An overview of physics
Physics is the science of the Universe. Since it is not even clear what exactly is the "universe", in the first place (for some people, it is one's very personal perception of a wider structure known as a "multiverse"), it is a science intrinsically rooted in empirical methods, approximations and abstractions.
As such, it differs from other (so-called "hard" or "exact") sciences such as Mathematics, that have a much more solid background in the form of axioms that serve to build an increasingly complex edifice.
Here is an example of what Mathematics is about: $\sqrt{2}$ is irrational.
As in any field of Science, one must know what one is speaking about. Here, we involve two concepts: $\sqrt{2}$ and "irrationality". The former is a notation for the number that, multiplied by itself, is 2. The Latter means something that is not a fraction of two integers: $p/q$. The Mathematical problem is therefore to prove that for all possible $p$ and $q$, we never find that:
$$\left(\frac{p}{q}\right)^2=2\,.$$
You may want to check that you understand how we arrived to formulating the problem in this way (we applied the various definitions and brought everything together). Now we are facing a puzzle. Mathematicians are typically people who like to solve puzzles and riddles. This is one of them.
It can be solved in this way:
The numbers are such that $p^2=2q^2$. That is to say, $p^2$ is even (it is a multiple of 2: this is the definition of "even" and that is precisely what is written). Now we cannot try all the possible $p$ and $q$ but we can explore what other properties they have, until we narrow it down maybe even to their actual value. It is clear that $p$ and $q$ cannot be both even, because then they are both multiples of 2 which can be cancelled in $p/q$ so that one at most is even, or they are both odd. But the square of an even number is also even (since no factor 2 appear in a product of numbers where it is absent). Therefore, since $p^2$ is even, so is $p$, which means that $q$ is odd. But if $p$ has a factor 2, its square has a factor 4. Therefore $p^2$ can be divided by 4, i.e., $2q^2$ can be divided by four, that is, $q^2$ can be divided by 2 which means that $q^2$ is even, which means that $q$ is even. This is a contradiction, therefore there are no two integers such that $p^2=2q^2$, i.e., $\sqrt{2}$ is irrational. Quod Erat Demonstrandum.
Here we have a typical example of a Mathematical reasoning. For some people this is a headache because you have to memorize various steps and follow a tight logical thread. It is however only a question of practice and when you are used to it, this is highly enjoyable. You will notice that we used intermediate results, in fact repeatedly, such as: "if a number is even then its square is also even" and vice-versa. These can be called theorems for convenience and with a collection of theorems, like a set of keys, one can try to break the problem, like one picks a lock.
Physics, on the other hand, accumulate with much less order and structure a body of knowledge. Sometimes purely from observations. Sometimes from an insight. Some other times from underlying mathematical reasoning. This body of knowledge must remain however strongly connected to scientific methods, such as the possibility to reproduce a phenomenon so that it can be studied and verified, and therefore also can be predicted and even controlled. Questions about this phenomenon can then be asked that can be answered not from intuition or personal belief but from unarguable methods such as experimentation or experimental proof. At such Physics differs from other (so-called "soft") sciences like Philosophy or Economy or Politics, that may not be resolvable except through common agreement between different parties, what usually results in no-agreement and the parties becoming "schools" defending their own view of a problem.
There is no clear boundary between the various sciences. For instance Mathematics are greatly involved in Physics, and the field that studies their point of closest encounter is called Mathematical Physics. Philosophy also is very much involved in Physics, although unlike Mathematics, a practicing physicist can often dispense Most planetary orbits are neafrom philosophical considerations. This is illustrated by the dictum "shut up and calculate". This rather brutal injunction arose in context with one of the major branch of contemporary physics: quantum mechanics, the physics of small objects (such as particles). The science of this object led to a formulation in terms of mathematical concepts whose interpretation was not clear. Namely, a so-called "wavefunction" $\psi$ is used to describe, say, an electron, and this takes the form of a complex-valued field, a sort of "wave" (as the name implies) but really a mathematical "function" (as the name completes) since unlike a sound-wave or a water-wave, it is not known what exactly is "waving". But it is not known if this wavefunction is an actual mechanical thing or a theoretical construct that allows to recover the information on the electron such as its position or speed.
Quantum mechanics is very successful to provide calculated values for experimentally measured data, and for one of the big applications of Physics, that is, engineering, this is all that is needed: a set of rules and tricks that work. It then became largely a matter of philosophy, what exactly is the wavefunction. The most famous debates are those between Bohr and Einstein
We have given above an example of a Mathematical reasoning. Since we are dealing with Physics, we must hurry to provide a counterpart for this field. From the countless possible examples, let us consider Kepler's laws. They say how a planet orbit its star:
Mermin said it here (he remembers it here where he also shares his favorite joke, that has a bearing on our discussion:
Question: What is the difference between theoretical physics and mathematical physics?
Answer: Theoretical physics is done by physicists who lack the necessary skills to do real experiments; mathematical physics is done by mathematicians who lack the necessary skills to do real mathematics.
http://www.nature.com/news/history-shut-up-and-calculate-1.14458#/b10
Portraits of physicists:
- Galileo * Newton * Boltzmann * Noether * Feynman * Hanbury Brown * Hawking * Witten
A three-year syllabus of physics:
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