프로그래밍과 경제

Searching for Quantum gravity - 1. Introduction

저자: 오영종

소개

요즘 입자 물리학의 주된 화제는 양자역학과 중력학을 통합할 궁극의 양자중력 이론에 대한 것이다. 궁극의 양자중력 이론을 찾기 위해 물리학계에서는 과거 수십년간 다양한 시도를 통해 여러가지 결과물을 만들어 내었고 많은 진보를 이루어내었지만 여전히 해소되지 못하고 있는 문제들과 부대끼고 있다. 왜 이렇게 양자역학과 중력을 통합하는 것이 어려운 것인가?

가장 큰 문제는 우리가 살고 있는 이 우주를 구성하는 가장 기본적인 요소인 시간과 공간에 대한 우리의 이해가 아직 부족하기 때문이다. 이것에 대한 수많은 토론이 이루어졌고 다루어지고 있지만 아직 모두의 동의를 얻을 수 있는 정확한 개념이 아직 형성되지 못한 것은 여기 https://www.youtube.com/watch?v=So6f4fTMWY4를 보면 잘 알수 있다. 관련한 목록은 셀 수 없이 많이 나온다. 이들을 보면 몇몇 독자들의 마음속에 현재까지의 정확한 이해에 대한 접근 방식이 만족스럽지 못하고 완전히 새로운 관점으로 모든 것을 근본적으로 바꿀 수 있는 새로운 접근 방식이 필요한 상황이 아닌가 하는 일말의 의심이 생길 법도 하다.

필자는 전통적인 물리학자들(String theory, Loop Qauntum gravity)의 연구결과에 정통한 사람은 아니다. 물리학을 전공하지도 않았고 이들 분야를 연구하기 위해 필수적인 배경 수학도 잘 모른다. 필자는 이런 면에서 중력에 대한 새로운 해석을 제시할 수 있는 철학자에 가깝다. Loop Quantum gravity로 유명한 물리학자 중 한명인 Carlo Rovelli도 새로운 해석을 찾기 위해 철학자의 도움이 필요함을 피력한 적이 있다. https://blogs.scientificamerican.com/observations/physics-needs-philosophy-philosophy-needs-physics/

필자는 지난 10년 동안 개인적인 사색을 통해 시간과 공간에 대한 기존과는 차별화되는 새로운 관점이 가능함을 알게 되었으며 앞으로 이번 시리즈에서 소개될 이 전혀 새로운 관점으로 기존 물리학자들이 궁금해하고 있는 많은 미스터리들(Twin paradox, 어떻게 시간과 공간을 양자화시킬수 있을까? Dark matter와 Dark Energy의 정체는?)을 직관적이고 일관된 하나의 프레임워크로 이해할 수 있게 되었다. 이번 시리즈는 그러한 필자의 연구결과를 공유하기 위한 목적으로 만들어지고 있다.

Searching for Quantum gravity. what is infinity? (6)

Oh Youngjong

(dmqcka @ gmail.com) 

(This article contains my own personal view and not finished yet so be noted that it may contain wrong information. It can be modified at any time without notice.)

What is infinity?

It is a new model for gravity which describes the fundamental nature of time and space ranging from Plank scale to cosmos scale. There are many papers concerning problem of time (POT) [1, 2 …] It is a most difficult and crucial problem in unifying Quantum theory and theory of general relativity because the notions of time in two great principles are mutually incompatible. In quantum mechanics, time is, especially in the time dependent Schrodinger equation (TDSE), absolute in that it is like a parameter fixed all the “time” which is continuous and differentiable. When we look at the continuous time axis (as far as I know, it is true) in TDSE, we are easy to get an impression that time flows at a fixed rate from past to future because there seems to be no finite region of special importance in this time dimension. On the other hand, time is relative and dynamical in the theory of general relativity. It is common sense that Einstein proved that time is relative, not absolute because he found that time can be distorted under influence of massive matter nearby. It is the outcome of GR that my time flow rate can be varied depending on where I am located in empty space or near surface of earth.

The problem of time must be resolved if we want to put together two great principles in physics but no one succeeded to produce a solution so far. Many difficulties in understanding the nature of time are listed in [1] but I will not recap those for two reasons. The first is I, as a hobbyist studying physics, don’t have enough knowledge and secondly that is not what I try to do. As I already stated many times, I think myself crazy enough to propose another model for gravity which will be different and perhaps batter that Einstein’s theory even I did not major physics in university. If you like some absurdity or are generous with a crazy mind like me, I will do my best to give you some fun and exciting stuffs concerning a whole new crazy idea on the most fundamental notions such as infinity, time, mass and energy. I will begin by explaining the notion of infinity which human cannot touch or measure.

I think many scientists will agree on that QM is so weird that no one understands it as Richard Feynman mentioned early. What makes QM so weird or why we feel difficult in understanding QM? From my study, I concluded it is because QM is a realm ruled by infinity which human do not have clear understanding or is an abstracted notion beyond out of reach. In daily life, it is impossible to see something infinite. There is no infinite money, energy, memory and time. In computer, the most basic error in calculation is dividing by 0 error because it is not defined. When we see infinity in calculation, then we try to find another way yielding no infinity if possible. We feel difficult in dealing with infinity because we do not understand what infinity actually means and how it work in nature. It has been true since Zeno’s paradoxes which were raised in dealing with the notion of infinity were introduced. Understanding infinity properly, I mean to find a whole new different view on infinity which no one noticed before, is the first key thing in explaining my new gravity model. It is not difficult but simple. It does not require any advanced mathematics but require you abandon all your biased knowledge and open minded to a new way of thinking.

The story begins with a simple question: In a dimension, does a point have size? I bet everyone will answer that a point does not have size. If someone says something different, all readers think it crazy. Never in my life have I seen any person arguing a point with non-zero size in a dimension. But I will be first crazy person arguing that and ask you staying with me. Why I think so? Firstly I need to mention I also believe that in principle a point has zero size but with one condition a point can have non-zero size. The condition is related with infinity. If a point is accompanied by infinity, then it becomes non-zero sized. This is first thing readers must be open-minded to. It is the key element to understand superposition in QM which is one of strange phenomena. If a particle is accompanied or given by infinite time, then it can many places at a single instance in “time” showing the property of unitarity. I think this can be reasoned by inspecting the Thompson’s lamp paradox carefully.

Thompson’s lamp with a switch has two states; on and off. Hit the switch once, it turns it on. Hit it again, it turns it off. Whenever the switch hit, lamp changes its state. Here is an endless process. Firstly, he hit the switch to turn lamp on. One second later he hit it to turn lamp off. In half second, he turns it on. At the next a quarter of a second, he turns it off. The story normally ends up with a question; at the end of two seconds, is the lamp one or off? It is the paradoxical because it cannot be easily answered. But here is the very point we need to be creative. My answer here is that the lamp has both states after two seconds. The two states of lamp can be thought as size-less points in a dimension having only two states. Logically, before two second, the state of lamp is simply one among two states; on and off but after two second there is no way to know the exclusive state so the size of state of lamp must be 2 not 1. But initially assumed, the state of lamp is exclusive one, not both of them so the lamp system must show the property of unitarity. The role of infinity here is the same thing that creates superposition in QM. My reasoning may sound weird and hard to believe but it will help you eventually understand deeper level of the nature. Another story concerning infinity will be introduced in the next post.

To be continued …

Reference

[1] PROBLEM OF TIME IN QUANTUM GRAVITY

Edward Anderson, APC AstroParticule et Cosmologie, Universit´e Paris Diderot CNRS/IN2P3, CEA/Irfu, Observatoire de Paris, Sorbonne Paris Cit´e, 10 rue Alice Domon et L´eonie Duquet, 75205 Paris Cedex 13, France, arXiv:1206.2403v2 [gr-qc] 16 Aug 2012

[2] Time in Quantum Mechanics

Curt A. Moyer, Department of Physics and Physical Oceanography, UNC Wilmington, arXiv:1305.5525v1 [quant-ph] 23 May 2013

Searching for Quantum gravity. what is infinity? (5)

Oh Youngjong

(dmqcka @ gmail.com) 

(This article contains my own personal view and not finished yet so be noted that it may contain wrong information. It can be modified at any time without notice.)

What is infinity?

Today topic which is concerning about infinity will confuse you and blow you out of mind because never previously have you heard of this new philosophical view what I will discuss. After reading it, you may think me mad, crazy and foolish so most will be ignorant but I am serious. In this series, I have wrote several articles describing the most basic fundamental thing such as the notion of distance, time and infinity because I believe that the so-called quantum gravity and theory of everything later which are expected to unify quantum mechanics and general relativity would be completed only after we have a clear picture on these basics fundamental concepts as already many scientists confessed.

Frankly speaking, many scientists don’t know if time is fundamental or not. One such view of Kate Becker, editor of NATURE OF REALITY is quoted below.

“Space and time are so fundamental to our understanding of the universe that they are woven into nearly every equation in physics. They are the words in which we speak the language of nature—so tried, tested, and true that we don’t even know how to talk about the cosmos without engaging space and time in the conversation.

But what if it turns out that space and time are not the fundamental infrastructure of our cosmos—what if they are themselves products of some deeper physics? This idea is called emergence. We see it in nature, as when birds flock. If you were only to study an individual bird, you would never predict how it would come together as part of a flock.  Yet each bird “knows” the simple rules that, when combined, create a wide range of agile and elegant behaviors. Could it be that physicists have been studying flocks all along, not realizing that it’s the birds that are truly fundamental?  That would mean we don't know if TIME is fundamental or not.”

Not only this, there are so many confessions from physicists about the problem of time. Especially the notion of time is used differently in two great principles, quantum mechanics and general relativity. In classical mechanics, time is treated as a fixed background parameter, independent of any system. The same treatment to time also can be found in the formulation of quantum mechanics. The state of system can be defined only on a certain instance of time and the raw of state evolution, dynamics of a quantum system can be determined solely by itself regardless of the existence of external system if there is no interaction with it. On the other hand, general relativity shows that space-time is actually dynamical. As can be seen in the gravitational wave experiments, matter guide space-time how to vary. The incompatibility in usage of time means that we are lack of enough knowledge on it.

In addition, the notion of infinity also has been problematic to human since its discovery in human history, perhaps introduction of Zeno’s paradoxes. In our daily life, we can see very large numbers but impossible to see the true infinity so it is just an abstracted idea residing only in our mind. Especially in physics if the prediction after mathematical calculation happens to be infinity which is quite normal in quantum mechanics and gravitational force, that means nightmare to physicists. In that case, they try to find a different approach not yielding infinity for the solution because they believe infinity does not exist in physical world or infinity is the fearsome monster we are hard to handle.

Time and infinity are the most basic fundamental notions we need to figure out but it is not easy thing to understand them. Without correct understanding them, the journey to the complete quantum gravity and theory of everything won’t be possible and that why I keep writing those subjects. From my previous study, I recognized that time and infinity are closely related and found a whole new way of thinking on what the infinity truly means to human and how to utilize it. With those understandings, I believe that I can show that Einstein’s relativity theory is incomplete due to the flaw in the principle of relativity, the first postulate of his special relativity. Repeatedly again, I will show the principle of relativity is not 100% true. I argue that must be testable whether an object under uniform motion is moving or stationary and will provide a full explanation in detail later how to test it. For example, a photon in vacuum is always under uniform motion and moving regardless of the choice of any inertial frames. Someone may say photon is not considered as a normal inertial reference of frame and the principle of relativity does not apply to it but I think the better principle will not treat the photon as the exception and will show later. Once you get the clear picture on what the infinity is and how time can switch its form in both QM and GR, then I am sure you will get step further to see the next revolution in physics.

What makes continuum and discontinuum?

Many physicists think time is emergent from unknown non temporal thing but don't know what it is. From my study, I believe that their guess is true and the non temporal thing is just another time. Sound crazy? or interesting? The non temporal hidden structure is actually the fixed time which is believed as undetectable by any mean available to human and the emergent time is what we can measure in the realm of GR.  My proposal of undetectable time as a reality may sound crazy and absurd to you but it is not. In fact, this view is influenced by the metaphysics, especially ontology what Parmenides of Elea, a pre-Socratic Greek philosopher proposed. 

Parmenides believed the by human sensory the true reality cannot be detectable but only the distorted illusory image can be sensed and touched. In this my own personal view, what I understand is that he saw a paradox that the existence of the true reality cannot be proved to be true experimentally because there is no way to see or touch it but only what human can see is the illusion which is considered as not existence. We can find similar cases from what we have experienced already. For example, imaginary number i in complex number theory is accepted as a useful concept by everyone although it cannot be detectable in our physical world. Also never in our life have we detected or measured the full complete digits of any irrational number such as π, e because it need infinity amount of time and storage to get complete digits. I interpret that the symbol of π is the absolute fixed unmeasurable reality and any approximated values such as 3.14, 3.14592653 are the emergent relativistic measurements which we can physically measure and feel. The number symbol π and its approximated decimal expressions above are actually two different aspects of the same thing and time also is considered to have two different aspects and one can be emergent from the non temporal thing. I hope it makes sense to readers. In the next post, I will continue discussion based on this observation.

To be continued ...

Searching for Quantum gravity. what is distance? (4)

Oh Youngjong

(dmqcka @ gmail.com) 

(This article contains my own personal view and not finished yet so be noted that it may contain wrong information. It can be modified at any time without notice.)

The main purpose of this series is to provide the fundamental principle helping readers to understand how quantum mechanics and general relativity can be unified together to form a single framework to make every weirdness in our universe understandable such as quantum superposition, the true meaning of dark matter and truth about dark energy and so on. Believe or not, I think I have a clear picture on these topics although I do not have any degree in physics and mathematics and know little about the details in many advanced topics in science. For examples, from what I have in mind, the dark matter is considered as the mass itself having a tendency sticking at a definitive point in empty space around near the boundary of ordinary matter and dark energy is not existent and illusory in that expanding universe which we can observe will turn out to be actually a fake. Quantum superposition which is one of the most counter intuitive concepts is believed as closely related with the (infinite) time. Once readers can have the clear picture on the notion of infinity in time, I am pretty sure the quantum superposition can be easily understood.

In fact, the physical meaning of quantum superposition and the true nature of mass have been full of mysteries to human and what we know about them is just the mathematical relationship with other parts. I think that people don’t know what the energy and mass truly is although people are used to think they are familiar with such the fundamental things. Without understanding what the true nature of mass, what can we pull out any useful things from dark matter which is a variant of mass? In this series, I offer my interpretation about the notion of time and mass and what the relation between time and mass exist. My interpretation which will be introduced later may turn out to be wrong or absurd but it is worth to note for now I feel satisfactory with it because it gives me the power to understand many weird behaviors in quantum world intuitively with high school level mathematics.

One such understanding is the nature of gravity. As many physicists argued, I also agree that gravity is not a force. I think gravitational behavior is all about time effect. To explain all details about gravity, it will take many pages but let me offer appetizer to pull readers interest by showing a brief partial introduction of my conclusion. In my view, there are three assumptions. First, any massive and mass-less object occupies a finite region in our 3 dimensional space is given a constant velocity which means uniform motion unless it is accelerated. Second, mass including dark matter is considered as a particle tending to rest at single point in our 3 dimensional space. The only difference between mass and dark matter is that mass is included in the bounded region of a matter but dark matter is placed in empty space near matter. Dark matter is also a particle having a strong tendency to rest at a single point keeping a constant distance away from the mass center of a matter. Simply to say, dark matter follows the matter. Third, every particle interacts with dark matter included within its bounded region and the result of interaction is to make the time flow of matter slower by the amount of proportional to dark matter’s energy.

With three assumptions, we can have a power to visualize the gravity. Let us suppose that there is an object under uniform motion in empty space. For simplicity, let’s divide whole bounded region of the object into two regions, left part and right part. Along the moving path, suppose there is a dark matter which is a particle resting at a point P as assumed in second assumption away from the object and In few time the left part of the object will overlap the point P where the dark matter rest. As the object moves, it will get close to the point P and soon it including the dark matter within its left part whiles the right part with no dark matter. If the dark matter is located within the left part of the object, the object will interact with it as assumed in third so the time flow rate of the left part will be slower than the right part. In such case, there will be same effect as friction prevents the movement so the object will be steering to the left slightly instead of going straight. It is the gravity I understand. In my view, the differences of time flow rate in parts of a body generate the gravitational effect on it. Max Plank introduced that energy is a quantum. From Einstein’s E=mc2, we can conclude that mass is also a quantum. With these well-known knowledge, my interpretation can show a way how gravity can be quantized by interacting with quantized dark matter. This is one among many things I would like to explain. Again it is just my imagination which may turn out to be wrong in the end but I hope you have fun with it.

To tell something about quantum superposition, I need to explain the infinity first which will be discussed in next post.

Searching for Quantum gravity. what is distance? (3)

Oh Youngjong

(dmqcka @ gmail.com) 

(This article contains my own personal view and not finished yet so be noted that it may contain wrong information. It can be modified at any time without notice.)

In the previous post, I argued a radical, sounding absurd idea that applying the mathematical abstraction directly to getting the measurable or observable property in the physical world such as finding distance between two separate points in space could be dangerous in that it can distort the true reality so may yield a wrong prediction.

To support this view, I adopted the notion of cost which is time for the case of determining distance in space and it can help us to recognize the pitfall. In mathematics, subtracting two numbers what is normally used to get the distance between two points over number line is just an abstracted description human can think of in mind and such abstracted description can be distinguishable from the specific physical implementation of it. Why? Because the mathematical abstracted operation is time free in that it does not care about the time cost needed for the determination of it. Meanwhile, the notion of time cost arises in the actual implementation in physical world. For example, computer can calculate the subtraction of two large numbers much faster than human with only bare brain. We cannot tell which one is better than the other and both are just valid but “approximated” implementations by either human or computer showing different time cost. For C++ programmers, the point that this distinction between abstraction and physical implementation must be treated cautiously can be easily understood. The distance between two points is just a final result or objective we want to see and mathematics do not care about what a specific route to final goal will be chosen to get the distance. We human need to make a choice on the various routes which will take much or less time to get there. Knowing that the time cost does not matter in mathematical abstraction which is ideal case and time cost actually matters in the physical implementation is crucial to keep going to next discussion.

For those who are still not sure about my reasoning so far, let me take another thought experiment. Here let assume that there are two observers living their own planets A and B separated at a distance of 1 billion light years. Also there is a very large rigid ruler connecting two planet so both observers know their location relative to the ruler by reading it. Here the ruler plays the same role described in the Einstein’s special relativity paper. By reading the ruler, observer A’ at A can read a scalar value X for the exact location in space and other observer B’ at B can read a scalar value Y. Also, at initial time t0, assume that they know others location that the distance between two is |X-Y|. For now let’s suppose that a new planet C suddenly appeared near B at t0 and observer B’ soon know C is created nearby. It is fine because it is thought experiment. Now the question is how to determine the distance between A and C. For observer B’ located at B near C, determining the distance between A and C can be done almost instantaneously by doing mathematical operation because he is very close to C. First he can read the approximated value for the location of C by reading the ruler, let’s say it is Z, and determine the distance by mathematical operation by subtracting two scalar values X and Z in almost no time.

Meanwhile, the observer A’ at the planet A at t0 when C just appeared at a distance of 1 billion light years away has a no way to know that event happened at B. If he tries to observe and take a photo to the direction of planet B soon after t0, what he can see in the photo at t0 is just only B at r0 even though C actually exists near B until 1 billion light years flow since t0. According to Einstein’s special relativity, nothing can move faster than light so if A’ want to measure the distance between A and C, he need to wait 1 billion light years and it’s the fastest way to measure although B’ can determine the distance between A and C without waiting 1 billion light years with mathematical abstracted operation.

From the exampled thought experiment, we can see there are two ways in determining the distance in space. The observer A’ can use only the physically feasible method of which time cost needed to complete the determination is proportional to the magnitude of distance but B’ at B near C can use the mathematical abstracted operation so that he can completed the determination much faster than any physically feasible way. I argue this shows clearly that there is some sort of inequality between the mathematical abstracted operation and the physically possible operation yielding almost same result and the gab is impossible to be filled by anything relevant to physical world.

The main goal in physics I think is to make a perfect prediction repeatedly. That being said, the main question I want to raise here is what applying mathematical abstraction to physical world directly will affect the prediction we want to see. Will it show us what really exists as it is without any distortion so we can observe the exact thing as predicted? Someone who knows well about quantum weirdness such as measurement problem, wave function collapse which is detectable at physically measuring state of the system may guess the answer would be negative. The double slit experiment shows that calculating the probability to find the location of elementary particle, the only one available option we can take for now, does not provide the precise prediction on where the particle to be found in near future. Simply putting, people do not have a clear understanding on what applying mathematical abstraction to physical world really means and what side effect we could not expect will arise when it is done in physical world.

What makes discrepancy between continuum and discontinuum?

In previous post, I argued that there is no physically feasible way to define the distance in continuum. Instead, we usually use a mathematical abstracted operation, subtracting two scalars which is the only one available option we know so far. And such mathematical operation does not limited by Einstein’s famous second postulate in his special relativity saying nothing moves faster than light as we can see previous thought experiment. Here what I want to do is to find the physical intuitive meaning of that mathematical operation can be completed much faster than speed of light which is the absolute limiting factor residing in every event happening in our universe.

To be continued …