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Everyone knows, or has at least heard, that our universe is expanding. It is also very common to read or hear that space is expanding. This is often used to explain the cosmological redshift as follows: since the space between us and a distant galaxy has "stretched" during the time that light took to reach us, the wavelengths of the photons have been "stretched" by the same ratio.
Figure 1: 
Figure 1 (from Relativity 4 Engineers) shows how every piece of space undergoes an equal amount of expansion as time goes on. This leads to Hubble's law, H = (recession velocity)/distance, normally expressed as km/s/Mega-parsec (km s-1 Mpc-1). It does not mean that for constant time intervals the expansion is always the same; it may vary over time, but for a given time, the expansion rate is on average the same all over space.
This notion of expanding space may (perhaps) be misleading. It may even be a fallacy, if we are to believe Prof. John Peacock of Edinburgh.[1] "The idea of an expanding universe can easily lead to confusion, and this section tries to counter some of the more tenacious misconceptions. The worst of these is the 'expanding space' fallacy." To be fair, the professor states that space on the global scale is expanding, but he holds that on a local scale, expanding space is a misconception. The space between the walls of your room, or between the Moon and us, or between nearby galaxies and us is not expanding, he says.
To me, Prof. Peacock's proof is not very convincing. He postulates a low redshift object that is somehow given a "push" directly towards us, with a velocity that just cancels out the cosmological redshift by means of a Doppler blueshift. Then he uses two approaches to analyze what will happen to the object as time goes on. One analysis shows that the "zero redshift" object will start moving away from us and obtain a redshift again. The other analysis shows that the object would actually pick up a blueshift and approach us.
It is important to note that he uses an Einstein-de-Sitter model[2] for the initial analyses, meaning that the cosmic expansion is slowing down 'just right' to prevent a contraction in the future. This result is then used to refute the "expanding space" notion. Shown below is a graph of the latter method, where the object approaches us.
Figure 2:
An object presently located at 100 million light-years from us is given a "push" so that it momentarily co-moves with us, meaning that it has the same velocity vector relative to the Cosmic Microwave Background (CMB) than what we have. The object will eventually reach us in a time depending on the rate of expansion. Shown here in blue is a distance curve for a decreasing expansion rate (Einstein-de-Sitter) and in green for comparison, the same curve with no expansion.
With Ho ~ 70 km s-1 Mpc-1, the required initial radial velocity relative to us is vr ~ -0.00715c. With Einstein-de-Sitter expansion, it will take some 45 billion years for the object to reach us. With no expansion (Ho = 0) it would have only taken some 0.1/0.00715 ~ 14 billion years (one Hubble time) for the object to reach us.[3] I feel that this says that space is expanding and not the contrary!
The said object will only be coming towards us in a universe with a decreasing expansion rate. This is perhaps of academic interest only, since the real universe seems to have an increasing expansion rate at present, meaning that the object in question would never reach us. It would drift away with the expansion and acquire a redshift once again. Prof. Peacock admits this in his article and comments that in this case one could possibly call it "expanding space".
Over a few meters, the present local expansion may be negligible - but the Moon is not quite "local". I calculated the pure Hubble expansion for the distance between the Moon and us, using the present Ho ~ 70 km s-1 Mpc-1 and I got ~27mm per year.[4] We know from laser ranging that the Moon is presently receding from Earth at ~38mm per year and all of this is normally attributed to tidal effects.
Figure 3: 
Figure 3 shows the mechanism of angular momentum transfer to the Moon, as viewed from above the South Pole. The blue band represents a hypothetical continuous ocean and the blue and red arrows indicate the average tidal current flows. The offset gravity vector, due to the tidal bulge (probably also aided by magma currents, causing the crust to bulge) transfers some of Earth's angular momentum to the Moon. This causes the Moon to slowly recede from Earth.
My question is: can we be sure about the size of this effect? Tidal effects on Earth's rotation are very hard to model with any precision. Earth's slowing rotation seems to be influenced more by movements of the tectonic plates than by the Moon, so who says we have the Moon's recession rate right? One cannot just take Earth's presumed loss in angular momentum and transfer that to the Moon. Maybe only ~11 mm/year is caused by the tidal gravity effects and the rest by spatial expansion.
Finally, if I have my sums right, a 10x10x10m chunk of local space should presently expand at a rate of 0.07 micron per century on each side. We would probably never notice that. Sadly, putting your money into such a piece of spatial "real estate" and waiting for it to expand is not useful. That is unless a "Big Rip" happens anytime soon and then your claim will be of no value anyway!
What do you think: has Prof. Peacock got it right or wrong?
Regards, Jorrie
Credits and notes:
[1] Cosmological Physics: additional topics by J Peacock.
[2] See the Einstein-de-Sitter page in Relativity 4 Engineers for more...
[3] Interestingly, the 45 and 14 billion years are only dependent upon Ho and not upon the distance. The speed required to be momentarily stationary relative to Earth scales automatically with distance, keeping the times constant.
[4] One Mpc is about 3.26 million light-years. The distance to the Moon is about 1.25 light-seconds, which converts to about 1.2 x 10-14 Mpc. Multiplied by Ho ~70 km s-1 Mpc-1, this gives ~8.5 x 10-13 km/s, or about 27 mm/year.
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