Physics Frenzy: Battle of the Equations - by "Perimeter institute" 2022 - Article revieww

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#1 Energy-momentum relation

E^2 = (pc)^2 + (m * c^2) ^2
1. This relation simplifies to the famous E = mc^2 for objects at rest,
How do you decide that an object is at rest?
Are both the Earth and the Earth at rest?
2. illustrating that mass and energy are two sides of the same coin and can be converted from one form to another.
This conversion is that something physical or mathematical?

#2 Maxwell's equations

div.E = rho/Epsilon 0 curl x E = - dB/dt
div.B = 0 curl x B = mu 0 (J + epsilon 0 * dE/dt)
1. If you're viewing this on a phone or computer, you can thank Maxwell's equations for making it possible.
Equations don't make something possible.
It are the physical processes behind these equations that make something possible.
Of primary importance are the people who invented these physical processes, or machines.

#3 Schrödinger equation

ih * d psi(r,t) /dt = H * psi(r,t) /dt
1. The bread and butter of quantum mechanics, the Schrödinger equation describes the wave function of any quantum system and therefore tracks the system's observable properties over time
This equation raises two questions: The first question is difficult to answer because all material or mass contains elementary particles like protons, neutrons and electrons. In that sense all objects are quantum systems.
The answer on the second question is: No.
But that more or less brings you back to the first question. Where is the border line between: which objects can be described by a wave function and which type of objects not.

#4 Newton's second law

F = m * a
1. If you've ever taken a high school physics class, chance are you remember Newton's second law.
You should not remember Newton's law, you should try to understand for what type of physical processes they apply.
2. It describes how an object's motion changes when a force is applied.
The most important part is the parameter a, called acceleration, which means increase in speed.
What the equation describes is: when there is a constant force the increase in speed for each unit of time is constant. That means the actual speed increases.

#5 Noether's theorem

{H,I} = dH/dti = 0 ==> {I,H} = dI/dt = 0
1. Stated Simply
There are no simple laws.
2. Noerther's theorem shows that symmetries in nature are intrinsically linked to conservations laws.
The only way to show something is by performing experiments.
3. This profound insight has guided every branch of modern physics
There does not something exists as modern physics.
The evolution of any physical process is not guided by something, specific not by any law or any mathematical equation.

The main problem with this law is that the law is very difficult to verify by means of an experiment because the law does not contain any direct measurable physical parameter.

#6 Uncertainty principle

delta x * delta p >= h/2
A prime example of the quirks of quantum physics, the uncertainty principle says that there is a fundamental limit to how well we can pin down certain pairs of quantities , such as a particle's position and momentum
It should be understand, that the uncertainty principle is not a physical law. All physical processes are in no way influenced or guided by this principle.
Its main 'importance' is that it is an expression of our human limitations to measure something.
For example: if you want to measure the position of any elementary particle, at the moment of measurement, the position of that particle is influenced, implying that its speed cannot be measured.

#7 Second law of thermodynamic

Delta S >=0
The second law of thermodynamics explains why your coffee goes cold and maybe even why we grow old: isolated systems can't grow more ordered over time.
If your coffee always goes cold there must be a physical reason for this.
There must also be a physical reason that coffee can be hot.

*8 Einstein field equations

G mu v + lambda g mu v = (8 pi G / c^4) T mu v
Believe it or thee are 10 equations formulating the general theory of relativity - all packed into this tidy expression of how mater energy and the geometry of spacetime interact to produce gravity

#9 Dirac equation

E^2 = (pc)^2 + (m c^2) ^2

#10 Newton's law of universal gravitation

F = G * m1 * m2 / r^2
1. For a couple of hundred years, this equation reigned supreme, explaining why the apple falls from a tree:
This equation does not explain why an apple falls from a tree.
The apple falls from a three we because we humans impose that there is a force involved
But that does not actual answer the question what is this force.
2. any mass is attracted to another with a force that depends on the masses and the distance between them.
What that means if you have two identical objects they will attract each other with identical forces and they will each have the same.
But that does not answer the question why does this happen.
The only good answer is, that this behaviour is observed by accurate experiments, but that is not a physical explanation.

#11 Friedmann equations

(da/a)^2 = (8 pi G)/3 * rho - k/a^2 + lambda/3

d2a/a = (4 pi G) /3 (rho + 3p) + lambda/3

1. Want to know the fate of the Universe?
What I want to know is the present state of the Universe. That already is extremely difficult because all what we can observe is the past.
2. Look no further than these equations, which describe hoe the universe will evolve based on how much stuff (matter and energy) is in it and the current rate of expansion.
This equation raises more questions than it solves.
The main culprit are all the parameters used in the two equations.
Specific: a, da, d2a, p, rho, k, and lambda.
All these parameters have to be calculated based on observations
If these parameters are not known but have to estimated, the predicted value of the equations is low.

#12 Boltzmann's entropy

F = G * m1 * m2 / r^2
1. This definition, which is carved on Ludwig's Bolzmann's tombstone, suggests that entropy is a thermodynamic property, much like pressure or volume.
The fact that entropy is a thermodynamic property does not say much
2.This subtle idea helps explain how microscopic phenomena relate to the macroscopic world.
Explains what? and how?

#13 Planck-Einstein relation

E = hv = hc/Lambda
1. This equation ties together the wave and the particle nature of light,
2. showing that the energy of a photon is related to its frequency and wavelength
What this equation tells us is that a photon also has a frequency and that how higher this frequency the more energy the photon has.
The equation does not tell us to what extend the Energy stays constant, or a photon can loose energy and the frequency drops.

#14 Eulers formula

e^iPhi = cos(phi) + i sin (phi)
1. Perhaps not technically a physics equation, this formula establishes a relationship between trigonometric functions and complex exponentials.
It is even worse. For all our understanding of the physical processes we don't need complex numbers.
2. The famous and beautiful Euler's density is derived from this formula.

#15 Hamiton's equations

dp/dt = = -dH/dq , dq/dt = dH/dp
Hamilton's equations can be used to describe the motion of a bouncing ball or predict its trajectory into the basket. As long as the ball is not too small or moving too fast, this formulation of classical mechanics has you covered.
What is missing is the realation between the parameters used in this equation and measurable quantities.

#16 Stefan-Boltzmann law.

L = 4pi * R^2 * sigma * T^4
Star light, star bright, the first star you see tonight .. can be described by this equation, which relates a star luminosity to its temperature and radius.
This equation is confusing because the observed brightness of a star is both a function of the size of star and the distance of the star.
A different question is: how is the temperature of the star established?

Reflection 1 - General

Understanding the physical processes that take place in the Universe or here on earth does not start by studying 'the laws of nature'.
Starting point should always be observing identical processes and identifying what the differences are.
A second strategy is, even more important, by performing identical experiments, each slightly different.

Reflection 2 - Three experiments and One question

One of the most important ways to get a better idea to understand how science works is by performing experiments. The proposed experiment consists of 3 experiments and one question. The main purpose is to describe and explain each experiment.

The experiment with waterwheel

The next experiment is to build a dynamo. To do that we need 4 bar magnets.

The bar magnet

We all know what a bar magnet is. We use it to guide us where we are on the surface of earth, because all bar magnets points in the same direction, to the same point, namely the north pole. There exists also such a point at the opposite side, namely the south pole.
A magnet can be a large or a small iron bar, but at its smallest scale, each bar always has a north and a south pole. But that does not mean that each piece of iron is a magnet. To make a large bar magnetic all the individual iron particles have the be aligned in the same direction. There are two ways to do that: This will magnetise the piece in your left hand.
A whole different way is to use an electric current. They are identical.
We still have one more experiment to perform, to get a better idea how to make a bar magnet. This explains what a magnet is.
To recapitulate there are two ways to make a bar magnet.

The Motor - part 1

When you know what a magnet is you can also perform simple experiments to explain how a dynamo works and how a motor works.
First we will explain a motor. This describes the basic principle of a motor: creating movement with the aid of a power supply i.e. an electric current.

The Dynamo - part 1

The previous paragraph was an introduction how a motor works. Now we have that knowledge it becomes easier to understand what a dynamo is. We can now come to two important conclusions: Both these conclusions are each other complement.

The dynamo and the motor part 2

Now we have the full picture: On purpose I did not use words like mechanical and electrical energy. The emphasis in this document what is physical involved.

The final question

The final question is: what happens if you increase the total number of motors used.
The only way to answer that question is: Try it out When you try it out you will actual see what happens.

Most readers will say: That is simple. The more motors you will connect the slower the other motors will rotate.
But how do they know that?

  1. They have already tried it out, with an experiment and observed that result.
  2. They have read that in a book where the experiment is described.
    But that raises the question: How does the writer knows that that is the correct answer?
  3. They have read in a book that a waterwheel per unit of time produces a certain amount of energy Ein and that each motor per unit of time requires a certain amount of energy Eout. That means when Ein < n * Eout, with n being the numbers of motors, the performance of the motors decreases.
    But how do you know that?
  4. By using differential equations. But how do they know that?
The answers on almost all these answers is by performing actual experiments. By studying these experiments you can get more detailed information what is actual physical involved.
Experiments increase our understanding.

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Created: 26 July 2021

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