John Valentine
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Algorithm Design: Optimising the Marbles

The previous post showed 3000 ball bearings being squeezed together. The app wasn't that efficient beyond 5000 particles, so needed optimising.

Good news: I've designed (reinvented!) a way of scaling this with linear complexity: space partitioning. Assuming a hex layout in a 2D space, about 15% of the collision tests will be positive, regardless of the number of particles.

e.g. for 10m particles, we'd use about 400m tests for 60m hits. This compares favourably against nested loop approach of complexity O(n^2), with 5Ã—10^13 tests, with 0.00012% of them being hits.ï»¿
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Following on from the "3000 ball bearings" video [1, ] that illustrates faults in physical sphere packing and crystal structures, I modified my "Spot 2" sim to use particles of identical size. Here are 3000 of them [2, pic]

[2] http://johnvalentine.co.uk/spot3.htmlï»¿
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This is sad, but I look forward to a future organisation performing the role, with all the 'free knowledge repository' ideals intact.

I have doubts about a .edu TLD being a commercial enterprise, and my instinct is to wish for domain registration to be denied.

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Flux Density, Gravitational Field, and Hubble's Law

tl;dr: (1) gravitational field is related to the gradient of flux density, (2) Is there a better fit to red-shift data?

In our previous post, we mentioned that flux density corresponds with Compton radius. It might then seem reasonable to think that you could test for blue-shifting of nearby massive objects, because they have a higher flux density. However, this is not necessarily the case.

We propose that the flux density in our neighbourhood (on the scale of galactic clusters or filaments) is very large when compared with the extra flux density that massive objects (like our Sun, or Jupiter) conduct. Incidentally, this makes gravitation quite weak when compared to charge-based effects that can harness more of the vacuum flux into a coherent current.

This means that, in our neighbourhood, there is a lot of flux to reduce the Compton radius, but a relatively small flux gradient (from source to receiver) that would contribute to blue/red-shifting. Local bodies are therefore not a good test for this hypothesis; instead, we must look further afield.

In a cosmological picture that assumes condensation rather than Big Bang, the red shift will be approximately proportional to distance [Hubble's Law], because the light from distant sources was emitted when the matter was in a rarefied flux.

It might therefore be interesting to examine measured red-shift values of sources against the expected vacuum flux conditions at the time of their emission, to see if it has a better fit than the general trend identified by Hubble's Law.

Perhaps more relevant to science, there are opportunities for disproof.

http://johnvalentine.co.uk/po8.php?art=gravitation
#vacuum #redshift #hubble #gravitation #fluxï»¿
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Expanding Universe / Shrinking Matter?

This post is hugely speculative, and covers the speculative part of my last paper [1], so put your Sceptic's Hat on, because we're going to suggest something silly...

...that red-shift (also) depends on the relative vacuum flux density at the source and at the receiver, and we don't need a cosmological constant if we take this into account.

In our description of the vacuum and fermion collapse, we suggested that a denser vacuum flux reduces the Compton radius of a fermion. We also proposed that photons are emitted from pairs of events, from structures that are also affected by vacuum flux density, which means that a receiver in a dense flux will see light that is red-shifted when compared with its emission frequency.

Our tentative proposal is that our environment has a denser vacuum flux than the red-shifted light sources that we observe, and that our composite structures are more compact, e.g. nulcei are smaller, fermions collapse faster, mass is more easily localised, and so on.

It offers us other insights:
* Gamma-ray bursts from black holes (greater in effect than gravitational red-shift)
* Our large-scale region of space might be compressing.
* Dark matter is generated by the same vacuum flux.
* An alternative to the standard cosmological model of the Big Bang: a 'big condensing', where inflation and expansion are not required.
* Varying vacuum conditions throughout the universe.

Yes, we are actively looking for good disproof!

[1] http://johnvalentine.co.uk/po8.php?art=index#papers [2014]

#darkmatter #cosmology #expansion #redshift #vacuumï»¿
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Dark Matter: observations as a statistical composite

Compare the composite image released here [1, 2], with the diagram of my previous post [3], and they look similar. However, I do not agree with the standard interpretation for it [4].

The community now needs to prove that their models are exclusively the only possible cause of this distribution of 'dark matter' between dense bodies.

[1] Seth D. Epps, Michael J. Hudson; The weak-lensing masses of filaments between luminous red galaxies. Mon Not R Astron Soc 2017; 468 (3): 2605-2613. doi: 10.1093/mnras/stx517

[4] http://johnvalentine.co.uk/po8.php?art=dark_matter - contains DOI refs.ï»¿
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A Dark Matter

The subject of Dark Matter has intrigued me, but I've never regarded it as a primary objective to devise a description for it, nor to use it as motivation when devising foundations.

However, I've found that my mechanism might provide an adequate explanation about the discrepancy between observations and our best standard theory (be that GR or MoND).

If we propose that the vacuum is filled with uncollapsed bosons with spherical symmetry, and that fermions are instantaneous snapshots of bosons (where uniqueness criteria apply), then in regions that contain lots of matter, there will be high levels of vacuum flux, which covers all flux: graviational flux, magnetic flux, and so on. This flux may self-interact to produce spontaneous, non-conserved fermions, and I believe that this provides the additional interactions (and localized sources) that Dark Matter tries to cover.

This picture also creates some interesting localised variables for the vacuum, as well as discrete origins for the statistics, where the standard theories expect the vacuum to be uniform and continuous. These variables will change Compton radius of conserved particles, create a flux gradient, cause red-shift, and change the periodicity of the way that matter interacts with the vacuum.

http://johnvalentine.co.uk/po8.php?art=dark_matterï»¿
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Phase Solver pt4: more interactive exploration, image export

New:
* Click to re-center
* Zoom in and out
* Export as PNG.
* Resolutions: 1/8 for speedy navigation, 8 for high-quality renders.

I started this session thinking I'd implement multi-threaded processing and async workers, but instead I improved the UI. I think that made a bigger difference to usability, but it still ties up the main thread.

There's a slight error on the vertical axis when re-centering.

http://johnvalentine.co.uk/app/phase/phase.htmlï»¿
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Phase Solver pt3: Have a play

I have a huge todo list for this HTML+JavaScript app.

http://johnvalentine.co.uk/phase2a.htmlï»¿
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Phase Solver, pt2: An imperfect implementation of a 'continued fraction'

I say "imperfect" because I haven't included the zero-th term, and I've limited 'n' to a small odd number. I also think I did it wrong, which is giving me the interesting result here.

Complex phase is mapped to greyscale, but is shifted. Again, imperfect.

I'll work again on this soon.ï»¿