Three time and one space dimensions for faster-than-light observers

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Observers moving faster than the speed of light would see a universe with one dimension of space and three dimensions of time — the opposite of how we perceive the world. This is the bizarre conclusion of physicists Professor Andrzej Dragan of the University of Warsaw and Professor Artur Ekert of the University of Oxford and their colleagues. The presence of faster-than-light observers, they claim, does not lead to anything “logically inconsistent”, and could help incorporate the basic principles of quantum mechanics — how nature behaves at the atomic scale — and the special theory of relativity that defines the relationship between space and time.

It was Professor Albert Einstein, shortly after the turn of the 20th century, who completely redefined the way that physicists understood time and space.

He established time as a fourth dimension on top of the three dimensions of space and paved the way for the concepts of space and time, previously seen as separate, to be treated as a whole — spacetime.

Prof. Dragan said: “In the special theory of relativity formulated in 1905 by Albert Einstein, time and space differ only in the sign of some of the equations.”

Prof. Einstein based his theory of special relativity on two assumptions — the first being that the speed of light in a vacuum is fixed, regardless of the motion of source or observer.

The second core tenet of special relativity is that the laws of physics are the same for all non-accelerating observers.

Professor Dragan adds: “Typically, this principle applies to observers who are moving relative to each other at speeds of less than the speed of light.

“However, there is no fundamental reason why observers moving in relation to the described physical system with speeds greater than the speed of light should not be subject to it.”

Profs Dragan and Ekert first explored what would happen if the world could be observable from a superluminal frame of reference — one faster than the speed of light — in a paper published back in 2020 in the New Journal of Physics.

At that time, they considered a simplified case in which both families of observers — sub and superluminal — existed in a hypothetical two-dimensional spacetime, one with one spatial and one temporal dimension.

In their new paper, however, Profs Dragan and Ekert and their colleagues have gone a step further — considering the ramifications of superluminal observers on four-dimensional spacetime.

The team started with the concept of spacetime that corresponds to our physical reality — one with three spatial dimensions and only one time dimension.

However, they said, from the point of view of a superluminal observer, only one dimension of the world would retain a spatial character — one along which the particles can move.

Prof. Dragan explains: “The other three dimensions are time dimensions.”

Paper co-author and University of Warsaw physicist Professor Krzysztof Turzyński added: “From the point of view of such an observer, the particle ‘ages’ independently in each of the three times.

“But from our perspective […] it looks like a simultaneous movement in all directions of space — i.e., the propagation of a quantum-mechanical spherical wave associated with a particle.”

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According to the researchers, factoring in superluminal observers requires the creation of new definitions for both kinematics and velocity.

Prof. Dragan said: “This new definition preserves Einstein’s postulate of constancy of the speed of light in vacuum even for superluminal observers. Therefore, our extended special relatively does not seem like a particularly extravagant idea.”

Furthermore, the team said, accounting for superluminal observers calls for a nondeterministic world — one in which particles move along not one but many trajectories at once, in accordance with the quantum principle of superposition.

Prof. Dragan added: “For a superluminal observer, the classical Newtonian point particle ceases to make sense, and the field becomes the only quantity that can be used to describe the physical world.”

With their latest study complete, the researchers are now looking to apply their results to better understand the Higgs mechanism that gives particles mass.

The full findings of the study were published in the journal Classical and Quantum Gravity.

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