Particle Physics for n00bs-Introduction to Standard model & Quarks

A long, long time ago in a galaxy far far away..some intelligent creatures discovered that an atom is NOT the smallest or from the literal meaning of 'atom' ( in Greek) the indivisible particle in our universe.

So these creatures found out that the aim can be further divide into protons, neutrons and electrons, but this was not the end of the story, in fact it was the beginning of the most confusing, wierd and one of the least elegant theories in the history of science-The Standard Model. Despite of  its enigmatic features it still remains one of the most successful theories that could explain 3 out of 4 of the fundamental forces in nature.

So according to the standard model there are fundamentally 2 kinds of particles fermions and bosons. One of the major basis of this classification is the kind of equations they obey, fermions obey the Dirac-Fermi statistics while bosons obey the Bose-Einstein statistics, and are, objectively speaking the 'force carriers', (so, yeah they belong to the skywalker family because the force is strong with them.)

First let's take up fermions. These include the particles most of us are acquainted with such as protons, neutrons and electrons. These particles are characterised by a half integer spin. Just to clarify, here spin doesn't mean that the particles are actually spinning, in fact we can't say anything about the conventional spinning of particles as we treat all of them as point masses and hence there is no meaning of rotation or spinning in the case of point particles. Now these fermions are further subdivided into two categories- quarks and leptons.

(From this point the following post will be dedicated solely to quarks.)

So these fascinating particles called quarks come in 6 different 'flavours' (yeah, that's what they call them.) These are up, down, strange, charm, top and bottom. Pretty awkward names for something you can't even see or 'taste', maybe they ran out of baby names...all fermions in the standard model are divided into 3 generations. Up and down quark belong to 1st gen, strange and charm belong to 2nd gen, and top and bottom belong to the 3rd gen, the basic difference between these generations is that the particles belonging to the 3rd gen. are considered to be more heavy,unstable and exotic. In fact up and down quarks are considered to be most stable in the quark family due to their less mass compared to others.

But how do we know these quarks even exist? You might ask that our whole standard model is based upon quarks and till now we haven't even observed a single quark in its own? Quite surprising isn't it. But what if I tell you it's not, scientists are so sure about the existence of quarks because we have observed their properties. We know that they exist because they produce some noticeable effects in their surroundings. For example it is observed that even neutrons possesses  magnetic moment, but how do they do it without having any charge? The answer is that they are made up of quarks which do have charges, a neutron is made up of 2 down quarks and 1 up quark, the charge on the down quark is -1/3 and the charge on the up quark is +2/3 which explains why a neutron as a whole is neutral but still possesses magnetic moment.

Now these quarks 'combine' to form hadrons. Hadrons are subdivided into 2 types-mesons and baryons. These hadrons can be defined as a group of quarks held together by the strong force ( one of the 4 fundamental forces). Baryons are the particles most of us are acquainted with-(neutrons and protons). Baryons are basically 3 quarks held together ina group and mesons consist of 2 entities-1 quark + 1 antiquark. Hey but wait, that doesn't look right. A quark and an antiquark should have  annihilated each other, not live together peacefully. This argument is correct to some extent, because most mesons are considered to be less stable than baryons and have a short life span. But it is not entirely true that the quark-antiquark pair annihilate, this is only the case in some mesons such as the neutral pion which is formed of a quark and its own antiquark. In fact most of the mesons are formed by a quark and an antiquark of some other quark. But they also decay due to weak interaction.

Pretty interesting,  isn't it? Fun fact before I leave- the name "quark" was taken by Murray Gell-Mann from the book "Finnegan's Wake" by James Joyce. The line "Three quarks for Muster Mark..." appears in the fanciful book. Gell-Mann received the 1969 Nobel Prize for his work in classifying elementary particles.

That's it for today. Stay tuned for the next part....

The Twisted Space-Part 2

So, in my last post I asked some questions for you to ponder upon, if you missed it you can scroll down and check the post Twisted Space Part 1 (you might need it ).
You may be thinking  that we might need some  3-d figure  and then maybe we can see for the discrepancies in its actual measured quantities and theoretically calculated quantities ( such as surface area) like we did for the triangle and the circle. If this was your thought process then you are on the right track. Let's do some analysis to narrow down our search for this 3-d figure. The thing with 3-d curvature is that it will have different values for different orientations i.e you might find a different curvature of space if you measure it in vertical direction and then maybe in horizontal direction. The curvature is said to have components along different orientations, just like a straight line in Cartesian plane having different components along the coordinate axes (obviously depending upon the angle). So it is advised to take a uniform geometry that can give us the average value of curvature in that region of space. That narrows down our search to 1 common 3-d figure- lo and behold........THE SPHERE! ........hey but wait, why are we even doing this, I mean why will  space even  have a curvature in the first place? The answer to this was given by einstien in order to explain gravity.the idea behind this is that any mass placed in space creates a curvature, and with curvature comes a gradient, and like any other phenomenon( like osmosis) a mass would like to go from a higher gradient to a lower gradient, hence by this notion a lighter object (which causes less curvature) would like to move towards an object of greater mass ( resulting in greater curvature).Here is a classic representation of curvature of space visualised in 2-d

                                   
But to give you a true idea of what a curvature in 3-dimensions would look like here is a nice visualisation which shows a concentration of "grids" around a mass, the grid here represents space.

                                 

Pretty interesting, isn't it?With the above facts known, it is obvious to think that a larger mass will have a larger curvature and in turn the deviation from Euclidean geometry will also be more. So this implies that the calculated radius from measuring the exact surface area will be much different from the actual measured radius. To quantify this fact einstien also gave the following formula:
Here r(meas) means the measured radius
M is the mass of the object( due to which there is a curvature)
A is the exact measured surface area
G and c have their usual meaning.

The Twisted Space-Part 1

Almost everyone has come across the  terms like space time curvature,gravitational lensing,black holes, singularities, etc etc. But what do they really mean? Are they just some sophisticated gibberish?

( ha see what I did there.....sophisticated gibberish... Oxymoron( if you didn't get it)) Or do they have some deep meaning that may even alter our perspective about reality. Let's explore !

Let's start with a classical analogy( it's good to have classical analogies as we can easily conceive it, human mind finds it easy to to recreate something that it might have experienced). Have you ever observed the longitudes of earth intersecting with the equator. You might have not observed it but they intersect the equator at right angles and still manage to intersect at the poles. This clearly means that the triangle formed by two  longitudes with the equator have a sum of angles greater than 180 degrees! And in fact if you measure the angle between two longitudes that intersect at right angles at the poles also, you will find that the sum of angles formed by these 2 longitudes and the equator is 270 degrees. Astonishing, isn't it?

But you might say, the lines are not even straight lines, rather they are curves, how can we even expect them to follow Euclidean geometry? Well that's because you are seeing it from a 3 dimensional perspective I.e we know that the surface is spherical (not straight), but what if we put some very intelligent bugs(who know Euclidean geometry) on such a spherical surface who can only perceive in 2 dimensions. When these bugs start drawing straight lines, in the way illustrated above they find that although their triangle looks like any other 2- dimensional figure( in our sense) still it doesn't follow some of the basic rules of geometry( the angle sum property) given by the Euclid of bugs ( of course there might have been a Euclid bug who introduced this geometry in their world......after all the bugs are super intelligent). Similarly the area of a circle won't be pi*r^2 where r is the measured radius of the circle. In fact it will be greater than pi*r^2.

Well that description was for geometries on a sphere, what about something with the opposite curvature like the surface of a saddle? Obviously the effects will be opposite. The angle sum of the triangle will be less than 180 degrees and similarly the area of circle will also be less than pi*r^2.

So far so good. We proved most of euclid's work (which he assumed was always true) wrong...in a few minutes....so yeah we are doing pretty good I guess.

Time to up the ante. What if our own 3-d space is distorted? What if we are the bugs in this experiment now? How are we supposed to measure the curvature of 3-d space, it was pretty easy in 2-d right? 

.....to be continued.

I will give you the opportunity to entertain yourself with these questions, till my next post.

Stay Tuned for part 2.

Star Stuff

Credits: ASAP Science

The Casimir Effect

We all know that things at the quantum level behave very strangely, yet they still manage to keep these funny organisms (namely Homo sapiens) captivated by their wonders.So here I am (back after a long hibernation) inspired by this cool Casimir effect.
Let's start with a classic analogy to explain this wierd phenomenon. In mid sixteenth century a sailor wrote a book - 'sailing for dummies' (of course that's not the name of the book). One of the salient phenomenon mentioned in the book was that in a rough sea two boats at rest tend to come closer to each other 'due to some mysterious force', but it was later explained that it was all because of the pattern of waves formed between the two boats.
It is observed that when a single boat is sailing in a rough sea it is equally likely to go left as well as right but due to random motion of the waves it just bobbles and stays in its position (unless the waves are moving in a particular direction in a uniform way) but when a second boat sails quite close to our first boat a limited number of waves can come from one side as compared to the other this is because the crests and troughs of these the waves will be of the form of an integer ( there won't be any 1/2 or 6/7 crests or troughs) i.e. Waves with longer wavelength won't be able to fit in the gap which in turn limits the number of waves formed between the two boats and hence pushes the boats towards each other because of the greater number of waves coming from the region outside the separation between the two boats.Similarly when two mirrors (or metal plates) are kept a few nanometers apart in vacuum the tend to stick to each other. Keep in mind that vacuum is not absolutely empty there are Electromagnetic waves(EM), disturbances in various fields (virtual particles) penetrating through that space. So now when the two mirrors are so close to each other there are only a limited number of waves penetrating the space between the two mirrors due to same reason as in the example of boats, i.e. the waves with larger wavelength won't even fit in the gap. hence due to biased direction of waves the two plates tend to come closer to each other.
Though this an interesting phenomenon it creates a lot of problems for nanotech. engineers. For example the nano scale electrical switches are so close together that they tend to remain in contact with each other that means they always stay in an on position (which of course is not the function of switches).
Stay tuned for more interesting stuff next week.



Credits: A friend of mine (Ishaan Joshi) brought this topic to my attention which intugued me. 

What are Pixels?

We have all come across the term 'pixel' in our everyday life. But do we really know what it is?

Pixels are all around us- in our computers, laptops, tablets. They are the very reason you are able to read this blog! 

The word pixel has been derived from the words 'picture element'. Going by the formal definition- 'a pixel is the smallest programmable/controllable element of a picture represented on a screen'. In layman's terms it is the smallest part of anything that you are viewing on your screens.Typically the colours you see on your screens have been formed by 3 primary colours- red, blue and green as shown in the picture-

But don't judge a book by its cover - these 3 primary colours combine in different proportions to give 16,777,216 different colour variations!!

Now we know that pixels are the smallest controllable elements. But how small they really are?

The answer is very interesting- pixels should be thought as a logical unit rather than a physical one. To explain this more clearly, I would like to introduce a new term- Resolution! (and no it has nothing to do with your new year's  resolutions)

Resolution is the number of pixels contained on a display monitor. The sharpness of the image on a display depends on the resolution and the size of the monitor. The same pixel resolution will be sharper on a smaller monitor and gradually lose sharpness on larger monitors because the same number of pixels are being spread out over a larger number of inches.So now you know why an image becomes blurred when you magnify it! The physical size of a pixel depends on how you've set the resolution for the display screen. If you've set the display to its maximum resolution, the physical size of a pixel will equal the physical size of a dot  of the display. If, however, you've set the resolution to something less than the maximum resolution, a pixel will be larger than the physical size of the screen's dot (that is, a pixel will use more than one dot).

Curiosity Matters

Curious stardust is the hangout place for all the curious creatures who are made up of stardust (and yes it includes human beings, which you possibly are and if you are curious you have landed in the right place, so congrats!).
This blog is devoted to all those who are always questioning everything, to all those who think they can make a difference because the ones who are crazy enough to think they can change the world are the ones who do!
It's good that you have read so far. It certainly means you are different which is a very good thing.
I also want to share a bitter truth with you- we are nothing but pieces of some star that lived long ago and will also disintegrate to that when the time comes. We are lost in this mysterious but still interesting universe. So why not explore and know this universe( or maybe even multiverse) better?
Let's jump into this endless ocean and endeavour to reveal its secrets!!

“I don't feel frightened by not knowing things, by being lost in a mysterious universe without any purpose, which is the way it really is, as far as I can tell. Possibly. It doesn't frighten me.”

----Richard Feynman