Teach clearly!

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Contents

What teachers can learn from managers

A successful business manager summed up his approach in the following way: "Simplify, execute, grow."

A famous teacher, Hartmut von Hentig, summed up his aim thus: "To fortify people, to clarify things."

Managers ensure that ideas and decisions are clear and that people have a future. So do teachers. Here are a few examples on what this means for the teaching of physics.

On infinite quantities

Numerous physicists finish their university studies without knowing that whenever a reasoning or a calculation yields a result of infinite size, then the reasoning and calculation is wrong. There are no exceptions. Nothing is ever infinite in nature. How could it be? The statement that something can be infinite cannot be verified; and it always easily falsified. Every single experiment falsifies it. In other words, 'infinite' is a false belief, an ideology, and never a fact. Some are so stubborn that the the point is best made like this: 'infinity' is always a lie.

If you falsely believe that infinity exists in nature, find the error in your assumptions - especially if you give lectures.

On force

Numerous physicists finish their university studies with a bizarre concept of force. In physics, force is the change of momentum with time, and momentum is a conserved quantity. Conservation means that a change in a volume of space can only happen through flow out of that volume. In other words, physics students need to learn that any force is due to the flow of momentum out of a closed surface.

Momentum is like electric charge: it is a quantity that is conserved, can accumulate, and can be exchanged. The change of electric charge is called current; the change of momentum is called force. The difference between charge and momentum is that charge is a scalar, and momentum a vector. But both current and force always imply a surface through which they are flowing. By far the clearest explanation of this point is the secondary school physics course by Friedrich Herrmann, found at http://physikdidaktik.uni-karlsruhe.de/ where it can be downloaded for free in several languages. To make this point especially clear, Herrmann introduces the unit "1 huygens=1 kg m/s" for momentum, and defines 1 newton as 1 huygens/second.

If you do not believe that force implies a flow through a surface, look at the equation for continuity in its integral form. The percentage of physicists who get this wrong is surprisingly large. Check yourself - especially if you work on general relativity and falsely believe that force does not exist as a concept.

On the wave function

Numerous physicists finish their university studies with a bizarre concept of wave function. In physics, the wave function describes the state of a quantum particle. In non-relativistic quantum mechanics, a wave function is, as Feynman explains, a little arrow at each point in space. Equivalently, the wave function is a cloud of rotating arrows. Students need to learn this.

If you do not have a intuition for non-relativistic wave functions, take some time to explore the website by Bernd Thaller, on visual quantum mechanics, at http://vqm.uni-graz.at/ and read his two books on the topic. And read Feynman's book "QED - the strange theory of light and matter". Check yourself - especially if you falsely believe in "many worlds" and similar nonsense.

On Feynman and simplification

Numerous physicists finish their university studies without learning anything form the career of Richard Feynman. When he was young, he was a calculator, i.e., a physicist who believed that calculation was the essence of physics. With age, he changed completely, and stressed clear concepts and foundations over detailed calculations. Only then did he became the famous teacher and popularizer of physics that he is remembered for. The older Feynman, like Einstein, had as motto: "simplify, simplify - without sacrificing truth". The same motto is helpful in all other sciences, in business, and in life in general. Students need to learn this.

If you do not believe the importance of simplification, read Feynman's book "QED - the strange theory of light and matter". The number of established physicists who follow the opposite path - obfuscation by calculation - is large. Check yourself - especially if you spent some time on string theory and falsely believed that you could do so without anybody ever clarifying its basic foundations.

On action as measure of change

Numerous physicists finish their university studies without a clear idea what action measures. Action measures the amount of change occurring in a system. The more changes, the larger the action. In fact, action should be renamed change.

If you have no intuitive idea for the concept of action, explore the issue and convince yourself - especially if you give lectures.

On action as an observable

Numerous physicists finish their university studies without knowing that action is a physical observable. Students need to learn this.

Action is the integral of the Lagrangian over time. It is a physical observable: action measures how much is happening in a system over a lapse of time.

If you falsely believe that action is not an observable, explore the issue and convince yourself - especially if you give lectures.

On relativistic invariants

Numerous physicists finish their university studies without knowing that the Planck constant h, the Boltzmann constant k, and the gravitational constant G are - like the speed of light c - observer invariant. Students need to learn this.

If you falsely believe that these constants are not relativistic invariants, explore the issue and convince yourself - especially if you give lectures.

On maximum force and the difference between fact and belief

Numerous physicists finish their university studies without knowing that there is a maximum force c^4/4G and a maximum power c^5/4G in nature. Students need to learn this.

First of all, students need to know what a force is; this issue is treated above. The maximum values are only realized with help of horizons. In simple words, horizons appear when mass is compressed to its Schwarzschild radius. Observing or realizing higher force or power values would imply reaching beyond a horizon. These maximum values, discovered independently by various people over the years, provide a test of logical reasoning for every physicist.

Some people do not believe in such a maximum value, but fail or even refuse to present a way to exceed it. They exchanged reality for a dream world.

Another class of people claim to have found a way to produce or measure a force value larger than c^4/4G without creating a horizon. Just check. They either overlooked a horizon or they do not reach the maximum value. For example, some people claim to be able to exceed the force limit c^4/4G with the help of boosts; well, in relativity, no boost can increase a force value to more than the force value seen by a comoving observer. Just check any book on special relativity.

Another example are people who think that forces simply add up. Well, this is true, as long a space is flat. But the systems producing a force curve space with their mass or energy. If you try to add up the force from so many systems as to exceed the force limit, you will see that the producing systems disappear into a black hole, or behind some other horizon. Test it by yourself.

In summary, if you falsely believe that maximum force and power do not exist, explore the issue and convince yourself - especially if you give lectures.

On Planck's natural units - 1: the foundations of physics

Numerous physicists finish their university studies without knowing that all observables are based on Planck's natural units. Students need to learn this.

Planck discovered in 1899 that all results of measurements - all units, all numbers, all quantities - can be constructed from the invariants c, G and hbar. This is the essence of our observation of nature. The business of modern physics is to find out where these multiples come from - and not much more! Concretely, modern physics has to find out where the coupling constants, the masses of elementary particles and their mixing angles come from. They are all multiples of Planck's natural units. (Note: these are the only multiples that are not understood so far; all others, and thus all other measurements, are understood.)

If you falsely believe that Planck units are unimportant, explore the issue and convince yourself - especially if you give lectures.

On Planck's natural units - 2: the impossibility to vary them

Numerous physicists finish their university studies without knowing that all observables are based on Planck's natural units. Students need to learn this.

All standards of measurement and all results of measurements are constructed from the invariants c, G and hbar. "Changing" the value of one of these quantities, has NO effect on our description of nature, because it also changes the measurement standards. There is no way to detect variations in G, hbar or c - neither variations over time nor dependences on location - because these changes would be compensated by the changes of the relevant measurement units and standards.

If you falsely believe that variations of c, G or hbar can be measured, explore the issue and convince yourself - especially if you give theory lectures.

On Planck's natural units - 3: the impossibility to exceed them

Numerous physicists finish their university studies without knowing that Planck's natural units are limits. Students need to learn this.

No single experiment yields local energy speeds larger than c, action values smaller than hbar, or forces larger than c^4/G; the same is valid for other combinations of them. This is the most hidden aspect of 20th century physics. For example, particles cannot have energies larger than the Planck energy.

If you falsely believe that c, G, hbar or their combinations can be exceeded, explore the issue and convince yourself - especially if you give lectures.

On pupils

A teacher should like his pupils. Pupils that are difficult are pupils that suffered a lot.

If you have trouble with your pupils, recall their suffering; then imagine them when they will be 50 years old. After that, do what is the most appropriate for them.