One of the challenging open questions of theoretical physics is how to unify general relativity and quantum theory to find a microscopic description of gravity. There are many approaches to find a solution to this fundamental question. It is however difficult to constrain all these possibilities because the relevant scales are far smaller than those accessible by current experiments. With the recent technological breakthroughs of the detection of gravitational waves and the direct imaging of a black hole, we are at the dawn of an era of strong gravity astronomy. It is therefore more important than ever to concentrate on finding observable features of quantum gravity that could in principle leave an imprint in future experiments. After a brief introduction of the fundamental aspects of quantum gravity, I will give an example of such a feature which seems to be a universal property of theories of quantum gravity. In many theories of quantum gravity, space-time has fractal properties near the Planck scale. A consequence which in principle could be observed, is that the effective dimension of space-time is a function of the scale that one is probing.

1. The search for quantum
gravity phenomenology
Marcus Reitz
Advanced Concepts Team - ESA
Science Coffee
07-05-2021

2. Why Quantum Gravity
• 20th century: two revolutions on the frontiers of physics.
• General Relativity on largest astronomical and cosmological scales.
• Quantum Theory on smallest scales of fundamental particles.
• Fundamental questions:
How are these theories connected?
What is the origin and form of gravity, space and time?
• First, summary of most important aspects ->

3. Description of Gravity
• Newtonian view on gravity:
• Masses attract each other.
• General Relativity:
• Space and time combined in space-time.
•
• “Form of space-time” = “Matter distribution”
• Gravity is the geometry (shape) of space-time
caused by the distribution of matter.
Note: Theory of space-time, not on space-time.

4. Description of Matter
• Classical view of particles:
• Fixed position and momentum.
• Quantum Theory:
• Probabilistic description.
• Electron orbitals give region of highest probability
to find electron.
• Alternative incarnation: “sum over histories”
•

5. Why Quantum Gravity
• Remember:
“Form of space-time” = “Matter distribution”
• On smallest scales we expect quantum space-time.
• Probabilistic “Sum over space-times”
•
• However, no complete probabilistic description of
space-time exists.
• Many approaches: ->

6. Why Quantum Gravity
• Non-perturbative quantisation:
e.g. Asymptotic safety, Causal Dynamical Triangulations, …
• New quantisation:
e.g. Loop Quantum Gravity, Spin Foams, …
• New degrees of freedom:
e.g. String theory, Group field theory, …
• Hard to constrain theory space in absence of experiments.
• Choice of approach should depend on questions asked.
• Causal Dynamical Triangulations, well suited for
numerical simulations and discovery of non-perturbative phenomenology,
e.g. running space-time dimension, more later…

7. The Planck scale
• Domain of quantum gravity from dimensional analysis:
• The Planck scale:
•
•
• Tiny scale, unfortunately far beyond current experiments.
• Note: still possible that this argument is too simple.

8. The era of strong gravity astronomy
Gravitational waves.
Direct image Black
Hole.
Non strong gravity:
Cosmic Microwave
Background.

9. The era of strong gravity astronomy
• Big future for gravity research:
• Multiple new faculty positions related to gravity in the Netherlands alone.
Strong groups in gravitational waves, black hole imaging,
quantum gravity/cosmology.
• Data collection and new generation of Experiments:
e.g. LISA, Einstein Telescope, …
• For quantum gravity: shift in focus on phenomenology.

10. What to measure if space-time
is quantum
• Seemingly universal property:
Space-time is “foamy” near Planck scale, sometimes fractal.
• Universal phenomenon first found by Causal Dynamical Triangulations:
running dimension, N.B. highly non-classical.
• Method of calculation: diffusion processes.
• Determined by heat equation and spectral dimension.

11. Running spectral dimension
• Diffusion is related to Random Walk.
• Governed by the Heat Equation.
•
• Gives Return Probability P(t):
Probability to return to starting point
after time t.
• Measure of dimension 𝐷𝑠 of space-time,
Spectral Dimension.
•
• N.B. Classically, space-time is 3+1 dimensional.

12. Running spectral dimension
• Dimension determined from simulations, as average over many quantum space-times.
• Result: running dimension (note σ = time).
• Near Planck scale (new physics).
•
• Large scale (coincides with classical physics):
•
• New result: running dimension can possibly
depend on type of matter:
MR, Ginestra Bianconi, J.Phys.A 53 (2020) 295001.
• Connection to experiments through ratio EM-wave/
gravitational wave luminosity distance or CMB:
Gianluca Calgani et al. JCAP 10 (2019) 012.
• Note: phenomenon is still likely Planck scale suppressed, but proof of concept.

13. Recap
• Gravity is the least understood force:
A microscopic description asks for a theory of Quantum Gravity.
• Many approaches exist, which propose different fundamental properties.
• Hard to constrain due to extremely small Planck scale .
• Start of new era of gravity research is an opportunity to make connection to experiment.
• Focus on universal properties of quantum gravity that can in principle be measured.
• Example is Causal Dynamical Triangulations with numerical simulations,
e.g. running spectral dimension, higher order spectral dimension.