Last night, the second installment of Nova’s program, “The Fabric of the Cosmos” aired. As expected, this episode, “The Illusion of Time,” was just as grating as the last one, “The Fabric of Space.”
The reason is that they treated space and time as “spacetime,” focusing on Einstein’s discovery of how vector motion affects time. It doesn’t occur to any of them, as far as I can tell (and I am familiar with the ideas of most of the physicists on the program), that the reason motion affects time is that time is an aspect of motion. Instead, they view time as something mysteriously apart from motion.
They make a big deal out of the arrow of time, and the fact that the forward direction of time is not incorporated into the laws of physics (i.e. the equations can be reversed as far as time is concerned without changing the result.) However, they don’t seem to notice that, if all motion stops, then so does time, since time can only be measured by motion.
Sitting there, I thought, what if all motion in the universe really did stop, so that it became frozen at absolute zero? Then, what if all the frozen objects were removed from the universe? Would anything be left? According to the big bang theory, the amount of space in the universe, as well as the amount of matter, is finite. Therefore, the amount of space in the emptied universe would be some measurable quantity.
Now, if this quantity of space in the emptied universe were to be subsequently increased somehow, it would have to be increased over time, or if the amount of space were decreased, it would have to be decreased over time. Clearly, there is no other way, and we know that space is indeed increasing in the universe.
Similarly, if time were increased… - but wait a minute - what does it mean to increase the amount of time in the universe? When all objects are removed from a frozen universe, does a finite amount of time exist in it at that point? I guess their answer would be that a certain amount of spacetime exists (imagine a loaf of bread containing slices of time), but what does this mean? Does it mean that for every cubic light-year of space there is a cubic light-year of time?
Certainly not. We can’t say this, because time is zero dimensional; that is, it is a scalar magnitude, with no direction in space. So, then, how much time is in the hypothetically frozen universe? The only way to express it is as a scalar quantity, a number that tells us how many moments passed since the beginning (i.e. since the big bang in their cosmology). But what does the number representing the elapsed time of the universal expansion mean, if not that a certain quantity of motion, or a certain increase of space over time, occurred since the big bang?
The trouble is, of course, this scenario requires a point of view that is outside the universe, since no observer can exist in the frozen universe by definition. However, if we admit this God-view, then it is clear that time would have to continue for the observer, but if we don’t admit it, then the observer’s observation stops at the moment the universe is frozen, and we must conclude that time stops as well.
But what do we mean, then, when we say space and time are frozen? Obviously we mean that the continuous increase of space and time has hypothetically ceased. Now, what should be just as obvious, is that the subsequent increase of either one cannot begin without the increase of the other; that is, an observable change in the magnitude of space requires some change in the magnitude of time, while an observable increase in the magnitude time requires some change in the magnitude of space.
One might argue that, while space can’t increase without a corresponding change in time, time could conceivably increase without a concomitant increase in space. The trouble with that argument however, is that one could never know. Time can only be measured over space, just as space can only be measured over time. Without a change in space, it’s not possible to detect a change in time. The bottom line here is that a change in space requires a change in time as well, and vice versa.
Yet, an LST physicists might want to still argue that motion is defined as a change of position, not a change in size, and in a universe without objects, motion itself is not detectable. How can one determine that the size of an empty universe is changing? There aren’t any grid lines to indicate a change of scale. He would be right, of course, but, by the same token, he would also have to believe that the space of a universe that was expanding with matter, could reasonably be expected not to expand without matter. This is a pretty difficult argument to make.
It’s easy to see that the discussion would quickly lead to consideration of the so-called dark energy and dark matter, but we will have to wait for a future episode of the program to get into that.