The team of Francis, Barnes, James & Lewis have published several very helpful papers in recent years about the expansion of space (with their names in various orders.) I suggested in a recent thread about their Radar Ranging article that they are trending away from explaining particle behaviors as resulting from "the expansion of space," toward explaining such behaviors as being motivated solely by gravity. They're still not admitting that they're all the way there, but I expect they will eventually, at a pace sufficiently measured to prevent their cosmology bretheren and sisteren from rejecting them out of hand as radicals.(adsbygoogle = window.adsbygoogle || []).push({});

In any event, in light of the evolution in their papers, it's not surprising that their earlier papers may lean a little too far towards rationalizing why "space itself" is expanding. Still, I am disappointed by one section in their 7/07 http://arxiv.org/abs/0707.0380" [Broken] "Expanding space: root of all evil?" in which they described a particular particle behavior as "cosmological tidal forces". I believe that their expanation and terminology on this subject (sec. 2.6.2) are misleading and confusing, perhaps in an effort to bend over backwards to justify that space itself is expanding. Here are pertinent quotes:

Clearly the only reason the particle string "expands" lengthwise is that it is being measured by an observer who is comoving with the Hubble flow. The comoving observer is Consider an object of many particles with no internal forces. It is shot away from the origin [tex] ( \chi = 0) [/tex] with speed [tex]v_{0}[/tex], the first particle leaving at time [tex]t_{0}[/tex] and the last at [tex] t_{0} + \Delta t_{0}[/tex]. The length of the object is [tex] l_{0} = v_{0} \Delta t_{0} [/tex]. The object travels to an observer in the Hubble flow at [tex]\chi[/tex], who measures its speed relative to him [tex] (v_{f}) [/tex] and the time of arrival of the first [tex] (t_{f}) [/tex] and last particle [tex](t_{f} + \Delta t_{f}) [/tex] in order to measure its length [tex] ( l_{f} = v_{f} \Delta t_{f}) [/tex].

... (equations) ...

Then, following the method of Barnes et al. (2006) to calculate [tex]v_{f} = \dot{\chi} (t_{f}) R (t_{f}) [/tex] and substituting forCwe have that

[tex]\frac{l_{f}}{l_{0}} = \frac{v_{f} \Delta t_{f}}{v_{0} \Delta t_{0}} = \frac{R(t_{f}) }{R(t_{0}) } [/tex]

Hence, the length of the object has increased in proportion with the scale factor.This result answers the question: what if an object had no internal forces, leaving it at the mercy of expanding space? This is a rather strange object — it would very quickly be disrupted by the forces of everyday life. Nevertheless, it is a useful thought experiment. The above result shows that the object, being subject only to expanding space, has been stretched in proportion with the scale factor. These are essentiallycosmological tidal forces.

We therefore have clear, unambiguous conditions that determine whether an object will be stretched by the expansion of space.Objects will not expand with the universe when there are sufficient internal forces to maintain the dimensions of the object.moving awayfrom the coordinate origin in terms of proper distance; so naturally he observers an increasing time interval between the passage of each particle and the subsequent particle in the stream.

As far as I can deduce, the proper distance between the particles in the stream does not change at all as a function of time, regardless of the expansion of the universe. How could it? This then is simply another example of a coordinate system-dependent calculation which does not reflect an underlying coordinate-independent physical reality. I strongly suspect that if the authors could do a "take-back", they would now retract this example, or at least significantly change their description of what it means

I think it is important to re-explain this sort of example, because I think the correct answer helps to illustrate two important points: (1) there is no need to consider space itself to be expanding in order to explain peculiar particle motions, and (2) peculiar particle motion in a flat, homogeneous dust-filled universe (per Gauss' law) demonstrates clearly that "spacetime curvature" exists even in the absence of any tidal forces. By definition, there are no differential gradients in the matter distribution, and therefore in the gravitational force, in such a universe. Tidal forces may = spacetime curvature, but a more complete statement is that spacetime curvature = tidal forces + nontidal gravitational forces.

Jon

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# Cosmological Tidal Forces

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