Symmetry for dummies!

Hi,
as I said, I will continue with the explanation of what I mentioned in some earlier posts. Today I will try my best to learn you what physicists mean when they say something about “symmetry”.


First of all, when you say symmetry you probably mean that it is the same on both sides.

On the next picture you have some shapes with the right and left “lines of symmetry”.
This means that you can flip them around this line and they will be exactly the same pictures.

Square has more than one line of symmetry, there are four of them [1].

This is what we think as symmetry but physicists use it in more kind of complicated way.

When somebody makes experiment with coca-cola and candy [2] it will explode. And it will explode in New York, Prague, under water, upside down if you do it properly and even in space. This is symmetry, it does not matter where you do the experiment. But it does matter what you do it with, if you would have used water instead of coca-cola, or chocolate bar you would see that there is no symmetry [2.5]! Because it is not going to work!

When we talk about particles we can say that there is a symmetry in them, for example you can have 3 quarks, labeled as Paul, Rick and Nick. It does not matter which one you will use, because all of them have the same properties! This is symmetry all quarks are same, all electrons are same and so on.

There is a symmetry in fundamental forces. For example in strong nuclear force there is symmetry in quarks and their colors [3]. It does not matter how you label one of three quarks, it can be red, green or blue.

Also charged particles are created in pairs. This means that you have to conserve the charge so if you create electron you must create positron or something else with positive charge.

Only weak nuclear interaction of all fundamental forces has special kind of symmetry. Weak force is the only force which makes difference between particles which are right and left handed.

Such a particles  are in pairs:

  • quark u ←→ quark d
  • quark c ←→ quark s
  • quark t ←→ quark b
  • electron ←→ electron neutrino
  • mion ←→ mion neutrino
  • tauon ←→ tauon neutrino

This is also called the breaking of parity.

So weak interaction breaks symmetry and behaves differently with right and left handed particles while other forces do not do this, take for example gravity, everything is attracted by it and it does not matter if it is quark u or quark d.

Of course those particles are diametrically different their mass varies a lot, but this is only because of what is called: Higgs field, and I am going to talk about it another time.

Dragallur


 

[1] Star has 5 lines of symmetry, triangle has 3 and arrow only 1.
[2] I do not know if it is in English mentos.
[2.5] This is also called “broken symmetry” if it would not be broken, in this analogy anything would work as the mentos candy and there would be no difference between coca-cola and oil.
[3] Quarks have colors as I mentioned in last post and also in post about strong nuclear force.
[4] Maybe you remember from chemistry how you were filling the orbitals with pairs of electrons: ↑↓. Those arrows mean that one electron has negative and second positive spin (but still the same value: 1/2  .. -1/2)

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