# Theoretical Predictions

Theoretical Predictions

# New Indications

New Indications

I.e. new things to look for, with unknown scale

“Qualitative predictions”

“Qualitative predictions”

## Discreteness of space/time

Discreteness of space/time

#### Propagation of photon in discrete space

Propagation of photon in discrete space

Highest energy 450 TeV [from Crab Nebula]

#### Propagation of protons in discrete space

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

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: scattering

#### Possible effect: dispersion

Possible effect: dispersion

Speed of light depends on frequency

Certainly if frequency ~ inverse scale size [[ cf edge of a Brillouin zone ]]

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??

Is there a logarithmic correction term??

#### Possible effect: birefringence ??

Possible effect: birefringence ??

#### Actual cutoffs in QFT

Actual cutoffs in QFT

Most are irrelevant because of renormalization

## Dimension change

Dimension change

#### Inverse square law on very large scales

Inverse square law on very large scales

#### Propagation of photons from CMB in a changing-dimensional space

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 ]

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)

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) )

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

Effects on primordial nucleosynthesis

[[ Which nuclei are stable? ]]

Effect on pions (e.g. chiral field theory etc.)

#### Effect on CMB fluctuations

Effect on CMB fluctuations

#### “Dimension waves”

“Dimension waves”

#### Effect on spin degrees of freedom

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)

[ => variations in the polarization of CMB that do not track variations in the temperature ]

(have to exclude Faraday rotation)

#### Effect on anomalies

Effect on anomalies

Effect on etc.

γ

5

#### [ Wave equation ]

[ Wave equation ]

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

#### Gravitational waves

Gravitational waves

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

#### Hydrogen atoms

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

E.g. Zeeman splitting will split into different numbers of lines

https://www.zarm.uni-bremen.de/uploads/tx_sibibtex/1999BurgbacherLaemmerzahlMacias.pdf

#### Einstein equations

Einstein equations

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

## Oligon-like particles

Oligon-like particles

## Non-particle excitations and structures

Non-particle excitations and structures

#### Dimension-change domain wall ?

Dimension-change domain wall ?

## CPT invariance ?

CPT invariance ?

## Corrections to Einstein’s equations

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]

(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?

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?]

[What happens to the singularity theorems?]

#### Very small black holes with naked singularities

Very small black holes with naked singularities

#### Black hole mergers

Black hole mergers

Neutron stars can emit photons to lose energy; BHs cannot

#### Would BHs only emit gravitational radiation?

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

Gravitational waves

#### Non-4D black holes

Non-4D black holes

Black saturns etc.

Supersymmetric black holes

Supersymmetric black holes

## Time dependence of cosmological constant

Time dependence of cosmological constant

## Existence of magnetic monopoles

Existence of magnetic monopoles

Dirac string in fractional dimensional space??

https://arxiv.org/pdf/hep-th/0505114.pdf ???

## Early universe dimension change

Early universe dimension change

## Very early universe anisotropy

Very early universe anisotropy

# Scale-Independent Phenomena

Scale-Independent Phenomena

## Photon correlations near a black hole

Photon correlations near a black hole

# Scale-Dependent Phenomena

Scale-Dependent Phenomena

#### Maximum entanglement speed ζ

Maximum entanglement speed ζ

## Quantization of mass, lifetime, ...

Quantization of mass, lifetime, ...

## Black-hole collapse with ζ < ∞

Black-hole collapse with ζ < ∞

# Specific Parameters

Specific Parameters

## Cosmological constant value

Cosmological constant value

## Particle masses

Particle masses

# [ Things to measure ]

[ Things to measure ]

## Expansion in branchial space

Expansion in branchial space

#### Comparison of quantum computing to classical

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)

do repeated measurements; how do the time increase?

Nominally: some polynomial in log (n)

## Excitations/deformations in spacetime

Excitations/deformations in spacetime

# [ How to measure things ]

[ How to measure things ]