Einstein and Euler foundational theories scrutinised using time distortion at the edge of the universe

A new method to test some of the most influential and far-reaching theories of physics has been devised. And it has to do with time distortion.

Few rank as high as Albert Einstein and Leonhard Euler in terms of lasting impact on the fields of physics and mathematics. But scientists are still trying to see if Einstein and Euler’s seemingly timeless contributions to the natural sciences stack up when you consider the more confounding phenomena: dark matter and the accelerated expansion of the universe.

Read more: Was Einstein slightly off? Cosmic-scale test of one of his main theories throws up strange result

Portrait of a man in a blue shirt with an odd white cap on his head
Portrait of Leonhard Euler (1753). Artist: Jakob Handmann, via Wikimedia Commons.

Euler (1707–1783) was a prolific mathematician. He is credited with founding the studies of graph theory and topology. His pioneering work in number theory, complex analysis and calculus led him to perhaps his most famous discovery, Euler’s number (e=2.71828) which is the base of the natural logarithm.

But another of Euler’s great feats was to develop equations of motion which have been a powerful tool for calculating the movements of galaxies.

Einstein’s (1879–1955) General Theory of Relativity tells us that the universe is not static, but the fabric of space-time itself is distorted by massive objects such as star clusters and galaxies.

But how do the theories of these Swiss masters (Einstein was born in Germany, but became a Swiss citizen in 1901) stack up when taking into account the problems thrown into the mix by modern physics?

Two discoveries in particular continue to put the models of Einstein and Euler to the test.

The first is the existence of dark matter. Astronomical observations suggest that 85 percent of all the matter in the universe is made up of this invisible substance, while only one-sixth of all matter is the stuff that we can see and interact with.

The second is the accelerating expansion of the universe, posited to be the result of dark energy – a mysterious force which counteracts gravity to stretch space-time itself out, causing galaxies to spread apart at an increasing rate.

Modern physicists in Switzerland are now trying to understand how the physical principles outlined by their forebears are impacted by what we now know about the universe.

Photograph of einstein in front of a blackboard
Albert Einstein during a lecture in Vienna in 1921. Photograph by Ferdinand Schmutzer, via Wikimedia Commons.

“The problem is that current cosmological data do not allow us to differentiate between a theory that breaks Einstein’s equations and one that breaks Euler’s equation,” says Camille Bonvin, associate professor at the University of Geneva. “This is what we demonstrate in our study. We also present a mathematical method for solving this problem. This is the culmination of ten years of research.”

Bonvin is first author on a paper published on the study in Nature Astronomy.

The researchers have taken the theories and applied them to one of the most extreme conditions: those that exist at the edge of the universe.

Read more: Einstein rings image reveal dark matter could be wave-like

Here, in particular, researchers have been unable to distinguish between the validity of the two theories because an “ingredient” was missing. So the University of Geneva scientists considered a never-before-used measure: time distortion.

“Until then, we only knew how to measure the speed of celestial objects and the sum of the distortion of time and space. We have developed a method for accessing this additional measurement, and it’s a first,” Bonvin says.

Tests are yet to be conducted, but the researchers know what to look for.

If the measurement of time distortion is not equal to the sum of the distortion of space and time, then Einstein’s General Theory of Relativity will be found to be incomplete.

However, if time distortion doesn’t correspond to the speed of galaxies at the edge of the universe calculated using Euler’s equation, then this Swiss master’s theories run into trouble.

“This will allow us to discover whether new forces or matter, which violate these two theories, exist in the Universe,” explains co-author Levon Pogosian, professor at Simon Fraser University, Canada.

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