# Why Are The Laws of Physics Not Symmetrical Between Left and Right?

1. Jun 5, 2013

### AlfieD

Greeting people of Physics,

Why are the laws of physics not symmetrical between left and right, future and past, and between matter and antimatter? I.e., what is the mechanism of CP violation, and what is the origin of parity violation in Weak interactions? Are there right-handed Weak currents too weak to have been detected so far? If so, what broke the symmetry? Is CP violation explicable entirely within the Standard Model, or is some new force or mechanism required?

Kind Regards,
AlfieD

2. Jun 5, 2013

### ZapperZ

Staff Emeritus
I'm not sure if anyone can give you a reason about the "why" part. But you have a misunderstanding here.

The laws of physics ARE symmetrical in the symmetry that you mentioned - except for some. That's the most important aspect. CP-symmetry is obeyed in the overwhelming majority of events except for rare decay cases, for example.

So it is incorrect to say that the laws of physics are not symmetrical. The more accurate question here is why it isn't symmetrical in these few cases.

Zz.

3. Jun 5, 2013

### Simon Bridge

I think the short answer to this one is "nobody knows".

The future past thing is a bit different though isn't it?
I think Newton's laws are time reversible, and Einstein Relativity ... but the distinction appears to be tied up with the way memory works, and entropy.

On the whole, I would prefer to see how you have attempted to find the answers yourself, and at what education level, before going into detail. Saves writing.

4. Jun 5, 2013

### AlfieD

Simon, to be honest, I haven't really attempted to find any answers myself; I wouldn't know where to start other than via the use of the famed 'Google Search'! As to what education level, I'm in Year 8 (Physics being my best and favourite subject; obviously) and do A-Level Physics on Fridays and I'm just curious as to how things work etcetera.

Kind Regards,
AlfieD

5. Jun 5, 2013

### The_Duck

There are two parameters in the Standard Model that each produce CP violation: http://en.wikipedia.org/wiki/Cp_violation#CP_violation_in_the_Standard_Model

In the SM the SU(2) part of the weak interaction only couples to left-handed fermions, and not to their parity partners, the right-handed fermions. This is the mechanism of parity violation. The SM doesn't provide an explanation for why the weak interaction should behave this way.

Not in the SM.

This seems to assume that P used to be a good symmetry and then it got spontaneously broken. I don't think there's any reason to believe the P was ever a good symmetry, though.

All existing accelerator measurements of CP violation can be explained as coming from the two CP-violating parameters of the Standard Model. One thing the SM doesn't seem to explain is the observed predominance of matter over antimatter in the universe, assuming the universe started out with equal amounts of both. I believe that this is thought to require new physics, as there is not enough CP violation in the SM to produce the observed abundance of matter.

6. Jun 5, 2013

7. Jun 5, 2013

### HomogenousCow

Certain equations don't stay the same when you make the transformation x --> -x'

8. Jun 5, 2013

### The_Duck

As the Wikipedia page mentions, the neutrino mixing matrix can have a CP-violating phase.

9. Jun 5, 2013

### Bill_K

Ok, thanks. The phase parameter in the PMNS matrix has not been seen yet, but I'm surprised to read that there's a proposed experiment (LAGUNA) that has a reasonable chance of detecting it.

10. Jun 5, 2013

### Simon Bridge

11. Jun 6, 2013

### AlfieD

Could you please explain matrix elements?

Kind Regards,
AlfieD

12. Jun 6, 2013

### Fredrik

Staff Emeritus
I wrote a FAQ post about it recently. You can find it https://www.physicsforums.com/showthread.php?t=694922 [Broken], but you will need to study more math before you can understand it. In particular, you need to understand vector spaces, linear independence, and bases for vector spaces, the kind of stuff that's taught in courses on linear algebra.

Last edited by a moderator: May 6, 2017
13. Jun 7, 2013

### Simon Bridge

That's what I thought :)

At "A-level"? That would take a while. Students normally meet these concepts in their second year of University. I might be able to give you an idea - at the risk of giving you the wrong one.

Hopefully you've met matrixes in math already?
And you know about writing a vector as a column of numbers - and you've seen matrixes transform vectors when you multiply them?

You can make make a vector out of a function by expanding it in a basis ... for example, if:
$$f(x)=\sum_{n=0}^N c_nx^n$$ ... then I can represent f(x) in the "polynomial basis" as an (N+1)-dimensional column vector of all the $c_n$'s. i.e. if $f(x)=5x^5+3x^2$ ... then that would be: $f=(0,0,3,0,0,5)^t$ as a 6D vector.

I don't have to use the polynomial basis - there are lots of them, some more useful than others.
The main advantage is that transformations of the function come from pre-multiplying the vector by a matrix... this can make all kinds of math involving multiple integrations by parts etc much easier.

In fact - if we define "vector" in terms of what it does rather than how we write it down, then a function actually is a vector and all we've done is changed the way it is written down.

If quantum mechanics the functions are normally complex-valued, so there's extra tricks for handling them. But in particular, if you know any quantum mechanics at all, you can use the eigenfunctions of an operator as a basis.

Have you met complex numbers?

If I have a set of complex numbers $\{z_n\}$ then I can multiply any two of them like this $a_{i,j}=z_i^\star z_j\; 0\leq i,j \leq N$ then all the $a_{i,j}$ will be real, which is handy, and I can represent them as the elements of an NxN matrix A.

If you examine A it has some handy properties. i.e. an element from the diagonal has the property: $a_{i,i}=|z_i|^2$.

I want to stop there - take a breath - it's a lot to take in. These concepts are usually introduced slowly with exercises at each step and I've glossed over a lot of stuff. The point here is to give you a glimpse, not to provide a complete picture, so be cautious about drawing conclusions.

Should give you an idea of what you are in for :D

In the meantime, treat "matrix element" as a special jargon.

14. Jun 7, 2013

### AlfieD

Will do! And thanks for the detailed answer, I'm sure it has probably helped me!

Kind Regards,
AlfieD