SPACE – PARTICLE RELATION PRINCIPLE S HUSSAINSHA1* Research Scholar, ECE Department, G PULLAIAH COLLEGE OF ENGINEERING & TECHNOLOGY, kurnool-518002, Andhra Pradesh, INDIA
Abstract: The principal objective of this paper is to solve the problems of absolute time and violation of Causal relation with respect to quantum entanglement in quantum mechanics. I solve these problems by introducing Space – Particle Relation principle in quantum mechanics. The result of this principle unites general relativity with quantum mechanics. This principle opens a new door to study universe completely in a different manner without modifying the existing concepts of quantum mechanics and general relativity. And finally I conclude universe is governed by the laws of quantum mechanics. Keywords: space – particle relation principle, Causality, Absolute Time, Quantum gravity, Pauli Exclusion Principle, Quantum Entanglement, Dark Matter, Expanding universe, Higgs Boson, Black Hole. PACS numbers: 04.60.-m, 04.20.-q, 03.65.-w, 03.65.Ud, 95.35.+d
Corresponding Author, E-mail:
[email protected]
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1. Introduction There are some problems facing in quantum mechanics. Those problems are absolute time, and violation of Causal relation due to quantum entanglement. Beside this we have Dark Matter problem, singularity problem, and expanding universe[3]. To analyze these problems in a new manner I am introducing the new principle called as; Space – Particle Relation Principle in quantum mechanics. In this paper I propose eight doable experiments (tests) to validate space – particle relation principle. In these eight tests two or three tests are considered as inferences. Though they are inferences I present them with interesting points. And remaining five tests are yet to do. I struggled a lot for many years in building this principle. From the beginning to now I have done many mistakes and solved many complex mathematical equations. After this experience I came to conclusion that no need of any mathematics to validate this principle. Therefore I am not going to introduce any new math in this paper.
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2. Birth Of Space – Particle Relation Principle In Quantum Mechanics 2.1.Space – Particle Relation Principle This principle is stated as; “two identical particles (fermions, bosons) cannot occupy the same position in a space”. If two identical particles occupy the same position; they are said to be entangled particles. (or) If two particles entangled with each other; they are said to be they are at same position. From this principle an expert of quantum mechanics can raise a question: What if particles have no defined position? E.g. if they are in a energy and angular momentum eigenstate (This is the situation that Pauli invented his rule for single particle approximation.)? For this question I can answer as follows; Note 1: I am introducing this principle in quantum mechanics for a pair of particles or single particle approximation. In quantum mechanics ‘state’ plays a crucial role which contains all the information. Quantum state contains definite information about either momentum or position but not both. Note 2: To validate space –particle relation principle either momentum or position is enough and no need of both. To validate this principle practically we have two choices to conduct an experiment. 3
Choice 1: you have to prove; two entangled particles are at same position. Choice 2: you have to prove; particles which share common point in a space are in entanglement. 2.2.Two Entangled particles and the First test of space – particle relation principle (choice 1) Choice 1: you have to prove; two entangled particles are at same position. Quantum entanglement: Two particles (x and y) are entangled when their quantum states are correlated in such a way that measuring the state of one particle immediately gives you the state of the other. Let us test choice 1 by taking two (x and y) entangled particles separated by a distance 100 meters. Case 1: if you have definite momentum and have no defined position. Now you calculate linear momentum of a particle x and let concentrate on direction but not on magnitude. If for suppose you got a measured direction of a particle x pointing from right to left as shown in figure 1. Particle x Figure 1: representation of linear momentum direction of x (pointing right to left). Then what may be the direction of linear momentum of a particle y? Without measuring linear momentum of a particle y I can say it’s direction points from left to right as shown in figure 2 when you measured along the same axis. Since
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particle x and particle y are in entanglement and so measuring the state of one particle immediately gives you the state of the other.
Particle y Figure 2: representation of linear momentum direction of y (pointing left to right). In a similar way if you know spin of a particle x in clock-wise then you can say spin of y in anti clock-wise without measuring the spin of y when you measured along the same axis. You may get a question, I know about these things and by this known data how can you say these entangled particles are sharing common point in a space? To answer this question I have a logical question in my mind. Why can’t be the spin of a particle y in clock-wise? And why can’t be the direction of linear momentum of a particle y from right to left? My answer for this logical question beside law of conservation: I assume they are sharing common point in a space. Due to sharing of common point in a space the linear momentum directions are opposite each other. In a similar way due to sharing of common point in a space the spins are opposite with each other. Though they are separated by a distance 100 meters; because of entanglement you have to assume they share common point in a space (100 = 0). If the distance between two entangled electrons (100 =0) is assumed to be zero implies; 1) Particle x should not follow particle y and vice versa. That is if measured linear momentum of y points from left to right then x should not point from 5
left to right. Otherwise distance between them is not equal to zero. Therefore the allowable directions of linear momentum of two entangled particles is (xleft to right, y-right to left), and (x-right to left, y-left to right). Case 2: if you have definite position and have no defined momentum. The same procedure is repeated here as explained in case 1 with one difference, the direction of linear momentum is replaced by the direction of position. Therefore the allowable directions of position of two entangled particles is (x-left to right, y-right to left), and (x-right to left, y-left to right). Why I assumed (100 = 0) or sharing a common point in a space? Because it works! Note 3: this principle also give better results for the special case of a single particle approximation with no electric charge and no spin. And this is similar to Pauli Exclusion Principle which gives better results for the special case of a single particle approximation with charge and spin. In the special case of a single particle with no electric charge and no spin, the orbital angular momentum operator[4] can be written in the position basis as a single vector equation given in equation (1)[4]:
L ir
(1)
Where; L = orbital angular momentum operator. r = position operator.
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2.3.Second test of space – particle relation principle (choice 2) Choice 2: You have to prove, particles which share common point in a space are in entanglement. Note 3 used as; We have practical evidence that, two electrons occupy the same molecular orbital. The coordinate parts of their wave functions are the same. That is, two electrons reside in the same orbital ( 2r ), they differ by spins. So according to Pauli those are not identical. But according to space – particle relation principle they are at same position. Therefore there exists entanglement in between those two electrons in the special case of a single particle approximation with no electric charge and no spin. That is, I am predicting that; if two or more electrons reside in the same orbital implies; those particles are entangled particles. To test this, for suppose imagine two electrons occupied same orbital. Now change the spin of one particle then spin of another particle also changes instantaneously when you measured spin along the same axis. By testing this prediction you can confirm my principle is correct. In this way space – particle relation principle can be applied to an atomic model in which electrons occupy states of definite angular momentum. General discussion: Imagine two particles x and y. due to uncertainty principle; x has no definite position and y also have no definite position. x may be anywhere and y may be any where or they may exist all over space. By adopting my principle; if finding a particle x is having a probability of 1/4 at some point in space; at that point y does not exist. If exist, those probabilities are said to be entangled. In a similar way if 7
finding a particle y is having a probability of 1/8 at some point in space; at that point particle x does not exist. If exist, those probabilities are said to be entangled.
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3. Quantum Gravity 3.1.Causality and the third test of space – particle relation principle By using space – particle relation principle it is possible to overcome the problem of causality. Einstein and others considered such behavior (quantum entanglement) to be impossible, as it violated the local realist view of causality. By using space – particle relation principle, I can say Quantum Entanglement is the subject of assuming all particles are at same point though they are separated by a large distance! For suppose take two entangled electrons separated by a distance 3000 meters. Now imagine you changed the spin of one electron from spin down to spin up then immediately give you the state of the other particle as; spin up to spin down when you measured spin along the same axis. This instantaneous communication violates causality. Therefore to overcome causality, what’s wrong if I assume those electrons are at same position though they are separated by a distance 3000 meters? That is, if I assume they are at same position, I can say; I am not only changing the spin of a single particle but it is assumed to be I am also changing spin of two electrons at the same time! Therefore communication is instantaneous. By this assumption I preserve causality. By observing instantaneous communication you can confirm my principle is correct. Because if they are not at same position you should observe some time delay in communication in between two entangled particles separated by large distance. Now here one doubt arises; what is the distance of 3000 meters if they are assumed to be at same position? For answer; see following section. 9
3.2.Time is absolute, Dark Matter and the fourth test of space – particle relation principle Now let us remove main drawback of ‘time is absolute’ in quantum mechanics which become hurdle to unify quantum mechanics with general relativity. By using space – particle relation principle; Quantum Entanglement is the subject of assuming all observers or particles are at same point though they are separated by a large distance! Therefore clocks of those observers read the same. That is the passage of time is same to all observers (time is absolute). In a simple language; under the condition of quantum entanglement; there is no other reference frame to prove time is not absolute. In this condition there is nothing wrong if you take time is absolute. For understanding purpose imagine two reference (frame 1 and frame 2) frames and the distance between these frames is 3000 meters. According to general relativity each reference frame has its personal measure of time depends on gravity therefore time is not homogeneous. Now take two entangled electrons with clocks and place them in each frame, I assumed that two entangled electrons share common point in a space though they are separated by 3000 meters, so based on this assumption two electrons have to share common reference frame. That is, two electrons have to be either in frame 1 or in frame 2. Therefore a question arises about; which frame is the common to those entangled electrons?
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For this question I can answer as; which frame shows greater impact that frame is the common to those entangled electrons. That is, for suppose if frame 1 have enough gravity to change the spin of electron and frame 2 not having enough gravity. Then frame 1 is common frame to both entangled electrons and so time measured in frame 1 is equal to time measured in frame 2. Which implies time is homogeneous. Let us do an experiment to confirm these arguments; we know that clock runs slow deeper in a gravitational well and fast at higher in a gravitational well[1][2]. Now take two entangled robots each with a clock. Place one robot at deeper in a gravitational well (reference frame 1) and another robot at higher in a gravitational well (reference frame 2). I am predicting that clocks of those robots read the same based on which reference frame shows an impact. Of course doing this experiment may not be possible. We may search for other alternative to prove time is absolute for entangled particles. After confirming this prediction you can conclude under quantum entanglement condition there is nothing wrong if you take time is absolute. Dark Matter: We know that dark matter problem arises due to gravity[3]. Yes I also confirm dark matter problem arises due to gravitational effects. Let take the same experiment; We know that clock runs slow deeper in a gravitational well and fast at higher in a gravitational well. Now take two entangled robots each with a clock. Place one robot at deeper in a gravitational well (reference frame 1) and another robot at higher in a gravitational well (reference frame 2).
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So reference frame 1 shows an impact due to more gravity. Therefore clock at higher in gravitational well read the same as compared with the clock at deeper in a gravitational well. Under the calculations of general relativity you get a doubt; though there is no enough gravity, why the clock at higher in a gravitational well reads equal to the clock at deeper in a gravitational well? What may be the reason? Of course you come to conclusion may be dark matter. Therefore you think there is a dark matter we can’t see but you feel its gravitational effects. For understanding purpose let elaborate this; Now bring observers in both the frames (frame 1 and frame 2) into the picture. Imagine observers of both frames don’t know about particle of frame 1 is in entanglement with the particle in frame 2. But observers of both frames know physics how to calculate spin of a particle and know how much energy or matter required to change the spin of a particle. I said that; frame 1 have enough gravity to change the spin of a particle and this frame satisfies observer with his calculations and frame 2 does not satisfy because there is no enough gravity to change the spin of a particle. Therefore observer thinks spin of a particle in frame 2 changing though there is no enough energy or matter. So after scratching heads finally observers come to conclusion that, this may be a Dark Matter. I raised a question in section 3.1 what is the distance of 3000 meters if they are assumed to be at same position? And the answer is; you should not take that 3000 meters distance into an account. This is the main reason behind constant orbital velocities of stars at the edge of galaxy though the distance increases. That is you 12
divide a galaxy into two reference frames (frame 1 and frame2). Frame 1 holds good without assuming Dark matter and frame 2 holds good if you assume Dark matter exist. But it’s not true. My opinion is; doing physics by assuming existence of Dark Matter is not a correct way. And the correct way is; don’t take distance ‘r’ in between these frames into an account where Dark matter is required so that two reference frames become single frame. The same is true for two galaxies revolving with each other. That is, divide the distance which is in between two galaxies which are revolving with each other into two frames and combine into single frame. This is the main reason behind universe is homogeneous! That is, reference frames looks the same. 3.3.Accelerating universe and the fifth test of space – particle relation principle In the above section I divided a galaxy into two frames (frame 1 and frame 2). Frame 1 holds good without assuming Dark matter and frame 2 holds good if you assume Dark matter exist. It’s true that frame 1 have more gravity than frame 2. As time passes; gravity of frame 1 still increases due to collapsing of stars. Therefore the velocities of stars present in frame two increases with time. This increase in velocity is named as accelerating universe. The same scenario is applied in between two galaxies. That is I am predicting that magnitude of dark matter rises with time as universe accelerates. Let do an experiment by assuming a star and a planet revolving around that star at distance of 3000 meters. I divide this star and a planet into two frames and I assume these frames are in entanglement. From the center of the star to some distance calculations of orbital velocity holds good without assuming dark matter. After that 13
distance you have to assume dark matter. Therefore planet revolves with greater velocity as compared with expected. This velocity still increases as star reaching to black hole. Therefore magnitude of dark matter rises as planet accelerates. The same scenario is applied to two revolving galaxies with each other. This is the main intelligence mechanism behind accelerating universe. If greater it’s velocity the planet has to escape from its orbit. Why it is not escaping? To answer this question let do another experiment; imagine a proton and an electron entangled with each other. I am predicting that the electron become heavier equivalent to proton due difference in their mass. Even I am predicting particles become heavier after entanglement. After doing this experiment you can confirm my principle is correct. The same experiment I use to explain why star cannot escape from its orbit though it has enough velocity to escape from its orbit. For suppose imagine a star and a planet entangled due to entanglement planet become heavier so its orbital velocity will be more as expected. When a planet tries to escape from its orbit due to having greater orbital velocity it has to take star also! That is a star have to move in opposite direction from its orbit equivalent to direction as planet moved. Therefore I conclude that complete universe is in entanglement and the punishment is observer don’t know this! Due to, at large scale quantum effects are neglected. Therefore the universe is governed by the laws of quantum mechanics.
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3.4.Black Hole and the sixth test of space – particle relation principle What is quantum gravity? Answer: We know that, “physics that seeks to describe the force of gravity according to the principles of quantum mechanics, and where quantum effects cannot be ignored (near Black Hole)”. Black Hole is subject of Einstein’s Space – Time where all particles packed in a single point. I can assume this Packing of particles in a single point as an aspect of quantum entanglement. That is quantum entanglement is also formed by forming Black hole. Inference from my principle: By using space – particle relation principle I can say Quantum Entanglement is the subject of assuming all particles are at same point though they are separated by a large distance. Therefore the distance between two entangled electrons is zero though they are separated by large distance.
If I substitute r = 0 in force equation ( F
mM ) I can get infinite force. Infinite r2
force implies infinite curvature according to general relativity. Infinite curvature is nothing but ‘a Black Hole’, a singularity. Therefore I can conclude formation of Black Hole is different aspect of an quantum entanglement. Now what happens after formation of singularity? Do experiment; take two entangled particles and observe the behavior of those particles with time. I am predicting the same thing happens after formation of singularity! 15
3.5.Expanding universe and the seventh test of space – particle relation principle. I assume here a particle never exists in absolutely rest or I assume movement is an inherent property of any particle. Under this assumption I apply my principle. That is entanglement means all particles are at same position. Let us take two entangled electrons. Due to inherent movement of a particle they both can’t move inwardly with each other. Because, there is no distance between them to move inwardly because of entanglement means sharing common point in a space. Therefore they move outwardly with each other called as expanding universe. This is the intelligence mechanism behind expansion of universe. Let us test this by conducting simple experiment. Take two entangled particles and separate them through a distance 100 meters. And let be there for a while. I am predicting that; as time passes due to inherent movement of a particle they both move outwardly with each other. Distance increases from 100 meters to some other value with time. Therefore by conducting this experiment you can confirm this principle is correct. 3.6.Existence of supreme particle and the eighth test of space – particle relation principle. This test can be considered as an inference because we already discovered supreme particle or Higgs Boson! Space – particle relation principle can be applied to an atomic model by assuming the special case of a single particle approximation with no charge and no spin principle. Therefore there exist a particle with no charge and no spin. This particle is said to be supreme particle or god particle.
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4. Conclusion Quantum Entanglement is a subject of studying single point where all particles reside and general relativity is a subject of making that single point and brings all particles nearer (gravity). Therefore Quantum Entanglement is the subject of assuming all observers or particles are at same point though they are separated by a large distance! Therefore clocks of those observers read the same. That is the passage of time is same to all observers (time is absolute). The result gives bran new way to unite quantum mechanics with relativity. I keep some of the consequences of this paper as my future work.
Acknowledgement
Author wants to thank Irfan, jagadish and ghouse for their cooperation in preparing this paper.
References Books: [1]
Stephen hawking, A stubbornly persistent illusion (running press book
publishers, Philadelphia, London). [2]
Albert Einstein, relativity, the special and the general theory (Mahaveer
Publishers, India). [3]
Lee Smolin, the trouble with physics (published by Penguin Group, London).
websites: [4]
https://en.wikipedia.org/wiki/Angular_momentum_operator
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