What is the most easiest way to understand the interaction of subatomic particles?

The easiest way to represent and understand the interaction of subatomic particles is by using Feynman Diagrams.

In theoretical physics, this method is used as a pictorial representation of the mathematical expressions of the behaviour of subatomic particles. This method was given by one of the famous scientist and lecturer Richard Phillips Feynman.

 


These diagrams are used to calculate the most difficult equations using diagrams.
For example collision of two electrons: When two electrons collide they interact with each other and scatter apart. The interaction happens as follows:
When two electrons are brought together they repel each other and move apart. This repulsion takes place due to the exchange of the gauge bosons. Gauge boson exchange is otherwise known as the exchange of particle or information. These are virtual particles.
Here photons are the exchange particle involved.
The photon released from one particle hits another electron and changes its path.

Thus represented by the given diagram below:




Rules to draw Feynman diagram are:
1. Time is always pointed upwards.
2. Space is on the x-axis moving forward towards the right.
3. Always start the incoming subatomic from down
4. The interaction or the process is represented in between
5. And the outgoing subatomic particles are represented at the top 


The below figure illustrates the representation used to represent different particles involved:





The diagrams can be more complicated for the above-given example if we consider the emission of photons before or after the process or else emission and reabsorption of photons before or after the process.



There can be a particle and antiparticle formation during the exchange of photons.





These diagrams are used to find more accurate equations for the phenomena occurred.
Each time a photon interacts with a charged particle the chance of the phenomena to happen is less likely. Single emission of photon drops to 1% of 1% i.e, 0.01%.



For more detailed understanding from the basic level of  particles involved in the standard model we take the example of :








With the emission of a W boson, the quarks change their behaviour and form a different subatomic particle.




The interaction of particles is a very interesting and vast topic.

For further understanding visit:

https://arxiv.org/pdf/1602.04182.pdf

https://simple.wikipedia.org/wiki/Feynman_diagram

Physics has a history of synthesizing many phenomena into a few theories. 

-Richard P. Feynman

The theory which is loved by every scientist around - THE PERTURBATION THEORY

Yes, this theory is opted by almost all the scientist and observers of different disciplines especially the domains which cannot give well-defined experimental results. This approach was given by Paul Dirac in 1927. It was later named as the Fermi's golden rule.

Perturbation Theory is a mathematical analysis to find an estimated solution from the exact solution to the similar and simplest problem.

THE BASIC IDEA BEHIND THE PERTURBATION THEORY

This simple example can cheer you up:

While making the tea we don't take a weighing machine to calculate the amount of tea powder to add to the milk boiling. We just take an approximate amount which we feel perfect.

This happens in science too !!!

As to understand this amazing approach in a more comprehensive mode we have to know a little mathematics.

The sine series 

This is the graph of a sine function.

The series equation is 

  

Here we take the expansion of sine series.

For a given value of x and computing it in x or in x - (x^3)/3! we can get a fair answer.

This is how the perturbation theory works.

For more transparency, we take the example of the shape of the earth.

We are taught in our schools that the shape of the earth is spherical with a radius of 6400km

 But it is not exactly spherical if we consider all the factors into account.

The rotation of the earth around its axis influences the distance from the poles and the distances from the equator from its centre.

The distances from the poles and equator to the centre of the earth turns out to be 6357kms and 6378kms respectively. The diameter is of the Earth is 42kms fatter than it is tall. The difference is only about 0.3% or 1/300th part.

Recognizing the Antarctic ice sheet squishing the bottom of the Earth and other effects the North pole bulges upwards about 17mts and makes a bulge of 7mts in mid-southern latitudes.

This method has given countless unsolvable enigmas with satisfactory answers and is still being used by everyone around the world.

Hope it was helpful!

For queries comment in the comment section below.

“LEARNING IS NOT ATTAINED BY CHANCE, IT MUST BE SOUGHT FOR WITH ARDOR AND ATTENDED TO WITH DILIGENCE.” ―ABIGAIL ADAMS

CHARACTERISTICS OF LASER

LASERs play a very vital role in many fields and industries.

What makes it so special?

It's characteristics.

Lasers have:

1.High directionality

2.High monochromaticity

3.A high degree of coherence

4.High brightness

So let's understand each one in detail.

1. High directionality:

The lasers are made of active medium placed in between two reflecting resonator mirrors one which can partially reflect and the other which can fully reflect the light.
Any photon travelling in a direction away from the cavity axis reflects away by the mirrors within a few reflections and is thus not allowed to propagate further, thus the beam drawn from the output mirror is highly parallel and directional. The degree of directionality is expressed as the divergence. 
Minimum spot point: The curvature of the mirror confines the light within the cavity and causes the beam to narrow down to a radius wo  and this is called a minimum spot point.

The beam of divergence phi is equal to 1.22*wavelength / 2*wo

The divergence tells us how rapidly the beam spreads when its emitted.

For a laser, the beam divergence is 1milliradian.

The angle of divergence = (a2-a1) / 2*(d2-d1)

where d1 and d2 distances from the laser window and a1 and a2 are the diameters of the spot.

HIGH MONOCHROMATICITY:

The light emitted from a laser is monochromatic, that is, it is of one wavelength (colour).

The emission or absorption of the photons whose frequency lies between f and f+df which is denoted as spectral broadening.

The three important mechanisms which rise to the spectral broadening are :

1. Doppler broadening: The atoms emitting and absorbing photons are not at rest. They move with some velocity in a probable region within the atom. Thus the frequency of emitted radiation changes slightly and this is called doppler broadening.

2.Collision broadening: During the emission or absorption if the atoms get collided then resulting frequency gets effected and this is known as collision broadening.

3.Natural broadening: In solid materials emitting photons leads to damping of the amplitude of the wave train and this is known as natural broadening.

Spectral width or line width is a quantity which is used to find the degree of monochromaticity of light.        

                                change in wavelength =                                                        - (c* change in frequency) / ((frequency)^2)

      For lasers change in wavelength is approx. 0.001nm and can be made much narrower.

Theoritical Understanding Behind the LASERS

LASER stands for Light Amplification through Stimulated Emission. The theoretical basis was given by Albert Einstein and the first laser was developed by T.H. Mainmann.

LASERs work on 3 main processes.

They are Stimulated Absorption, Spontaneous Emission and Stimulated Emission.

Stimulated Absorption:

When a photon with energy hf, is incident on an electron of an atom present in the ground state, the electron excites to higher energy levels by absorbing the photon. This process is directly proportional to the number of electrons in the ground state. 

Spontaneous Emission:

The excited electron stays for 100 nanoseconds in the excited state and then emits a photon i.e, releases energy which is equal to the difference between energies of the higher energy level and the minimum energy level, to get back to ground state. This process is directly proportional to the number of electrons in the excited state.

Stimulated Emission:

When the electron moves to a metastable state from the excited state by releasing no radiation but some ignorable amount of energy it stays for more than 100 nanoseconds. So then when we incident a photon towards the electron in the metastable state it emits a photon which has a similar phase with that of the electron incident. This creates coherent light waves with high directionality.

This process is directly proportional to the number of electrons in the excited state or in the metastable state.

The principle behind the working of the principle is population inversion.

 

POPULATION INVERSION: 

 

In general, an atom has more number of electrons in the ground state than in the higher energy levels. But after excitation of more number of electrons into the higher energy levels they settle down in the metastable for a longer time and that is known to be population inversion. In simple words, there will be more number of electrons in higher energy level than in lower energy levels.

As the Stimulated Emission is directly proportional to the number of electrons in the metastable state this process enhances and accelerates the process.

This population inversion can be achieved by pumping mechanisms or techniques. They are :

 1.Optical pumping

 2.Electrical discharge pumping 

 3.Chemical pumping

 4.Injection current pumping

Einstein's coefficient (EC):

Let the number of electrons in the ground state is N1 and the excited state is N2.

Let energy density p(f)= nhf where n is the number of photons per unit volume at frequency f such that E2-E1=hf.

Absorption = B12*N1*p(f)

where B12 is EC of absorption.

Spontaneous Emission = A21*N2

where A21 is EC of spontaneous emission.

Stimulated emission = B21*N2*p(f)

where B21 is EC of stimulated emission.

Absorption is an upward transition and the other two are the downward transition processes of the electron.

In equilibrium both the transitions become equal i.e,

 B12*N1*p(f) = A21*N2 +  B21*N2*p(f)

 B12*N1*p(f) -  B21*N2*p(f) = A21*N2

 p(f) [ B12*N1 - B21*N2] = A21*N2

 p(f)*B21 [ N1 - N2] = A21*N2

 p(f) = (A21/B21)*(N2/N1-N2)

 p(f) = (A21/B21)*(1/(N1/N2)-1)

 

 From Maxwells Boltzmann distribution law :

N1/N2 = e^(E2-E1)/KT

p(f) = (A21/B21)*(1/(e^(E2-E1)/KT-1))

p(f) = (A21/B21)*(1/(e^(h(f))/KT-1))   ---------eqn1

By comparing  eqn1 with Plank's radiation formula we get :

The above relations are referred to as Einstein's relations.

This is the theoretical explanation behind the lasers.

For more interesting and easy explanations of physics comment in the comment section.

Energy is liberated matter, matter is energy waiting to happen

WHAT DOES UNCERTAINTY ACTUALLY MEAN?

       

 HEISENBERG'S UNCERTAINTY PRINCIPLE  

It becomes a bit perplexing and puzzling to know that if you are reduced into a quantum sized body then your position and momentum are not certain. If you are not aware of anything like this before then it surely puts your mind into the blank area where this statement raises numerous questions and some don't even agree with this.

But this statement is the foundation of the quantum theories which have remarkably and marvellously changed the entire world's thinking towards science.

It looks nonsensical to say that you are present everywhere in a probable region and your position is uncertain till someone measures it at a certain time. But it is true no matter what we think.

The statement says that we cannot know both the position and momentum of a subatomic particle simultaneously.

This theory says that the change in momentum times the change in position is always greater than or equal to planks constant times 1/4(pi).

This principle also holds true for conjugate pairs of physical quantities such as Energy and time and also angular momentum and angle.

This principle stands as the base for the whole quantum physics thus this fundamental theory is very important to understand the more complicated theories.

For more interesting topics explanations suggest me in the comments section.

“Look up at the stars and not down at your feet. Try to make sense of what you see, and wonder about what makes the universe exist. Be curious.” 

What does Imaginary Time mean?

Imaginary time is not like the Real-time we experience in our day to day life which is classified as past, present and future. It is a very bizarre idea introduced by Stephen W.Hawking.

Imaginary time is right angled to real time. It was introduced to eliminate the theory of Creator of God from the Universe.   

It is used to remove singularities which avoid the laws of physics to break. It can be seen in MINKOWSKI SPACE-TIME model which was adopted by the theory of relativity.

Real-time has a beginning which is called a big bang and an end which is called a big crunch. But Imaginary time has no beginning and no end rather it has a closed surface like a sphere. We do not have a start and end for a sphere.

The imaginary time direction could be from the south pole. As one goes towards the north from the south pole, the latitudes which are uniformly placed inflates and reach the maximum at the equator and again contract to a single point at the North pole. Even though the universe is zero at the poles it would not be a singularity. This helps us to understand the origin of the universe in the imaginary time can be at a random regular point on the spacetime.

We now consider Imaginary time as a new dimension added to the regular time.

Stephen Hawking popularised this concept in his famous book " The Brief History of Time". 

Can purchase this book here:

 https://www.amazon.in/Briefer-History-Time-Stephen-Hawking-ebook/dp/B00351YEZS?tag=googinhydr18418-21&tag=googinkenshoo-21&ascsubtag=_k_Cj0KCQjwxYLoBRCxARIsAEf16-tDBN60xipDXHEAMkuQGIQ4eXGWHz7WxMUx1t-A-u8jh0CSGUd1YAUaAvtyEALw_wcB_k_&gclid=Cj0KCQjwxYLoBRCxARIsAEf16-tDBN60xipDXHEAMkuQGIQ4eXGWHz7WxMUx1t-A-u8jh0CSGUd1YAUaAvtyEALw_wcB

He personally thinks that individual particles can travel through imaginary time and arrive back at an earlier real-time but not that people can travel back in time like in films such as Back to the Future.

Do you agree with him?

Do you think time travel is possible?

Comment below.

All of physics is either impossible or trivial. It is impossible until you understand it, and then it becomes trivial.

What are Gravitational Waves ?

Gravitational Waves are assumptions from the curious minds ever, Albert Einstein. They are the ripples caused in space-time sheet due to the motion of masses.

Gravitational waves are produced whenever masses accelerate, changing the distortion of space-time fabric. Everything with mass and /or energy can cause ripples. As gravitational waves rolls by it will squeeze and stretch anything in its path but in a very infinitesimally small change which makes it extremely difficult to detect.

So to detect these ripples we use the idea of the time taken by the light to travel is more when the distance increases and less when distance decreases, which is what the principle used in the interferometer. Thus LIGO experiment comes into the picture.

LIGO - Laser Interference Gravitational-wave Observatory.

Here 4km long tunnels are set up where lasers are used to measure the change in distance between the ends of the tunnels.

So when Gravitational wave comes in contact, it elongates space in one direction and squeezes in another direction. By measuring the interference of lasers physicists can precisely conclude about these waves and its incredible as we surely need a smart analysis as it can easily be confused with the other existing waves and disturbances as they are very minuscule.

 Here is the data recorded from LIGO Livingston and LIGO Hanford.

Gravitational waves are helpful in detecting the universe in a whole new way. 
They are significant.


So to know more deeply :
https://physics.aps.org/featured-article-pdf/10.1103/PhysRevLett.116.061102






“The important thing is not to stop questioning. Curiosity has its own reason for existence. One cannot help but be in awe when he contemplates the mysteries of eternity, of life, of the marvellous structure of reality. It is enough if one tries merely to comprehend a little of this mystery each day."

How is Schrodinger's cat dead and alive?

SCHRODINGER'S CAT is a thought experiment by Erwin Schrodinger to make the world understand that quantum particles exist in a superposition.

Quantum theory states that quantum particles can achieve more than one state simultaneously.

SCHRODINGER'S CAT EXPERIMENT:

If we put a cat in a strong box with a radioactive sample which has 50 per cent of chances of decaying and closes the box, it is very confusing for the observer outside to guess whether the cat is dead or alive after a period of time.   

         

So before opening the box, we can say that the cat is in superposition. That is it's in the state of both dead and alive. But if we open the box and observe we may find the cat in only one state that is the state of dead or alive.



This means that quantum particles exist in different states but when observed takes a single state.
And according to multiverse theory or many worlds theory, the universe achieves all the possible outcomes by splitting itself and making its copies. So from the thought experiment, we can say that the cat is alive and dead in the split universe. 
That means the quantum particles achieve all the possible positions one in each copy of the universe.


For further understanding :
https://www.aps.org/units/maspg/meetings/upload/franson-021815.pdf
https://www3.nd.edu/~jspeaks/courses/2007-8/20229/_HANDOUTS/quantum-mechanics.pdf

Physics tells us observations can't be predicted absolutely. Rather, there's a range of possible observations each with a different probability.     

Schrodinger Wave Equation explained in simple words

Newtonian Mechanics don't work in the quantum world.
Quantum objects are very microscopic that they can't be located but they can be probably located. And this probability can be determined by using wave functions of the quantum particles




Wave function gives us the probabilities of where the electron is likely to be. The act of not knowing where the electron is, allows its probability distribution to be spread out over a large space kind of wave. Therefore wave function is the function which describes the wave shape of the probability distribution of the electron.


The Heisenberg Uncertainty principle says that we can't predict the exact position and momentum of the quantum objects. But we can know about things like Energy levels and wave functions.
THE SCHRODINGERS WAVE EQUATION :

                                                                                                          = Wave function (psi)                    E= Energies of the electron is allowed to have 

E[(psi)(x)] = The energy levels of the wave function of the electron 

If we consider an electron inside a box where it is confined to only a few frequencies the wavefunction always needs to be 0. In other words, the electron has 0 probability to be found outside the box.

 

And we know the famous Einsteins equation  E=hf where h is Planks constant. Since only a few frequencies are allowed only certain energy levels are allowed.
That is what is meant by QUANTISATION.

Derivation :

For more detailed information :
http://physics.mq.edu.au/~jcresser/Phys201/LectureNotes/SchrodingerEqn.pdf
http://lejpt.academicdirect.org/A26/031_048.pdf

"No one undertakes research in physics with the intention of winning a prize. It is the joy of discovering something no one knew before."

Casimir Effect

Scientists are often astonished observing the moment of things around, on their own with no visible force acting on them. 
When two mirrors which are later called the Casimir plates, placed in a strong box maintaining one-atmosphere pressure at 100 nanometers apart move towards each other with no well-known forces between. Here comes the Casimir effect into the picture.
This was discovered by Hendrick Casimir in 1948 and named after him.

To understand the Casimir effect we have to first know these bullet points:

• Heisenberg's Uncertainty Principle proposes that both the position and momentum of a subatomic particle cannot be determined simultaneously.                                                                                                                                                   And also energy and duration cannot be predicted simultaneously. Thus particles don't have both nill energy and duration. Therefore particles that don't exist can even have a high chance of having huge energy causing duration and forcing them to exist for a very short period. These are called virtual particles which further turn up into matter and antimatter to annihilate rapidly.
• Wave-Particle Duality says us that particles can turn into waves and again into their particle nature.
• Stationary wave theory tells us that only a finite number of waves can exist in closed space which is generally termed as Harmonics.
• Infinities are distinct which means decimal infinities are greater than real number infinities. Thus a number of waves exist outside the mirror
• Force exerted is generally defined to be the change in momentum times the inverse of time. We know that there are a number of virtual particles outside the Casimir plates than in between and thus they exert more force than the particles in between them.