Advice for Young Physicists

There are some people for whom physics is the only way to move forward in academia. Physics is the only subject that addresses some of the most fundamental questions that we sometimes ask ourselves and ask about the Universe around us. If you are young and planning for a career in theoretical physics then I have some advise for you.

First of all, from a more practical perspective, make sure you have an additional skill that has more applications in industry. The job industry in theoretical physics is a disaster. Secondly, if you are planning to pursue a PhD in physics then get ready to say goodbye to your creative skills. The general approach in academia these days is that you decide on what topic to major in and then find a suitable adviser who will guide you in learning that subject and publish papers on that topic. I have noticed that once students start research they tend to focus so much on a particular topic that they loose their creative skills or they cant use these skills out of the very narrow topic they chose for their PhD. They continue to collaborate with the same group their whole life and work on the same topic. (There are clearly exceptions but I am addressing the more common occurrences here.)

This is my advise to graduate students. Once you are done with your course work try to build your own world out of the knowledge you have gained. Every subfield in theoretical and applied physics has a vast amount of literature and one can spend their whole life exploring and understanding just the present status of that theory. So even if you have started research on a standard topic, try to discover something out of the knowledge you have obtained as a graduate student. In my view, at present, physics is in crisis and the only way out of this is for the young to be more creative and they should be willing to take risks by proposing new ideas.

Lorentz Violation and Condensed Matter Physics

In one of my papers titled "Lorentz Violation and Condensed Matter Physics" I pointed out several operators in condensed matter physics that arise from Lorentz violation in the Standard Model Extension. The coefficients of these operators employed in condensed matter physics are clearly enhanced, as shown from different references in the paper.

I have a feeling that we are missing something very fundamental in our understanding of Lorentz symmetry. At the heart, it makes complete sense and it is important that physics remains the same independent of the frame of reference, but one subtle point about the principle of relativity is that it is formulated for the vacuum. What if we perform a Lorentz transformation and end up in a condensed matter system where the speed of light can be slower, the mass of the electron can be different? The physics has clearly changed to some extent. This might be the reason we see an enhanced value of the coefficients of Lorentz violating operators in condensed matter.

[1] https://arxiv.org/abs/1403.7622

A great lecture: "The Astonishing Simplicity of Everything"

I recently saw this lecture by Neil Turok on youtube and was amazed by the elegance with which it was presented. I believe that every student of science and in particular physics should listen to it. Professor Turok starts with some simple math and basic questions, like the length scales in the Universe. He also present a simple introduction to quantum mechanics and then moves on to the idea of the multiverse and cyclic universe. Give it a listen!

Following are some of his quotes I liked:

"Its (nature) so simple, we don't know how nature got away with it"

"If you are a theorist you should be happy when you are wrong. It means your idea was testable. It was worth talking about"

A New Approach in Quantum Mechanics

A paper of mine was recently published in the journal "Foundations of Physics". In this paper I introduced an equation from which the Schrodinger equation can be derived. This is a new approach with which known problems in quantum mechanics (such as scattering problems) can be solved with new insights. For example, the equation introduced in this paper takes into account the spin of the particle in scattering problems and makes specific predictions on how a particle with spin can scatter from a step potential. The equation can be used to solve other problems in quantum mechanics as well. This equation can have notable implications for physics in the non-relativistic limit.

Following are the comments of one of the reviewers of this paper:

" This article is an important work, and should be published as soon as possible. Dirac deduced his equation ---the Dirac equation by introducing 4*4 matrices, which is first order both for time and space and can deduces the Klein-Gordon equation. The Schrödinger equation is first order for time and second order for space, it has been used for a century to treat non-relativistic quantum mechanical problems. No one was aware of looking for a Dirac equation analogue of the Schrödinger equation. The author the first time proposed an equation with first order time and first order space for the Schrödinger equation, it is brand new idea and work."

Here is the link to a translated version of a blog post on this article originally written in Chinese.

Following is the 3D version of the equation in momentum space


 

The matrices η are 4 dimensional matrices and \gamma_i are the Dirac gamma matrices. (Note that η can also be 2x2 matrices but in that case the 3D version of the equation is not possible because there is no fourth matrix that anticommutes with the Pauli matrix. The 1d version is possible and agrees with standard quantum mechanics.)

In another recently published paper I have also shown that this first order equation is the non-relativistic limit of the Dirac equation and the Pauli equation can be derived from it:

http://www.ijqf.org/archives/3480

I have therefore proposed that this equation is the non-relativistic equation for fermions and Schrodinger equation more appropriately describes scalars in the non-relativistic limit. This equation allows for the description of fermions and boson in the non-relativistic limit. The Lagrangian for free fermions and scalars in the non-relativistic limit can therefore be written as





Note that the scalar and fermion wave functions have dimensions of Energy^(3/2) in the above Lagrangian density. In the presence of interactions, for example, for scalars we can have a phi^4 like interaction term which would lead to the non-linear Schrodinger equation which is employed in the description of the Bose-Einstein condensate.

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[1] http://arxiv.org/pdf/1502.04274v2.pdf