When white light passes through a prism, the rainbow at the other end exhibits a rich palette of colors. The theorists of the Faculty of Physics at the University of Warsaw have shown that models of the Universe using any quantum theory of gravity should also have a kind of "rainbow", consisting of different versions of space-time. This mechanism predicts that instead of a single and common spacetime, particles of different energies should experience slightly altered versions of it.
We've all probably seen the experiment: when white light passes through a prism, it decays to form a rainbow. This is because white light is a mixture of photons of different energies, and the higher the photon energy, the more it is deflected by the prism. Thus, we can say that the rainbow arises because photons of different energies perceive the same prism as having different properties. For many years, scientists have suspected that particles of different energies in models of the quantum universe essentially sense different structures of spacetime.
Physicists in Warsaw used a cosmological model containing only two components: gravity and one type of matter. Within the framework of general relativity, the gravitational field is described by deformations of space-time, while matter is represented by a scalar field (the simplest type of field in which only one value is inherent in each point in space).
“There are many competing theories of quantum gravity today. Therefore, we formulated our model in the most general terms so that it can be applied to any of them. Some might suggest one type of gravitational field - which in practice means spacetime - suggested by one quantum theory, another might suggest another. Some mathematical operators in the model will change, but not the nature of the phenomena occurring in them,”says Andrea Dapor, a graduate student at Warsaw University.
“This result is amazing. We start with the fuzzy world of quantum geometry, where it’s even difficult to say what is time and what is space, but the phenomena occurring in our cosmological model seem to occur in ordinary space-time,”says another graduate student Mehdi Assaniussi.
Things got even more interesting when physicists looked at scalar field excitations that were interpreted as particles. Calculations have shown that in this model, particles that differ in terms of energy interact with quantum space-time in a different way - just like photons with different energies interact differently with a prism. This means that even the effective structure of classical space-time is perceived differently by individual particles, depending on their energy.
The appearance of an ordinary rainbow can be described in terms of the refractive index, the magnitude of which depends on the wavelength of light. In the case of a similar rainbow of space-time, a similar relationship is proposed: the beta-function, a measure of the degree of difference in the perception of classical space-time by different particles. This function reflects the degree of non-classicality of the quantum space-time: in conditions close to classical, it tends to zero, while in true quantum conditions it tends to unity. Now the Universe is in a classic-like state, so the beta value is close to zero, physicists estimate it as not exceeding 0.01. Such a small value of the beta function means that the spacetime rainbow is currently very narrow and cannot be detected experimentally.
A study by theoretical physicists at the University of Warsaw, funded by grants from the National Science Center of Poland, led to another interesting conclusion. The spacetime rainbow is the result of quantum gravity. Physicists generally agree that the effects of such a plan will be visible only at gigantic energies close to the Planck energy, millions or billions of times higher than the particle energy to which the Large Hadron Collider is now accelerating. However, the value of the beta function depends on time, and at moments close to the Big Bang, it could be much higher. As beta approaches zero, the time-space rainbow increases significantly. As a result, under such conditions, the rainbow effect of quantum gravity can potentially be observed even at particle energies that are hundreds of times lower,than the energy of protons at the modern LHC.
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