Showing posts with label mathematics. Show all posts
Showing posts with label mathematics. Show all posts

Sunday, August 13, 2023

Could white holes exist?


Could white holes exist, and why can't we see them? Mathematically, white holes or anti-black holes exist, but they are extremely unstable. The thing is that the white hole might misunderstand some of those visions. A white hole is theoretically the opposite of a black hole. It's the point where the material comes out of the wormhole that is the quantum energy channel through spacetime. The white hole has singularity, as well as black holes, do, but the white hole acts oppositely to black holes.

Time dilation stops time at the point of the white hole. That means we can only see flashes, and then we would travel through that thing in time. So when particles come out of the wormhole, they release their extra energy as a shockwave that we can see as a flash.


"White holes are theoretical cosmic regions that function in an opposite way to black holes. (Image credit: Future/Adam Smith)" (Space.com/Could white holes actually exist?)

(Space.com/Could white holes actually exist?)


The idea of a wormhole is that there is a quantum tornado in space. And there is a quantum vacuum ahead of objects that travel in that "tube". That means all particles, including photons, travel at the same speed in that strange phenomenon called a wormhole or Einstein-Rose bridge. Wormholes follow the principle of quantum entanglement. And information can travel through those energy bridges only if one side is at a higher energy level than the other.

The white hole pushes material away from the hole, and the point where the speed of that material that travels in a wormhole decreases below the speed of light is the point where the wormhole ends. So at that point, the matter again reaches the speed of light. And the thing is that time is also frozen at the point of the white hole.

If we think that time is a river, a white hole is like a stone in that river. A river called time takes all matter with it. And we can see that stone only once. And maybe the flash of the supernova is the moment when a white hole opens in spacetime. And that means we could see that thing only once.

The white hole interacts in a similar way as black holes, and at the point where the speed of matter is the speed of light, time is frozen. Time dilation stops time at that moment. When matter comes out of a white hole, it causes a shockwave that is seen as a flash.

So because time is frozen at the end of a wormhole, we might say that white holes are frozen at a certain point in spacetime. So the white hole is in a stable position, but time travels around it. When we think about white holes from the point of view of an observer who stands in a regular universe, the white hole is just a flash in spacetime. That means a white hole exists, but it exists at a certain point in spacetime.


https://www.space.com/could-white-holes-exist-space-mysteries

Thursday, January 6, 2022

Imaginary numbers are turning true in quantum physics.

   

 Imaginary numbers are turning true in quantum physics.



(Above) An illustration of the complex number z = x + iy on the complex plane. The real part is x, and its imaginary part is y.(Wikipedia/Complex numbers)

The mode of complex number is z = x + yi. The term yi is an imaginary part of a complex number. There are theoretically no limits in the number of those imaginary parts. And that is the description of the pure complex number. If the imaginary part is 0 the number is a so-called imaginary number. 

There are many times made mistakes with complex and imaginary numbers. An imaginary number is the square root of a negative number or zero. So imaginary number is the complex number that the real part is zero. Normally is impossible to take the square root from a negative number but if a negative number is part of the complex number there is an answer. 

The complex numbers are also imaginary numbers but sometimes the complex number whose imaginary part is zero is mentioned as imaginary numbers. And complex numbers whose imaginary part is bigger than zero (i>0) are pure complex numbers. In quantum physics that imaginary part is needed for calculating the quantum states. 


The imaginary numbers are in use because there must be an answer for the formula sqrt(-a)= i(sqrt)-a   (sqrt)=square root

There i is an imaginary unit that implements the equation i=-1^2. 

The imaginary numbers are created because they are offering the answer to the equation  x^2+a=0 if a>0


"In mathematics, a complex number is an element of a number system that contains the real numbers and a specific element denoted the i, called the imaginary unit, and satisfying the equation i2 = −1. Moreover, every complex number can be expressed in the form a + bi, where a and b are real numbers. Because no real number satisfies the above equation i was called an imaginary number by René Descartes". (Wikipedia, Complex numbers)

"For the complex number a + bi, a is called the real part, and b is called the imaginary part. The set of complex numbers is denoted by either of the symbols {\displaystyle \mathbb {C} }\mathbb {C}  or C. Despite the historical nomenclature "imaginary", complex numbers are regarded in the mathematical sciences as just as "real" as the real numbers and are fundamental in many aspects of the scientific description of the natural world" "Wikipedia ´, Complex numbers", 

Complex numbers allow solutions to all polynomial equations, even those that have no solutions in real numbers. More precisely, the fundamental theorem of algebra asserts that every non-constant polynomial equation with real or complex coefficients has a solution which is a complex number. For example, the equation {\displaystyle (x+1)^{2}=-9}{\displaystyle (x+1)^{2}=-9} has no real solution, since the square of a real number cannot be negative, but has the two nonreal complex solutions −1 + 3i and −1 − 3i.

"An imaginary number is a complex number that can be written as a real number multiplied by the imaginary unit i,[note 1] which is defined by its property i2 = −1.[1][2] The square of an imaginary number bi is −b2. For example, 5i is an imaginary number. And its square is −25. By definition, zero is considered to be both real and imaginary". (Wikipedia/ Imaginary numbers)

This is a great day for quantum physics and mathematics. The complex numbers are turning real numbers that have a purpose in the real world. Researchers need Those numbers for calculating the quantum states of the material. And at least those numbers that have the "extra" or "imaginary" part are turning to "real numbers". 

In regular mathematics, a number has a certain place in number straight. But the complex number has two places in the coordinate system. Or the complex numbers can have many places in the 3D coordinate system. The number of the positions of complex numbers depends on the number of imaginary parts of the number. 

In most examples, there is only one imaginary part in complex numbers. But nothing limits the number of those parts. The problem is that the 3D coordinate system is impossible to draw on the 2D layer. 




https://www.sciencenews.org/article/quantum-physics-imaginary-numbers-math-reality


Complex numbers. https://en.wikipedia.org/wiki/Complex_number


Imaginary numbers: https://en.wikipedia.org/wiki/Imaginary_number#:~:text=An%20imaginary%20number%20is%20a%20complex%20number%20that,is%20considered%20to%20be%20both%20real%20and%20imaginary.


Image:https://en.wikipedia.org/wiki/Complex_number


https://thoughtandmachines.blogspot.com/

Friday, December 31, 2021

Can machines predict the future?

 Can machines predict the future? 



In the beginning, I must say that the world is changing. The great mathematicians like Ludwig Boltzmann (1844-1906) had not had quantum computers. 

And maybe quantum computers are allowing us to create the calculations that are making it possible to predict the behavior of human society. But there is the possibility that those systems could predict the behavior of a single person. 


Can we predict the future of material?


When we are thinking about the shape of the universe and material. The behavior of material should follow a certain formula. Making predictions of the things that are going to happen. Seem the easiest thing in the world. We should know the trajectories of the particles and objects very well. The problem is that the universe is full of wildcards like supernovas and other things like gravitational waves that might have a bigger influence than nobody predicted. 

If we are thinking about things like electrons. Those are monopolar particles but they can connect in one entirety by using quantum gravitation. Those quanta gravitational connections might be extremely weak. And the gravitational waves can cause that the electron structure will blow away. There is also another way to connect electrons with other electrons than quantum gravitation. And that thing might be even more sensitive. 

The electron is a particle that has multiple poles. And if two electrons would position that the main pulling effect of the poles are between the poles of another electron that thing can make it possible to create electron chains. But if something pushes that object that causes that the poles of electrons are pointing to each other. That causes that electrons would start to repel each other. 

The answer to the questions is why we cannot predict the movements of the particles. Is that we cannot predict supernovas. And other highly energetic reactions like impacts of black holes. The missing parts of the universe. Are making it impossible to predict. What would be the end of the Universe? Those missing parts are dark matter and actually, we don't know even how many black holes are in the universe. 

There is the possibility that in the black holes is a large mass of material of the universe. The fact is that the only known common phenomenon between dark and visible material is a black hole. Theoretically is possible that dark matter forms a black hole. Suddenly in the middle of some solar system. But nobody has seen dark matter yet and that is the hypothesis. 


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Can AI predict the future?


The idea of the mathematical method. For predicting how gas is moving in certain conditions created Ludwig Boltzmann. His formulas are introducing very well how the large gas masses are behaving. But the problem is to calculate the position of the single gas atom in the space. Calculations are made by using the Boltzmann constant gives more accurate answers when the gas mass is higher. 

The thing is that quantum computers are making thermodynamical calculations more accurate. So maybe we can try to calculate the position of a single gas molecule very accurately by using quantum computers. 

So somebody introduced an idea that maybe those calculations are made for thermodynamics. Can benefit from predicting the future of society. The problem in society is the human effect. But humans can also be thought of as atoms and particles. Predicting the behavior of one person is not possible. But predicting the behavior of great entirety is possible. 

The ability to predict the future is one of the most interesting things in the world. Theoretically, a thing called "Psychohistory" which introduced in the fictional novel series "The Foundation" by Isac Asimov. Is possible to make. 

Artificial intelligence can find all data that predicted some upheavals in history. Then the artificial intelligence can search the similar markings in the environment. And that thing can give warning that something will happen again. 

So could we deny something bad happening again? The thing is that we can analyze the society that made something happen. We can search for things that made people support leaders and try to remove or replace that thing from society. 


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Black swans and wild cards are making predictions of the future difficult. 


But if we want to create predictions of the things that are happening to human civilization. We are facing too many wild cards and black swans. 

Black Swans are the effects that happen only once and they have a great influence on the entirety. Nassim Nicholas Taleb introduced that term. And that term Blac Swan means extremely extraordinary but still existing possibility. And one of the best examples of that kind of effect was the 9.11.2001 terror attack. That single thing caused effects that still influence global politics. 

Another thing is wild cards. The most effective wild card is the internet. Things like social media and other things are not predicted things. The internet is like the string where is hanging all the time new services and other kinds of things. So the internet offers the term "wild wire". It's like the wire that connects multiple things. 

The internet is the instrument that makes it possible to create new services and new systems even without budgets. Computer program codes and technical manuals are easy to find if a person knows where to look for them. At this moment nobody controls the development of Artificial intelligence. 

So fast that nobody can imagine or respond to that thing. The information is free on the Internet. That means the development of new technology is free. And R&D (Research and Development) precesses are turning self-controlled. The computers are cheap and every flat has an internet connection. So everybody can make what they want on the Internet. 


Sunday, December 5, 2021

The key is: how to prove the solution?


The key is: how to prove the solution?


Carl Friedrich Gauss (1777-1855)

Prime numbers from Gauss to Riemann. And from RSA encryption to quantum computers that can break any code in the world. 


Carl Friedrich Gauss (1777-1855)(1) was a mathematician who spent a couple of hours each day trying to create prime numbers. His student Bernhard Riemann  (1826-1866) (2) created his "Riemann hypothesis" (3) that is also known as Riemann's conjecture that used to create the series of prime numbers. The question is where Gauss and Riemann needed those prime numbers? 

Those two famous mathematicians were not the first persons who were try to create so many prime numbers as they could. There were many people like Stanislaw "Stan" Ulam (1909-1984) (4). That man is better known for his work with Edward Teller and the hydrogen bomb. Who tried to create the geometrical model of how the prime numbers divide into spiral structures. That model is called Ulam's spiral(5). 

Even if the answer for Riemann's conjecture is 1/2 there is the possibility to chain the algorithms. The thing is that in point 1/2 the Riemann's conjecture is giving non-trivial zeros. If there are points where the answer is not a prime number or the answers are turning easy to predict that is the end of the use of pure Riemann's conjecture in cryptography. But that conjecture can connect with other mathematical formulas. 

So when we are going to Riemann's conjecture that is giving prime numbers all the time that the formula is driven there is also the possibility that there are prime numbers also outside the series that the Riemann's conjecture is giving. When the series of the prime number ends is unknown. That thing is possible because when the numbers are turning bigger. And there might be some prime numbers between the answers generated by using Riemann's conjecture. 

The sequence between those solutions is turning longer. And that means there is the possibility. That Riemann's conjecture is leaving some prime numbers away from the series that the formula is giving. The thing that makes that formula so impressive, interesting and mysterious is, where Riemann or Gauss needed those numbers. The modern RSA encryption requires Riemann's conjecture. 

If Riemann's conjecture is used purely. That makes secrecy quite easy to break. Purely used conjecture is easy to break simply by using fast computers that are calculating prime numbers. And then the system can simply try every prime number to the captured message. That is called a brute force attack. But if Riemann's conjecture is connected with other mathematical algorithms and functions. That thing makes the algorithm safer and harder to break. 


(1) https://en.wikipedia.org/wiki/Carl_Friedrich_Gauss


(2) https://en.wikipedia.org/wiki/Bernhard_Riemann


(3)https://en.wikipedia.org/wiki/Riemann_hypothesis


(4)https://en.wikipedia.org/wiki/Stanislaw_Ulam


(5) https://en.wikipedia.org/wiki/Ulam_spiral


Image: https://en.wikipedia.org/wiki/Carl_Friedrich_Gauss


And finally, what people should do when they try to solve mathematical problems? 


The key element in mathematical problems is to show people how to get the answer? How to prove that some solution is right or some solution is wrong. Must be done by using a methodology that is accepted in mathematics. 

That thing means that only the answer is not enough. Proving the solution is the key. And the thing that is making that thing. Is that every stage of the calculation must write to the paper. The idea is that the inspector can retake those calculations. And the solution should be the original numbers. 

When some person is making those calculations. The thing is that every part of the formula must make exactly correctly. If something is left outside the mark the answer is always wrong. And the thing is that if the person makes a little bit too much work. 

That thing gives better or correct answers than just removing the "unnecessary parts". Like some "meanless" square root marks from the calculations. In formulas or algorithms is not unnecessary marks. 

And the thing is that proving the thing is the key element. If somebody presses some button unnecessarily that thing is not a mistake. The mistake is that if some mark is lost. And that thing causes horrible errors in the calculation. In mathematics is many things that are sure or they are not sure. But there are also unsolved answers. 


https://thoughtandmachines.blogspot.com/


By the way, how to solve the quadratic algorithm?

 

 By the way, how to solve the quadratic algorithm?




The most common mistake is just trying to combine the formula that is under the square root mark. The square root is marked in this text as the "sqrt". That is the C++ mark for square root. Forgetting the brackets is fatal in this kind of calculations. So solving this mystery formula happens like this:


x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x


That is how the numbers must be input in pocket calculators:


     -b + sqrt (b^2-4ac)=ANS and then ANS/2a

     -b - sqrt( b^2-4ac)=ANS and then ANS/2a



      -b + sqrt(b^2-4ac)

x=_________________   

2a

 Using pocket calculator:   


-b + sqrt (b^2-4ac)=ANS and then ANS/2a

or 

              

-b-sqrt(b^2-4ac)

_________________

              2a

Using a pocket calculator:


-b - sqrt (b^2-4ac)=ANS and then ANS/2a


The terms below the square root can mark like this:


-b + (sqrt b^2- sqrt(4ac) The calculation is:      -b+(sqrt b^2- sqrt(4ac)

     x=__________________________

2a


or


-b - (sqrt b^2- sqrt(4ac) The calculation is:           -b-(sqrt b^2- sqrt(4ac)

       x=________________________

2a


The sqrt is the square root. And don´t forget brackets.


x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x


And the most common mistake is that the person tries to calculate the calculations at both sides of the minus mark as the entirety. Or they simply forget to take the square root from both sides of the marks that are below the square root. 


So marking both of the parts under the square root mark by using their square root mark is making it simple to understand the idea of the quadratic algorithm. Combining those terms is not possible because there is a "minus" mark between them. Both of the numbers that are below the square root must calculate separately. 

Dark dwarfs can erase dark matter. And get energy from that reaction.

 Dark dwarfs can erase dark matter. And get energy from that reaction.   "A newly proposed type of stellar object, called a dark dwarf,...