About changes in the size of the universe …
As this is the second time one of my relations raises the topic of expansions and compressions of our dear world, I conclude that this matter should interest my contemporaries and it may be worth taking care of it.
Not without a little a great sadness … How could we forget what the Greeks, the Hebrews and others KNEW 2500 years ago?
As my familiar readers can expect, I will use my darling jingle after the Book of Wisdom: “Examine all things”, and we will therefore examine this: I can already tell you that you will have some surprises…
How do we measure the universe?
Like anything else: by choosing a reference size and assessing the proportion between what we want to measure and this reference.
So if the universe has an erection or shrivels, we will have to find a reference length that has the good taste to remain constant when everything else changes. Could we imagine that our reference length will undergo the same variations in size than the rest, or would you prefer that I wait until you miraculously find that fixed and absolute length?
In other words, whatever the size of the universe and its variations, the proportion between it and our reference will remain the same, and we have NO way of knowing whether this size varies as its measure, the only thing we can know of it, does not vary!
The Greeks knew it, I said! “If you want to use the universe to understand the universe, you will only have information on the interactions in this universe!”….
So, what are the interactions between lengths? Their proportions!
The Hebrews too! (Again the Book of Wisdom): “Everything was done according to weight, measure and number!”
What are the weights and measures? Proportions!
Ah, some are following…
As for numbers I loosely refer you to my books, quite another story…
But it was found again lately by some Heisenberg guy with his “Uncertainty Principle”! Note that basing the knowledge of the universe on uncertainty was pretty swollen! But at least we know what we can expect of this science!
What did Mr. Heisenberg say? That: “In this world we can know only quantities that have the dimension of an action”! And what is that thing? Without going into detail, you have physics teachers for that, the dimension of an action is a combination of a mass, a length and a duration. So we cannot know any of its components separately.
Although we therefore cannot know precisely the masses, the proton is estimated at 1,672622 10-27 kg; neither sizes, but the proton is 0.84184 fm (a femto is 10-15)! Strange principle that everyone seems to mock.
Note, however, that the most accurate known mass is that of the photon with .00000000000000000000000000 … kg (put there as many significant digits you want, as long as they are zeroes!) Except that the photon’s energy, which characterizes it, depends on the observer and his traveling, through its frequency or its wavelength, a feature used by cops and doctors, the first for extending you a ticket and the others to know if you are still alive without asking the question: it is the Doppler effect!
But I announced some surprises. So let’s go! Consider a circle of radius R and be vicious so that R can be a “pure number”, a “scalar” or a “dimensionless” number, as they say… and let’s say that the measure of the radius is R×Lr the dimension of the length being carried by Lr, a “reference length” to which we will report our measurements. If you want to see it as a stallion, nobody prevents you to consider it as a unit (of length)… Finally!
The circumference of the circle will be 2×π×R×Lr and you will notice that 2, π and R are “dimensionless” numbers through the use of our magic length. Now seek the ratio between the circumference and its radius i.e. 2×π×R×Lr/R×Lr. We see that our Lr evaporates, which leaves us with only dimensionless numbers, and that’s good because a proportion itself is a dimensionless number! There is perhaps no need to be graduated from the MIT to know that this is 2×π×R/R, and so just 2×π. So this proportion is independent of the length of the radius R! And that’s good, it means that this proportion will not tell us anything about the size of the circle, just as we have seen for the universe!
And what if R was null?
The formula 2×π×R/R becomes 0/0, what mathematicians call an “indeterminate form” Remember a bit: doing a division of A by B is to find which number multiplied by B gives A. Now you can multiply anything you want by 0 (well, as long as it’s really a number), it will always be 0. So: we do not know!
Uncertainty is okay, but ignorance is intolerable for a scientist, even for a maths.
So they found the trick: if a ratio of two functions (continuous, but let’s be modest, I pass… lengths are such…) becomes indeterminate, the “true value” is that of the ratio of derivatives. Still not enough to have to come from MIT, but if you do not know what a derivative is, just trust me … The derivative of 2×π×R is 2×π, and that of R is 1. So the “true value” when the radius is zero is 2×π. Funny, right? It is the same!
Let get vicious.
We’re coming up to the surface…
Now let’s seek the ratio between the surface of that circle and that of a square of side R, since we compared the perimeter with a length. They are π×R×R and R×R respectively, again our reference lengths are removed, and the result is just π. What will happen if the radius is zero? We fall back on 0/0, but we have the ultimate weapon, let’s take the derivatives: 2×π×R and 2×R. Proportion: 0/0 again! Sh…!! Well, we derive again: 2×π/2, so π remains as when the radius was not zero !!!
Can’t hear, let’s turn the volume up!
Come on, once more and then I’ll stop. The proportion between the volume of a sphere and a cube with an edge of R? 4/3×π×R×R×R and R×R×R. Wouldn’t it be 4/3×π?. Obviously if R is zero we get our 0/0. Go on, go derive up and derive down! 4×π×R× R and 3×R×R. No surprise it is 0/0 again! Once more: 8×π×R and 6×R! Still no surprise and in the end we get : 8×π/6, just in case, it is also equal to 4×π/3, the same proportion as when the radius was not zero!
That is: ALL proportions are retained even if the dimensions are zero… whatever the stuff, straight or curved, which are compared.
So why would not the size of the universe be zero? Since “seen from within”, it would not change anything to what we perceive?
Oulah, oulah! I know pretty well it is not zero since I am in it!
Readers of my “Be logical” that have had the patience to go that far, remember perhaps my sensational experience: the mirror placed on the ground outside by a cloudless night where you could contemplate in the mirror the reflection of the “half” of the universe situated above it.
Well, you can see this reflection indeed? And in 3D? Yet there is no volume in the plane of the mirror, and since you’ve put it on the floor it has not bungled the tar or the grass if you are in the countryside, so that volume is pretty much visible and yet it DOES NOT EXIST.
But you can do worse. Go get a computer engineer of your friends and ask him to make you a video game imitating a game of bowling. He will need spheres, but he knows how to create them and display them as circles on the screen. However, there is a constraint to be respected: the distance between the centers of any two spheres cannot be less than the sum of their radii! Once he has programmed it, your spheres have become solid! I.e. they behave like solid spheres, the way of your “real” bowling balls. Whereas there is nothing solid in your video game but the screen of course. There balls are even just ideas “frozen” in a software that can produce nothing without a compatible hardware!
Are you still sure that what you believe exist is more “real” than reflections or “virtual” video games? We can only know the interactions of the universe with itself, and in fact we can only know its apparent behavior…
Incidentally, this illustration of reflection also applies to “intellectual” thinking, or let’s say “mental”. As much fresh thinking from a spirit can produce material results, the products of reflections are powerless to manifest anything… It is no longer but an illusion of thought. We lost a dimension… But this is off topic!
And so is life, we think we see plants and critters, because we do not see that they are only a digestion (assimilation) process, extremely slow, and they are but appearances taken by the phenomenon of Life…
On the other hand, if the size of the universe is zero, it suits many things. Because it makes it compatible with its possibility. The fact that the universe exists shows that it is possible! The only reason for its existence… But a mere possibility does not take any place or volume because it does not (not yet!) exist. In other words, the very real possibility of the existence of the universe is invisible whereas the depth of the image in the mirror is quite visible but corresponds to nothing existing! So a zero size universe can easily enter a possibility of the “same size”! As the Verb which St. John tells us that He is IN the Principle. The Verb is what makes the world itself out of its possibility, and this Principle is the “possibility” of ALL, not just of this universe… or it is ALL the possibilities, up to you…
For educated people, you see now why Hindus consider this universe as a Māya, an “illusion”?
And if it reminds you why some explain that our vision of reality is inverted, because the tree of reality has its roots in heaven, is it eagerness?
Okay, well, I enjoyed myself a lot, and I promise you that this is the last opportunity I take to waste my time evaluating my space … And I suggest you drop the issues you may not have the answer of, because a well-conducted “examination” (= digging to extract the light of what we study) will result in intelligence (= the ability to read in the depths of things) and that is not so stupid to know that something is absolutely useless!
Good night for now!