How large is the universe, and how old is it?

This has nothing to do with electronics, but it is still a very fascinating question. The reason is, the numerics for this are accessible to anyone with a calculator, and basic understanding of mathematics. Once you start to make some calculation, you will see you are getting some results easier as you expect, and the only thing you need is input data for you calculations.

Specially with things like time and position, it makes me realize on what a truly unique place and moment we live here and now, in this universe and time. This requires such a fabulous coincidence, that it makes me wonder if such a coincidence is possible at all. Mathematically speaking, there is a limit with probability, saying that something with a chance smaller than 1: 10^50 could never have happened in the past. ( 10^50 is a one with 50 zeroes behind it). That is because the time the universe excited so far, was around 10...20 Billion years. When looking into the future, an occurrence with a probability of 1:10^50 can take place, if you just wait long enough, like thousands of millions of billions of years. However for the past, time is limited to the birth of the universe. What was before that, we don't know, but it sure was not the world we live on. So there is indeed this validity, saying a change smaller than is 10^50 means it has not happened. This is important to understand that probability with respect to future, is another one as with respect to the past. Simply because there are more years to come, as have passed yet.

First let me bring up this: A few hundred years ago, scientists were able to calculate the ratio of the distance of the earth to the sun, and the diameter of the earth, just based on the length of shadows. It is only the RATIO they knew, from old formulas of land measuring. The only problem was, the diameter of the earth was not known precisely. They had some idea bout it, but no method would give something near precise. Getting this precise number though, would give what you need to scale the whole solar system. So they felt it was important to know. Believe it or not, the british scientist CAVENDISH spend years measuring a part of the earth with his own hands, using a long piece of rope that he layed on the ground, and rolled it up again, etc. Like that he measured a very long piece of land in England, that he knew the coordinates from. Well it was worth it! Now he knew the diameter of the earth relatively precise. WIth that he could calculate the distance to the sun. With the diameter of the earth, he could also calculate diameter of the sun, and from that estimate it's weight. Actually he could scale the whole solar system. All pieces of information could be brought in relation to each other. For instance there is the relation between the distance of Mars to the Sun, the weight of the sun, and the length of one Mars Year. The whole solar system could be charted now, but also the solar system was where the calculations ended.

Cavendish with a Gravity scale. He measured the gravity force between two objects. Gravity is extremely small. If you take a weight of 1kilogram, the gravity that the whole planet earth gives on it, is only "one kilogram force". This is not much, given the size of the planet. So you see what extremely small forces Cavendish was measuring here. Just the force between two weights hanging from a cable. Here is a link to his work, when you like reading such things. On the last page you see the instrument he used. The thing was sealed into a building without doors, so inside it was dead silent, no air movement. From the outside, he could look through some sort of microscope, and see the small movements of the small weights, while he turned the big weights with a handle. He was the first to precisely measure gravity.

So how far away is a star? They still did not know. The problem is the same as described above. They could calculate ratios, like the distance of star "A" to star "B" is 1000 times more than "C" to "D". However they had no (good) reference to scale the universe. Interesting is, if you just have some small beginning somewhere, and you know this number is very precise, you can start to make good estimations though. So suppose you know the distance from "A" to "B", then you can derive from that the distance from "C" to "D". etc, and scale parts of the universe. However there was never a break through with that.

The dimension of the universe is largest "size" that exist in a real (not virtual) environment. This dimension is huge, and today we think we know it's size. Nobody ever was able to verify it, and even if we could, this dimension breaks it's won record every second. That is because the universe expands with the speed of light. This was a discovery by a modern scientist named Hubble. He calculated the size of the universe after he found out the universe is expanding, and he also found at what speed. With this simple idea he could take a specific very far away star, and say how fast is moves away from us, and from that calculate it's distance. The human brain is capable of doing this method in a natural way. When you would hear in a headphone a good stereo recording of a car passing by on the street, you can say if this car was driving very slow or very fast, and also if it passed by in short distance from the microphone or in long distance. So actually you can come up with an estimated speed and an estimated distance. Things like the Doppler effect are evaluated by the brain in a natural way, even if you don't realize it. It's as if you just "hear" the distance and the speed, but it's the Doppler effect that makes you hear it. It is this method that Mr. Hubble used on stars, which all seem to move away from us.

With that he could go even further and calculate the size of the universe. So what is the size? If we know the size the universe has today, then one year later it has grown a tremendous distance, with the speed of light. You may know the speed of light in vacuum is very high. It is 299.000 kilometres per second. Now first 299.000 kilometres is quite a distance to lay back in one second, and a year has very many seconds. So it expands a tremendous distance every year. Add to this the universe is incredible old, it must have a huge size after ten thousand millions of years.

So in one year the universe will grow 9,43·10¹⁵ meters. (take your calculator and verify it). As you see now, it is not hard to make such calculations. 9,43·10¹⁵ meters means you need to drive in a car 235 millions times around the earth. Suppose you take the total distance that all cars that were ever made, have driven, and add to that the the distances that existing cars on earth will drive, and you drive them until they won't go any more. That total distance is about how much the universe expands each year. This makes the number more touchable. So it's a lot, but something our imagination understand. Anyway, the precise real number is 9,43·10¹⁵ meters per year.

So we know now, at the edges the universe expands with 9,43·10¹⁵ meter per year. The more you move to the center of the universe, the lower the expansion speed gets. Good old Mr. Hubble discovered this expansion, by the Doppler effect. He noticed, the further away a galaxy is, the more it's color shifts into the red, meaning further away galaxies move faster away from us then near by galaxies. You need to digest this: Hubble noticed, the further away galaxies we look at, the faster we see them move away from us. This has a lot of meaning to how we must see the universe, and from this we can derive its age and size even!

Here is a simple way to demonstrate this. Suppose an ant stands on the left end a stick of 1 meter, which expands with 10% per minute. The ant would see the marks: 1cm, 2cm, 3cm, etc, and at the end of the stick he sees 100cm. Now he sees the mark "1cm" move away from him with 10% per minute, so 0,1mm per minute. The mark "2cm" he sees move away from him with twice that speed. and the end of the stick moves away from him with full 10cm per minute (and we already knew that). Now, suppose we take a much longer stick, and it's expanding with the same ratio. The longer the stick gets, the faster the ant will see move the end away. Suppose it is not 1 meter long, but 10km long, and expands 10% per minute, the ant would see the end move away from home with 1km per minute. That is as fast as a leopard at full speed. Far beyond the ant's imagination. Still the 1cm mark would only move 0,1 mm per minute away from the ant, and the ant sees nothing special. Suppose our "10% per minute expanding stick" would be 10000 kilometer long, or more and more. You come to a point where it's end expands with the speed of light, and that would determine either the maximum length of that stick or the maximum expansion speed. So you already see the relation coming between up expansion speed, total size, and how long has this been going on. These relations are very interesting.

Mr. Hubble applied his method not on a stick, but on the whole universe. He calculated when you know the distance to a certain galaxy and when you know how fast it moves away from us, we can calculate the size of the universe, by assuming the end of the universe moves away with the speed of light. (and there are many observations saying it really does so). Also we can calculate the age of the universe by this. It takes about 20 lines with difficult calculations, and there is some small limitation to the precision, but the result is:

The universe is somewhere between 9,3·10²⁵ and 1,9·10²⁶ Meter wide (Hubble's method).

I found another way to calculate the size of the universe, which I have never seen elsewhere before. I do not say nobody had that idea before, it's just that I haven't seen it before, and may be I haven't looked well enough. The idea works very simple. The moon circles around the earth, and creates tide energy on earth, so the water of the see is moved by the moon. Now that is a considerable amount of energy, and it it will eventually slow down the moon, and it would collapse on the earth when its speed gets too low. Before that happens, it would approach the earth. Like a few meters or microns each year. Now, the NASA was interested in that and has put reflectors on the moon. With those the distance earth-moon can be measured very precise with the help of a laser beam.

Interesting the results are unexpected. The moon moves away from the earth, and not just a little bit. It moves away 3.8 cm per year, which is a lot when you consider it over lets say one Millions of years, and it is 3800 km then. You can find on the NASA web site. The moon moves away from us with a speed of 1.2 nanometer per second, I calculated from this. However this speed is there, and we know it very exact. This phenomena can not be explained very good. Suppose, this is the expansion of the universe....?! Just suppose we see the moon move away because of that. This expansion speed will be larger when we take a larger distance than "just" moon to earth. At it's largest, this speed is the speed of light, and the point where this happens, is where we reached the end of the universe. We can not expand beyond that, because light speed can not be exceeded. The ratio for the size of the universe to the distance moon-earth can be found by the ratio of the expansion speed. For that we divide the speed of light by 1.2·10^-9 M/sec which gives a ratio of 2.48.10¹⁷ .This ratio we multiply by the distance moon-earth and we get:

9.5.10²⁵. As you see, this fits inside the window as calculated by Hubble

Now this may have gone a bit too fast for you, and perhaps the result means not much to you. To understand it, just make a drawing of the earth with the moon , and put the numbers in there, and you will understand it then. Then get out of the internet what is the size of the universe, and you will see it is exactly the number I found with this method.

If there is anyone with some useful comment on this, I would be interesting to hear about it!

With this number 9.5.10²⁵ you can also calculate backwards and see how long it takes to expand that far, with the speed of light, and you have found the age of the universe. From what I initially tried, it seems to give a realistic number. So divide 9.5.10²⁵ by the speed of light and you get the age of the universe. The result is 9.5.10²⁵ / 3.10⁸ = 3.16.10¹⁷ seconds, or 10 billion years. I find in the internet variations ranging from 10...20 Billion years. So my calculations are not so bad, and they all depend on this mysterious increase of the distance of the moon to the earth and nothing else.

However we must realize we talk about the age of the universe observed from our position "earth". What do I mean by this? At the outer edges where the universe expands, it is fresh born. Only the strange part is, it is "new" born at the outer edges, but made from materials that are not new at all, but just needed 10 billion years to get there. So the age of extremely far away objects obviously depends on from where you observe them. It means the speed of which clocks tick at any position in the universe is not the same, as we see it from where we are here at earth. They tick with exactly that speed difference to make the things possible that we can't explain otherwise. So relativity comes in here, which will make me get stuck with the item if I only try. Well I am glad I know more about electron tubes.