Register to reply

A Singular Question

by TalonD
Tags: singular
Share this thread:
Nov24-08, 11:21 PM
Sci Advisor
PF Gold
Chronos's Avatar
P: 9,491
When space expands, a photon redshifts. This nicely fits the conservation of energy principle. The total energy of the photon is diluted across a larger volume of space. Incidently, this phenomenon refutes the notion of space as a propogation media for photons [i.e., aether]. If space were such an entity, photons would blue shift when it was tensioned - like the note emitted by a guitar string being tightened. If space behaves more like a fluid, you should get shear when it is stretched. In that sense, dark energy could be equated with turbulence.
Nov25-08, 07:32 AM
PF Gold
mysearch's Avatar
P: 522
I hope you don’t mind, but I thought your previous response was so useful I made a reference to it in the sticky thread at the beginning of this forum. See following link: As implied, I found this to be a very useful summation of the state-of-play concerning what appears to be some of the more critical assumptions of the LCDM model.

I might still be a little sceptical of the `serendipity` theory regarding the energy density of dark energy at this time, but need to research some of the background issues a little more before commenting. Therefore, started to do some figures on the energy issues related to the observable universe now and at CMB decoupling, i.e. z-1090, as the following figures can be checked against the cosmological calculators. However, I was wondered if anybody had any comments on the results so far?
Energy Density at z=0;
Observable radius = 4.558e10 LY = 4.312e26 m
Observable volume = 3.965e32 LY^3 = 3.358e80 m^3

Baryons = …4%; ……….3.41e-11 joules/m^3; …1.145e70 joules
CDM = …...23%; ………1.96e-10 joules/m^3; …6.581e70 joules
Radiation = 0.00824%; …7.03e-14 joules/m^3; …2.360e67 joules
Lambda = …73%; …...…6.23e-10 joules/m^3; …2.092e71 joules
Total = …..100%; ……...8.53e-10 joules/m^3; ….2.864e71 joules

Energy Density at z=1090
Observable radius = 4.180e7 LY = 3.954e23
Observable volume = 3.059e23 LY^3 = 2.589e71 m^3

Baryons = ..11%; …4.53e-2 joules/m^3; ….1.172e70 joules
CDM = …..64%; …2.60e-1 joules/m^3; …. 6.731e70 joules
Radiation = 25%; …1.02e-1 joules/m^3; …. 2.640e70 joules
Lambda = …0%; ….6.23e-10 joules/m^3; …1.612e62 joules
Total = ….100%; ….4.08e-1 joules/m^3; ….1.056e71 joules
So we are considering a comoving volume expanding from 41.80 million lightyears to 45.58 billion lightyears. Therefore, we can estimate the unity change in energy of this volume as follows:
Baryon:… 1.145e70 / 1.172e70 = 0.977
CDM: .…. 6.581e70 / 6.731e70 = 0.977
Radiation: 2.360e67 / 2.640e70 = 0.00089
Lambda:…2.092e71 / 1.612e62 = 1.297e9
Total: ……2.864e71 / 1.056e71 = 2.712
So under expansion and within the limits of accuracy of the calculation, the baryon and cold dark matter energy within this comoving volume remains unchanged, as we would expect. The radiation energy falls due to the additional (1/a) wavelength expansion factor, while there is an exponential increase in dark energy because it scales with volume. However, the bottom line appears to be that our comoving volume now has 2.7212 times the energy at decoupling, i.e. +370,000 years!
I guess one immediate question that comes to mind is whether this energy analysis should consider any change the gravitational potential energy due to expansion?

I haven’t really had time to consider this issue, but as a generalisation, any increase in potential energy would be negative, therefore I was wondering if this might, in any way, offset the apparent positive increase in energy?
After reading Chronos` post could I clarify a few points:
In the context under consideration, the expansion of space, wherever that means, leads to an increase in the wavelength of a photon in transit. As frequency is the inverse of wavelength, it falls as a function of expansion and so does energy by virtue of E=hf?

Irrespective of the guitar string analogy, the expansion of space does seem to affect the photon. If we assume that the speed of light [c] doesn’t change, then I assume we must assume the product of permittivity and permeability of space doesn’t change. So what caused the photon to change frequency?
Nov26-08, 06:46 AM
P: 622
Quote Quote by mysearch View Post
I thought your previous response was so useful I made a reference to it in the sticky thread at the beginning of this forum.
Hear! Hear!

Mysearch: You originally asked:
Is Hubble’s constant [H] primarily established based on observational measurements and then the critical density calculated from Friedmann’s equation?
and Marcus replied simply "Yes"---- which is quite true ---- as far as it goes. But adopting a different perspective warns of how incomplete our present understanding of cosmology still is:

The actual observational measurements are (a) H now (finally well-established by observation at 72 Km/sec/Mpc) (b) the Universe's flat spatial geometry (inferred from the WMAP power spectrum) and (c) the observed matter density (via the complex of observations discussed by Coles and Ellis in Is the Universe Open or Closed?; C.U.P. 1997), together with more recent observations of gravitational lensing caused by dark matter).

When these observations are interpreted in the usual way with GR, assuming the isotropic-everywhere cosmological principle, they determine the present value of Lambda --- and rightly focus attention on the puzzle of why that most mysterious quantity (or H, if you prefer) has the value it does.
Nov26-08, 09:26 AM
PF Gold
mysearch's Avatar
P: 522
--- and rightly focus attention on the puzzle of why that most mysterious quantity (or H, if you prefer) has the value it does.
More by way of a footnote: If, as indicated, H is primarily determined by observation and measurement, then it would seem the Friedmann’s equation does not really explain the value of H, only how the corresponding critical density is calculated from its value at any point in time. While the positive or expansive nature of H may be obvious from observation, what still puzzles me is why the Friedmann equation implicitly assumes that the value of H is positive, i.e. an expansive velocity, when the component energy densities of this equation only seem to suggest a universe that must collapse under gravitation, prior to +7 billion years. The following thread provides my rationale for asking this question:

Register to reply

Related Discussions
Singular / nonsingular question Linear & Abstract Algebra 7
Singular Value Decomposition question Calculus & Beyond Homework 0
Non singular Linear & Abstract Algebra 1
Singular matrix ? General Math 1