Einstein Field equation

#Einstein_field_equation

Today I will try to write about a thing that those who are in physics in this forum will smile a little when they hear, you can laugh even if you say yes. That possibility is good. Let it be. Today I will try to write about Einstein's field equations of general relativity. No, no. Don't be afraid. By no means do I want to convey that I recommend for the mother to be inactive. Then I will catch myself because I do not understand them. I will try to give a vague idea without them. Does it actually eat or not? I wrote about general relativity and that was my first post. Although it has a lot in common with that writing, it will differ a little. I tried to say theoretically there but actually ignored the physical meaning of the equations. That will be an attempt to write today. I have tried to say at the end what it actually means and I have tried to create a ground to understand it with the previous paragraphs. If you don't know these things, you won't find the fun.

.. Co-ordinate system on flat surface 6

Let's try to give analogy. Suppose you are one man but two people who love you. Bindas for you. So you're in for a treat right now, aren't you? One day he went for a walk around Dhanmondi Lake and saw the two of them together (Giligili). Suppose you step on the door of a shop and then you notice one sitting on the right side and one on the left side. Perfect triangle love. Not only from the point of view of the three of you but also made a nice triangle and form in that location. Now one thing to note is that if the three of you are the three corners of that triangle, it also means that you have three precise locations. You occupy three very specific spaces in this universe. At first it looks small. I think if I want to show you a graph of where you are in the respect of the shop, but I can show it very easily. All you have to do is imagine the x axis along the length of the store and the y axis along the width of the store, one graph at a time, you have to put three coordinates of the three of you. Co-ordination means that each of you is within a distance of respect to the origin point (x = 0, y = 0) of this graph. Your distance from the origin point along the x axis will be your x value and similarly your distance from the origin point towards the y axis will be your y value. And this X and Y value will be the respect of the original point that your co-ordinator imagined and in this graph.

.. Distance on flat surface 6

Above we actually saw how it is possible to know the price position (or location) of the three of you and explain it in the book. Now suppose you thought to yourself, Dad, it's been a long time, and no more. There is no benefit in hiding like this. Both of them will go later. You have decided that you will love the one between these two whose distance is less than your position from today. So how do you figure it out? You have to measure. You can easily find out who is closest by bringing measuring tape. But this is the Sabu method. If you are Uncle Chowdhury, think a little differently. You may think, I read a formula in class 8 or 9. If the coordinates of the two positions are known, then the distances between those two positions can be calculated by inserting the values ​​of the coordinates in that formula. And since Uncle Chowdhury's intellect is sharper than a computer, it won't take you a minute to figure it out. You already know everyone's position, now just drop that formula and find out everyone's distance with each other.

So the point is that if someone is standing in one position on a flat surface, the distance can be calculated by respecting his or her position and respecting another position. You saw the pure geometry here that we all learned at a very young age. This is called Euclidean geometry as far as possible. Here is an important observation that you have applied this procedure for a flat surface. The surface of the shop should be completely flat, right?

.. Distance on bumpy surface 6

Now imagine a little differently. You think the three of you are standing in the mountains eating the bushes of the elders. No need to take a beer tear. And the mountains are not a flat surface. Uchunichu. Now think about it, will the formula with which you calculated your distance be applicable here? Once upon a time. Never. Why? Because the distance is from one position to another and your previous surface was flat. How many things can happen on a bumpy surface. The position of you and one person may be close but maybe there is a 10 feet high hill between the two of you. So if the distance between the two positions is 5 feet (5 feet + 10 feet (one side of the tiller) + 10 feet (the other side of the tiller)) = 25 feet. The other one may be standing 10 feet away but you have a 3 feet high hill inside. Then the distance of your dozen positions will be (10 feet + 3 feet (one side of the tiller) + 3 feet (the other side of the tiller)) = 18 feet. So your inner distance is only 18 feet which is less than the other (25 feet). The point I want to make is that even if you are standing close, your distance may be higher and even if it seems far away, your distance may be less. And it's all happening because you're standing on a hilly surface. If you were on a flat surface, it would not be so adulterated, you can find out by using a simple formula, but if the surface is not flat, then you can't find out with that simple formula or it will be wrong. And here is Einstein's real miracle.

.. Elevated Surface Analysis 6

If you understand the above, then in fact 80% of Einstein's field equations have understood. Though I have been thinking about shops and mountains for so long, now I am thinking about this universe. Einstein (God knows what was in his head) thought of this universe as a fabric where stars, galaxies are all there. Physically speaking, if you tie the four corners of a sheet somewhere, it is the type of flat that will create a surface. He saw this sheet as the Universe and placed the star, the galaxy, on top of this sheet. He saw this sheet as an object that bends, expands, contracts, meaning no solid thing. In other words, the sheet is not made of any iron but is made of yarn which we can do whatever we want. Now if you put an iron ball on the sheet, the sheet will fall off, won't it? Uni also remembered. He thought these iron balls were a star or a galaxy. Now the sheet is left with an iron ball because these balls have a weight. And if the stars and galaxies hold an iron ball, then they actually have a weight. So they have to sink this universe in places. Then the surface of this universe is no longer flat but is getting bumpy and that simple formula will not work. He thought, thought, thought, 10 years. He thought something out. Guys.

.. Einstein Field Equations 6

Now that you know that the surface of this universe is not flat, it cannot be said or even thought that any part of it has a specific geometric shape. It needs to be figured out. Because somewhere there may be a lot of debris for a big galaxy and somewhere there may be a little bit of debris for a small world. Einstein discovered some tensors and brought them into his equation. You don't need to understand what tensor is, just keep in mind that it is a quantity that if you are in an equation, you can measure the distance from one position to another without measuring with measuring tape on a bumpy surface. So if you want to know how far Mars is from Earth, put different constant values ​​in Einstein's equation. You will get. You want to know how much space there is for the mass of Jupiter? Put in Einstein's equation. All flickering like Philip Batti. Not noticed now but the accuracy of the value obtained by putting it in his field equation seems to be around 100% or so. Think once.

Whatever. He has known for a long time what can be done physically with his equations. Now let's see what his equation actually says. Like all other equations, this equation has a left hand side and a right hand side. The left hand side tells you what the geometry of this universe is like and the right hand side tells you how much mass and energy it will take to create that geometry. Or in other words, if you put a galaxy somewhere in the universe, how it will change that space in the universe can be found out with its equations. In other words, if you put an iron ball weighing 1 kg on top of the sheet, then the sheet will sink in the same way, and if the weight of the iron ball is 2 kg, then the sheet will come in a different way or a little different way and will curve the adjacent places These are the things you can precisely measure or say with Einstein's field equations. Have you ever wondered what is strange? He has shown how the sun is sinking this universe while sitting at home. He didn't just stop, he proved. Not once, thousands of times, millions of times. People still apply this theory to him and it still gives the right results. There is a term here called cosmological constant. It is very important but it should not be caught now. There is no way to write about it without giving a separate article.

I am not a student of physics and I can go to a certain stage of that equation derivation. I couldn't even try a few more times but very willingly understood. Of course, if you understand, no one else will pay, so even if you don't understand the consolation, it will work.

Einstein took about 10 years to figure it out. Of course he took the help of a mathematician friend because he was not a math student himself. It was a matter of extreme sensitivity. Has published wrong papers several times, slowly submitted them again later. I don't know if it's true but I read it. I think he wrote the equation in the second year of his endeavor. He then thought that he might have misunderstood or that something was wrong. There are many more things in his equation that he said nothing about. You read it. And later, if I get the time and desire, I will definitely write slowly. But try it yourself, read it a little, don't read so many nice things - how is it possible?

.. Equation and we 6

This equation is placed right in front of my office desk. It's better to look, not to feel gut-type. As much as it is more than equation, it is the work of a human being behind it, patience that matters. I don't have these qualities but for a little person dearer than my own life, I need them very much. For 10 years a man has been following a lifeless equation. Tried to understand, wrote wrong, wrote correctly after being caught wrong, it was seen a year later that wrong writing was done in the beginning Fix it again. By doing so, he has finally succeeded. If it takes 10 years for a person to understand behind a lifeless equation, then why don't we try to understand our dear people, who laugh, play, get angry for 100 years, why don't we give time, why can't we stick? Of course, inshallah I can. Because we are ordinary people, sometimes we will stumble, fall, we will not want to get up, but we will stand up straight again, we will love again.