By Marcel van der Veer
October 2022

Published in Science

More on Physics, Tutoring

Hardly anyone will dispute that Einstein's general theory of relativity is well established now. It is very successful in explaining observations and predicting them. Whether general relativity is the ultimate theory on gravity is a different discussion. Astronomers cannot find enough mass to explain the large-scale structure of the universe hence assume it is full of elusive dark matter - or did Einstein not conceive the ultimate theory on gravity?

Bright minds like Verlinde have proposed intriguing new theories on gravity without needing ghostly particles. Others like Hossenfelder suggest that the matter remains elusive because the wrong people are working on it - condensed matter physicists might provide important insights if they would work on the structure of the cosmos, which they do not. Only history will tell, but let's return to today's subject.

Because of Einstein's success it is generally understood that light speed is the speed limit in space. Light speed is ridiculously high, roughly three hundred thousand kilometers per second. Can you imagine such speed? I cannot. It would require an infinite amount of energy for matter to be propelled to light speed. Hence you could only approach it, not reach it.

Can nothing move faster? Well, matter cannot, but space evidently is not matter. Modern insights in the inner workings of a black hole suggest that space itself would cascade over the event horizon, exceeding light speed beyond it. That explains why light cannot escape from a black hole - compare captured light to salmon trying to go against a stream flowing faster than they can swim.

To put the incredible speed of light into perspective, let's reduce astronomical scales to translate light speed into a value we can relate to. Suppose the Sun were a regular thirty-two-panel football, some twenty-two centimeters in diameter, in the center of Amsterdam (the city I live close to, so that's why I imagine the model Sun over there). On this scale, Earth is a grain of sand about two millimeters in size, orbiting the football Sun at a distance of twenty-three meters.

The nearest star to the Sun is Proxima Centauri. Its light takes four years and three months to reach us. This means that the closest neighbor to the small Sun in Amsterdam would be a same-sized football more or less in Detroit or Delhi. In our football universe, light speed would amount to circa four kilometers per day. A light-year, the distance light travels in a year, would be the distance Amsterdam-Madrid. You could walk that distance in less time. This comparison puts light speed into perspective, and on the other hand illustrates how far we are from anywhere in space.

The creators of Star Trek thought up an ingenious way to travel faster than light. Fans of this franchise know that warp one means light speed, and somewhere in the series infinite speed was set to warp ten, at which you would be everywhere in the universe at the same time. In Einstein's universe however, matter cannot exceed warp one. This brings us to the question why there would be a speed limit at all.

The reason from Einstein's theory is that there is no such notion as maximum speed. In fact, light speed is not some maximum speed, it is the only speed. Many people do not realize that in general relativity all matter travels at one same constant speed through spacetime. Why matter would do this is not known, for the moment we must assume that this is the way the universe works. Speed has a component in space and a component in time, like you could analyze your speed in a car in terms of speed going north-south and speed going east-west. The combined total speed in space and speed in time, always has that one same magnitude.

If you would stand still in time, your speed in space would be that one constant speed. If you would stand still in space, your speed in time would be that one constant speed. Photons, the particles that make up light, are ageless, they are frozen in time. So their speed in space must be the maximum velocity attainable, which we have come to call light speed, obviously. We ourselves move relatively slowly through space, consequently we must move at almost warp one through time. Think about this for a moment; this is about as cool as physics gets.

Top picture: The Sun, captured by NASA's Solar Dynamics Observatory (source: NASA).

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