The ## \bar{x^1} ## grid squares are twice as big as the ## x^1 ## grid squares so the ## \bar{V^1} ## component should be half as much to compensate for that (contravarient), right?
Okay. I found online that you get a transformation matrix as an answer but how do I use that to get the...
Okay, now I think I understand this. I just have one question.
Above I wrote ## \bar{x}^1 = 2x^1, \bar{x}^2 = 2x^2 ##
Now if I use the formula for calculating the components of the vector ## V(1, 2) ## (which uses ## x^1 ## and ## x^2 ## coordinates) in ## \bar{x}^1 ## and ## \bar{x}^2 ##...
Let's say I have coordinate system ## x^n = (x^1, x^2) ## and another ## x'^m = (2x^1, 2x^2) ## . I know this isn't the best example. Let's say I have a vector ## V=(1,2) ## Now according to the formula:
## V'^m = /frac{/partial x'^m}{/partial x^n} V^n ##
Now if I'm looking for the first...
Okay, thanks a lot for your help on this. I bought a textbook on QFT and this is one of the things I need to know. I'm 16 so buying the textbook was a bit ambitious looking back but I'm still going to give it a shot. Thanks for the link btw. Have a nice day :D
@PeroK ok, so after scratching my head for a couple of hours I think I get it now. Is this correct?
Suppose we have a coordinate system ## x^n = (x^1, x^2, x^3) ## and another ## \bar{x^m} = (x^1 * sin(x^2) * cos(x^3), x^1 * sin(x^2) * sin(x^3), x^1 * cos(x^3)) ## .
As you can see, ##...
Okay. Sorry, but this is all very new to me.
So let's assume that I have a vector ##V## in the ## x^m ## frame of reference and it's components are:
## \left( 1, 2, 3 \right) ##
With the basis vector ## \hat{i} , \hat{j} ,\hat{k} ## one can write ## V = 1 * \hat{i}, 2 * \hat{j}, 3 * \hat{k}...
Ah ok. But if I'm trying to convert a Vector from one reference frame to another, how can I know the component of the vector in the new reference frame. Isnt that what I'm calculating? And what is the difference between V^m and x^m ?
Hello,
I have a question regarding the contravarient transformation of vectors.
So the formula:
V'n = dx'n / dxm Vm
So in words, the nth basis vector in the ' frame of reference over the mth (where m is the summation term) basis vector in the original frame of reference times the mth...
If time slows down for an observer traveling at some speed relative to your proper time, shouldn't the traveling observer also see your time slow down relative to his proper time? Or does the observer see your time speed up relative to his proper time.
Also, is dilation exactly the same in...
Let's assume I have a ball moving at a constant velocity and it collides with a spring and the spring compresses n cm. If I know how much mass the ball has and the spring constant D, how would I calculate the Force? I mean since F = dp/dt I would have to know the time in which the stopping...
The distance that separates the slits is a factor, as is the distance from the slits to the wall at the back. Magnetic fields, charge etc. is not taken into account. If you are talking about the double slit experiment with light, then these two factors have no meaning, as light is not influenced...
You need a lot of energy to create a significant amount of mass. You need very little mass to create a very large amount of energy (as evidenced by the atomic bombs). When measuring the mass of a system, for extremely accurate measurements it is necessary to take the energy into account.
Fun...
Update: I got The Theoretical Minimum on Classical Mechanics by Leonard Susskind and I find it challenging enough to enjoy it. I am now aware that I have quite a long way to go :D
Hello,
So I was reading about Hawking radiation and I read a QFT interpretation of it. It went something like this:
A vacuum contains virtual particles (vacuum energy), which in qft can be described as waves that are out of phase and cancel each other out (matter and antimatter). I a black...
Hey guys,
so I was on this thread on tips for self studding physics as a high schooler with the aim to become a theoretical (quantum) physicist in the future. I myself am a 15 year old who wants to become a theoretical physicist in the future. A lot of people in the thread were saying that...
Hello,
So I read that a person in a rocket accelerating at 9.8m/s^2 would feel the same pull downwards as a person standing on the Earth's surface.
However, I can think of a few instances where you could tell the difference:
- If you measure g (9.8N/kg) on Earth, you will notice that the...
Hi,
I'm a 15-year-old high school student and I was wondering what textbook you guys recommend for Special- and General Relativity. I'm familiar with the concept of the Metric Tensor and Christoffel Symbols, but I wanted a good textbook where I can really learn derive it all and gain a deeper...
If there are no flavor changing z0 weak interactions, how do we even know that the particle exists? I thought that we could only tell which particle was exchanged by the particles it decays into. Is this wrong?
I've been reading about Quantum Mechanics for years now and I think it's time I bought a textbook and really learned the math. I'm 15 y.o. and have a working understanding of Derivitives, Integrals and Vectors. Is this textbook a good one to start with or is it too complex? Which one would you...
Quantum by Manjit Kumar
I read that there are energy levels n = 1, n = 2 (...) and that each energy level contained n amount of sublevels, so n = 2 is made up of two sublevels and n = 3 is made of 3 sublevels etc. Is this correct?
So I read that Bohr's atom has discrete energy levels that an Electron can orbit at and that each level has n amount of sublevels (if n = 2 then there are 2 sublevels). Does the sublevel that the Electron is in have to do with it's mass? Does an electron in energy level l and sublevel d have...