CONSERVATION LAW.

“For temperature, these small scale entities are kinetic energy and particle collisions, at which the sum of the energy is conserved.”

GIANT GRADIENTS.

“That precise conservation gives rise to the existence of steady-state linear gradients on the large scale, and the expectation value of the kinetic energy (per particle) connects to temperature through the Boltzmann constant, e.g. with ⟨Ek ⟩ = 32 kB T in the kinetic theory of gases.”

LIMITS.

“Now, to claim that kinetic energy and its properties are defined or governed by the classic thermodynamic model of temperature would be misleading.”

MORE LIMITS.

“To construct a model of kinetic energy exchange between particles based on temperature would be to lose detail as well.”

INSULATION.

“Insulation divides unconnected and separately equilibrating subsystems, and in the temperature model it needs to be assumed separately, and be put in by hand.”

EQUILIBRATING SUBSYSTEMS.

“In the particle interaction picture, however, insulation arises naturally in the limit where interactions are suppressed. In addition, it naturally leads to a disruption of a theory modelled on a region with only regular interactions, i.e. without insulation.”

LEANING TOWARDS FLUCTATIONS.

“At the quantum level, the basic suggestion is to replace the metric tensor of general relativity (in its role of giving rise to ds2) with interactions between pairs of quantum particles, including (and heavily reliant on) quantum fluctuations.”

THE BRIDGE.

“For a connection to the metric, we look to rates of information exchange.”

VISUALIZING THE MODEL.

“An equilibrating process is assumed to exist, so that gradients are suppressed, and to begin with the points of reference can be thought of as on a lattice.”

THE GAP.

“An origin of space-time in information exchange (interactions) would have consequences at the classical level beyond what is described by general relativity, and not limited to event horizons or curvature.”

NOT A REPLACEMENT.

“Note that while the emergent theory in classically safe regions (far away from not only high curvature, but even curvature giving rise to event horizons) must be compatible with general relativity, it is allowed to be more detailed, e.g. fitting within the diffeomorphism invariance of general relativity.”

A CONSEQUENCE.

“The simplest example of a direct consequence is in settings where flat space-time is a good approximation and general relativity would not distinguish between regions with vacuum vs a presence of obstacles to information flow.”

FLUCTUATING SPACE-TIME.

“With vacuum, we here mean empty space-time where only quantum fluctuations are present, and the optionally present obstacles are extended objects made of matter, not sufficiently massive to prevent flat space-time from be a good approximation on the scales considered.”

FLAT SPACE-TIME.

“General relativity would not make a distinction between these two scenarios since it is a theory of curvature only.”

INFORMATION FLOW.

“However, any model based on information exchange must depend on how information is transmitted through regions, and so a presence vs absence of obstacles to information flow must give qualitatively different results for the space-time configuration.”

RELATIVE GEOMETRY.

“With information propagation restricted due to matter, the shortest path is around rather than across an obstacle. This property of information exchange implies non-trivial structure of the associated flat space-times, relative to the case without obstacles. We will call this relative geometry, and model it on the connectivity of flat space-time, leaving dt constant.”

FLAT SPACE-TIME.

“If an obstacle describing a surface extending only through a fraction of the region is placed within the region, an information origin of space-time would mean a bending of the light rays around the surface edges, relative to the reference frame set by the vacuum behaviour.”

BENDING LIGHT.

“This would happen since the surface would describe an ‘insulating’ surface (using the temperature analogy) in terms of the interactions present, which would be cut off in one space dimension along the surface (the object).”

BOUNDARY EFFECTS.

“At the edges, the shortest path for information flow would be around the edges, and that information exchange would reshape the space-time compared to its shape in the vacuum configuration.”

ANALOGOUS SYSTEM.

“This bending can be also be compared with how heat flows past edges of insulating surfaces vs how it would flow in an absence of insulation, in the temperature analogy.”

BLACK VS WHITE.

“Note that relative geometry refers to the space-time configuration, and ‘relative’ refers to that it only makes sense as a comparison between obstacle vs pure vacuum scenarios.”

FLAT VS CURVED.

“In modelling relative geometry, we will use vacuum configurations as reference frames for the metric configurations, illustrating metrics that are flat, but different relative to a set of reference points.”

THE WEFT.

“To describe the different space-times, it is necessary to discuss particle paths delineating the space-time configurations. Light rays are frequently employed for that, but any particle path would be affected by a change in the space-time metric.”

FOOTNOTE.

“The relative geometry is not defined by particle motion. Particle motion is only an effect of the metric.”

THE RELATIVE GEOMETRY.

“The relative geometry is defined by the configuration of the present obstacles, and by the interaction properties at the quantum level. In this, light just happens to have two roles, first as one example of information flow (information exchange with massless properties) and secondly as light rays delineating the metric.”

IT FOLLOWS THAT.

“Since flat space-time is well-known, any observable effects should be well-known as well.”

DIFFRACTION GRATING.

“Interestingly, our example of an insulating surface above has a direct parallel in e.g. a disc giving rise to particle diffraction, an example of the wave-particle duality. This type of effect is present for any configuration of apertures or edges.”

BOUNDARY EFFECTS.

“If the discussion above appeared too unspecific, simply replace ‘obstacles to information flow compatible with approximately flat space-time’ with a tabletop experiment looking at the effects edges/apertures have on light rays, compared with how light propagates when those objects are removed.”

THE COMPARATOR.

“The difference is observable in relation to a set reference frame where light rays describe straight lines in the absence of the objects in question.”

OBSERVABLE EFFECTS.

“Among the observed classical, flat space-time physics, the wave-particle duality is a good candidate for an effect coinciding with that of relative geometry. It is also the only one. Because of this, we model relative geometry on the observed distortion of light rays near apertures and edges.”