Greetings,
Completing Bachelors in Engineering this June'19, I thought I'd start with Masters/PhD in Gravitational Physics this fall but I received rejections from almost every graduate school I applied to. To where I received an offer from, I won't be able to pay off the tuition fees.
Of course I knew that to receive an offer, one needs to have some experience with the subject. With the engineering curriculum on one hand, I tried to manage my interests in gravity. From watching lecture videos by Frederic Schuller and Leonard Susskind to reading books by Sean Carrol and to even doing a summer research internship on black hole geometries, I tried to gain experience on the subject.
I wish to understand relativity from a mathematical point of view.
" A good course in more abstract algebra dealing with vector spaces, inner products/orthogonality, and that sort of thing is a must. To my knowledge this is normally taught in a second year linear algebra course and is typically kept out of first year courses. Obviously a course in differential equations is required and probably a course in partial differential equations is required as well.
The question is more about the mathematical aspect, I'd say having a course in analysis up to topological spaces is a huge plus. That way if you're curious about the more mathematical nature of manifolds, you could pick up a book like Lee and be off to the races. If you want to study anything at a level higher, say Wald, then a course in analysis including topological spaces is a must.
I'd also say a good course in classical differential geometry (2 and 3 dimensional things) is a good pre-req to build a geometrical idea of what is going on, albeit the methods used in those types of courses do not generalise. "
- Professor X
^I am looking for an opportunity to study all of this.
I would be grateful for any opportunity/guidance given.
Thanking you
PS: I really wanted to do Part III of the Mathematical Tripos from Cambridge University, but sadly my grades won't allow me to even apply :p
There are two sides to your problem: the practical and the ambitional. You will have to look after both. Recognize the practical issues but don't let go of your ambition. You may have to get a temporary job just to live, but that does not mean you give up on your dreams.
Your problem is not unique and has been overcome by famous scientists. Faraday started working for a bookbinder and ended as a revered scientist. His personal drive got him through. Dirac got a first degree in electrical engineering and ended as a revered theorist. Einstein worked early on in a Patent office and ended as a revered theorist. Other examples can be found, such as Ramanujan. Now there's a great example of talent beating disadvantage. So you see, it's not the end of the world if there are practical difficulties in your way at this time in your life. If you keep your spirits high, focused on what really interests you, you may succeed. It may be very hard, but don't give up.
You should understand that training is not enough. You have to practice being creative. Some people on this forum will probably disagree with the following suggestion, but have a go at writing a paper on a novel topic and seeing the reaction. It may take time to find a problem that you can work on, and you may very well get rejection. But having a go will teach you more than doing a lecture course on analysis. Papers do not all have to be in quantum field theory or relativity. Go on the arXives and see what sort of topics are viable for you. Most likely, at this stage, it might be in the General Physics section. But at least you might start from there.
Good luck in your ambition. Never give up.
George Jaroszkiewicz
my dear Ayush Paliwal it is good step from you...in a layman perspective GR is simple but horrible in math perspective if and only if you are bad in math.. at present Leonard Susskind is a better choice....
Dear Ayush:
I am a 78 years old chaos researcher who always was only interested in finding new things.
While it is impressive what you want to study (and probably can study when you follow the above-given advice), I feel it is perhaps not unfair if I tell you also that in my old years I have found that much of what the current curriculum in physics is teaching absolutely false stuff. So learning to reproduce it is really a sin against your own self.
While I cannot give you a stipend or position, I can tell you a result which I found in the last decade that no one believes but nonetheless is true. It has the asset that those who are not interested run the risk of losing earth soon with a certain finite probability.
So specializing in this result as a topic to check is, while offering no bread directly, possibly the ultimate bread-giving activity for the whole planet.
This sounds crazy.
Can I nonetheless elaborate a bit?
It has to do with the young Einstein when he was still an outsider.
He had this mental imagination that is unsurpassed ever since.
He pictured in his mind a rocketship in outer space with constantly roaring motors (acceleration) and looked at the behavior of a light ray inside. The point: Light has a universal constant speed c.
That is all. He found a few implications which made him famous after some years. But he also overlooked some implications because his mind was not as powerful as a modern computer implementation can be or will eventually prove to be (I dare say).
So I tell you first what he found, and then what he overlooked. And what he overlooked is of course much more important.
He found three things at the very end of his long but otherwise not interesting (only hard-working) paper of 1907 in the yearbook of radioactivity (he has only one big paper that year and it is in translation on the web).
1) The light emitted vertically at the bottom arrives at the tip when the tip, along with the whole spaceship, has acquired a fixed speed away from the original emission point. This causes a Doppler effect -- the frequency of the emitted light is reduced like that of a departing siren.
After 5 decades this result got first directly confirmed by measurement (of course). It is called "gravitational redshift." Red because redder light has a lower frequency (to have a fitting name for the effect). For example, clocks in a high-up satellite are having a higher frequency.
2) If the light is emitted horizontally somewhere in the middle of the rocketship in full blast, the light ray looks bending downwards (not so important and already seen a hundred years before by von Soldner who otherwise is forgotten.
3) When the light ray hugs the floor, the lower frequency is not all. The speed of light appears to be reduced when watched from above. (This has never been observed but no doubt is true.)
This third result led Einstein and the whole physics community astray ever since. It is rare to find a real mistake in science. And the consequences are potentially vital. In the present case, everyone is betting the planet on this result being true, it turns out.
I wrote many things on this on ResearchGate, but few people are interested as you can see from the small number of readers.
The third result is true but the conclusion -- that the speed of light is lower downstairs -- is not true. Only everybody thinks it is. Ask anyone in physics.
The explanation is: As the light ray crosses the bottom while watched from the tip, the bottom is constantly faling away from the tip even though keeping its distance (as we already saw with Einstein in the case of the vertical light ray). The seeming contradiction can give one a headache as Einstein complained, but here in the horizontal rather than vertical case we have a new problem.
The explanation for the observable slowdown is that the bottom is constantly falling away from the tip even though the distance is the same (as we saw).
That is, the light ray that is progressing horizontally to the side does so along a floor that is constantly falling back as we saw. Right?
So the same recession of the bottom which causes the famous gravitational redshift also causes the famous slowdown of light downstairs.
But this slowdown is now not a slowdown at all, but only a projection effect since relative to the tip, the light hugging the bottom follows a slanted course!
Therefore, the speed of light downstairs is not reduced, although this is the official teaching for 112 years.
It is unlikely to find such a common mistake made by the whole planet and adhered to for more than a century. It took me decades to see it clearly and I have the privilege of hindsight by more than a century. So my IQ is not exceptional.
But you suddenly see the limited IQ of the whole of science and the whole of humanity for 112 years.
Forgive me that I felt the urge to tell you this story.
One such error now has the most far-reaching consequences:
No Big Bang is the biggest. No finished black holes comes next. No gravitational waves despite the Nobel prizes for them is next. Ten Nobel medals for cosmology prove inapplicable, too.
I come to an end. It makes no sense to try to find mistakes. It only makes sense to think clearly oneself.
Nowadays, computer simulations can be used to at last fully understand the Einstein equivalene principle, But strangely, no one thought of checking the latter by computer power so far.
Forgive me that I wrote so much,
Take care,
Otto
March 24, 2019
Not much new research is done in gravitational physics. You must do original new research to get the Doctorate and usually also for the Masters. So choose a different topic for research and specialty of your major field.
Gravity Physics makes a good hobby, and you can get a good understanding of it from electives study.
Mathematically general relativity is not terribly difficult as it once was because many writers have explained it well. All of GR is developed from the gμν which Albert Einstein introduced without proper explanation.
On Gr the place to start is multilinear analysis gμν are developed as dot products of unit vectors in curved and flat coordinate systems. In the same book the Reimann tensor should be developed from gμν and the Christoffel symbols should also be developed. Also the meanings of covariance and contra variance are given. The same book should show how to manipulate tensors to raise and lower the indices.
By the time you have mastered multilinear analysis GR should not be especially difficult and Einstein developed it well enough in his books that a lot of other sources are not needed or helpful.
You should consider how to earn a living and study that field with technical electives covering your interest in gravity and GR.
There are two sides to your problem: the practical and the ambitional. You will have to look after both. Recognize the practical issues but don't let go of your ambition. You may have to get a temporary job just to live, but that does not mean you give up on your dreams.
Your problem is not unique and has been overcome by famous scientists. Faraday started working for a bookbinder and ended as a revered scientist. His personal drive got him through. Dirac got a first degree in electrical engineering and ended as a revered theorist. Einstein worked early on in a Patent office and ended as a revered theorist. Other examples can be found, such as Ramanujan. Now there's a great example of talent beating disadvantage. So you see, it's not the end of the world if there are practical difficulties in your way at this time in your life. If you keep your spirits high, focused on what really interests you, you may succeed. It may be very hard, but don't give up.
You should understand that training is not enough. You have to practice being creative. Some people on this forum will probably disagree with the following suggestion, but have a go at writing a paper on a novel topic and seeing the reaction. It may take time to find a problem that you can work on, and you may very well get rejection. But having a go will teach you more than doing a lecture course on analysis. Papers do not all have to be in quantum field theory or relativity. Go on the arXives and see what sort of topics are viable for you. Most likely, at this stage, it might be in the General Physics section. But at least you might start from there.
Good luck in your ambition. Never give up.
George Jaroszkiewicz
My proposal of a computer simulation on Einstein 1907 makes maximum sense in our current age -- right?
https://www.researchgate.net/post/Going_back_to_Einstein_1907_in_the_modern_Computer_Age_Submitted_to_PRResearch2
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