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 ]