I can see that by the tensor transformation law of the Kronecker delta that
##\frac{\partial x^a}{\partial x^b}=\delta^a_b##
And thus coordinates must be independent of eachother.
But is there a more straightforward and fundamental reason why we don’t consider dependent coordinates? Is it...
I’m worried I’m going to get my PhD knowing GR but having a less-than-undergrad grasp on the other core topics like stat mech and QM. I feel like “forgetting” most of core physics makes me a bad physicist.
Or is this normal when you specialize?
How do y’all stay sharp on these topics?
Summary: Does the "problem of time in quantum mechanics" go for Lorentz-invariant quantum mechanical theories like QED?
Everything I read about "the problem of time in quantum mechanics," i.e. absolute time in QM clashing with relativity's relative time coordinate and relativity of...
I'm studying how derivatives and partial derivatives transform under a Galilean transformation.
On this page:
http://www.physics.princeton.edu/~mcdonald/examples/wave_velocity.pdf
Equation (16) relies on ##\frac{\partial t'}{\partial x}=0## but ##\frac{\partial x'}{\partial t}=-v##
But this...
I use the ##(-,+,+,+)## signature.
In the Schwarzschild solution $$ds^2=-\left(1-\frac{2m}{r}\right)dt^2+\left(1-\frac{2m}{r}\right)^{-1}dr^2+r^2d\Omega^2$$ with coordinates $$(t,r,\theta,\phi)$$ the timelike Killing vector $$K^a=\delta^a_0=\partial_0=(1,0,0,0)$$ has a norm squared of...
I'm a PhD student who's taken GR, so I have studied gravity and cosmology, and we have the underlying assumption of homogeneity and isotropy, but since this assumption comes from how we've calculated the distribution of galaxies in the visible universe I want to make sure I really understand it...
Let's say I'm getting a PhD in an area of gravitational physics. Upon getting that diploma, what is expected of me in terms of knowledge of GR? I hope my question can be useful to other students in other concentrations, so substitute QFT, or condensed matter, or whatever.
For example, is it...
I understand how we associate high energies with small wavelengths and thus small distance scales, but we also tend to associate small distance scales with ordinary quantum mechanics, and hence low quantum numbers (low energy). Also, many high-energy processes are active across large distance...
I tried a cursory search for this but couldn't find it.
I was talking with my advisor about 5D theories such as those of Paul Wesson and Randall-Sundrum, and he said that I shouldn't spend too much time studying those theories because they are unstable, or require so many corrections to...
Grad school is *not* what I was hoping it would be. I wanted to study GR and was fortunate enough to get accepted in a program with an advisor who is a gravity theorist. I have the best fellowship awarded to grad students at my school. I passed all my prelims on my first try. My grades...
I'm in gravity (cosmology, GWs, etc.) and starting my fourth year and only just recently took GR for the first time. I'm wondering what standard I should set for myself WRT GR. It feels like you'd need to be an expert in GR just to identify worthwhile problems to work on, and I'm expected to...
I'm a grad student working on a PhD in physics at an accredited university in the US. I have the opportunity this Summer of doing a side research project or two under the auspices of a physicist who works at a private research outfit funded by another physicist who was involved in "paranormal"...
I hope my question doesn't sound bitter, it's not meant to be, I'm just a grad student wanting to get some opinions on how things are. I'm especially interested in hearing from people outside academia as well, since I assume people *within* academia might have an unrealistic view of what the...
I am studying a paper and a math step like this was used:
dt'=(1+\frac{h}{2}sin^2(\theta))dr \\
\int^{t1}_t dt'=\int^d_0 (1+\frac{h}{2}sin^2(\theta))dr \\
where\\
h=h(t-\frac{r}{c}-\frac{r}{c}cos(\theta))
This seems wrong because it seems to me that you're not doing the same thing to both...
Maybe "dunce" is the wrong word, but I'm pretty weak on stat mech/thermo. I've had a few courses in them but not to the point where I can understand anything but the most rudimentary basics (each time I took a course in them I happened to have been distracted with other things). I'm a thirdish...
I need to learn more about optical clocks, frequency combs, atom trapping, atom interferometry, etc., and I'm wondering if there are good books or review papers you recommend? The papers I'm reading can be hard to understand and often assume knowledge I don't have. I'm a grad student if that...
Homework Statement
The problem is from D'Inverno's book on GR, problem 5.6. We're using the Jacobian/transformation matrix to convert the tangent to a circle centered at the origin of radius A from Cartesian to polar coordinates. I can do the problem and get the book answer, that's okay...
Hi. I hope this is the rightplace to ask this. Sorry if it isn't. I'm looking for a resource (book, web page, etc) and I don't know if it exists so I'll describe it.
I want something that lists actual experiments that complement or back up the topics listed in a typical QM textbook, so I can...
Tried searching for equivalent question but couldn't find it.
Presumably, a potential (like a Coulomb one) comes from another particle, which has its own momentum/position uncertainty, but in the Schroedinger equation the potential is well-defined either in terms of some coordinate system or...
Let me define the question better. For my purposes I'm saying a person "understand quantum mechanics" when they have what it takes to write a basic graduate level QM textbook. Maybe I'm setting the bar too high, but I'm a first-year physics grad student who can get good grades in QM classes...
I did a search but couldn't find what I was looking for. I'm a physics student studying QM at the graduate level. I'm aware that "nobody truly understands QM" but I'd like to get as much insight and intuition as possible. Textbooks are good for learning to solve problems and learning the...
I'm trying to get a feel for what's important and what's not so important. For example is memorizing the Frobenius method important or is it something you don't use much? I'm asking from the perspective of a grad student.
I am in a graduate class taught by a super genius who advises us to just keep rereading Gottfried (it's the sole text and all HW comes from it) if we don't understand.
Me and my classmates feel like we aren't learning QM because the text is inscrutable and the HW isn't teaching us anything...
It's not just in physics, it's mainly in math IME, but a lot of older books (pre-1980) for upper-division topics are usually thin. Not giant tomes like you get today. Hence I was thinking of using a lot of these older books to teach myself some things (mainly in math and classical physics...
What do you peeps think of the ranking of one's PhD-granting institution and non-academic jobs? We all know that academic jobs are biased in favor of the prestige of one's school first and foremost. I met a recently-granted PhD student from a low-ranked university with eleven relevant...
For example, if your advisor specializes in gravity, but has a subfield specialty (like Horava-Lifschitz gravity) and most of their papers for the last several years are about that subspecialty, does that mean your thesis research will be about that, or could it be about any gravitational thing?
Undergrad here. I'm filling out grad school apps and my BIG interest is GR, most likely numerical relativity.
But I have heard that this is a dead field, that professors working in it don't take on new students, etc.
But it's the reason I'm in physics in the first place. I'm applying to...
For example, I want to work on quantum gravity and things like Brane cosmology (but not necessarily string theory). I'm really interested in sinking my teeth into differential geometry, general relativity, the shape of the universe, stuff like that. But if I were to go to a grad school that...
I'm taking stat mech right now (Kittel book) and..........I might hate it. I love e&m, quantum, classical, relativity, but I like almost none of what we're doing in this class. It's not the type of physics I'm interested in and it's abstract in a way I don't like (I normally like abstraction)...