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The common way to divide physics into two parts where one is 'Modern Physics' has the other part as 'Classical Physics' (not 'Early Physics'). 'Early Physics' is not a widely-used expression though it might be considered the work of the ancient Greeks. 'Classical Physics' will be assumed hereon.

Classical physics is the common (and often relatively common-sense) physics that we observe around us. It is the physics of televisions and refrigerators and rainbows and air planes. It explains the orbit of the Earth around the Sun and why the sky is blue and how engines and microwave cookers and bicycles and anti-lock brakes work. The fundamentals of electronics and semiconductor and computer technologies (but not the fine details) can be derived using classical physics. Much of the basic operation of lasers and the fibre-optics technologies (but again not the fine details) can also be explained by classical physics.

Traditionally, physicists consider the main branches of classical physics to be mechanics (motion), electromagnetism (electricity and magnetism), optics (light, lenses, waves, propagation) and thermodynamics (heat, order and entropy). Note that in principle, optics could be included in the electromagnetism branch but it is generally understood to be important enough to be considered a separate one.

Modern physics began to appear around 1900 when phenomena started to be observed that classical physics could describe, but only quite approximately. A notable year was 1905 when Albert Einstein published his paper on what we now call Special Relativity. Later he presented a generalisation of it, aptly enough called General Relativity. This was followed in the 1920s by even more astounding - and profoundly different - work by Schrödinger and Heisenberg that led to what we now call Quantum Physics. These - Quantum Physics and General Relativity - are considered the two main branches of modern physics.

In a paragraph above classical physics was described as the common (and often relatively common-sense) physics. Modern physics, though, describes 'worlds' that are not at all common (and are often very counter intuitive) for us. General relativity typically starts to give results that are significantly different from classical physics (Newtonian mechanics) only when masses are many times that of our Sun or velocities are a significant part of the speed of light. Quantum physics - which is notoriously difficult to intuit - often only gives different results from classical physics when the spatial scales are tiny; that is when we are considering particles or systems the size of small molecules or atoms or smaller.

In fact, through recent efforts it is possible to absorb all of classical physics into general relativity.

It is also possible now to absorb all of classical physics into quantum physics. However the distinguishing parts of General Relativity and Quantum Physics continue to stand apart and seem difficult to absorb into a unified theory. String theories are some of the most promising recent efforts at the unification and some are candidates for a Theory of Everything (TOE) in physics.

While the applications of modern physics are in some ways still in their infancy, General relativity has given us a much richer understanding of the Universe than classical physics gave us. Quantum physics has been important in the development and refinement of the electronics, computer and information technologies. Both are providing us with a greater understanding of the Universe, perhaps while reminding us, with their often counter-intuitive perspectives, that things in this world may not always be the way that they initially seem to be ... That 'truth' can be more wonderful and seem vastly more imaginative than fiction.

DonB

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By physical physics, you're probably talking about continuum mechanics and classical mechanics. And by modern physics you are probably talking about quantum mechanics and special and general relativity. Which includes some relatively new theories about sub-atomic particles like quarks, and strings.

Classical mechanics is the study of the motion of objects which are above the size of the atom. It is called classical, because it is based on the older classic ideas developed by scientists like Isaac newton. Hence the term Newtonian mechanics which is the term for the ideas about motion Newton is said to have developed.

Continuum mechanics is the idea of dealing with the movement of objects ignoring the idea that they are made out of atoms, but instead treating objects as continuous materials. It includes solid and fluid mechanics. Archimedes, Evangelista Torricelli, Isaac Newton, Blaise Pascal, Claude-Louis Navier and George Gabriel Stokes all developed ideas on fluid mechanics. Solid mechanics deals with how solid materials behave when forces are applied to them. These ideas still work for most normal sized physical objects today.

Modern Physics likely includes fields like relativity and quantum mechanics, the study of sub-atomic behaviour like waves and sub-atomic particles such as Hadrons. And the building blocks of hadrons, quarks and their various types (up, down, charm, strange, top, bottom). Bosons (force particles) like gluons and photons.

Modern physics would include new theories of unification such as string theory. Unification is the aim of creating a general theory that describes the behaviour of objects both above and below the size of an atom. Effectively unifying classical and quantum mechanics.

Part of the aim of the Large Hadron Collider (LHC) is to try to further investigate areas of physics such as quantum mechanics and string theory.

In conclusion most ideas after the dawn of the 20th Century would be considered Modern Physics. The ideas before the discovery of atoms would probably be considered 'physical' physics.

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