Say the universe continued accelerated expansion. Would there be any tidal effects?
Would elephantification happen?
....^
<- O ->
.....V
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Say the universe continued accelerated expansion. Would there be any tidal effects?
Would elephantification happen?
....^
<- O ->
.....V
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Sounds like you're thinking about the Big Rip scenario.
Conserve energy. Commute with the Hamiltonian.
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Also, note that if we adopt the cosmological principle, that says everything is more or less the same everywhere at a given age, then "tidal effects", which you would normally interpret as local in the absence of a cosmological principle, become the same thing as what is happening globally to the whole universe. So there aren't two questions there, what is happening to the whole universe and what are the tidal effects-- there's just one. But it sounds like you are also asking how large would the local effects get, and that's where the "big rip" idea comes in-- as in that model, the expansion can be so drastic that the local effects get very large.
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Lineweaver & Davis (440KB pdf) say that accelerating expansion results in an expansive force, which is tiny at galactic scales in the present epoch. In an accelerating Universe, we're very slightly taller; in a decelerating Universe, we're very slightly shorter.
I'm interpreting this as follows:
In a Universe undergoing constant expansion, an extended object could maintain a constant size without experiencing tension or compression, since its two ends are moving at constant velocity with regard to their local Hubble Flow. In an accelerating Universe, the object maintains constant size only by constantly nudging its ends to higher velocity with regard to their local Hubble Flow. To generate the necessary force, it needs to develop internal tension. (Reverse the reasoning for the case of the decelerating Universe.)
Grant Hutchison
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What doesn't quite scan about that description is that getting taller implies a stretch that implies a compressive internal tension. That wouldn't nudge to higher velocities. So I think one would have to say that there are tidal forces on the individual that are the same as the tidal effect on the universe as a whole that is accelerating the expansion. So just as the universe does not maintain a fixed size relative to a rigid standard, neither does the individual. This would make the effect similar to the bulging of the Earth's oceans in the lunar tide-- tidal forces create a net outward stretching that, once steady state is achieved, require an additional internal compressive force created by the deformation of the Earth. For the Earth, that's a self-gravity, but for a person, it would be the elastic compressive force associated with stretching our height.
In other words, the cosmological principle dictates that our bodies should keep pace with the universal expansion, relative to a local rigid standard, but our bodies, having some rigidity of their own, resist that. This means we are less tall than we would be had we followed the expansion, but more tall than we would be if we were perfectly rigid. Your point is that we must distinguish constant expansion from accelerated expansion, because constant expansion would allow all points of our body to remain inertial-- that's a good point, it's not the expansion itself that our bodies would tend to follow, but rather its tidal component (acceleration). I think you meant to say the object nudges its ends to lower velocities relative to the Hubble flow to escape its tidal influences.
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And just so it's clear, tommac, if you're talking about the effects on people or planets, these effects are tiny. Minuscule. Far too small to measure. It's only if we got to a point where the acceleration was much larger than it is now that we'd be able to observe any kind of local effects at all, and the authors of the original paper introducing the idea of a "Big Rip" as a possibility point out that the data do not suggest that it is a very likely possibility.
Conserve energy. Commute with the Hamiltonian.
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I'm pretty sure I didn't mean to say that: so either I'm describing it badly or visualizing it wrongly.Originally Posted by Ken G
We have a chain of comoving observers, locally at rest in the Hubble Flow. A rope runs parallel to these observers, and they are each able, successively, to assess the relative velocity of one or the other of the rope's ends as the Hubble Flow carries the observers along the length of the rope and then outwards beyond its ends. For a rope a megaparsec long, and plugging in the current value of Hubble's constant, the observers currently at the rope's ends would see them moving at 74/2 = 37 km/s relative to their local standard of rest in the Hubble Flow, and the velocity vectors for the two ends point towards each other. If the Universe continued to expand at a steady 74 km/s/Mpc, then each successive observer would measure the same velocity as the rope's ends went past, and they'd therefore see that the rope's ends were moving inertially. But if Hubble's constant increases with time, each successive observer measures a higher velocity for the rope's ends. The rope's ends are accelerating past the chain of comoving observers, each of them in the direction of the rope's middle. To maintain that "centripetal" acceleration, the rope must be under tension, and will be slightly stretched as a result.
No?
Grant Hutchison
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Ah, I see, it's all an issue of the reference being used for the "higher velocity". You are taking comoving observers as your reference system, so tidal effects show up in the distances between them, rather than in any motion-- nothing that is free to move appears to ever move if it starts off comoving. That's an inertial-based approach. I was taking a rigid standard as my reference system-- appropriate to non-comoving observers, like the people on Earth. People on Earth would say their height is expanded by the need to have compressional forces that counter the tidal effects of accelerated expansion, whereas comoving observers would say the height of a person is expanded by the need to have growing speeds at the ends of the person that are pointed toward the center of the person, as you describe above. The rigid standard has the stretched person as never really having much of a velocity at its ends (only what is needed to get the stretching), whereas the comoving-frame inertial observers see all that additional velocity relative to the Hubble flow (which of course is also miniscule, but we are magnifying the effect to picture it).
So yes, if one uses comoving observers to measure the height of people on Earth, they would indeed see a stretch that is needed to nudge the speeds of the person's ends to increase inwardly toward the center of the person, relative to the Hubble flow that the person's body is resisting. Your language was correct. Interestingly, one gets a very different picture when one adopts the standard of reference of observers aligned along the length of a rigid standard of some kind, which is more appropriate for observers on Earth-- there, one says that it is the Hubble flow that is accelerating, due to the tidal gravity, and the person needs to be stretched to maintain a lower velocity, relative to this other set of observers, so as not to participate in the Hubble flow. The language that "space itself is expanding" is native to this second class of observers-- comoving observers would tend toward the language that rigid matter is shrinking (though in fact we rarely use that language because we never actually communicate with comoving observers, nor do we take their perspective literally, which is an interesting point in itself as much as comoving observers are used in cosmology).
In other words, your way of describing the situation leads me to see that the usual language we see use in cosmology is a kind of unholy alliance of the perspectives of rigid-standard observers, who would tend to allow space to expand, versus the natural language of comoving observers, who should interpret their positions as stationary and hence require that rigid matter be shrinking (after all, how can the space expand between mutually stationary observers?). It's as though the comoving observers have rigid rulers in their pockets, which they imagine stay of fixed length when they interpret what "space is doing", but they don't apply that same standard to talking about what the endpoints of a person are doing, referring instead to the other comoving observers for that.
This means there is a kind of tension between the rigid standards we use to establish what distance means, and the cosmological principle we use to establish what inertial means. How we walk the line of that tension controls how our language comes out, and whether the endpoints of a person in an expanding universe are increasing in speed against the inertial standard of the Hubble flow, or resisting changes in speed against the rigid standard. Your language, which is the standard in cosmology so is used on the largest scales, asserts that velocities should be referenced to the inertial comoving standard, whereas lengths should be referenced to the local rigid standard. The cost, naturally, is that velocities are no longer the time rate of change of lengths.
However, if one simply allows that comoving observers, as a convention-setting bunch, should consider the local rigid standard as itself shrinking with age, then one can recover the idea that velocities are still the time rate of change of lengths, simply by saying that length is the product of the standard of length times the number of such units you'd need to lay out end to end. In other words, it seems to me that the natural interpretation of our own conventions about when to use comoving observers and when to use rigid standards is that the rigid standards are shrinking with age, not that space is expanding.
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Yeah, I'd say when talking about local tidal effects, it's best to stick with meaningful local coordinates (your basic "frame field" in the language of GR's differential geometry) and not comoving language.
With an accelerating expansion, we have what I like to call a "rip tide", radially outward in spherical coordinates. With no cosmological constant (or when the regular matter density dominates), we've got a compressive tide.
You can see this in static deSitter coordinates, where the magic metric factor (g_00 and 1/g_11) is (1 - r^2/R^2), where R is the cosmological horizon (note the "inside out" black hole analogy), given by 1/R^2 = Lambda/3 (in geometric units, there will be a c^2 factor there in regular units). Note this looks just like the Newtonian potential for a spherical negative mass density distribution. About r = 0, things fly away radially, unless you accelerate them to hold them a constant distance according to your local rigid ruler.
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Ah, that makes sense.
Edward Harrison wrote an interesting paper connected to all this: Mining Energy In An Expanding Universe.
Grant Hutchison
Last edited by grant hutchison; 2010-Nov-17 at 10:49 PM. Reason: provided quote for context
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Actually, I think that even in MKS units, there is no c^2 in the de Sitter metric factor. That would only come about if you expressed Lambda in terms of its equivalent energy density, which adds a factor of c^2. Going back to straight Lambda, that c^2 cancels. My brain just isn't in the mood to fool with dimensional crap now. Oh what the heck.
The RHS of the EFE in MKS has a factor of G/c^4 times the stress-energy tensor, which has units of energy density. Divide through by one c^2, and you get units of mass density, so the RHS has units of G/c^2 times mass per volume. We know mass times G/c^2 gives length (as that's the Schwarzschild radius form, GM/c^2), so the RHS has units of length per volume, or 1/length^2.
Since the metric is dimensionless, that means Lamdba must have units of 1/length^2. Thus it can go into the deSitter "magic metric factor" directly with no c^2 needed. IOW, the way the EFE is written, the G/c^2 factor is "already applied" to Lamdba. You have to take it out to get an equivalent "dark energy" density.
-Richard
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Yes exactly. I guess the question would be would or why would the big rip tear apart planets and atoms if expansion is the net effect of a co-moving system? Would there be the equivalent of tidal forces pulling apart all mass in all directions? Is this tidal force similar to the one exerted by a black hole EXCEPT in direction, as it is not being pulled to a point? If not how is it different?
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Not sure if I understand correctly but wouldnt the hubble flow be accelerating also?
Also are these forces similar to a Black hole tidal force but with arrows in all directions?
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Regardless of its likelyhood I would like to understand what is causing the tidal pull planets and atoms.
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How different is that than tidal forces ( ignoring the arrows )?
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That is what I am terming "elephantification" as a play on similar forces from "spaghetification" ( just with the arrows of acceleration point raidally outwards rather than towards a point.
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Yes, it's the accelerating Hubble Flow that causes the expansive forces.
Yes, if the Universe is expanding isotropically, the resulting forces will be of equal magnitude along all axes.
Grant Hutchison
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Like fan out acceleration rather than fan in acceleration of a black hole.
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I have no idea what that means.
Grant Hutchison
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fan out = forces will be of equal magnitude along all axes and pointing outwards from a point. ( accelerating expansion )
fan in = forces will be of equal magnitude along all axes and pointing inwards to a point. ( Black hole )
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Tommac,
The tidal forces of a black hole are not "fan in". The tidal force is radially stretching, and tangentially compressive. Turns out the tidal forces experienced by radial free fallers in Schwarzschild is exactly the Newtonian inverse square tide (this is not true for orbiting observers, however). The radial stretching tide is -2GM/r^3, and the tangential compressive tide is GM/r^3. In terms of the tidal tensor (expressed in the correct coordinates), one can write GM/r^3*diag(-2, 1, 1), where the "diag" represents a diagonal 2x2 tensor matrix representation. Note the trace of that is zero. That is a (required) property of a vacuum field (no Ricci curvature, only Weyl curvature, in GR's language).
A "fan out" tide as you say would be expressed as some some diag(1, 1, 1). A "fan in" tide would be diag(-1, -1, -1) (the sign convention here could be the other way, and I forget which one actually makes the most sense, depends on if you're talking about the tidal coordinate acceleration or the proper accelerationr required to resist it).
A cosmological constant gives us the former tide, while the tide inside a spherical symmetric mass distribution gives the latter. Note in these cases the trace does not sum to zero. That means the field has divergence (Ricci curvature in GR's language), which means matter is present and we're not a vacuum field. In the case of Lamdba, the effect is to force the vacuum to have Ricci curvature.
-Richard
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Wow ... awesome post!
Banned
@ Tommac We call it Dark Energy because we do not have a better description. That it is a observed as confirmed is the main stream view...
That it works across the universe in a manor we do not understand on all that is not gravity bound...
Once outside the weak and strong nuclear forces and beyond the influence of a gravity well. Accelerated expansion is apparent.
It does not change the answer to change the question... We do not know.
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