Challenging to solve the double slit experiment puzzle
Oh YeungJong (dmqcka _at_ gmail _dot_ com)
Note: This paper is intended to introduce my private view in a hope helping others to build the theory of everything. Please be noted that this has some radical or crazy ideas and may have wrong statements. I want to celebrate the 100 anniversary Einstein's general theory of relativity before the end of 2015. Welcome any comment and further discussion.
One of the weirdest things in Quantum Mechanics (QM) would be the subatomic particle’s behavior which can be observable in the double slit experiment. The microscopic scale particle such as photon and electron appears as a particle whenever we measure them but if single subatomic particle is not observed, then it seems to exist at multiple places at the same time. This observation confused many scientists. One major figure in modern physics, Richard Feynman mentioned in his physics lecture series [1] that (this) “phenomenon which is impossible, absolutely impossible, to explain in any classical way, and which has in it the heart of quantum mechanics. In reality, it contains the only mystery. We cannot explain the mystery in the sense of “explaining” how it works.” For now, it is common belief that there is no one who can explain “how it works” in the double slit experiment similar to the Figure 1 introduced in his lecture.
With Schrödinger's Cat thought experiment, they are showing one famous counter-intuitive feature about quantum superposition and collapse. In quantum mechanics, superposition is a fundamental principle stating that a point like particle such as photon or electron exists in several different positions at the same time and collapse means that measurement gives a result corresponding to only one of the possible state. This observation has been so weird to many physicists including Feynman but it is a fact no one can deny.
How can a point like particle exist several places at the same time? This question based on the reality has confused many physicists since the discovery of quantum mechanics and still remains unanswered. Problem is that even though many physicists tried to understand the weird behavior during last few decades, there is no working model which can give us a reasonable explanation of the quantum superposition yet. Is it possible to think about such a physical model explaining quantum superposition and collapse using two great principles of quantum mechanics and theory of relativity?
Figure 1: Double slit experiment with electrons. [1]
Here I present a bold argument that there is another essential principle missing in building a theory of everything which will unify quantum mechanics and relativity. Without serious consideration for it, I argue no one will have clear picture on the fundamental structure beneath Quantum mechanics. I am pretty sure that if many scientists seek for something beyond the standard model to build the theory of everything, the first candidate must be the chaos theory and I hope the following discussion will make it clear. To show the usefulness of chaos theory, I begin by introducing a classical example which could be a hint for particle superposition similar to the quantum superposition and collapse.
Before delving into the discussion of a new model concerning quantum superposition, it would be helpful for understanding it to consider an mechanism to display Arabic number with a 7 segment display as a classical example which can show the same pattern with the superposed particle.
Figure 2: An example for particle superposition effect in 7 segment display utilizing Persistence of Vision
In the left of Figure 2, a typical numeric display device known as 7 segment display is shown and in it there are 7 lights which are tagged as a, b, c, d, e, f and g. It is used to display any single Arabic number among 0-9. In order to display number 5 as in the figure 2, we can choose one of two possible options. First is to turn on all 5 lights at a, c, d, f and g at the same time. It obviously consumes 5 times energy than turning on single light. To reduce the required energy, with help of persistence of vision, we can take the second option to turn on only one light at any instance time. The right of the Figure 2 shows the timing sheet showing how to schedule to turn a light in 7 segment display. The used algorithm is something like as follows.
Let suppose there is a system which can display a number 5 with 7 segment display and it has 7 states named from a to g. It is assumed to be in one state at certain instance time and change its state at a discrete time interval or tick t. With these limitations, it requires 7 ticks in minimum to visit all states so let assume its transition is always periodic with period 7. Basically it is scheduled to turn on ‘a’ during first tick out of period 7 and ‘b’ during second tick and so on. In order to display 5, it can visit ‘a’, ‘c’, ‘d’, ‘f’, and ‘g’ sequentially except ‘b’ and ‘e’. As described in the previous assumption, it is scheduled to keep the previous state during interval for ‘b’ and ‘e’.
With these preparations, when we exploit the persistence of vision, one characteristic of the human eyes, we can experience the same effect as in the first method. If the unit period time T is decreased below a certain threshold value, fairly less than 1/60 second, human eye feels difficult to distinguish the observed behavior of it from one of turning on all lights and its appearance will be almost same as the interval of unit time tick is decreased to zero. Even though human eye can see the same effect as all lights are turned on with extremely short interval of unit time tick, whenever we try to stop the system running and see what state it show, we always observe one state instead of many states. Here the probability we can calculate and measure for all possible states are shown in Table 1. The example model used here gives us a hint in building a model deceiving us that a single particle can show up multiple places at the same time with the predictable probabilities but is detected at only one place.
|
|
a |
b |
c |
d |
e |
f |
g |
|
Probability |
2/7 |
0 |
1/7 |
2/7 |
0 |
1/7 |
1/7 |
Table 1 Probability to be in one state out of 7 states of 7 segment display system showing number 5.
A physical model explaining quantum superposition and collapse
My purpose here is to introduce a model describing properties of the most fundamental building block in our universe probably scale down to the plank scale distance using three theoretical frameworks; quantum gravity, relativity and chaos theory. It is expected to explain many weird behaviors what many physicists want to understand and the nature of time, space and mass. As like other great theories require certain number of postulates, my model needs many postulates but I think the number need to be decreased significantly as study goes.
Postulates
1. Revival of Newton’s absolute time. Newton’s view on absolute time that absolute time exists independently of any perceiver and progresses at a consistent pace throughout the universe is a basis for further reasoning. Full range of absolute time can be mapped into continuous real number and absolute time flows always to the future at a uniform rate independently of any inertial frame of reference.
2. Revival of Newton’s absolute space. According to Newton, “absolute space, in its own nature, without regard to anything external, remains always similar and immovable.” Full range of absolute space can be mapped into continuous real number.
3. Similar to what string theory suggests, the time evolution of every elementary entity in 3 spatial dimensional space defined in the standard model such as electron, photon, dark matter and dark energy can be described as mathematical language and all share a common mathematical form and the general form can be rearranged as a set of first order differential equations defined in 11 dimensional space whose Eigen vectors include:
A. 3 absolute spatial vectors x, y, z
B. 1 absolute time vector t
C. 3 spinning forces fr, fg, fb at position p= (x, y, z).
D. 3 directional forces fx, fy, fz at position p= (x, y, z).
E. 1 energy vector E as a power source driving the time evolution.
| $$Ω(x,y,z,f_x,f_y,f_z,f_r,f_g,f_b,t)=E$$ |
(1) |
4. The general form in 3 for any elementary entity in can be simplified as follows:
| $$E=phν+qmc^2$$
|
(2) |
, where h is plank constant, ν is light frequency, c is the speed of light in empty space and m is mass. This equation reflects the wave-particle duality. For a pure photon with energy E=hν, if it is got absorbed by a balckhole, it's wave like energy will turn into a pure mass form with $$E=mc^2$$. So m and ν are related as $$E=hν=mc^2$$.
5. The p and q in equation (2) has the relation of
| $$p+q=1$$
|
(3) |
6. Dark matter which is well known term in cosmology is assumed to be a point like particle with q=1 in the equation (2) and the pure photon with constant light velocity is considered as a point like particle with p=1 in the equation (2).
7. Of any elementary particle system, Einstein’s relative time tr and relative space xr are related with Newton’s absolute time t and x as in what follows:
| $$m=\frac{t_r}{t}=\frac{x_r}{x}=\frac{y_r}{y}=\frac{z_r}{z}$$
|
(4) |
, where m is the mass term and m-1 is called as a world evolving rate. For a photon, m=0.
8. Of any system of elementary particle, the mass term m in equation (3) and (2) is defined as a sum of all interaction with dark matters included within its bounded area over a unit interval of absolute time domain. The full set of possible states of the system governed by the rule of equation (1) is known to be finite or bounded in the state space. [Refer to 2].
9. The definition of measurement is to synchronize two different world evolving rates of two different inertial reference frames. For example, If a detector system with the world evolving rate r1 try to measure or detect a photon with the evolving rate r2=∞, then the measurement can be completed only after setting r2 to r1.
[2016-206. Added]
10. The term "dark matter" mentioned in the postulate 8 can be thought as a particle having a tendency to stand still to a inertial reference frame and its role is generally to put some amount of mass to an encompassing particle. It is defined as the linear sum of 3 spinning forces fr, fg, fb at a spatial position p= (x, y, z).
$$D=a_1f_r+a_2f_g+a_3f_b$$ | (5) |
Explanation for the postulate 10.
In my view, the dark matter seems to play the same role what the "Higgs particle" is expected to show. The most important thing is this dark matter is also the source of gravitational lensing effect such as bending space-time as most physicists think. My understanding is that the major view point shared by most physicists are that Higgs particle and dark matter are two different things and not the same one but I argue they are the same thing. Then the question is how it, whatever is called as dark matter or Higgs particle, can play both roles; putting a some amount of mass to a particle or bending space-time.
I think if the dark matter particle is included within the bounded area of a particle or object, then the object will get the mass equal to the sum of the interaction with the dark matter particle. So the mass of our body is believed to be the sum of interaction with the dark matter enclosed by our body. In this view, any physical shape including us are the total sum of lights, massless particle, interacting with the dark matter particles within a bounded area in 3 dimensional space. If a massive rigid body occupying a finite area in space is in a consistent motion with the same velocity, we say it is associated with a inertial reference of frame IRF and the dark matter particles contributing the mass of it tend to standing still to IRF. This view shows the role of Higgs particle is expected to play. I think the mass created from the interaction with dark matter particles bounded within a thing(i.e electron, proton and etc) is the rest mass or invariant mass of the thing most physicists mean.
Another role which dark matter plays is to change the motion of a particle or bend the space-time. Let me describe what I have in mind. Dark matter can reside any point in 3D space and shows a tendency to stay still relative to a inertial reference of frame. It makes me to think the eye of typhoon, a floating force trying to pull everything nearby into its center. The dark matter distributed not only within the bounded area of a rigid body but also near out side of the rigid body constituting a field. The distribution of dark matter near a massive body of mass M is believed to meet the condition described in the postulate 5 and suggested by general relativity.
For better understanding, let me give you a classical analogy. Suppose, in the center of ocean, that a ship is sailing with constant velocity v and will pass nearby a whirlpool strong enough to change the sailing direction of a ship. In this case the future life of the ship will be determined by the closet distance between the ship and the center of whirlpool with the assumption that the the whirlpool power is constant and no driver controlling the ship on board. As it gets to the center of the whirlpool, it will need more energy to escape from it. Here we need to change our classical view that the eye of typhoon is just one. Instead, we can think there are finite but infinitely many number of eyes within the bounded area of typhoon and each eye having different magnitude is orderly distributed so that its pulling power is inversely proportional to the distance to the center of typhoon. This view resolves the problem of acting with object at a distance which Newton want to know. I believe this classical example helps readers understanding intuitively the space-time curvature what Einstein recognized firstly 100 years ago.
So it is the source to give rise in the rest mass of a rigid body that the dark matters enclosed by it and standing still relative to the center of mass of it. The minimum distance between two dark matters is estimated to be the Planck scale distance 10-35m. No matter where the rigid body moves, its paired dark matter will follow standing still to the IRF of it so there will be no change in the rest mass. Of course, near out side of the rigid body, there will be dark matters distributed consisting a gravitational field due to the rigid body. Returning to the classical example of the ship sailing near by a whirlpool, the ship can be thought as the rigid body and whirlpool as a black hole exerting humongous gravitational field. In such case, the space-time curvature what Einstein described in his general relativity can be described as the distribution of two groups of dark matters which are originated from the rigid body and black hole in space. This distribution which is continuous in space can provide definitely the guiding passage for the rigid body in its world line. Unfortunately, I don't have enough skills to describe it with a strict mathematical form for now but I believe some experts can derive it easily based on the description above.
It would be worth to note one additional philosophical view that nature hates sudden discontinuity and I agree on that. On the boundary of a massive rigid body, I think it would be nice and beautiful that the distribution of dark matter is decreased gradually as the distance from the boundary increases.
The dark matter seems to be a singularity attractor pulling any particle moving near by and black hole is believed to be a dark matter particle with huge energy. I borrowed the concept of attractor from the chaos theory. Some characteristics found in attractor such as the new concept of frequency of a strange attractor are especially important to understand the true nature of our universe but I will leave it here and discuss in another thread.
In my view, all Higgs particle and dark matter and black hole are actually the same thing with magnitude variations: a energy force trying to pull any object passing near by into its center. I think most physicists will agree on that a physical model with fewer assumptions is better than one with more assumptions. From my intuition, it seems to prevent the time evolution of a particle and shrink its perception on the spacial space similar to what special relativity proposes.
[/2016-206. Added]
How can quantum superposition and collapse be interpreted using the above postulates?
For simplicity, I will begin with the most basic element particle, a massless photon, other than electron with rest mass. From postulate 3 and 8, a photon evolves in time in a bounded volume of 3 spatial dimensional space deterministically ruled by a set of ordinary differential equation. Bounded area means that the photon oscillate within a bounded area or has a finite size instead of a point independently of any perceiver.
As quantum mechanics already discovered that the probability to find a photon at certain volume area can be predicted, the previous work with chaos theory [3] showed that the probability distribution of a particle moving along the trajectory of chaos system such as Lorentz system can be determined by means of numerical analysis before actual measurement.
The size of a photon is appeared as almost zero to any perceiver close to human scale but in absolute time and space, the bounded area of a photon is non-zero volume and remains unchanged if there is no interaction with any external energy form.
What is the frequency of light in free
space and is it quantizable?
This is next topic.
[Added 2016-01-03]
See the recent comments in the additional part in 2016-2-06.
I missed one important postulated so here I add more postulate about the distribution of dark matter in absolute space. Dark matter which is known as a hypothetical kind of matter causing gravitational effect in cosmology is, in my model, a sort of frictional like energy particle instead of matter. It is made up of the linear combination of fr, fg, fb. It is same with the inertial mass in classical mechanics.
Postulate 10.
Given a point like matter with mass m, assuming 1 directional space, dark matter is distributed around it in decreasing way as the distance r from the mass position: Unfortunately, I don't have the exact equation for the dark matter distribution but my guess is that it could be a equation whose integrals from 0 to infinity distance is matched with the rate of percentage of dark matter over visible matter:
Figure 3. Conceptual image for dark matter distribution. The integral of the distribution between 0 to infinity is expected to be matched with the rate between the percentage of dark matter and visible matter.
Understanding quantum superposition in double slit experiment with the new model.
From postulate 3, it is known that any particle system of which time evolution is governed by the set of ordinary differential equations is oscillating in a bounded area in absolute time space in similar way to the strange attractor. It means it is possible that the bounded area of the particle is bigger than the distance between two slits. Figure 5 shows such a case.
Figure 4. A conceptual image. An oscillating particle in the bounded area is passing through double slits with light velocity c. The trajectory of the particle is big enough to contain the wall between two slits.
As can be seen in the previous example of 7 segment display system, for a system which can have only one state at any instance time, it can produce an illusionary effect as if it can have multiple states at the same time by reducing the duration of a unit tick to zero. Same principle can be applied with the double slit experiments with photon. What important information is that a photon has no mass and a world evolving rate $$ \alpha = \frac{t}{t_r} = \infty $$
What the world evolving rate α of a system is infinity means that it takes no time to complete the evolution which is analogous with increasing the clock speed of CPU to infinity or decreasing the duration of a unit tick. It should be noted that any system experience only relativistic time and space and there is no way to measure or observe the absolute time and space. It is similar to what we are unable to measure π. Instead of using ideal symbol, we can only use the approximated value of π in a calculation and the approximated value is normally relativistic to who make a decision of the level of approximation.
Back to the double slit experiment, due to the mass of wall included in the bounded area of photon particle, the world evolving rate will be decreased but negligible because the mass is small and still it's moving from one slit to other along its trajectory will take almost zero time.
I think the model described so far using chaos theory and special relativity is the only available non-mathematical explanation about the quantum superposition and easy to understand.
[/Added 2016-01-03]
1. [↑] Feynman, R.P., Leighton, R.B., and Sands, M. (1965). The Feynman Lectures in Physics Volume 3, Section 1–1, Addison–Wesley.
2. Chaos. http://plato.stanford.edu/entries/chaos/
3. Jos Leys, É. G. (n.d.). Chaos-viii-statistics. Retrieved from CHAOS: http://www.chaos-math.org/en/chaos-viii-statistics
