When white light is passed through a prism, the rainbow on the other side reveals a rich palette of colors. Theoretical physicists, who have increasingly migrated toward making up stuff using math, now claim using such numbers that quantum theories of gravity must also have a 'rainbow' of sorts, composed of different versions of spacetime. They further predict that instead of a single, common spacetime, particles of different energies essentially sense slightly modified versions.

Most of you have seen prism experiments. When white light passes through a prism it splits to form a rainbow, because white light is a mixture of photons of different energies, and the greater the energy of the photon, the more it is deflected by the prism. It could be said that the rainbow arises because photons of different energies sense the same prism as having slightly different properties.

Some theoretical physicists have speculated that particles of different energies in quantum universe models essentially sense spacetimes with slightly different structures, based on guesses rather than a quantum theory/hypothesis. Currently, a group of physicists from the Faculty of Physics, University of Warsaw, led by Prof. Jerzy Lewandowski, has formulated a general mechanism responsible for the emergence of such a spacetime rainbow.


Quantum particles of different energies sense different properties of spacetime. The effect is similar to the dispersion of light in prism: photons of different energies sense the same prism as having slightly different properties. (Source: FUW, jch) Credit: Source: FUW, jch

In the current discussion the Warsaw physicists are using a cosmological model that contains just two components: gravity and one type of matter, which sends off alarm bells in the real world physics community. Under the general theory of relativity, a gravitational field is described by deformations of spacetime, whereas matter is represented as a scalar field (the simplest type of field where every point in space is assigned only one value). 

"Today there are many competing theories of quantum gravity. Therefore, we formulated our model in very general terms so that it can be applied to any of them. Someone might assume the kind of gravitational field - which in practice means spacetime - that is posited by one quantum theory, and someone else might assume another. Some mathematical operators in the model will then change, but this will not change the nature of the phenomena occurring in it," says PhD student Andrea Dapor.

They mean hypotheses, of course. Gravity is a theory, gravity is a theory, quantum gravity is not.

The model so devised was then quantized numerically (on a computer) - in other words continuous values, which may differ from one another in terms of any arbitrarily small amount, were converted to discrete values, which may only differ by specific intervals (quanta). Research on the dynamics of the quantized model revealed an amazing result: processes modeled using the quantum theory on quantum spacetime turned out to exhibit the same dynamics as when the quantum theory takes place in a classical continuous spacetime, i.e. the kind we know from everyday experience.

"This result is simply astonishing. We start with the fuzzy world of quantum geometry, where it is even difficult to say what is time and what is space, yet the phenomena occurring in our cosmological model still look as if everything was happening in ordinary spacetime!" says PhD student Mehdi Assanioussi (UW Physics).

They then looked at excitations in the scalar field, which are interpreted as particles. Calculations showed that in this model, particles that differ in terms of energy interact with quantum spacetime somewhat differently - much as photons of different energies interact with a prism somewhat differently. This result means that even the effective structure of classical spacetime sensed by individual particles must depend on their energy. 

The occurrence of a normal rainbow can be described in terms of a refractive index, the value of which varies depending on the wavelength of light. In the case of the analogous spacetime rainbow, a similar relationship has also been proposed: the beta function, a measure of the extent to which the structure of classical spacetime differs as experienced by different particles. This function reflects the degree of non-classicalness of quantum spacetime: in conditions similar to classical it is close to zero, whereas in truly quantum conditions its value is close to one. Today the Universe is in a classical-like state, so now the beta value should be near zero, and estimates performed by other groups of physicists indeed suggest that it does not exceed 0.01. This small value for the beta function means that currently the spacetime rainbow is very narrow and cannot be detected experimentally.

As is often the case, the groups now says it is up to particle physics to prove them right.