If energy is quantized, then why not other things, like space and time? Could one find compelling arguments for postulating that this is the case? Could an experiment be constructed to prove the quantized nature of things? In the below, Rudolph Draaisma tells us why he believed that time is indeed quantized.
Quantized time, space and eternity have been and still are hot subjects in the science of cosmology and philosophy and in discussions about religion as well. In the following I make a different approach, by trying to go down to basics and deductively build up a theory that concludes by exclusion. If you don’t know what is, but can figure out what cannot be, then what is left must be what is.
You probably have sometimes heard the paradox about an arrow or bullet, that never can reach its target, because it first has to travel half the distance, then half of the remaining distance, half of the next one and so on. As there thus always will be an however small rest-distance left, the target cannot be reached. Nevertheless, hardly anyone would volunteer to be the target, just to check this out, because we all know by experience that the target will be hit. How do we solve this apparent paradox?
Well, let’s say that we film the flight of an arrow with a camera, that takes 16 pictures per second. If we play that film later with the same speed, 16 pictures per second, we will basically see the same event as it happened during filming. Our brain cannot separate the individual slides, that the eyes see and so we see a continuous motion. If we would play the film very slowly, slide by slide, we will see that the arrow moves sort of with infinite speed from one location to the next. In the last 1/16 second, before impact on the target, the arrow is on a certain minimal distance and the next, final slide, shows the impact – there are clearly no half-distances to consider.
This is intriguing, so we repeat the experiment with a high-speed camera, say at a 1000 pictures per second. If we play it again with the same speed, 1000 pictures per second, we will see no difference with the previous film of 16 pictures per second – the event appears as it really happened (provided the human brain can handle the 1000 pictures per second – I don’t know). If we however play the high-speed film with the normal 16 per second speed (slow-motion), we will see the arrow move very slowly; it takes minutes, where the original event took seconds. Surely, if anything happened during the event, that lasted anything longer than 1/1000 second, we will see it on the high-speed film in slow-motion. It gives thus more information than even the naked eye could observe, which is the purpose of using high-speed cameras at all. However, it doesn’t solve our problem. Only the time intervals between the slides have become shorter, but the arrow is still “moving” with infinite speed from its position on one slide to that on the next.
To get around this, let’s make an imaginary experiment by using a high-speed camera with an infinite number of slides per second, so we will be able to see the “real” continuous motion. Alas, because how much is the time interval between two slides? Exactly, it is zero. If it would be anything, however little larger than zero, an infinite number of such slides would take an infinite time, not just one second. Hence, not even an imaginary camera can run with an infinite number of slides per second – it is a meaningless statement. There is only one conclusion possible and that is to realize that continuous motion does not exist, which solves the paradox. The possible number of shortest time intervals during any event must be finite and so there must be a shortest time interval, that is indivisible; a time-quantum. We also have a probable measure for it, the Planck time, being 10–43 seconds. Our physical laws are not defined for shorter time intervals, which may no longer surprise us, does it?
Mind that a time-quantum simply is the partition between past and future and in essence what we call the present moment… in which everything exists. Compare with the film strip. Any slide is a present moment, the previous ones are the past and the next ones are the future. A moving object, that as such has different positions on subsequent slides, “jumps” from one position to the next, sort of at infinite speed. But then, also “infinite speed” is a meaningless concept, because however short the duration of the according motion, the traveled distance would still be infinite. If something changes position in no time, it cannot be related to any speed (being a function of time)
Moreover, whatever is infinite, must have had a start. If there is no start and we so would talk about infinity in the past, then whatever it is, can’t get even a second older than it is now. Hence, time itself must have had a start, by which it can be infinite in the future, or have an end there as well. This also means that eternity, being an infinite notion, must have had a start. “Infinite past” is a meaningless concept also; it is a void.
We can now understand that any idea of an infinite speed is unrealistic – it cannot exist. Hence there must be a finite speed, that cannot be exceeded, today acknowledged as the speed of light in vacuum – approximately 300,000 km/s. The speed of light was measured – there is no physical theory from which it can be calculated. Inversely, the Planck time was calculated – it cannot be measured.
What then is speed – is there a speed quantum also? No, there isn’t. Speed is simply traveled distance per unit of time, but the motion is not continuous, but intermittent. If the motion lasted one second, there were 1043 steps. From this we can conclude that for something moving at the speed of light during one second, the length of each step would be: 3.108 x 10–43 = 3.10–35 meter. Mind, that this length is in fact total distance, divided by number of steps and NOT the range of the speed of light and a time-quantum, even though it mathematically gives the same expression. This length is the jump in space that an object at the speed of light makes, from one INDIVISIBLE present moment to the next, just as it is on the slides of a film strip.
I said “a jump in space”. A photon “jumps” through space, from one indivisible present moment to the next, 1043 times per second. As we speak of light years, being the distance that light travels in one year, or light seconds for the traveled distance in one second (the Moon is 1.6 light seconds away from Earth), we now also can speak of “light time-quantum” as a distance. This would be an unfortunate term though, because it is a “jumped” distance and not one traveled by a (continuous) speed, as we perceive photons to have. Within a time-quantum nothing moves, nothing happens; there is only “time-less existence”. Hence, we can replace the inadequate term “light time-quantum” with “space-quantum” and we must conclude that space also is quantized. If so, then the smallest particle that can exist, has the size of just that space-quantum (3.10-35 meter) and is then also an INDIVISIBLE particle.
From this again follows that the observable universe expands at the speed of light. The diameter of the observable universe increases with 3.10-35 meter for every subsequent time quantum, 1043 of them per second. Yes, this means that everything moves at the speed of light, but because we, as observers, do that too, we can consider ourselves to be at rest and so objects moving at speeds lower than that of light, are just doing that relative us, or relative any source of reference we choose instead. As such motions cannot be in-line with the universal expansion at the speed of light, we must conclude that time is 3-dimensional, allowing relative motions to occur in a perpendicular direction (in 3D-time), creating the (illusion of) a 3-dimensional spatial universe, that we perceive to expand as a function of scalar time. In other words, quantized 3D-spacetime is the source of 4D-timespace in Einstein’s relativity theory.
This view explains why the maximum possible speed is finite, because it is bound to the quantized (intermittent) flow of time; space and time are equivalent! So, we should actually talk about “quantized spacetime” and “spacetime-quantum, being 3.10-35 meter.
Whatever particle exists, detected or not, cannot be smaller than this 3.10-35 meter. Compare this with the size of the smallest nuclei of atoms, being around 1.2.10–15 meter, which is 4.1019 larger (40,000,000,000,000,000,000). An atom appears the size of a galaxy for a spacetime-quantum!