When it comes to understanding the dimension of time, definitions are as diverse as those who ponder it. Famous philosopher Augustine of Hippo (354–430 AD) said, ‘Everybody knows what time is until they try to define it’. Fifteen centuries after Augustine came Einstein, who manufactured a definition of time to suit his special relativity theory.

‘The primitive subjective feeling of time flow enables us to order our impressions, to judge that one event takes place earlier, another later. But to show that the time interval between two events is 10 seconds, a clock is needed. By the use of a clock the time concept becomes objective. Any physical phenomenon may be used as a clock, provided it can be exactly repeated as many times as desired. Taking the interval between the beginning and the end of such an event as one unit of time, arbitrary time intervals may be measured by repetition of this physical process. All clocks, from the simple hourglass to the most refined instruments, are based on this idea.’ ^{1}

For Einstein, ‘what clocks measure’ didn’t just provide an understanding of time; it somehow was time. In special relativity, when a clock slows down, time itself slows down. Essentially, Einstein was clothing the concept of time with physical characteristics.

French philosopher Henri Bergson, a contemporary of Einstein’s, disputed relativity’s portrayal of time by arguing that there is a difference between time itself and what clocks display.^{2} Clocks display arbitrary fractions of periodic events such as the motion of the Sun across the sky (as shown on a sundial), grains of sand moving through an hourglass, the number of swings of a pendulum, or the number of oscillations of a caesium atom (the current standard), but this is not the physical reality of time itself. The physical reality of time is the standard against which we can compare these events, which is not just a made-up ‘psychological definition’ as Einstein had contended.

In 1987, following in Bergson’s footsteps, professor of Electrical Engineering at the University of Colorado Petr Beckmann wrote:

‘Clocks are not time, and they do not define time; they are simply measuring devices, keeping a record of arbitrary divisions of the day. There is an element of sympathetic magic in the connection between time and clocks which generated the irrational character of time and space woven into the mathematics of special relativity. What happens to Einstein’s clocks is what happens to time. But Einstein is detaching himself from physical reality in his theoretical imaginings.’ ^{3}

## Time Meets Space

Once Einstein had clothed time with physical characteristics, it was a small jump to connect it to the three dimensions of physical space. This was achieved in the years following the publication of special relativity by Einstein’s former mathematics professor, Hermann Minkowski. In Minkowski’s new union of the four dimensions, an object’s frame of reference was pictured to transform between two events, meaning that coordinates for its location in space as well as its instant in time were specified. This came to be called ‘spacetime’.^{4} Minkowski’s four-dimensional spacetime model allowed for a ‘geometric’ representation of the effects of relative motion, particularly those involving high speeds.

Spacetime was not without criticism, however. One of the main objections was the argument that it isn’t physically real, that it is purely a mathematical construct. Yes, it can be precisely defined in the language of mathematics, but what do those equations actually represent in the real world? We can imagine spacetime to be some sort of malleable interactive substance for the sake of the numbers, but what is it really?

Although Einstein wasn’t initially happy with the concept of spacetime, he justified its existence by saying it was not something we could separate from physical objects. Rather, spacetime was an extension of the objects themselves:

‘I wished to show that spacetime is not necessarily something to which one can ascribe a separate existence, independently of the actual objects of physical reality. Physical objects are not in space, but these objects are spatially extended… In this way the concept “empty space” loses its meaning’.^{5}

In this view, empty space cannot be thought of as nothingness; instead, it is some esoteric property of the physical objects spatially separated within it. This is a difficult concept to grasp because intuitively, we think of space as ’emptiness’, not having a shape or curvature of its own. This is how it was viewed in classical physics – an emptiness between the Earth and the Sun, for example. But when contemplated in the physics of relativity, the emptiness becomes an aura-like augmentation of the masses of the Earth and the Sun. By extension, since it is not independent of an object’s mass, it becomes some inexplicable property of the mass-energy equivalence. But if the math works, how can it be wrong?

Minkowski may have done Einstein a big favour by mathematically showing that time could be connected to space, but in the long run, this link does physics a disservice because spacetime does not represent any physical reality. Spacetime exists only as an idealized mathematical construct. It is an example of mathematicism, the metaphysical belief that mathematics underlies and determines the nature of physical reality.

Refuting Relativity,^{6} points out that the operational definition of time used in Einstein’s relativity does not address the more fundamental aspect of time borne out in the extremely small intervals of quantum mechanics (chapter 2). At the quantum level, ‘time’ is not something that can be slowed down or interact with space. In quantum mechanics, time is treated as a universal and absolute parameter. It does not vary according to the observer’s motion but is the same for everyone, everywhere.

Thanks to quantum mechanics, spacetime is doomed. This was one of the conclusions drawn by cognitive psychologist and popular science author Donald Hoffman.^{7} Although not the central topic of his discussion, Hoffman quotes several top voices in the physics community who are ready to ditch spacetime. Watch a highlights version of Hoffman’s argument in this video.

Please let me know your thoughts in the comments below.

#### References

- Einstein, A. (1952) Relativity: The Special And General Theories. 15th edition, 5th Appendix, June 9, 1952.
- Bergson, H. (1922) Debate at the Société Francaise de Philosophie. Cited in: Nathan, M. Does anybody really know what time it is? From biological age to biological time. Published: February 22 2021.
- Beckmann, P. (1987) Einstein Plus Two. Golem Press, Box 1342, Boulder, CO 80306, 1987.
- Minkowski, H. (1907) ‘Spacetime’ quote. Cited In: Siegfried T. It’s Likely That Times Are Changing. Science News August 29, 2008.
- Einstein, A. & Infeld, L. (1938) The Evolution of Physics: The Growth of Ideas from Early Concepts to Relativity and Quanta. Vol. 10 1938, p.186-189. Simon and Schuster.
- Shadbolt, B. (2024) Refuting Relativity. Chap 2.
- Hoffman, D. (2024) Perception as a fantasy, Reality as Illusion. Talk given at the Institute of Art and Ideas. Last accessed 11/05/2024.

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