Could Velocity Exceed c in Comoving Worldlines?

[Finny]

Yes. But the CMBR is not a locally bound system; it is very well approximated as a homogeneous and isotropic "fluid" of radiation filling the universe. So the overall dynamics of the expanding universe should describe the CMBR very well.

Yes, no issue with that...Thanks for the observation, but I was on a different topic when I posted about the universe expansion by a factor of 1,000...merely wondering if Chronos' calculation wasn't wildly too big regarding the solar system in comparsion with such distant expansion. Now that I think about it, my comparison is not so good as his is in a much more recent timeframe. Mine started shortly after the big bang, his only 4.5B or so years ago...apples and oranges...

Anyway, no issue about CMBR being homogeneous and isotropic...fits that description well...lots better than matter I think. .

 

[PeterDonis]

merely wondering if Chronos' calculation wasn't wildly too big regarding the solar system in comparsion with such distant expansion

The solar system is a locally bound system, whereas the CMBR is not. You should not expect observations of the two to show similar effects from the universe's expansion. Chronos' calculation was merely confirming that, by showing what "similar effects" would look like--i.e., what we would expect to observe if the solar system had expanded over the past 4.5B years at the same rate as the universe as a whole. Obviously it hasn't, which is why this calculation gives an answer very, very different from what we actually observe.

"...Cooperstock et al computes that the influence of the cosmological expansion on the Earth's orbit asround the sun amounts to a growth by only one part in a septillion over the age of the Solar System."

This calculation takes into account the fact that the solar system is a locally bound system. Chronos's calculation does not, which is why it gives a very different answer.

my comparison is not so good as his is in a much more recent timeframe. Mine started shortly after the big bang, his only 4.5B or so years ago...apples and oranges...

That makes a difference, but it still leaves a large variance between the expansion of the universe as a whole (which is, IIRC, about a factor of 2 over that time period) and that of the solar system (which is much, much, much less, as the Cooperstock calculation shows--see above).

 

[ohannuks]

I guess another interesting question would be what it would imply if we events propagating faster than the speed of light locally. Particles with negative mass? Tachyons? :)

 

[Chronos]

How would you propose to detect tachyonz?

 

[timmdeeg]

This calculation takes into account the fact that the solar system is a locally bound system. Chronos's calculation does not, which is why it gives a very different answer.

That makes a difference, but it still leaves a large variance between the expansion of the universe as a whole (which is, IIRC, about a factor of 2 over that time period) and that of the solar system (which is much, much, much less, as the Cooperstock calculation shows--see above).

http://arxiv.org/pdf/astro-ph/9803097v1.pdf

Quote:

"However, it is reasonable to pose the question as to whether there is a cut–off at which systems below this scale do not partake of the expansion. It would appear that one would be hard put to justify a particular scale for the onset of expansion. Thus, in this debate, we are in agreement with Anderson (1995) that it is most reasonable to assume that the expansion does indeed proceed at all scales. However, there is a certain ironical quality attached to the debate in the sense that even if the expansion does actually occur at all scales, we will show that the effects of the cosmological expansion on smaller spatial and temporal scales would be undetectable in general in the foreseeable future and hence one could just as comfortably hold the view that the expansion occurs strictly on the cosmological scale. ...

The purpose of the present paper is to provide a clear quantitative answer to the problem. The motion of a particle subject to external forces in the (approximate) LIF using Fermi normal coordinates is analyzed. It is the locally inertial frame based on a geodesic observer and it continues to be locally inertial following the observer in time. This is the frame in which astronomical observations are performed, and we compute the corrections to the dynamics due to cosmology. In this paper, we assume that homogeneous isotropic expansion is actually universal and we analyze the consequences of this assumption."

If I understand Cooperstock et al correctly, they talk in the subjunctive mood. Their calculation is based on the assumption that the expansion occurs "at all scales", thus obviously including the solar system. So it seems the result that the expansion of the solar system is negligible (but not zero) doesn't prove or disprove this assumption.

They don't mention tidal forces at all and presumably their assumption is not related to tidal forces, because probably no one would doubt their existence on small scales like the solar system, following your arguments. From this I suspect that Cooperstock takes into consideration that it is an open question whether or not gravitational systems do participate in the cosmological expansion.
On the other side they mention "external forced"; what is the meaning, if not tidal forces. To me it's a puzzle, so I would be glad to know your opinion.

 

[ohannuks]

How would you propose to detect tachyonz?

Gravity ;)

Imho, I'm not confident enough in particle physics to give an intelligent answer to this.

 

[PeterDonis]

Their calculation is based on the assumption that the expansion occurs "at all scales", thus obviously including the solar system.

Not really. Their calculation assumes that the effect of the expansion would have to show up as "external forces" (see below). It completely ignores the fact that, if the solar system were expanding at the rate of the universe as a whole--i.e., if the sun and each of the planets were moving on "comoving" worldlines--it would have had to double in size, more or less, over the past 4.5 billion years. Clearly the solar system has not actually expanded by such a factor, or by anything within orders of magnitude of such a factor. So clearly the individual objects in the solar system cannot all be moving on "comoving" worldlines, or anything close to it.

But the assumption that the expansion occurs "at all scales", if made consistently, would force us to assume that the individual objects in the solar system are moving on "comoving" worldlines--that's what "expansion" in this sense means. Cooperstock et al. are clearly not assuming that, or anything close to it, by many orders of magnitude. So, regardless of what they say, they are clearly not assuming that "expansion occurs at all scales" in the relevant sense.

They don't mention tidal forces at all and presumably their assumption is not related to tidal forces

Actually, it is. See below.

On the other side they mention "external forced"; what is the meaning, if not tidal forces.

The "external forces" are tidal forces. Basically they are trying to compute the tidal forces induced by the rest of the matter in the universe on the solar system.

 

[timmdeeg]

Not really. Their calculation assumes that the effect of the expansion would have to show up as "external forces" (see below).

Ok, if they say expansion, their have tidal forces in their mind. It's not really important, but remembering "... even if the expansion does actually occur at all scales, we will show ..." they seem to believe that there is no clear theoretical foundation to assume the existence of tidal forces (thereby neglecting the dark energy), otherwise "even if" makes no sense.

The "external forces" are tidal forces. Basically they are trying to compute the tidal forces induced by the rest of the matter in the universe on the solar system.

Hmm, and also induced by the dark energy, right? Otherwise the universe wouldn't expand accelerated.

But on this scale the tidal forces should be computed with respect to the effect of the dark energy only, correct? And this correction to the acceleration of the Earth towards the sun should yield a larger value then.

 

[PeterDonis]

and also induced by the dark energy, right?

I don't think their calculation includes dark energy; they seem to be using the matter-dominated FRW model. Including dark energy does change the tidal forces, yes. See below.

on this scale the tidal forces should be computed with respect to the effect of the dark energy only, correct?

Once again, it depends on what assumptions you make. Cooperstock et al. appear to be making the assumption that the individual objects in the solar system are not moving on "comoving" worldlines, which means they are not assuming that the matter in the universe is exactly homogeneous and isotropic--if it were, every single piece of matter everywhere in the universe, on all scales, would be moving on a "comoving" worldline. If that were true, we would be able to see tidal forces on any scale due to all of the matter and energy in the universe, whether it was ordinary matter, dark matter, radiation, or dark energy.

In our actual universe, individual pieces of matter do not move on comoving worldlines; the "comoving" worldlines only describe the average motion of the matter in the universe on very large scales (hundreds of millions to billions of light years). So on much smaller scales, we would not expect tidal forces due to the matter to be significant (and Cooperstock et al.'s calculations appear to show that). But the density of dark energy is constant everywhere, so effectively, dark energy moves on "comoving" worldlines everywhere, and tidal forces due to dark energy should be present on all distance scales. (But on the scale of the solar system, they are still very small.) However, as above, I don't think Cooperstock et al. included dark energy in their calculations.

 

[timmdeeg]

I hope that I don't bother you. I don't aim to criticize this paper, of course, but think it has pedagogical value to deal with it.

I don't think their calculation includes dark energy; they seem to be using the matter-dominated FRW model. Including dark energy does change the tidal forces, yes.

In this case it seems, they talk expansion (effect of accelerated expansion) but calculate deceleration.

Once again, it depends on what assumptions you make. Cooperstock et al. appear to be making the assumption that the individual objects in the solar system are not moving on "comoving" worldlines, which means they are not assuming that the matter in the universe is exactly homogeneous and isotropic--if it were, every single piece of matter everywhere in the universe, on all scales, would be moving on a "comoving" worldline. If that were true, we would be able to see tidal forces on any scale due to all of the matter and energy in the universe, whether it was ordinary matter, dark matter, radiation, or dark energy.

In our actual universe, individual pieces of matter do not move on comoving worldlines; the "comoving" worldlines only describe the average motion of the matter in the universe on very large scales (hundreds of millions to billions of light years). So on much smaller scales, we would not expect tidal forces due to the matter to be significant (and Cooperstock et al.'s calculations appear to show that). But the density of dark energy is constant everywhere, so effectively, dark energy moves on "comoving" worldlines everywhere, and tidal forces due to dark energy should be present on all distance scales. (But on the scale of the solar system, they are still very small.) However, as above, I don't think Cooperstock et al. included dark energy in their calculations.

I think there are 2 scenarios only , if dark energy is not included.

1. All matter is homogeneous on all scales as according to the FRW model, with the exception of the solar system. In other words, the solar system is 'suspended' in the matter fluid. Then all matter is comoving with the exception of the planets. This picture is probably unphysical due to the gravitational influence of the sun and the planets on the matter fluid. However neglecting this, one obtains a theoretical value of the tidal force on the solar system induced by the fluid.

2. There is no fluid, the universe is structured like ours instead. Then "we would not expect tidal forces", as you say.

I don't understand jet, why the effect is not exactly zero in scenario 2., how would tidal forces be founded theoretically, even if very, very small? Did Cooperstock use scenario 1. eventually?

 

[PeterDonis]

they talk expansion (effect of accelerated expansion) but calculate deceleration

Expansion does not necessarily mean accelerated expansion. As far as I can tell, by "expansion" they mean the kind you see in a matter-dominated model, which decelerates. They do not mean the kind you see in a dark energy-dominated model, which accelerates. If you think they mean the latter, please give specific quotes.

Cooperstock use scenario 1. eventually?

Not explicitly, but I think that's what their analysis amounts to. They are basically trying to see what "comoving" worldlines would look like in local coordinates centered on the worldline of the solar system's center of mass.

 

[timmdeeg]

Not explicitly, but I think that's what their analysis amounts to. They are basically trying to see what "comoving" worldlines would look like in local coordinates centered on the worldline of the solar system's center of mass.

This would make sense, in contrast to scenario 2. (universe structured) in my opinion.
Thanks for your helpful comments!