- #1
jonmtkisco
- 532
- 1
I would appreciate help in objectively disproving the following "alternative physics" proposition: "The large-scale geometry of the universe is compelled to be eternally flat because gravity causes the universe to expand at exactly the escape velocity of its mass/energy contents." This proposition could be disproved, among other means, by proving that the universe must be capable of non-zero curvature at large scales. Or by proving that gravity cannot be the source of spatial expansion.
Of course I recognize that even if a proposition isn't readily disproved, doesn't mean that it's actually true. By the way,anyone who has read my posts on the cosmology forum is aware that my math skills don't go much beyond basic calculus, but I have spent some time studying cosmology. You don't need to remind me that in standard general relativity, gravity is supposed to slow down expansion, not propel it. And that once initiated (presumably by inflation), expansion is supposed to possesses a sort of momentum that would keep it expanding eternally but for the retarding effect of gravity. I also understand that cosmologists prefer to work with mass/energy densities rather than with absolute values of total mass/energy used in the escape value formula. The "escape velocity" formula:
[tex]\dot{r} = \sqrt{\frac{2GM}{r}}[/tex]
is a trivial variation of the Friedmann expansion formula, substituting M/V for rho (density). In this approach, the cosmological constant is automatically included by incorporating its mass/energy component, without any need to separately account for its negative pressure component.
To make a long story short, inflation theories are designed to deliver a flat initial universe expanding at exactly the escape velocity of its mass/energy contents. At its peak expansion rate, inflation "dumps" precisely the initial amount of radiation and matter plasma into the universe, the escape velocity of which matches the inflationary expansion rate.
It is implicit in the Friedmann expansion equation that spatial expansion (at escape velocity) depends on, and derives from, the mass/energy of the contents. In effect, mass/energy must be the "repository" of the ongoing expansionary "momentum." (There are good reasons to reject any concept that the "momentum" of expansion resides in vacuum space itself.) The expansion of space involves no peculiar motion of mass/energy through vacuum space. This suggests that each particle of mass/energy is causally connected directly to the expansion of the vacuum space around it, at the escape velocity of that particle. (If many particles are gravitational bound together, the gravitational binding energy constituting their collective "mass defect" do not contribute to the expansion rate.)
My proposition is that post-inflation, pre-dark energy-dominated expansion is NOT a "momentum" leftover from inflation. This proposition has the following key elements:
1. So-called "negative pressure" components such as inflation and the cosmological constant DO NOT impart any expansionary momentum to the universe.
2. Gravity DOES NOT act to restrain the expansion of space.
3. Instead, the gravity of mass/energy actively causes real-time expansion of the space within its gravitational field, at exactly the escape velocity of that mass/energy.
4. If an object with mass/energy departs an otherwise empty region of space, expansion of that region ceases immediately. When the object enters a new region of space, that region immediately expands at escape velocity. Thus there is no concept of retained momentum or inertia of expansion. Acceleration and deceleration of local expansion occur instantaneously.
5. The cosmological constant accelerates the expansion rate merely by virtue of possessing simple mass/energy. There is no need for a negative pressure component.
6. Because gravity actively maintains the instantaneous local expansion rate exactly equal to escape velocity, it is impossible for the large-scale geometry of space to ever be anything other than perfectly flat.
I'll offer a couple of related points.
The observable universe currently is deemed to be flat or nearly flat, and theory requires that it was no less flat at any time in the past (since inflation). Although a firm mathematical relationship between spatial expansion and curvature of space has been a central element of general relativity since its inception, isn't it still is an entirely theoretical construct which has not been proven empirically or by observation? Assuming that local curvature is a valid construct of GR to explain gravity, it seems to me that one is not compelled to also accept that holistic curvature of the universe is a necessary corollary. Specifically, with respect to two objects in the observable universe which are not gravitationally bound to each other in the context of rapidly expanding space, why isn't it reasonable to say that their individual gravitational fields are NOT in causal contact with each other (particularly across event horizons), and therefore cannot additively reinforce each other's contribution to the shape of the overall manifold of the universe?
If my proposition were correct, then I think the 'equation of state' in GR and the Friedmann equations would need to be partially recast to reflect a different (real-time rather than static) expansion mechanism, but not different physical results. In particular, I don't see any need for the pressure terms, because the Friedmann deceleration equation can be modeled as a simple change in total mass/energy over time (for example, due to redshift of free radiation). I need to understand whether a change of that kind would cause conflicts in other aspects of physics -- such as the physics of perfect fluids.
I would really appreciate some constructive comments. If your response is going to be to tell me I don't understand the first thing about physics, one sentence will be sufficient, no piling on is allowed.
Jon
Of course I recognize that even if a proposition isn't readily disproved, doesn't mean that it's actually true. By the way,anyone who has read my posts on the cosmology forum is aware that my math skills don't go much beyond basic calculus, but I have spent some time studying cosmology. You don't need to remind me that in standard general relativity, gravity is supposed to slow down expansion, not propel it. And that once initiated (presumably by inflation), expansion is supposed to possesses a sort of momentum that would keep it expanding eternally but for the retarding effect of gravity. I also understand that cosmologists prefer to work with mass/energy densities rather than with absolute values of total mass/energy used in the escape value formula. The "escape velocity" formula:
[tex]\dot{r} = \sqrt{\frac{2GM}{r}}[/tex]
is a trivial variation of the Friedmann expansion formula, substituting M/V for rho (density). In this approach, the cosmological constant is automatically included by incorporating its mass/energy component, without any need to separately account for its negative pressure component.
To make a long story short, inflation theories are designed to deliver a flat initial universe expanding at exactly the escape velocity of its mass/energy contents. At its peak expansion rate, inflation "dumps" precisely the initial amount of radiation and matter plasma into the universe, the escape velocity of which matches the inflationary expansion rate.
It is implicit in the Friedmann expansion equation that spatial expansion (at escape velocity) depends on, and derives from, the mass/energy of the contents. In effect, mass/energy must be the "repository" of the ongoing expansionary "momentum." (There are good reasons to reject any concept that the "momentum" of expansion resides in vacuum space itself.) The expansion of space involves no peculiar motion of mass/energy through vacuum space. This suggests that each particle of mass/energy is causally connected directly to the expansion of the vacuum space around it, at the escape velocity of that particle. (If many particles are gravitational bound together, the gravitational binding energy constituting their collective "mass defect" do not contribute to the expansion rate.)
My proposition is that post-inflation, pre-dark energy-dominated expansion is NOT a "momentum" leftover from inflation. This proposition has the following key elements:
1. So-called "negative pressure" components such as inflation and the cosmological constant DO NOT impart any expansionary momentum to the universe.
2. Gravity DOES NOT act to restrain the expansion of space.
3. Instead, the gravity of mass/energy actively causes real-time expansion of the space within its gravitational field, at exactly the escape velocity of that mass/energy.
4. If an object with mass/energy departs an otherwise empty region of space, expansion of that region ceases immediately. When the object enters a new region of space, that region immediately expands at escape velocity. Thus there is no concept of retained momentum or inertia of expansion. Acceleration and deceleration of local expansion occur instantaneously.
5. The cosmological constant accelerates the expansion rate merely by virtue of possessing simple mass/energy. There is no need for a negative pressure component.
6. Because gravity actively maintains the instantaneous local expansion rate exactly equal to escape velocity, it is impossible for the large-scale geometry of space to ever be anything other than perfectly flat.
I'll offer a couple of related points.
The observable universe currently is deemed to be flat or nearly flat, and theory requires that it was no less flat at any time in the past (since inflation). Although a firm mathematical relationship between spatial expansion and curvature of space has been a central element of general relativity since its inception, isn't it still is an entirely theoretical construct which has not been proven empirically or by observation? Assuming that local curvature is a valid construct of GR to explain gravity, it seems to me that one is not compelled to also accept that holistic curvature of the universe is a necessary corollary. Specifically, with respect to two objects in the observable universe which are not gravitationally bound to each other in the context of rapidly expanding space, why isn't it reasonable to say that their individual gravitational fields are NOT in causal contact with each other (particularly across event horizons), and therefore cannot additively reinforce each other's contribution to the shape of the overall manifold of the universe?
If my proposition were correct, then I think the 'equation of state' in GR and the Friedmann equations would need to be partially recast to reflect a different (real-time rather than static) expansion mechanism, but not different physical results. In particular, I don't see any need for the pressure terms, because the Friedmann deceleration equation can be modeled as a simple change in total mass/energy over time (for example, due to redshift of free radiation). I need to understand whether a change of that kind would cause conflicts in other aspects of physics -- such as the physics of perfect fluids.
I would really appreciate some constructive comments. If your response is going to be to tell me I don't understand the first thing about physics, one sentence will be sufficient, no piling on is allowed.
Jon
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