Lambda-CDM theory - Woo or not?

[ben m]

Yep, it's an interesting one for all sorts of reasons. Like this: neutrinos are more like photons than electrons.

Nope. Let's review:

Electrons: Fermions. Massive. Couple to the neutrinos via the weak charged current. Carry conserved lepton number. Charged.

Neutrinos: Fermions. Massive. Couple to the electrons via the weak charged current. Carry conserved lepton number. Neutral.

Photons: Bosons. Massless. Couple to all charged quarks and leptons. Couple to the weak interaction via the triple-gauge and quadruple-gauge couplings. Mixes with the Z boson. No conserved quantum numbers. Neutral.

 

[Michael Mozina]

I might come back to other stuff later but - errr? How? Other than being neutral?

Speed too.

 

[Michael Mozina]

Most things are. That's why we talk I suppose.

Yes indeed.

Vacuum fluctuations are real enough, as demonstrated by the Casimir effect. But that isn't what keeps the electron and proton together in a hydrogen atom. They aren't actually exchanging virtual photons. They're just the accounting units. A nice analogy is that there are no actual virtual pennies flying into your bank account when your salary gets paid in. Search google on this, but it's maybe one for another thread.

I guess the best way to explain my position is that I'm inclined to believe that those real fluctuations (I agree they occur) are caused by interactions of quite REAL particles that are already traveling through the experiments.

I skimmed the paper. I don't like it I'm afraid. Brooklyn doesn't expand for the same reason a galaxy doesn't expand or an electron doesn't expand, because it's "bound". The simple analogy is that of the rubber-sheet universe with a knot in it. Stretch it and the knot doesn't expand with the rubber sheet. But the paper treats space as absolutely empty. That isn't in line with Einstein's Leyden address, where he talked of inhomogeneous space and said has, I think, finally disposed of the view that space is physically empty. Space isn't the same as nothing, it sustains fields and waves, from which we can make matter via pair production. There's energy in it, that energy has a mass equivalence, the vacuum isn't the same as nothing.

Well, in real life no. For purposes of the paper, yes. Not liking it and finding a mathematical flaw in it are two entirely different things by the way. I see however that you have your hands full at the moment, so we'll take it up at a more appropriate time. Suffice to say I don't buy the idea that a NON empty vacuum expands faster than light. Of course if those neutrino results hold up....

This touches on what I mentioned earlier about space just having to expand. The universe as a whole is not bound, and there's stress-energy in the space, even in an "empty model". Stress is measured in Pascals like pressure, the dimensionality of energy is pressure x volume, so the universe starts with a high spatial energy density, like a high pressure, and there's nothing to confine it or bind it, and it just has to expand. So switch from the rubber-sheet analogy to a stress-ball universe. Squeeze it in your fist and let it go.

I don't have any problem with your analogy, other than to point out that nothing we know of (yet) travels faster than light. While it can expand, it's unlikely (IMO) that it's expanding any differently than plasma due to plasma pressure. It's still limited by the speed limits of mass.

They're probably expert in the MTW version, which is subtly different to Einstein's original.

Ya, I agree. Einstein's version just had a constant which he preferred to be set at zero. They stuffed a whole bunch of "dark energy" in there.

Have a look at Golden age of general relativity and note the paradigm shifts. One was the big bang, which I'm happy with. Another is the role of curvature in general relativity, which I'm not. I think it causes problems for cosmologists.

I think I'll try to see your side of the argument as you discuss the issue with sol and see if I can help in any way. I'm more likely to be sympathetic to your viewpoint since I'm not a fan of Lambda-CDM theory. They are typically more of the 'hardcore believer' sort of folks.

FYI, sol is very knowledgeable, particularly with GR theory. If you intend to stand your ground, be sure you're listening to his argument carefully and responding accordingly. He'll come around eventually if there is any merit to your argument. Edd is great by the way. There's never an ego battle with edd. He never barks, but if he bites you, he's like a pit bull and you're probably in trouble.

You might just as well forget about RC and some of the folks that rub you the wrong way. I'd love to see you and sol discuss your ideas. We'd all learn a lot. Stay focused with edd and sol. This could get fun......

 

[Reality Check]

Ya, I agree. Einstein's version just had a constant which he preferred to be set at zero. They stuffed a whole bunch of "dark energy" in there.

Ya, you are still ignorant about dark energy.

Dark energy is the term for the cause for a set of observations about the universe, e.g. the rate of expansion is measured to be accelerating.

Einstein's version had a zero cosmological constant and resulted in invalid solutions from it (its solutions for a static universe were unstable so that any perturbation lead to an expanding or contracting universe).

A non-zero cosmological constant is a possible cause of dark energy. It is regarded as the best solution because it is the simplest, e.g. involves known physics. The alternatives mean wandering into more exotic physics.

A non-zero cosmological constant exerts the negative pressure that dark energy needs to have.

Independently from its actual nature, dark energy would need to have a strong negative pressure (i.e. effects, acting repulsively) in order to explain the observed acceleration in the expansion rate of the universe.
...
The cosmological constant has negative pressure equal to its energy density and so causes the expansion of the universe to accelerate. The reason why a cosmological constant has negative pressure can be seen from classical thermodynamics; Energy must be lost from inside a container to do work on the container. A change in volume dV requires work done equal to a change of energy −P dV, where P is the pressure. But the amount of energy in a container full of vacuum actually increases when the volume increases (dV is positive), because the energy is equal to ρV, where ρ (rho) is the energy density of the cosmological constant. Therefore, P is negative and, in fact, P = −ρ.

 

[Michael Mozina]

Ya, you are still ignorant about dark energy.

So what? So are you. You can't even tell me where it comes from!

 

[W.D.Clinger]

Einstein's version had a zero cosmological constant and resulted in invalid solutions from it (its solutions for a static universe were unstable so that any perturbation lead to an expanding or contracting universe).

Uh, no. Einstein's original version of the field equations omitted the cosmological constant. Einstein added the cosmological constant two years later, partly because his original equations had no static solution. It was Einstein's cosmological constant that made the static solution possible.

Mathematically, omitting the cosmological constant is analogous to omitting the constant from a solution to an indefinite integral. The omission rules out perfectly good solutions for no good reason. As Michael Mozina and others are fond of telling us, we should let empirical physics decide such things. At the moment, it looks as though empirical physics is telling us the cosmological constant is nonzero.

 

[Wangler]

So, are you interested in learning that, or not? And do you or do you not know enough basic vector calculus to follow a simple derivation involving Newtonian gravity and a few aspects of Maxwell's equations?

Yes, and yes!

This is an opportunity not to be missed.

I hope Sol continues!

 

[Reality Check]

So what? So are you. You can't even tell me where it comes from!

Wrong. I know about the evidence for dark energy just as anyone who can read can find out about the evidence for dark energy. That does not seem to be you though!

I can tell you where it comes from: probably a non-zero cosmological constant, maybe quintessence or a couple of more exotic theories.

 

[sol invictus]

No offence, but Sol doesn't know as much as he thinks.

That is probably true. Nevertheless, your posts make it plain that I know far more about this than you do.

I reiterate: if you assume that the universe is homogeneous and isotropic, there's absolutely no gravity in it, spacetime is flat.

That is flat-out false, as W.D.Clinger and others pointed out. To see that it is false, all one needs to do is compute the curvature - which for FRW solutions is extremely easy - and note that it is not zero.

Lay it on me, sol. But do note that understanding the simple case relates to axioms, essentially undertstanding the terms. That's sometimes an issue.

Sure. I have a deep understanding of say this that gets right down to the fundamentals.

Good. Very well. Start from Newtonian gravity, because general relativity reduces to Newton in the limit of weak gravity (as any potentially valid theory of gravity must). Here's Newtonian gravity:
[latex]$\vec \nabla \cdot \vec g = -4 \pi G_N \rho_m$[/latex], where rho_m is the matter density, [latex]$\vec g = \vec \nabla \Phi_N$[/latex] is the gravitational field, and G_N is Newton's constant.

Note that if you map the gravity field to the electric field and mass to charge, this is identical to Gauss' law in electrodynamics, which the exception of the minus sign (which means positive masses attract each other instead of repelling).

Now, we know gravity should act on all forms of energy, including the energy in the gravitational field itself. So if we want to include the effect you mentioned, we should start by adding a term to the right hand side that encodes the energy in the gravity field. But what term should we add? Well, first let's recall what the energy density is in an electric field:
[latex]$\rho_E = (1/2)\vec E^2 = (1/2) (\vec \nabla \phi)^2$[/latex],
where phi is the electric potential and E is the field.

Question: what is the energy in an gravitational field? The obvious guess is that it should be given by this same formula, namely [latex]$\rho_g = (\alpha/2)\vec g^2 = (\alpha/2) (\vec \nabla \Phi_N)^2$[/latex], where alpha is some constant. So, let's see what happens if we add this term to the right hand side of Newton's equation:

[latex]$\vec \nabla \cdot \vec g = -4 \pi G_N \rho_m + c^2(\vec g)^2/2$[/latex], where c^2 must be there by dimensional analysis (the fact that it's c^2/2, and not c^2/53 pi or something cannot be derived from this, but if you're more careful and check the constant I believe that's exactly what you find).

A couple of things to notice about this formula.

First, since the second term on the right is quadratic in g, it's not important when g is small. That had to be the case since the theory needs to reduce to Newton in the weak field limit.

Second, if the field g is weak, we can easily estimate how important the second term is. All we need to do is calculate what g would be in Newtonian gravity, plug that into the second term, and compare it to the G_N rho_m term to see how much it matters.

Before doing that for a galaxy or other interesting object, I'll pause and make sure you're following so far.

 

[Wangler]

Before doing that for a galaxy or other interesting object, I'll pause and make sure you're following so far.

I think so...that is beginning to look like a diff. eq. that I seem to remember from somewhere.........

 

[Farsight]

I guess the best way to explain my position is that I'm inclined to believe that those real fluctuations (I agree they occur) are caused by interactions of quite REAL particles that are already traveling through the experiments.

I don't think there's a problem in saying that vacuum fluctuations are real. I'd say the problem comes when people equate them to the QED virtual photons which are said to bind the electron and the proton in a hydrogen atom. They aren't the same thing. There aren't any real photons flitting back and forth between the electron and proton.

Well, in real life no. For purposes of the paper, yes. Not liking it and finding a mathematical flaw in it are two entirely different things by the way.

Definitely. There can be some big issues in interpretation, wherein the same mathematics can deliver two entirely different meanings, and does not distinguish between the two.

I see however that you have your hands full at the moment, so we'll take it up at a more appropriate time.

Maybe we need a separate thread for the neutrino issue.

Suffice to say I don't buy the idea that a NON empty vacuum expands faster than light.

Humour me on this, it's important to the discussion.

I don't have any problem with your analogy, other than to point out that nothing we know of (yet) travels faster than light. While it can expand, it's unlikely (IMO) that it's expanding any differently than plasma due to plasma pressure. It's still limited by the speed limits of mass.

Let's park that one and come back to it another time. The main point is that if space has an innate "pressure" and is not bound because there's nothing outside it, it's reasonable to expect it to expand.

Ya, I agree. Einstein's version just had a constant which he preferred to be set at zero. They stuffed a whole bunch of "dark energy" in there.

Check out the vacuum catastophe. It's important.

I think I'll try to see your side of the argument as you discuss the issue with sol and see if I can help in any way. I'm more likely to be sympathetic to your viewpoint since I'm not a fan of Lambda-CDM theory. They are typically more of the 'hardcore believer' sort of folks.

Like I said, belief is kinda weird. The crucial point is this: you can't trust your own beliefs. Trust me on this.

FYI, sol is very knowledgeable, particularly with GR theory. If you intend to stand your ground, be sure you're listening to his argument carefully and responding accordingly. He'll come around eventually if there is any merit to your argument.

I'll listen carefully and respond accordingly.

Edd is great by the way. There's never an ego battle with edd. He never barks, but if he bites you, he's like a pit bull and you're probably in trouble.

LOL, I'm looking forward to this.

You might just as well forget about RC and some of the folks that rub you the wrong way. I'd love to see you and sol discuss your ideas. We'd all learn a lot. Stay focused with edd and sol. This could get fun......

Tim's the one I want to get the message across to. He sounds like a cosmologist who knows his stuff, but who has been ill-advised on the fundamental physics.

 

[Farsight]

In actual fact it is the other way around.
Neutrinos started as more like photons in that they were massless. The observation of neutrino oscillations means that they have mass. So they are more like electrons in that they have mass. However in all other respects thay are not like electrons, e.g. they have no charge. The hint that they may travel slightly faster than the speed of light would rule out neutrinos as being anything like photons since photons travel at the speed of light.

Let's talk about neutrinos on another thread another time.

What is so special about Einstein's original version?

He gave the equations of motion rather than the equations of curved spacetime, and took the view that the speed of light varied with gravitational potential, qualifying his SR postulate. This isn't the modern view. See this article and look at the section on General Relativity.

Sceince always improves on original concepts. The MTW version is an improvement on Einstein's original, e.g. adds the cosomological constant.

Don't you believe it. Wheeler said "Matter tells space how to curve. Space tells matter how to move", which is trash.

Why are you not happy with the fact that people have grown to appreciate the importance of spacetime curvature in GR?

Because they confuse cause and effect.

I think it causes no problems for cosmologists. As that Wikipedia page states - they appreciate it!

We'll have to agree to differ on that.

 

[edd]

Edd is great by the way. There's never an ego battle with edd. He never barks, but if he bites you, he's like a pit bull and you're probably in trouble.

Eeesh, don't build me up too much. I'm much more an observer and my GR knowledge doesn't actually compare to a lot of people here.

 

[Farsight]

Wrong: Any mass or energy results in curved spacetime. A concentration of energy results in a more strongly curved spacetime. This implies that you have never seen Einstein's field equations, so here they are...

Of course I've seen them. The issue is in the interpretation, what the individual terms actually represent, what curved spacetime really is, and seeing the underlying simplicity. Let me try to get this across with a trivial example. You have a massive body in space. The energy present in this body "conditions" the surrounding space, the effect diminishing with distance, such that a light beam curves as it transits this space. Now add another massive body near to the first one, and shoot your light beam through the gap between them. It doesn't curve. However you can detect a Shapiro delay, so you can assert that spacetime is still curved. Now chop up your massive bodies into infinitesimal parts and distribute them evenly throughout the universe. Shoot a light beam through it, and that light beam doesn't curve. And you can't detect a Shapiro delay either. Forget about the expansion of the universe for a minute, and think about it. Light moves uniformly, in straight lines: your spacetime curvature has gone.

 

[Farsight]

Clicking on the link above reveals a post in which I didn't write those two sentences you attributed to me.

Sorry, my mistake, that was RealityCheck.

The evidence of your recent posts shows you are misrepresenting the FLRW solutions. That fact can be checked by anyone who has access to the standard references I cited. If you believe those standard references are incorrect on this point, it's your responsibility to explain why they're wrong and you're right.

I'm not misrepresenting them, I'm pointing out a clear issue. Here's the Einstein quote again followed by the quote from wiki:

”According to this theory the metrical qualities of the continuum of space-time differ in the environment of different points of space-time, and are partly conditioned by the matter existing outside of the territory under consideration. This space-time variability of the reciprocal relations of the standards of space and time, or, perhaps, the recognition of the fact that ‘empty space’ in its physical relation is neither homogeneous nor isotropic, compelling us to describe its state by ten functions (the gravitation potentials gμν)...

"The Friedmann–Lemaître–Robertson–Walker (FLRW) metric is an exact solution of Einstein's field equations of general relativity; it describes a homogeneous, isotropic expanding or contracting universe..."

To expand on that, the FLRW solutions include "dusty" solutions in which matter dominates radiation, so we can approximate the density of matter by a positive number rho while approximating radiation by zero. Since the solutions are homogeneous and isotropic, given any point in the universe we can choose a local coordinate system in which T⁰⁰=rho but all the other coordinates of the stress-energy tensor are zero. By the Einstein field equations, the Ricci tensor, curvature R, and cosmological constant cannot all be zero. Conclusion: You get to choose between curvature and Einstein's unstable steady state cosmology.

Einstein seemed to have a bit of a blind spot when it came to cosmology. I don't know if you've read The Meaning of Relativity, but there's a "dusty" chapter there.

(As I was about to post this, I saw that Reality Check has already said pretty much what I said in my paragraph above. That just goes to emphasize how obvious this should have been to Farsight.)

See my reply. Think it through.

ETA: Actually, you don't even get the choice I stated in my conclusion above. As Reality Check said, the Einstein field equations (together with the assumption that metrics have Lorentzian signature) imply curvature for all of the "dusty" FLRW solutions.

So you've got light moving uniformly in straight lines. Where's your curved spacetime gone? Space is homogeneous. There's no gravitational field. There is no gravity to make this universe collapse, even when it was much smaller, with a much higher energy density. And let's face it, if it had done, we wouldn't be here.

 

[sol invictus]

Of course I've seen them. The issue is in the interpretation, what the individual terms actually represent, what curved spacetime really is, and seeing the underlying simplicity.

"Curvature" has a specific mathematical definition, Farsight. Reality Check is correct - Einstein's equations guarantee that the curvature is non-zero if the energy density is, because they equate a certain combination of curvature components to it. That makes you wrong by definition.

Let me try to get this across with a trivial example. You have a massive body in space. The energy present in this body "conditions" the surrounding space, the effect diminishing with distance, such that a light beam curves as it transits this space. Now add another massive body near to the first one, and shoot your light beam through the gap between them. It doesn't curve. However you can detect a Shapiro delay, so you can assert that spacetime is still curved. Now chop up your massive bodies into infinitesimal parts and distribute them evenly throughout the universe. Shoot a light beam through it, and that light beam doesn't curve. And you can't detect a Shapiro delay either. Forget about the expansion of the universe for a minute, and think about it. Light moves uniformly, in straight lines: your spacetime curvature has gone.

Beam some light between a receiver A and an emitter B in an expanding FRW spacetime. If the receiver and emitter are at rest in comoving FRW coordinates, the received light will be redshifted.

That can only happen in a flat spacetime if A and B are in relative motion (moving away from each other). Let's say after hearing from B that there's a redshift, A fires a rocket to accelerate herself towards B, and then emits light. If A is moving at just the correct velocity, the light received by B will not be redshifted or blue shifted. But, after some time passes (during which neither A nor B fires any more rockets), the light will go back to being redshifted. That cannot happen in flat spacetime, therefore the spacetime is not flat.

I can give lots of other physical examples of how you can measure the spacetime curvature of FRW, but that's a pretty simple one.

 

[Farsight]

That is probably true...

Sorry sol, I have to go. I'll reply another time.

 

[W.D.Clinger]

Of course I've seen them.

You've seen the Einstein field equations, but you don't understand them. There's no shame in that, because you can't understand the field equations until you understand the mathematics underlying their notation, and that mathematics is fairly advanced. In particular, you can't understand the Einstein field equations until you understand the mathematical notion of a manifold's intrinsic curvature.

Let's start with a simple example (although you'll have to imagine a more extensive land mass than exists on earth): Stand at the equator, facing north. Walk straight ahead until you get to the north pole. Turn left exactly 90 degrees. Walk straight ahead until you get to the equator. Turn left exactly 90 degrees. Walk straight ahead until you get back to where you started. Your path consists of three fragments of geodesics that describe a triangle. What's the sum of that triangle's angles? 270 degrees.

On a 2-dimensional manifold without curvature, every triangle's angles sum to 180 degrees. The discrepancy between 270 degrees and 180 degrees indicates curvature. That discrepancy can be converted into a mathematically well-defined measure of curvature via careful definitions and taking limits of certain ratios as the size of the path goes to zero. It turns out that the surface of a sphere has constant curvature.

In general, however, the curvature depends on the direction of the path, so the general definition of mathematical intrinsic curvature is more complicated. That more general definition of intrinsic curvature is called the Riemann tensor. A simplification of the Riemann tensor, obtained by contraction, is called the Ricci tensor. Simplifying the Ricci tensor to a scalar via contraction yields the scalar curvature. Although the full Riemann tensor does not appear in Einstein's field equations, the Ricci tensor and scalar curvature do appear. If the scalar curvature is nonzero, then the spacetime manifold is curved by the very definition of curvature. If the Ricci tensor is nonzero, then the spacetime manifold is curved by the very definition of curvature.

The issue is in the interpretation, what the individual terms actually represent, what curved spacetime really is, and seeing the underlying simplicity.

There is no interpretation needed: The Ricci tensor and scalar curvature are mathematically well-defined. You just need to learn those definitions. Only then will you understand what the individual terms actually mean, and what curved spacetime really is.

So you've got light moving uniformly in straight lines. Where's your curved spacetime gone?

You're like the fellow at the bowling alley who says the bowling lanes can't be curved because you don't see them bending to the left or right. If I suggest they be lengthened to make the curvature more apparent, he says they won't bend to the left or right no matter how long you make them. If you make them long enough, however, the pins will be set up only 3 meters behind him.

That analogy isn't exact, because the bowler can say the two-dimensional surface of the earth is embedded within a 3-dimensional Euclidean space. Spacetime, however, is not Euclidean. Spacetime is Riemannian.

Space is homogeneous. There's no gravitational field. There is no gravity to make this universe collapse, even when it was much smaller, with a much higher energy density. And let's face it, if it had done, we wouldn't be here.

Cosmologically, the curvature/gravity of an FLRW "dusty" solution manifests itself as a reduced rate of expansion. If the matter density is less than or equal to the critical value, the universe will expand forever, but it will expand slower than it would have without the curvature/gravity due to matter. If the matter density is greater than the critical value, the universe will eventually collapse.

As for the fact that we're here: Obviously the universe hasn't yet collapsed completely, and doesn't appear to have begun a collapsing phase, and may never begin a collapsing phase. On the other hand, the mass/energy density of the universe appears to be very close to the critical value. Why that should be so is one of the great mysteries of cosmology.

 

[Farsight]

Start from Newtonian gravity, because general relativity reduces to Newton in the limit of weak gravity (as any potentially valid theory of gravity must). Here's Newtonian gravity:
[latex]$\vec \nabla \cdot \vec g = -4 \pi G_N \rho_m$[/latex], where rho_m is the matter density, [latex]$\vec g = \vec \nabla \Phi_N$[/latex] is the gravitational field, and G_N is Newton's constant.

That’s Gauss’s law for gravity in differential form, see wiki. Newtonian gravity is usually described in a different fashion, such as... (is there a problem with frac and over on this latex? F = G \frac{m_1 m_2}{r^2} and another expression doesn't seem to parse, maybe it's me).

Note that if you map the gravity field to the electric field and mass to charge, this is identical to Gauss' law in electrodynamics, which the exception of the minus sign (which means positive masses attract each other instead of repelling).

I’m not fond of that mapping. Yes [latex]\nabla \cdot \mathbf{E} = \frac{\rho}{\varepsilon_0}[/latex] but remember that it’s the electromagnetic field, which has curl, whilst a gravitational field hasn’t. This could take into the issue of curved space versus curved spacetime, but let's come back to that.

Now, we know gravity should act on all forms of energy, including the energy in the gravitational field itself. So if we want to include the effect you mentioned, we should start by adding a term to the right hand side that encodes the energy in the gravity field. But what term should we add? Well, first let's recall what the energy density is in an electric field:
[latex]$\rho_E = (1/2)\vec E^2 = (1/2) (\vec \nabla \phi)^2$[/latex],
where phi is the electric potential and E is the field.

Sorry, I’m not familiar with that expression. But given that [latex] u_{em} = \frac{\epsilon_0}{2}E^2 + \frac{1}{2\mu_0}B^2 \,[/latex], no matter, an electromagnetic field has an energy density, the energy is there in the space, and it’s related to electromagnetic four-potential A^α in which Φ plays a part.

Question: what is the energy in an gravitational field? The obvious guess is that it should be given by this same formula, namely [latex]$\rho_g = (\alpha/2)\vec g^2 = (\alpha/2) (\vec \nabla \Phi_N)^2$[/latex], where alpha is some constant.

Pause there. Don't guess. Think about a single electron. There’s electromagnetic energy in the space surrounding the place where we say the electron is located. Now add a proton. It also comes with electromagnetic energy in the surrounding space. Now you’ve got a hydrogen atom, still with electromagnetic energy in the surrounding space. The two opposite fields mask one another, the energy doesn’t vanish from the space just because the electron and the proton are close to one another. So recast your expression saying [latex]$\rho_g = (2/2)\vec E^2[/latex]

So, let's see what happens if we add this term to the right hand side of Newton's equation:

[latex]$\vec \nabla \cdot \vec g = -4 \pi G_N \rho_m + c^2(\vec g)^2/2$[/latex], where c^2 must be there by dimensional analysis (the fact that it's c^2/2, and not c^2/53 pi or something cannot be derived from this, but if you're more careful and check the constant I believe that's exactly what you find).

Sorry, you lost me there. How do you go from a constant alpha to c²? Because it relates energy E to mass m and you’re talking in terms of gravitational charge? Like I said, I’m not fond of that, and the point I was making earlier still holds: Einstein asserted that c varies with gravitational potential, which means it isn’t a constant.

A couple of things to notice about this formula.

First, since the second term on the right is quadratic in g, it's not important when g is small. That had to be the case since the theory needs to reduce to Newton in the weak field limit.

That’s sounds like circular reasoning. If you look at a plot of gravitational potential there’s a flat bit at the bottom of the upturned hat. That’s where gravitational potential is lowest and energy density is at a maximum. When you’re in a void at the centre of the earth there’s no discernible gravity because you’re in region where there’s no gradient in energy density. And you can’t tell locally what the energy density is.

Second, if the field g is weak, we can easily estimate how important the second term is. All we need to do is calculate what g would be in Newtonian gravity, plug that into the second term, and compare it to the G_N rho_m term to see how much it matters.

In a void at the centre of the earth the field g is so weak it’s undetectable. It’s essentially zero. But the energy density in the space at that region is higher than anywhere else.

Before doing that for a galaxy or other interesting object, I'll pause and make sure you're following so far.

I’m following. But again I have to go. Sorry.

 

[Michael Mozina]

I don't think there's a problem in saying that vacuum fluctuations are real. I'd say the problem comes when people equate them to the QED virtual photons which are said to bind the electron and the proton in a hydrogen atom. They aren't the same thing. There aren't any real photons flitting back and forth between the electron and proton.

Definitely. There can be some big issues in interpretation, wherein the same mathematics can deliver two entirely different meanings, and does not distinguish between the two.

Maybe we need a separate thread for the neutrino issue.

Humour me on this, it's important to the discussion.

Let's park that one and come back to it another time. The main point is that if space has an innate "pressure" and is not bound because there's nothing outside it, it's reasonable to expect it to expand.

Check out the vacuum catastophe. It's important.

Like I said, belief is kinda weird. The crucial point is this: you can't trust your own beliefs. Trust me on this.

I'll listen carefully and respond accordingly.

LOL, I'm looking forward to this.

Tim's the one I want to get the message across to. He sounds like a cosmologist who knows his stuff, but who has been ill-advised on the fundamental physics.

Believe me when I tell you that I will give you the benefit of the doubt. Especially after the neutrino debates, I'm open to new ideas.

FYI, if you convince sol, you'll definitely reach Tim and everyone else following this thread.

The best advice I can give you is to stay cool and don't let the hostility bother you. Just stay focused on the key points that you're trying to make and I'm sure that your points will be heard. Don't be afraid to repeat your key points however if they were simply ignored or not addressed adequately the first time.