loss of solar mass loss over the same period of time. Cosmological affects due to dark energy are totally insignificant over such short distances.
Mark M said:Expansion has no effect on the orbit of the earth. What can is dark energy. One way to see why is the fact that dark energy is a uniform negative pressure, so it functions as a kind of 'anti-gravity' (of course, it may be just a constant curvature, which amounts to the same thing.) So, you must take that force into account for, say, the orbit of a planet. But it is negligible. However, nothing affects the size of atoms. The strong force is far to powerful.
phinds said:Yes, Chronos has alerted me to this. One thing I'm still not clear on is that I have heard both of the following regarding the effect of dark energy / the cosmological constant and I'd like to hear what you guys have to say (also see post #10)
1) the effect on the Earth's orbit is tiny and has gotten as big as it's going to get [I have no idea why]
2) the effect on the Earth's orbit is tiny and will contrinue to grow (but still be negligible)
regular expansion does not affect gravitationally bound objects. Dark energy does.
Mark M said:It depends on the nature of dark energy.
Firstly, keep in mind that even without dark energy, the orbit of the Earth will grow. That's because the Sun and the Earth emit gravitational waves over time, and exhibit gravitational recession, a consequence of general relativity. But let's ignore that.
Next, let's assume dark energy has a constant strength, so that it doesn't vary with time. With that in mind, I would have to say two is correct. Let's say we had two objects moving through a region in which dark energy was extremely strong (just a thought experiment). Since the force from DE is constant, the two objects will accelerate away, diverging to infinity.
So, we should be able to conclude that two is correct.
Naty1, regular expansion does not affect gravitationally bound objects. Dark energy does.
Naty1 said:So it still seems to me we instead say something like 'gravitationally bound systems and things inside them are not thought to expand [or are generally not considered to expand] but we have no exact solution, no good model, for such conditions.
We have presented a simple definitive question about the influence of the expansion of the universe on a very particular system: a classical “atom.” ... atoms are in no danger of being disrupted by cosmological expansion.
Take a look at the paper you posted - exponential expansion affects bound objects, however slightly.
...And we have found a simple definitive answer: Expansion forces increase with increasing atomic radius, while atomic forces decrease. This amounts to an instability with respect to the disruption of an atom. If the atomic accelerations are initially stronger than the cosmological, then the subsequent expansion will become less and less important. The atom will not “partially” take part in the expansion. If, on the other hand, the cosmological effect is initially stronger, the atomic radius will increase and the atomic forces will become less and less important. The atom will fully take part in the expansion...atoms are in no danger of being disrupted by cosmological expansion
Due to the exponential increase in a(t), the physical radius grows without bound.
Naty1 said:Mark M: Is that equation in your post within the quoted article? I am not familiar with that equation...is that available in say Wikipedia?... I have no idea about the assumptions from which it is built.
George Jones said:The weak-field limit of Einstein's equation without cosmological constant/dark energy leads to Poisson's equation,
\nabla^2 \Phi = - \vec{\nabla} \cdot \vec{g}= 4 \pi G \rho,
where \Phi is gravitational potential and \vec{g}= - \vec{\nabla} \Phi is the acceleration of a small test mass.
The weak-field limit of Einstein's equation with cosmological constant/dark energy \Lambda leads to a modified "Poisson" equation,
\nabla^2 \Phi = 4 \pi G \rho - \Lambda c^2.
For a spherical mass M, the divergence theorem applied to the above gives
\vec{g} = \left(-\frac{GM}{r^2} + \frac{c^2 \Lambda}{3} r \right) \hat{r}.
The second term is a "springy" repulsive term for positive \Lambda.
George Jones said:Yes. I also posted something similar in
https://www.physicsforums.com/showthread.php?p=2799641#post2799641.
I don't know of any online sources, but it is given in the books:
General Relativity: An Introdution for Physicsists by Hobson, Efstathiou, and Lasenby;
Gravitation: Foundations and Frontiers by Padmanabhan.
Mark M said:Dark energy is what I've been speaking about - since it's a uniform negative pressure (or a constant negative curvature), it affects everything. However small these effects are (small enough that they won't even affect atoms), they can increase orbits, by an extremely small margin.
Drakkith said:Here's how I'm interpreting this. Expansion can be seen as a slight reduction in the "force" holding things together. Meaning that the Earth is very very slightly further out than it would be if there were no expansion. The effect of dark energy, or the acceleration of this expansion, results in an increase in the rate of this expansion, further reducing the attractive force between objects.
How's that sound?
Mark M said:Well, normal expansion has absolutely no effect inside of galaxies. See the website I posted above by John Baez.
Think of the force from dark energy as repulsive gravity. But, the key difference is that it exerts this repulsive gravitational force at every point (or, in the language of a cosmological constant, there is a constant curvature at every point.). So, it continually expands the orbit of the Earth at a constant rate.
Drakkith said:Ah I see. The FRW spacetime simply doesn't apply at the local scale. So how does one reconcile the two different spacetimes from the article? If the universe as a whole is expanding, but locally it has zero effect, where's the middle ground? How weak does gravity need to be between two objects for expansion to occur?
Mark M said:It needs to be extremely weak, and there needs to be a sufficiently large distance in between the objects. Unfortunately, it's a grey line. It's like asking 'When do we start using global coordinates instead of local coordinates?'. There isn't a well defined answer.
Well, normal expansion has absolutely no effect inside of galaxies. See the website I posted above by John Baez.
Neither Brooklyn, nor its atoms, nor the solar system, nor even the galaxy, is expanding.
...You can see that the cosmological constant reduces the attractive force of gravity by some small amount. For atoms, this would have the effect of making atoms ever so slightly larger than they otherwise would be (the difference really is utterly negligible, however).
The FRW spacetime simply doesn't apply at the local scale.
...regular expansion does not affect gravitationally bound objects. Dark energy does.
So how does one reconcile the two different spacetimes from the article? If the universe as a whole is expanding, but locally it has zero effect, where's the middle ground? How weak does gravity need to be between two objects for expansion to occur?
It needs to be extremely weak, and there needs to be a sufficiently large distance in between the objects. Unfortunately, it's a grey line. It's like asking 'When do we start using global coordinates instead of local coordinates?'. There isn't a well defined answer.
a negative pressure dark energy is the same thing as a cosmological constant.
The difference is that the curvature from the cosmological constant is intrinsic, it's just there. With a dark energy case, the negative pressure creates the curvature.
Do you agree that regular metric expansion (as in FRW) does not have an effect within gravitationally bound systems?
Well, you could think of a cosmological constant as being a geometric feature of the particular space-time. For example, a space with a cosmological constant and no matter is a de Sitter space. A de Sitter space just comes with this constant force (the cosmological constant). Nothing present in the space causes this, it's 'built in' to it's equations.Naty1 said:Was not aware of such a distinction...but it makes no sense to me...'intrinsic' usually means we have no good ideas! In this case, assigning such a 'constant' factor of integration and ascribing a specific physical meaning amid the mess of GR is byond my paygrade!
It comes from the normal Einstein Field equations. Take a look: R_{\mu \nu} - {1 \over 2}g_{\mu \nu}\,R + g_{\mu \nu} \Lambda = {8 \pi G \over c^4} T_{\mu \nu} Now, say no matter is present, so we can ignore the the Ricci tensor and scalar. (Those are the two 'R's, the tensor has a subscript). Now the equation becomes g_{\mu \nu} \Lambda = {8 \pi G \over c^4} T_{\mu \nu} Using a little algebra, you can solve for the stress-energy tensor (the 'T'), and get this T_{\mu \nu} = - \frac {\Lambda c^{4}} {8 \pi G} g_{ \mu \nu} From which you could derive the expression I posted above.the exact mathematical relationship between vacuum energy and the cosmological constant is interesting...have not seen it...
They most definitely don't apply for non-homogenous distributions of matter, such as galaxies. So, as John Baez explained on that page, we say that no expansion is occurring in the galaxies (dark energy is a different matter).Do you think the assumptions that go into the FLRW metric solution
to the EFE apply within gravitationally bound systems?
If anything there is a vanishingly small FRW element to the metric of bound structures. If the FRW metric 'prevail(ed) on all scales and everywhere, even inside gravitationally bound structures or within atoms' then why do galaxies maintain a constant size as the distance between them expands? Commonly we are told that the local mass concentration 'overcomes' the expansion preventing this from occurring. This is one of the worst and most fallacious explanations you could possibly give someone! What really happens then?
The FRW metric is the inevitable result of the cosmological principle, CP. which is that the universe is homogeneous and isotropic. The metric is only valid if these principles hold. Consider now a galaxy, solar system or planet. Does the CP hold? No. Is it a remotely useful approximation? Not at all! Unsurprisingly then the dynamics of bodies in these systems and on these scales bears no resemblance to the dynamics of galaxies. So for instance, there is no redshift of light due to a(t) when we observe light from the other side of our galaxy, or from say Andromeda. The FRW metric simply is not valid on these scales.
….. The better way to look at it is that the presence of the mass in the galaxy gives the metric of space-time around this mass a form that would look much more like a Schwarzschild metric than FRW (though we cannot fully solve GR for a galaxy.). The point is though that there is not expansion to 'overcome' since the 'expansion' is merely the result of the metric [variable over time] formed by a homogeneous and isotropic mass distribution. If the mass doesn't obey these principles we shouldn't be surprised that we don't see any 'expansion'.
If you don't believe me hold an object in each hand with outstretched arms. When you let them go what happens? I think you will find that they both plummet towards the local centre of mass (the centre of the Earth) rather than drift off into the Hubble flow! The local mass concentration can hardly be described as a mere perturbation to the FRW metric!
….the 'expansion' (which we both definitely agree is a bad term for it!) is a result of the FRW metric, in particular a(t). The metric in the region of bound structure looks nothing like the FRW metric, in particular it has no global time dependence (though will of course evolve). For this reason I stand by the statement that the FRW metric is not valid on scales which are significantly inhomogeneous, since the metric has no component that reflects the global a(t), and hence the FRW picture does not relate to the dynamics of the system.
Well, you could think of a cosmological constant as being a geometric feature of the particular space-time. For example, a space with a cosmological constant and no matter is a de Sitter space. A de Sitter space just comes with this constant force (the cosmological constant). Nothing present in the space causes this, it's 'built in' to it's equations.
