The Cosmic distance ladder is something you should already know about since learning about the mainstream is part of the process of creating an against the mainstream idea. You should certainly know how Hubble measured extra-galactic proper distance (Cepheid variable stars) given the number of times that I have cited Hubble's law.
Last edited by Reality Check; 2017-Mar-27 at 09:02 PM.
We can get recessional velocity V_r from this alternate model with this form:
then using hubble's law, we can divide this speed by H_o to yield Proper distance.
So there's Proper Distance. I've graphed them out to z=10 against the equation from conventional cosmology: recessional velocity, Proper Distance
Realitycheck, I believe you are in error about the measurability of proper distance on extragalactic scales:
"With few exceptions, distances based on direct measurements are available only out to about a thousand parsecs, which is a modest portion of our own Galaxy. For distances beyond that, measures depend upon physical assumptions, that is, the assertion that one recognizes the object in question, and the class of objects is homogeneous enough that its members can be used for meaningful estimation of distance."
"While the Hubble law distance is in principle measurable, the need for helpers all along the chain of galaxies out to a distant galaxy makes its use quite impractical. Other distances can be defined and measured more easily."
Hubble's law is also an approximation that doesn't accurately describe our universe observationally on large scales. The Proper distance that you are referencing is absent from the cosmology calculators and is not defined mathematically in the wikipedia articles that you are linking. Maybe proper distance=luminosity distance in gravitationally bound regions, but if you are measuring luminosity, as is the case in virtually every extra-galactic measurement technique including cepheids, you are yielding luminosity distance.
, again, note the D_l.
It is the empirical Hubble's law that states that your ATM idea is wrong because all galaxies do not recede from us at the speed of light: v = HD where v varies with distance.
ETA: Starting with a formula that seems to appear from nowhere is not wise.
Last edited by Reality Check; Today at 03:13 AM.
cosmic distance ladder.
The Ned Wright page you cited has:
Hubble's law is an approximation that accurately describes our universe observationally on large scales. There are deviations from it which is why we say that the expansion of the universe is accelerating.Many Distances
With the correct interpretation of the variables, the Hubble law (v = HD) is true for all values of D, even very large ones which give v > c. But one must be careful in interpreting the distance and velocity. The distance in the Hubble law must be defined so that if A and B are two distant galaxies seen by us in the same direction, and A and B are not too far from each other, then the difference in distances from us, D(A)-D(B), is the distance A would measure to B. But this measurement must be made "now" -- so A must measure the distance to B at the same proper time since the Big Bang as we see now.