# Day 5: Conservation Laws and Symmetry

Symmetry and Nature are related on the deepest level . The Conservation

laws of Physics can be derived from considerations of symmetry of

different types . This means that since our Universe has certain kinds

of symmetry THAT IS WHY it has the corresponding kinds of conservation

laws .

Law of conservation of linear momentum is related to linear symmetry

or putting it in other words : conservation of p is related to

Law of conservation of angular momentum can be derived from

rotational symmetry . conservation of L is due to symmetry of theta.

In other words : since space has no preffered direction and is homogeneous

so it causes these kinds of conservation laws .

Law of conservation of Energy is because all eqns of physics are

same when we add or subtract time from them . conservation of E

is bacause of symmetry wrt t .

Also notice that these conservation,symmetry pairs cannot be measured

at the same time ie the Heisenberg’s uncertainty principle applies

to them .

so u cannot measure x and p at the same time .

u cannot measure E and t at the same time .

All the other conservation laws too are due to some or the other

symmetry . The conservation of charge for example , is related

to something called gauge symmetry .

See how deep symmetry is embedded in the fabric of the universe !!!!!

And that is the end of the Conservation Laws Week .

# Day 4: Conservation Laws Poetry

We had nothing planned for today so we are going to have a “fun” session.

I tried to find some poetry related to Conservation Laws . I found some interesting stuff . Here it is for you and the MHFL folks to enjoy :

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The first poem illustrates the Baryon family number conservation law .

We said yesterday that the proton is the lightest baryon . So it cannot decay into anything . Because to conserve the Baryon number it has to becay into a lighter baryon and that is not possible. Why the proton does not decay was a mystery for Physicists before they discoved this Conv law . And the Limmerick is by David Halliday of the “Resnisk and Halliday “

fame :

Proton Decay

by David Halliday

A proton once said, “I’ll fulfill

My long-term belief in free will.

Though theorists (may) say

That I ought to decay

I’m damned if I think that I will.”

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The second poem illustrates what happens what happens when an electron meets its antiparticle the positron . Both particles vanish and and only light is produced . The electron family number is conserved because the electron has +1 and positron has -1 and light has 0 . The process is :

electron + positron -> light

And Then There Were Photons

by William Rolnick

An electron, while trav’ling in space,

Met a positron there “face-to-face.”

The electron then sighed,

At the sight of his bride

And they “died” in a loving embrace.

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The third poem is very loosely connected to conservation laws . It is about Einstein and his famous E=mc^2

There once was a man with strange hair.

He said, “Anything other than physics, don’t care.”

He sat down with a book,

And he realized that E equals m c square !

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The last one was not probably written for the Conservation laws but the

spirit of this poem comes so close it :

TWO LENGTHS

TWO lengths has every day,

Its absolute extent —

And area superior

By hope or heaven lent.

Eternity will be

Velocity, or pause,

At fundamental signals

# Day 3: The subatomic particle Conservation Laws

Nothing exists except Atoms and Empty Space , Everything else is opinion

– Democritus

Today we will talk about the more “complicated” conservation laws .

These laws were discovered after people could make giant accelerators to “make” subatomic particles.

a) Baryon Family Number conservation : The larger/heavier elemantary

are called baryons . These are protons , sigma , neutron etc.

These particles are said to have a baryon number of 1 . Their

antiparticles are said to have a baryon number of -1 . The particles

that do not come in the baryon family have a baryon number of 0 .

proton + proton -> proton + sigma + kaon

is a valid physical phenomenon  because there are 2 baryons on before

the “reaction” ( 2 protons ) and 2 after it ( proton and sigma ).

All baryons(except proton) undergo spontaneous disintegration into

lighter baryons . But the proton is the lightest baryon . So it cannot

decay into anything . This is a very remarkable thing . The proton

is a very heavy particle and there are so many particles lighter

than it . The proton is almost 1837 times the weight of an electron .

But since it is the lightest baryon it CANNOT decay . It is stable.

Its enourmous energy is locked in it forever .

The stability of the proton accounts for the stability of nucleus and

the reason why atoms , molecules etc are formed and they stay .

The reason why we have a world .

b) Electron Family number conservation:

The electron family consists of only 2 particles . The electron and

its antiparticle the neutrino .

This number is also conserved .

neuton -> proton + electron + neutrino

shows that there are 0 electron family particles on the LHS . And there

are 0 on the RHS ( because the electron has +1 electron family no

and the neutrino has -1 electron family no . So they cancel ) . The

neutron and proton are baryon and have 0 electron family no .

c) Muon Family number :

There are two particles in this family: muon and its antiparticle .

And their number is also conserved .

This completes our list of the 7 conservation laws . In any “reaction”

/ phenomenon all these conservation laws must hold .

There is another conservation law : The conservation of strangeness.

Some particles ( called strange particles đź™‚ )  have a strangeness

number and it is partially conserved( conserved only in some processes

called “strong interactions” ) . We will not cover it here .

# Day II : The “simple” laws

Today we will take a look at 4 Conservation Laws : Energy , Momentum , Angular Momentum and Charge . Most of us have studied these laws in our school days . But we will also be answering the important question ” Why is the Electron stable ? “

a) Energy : How do you define Energy ? I dont know ! How about this :

” It is the ability to do work . ” Not very convincing . Anyway we

all kinda know what energy is . The formula is E = m (c ^ 2 ) .

Mass is a kind of Energy because it can be converted into Kinetic

Energy . This is a conserved quantity .

b) Momentum : Now this is trickier . Momentum is defined by mass times

velocity . This is a vector quantity and has to be added vectorically.

c) Angular Momentum : This is the amount of “circular” motion contained

in a body . There are two kinds of angular momentum :

i) Orbital Angular Mom : This is the momentum of a body that revolves

around another body .

ii) Spin : This is the momentum of a body that spins or rotates about

its axis .

The sum total of Orbital and Spin Angular Mom has to remain constant .

elementary particles( electrons , protons etc ) also have spin . But

this is not the normal spin . No one has ever seen an electron

rotating ! In elemantary particles spin is defined as some sort

of intrinsic angular momentum . This is nothing like we can ever imagine

But it is there .

d) Charge : The total amount of charge that a system contains is always

conserved . The smallest unit of charge is that contained by the

electron . We call it -1 .

We can have reactions like :

neutron(charge 0) -> proton( ch +1) + electron(ch -1) + antineutrino( ch 0)

The total charge on both sides of the equation is 0 .

These kinds of reactions are called decay . In the above reaction

the neutron has decayed into three particles .

The electron is one of the very rare particles that never decays !

The reason is that it is the lightest charged particle . So if

it decays into a set of smaller particles their charge will have to

add upto the electron’s charge . But there are no lighter charged particles

than the electron . So the electron NEVER decays . One experiment

estimated the life of an electron to be 10 ^ 25 years . which is :

10000000000000000000000000 years . Now this is huge !!!

Tomorrow we will do the more exotic conservation laws : Baryon family no

electron family no and the muon family no .

# Day 1 : The Philosophy of Conservation Laws

There are two kinds of laws in Physics : a) Laws of permission

and b) laws of restriction .

Lets take an example of a party with some people in it . People

keep coming and people keep going .

A law of permission may say that the rate of people coming to

the party depends on their economic condition(E) , the distance

from the venue of the party(d) and the no of invitations that were

sent out(n) and a physical constant (k )

so the formula can something like :

R = k * E * n * t / d

You can calculate the no of people coming between any two times

using this formula .

Most of the laws in Physics are laws of permission and tell u

how to predict something given the initial conditions .

The laws of restriction on the other hand restrict certain things

happening . Our conservation laws are laws of restriction .

Suppose at the party we had a law of restriction which said that

the number of kids ( below 12 ) always remains constant at the

party .

Now this law means that no matter how many people come in or go and

at what rates or at what times but the number of kids at any time has

to remain the same ( whether u count at 5:00 or 7:15 or 8 or whenever )

See we just have a sweeping statement about what cannot happen . This

statement tells us nothing about the rates of people coming or

going . And it does not tell us how many kids are at the party .

But it tells us that if u count the no of kids at any time

at all later times the no of kids is the same .

So this also means that no of kids coming in has to be equal to the

no of kids leaving .

That means that if 2 parents and one kid want to leave the party they

have to wait for any number of parents but only one kid to arrive !

The conservation laws are laws of restriction . In any system

some things have to remain a constant . These are our laws

of conservation .

Some people feel that the laws of conservation may be the definition

of any particular universe ie all laws should be able to be derivable

from these laws of conservation .

We know the following laws of conservation in our Universe .

They have NEVER been violated :

1. Conservation of Energy

2. Conservation of momentum

3. Conservation of Angular Momentum( including spin ) 4. Conservation of Charge 5. Conservation of Baryon Family number 6. Conservation of Electron family number 7. Conservation of Muon Family number .

Just these 7 .

The universe is like a a man with these 7 restrictions and has

only one course of action available .

Tomorrow we will talk about the first 4 laws .

# Conservation Laws week starts

VERITAS is going to have its first theme week . The topic is “Conservation laws ” . We will talk about the 7 most fundamental laws of Physics called the Conservation laws . The agenda for the week is :

Mar 6 ( Monday )  : The philosophy of COnservation Laws

Mar 7             : Conservation of Energy , Momentum , Angular Momentum

Charge( and the anawer to the question : “why is the

electron stable?”

Mar 8             : Conservation of Baryon Family number , electron Family

number , muon family number .

Mar 9             : < dont know >

March 10          : Conservation laws and symmetry

So Ladies and gentlemen , please fasten ur seat belts because we are going to go study the “fabric of the Universe ” . The deepest and the most powerful laws of Physics . The thought process of God .