However, the rigors of this subject are toned down as
per the requirements of the objectives of the study. Then, we call this new
branch of physics as mathematical physics. This article tries to gain further
insight on this topic.
Mathematical
Physics:
·
According to the famous Physicist Paul Dirac,
nature has certain mathematical quality and requires mathematics for its
description.
·
The mathematical equations representing
the laws of nature are simple in nature.
·
In this way, a physicist is provided by
a principle of simplicity of mathematical equations which he can use in
scientific endeavors.
·
Mathematical beauty in an aesthetic sense
takes precedence over simplicity of equations though.
·
The abstract concepts of mathematics are
provided certain physical sense in their application in a physical theory.
·
In most of the cases, the initial and
final steps of the solution of a mathematical expression hold utmost importance
as they represent certain information on the state of the system.
·
The precision and rigor of mathematics are
replaced by frequent approximations in mathematical physics.
·
The branch of mathematical physics as such,
is a system of mathematical concepts which can be brought to use either for reasoning
or for representation.
Role of Mathematics in
Physics:
1.As a Tool of Abbrevation:
- · The equations of mathematics represent the ideas of Physics in a concise manner unlike words.
Ex:
Newton’s Second Law: F = m*a.
2.As a Tool of Connection
of Physical Quantities:
- · The equations of mathematics connect the physical quantities to each other ceasing their independent existence.
Ex:
The equation F =m*a says that the net external force acting on a physical system
is related only to its mass and acceleration.
3.As a Tool of Mechanized
Thinking:
- · Mathematics mechanizes the process of scientific thinking.
- · If the original statement of thinking is correct and represented mathematically, then certain rules of mathematics are to be strictly followed thereafter.
- · This results in arriving at a final statement which is equally correct and can be ultimately interpreted for a physical sense.
- · This is solving problems in mathematics or thinking scientifically about nature.
- The power and beauty of mathematics is that it saves us from following the painstaking process of analyzing a process purely on thinking from the initial conditions to final conditions.
- · Instead, we represent the initial state in an expression and faithfully follow the rules of mathematics in the intermediate stage.
- · We are then certainly taken to the final stage where we only need to interpret the expression at the final stage physically.
Ex: Newton’s Second
Law: F = m*a (Original Statement)
ð F
= m* d/dt v (alternative representation of “a” using calculus)
ð F*dt
= m*dv (cross multiplication)
ð F*dt
= m*(v2 –v1) (Notation for change)
ð F*dt
= m*v2 – m*v1 (Multiplication)
I =
Δp(Final Statement)
- · Physical Interpretation: Impulse acting on a physical system changes its momentum.
Resources:
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