There is a good summary of phrases to use when writing journal papers.
English for writing research papers (.pdf file) can be downloaded from this Springer site.
Time - What is it?
Intriguing question related to time are
- What really time is?
- Was there time before the Big Bang event?
- We use motion to measure time. Thus intution says that there won't be time without motion (zero-point vibration protected by the Heizenberg's uncertanty principle). Is it possible to create something called no time
- It is found that the particles/waves moving at the speed of light does not experience time. How far it is true?
- Apart from photons (e-m waves), what are the other particles that has such property (no time)
Recently, I happen to read the article by Prof. Gabriele Veneziano (the father of String theory) titled String Theory Predicts a Time Before the Big Bang". I remember that there was debated during the big bang theory discussion like "the question about before the big bang is stupid" because time itself starts after the big bang. But, Prof. Veneziano has written article on "Time before the bigbang".
Why do we use 360 degrees for a complete circle?
Sumerians, Greeks and Babylonians were the forerunners in observing the astronomical objects, may be for omens initially and later for calculating time. Sumerians observed that the sun takes a circular path and it takes approximately 360 days for one cycle (which is exactly 365.15 days which we call a year). This may the starting point for using 360. Obviously, others may have tried to change this to some other number. However, there are many reasons to stick to 360 degrees.
- It is divisible by 1, 2, 3, 4, 6, 8, 9, 10, 12, 16.
- Babylonians used base 60 numbers which is favourable to 360 degree
- The Greeks devided the the total number of days in to 24 hours.
- Later Babylonians devided each hour in to 60 minutes and each minute in to 60 seconds (which is their base system)
Vectors
What is a vector?
In everyday life, we measure things. For example, what is the size of something, what is the volume (how many liters) of the water bottle. When we buy things from shops, we ask 100 grams or 1 Kg etc. Assume that we need sugar. We will use just a number for example 2 Kg. But, there are some quantities which need not only a number but direction also. For example, if we ask where is this building, we may get a response like this: Go straight in this street. At the end, turn left and then first right. There you can find that building. Look at this explanation. Here, the location (length of the distance is hidden) includes right and left. These are the directions.
This is in everyday life. In physics, there are so many such quantities which need direction as well as some number. These are called vectors. There are quantities for which just a number is enough to denote them. Those are called scalars. Now what are the vector quantities?
In everyday life, we measure things. For example, what is the size of something, what is the volume (how many liters) of the water bottle. When we buy things from shops, we ask 100 grams or 1 Kg etc. Assume that we need sugar. We will use just a number for example 2 Kg. But, there are some quantities which need not only a number but direction also. For example, if we ask where is this building, we may get a response like this: Go straight in this street. At the end, turn left and then first right. There you can find that building. Look at this explanation. Here, the location (length of the distance is hidden) includes right and left. These are the directions.
This is in everyday life. In physics, there are so many such quantities which need direction as well as some number. These are called vectors. There are quantities for which just a number is enough to denote them. Those are called scalars. Now what are the vector quantities?
- velocity
- momentum
- angular momentum
- acceleration
- force
- torque
Symmetry and Emmy Noether's theorem
Emmy Noether's theorems provide profound relation between a system having symmetry and constancy of a physical quantity. That is, there is a corresponding conserved quantity for any symmetry the system posses.
Following video from the YouTube channel "Looking Glass Universe". There, the title says "The most beautiful idea in physics - Noether's Theorem". The concept of symmetry is one of the ways to attack a problem as Feynman says.
Here is the video.
Following video from the YouTube channel "Looking Glass Universe". There, the title says "The most beautiful idea in physics - Noether's Theorem". The concept of symmetry is one of the ways to attack a problem as Feynman says.
Here is the video.
An easy way to find Latex code
There exists an excellent site on which you can find out the key for most of the $LaTeX$ comments.
The site is Detexify Latex handwriting.
The page says:
"Anyone who works with LaTeX knows how time-consuming it can be to find a symbol in symbols-a4.pdf that you just can't memorize. Detexify is an attempt to simplify this search."
What you have to do is just draw the symbol (on the portion given in the site) for which you want to know the comment.
You will be given the latex-code for that symbol.
Conservation of angular momentum
It is interesting to see the demo for "Conservation of angular momentum". The MIT2K series has an excellent video on the conservation of angular momentum.
When he rotate the wheel, it has an angular momentum say $L$. The angular moment is given by $L=r\times \omega$ where $\omega$ is the angular frequency (which can be rewritten as $2\pi \nu$). This quantity is constant as for as no other forces acting on it. Now, when he flip the wheel, what happens? Isn't that really amazing? He starts to rotate. Why he starts to rotate? Because, when he rotate the wheel, the angular momentum directs downward (previously upward). Since angular momentum is conserved, it has to still $L$. So, the system make the demostrator to roate (with an angular momentum of $2L$ so that the total angular momentum is still $2L-L=L$. Gotcha...
Isn't that really amazing!!!
Questions:
How angular momentum conservation plays role in magnetism?
In a magnet, the angular momenta of all the electrons is alighted up. If we flip the magnet, does this has the same effect (i mean similar effect) as in the case of the rotating wheel here?
Is there any relation to the quantum hall effect, fractional quantum hall effect?
Questions:
How angular momentum conservation plays role in magnetism?
In a magnet, the angular momenta of all the electrons is alighted up. If we flip the magnet, does this has the same effect (i mean similar effect) as in the case of the rotating wheel here?
Is there any relation to the quantum hall effect, fractional quantum hall effect?
Notes on Fermi-Dirac distribution
As per my knowledge, in our universe, number of Fermions are more than Bosons (correct me if I am wrong). Apart from this, my interest to write on this topic is rooted on the fact that atoms consists of electrons, nucleons (proton and neutron), which in turn made of quarks which are also Fermions. Thus, in this page, I try to write on Fermions and their distribution function.
The Fermion distribution function at some temperature $T_{balance between the energy and entroy}$ is given by:
The Fermion distribution function at some temperature $T_{balance between the energy and entroy}$ is given by:
Notes on Dark matter and Dark energy
Dark matter and dark energy are one of the intriguing problems which keep awake theoretical physicists.
See this picture for a schematic of the accelerated expansion of the universe due to dark energy.
There are many attempts to demystify the truth behind these concepts. For first account on these topics, click following links from Wikipedia. I try to give a clear picture in the coming days.
1. Dark Matter
2. Dark Energy
There are attempts to unify these two concepts. For example, a recent arXiv pre-print titled "Unified description of dark energy and dark matter in mimetic matter model" by Jiro Matsumoto from Institute of Physics, Kazan Federal University, Russia attempts in this direction.
The abstract reads as follows:
"The existence of dark matter and dark energy in cosmology is implied by various observations, however, they are still unclear because they have not been directly detected. In this Letter, an unified model of dark energy and dark matter that can explain the evolution history of the Universe later than inflationary era, the time evolution of the growth rate function of the matter density contrast, the flat rotation curves of the spiral galaxies, and the gravitational experiments in the solar system is proposed in mimetic matter model."
While discussing dark matter and dark energy, we may need to consider the cosmic mirowave backround radiation (CMB radiation). In general, the CMB radiation picture is shown with a lot of variations. But, it is a difference with the actual image. The real image is completely red. What is shown in the Figure is just the variation (less than 4 K ?).
If dark matter is a boson, its masss in lower limit is 10>-22 eV.
If it is Fermion, its Fermion, is lower limit is a few eVs.
The upper limit for the mass is 10^3 solar masses (huge!!!!).
Types of Dark Matter:
Bananas Dark Matter:
(This page will be updated gradually...)
See this picture for a schematic of the accelerated expansion of the universe due to dark energy.
There are many attempts to demystify the truth behind these concepts. For first account on these topics, click following links from Wikipedia. I try to give a clear picture in the coming days.
1. Dark Matter
2. Dark Energy
There are attempts to unify these two concepts. For example, a recent arXiv pre-print titled "Unified description of dark energy and dark matter in mimetic matter model" by Jiro Matsumoto from Institute of Physics, Kazan Federal University, Russia attempts in this direction.
The abstract reads as follows:
"The existence of dark matter and dark energy in cosmology is implied by various observations, however, they are still unclear because they have not been directly detected. In this Letter, an unified model of dark energy and dark matter that can explain the evolution history of the Universe later than inflationary era, the time evolution of the growth rate function of the matter density contrast, the flat rotation curves of the spiral galaxies, and the gravitational experiments in the solar system is proposed in mimetic matter model."
While discussing dark matter and dark energy, we may need to consider the cosmic mirowave backround radiation (CMB radiation). In general, the CMB radiation picture is shown with a lot of variations. But, it is a difference with the actual image. The real image is completely red. What is shown in the Figure is just the variation (less than 4 K ?).
If dark matter is a boson, its masss in lower limit is 10>-22 eV.
If it is Fermion, its Fermion, is lower limit is a few eVs.
The upper limit for the mass is 10^3 solar masses (huge!!!!).
Types of Dark Matter:
Bananas Dark Matter:
(This page will be updated gradually...)
Heizenberg's Uncertainty Principle
Nobel laureate Weinberg (Ref. 7 of the English translation of the original paper by Heisenberg's paper) has written as follows:
‘If the reader is mystified at what Heisenberg was doing, he or she is not
alone. I have tried several times to read the paper that Heisenberg wrote on
returning from Heligoland, and, although I think I understand quantum mechanics,
I have never understood Heisenberg’s motivations for the mathematical
steps in his paper. Theoretical physicists in their most successful work tend
to play one of two roles: they are either sages or magicians....It is usually not
difficult to understand the papers of sage-physicists, but the papers of magicianphysicists
are often incomprehensible. In that sense, Heisenberg’s 1925 paper
was pure magic."
So, it is very difficult to understand the Uncertainty principle from original paper. The paper in the above link try to give the method that Heisenberg may have used.
So, it is very difficult to understand the Uncertainty principle from original paper. The paper in the above link try to give the method that Heisenberg may have used.
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