- #1
jonmtkisco
- 532
- 1
As a thought experiment, let's imagine assembling a 300 Mpc long rod in intergalactic space, made of an astounding future material which enables it to be both rigid and nearly weightless, while somewhat "stretchy" and "compressible" longitudinally. The rod is centered at the origin of our proper distance coordinate system, and is assembled progressively from the origin. At the origin, we observe the rod to be locally at rest with respect to the Einstein-de Sitter universe with [tex]\Lambda = 0[/tex] and [tex]\Omega = 1.[/tex]
Will the ends of the rod be stretched apart longitudinally by the expansion of space? No, because the expansion of space does not act like a "force" or "viscous liquid." The expansion of space is the result, not the cause, of the expansion of the universe. The expansion of the universe is best explained simply as the kinematic (or momentum-like) movement of massive objects away from each other because they previously were moving away from each other.
Conversely, will the ends of the rod be compressed inward longitudinally by the deceleration of the expansion rate? After all, observers at each end of the rod will observe their rod end having peculiar motion longitudinally towards the origin, with respect to the comoving coordinates of local space. I think the answer is no. I think the locally observed peculiar motion at the ends of the rods is "real" only with respect to the observed kinematic recession of local galaxies away from the origin in comoving coordinates. But the rod ends aren't in proper motion with respect to the coordinate origin, and therefore they do not experience acceleration with respect to the origin either; their proper motion and acceleration both are zero. The rod was constructed ex post facto, and therefore never inherited the original recessionary "momentum" of the decelerating expansion.
If Lambda (with equation of state w = -1) is added to the universe, will the rod ends be stretched away from the origin? I think the answer depends on whether the cosmological constant can "co-inhabit" the same physical space as the rod matter. If it can, then the rod feels expansionary stretching. If it can't, then the cosmological constant is not directly interposed between the origin and the rod ends, so the rod ends to not experience stretching in proper distance.
...
Now let's imagine two galaxies in the same universe, which are far enough apart not to be gravitationally bound together. The first galaxy is located at the coordinate origin. The second galaxy is tethered to the first by a slack rope (please don't ask how!) A winch at the origin galaxy gently tightens the rope until it just smoothly stops the tethered galaxy from moving away in the Hubble flow (i.e., without jerking or pulling it), and then the rope is released. What will the tethered galaxy do, when observed in proper distance coordinates?
I submit that it will behave exactly like the long rod in the example above. If Lambda=0, the (formerly) tethered galaxy will exhibit NO proper motion towards or away from the origin galaxy even if the expansion is decelerating. It's initial condition is NOT proper motion towards the origin galaxy; it is specifically released at rest with respect to the origin galaxy. Because it has zero proper velocity towards the origin galaxy, it has no proper velocity to decay. Proper velocity and acceleration remain at zero. Certainly the tethered galaxy experiences peculiar motion with respect to the locally comoving expansion, but this is entirely consistent with zero proper motion with respect to the origin galaxy.
If there is Lambda with (w = -1), then the tethered galaxy will experience proper motion away from the origin galaxy, as a result of the expansionary "force" of the cosmological constant energy interposed between the origin and the tethered galaxy.
So, I question whether J. Peacock, A.B. Whiting, Davis & Lineweaver, and Francis, Barnes, et al have explained the deceleration scenario correctly in their respective papers.
Jon
Will the ends of the rod be stretched apart longitudinally by the expansion of space? No, because the expansion of space does not act like a "force" or "viscous liquid." The expansion of space is the result, not the cause, of the expansion of the universe. The expansion of the universe is best explained simply as the kinematic (or momentum-like) movement of massive objects away from each other because they previously were moving away from each other.
Conversely, will the ends of the rod be compressed inward longitudinally by the deceleration of the expansion rate? After all, observers at each end of the rod will observe their rod end having peculiar motion longitudinally towards the origin, with respect to the comoving coordinates of local space. I think the answer is no. I think the locally observed peculiar motion at the ends of the rods is "real" only with respect to the observed kinematic recession of local galaxies away from the origin in comoving coordinates. But the rod ends aren't in proper motion with respect to the coordinate origin, and therefore they do not experience acceleration with respect to the origin either; their proper motion and acceleration both are zero. The rod was constructed ex post facto, and therefore never inherited the original recessionary "momentum" of the decelerating expansion.
If Lambda (with equation of state w = -1) is added to the universe, will the rod ends be stretched away from the origin? I think the answer depends on whether the cosmological constant can "co-inhabit" the same physical space as the rod matter. If it can, then the rod feels expansionary stretching. If it can't, then the cosmological constant is not directly interposed between the origin and the rod ends, so the rod ends to not experience stretching in proper distance.
...
Now let's imagine two galaxies in the same universe, which are far enough apart not to be gravitationally bound together. The first galaxy is located at the coordinate origin. The second galaxy is tethered to the first by a slack rope (please don't ask how!) A winch at the origin galaxy gently tightens the rope until it just smoothly stops the tethered galaxy from moving away in the Hubble flow (i.e., without jerking or pulling it), and then the rope is released. What will the tethered galaxy do, when observed in proper distance coordinates?
I submit that it will behave exactly like the long rod in the example above. If Lambda=0, the (formerly) tethered galaxy will exhibit NO proper motion towards or away from the origin galaxy even if the expansion is decelerating. It's initial condition is NOT proper motion towards the origin galaxy; it is specifically released at rest with respect to the origin galaxy. Because it has zero proper velocity towards the origin galaxy, it has no proper velocity to decay. Proper velocity and acceleration remain at zero. Certainly the tethered galaxy experiences peculiar motion with respect to the locally comoving expansion, but this is entirely consistent with zero proper motion with respect to the origin galaxy.
If there is Lambda with (w = -1), then the tethered galaxy will experience proper motion away from the origin galaxy, as a result of the expansionary "force" of the cosmological constant energy interposed between the origin and the tethered galaxy.
So, I question whether J. Peacock, A.B. Whiting, Davis & Lineweaver, and Francis, Barnes, et al have explained the deceleration scenario correctly in their respective papers.
Jon
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