General relativity: Cosmologist discusses Einstein’s theory
Extra dimensions may be required to explain how gravity worked in the early universe — and led to the conditions we experience today. This is the conclusion of a pair of researchers from Japan, who are trying to reconcile superficially conflicting theories from different areas of physics. Such includes Albert Einstein’s theory of general relativity, which concerns how objects with mass distort the fabric of space and time — an effect that we experience as gravity.
While general relativity successfully explains how gravity works in most cases, the theory begins to break down in certain extreme conditions.
(Such include within the singularities at the heart of black holes and the primordial “cosmic soup” from which all the visible matter and energy in the universe originally formed.)
It may be possible to resolve many of these problems through “superstring theory”, via which some physicists hoped to explain both all particles and the fundamental forces of nature as vibrations of tiny, one-dimensional objects called “strings”.
In this way, superstring theory could provide an avenue to reconcile general relativity — in which events are continuous and deterministic — with quantum mechanics, in which events occur via quantum jumps and outcomes are probabilistic.
The problem, however, is that the evidence required to support this proposal has so far proven elusive.
A new study led by Professor Yasuaki Hikida of the Yukawa Institute for Theoretical Physics at Kyoto University, however, may help pave the way to a validation of superstring theory.
In their study, the researchers have been exploring a concept known as “de Sitter space” — after the Dutch astronomer Willem de Sitter, who was a colleague of Einstein’s in the 1920s.
Professor de Sitter’s theoretical models describe the simplest cosmological solution to Einstein’s field equations, which relate the geometry of spacetime to the matter within it.
In de Sitter space, the three-dimensional, spatial universe is flat (although curved in four dimensional spacetime) and ordinary matter is neglected.
Accordingly, the dynamics of the de Sitter universe are dominated by the so-called cosmological constant, the part of the field equations that accounts for the expansion of the universe.
What Prof. Hikida and his colleague Heng-Yu Chen have done is to develop a concrete method for computing so-called “correlation functions”, which describe the distribution of matter and galaxies across the cosmos, for the fluctuations of the early universe.
They did this using holography — in which higher dimensions exist as a projection on the three-dimensional, spatial universe, much as the security holograms on credit and debit cards appear to show three-dimensional images on a two-dimensional surface.
(Higher dimensions, incidentally, are a common feature of superstring theories — which call for the universe to have at least six extra, “hyperspatial” dimensions in addition to the more familiar three spatial dimensions and the fourth dimension of time.)
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The researchers started with existing methods for handling gravity in so-called “anti-de Sitter space” — in which spacetime is curved in the opposite direction to that of “regular” de Sitter space —,and reshaped them to work in the latter model.
Prof. Hikida said: “We came to realise that our method can be applied more generically than we expected while dealing with quantum gravity.”
With their initial study complete, he added, the team is “now extending our analysis to investigate cosmological entropy and quantum gravity effects.”
While the present study only considered a three-dimensional universe as a test case, the analysis can “easily” be extended to a four-dimensional cosmos, the researchers said.
This may allow the team to extract information on the real world.
Prof. Hikida concluded: “Our approach possibly contributes to validating superstring theory and allows for practical calculations about the subtle changes that rippled across the fabric of our early universe.”
The full findings of the study were published in the journal Physical Review Letters.
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