Quite interesting. Though it is not within area of my expertise..but I don't think so the same entropy across different fractal structures through my limited knowledge on the issue..

Thanks Anoop

See also https://www.newscientist.com/article/dn19429-laws-of-physics-may-change-across-the-universe/

No idea

As you know Tony I like and identify with the approach you are taking because it has the inherent capability of breaking us out from our existing conceptual models.

For me the critical word is 'seen'.

Entropy: Entropy may be understood as a measure of disorder within a macroscopic system. (wiki)

Within vision there is no information structure 'blur' - its disorder. The amount of disorder varies with distance from fixation i.e the principle data-set to the phenomenon of vision presents a ramped radial field of disorder with the degree of disorder dependent on how far the the surface in the real environment being presented within the phenomenon is from the object being fixated upon. We (the observer) are also factored into this field. We see the world in relation to ourselves. The field presents spatial relationships on an implicit basis including the sentient being. Thus we instantaneously achieve 'orientation' via a field of proximity cues.

The structure of this field is self-similar (attached). This pattern is ubiquitous (so I am told) across the brain and even in neuronal configurations.

Is what's referred to in your question as 'seen' this structure and does this hold relevance to the concept of entropy? Does the field structure relate to the physics universe by virtue that it's related to the relationship between the two components of EMR?

We can't take ourselves out of an act of observation because we are embedded within it - thank Vishnu!

Hi John

That's an interesting take on 'chaos' and entropy. I think you're right.

I think 'seeing' is important in the sense that we have to observe such a fractal structure within cosmology. Our perception has so far been flavoured by our scientific history. We started with Newtonian gravity and chemistry some two centuries ago; first came Planck's Blackbody work that demonstrated the particle nature of photons, then came Jeans' instability criterion which showed how gas clouds could provide 'baby galaxies'; all this was in accordance with second law of thermodynamics.

But more recently however we have started to examine the nuclear forces and the gravitational forces more carefully. It seems entropy as we know it may only be related to those structures with hot centres, like stars, or something that might resemble neutron stars at the super cluster level (super neutron stars?); while those structures which provide negative energy, like galaxies with blackholes at their centres can cause a cooling where the 'arrow of time' would be reversed; a crystalization of matter into galaxies as time proceeds.

In Einstein's general relativity we have made the assumption that the Universe is isotropic and homogeneous (and so is chopped liver by the way - no disrespect meant to Albert, one of my scientific heroes) so we can model it approximately by a homogeneous model.

It is by observing the Universe as INhomogeneous models (WAMP and COBE) that we can actually learn more about the Universe and its structure.

It was only recently that I realized that such a fractal structure might give us a clue about climate change being perhaps linked to nuclear radiation form our Galaxy. At the same time we must fully realize the damage caused by human 'exploitation' of the natural world including the unsustainable level of pollution we are causing e.g. plastics in the ocean.

Take a look at this Tony:

Article Entropy: A concept that is not a physical quantity

Entropy and homeostasis are related but I have nothing like the dept of insight required to isolate the pertinent issues as they 'appear'er 'present' in cosmology.

'It is by observing the Universe as INhomogeneous models (WAMP and COBE) that we can actually learn more about the Universe and its structure."

What's that saying.... "without looking out of the window we can know the ways of heaven"!!

Hi Aparna

I've been thinking how would statistical mechanics have to be adjusted to account for the nuclear radiation from galaxies; any ideas? or references?

and John

Fantastically relevant report ; I will have to read this article very carefully.

Tony, The math involved is totally beyond me I am afraid! Please let me know what you find and lay it back on me in terms that I might understand! Cheers

Probably not. For entropy you get two definitions:

dS = dQ/T

In randomly sampled thermal systems,

and

S = k Ln (Ω)

In randomly filled energy levels.

dS = k dΩ/Ω

Ω dQ/ dΩ = kT

Fractals are not random energy quantities. So you get no entropy defined for them.

Thanks Arpana and Jerry

We need to look carefully at the mathematics of what is being said.

(any references Jerry?)

We seem to have a quantity that may or may not be defined in regions of the cosmos depending on the mathematics we use.

Looking at the physics within the cosmos, galaxies crystallize out of clouds that are 'hot'!!.

At the end of the day I'm very interested in what I call 'cosmostasis' a dynamic equilibrium of the entire Universe and cosmos. I would imagine that entropy is also 'static' (in a dynamic sense) in this situation.

Dear Arpana

I found the following within the conclusion of the paper by Rothman and Anninos Hamiltonian dynamics and the entropy of the gravitational field (file attached). What it says is that the expressions they find for entropy and its Hamiltonian behave as expected. In particular they find the Hamiltonian is an even function (as expected) and therefore positive as I suggested. They equate the crystalization process as more entropy since it is 'more inhomogeneous'. I find this a strange mix of concepts; I think crystalization is order rather than disorder.

I would go further and say that we need to redefine the Hamiltonian (energy density) and entropy function for 'odd' gravitational regions.

Thanks Arpana

So we are saying entropy is related to scattering; the eigenvalue for a 'crystal' is different to a homogeneous medium; I understand what you are saying and what you say is the proper way we have looked at this quantity for the past 150 years. What we would expect is that the most 'ordered' way in which the cosmos can evolve is to slowly disintegrate until only homogeneous radiation remains; the 'arrow of time'.

But look at my point of view in this:

The Big Bang began with a 'crystal', if you will. Gamow called this 'Ylem' (from memory). I would call this the 'Cosmic Egg'. Now this is energy packed into a much smaller space than we have now. Now when the energy fell below a certain quantum level, or alternatively when the 'cosmic guitar player plucked the strings' the energy was dispersed over the entire cosmos; we see the CMBR (cosmic microwave backgroud radiation) to prove this and we can look back over the whole of time (almost).

No energy has been created except what was there in the beginning; so from conservation of energy we can say that over time the integral over volume of the Hamiltonian has not changed.

We began with a condensed 'egg' which I call 'order' and the Big Bang blew it into the Cosmos, and I call this 'disorder', not order.

So my definition of entropy would allow for all these issues. Maybe I should call it a different entity such as 'self-field entropy'

Homeostasis!

Dear Arpana

I think the trouble is that 'entropy was invented during the 'chemistry era' when everything was being analyzed via its EM spectroscopic content. All we needed to do was to detect the frequency signature of the cosmic 'noise'; we could then detect and analyze the EM details and the results were seen in WMAP a heterogeneous model of the early cosmos. https://en.wikipedia.org/wiki/Baryon_acoustic_oscillations#/media/File:Ilc_9yr_moll4096.png

We now suspect that part of the spectrum is acoustic and another part is nuclear, certainly recent cosmological research is pointing this way. https://arxiv.org/pdf/1203.6594.pdf.

Therefore our theories about entropy appear not to be complete. Somehow we need to measure these other parts of the spectrum and combine the results within the standard model of the sky.

Perhaps by combining a search for neutrinos and acoustic fields across a wider spectrum we may build up a gravitational structure of the Universe perhaps to match what self-field theory suggests.

Dear Tony,

This is an excellent observation; in order to "detect the frequency signature" we can use some elements of the information theory and the corresponding definition (definitions...) of entropy. The review of this subject is presented in the paper by Zmeskal et al. (2013): Entropy of the fractal systems, Computers and mathematics with applications, vol 66, no. 2

http://www.sciencedirect.com/science/article/pii/S0898122113000345

The ideas expressed in this paper point directly to the link between the entropy of the Universe and information theory. This connection was also proposed in 1960s by Buchel in the paper: Entropy and Information in the Universe (Nature 213, 319–320 (21 January 1967).

Probably not. The fractal dimension and entropy seem to be related but not quite correlated. I'll answer it by giving an entirely different example.

We did a research in the past to check the correlation between entropy and fractal dimension in melodies which are quite correlated systems. There were no significant correlation. Yes, the universe has fractal structure and one can probably find out the fractal dimension and the structural entropy of a galaxy, but if one plots the structural entropies w.r.t. fractal dimensions for a number of galaxies I think no correlation will show up. It will be interesting for me to know if somebody proves the reverse.

(Adnan Aydemir and Güngör Gündüz, Fractal Dimensions and Entropies of Meragi Songs, in Nonlinear Phenomena in Complex Systems: From Nano to Macro Scale, editors: Davron Matrasulov, H. Eugene Stanley, Chapter 6, Publisher: Springer)

Entropy: A concept that is not a physical quantity

https://www.researchgate.net/publication/230554936_Entropy_A_concept_that_is_not_a_physical_quantity