Cosmological Expansion and Laboratories
Also, the analogy I used earlier about the 13 billion lightyear long string, was that an accurate one, do you think? Or do I need to modify it?
That would be ...
Let's say I have a string thirteen billion lightyears long. It's got a bit of a flex to it. Let's say for every inch of that string, it's stretching exactly one planck length. That's pretty much unmeasurable at our level. The ends of the string, however, would be moving away from each other at superluminal speeds.
The idea is OK, but needs a small modification. Just look at the units for the
Hubble Constant, around 70 km sec
-1 Mpc
-1. The dimensionality is
distance/(time x distance) and so can easily by simplified to just
1/time, but as presented, we see
velocity/distance. So for each Mpc of distance we pick up about 70 km/sec of speed. In your analogy there is no mention of time, so you get a stretch but not a velocity. Now if we re-write that as 1 Planck length per second per inch we are in business. Over a distance of 1 mile (about the largest practical "laboratory" distance it seems to me; the original
SLAC was 1 mile long) or 63,360 inches, the string would appear to stretch 63,360 Planck lengths per second. That comes out to 4.03x10
-29 inches per second (1.02x10
-30 meters/sec). That's about 10
-14 of a typical nuclear diameter, and I think one would be justified in saying that such an effect would not be measurable with today's technology. Do it in a smaller lab and it just gets harder.
The string is definitely stretching, you just can't measure it, so local observations alone don't tell you what it's really doing. Now if we look again at the Hubble constant, 1 Mpc is about 3.09x10
19 km. So just do (70 km/sec)/3.09x10
19 km (and don't rationalize the units so you can see what's happening more clearly), you get 2.27x10
-18 km/sec of velocity per km of distance. That's 2.27x10
-15 meters, and that's a nuclear diameter distance scale. I have heard that one might be able to measure such an effect using
quantum non-demolition techniques, but I don't know if that can really be done. In any case, it is obviously either just plain impossible to do, or just can't be done with current technology.
But that all assumes that the cosmological expansion is not fighting any resisting effects at local scales, and that assumption is wrong. It is well established that bound structures, up to the sale of galaxy clusters, will not feel this effect at all (absent
cosmic rip scenarios, and they appear to be ruled out by observation). So for
Mozina to constantly complain that it can't be empirical because you can't see it in a lab is both monumentally ignorant, because he has never even bothered to think about what really needs to be measured, and monumentally stupid because he re-defined the concept of empiricism so he could feel like he has an excuse not to think bout anything.