Yikes! Physics! What a Pain!

Figure 1.1: Physics: Where the Real World and Math World Meet.

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The subject of Physics is generally considered difficult. In mathematics, there are proofs, in physics you are asked to sit through many ``derivations".

The idea is to start from Fundamental (often Mathematical) Principles, and apply them to a situation of interest. In the first term of General Physics, the Fundamental Mathematical Principles used are known as ``Newton's Laws of Motion." The power of physics (and all of science for that matter) is that one can apply these general principles to a wide variety of situations (many more than envisioned by the original investigator).

For example, Newton developed his Laws while examining ordinary sized objects. But those laws have been applied to the motion of electrons, planets, objects going in a circle, systems of particles, rigid bodies,... Another example of this for biology comes from the monk Gregor Mendel, who discovered the laws of genetic inheritance. He did this carefully dissecting and growing plants. However, these inheritance laws apply to many other biological systems including people!

So, why is physics hard again? Because the laws of physics almost universally involved mathematics. Not just adding and multiplying numbers, but differential equations! (i.e. ``hard" math).

So, mathematicians are great physicists, right? Not necessarily. To see why, let's examine how physics problems are solved:

Step 1

Convert the real world problem to idealized mathematical abstractions.

Step 2

Solve the governing mathematical equations for the unknown(s) of interest.

Step 3

Convert the abstract mathematical result to the real world.

So, while an applied mathematician may be great at step 2, he/she may struggle mightily with steps 1 and 3. So what we have here is two types of common sense - Mathematical Common Sense and Physical Common Sense. Sometimes these are at odds at each other and this is another reason why physics is hard.

It should be noted that there are many assumptions and/or constraints involved in all of the three above steps. Let's take a simple (but silly) example.

Johnny has 5 pencils. He gives two to Sue. How many pencils does Johnny have?

The physicist answer (and the ``Smart Alec" answer) is that you don't have enough information to solve the problem, but, without knowing anything else, the probably correct answer is 3. Assumptions must be made. When exactly did you measure Johnny's number of pencils? Suppose you measure it 1 hour after the transaction. Johnny could have

• lost some pencils.
• obtained more pencils.
• both of the above.
• died!

Those things would all change the answer. What if we measure only 0.5 seconds after the transaction? All of the above still apply. Thus, we must assume that

• nothing relevant happened during the transaction.
• nothing relevant happened between the time of the tranaction and the measurement.
• nothing relevant happened during the measurement.

Put another way, we must either

1. Assume that nothing relevant happened, or
2. Constrain our results to situations where nothing else relevant happens.

A problem is that in the ``Real World", other things are ALWAYS happening. It is the job of the physicist to determine whether these things are relevant, and to what extent. ``Normal" people don't have to think about this stuff, physicists do!

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Some Good News!

It is NOT assumed that you've had any previous physics experience!

Figure 1.2: There are many, many details in physics. It is often difficult to ``see the forest from the trees." This is why it is extremely important to constantly look at the larger picture! This process, which is emphasized in this course, is extremely valuable, and students are encouraged to apply this to other aspects of their lives.

Another way to describes this whole process comes from the wikipedia:

Physics is closely related to mathematics - mathematics provides the logical framework where physical laws can be precisely formulated and their predictions quantified. Physical theories are almost invariably expressed using mathematical relations, and the mathematics involved is generally more complicated than in the other sciences. The difference between physics and mathematics is that physics is ultimately concerned with descriptions of the material world, whereas mathematics is concerned with abstract patterns that need not have any bearing on it. The distinction, however, is not always clear-cut. There is a large area of research intermediate between physics and mathematics, known as mathematical physics, devoted to developing the mathematical structure of physical theories.