As one turns the scale to the atom level, the behavior of a particle
becomes very unpredictable. Quantum mechanics has a
better description of microscopic properties than classical mechanics for this
scale. It brings us the most precise and successful numerical predictions in
the history of science. But a contradiction accompanied with the development of
quantum mechanics was brought to light, and has been queried from realists. It is certain that the probabilistic
interpretation contravenes the law of causality, and is unable to delineate the fundamental physical process of the universe. According to
quantum mechanics, measurements of some properties, such as a particle's
momentum for example, can yield a range of possible results with varying
probabilities. In other words the objective physical
process, once physicists took it for granted to
possess definite properties that suitable observations can reveal, is no longer
adaptable in the microscopic world.

The most profound conceptual difficulties
of quantum mechanics are those that originated from conflicting non-causations.
The compelling results unearth the incompleteness of quantum mechanics revealed
by the EPR experiment^{1} and the double-slit experiment, where the
former lies in the inadmissible awareness of definite position and momentum at the same time; while the latter designates the wave-particle duality, which is
the most unusual character of quantum particles. Moreover, this is just the
outset of this battle to uncover the covert facts behind quantum mechanics.
More quantum strangeness is rooted in the relevance of causation at a microscopic level,
such as the uncertainty principle, entanglement, tunneling effect and so on, which
have been proposed since. These phenomena profoundly violate the standpoint of
human experience to our orderly, causal universe. It seems that the usage of
quantum mechanics has been widely accepted while ignoring its essential
features. This metaphysical quantum theory perfectly
interprets experimental results, however, addresses nothing which approaches
the realistic description with regards to the nature of
quantum world, and yet becomes the most wizardly of theories.

The need for a more complete theory is revealed as our understanding of
the physical universe has deepened profoundly, and, in particular, as the desiderative
exploration of the very
beginning of our universe has been carried out. One of the possible theories is
the “hidden variable theory” proposed by D. Bohm. An insinuation of invisible
variables revises empirical
grounds and preserves the causality
on the subject of quantum behavior based on a wave conception. It provides a possible
sketch of the parentage of “multi-path” methodology, which is an alternative perspective
on the issue of a particle’s wave-like property proposed by R. Feynman. His
standpoint concurs exactly with all that went before from the numerical
predication point of view, but presented in a causal way. It concludes that
there are a lot of trajectories between two fixed points, and becomes only one
trajectory, the classical one, at the macroscopic level. However, this causal
manner emerges from a contradiction of quantum theory, and has not yet been
fully understood from the anthropocentric
viewpoint. In terms of physical
laws in the objective physical process, it appears that an invisible physical
strength acts on a particle and draws forth all
possible trajectories. Obviously, more questions arise from the deterministic viewpoint
to this hidden variable theory, such as: “What is matter wave exactly?” and “Why
is there an invisible part which does generate an effect on particles?” and so
on. Those puzzling questions could be straightened out if we could visualize
this invisible portion in some way. Therefore, the primary research to be
addressed next is how to convert hidden variables into realistic physical
quantities and to provide a concrete depiction that can bring a convincing
theory forth, which would account for all wired quantum phenomena and describe
every property of the quantum world.

The main purpose of this introduction is to explore the process of visualizing hidden variables, and to represent a complete theory within microscopic physics. One can imagine that there is a bee in a house with no window. The bee has a special power allowing it to pass through walls to go outside. Of course, we cannot see the bee while it stays outside the house and we are inside. It can only be seen after passing through the wall and coming back into the house again. Hence, what we can observe is that the bee appears all of a sudden and disappears later if it passes in and out of the house. In such a condition, we have no idea about when it will come back to the house for the reason that we cannot see anything outside the house, but what we can do is to estimate the probability of being stung by the bee according to the position we are in inside the house. This is the probabilistic interpretation proposed by quantum mechanics to describe a quantum system.

On the other
hand, let us replace all the walls of the house by transparent glass then there
will be no doubt that we can see everything outside the house as we stay
inside. Now, we still can observe where the bee is and even how it moves after
it is passing through the glass wall to go outside. There is no problem for us
to predict its flight path, position, velocity and heading. In other words, we
can be told when and where the bee comes back into the house in a deterministic
way, without estimating the stinging probability. A contrast can be made here
that transparent walls symbolize the visualization process; it can reveal
motions of the bee outside the house in the former case in an objective
physical process. Consequently,
a continuous and deterministic interpretation of the quantum world can arise if
we can find some method of replacing the invisible border.

It is
straightforward to think of extending dimension to bring transparent walls into
existence. To deliberate on the imperceptible part to the sense at quantum
level, a rational speculation of complex domain could strike a bargain, in
which its imaginary part can represent the invisible world. In fact, it is not
an unrestrained attempt originated from an intuition only. The complex concept was objective in Schrodinger’s
equation and can be made aware of by the appearance of the imaginary factor “i”,
and has been permitted as a genuine mathematical tool. In fact, the ignoring of the imaginary sign in wave
mechanics can be attributed to practical experimental results, which cause
people’s attention to delve into the atom scale. Owing to the limited
observable dimension, imaginary features of nature which could dissolve the consequence
of experiments has been eliminated by empiricists. However, no thorough canvass can be addressed if our understanding of nature contains a
one-legged version of the full view. This is the main reason why quantum
mechanics is an incomplete theory, for its grounds for existence lie on
observation that has been criticized from the philosophical aspect and the
causality of its nature.

In pioneering work approaching causal quantum physics, a remarkable achievement based on the complex concept has been
proposed by C. D. Yang. In his study of the physical process in a complex
domain, astonishing results
have been acquired. They reveal that Schrodinger’s equation is a deformation of
the Hamilton-Jacobi equation when considering the existence of a complex
dimension. There is no fortune at all in this since it is the only way to manifest
the true face of its nature after a long struggle for a unified description of
the causal universe up to now. General relativity and causal quantum physics
can for the first time be on an equal footing in the foundation of the Hamiltonian
outlook on causal physical processes. The biggest difference of Hamiltonian in the
microscopic world is its additional term, namely quantum potential, as compared
to the classical one. It states that there is a special field in the atom
scale. It is on the decrease along with increasing mass, and finally vanishes
in our daily scale. This field is so-called the quantum field, which can take responsibility
for all marvelous quantum phenomena from the perspective of causality. Thus, a
concrete object having specific physical quantities can be discussed after a
complete description of carried energy has been expressed. In other words, it
can be regarded as a classical particle for those who once considered it as the
most bizarre particle in the quantum scale.

One of the most elusive parts of this causal
quantum physics, or so-called quantum

Therefore, the wave function decided by Schrodinger’s equation describes a particle’s motion statistically
and cannot provide more detail about each trajectory. It is clearer to think of
it as a water flow; since we cannot know a specific molecule’s motion by
observing its whole flow, and can only understand the probability of this
molecule passing by a specific area. This is the limitation of describing a
quantum motion based on wave mechanics since it provides a macroscopic
observation which cannot be overlooked. On the contrary, a fully informative
view of a particle’s motion can be presented in terms of causal description
from the same wave function. We can observe a specific particle’s motion with
the help of quantum

In summary, the revolutionary viewpoint of the complex dimension not only visualizes hidden variables but also provides them with a realistic physical meaning. As a causal theory, quantum Hamilton mechanics can be fully understood based on the classical standpoint, and invigorates complete description of the microscopic nature. However, this complex extension should be amenable to revision on empirical gounds as a scientific hypothesis. The prediction of small perturbation of the electron's spin momentum can be one of the crucial testmonies, waiting for the comparison with experiments. On the other hand, the flying time of a photonic tunneling effect can be brought out by solving the equation of motion of the photon, which can be examined by the experimental data. The oscillation period of ammonia molecular can be estimated precisely by averaging the time that a trajectory cycle has made. Those issues have been executed in our laboratory recently, and could be worked out in the near future. We can conclude that quantum mechanics is a theory of phenomenology which gives average values for observed quantities; while quantum Hamilton mechanics is a theory of fatalism presenting specific particles and trajectories. Quantum Hamilton mechanics as a causal theory extends our understanding of the true nature of the microscopic world. It defends the causality, preserves physical laws while revealing the most mysterious feature of nature, indicating what is behind quantum mechanics.

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