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Kinematics and Dynamics of a Material Point
A classical particle or, as it is also referred to, a material
point, is an abstraction that does not have a genuine counterpart
in nature other than as an idealisation that can be mapped on certain
physical systems in some circumstances.
Planets, for example, are so far away from each other and from
the Sun that their movements can be described fairly accurately
by treating them as material points. But a planet-moon system can
no longer be analysed in these terms, because the bodies are sufficiently
close to "see'' each other's angular dimension and that has a profound
effect on the dynamics of a planet-moon system.
All physical bodies, which we encounter in our every-day life have
some physical extent, and thus the description of their motion and
their interaction with other bodies becomes a very complex issue.
The use of the word "particles'' as applied to Quantum particles
is a misnomer, that tends to evoke quite inappropriate Classical
Physics connotations. Quantum particles are very strange objects.
Although they tend to interact with macroscopic apparatuses in a
point-like manner, which is why the term "particle'' has been slapped
onto them, more sophisticated experiments reveal their extended,
highly non-local nature. In one of those experiments a quantum particle
has been demonstrated to "stretch'' over a distance of 15 km and
seemingly pass some sort of a communication (not readily accessible
to us though) within that stretch at an infinite speed. Quantum
Mechanics, as it has been formulated so far, suggests that a quantum
particle may even "stretch'' like that over the entire universe,
which really forces us to revise the very notions of space and time,
notions that are intrinsically classical and therefore essentially
incompatible with the realm of Quantum Mechanics. Yet we continue
to cling to those notions even in Quantum Field Theory, because
we have nothing better to replace them with.
The clash between the concepts of a classical space-time continuum
and Quantum reality is ultimately responsible for most mathematical
difficulties in Quantum Field Theory. But to discuss those interesting
issues in more depth would take us too far from the topic of this
chapter, which is numerical simulation of a material point.
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