Theoretical Predictions

New Indications

I.e. new things to look for, with unknown scale
“Qualitative predictions”

Discreteness of space/time

Propagation of photon in discrete space

Highest energy 450 TeV [from Crab Nebula]

Propagation of protons in discrete space

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10^-26 m Compton wavelength
Is there shot noise from the discreteness?
“Scattering” from the discreteness:
cross-section is of order (elementary length)^2 [ 10^-172 barns ]
scattering event frequency n σ v
What is mfp for scattering from the discrete background? [compton wavelength vs. elementary length]

Possible effect: scattering

Possible effect: dispersion

Speed of light depends on frequency
Certainly if frequency ~ inverse scale size [[ cf edge of a Brillouin zone ]]
Analogy: propagation of phonons in an amorphous material
Is there a logarithmic correction term??

Possible effect: birefringence ??

Actual cutoffs in QFT

Most are irrelevant because of renormalization

Dimension change

Inverse square law on very large scales

Propagation of photons from CMB in a changing-dimensional space

Huygens principle would have spheres of different dimension
1/r^(d-1) [ d space dimensions ]
Is this effectively like a changing speed of light (AKA refractive index)
Warping in string theories etc. might be an analog
https://en.wikipedia.org/wiki/Randall%E2%80%93Sundrum_model
(e.g. you have d+p dimensional spacetime, where the p dimensions have varying curvature)
V(X, r) ~ r^d
We want: V(X, r) ~ r^(d+p(X))
RS: V(X,r) ~ r^(d+p) ( 1 - r^2 / R(X) )
If you go through a region of differing dimension, geodesics (aka rays) will diverge or converge

Effects on primordial nucleosynthesis

[[ Which nuclei are stable? ]]
Effect on pions (e.g. chiral field theory etc.)

Effect on CMB fluctuations

“Dimension waves”

Effect on spin degrees of freedom

Photons have d-1 polarization states?
A massive spin-1 particle should have d polarization states in d dimensions
https://link.aps.org/pdf/10.1103/PhysRevD.97.024004
Spin 1/2 : 2^(d/2) ?? [ i.e. number of components for a Dirac spinor ]
Graviton : d (d-3)/2 [[ possibly polarization of gravitational waves measurable with LISA ]]
In variable dimension space, there might be “rotation” between physical directions and spin direction.... Some form of “dimensional precession”
[ => variations in the polarization of CMB that do not track variations in the temperature ]
(have to exclude Faraday rotation)

Effect on anomalies

Effect on
γ
5
etc.

[ Wave equation ]

https://www.wolframscience.com/nks/notes-4-9--pdes-in-higher-dimensions/

Gravitational waves

https://arxiv.org/pdf/1704.07392.pdf

Hydrogen atoms

Spectral lines?
As dimension changes, the orbital angular momentum states will work differently. Multiplicity of spectral lines will be different
E.g. Zeeman splitting will split into different numbers of lines
https://www.zarm.uni-bremen.de/uploads/tx_sibibtex/1999BurgbacherLaemmerzahlMacias.pdf

Einstein equations

Does the 8π change (2 for graviton degrees of freedom)

Oligon-like particles

Non-particle excitations and structures

Dimension-change domain wall ?

CPT invariance ?

Corrections to Einstein’s equations

Presumably of order κ = (elementary length)/(scale size) or κ^(2-d)
Could there be a logarithmic term? In log(κ)
Do the corrections imply curvature singularities cannot form?
Do the corrections imply an effective equation of state even for the vacuum?
(cf MECOs with weird “bouncing” equations of state) [compact object without horizons]

Does the graviton have a mass; i.e. should the gravitational potential be a Yukawa potential?

Do they lead to a mass gap for gravitational waves?
The most obvious version would have a dispersion relation
ω^2 = c^2 k^2 + ϵ k^4 ??

[What happens to the singularity theorems?]

Very small black holes with naked singularities

Black hole mergers

Neutron stars can emit photons to lose energy; BHs cannot

Would BHs only emit gravitational radiation?

Could they emit “dimensionons”?
Anything with the quantum numbers of the vacuum could be radiated outside a black hole. We might call any classical excitation of the vacuum a gravitational wave.
What about oligons?

Gravitational waves

Non-4D black holes

Black saturns etc.
Supersymmetric black holes

Time dependence of cosmological constant

Existence of magnetic monopoles

Dirac string in fractional dimensional space??
https://arxiv.org/pdf/hep-th/0505114.pdf ???

Early universe dimension change

Very early universe anisotropy

Scale-Independent Phenomena

Photon correlations near a black hole

Scale-Dependent Phenomena

Maximum entanglement speed ζ

Quantization of mass, lifetime, ...

Black-hole collapse with ζ < ∞

Specific Parameters

Cosmological constant value

Particle masses

[ Things to measure ]

Expansion in branchial space

Comparison of quantum computing to classical

Make the best Shor’s algorithm quantum computer:
do repeated measurements; how do the time increase?
Nominally: some polynomial in log (n)

Excitations/deformations in spacetime

[ How to measure things ]