Do sub-atomic particles obey Newtons Laws of motion?
In general, the behavior of the sub-atomic particles cannot be described by
The basic picture of the Newtonian mechanics can be described as follows. There are
particles, with specified positions and velocities, interacting with each other by
means of forces. There are several kinds of forces in Nature. These forces can act
between two particles, and their strength and direction depend on the positions and
the velocities of the particles. Second Newton's Law connects between the forces
acting on a particle and the resulting acceleration. Knowledge of the positions and
the velocities of all the relevant particles at a specific moment of time allows to
predict the positions and the velocities at any other time.
The laws which govern the behavior of the sub-atomic particles are completely
different. It is impossible to assign a specific position and velocity to a
particle. Each particle can be in a superposition of different states, which means
that in some sense it is located at the same time in a whole region of space and
has a whole range of velocities. If you measure the position (or the velocity) of
the particle, you just get one of the values from that range, in random (possibly
with different probabilities for each value). However, this is NOT because the
particle actually HAD that position and you just hadn't known that, but the
particle really HAD a whole range of positions the moment before the measurement.
This is something strange and beautiful.
The ability of the particle to be in several different states simultaneously
results in a well-known wave-particle duality: the sub-atomic particles (electrons,
neutrons and other) can behave like waves and show interference. Suppose we have a
particle source aimed towards a wall with two slits where the particles can pass,
and a detecting screen beyond this wall. First we allow the particles to pass only
through one of the slits, and then only through the second one. In a third
experiment, the particles can pass though both the slits. When looking at the
results, the results of the last experiment seem to be completely unrelated to the
results of the first two. This happens because when particles are allowed to pass
through both slits it's not that some of them pass through the first slit and some
of them through the second one, but in some sense each particle passes through both
of them. On the detecting screen we see a picture identical to one which is
obtained from interference of waves.
The theory which is able to describe the sub-atomic particles is the Quantum
Mechanics. In Quantum Mechanics, a system (sometimes a single particle) can be
described by a wave function (or by a vector in a multi-dimensional space). The
information contained in the wave function is just the weight of each possible
state in the current state of the system (actually there is something more: the
phase of each state, which I will not discuss here). The wave function allows to
calculate the possible results (and their probabilities) of any measurement which
can be performed on the system. The development of the wave function in time is
described by Schroedinger's Equation (which is analogical to Newton's Laws), given
the initial wave function and the so-called Hamiltonian operator of the system
(which takes into account the interactions between the particles).
Newtonian Mechanics turns out to be a private case of Quantum Mechanics. In some
situations, the behavior of the sub-atomic particles can be described well enough
by Newton's Laws, but the more general theory is the Quantum Mechanics. To see the
beauty and understand the basics of Quantum Mechanics, I would recommend reading
about it in 'Feynman's Lectures on Physics' by R. P. Feynman or in 'The Principles
of Quantum Mechanics' by P. A. M. Dirac.
Yevgeny Kats, Physics Grad Student, Bar-Ilan University, Israel
'The true spirit of delight, the exaltation, the sense of being more than Man, which is the touchstone of the highest excellence, is to be found in mathematics as surely as in poetry.'