Latest word from Lewis, Francis et all on radar ranging

[jonmtkisco]

Holy smokes, just when we needed it, http://arxiv.org/PS_cache/arxiv/pdf/0805/0805.2197v1.pdf" is the latest paper hot off the press from Lewis, Francis, Barnes, Kwan & James, "Cosmological Radar Ranging in an Expanding Universe." This is mandatory reading for everyone interested in expanding space. Abstract:

While modern cosmology, founded in the language of general relativity, is almost a
century old, the meaning of the expansion of space is still being debated. In this paper,
the question of radar ranging in an expanding universe is examined, focusing upon
light travel times during the ranging; it has recently been claimed that this proves
that space physically expands. We generalize the problem into considering the return
journey of an accelerating rocketeer, showing that while this agrees with expectations
of special relativity for an empty universe, distinct differences occur when the universe
contains matter. We conclude that this does not require the expansion of space to be
a physical phenomenon, rather that we cannot neglect the influence of matter, seen
through the laws of general relativity, when considering motions on cosmic scales.

I find it portentuous that with each succeeding paper, this team seems to be edging further and further from expressing confidence that the expansion of space is a real physical phenomenon. They're not abandoning it entirely, but they conclude that "While the expansion of space is a valid (but dangerous picture when working with the equations of relativity, any attempts) to obtain observations to address the question of whether galaxies are moving through static space or are carried away by the expansion of space are doomed to failure."

Their primary conclusion is that any non-symetrical results observed in radar ranging result from the effects of the gravity of the background dust cloud, not from the expansion of empty space.

I note that much of their analysis uses conformally flat coordinates and there are several approving references to Chodorowski's pioneering work on radar ranging.

Jon

 

[jonmtkisco]

The somewhat excruciating effort (ouch!) that some of us made to understand what the Shell Theorem predicts in a flat, expanding, homogeneous, Lambda = 0 dust universe may pay off after all. Regarding a rocketeer who accelerates away from the origin and then back to the origin, and then stops, Lewis & Barnes find that they can explain the asymmetry of the "out" and "back" legs of the journey quite simply using the Newtonian Shell Theorem (which is equivalent to Gauss' Law):

In any case, we might naively expect that if space is expanding, then the journey is longer on the way back than it was on the way forwards... and hence we might predict under-shooting, rather than over-shooting, the origin. It must be emphasized that this over shoot is no different in the Newtonian limit of the FLRW metric without expansion; using Gauss’s law we can see that at a given radius R from the origin, the rocketeer experiences a gravitational acceleration toward the origin due to the mass contained by a sphere of radius R. This imaginary sphere changes size throughout the journey but the acceleration from gravity remains pointed toward the origin during the entire trip. Thus in addition to the thrust provided by the rocket, the rocketeer receives at all times an additional push toward the origin. We should not, therefore, be surprised to find the rocketeer overshoots. Thinking very simply about the effects of gravity, rather than the more nebulous expansion of space, gives a much simpler intuitive view.

Makes me wonder whether a relativistic calculation analogous to the Shell Theorem could also explain the observation of superluminal recession as an asymmetric gravitational effect on light, rather than as a result of expanding space. Arising because the Shell Theorem shows the dust cloud's gravity pulling towards the (arbitrary) coordinate origin on both legs of the trip, possibly coupled with the fact that the matter density is higher on the distant galaxy's "out" trip than on the light's "back" trip. Hmmm, gravitational redshift would NOT be caused by a pseudo-gravitational well at the coordinate origin, that would cause blueshift. The rocketeer overshooting the origin on the return trip is analogous to blueshift (coming in hot). But something along these lines.

Jon

 

[chronon]

It certainly does look as if they are backtracking on the idea that expanding space is the way to understand the universe. I'm fairly certain that a 'natural' coordinate system would have all matter moving subluminally, but I'm not sure what this is. or how you would persuade anyone that it is 'natural'. I'm still trying to figure out how their coordinate system gets subluminal motion in the (0,0) universe, but superluminal in one containing matter. It may be something along the following lines:

If you take a large enough sphere then the matter inside it should form a black hole. For matter to escape from a black hole it needs to have superluminal motion. Hence the matter we see going beyond this sphere must be moving superluminally.

 

[jonmtkisco]

Hi chronon,

If you take a large enough sphere then the matter inside it should form a black hole. For matter to escape from a black hole it needs to have superluminal motion. Hence the matter we see going beyond this sphere must be moving superluminally.

Interesting. Well as I understand it, the Schwarzschild radius of our observable universe is equal to its particle horizon, which is the definition of the total radius of our observable universe. So if your theory were the explanation for the situation, there would be no superluminal recession within our visible universe. But it is indeed observed (whether it's "physical" or not) everywhere beyond about z=1.46.

If our universe began as a singularity full of today's mass-energy, and then needed to "explode" outward, there's no doubt that superluminal velocity would be required to break the grip of that ultimate black hole. But of course inflation theory says that the expansion momentum came first (during the inflation phase) and then mass appeared later (during the reheating phase). In the inflation scenario therefore, no superluminal expansion is required, except of course to the extent we actually observe (or calculate) its existence. (Assuming it is not an optical illusion of sorts.)

In SR, superluminal velocity is prohibited only within a given inertial (non-accelerating) frame. In GR, if the universe is homogeneously filled with gravitational sources, then no local frame is truly inertial even at near-zero size (since at any size it feels gravitational acceleration). Any significant amount of distance will span many such local frames. GR theory does not rule out light moving in one frame at a superluminal rate compared to another distant frame. That's true regardless of whether the universe is expanding. So in that basic sense, I do not think that superluminal expansion actually requires or mandates an expanding universe, it just requires gravity and GR. For example, it seems to me that it ought to be theoretically possible to observe superluminal peculiar velocity at a distance even in a static universe.

Jon

 

[chronon]

Hi chronon,
Interesting. Well as I understand it, the Schwarzschild radius of our observable universe is equal to its particle horizon, which is the definition of the total radius of our observable universe. So if your theory were the explanation for the situation, there would be no superluminal recession within our visible universe. But it is indeed observed (whether it's "physical" or not) everywhere beyond about z=1.46.

Well I wouldn't call it a theory, I'm just searching for ways to make intuitive sense of the confusion of coordinate systems. In particular, why should superluminal motion appear once you've got mass in the universe? But remember that we are no longer dealing with comoving coordinates here, but for Lewis's et.al. version of conformal coordinates. Thus the superluminal limit will not be at z=1.46 but further out. At first I thought that their superluminal limit might be the particle horizon. If this were the case then it would be a serious flaw in their argument because it would put the superluminal motion before the big bang. However, I don't actually think that this is the case, so my black hole analogy probably isn't a good one.

 

[jonmtkisco]

In GR, if the universe is homogeneously filled with gravitational sources, then no local frame is truly inertial even at near-zero size (since at any size it feels gravitational acceleration).

Oops, I made a stupid misstatement here. In GR, any local frame can be defined as a truly inertial SR-compliant frame. All that's needed is to define a personalized coordinate system with the desired local frame as the coordinate origin. Then the Shell Theorem says the origin point feels zero acceleration from the gravity of the surrounding dust cloud.

So in that basic sense, I do not think that superluminal expansion actually requires or mandates an expanding universe, it just requires gravity and GR. For example, it seems to me that it ought to be theoretically possible to observe superluminal peculiar velocity at a distance even in a static universe.

Based on my first correction, I need to revise this statement. Nothing can move faster than light in a local inertial frame, so superluminal motion is not possible unless the background dust cloud in one local inertial frame is in motion relative to another local inertial frame. The most general scenario for that to occur is in an expanding or contracting universe.

HOWEVER, let's consider a rotational universe which is static (i.e. not expanding or contracting). An observer located near the axis of rotation should be able to detect that it, together with the entire dust cloud, is rotating relative to the observer's local CMB frame (especially if there is rotational shear). The further out an observed galaxy is located radially along the equatorial plane of rotation, the faster its rotation will be calculated to move relative to the observer's CMB frame, so beyond a certain radial distance that relative motion will be superluminal.

Whether or not it is technically correct to refer to the rotational motion of such a dust cloud as "peculiar motion", I think this is a valid example of how (apparent or calculated) superluminal motion could theoretically occur in the absence of any expansion of space.

Jon

 

[jonmtkisco]

I quoted this passage from the Lewis & Barnes Radar Ranging paper earlier in this thread, where he describes a rocketeer who applies the same thrust for the same time on both the outward and return journeys, and discovers that on the return path he has overshot the origin:

In any case, we might naively expect that if space is expanding, then the journey is longer on the way back than it was on the way forwards ... and hence we might predict under-shooting, rather than over-shooting, the origin. It must be emphasized that this over shoot is no different in the Newtonian limit of the FLRW metric without expansion; using Gauss’s law we can see that at a given radius R from the origin, the rocketeer experiences a gravitational acceleration towards the origin due to the mass contained by a sphere of radius R. This imaginary sphere changes size throughout the journey but the acceleration from gravity remains pointed to wards the origin during the entire trip. Thus in addition to the thrust provided by the rocket, the rocketeer receives at all times an additional push towards the origin. We should not, therefore, be surprised to find the rocketeer overshoots. Thinking very simply about the effects of gravity, rather than the more nebulous expansion of space, gives a much simpler intuitive view.

Another way of describing the overshoot occurs to me which amounts to the same conclusion as the authors'. Just think of the rocketeer as being a tethered galaxy in the Tethered Galaxy exercise. When the rocketeer is exactly at the turnaround point, his proper velocity toward the origin is zero. In a matter-only decelerating universe (which is what the paper uses), the Tethered Galaxy exercise says that the rocketeer would eventually (after a long elapsed time) find himself accelerated back through the origin and out the other side - even if he applied no return thrust at all after coming to proper rest relative to the distant origin! So applying thrust on the return leg only exacerbates the inevitability that he will overshoot the origin on the return.

Another noteworthy aspect of this exercise is that at the turnaround point, the rocketeer will not observe himself to be at proper rest with respect to nearby galaxies which are themselves at rest in the local cosmic Hubble flow. Instead, with respect to such privileged comoving galaxies, he will observe that his deceleration on the outbound leg will be more than that required to be at rest with nearby galaxies; in this relative sense he'll see himself already moving in the direction of the origin. This illustrates the difference between being at proper rest relative to the local Hubble flow, as compared to being at proper rest with respect to the Hubble flow at some distant coordinate.

Apparently it is accurate to describe any "peculiar velocity" as simply being an ordinary "comoving velocity" whereby the moving object is spatially displaced away from the coordinate location where its relative velocity would put it at rest with respect to local Hubble flow. Every peculiar velocity must correspond to a specific such spatial displacement vector, characterized by both a unique proper distance and a unique coordinate direction. In fact, the displacement vector at any particular point in time is just the summation of all of the real spatial displacements which have occurred to an object (and its constituent particles) over the history of the universe, from their originating point(s) where they were at rest with the local Hubble flow. This is because in theory the very early universe had very high homogeneity - e.g. almost no peculiar motion.

Jon