currently very suspicious about the well-known formula for a time derivative of a rotation matrix $$\omega \times R$$. Seems like it'll just blow up the determinant of R.
@ScientistSmithYT I'm confused. Your previous questions sounded like you know almost nothing about fusion, but now it seems that you're claiming that you've been able to achieve fusion, somehow. FWIW, it's not that hard to make deuterium fuse. The hard part is to get more energy out than what the reactor consumes. From en.wikipedia.org/wiki/Fusor here's a picture of a home-made fusor:
Also see fusor.net which is a site for amateurs who build fusion reactors. Unfortunately, that site is a bit of a mess, with quite a few broken links.
@AjayMohan hi. For questions about CFT @ACuriousMind is probably the best person to ask, though he is usually only around in the afternoons (European time).
@AjayMohan you can also ask whatever you want to ask now and I'll answer it when I have time, that way we can't miss each other. (I'm just stopping by briefly right now)
@ACuriousMind Every transformation tells us how both the coordinates and the fields transform. In translations, it's $x' = x+a$ and ${\phi'}^A (x)=\phi^A (x-a)$. In dilatations, it's $x'=\lambda x$ and ${\phi'}^A (x)= \lambda^{-\Delta} \phi^A (\lambda^{-1}x) where $\Delta$ is the scaling dimension of the field $\phi$. In a similar manner, how do the fields transform in a finite special conformal transformation?
The definition of a SCT should contain both how the coordinates transform and the fields transform, right? One can't derive how the field transforms in a SCT, right? It's a definition.
I have read Philippe Francesco's book to understand this but I'm unable to understand them. I'm going to assume you have the book so you can look up the relevant formulae (let me know if you don't) :
The generators in (4.18) are calculated assuming the fields transform as ${\phi'}^A (x') = \phi^A (x)$ (**) and these generators can be verified to satisfy the commutation relations in (4.19). The commutation relations in (4.19) are used in section 4.2.1 to derive how the generators $P^{\mu}, L^{\mu \nu}, D, K^{\mu}$ act on a field $\phi(x)$ (4.28) and (4.31). Does this information give us how a field transforms under a symmetry transformation?
(contd.) But it shouldn't be the case right? How a field transforms under a transformation is a part of the transformation's definition and in the above passage describing the flow of information in the book, I don't think he has put that anywhere by hand. Therefore, it implies that the answer to "Does this information give us how a field transforms under a symmetry transformation?" is No.
What I've described about is my thoughts on Question 1. Question 1 : How do fields transform in a finite special conformal transformation?
I have another question too. My teacher told me that a field $\phi(x)$ is "primary" if it satisfies the following three commutator relations: $[D, \phi^A(0)]=0, [M^{\mu \nu},\phi^A(0)]={(S_{\mu \nu})^A}_B \phi^B(0), $ and $[K^{\mu},\phi^A(0)]=0$. Question 2 : Can this be taken as a definition of primary field?
Nevermind. My words are just too messy. You don't have to answer it. I'll refine it further and ask it on SE (preferably) later.
I have come across two similar definitions of primary fields in conformal field theory. Depending on what I am doing each definition has its own usefulness. I expect both definitions to be compatible but I can't seem to be able to show it. By compatible I mean definition 1 $\iff$ definition 2. I ...
Why electromagnetic force works even in a dark room constructed of thick concrete walls?
If photons do not enter Earth’s core, why rocks, silicon, magma, iron, oxygen, are present there which requires electromagnetic force for atomic bonding?
Each night, when we are completely opposite of the Su...
@KyleKanos Hmmm. I suppose the OP doesn't know about virtual photons. How do you answer a question like that without writing half a textbook? And without knowing what misconceptions the OP has that led them to asking that question? I'm tempted to VtC it as Too Broad. OTOH, I suppose it might elicit some great answers. If it does, it'll surely hit the HNQ...
@PM2Ring I VtC as unclear. I think OP largely misunderstands EM force and we're unlikely to be able to help, I think. Too Broad might also be right here
And I would hate that query even more if it managed HNQ. We already have a problem with HNQ (mostly not even physics questions getting promoted) and giving such a LQ post as an example of types of "good" questions would be terrible for us
@AaronStevens Part of me thinks that sounds really interesting and I would like to know more about it. The part of me that failed Numerical Methods the first time is terrified.
i didn't want to consider BC's in my PhD work, so i literally just "zoomed out" and ignored them. the fluid of interest never touched the boundary, so all was well
But then they can react with other species bound to a surface
So the boundary conditions of how the diffusible species "move on and off" the surface depends on how the other species that are on the surface are behaving
hey guys, is there a compressed notation similar to einstein notation using products (and tbh on that end is there a name for when you use the product operator, kinda like how summations are said to be in sigma notation)
@AjayMohan 1. The definition of a transformation a priori only includes its action on coordinates. These transformations then form a group in whose representations fields can transform (or not). 2. The requirement that $\phi'(x') = \phi(x)$ is precisely the requirement that the field transforms in a proper representation.
3. The action of the generator of a transformation on the field encodes the behaviour under the transformation - the generator $G$ is the infinitesimal version of the symmetry and you can "integrate" it to get the finite transformation. joshphysics demonstrates this for the SCT on the coordinates here - to get the transformation of a field, you need to replace the $G_b(x)$ with whatever the transformation of the field under the generator is
@AjayMohan Yes, this is a definition of "primary field". A more insightful definition could be made once you know the structure of the conformal algebra in terms of raising/lowering operators, but it's still a definition.
@Skyler It's pi notation (or big pi notation). I suppose you can just say "using the Einstein index convention" & people will know what you mean. Alternatively, use logs to convert your product to a sum. ;)
@JMac Yeah I am not too skilled in numerical methods myself. I rely heavily on the automated methods Mathematica uses. It is something I am not entirely proud of, but I honestly don't have the time to get into the gritty details of the numeric solver
@KyleKanos For a terrible piece of software it's sure earned Wolfram a few dollars. I've never used it (apart from indirectly, via Wolfram Alpha), but I really don't like the look of the Mathematica language.
@PM2Ring The language takes some time to get used to. But it can be very powerful when used in the right way (which I probably still have not fully picked up on)
Yeah it has a lot of built in functions, so it is useful for "lazy" people I suppose. I view it as being useful for those who don't need to get into all of the details of everything.
it does differentials and integrals nicely (which i largely imagine consists of most undergrad uses), but you can do that in julia, sage, sympy, etc all for free
but teachers at unis, for whatever reason, never advocate that, but push for matlab, mathematica, etc
@AaronStevens almost all of my doctoral work was in Fortran 90. I did use some C++ and Python. Never once need to touch anything like mathematica/matlab/maple/etc
and now i'm a real programmer using C++, Java (barf) 8 & Python
@KyleKanos I took a C++ class in undergrad, but it really was essentially just an "intro to programming" class that used C++ to teach basic programming principles
We really didn't get into anything that made C++ unique
It was my first programming class, so I was fine with it I suppose. Looking back I wish it had been different
I did take a Java class too though that was much better at being an actual Java class
it says at the bottom (Viewable by the post author and users with the close/reopen votes privilege); kinda curious what insufficient privilege users see
"We’ve heard in feedback from users that receiving this feedback in public is not helpful and can contribute to negative experiences on the site. We’ve also heard from users who vote to close questions that they don’t necessarily like their names being put on display, either. Plus, we’re confident not everyone viewing a question needs to see this information. So, we’re now only displaying these names to authors and privileged users who sometimes still find this information useful."
I like putting the notice right at the top. I'm ambivalent about hiding the close voters. But I definitely dislike hiding the long text of the post notice from public view - that means that our hand-crafted notice for closing HW questions with links to the faq meta posts isn't visible to other new users who might look at such a question and wonder why it's been closed.
Declined: there are legitimate reasons to show close reasons for the public view. However, we are not going to do so at this time. The vast majority of users who will view these (without privileges to reopen) are not going to be acting on it. And we have plans to change the close workflow very soon in ways that will hopefully be more effective in achieving our objectives than this change will. We will be concentrating our efforts there. — Yaakov Ellis ♦Nov 5 at 12:13
@AaronStevens I think hiding the downvoters would be defensible - if they were also hidden from low-rep authors, since they are the most likely to get upset at the specific persons closing their question. The place where I've seen the most aggression towards close voters is from new OPs whose successive questions were closed by the same user(s).
Oh, sorry, I was talking about the hiding of close voters, no about your jest...probably shouldn't have replied to that message, I see how that was confusing :P
Downvotes should always be shown - users need to know their questions are downvoted, how else should they know people are being mean to them they aren't posting content the community considers acceptable.
@PM2Ring Sorry if I made it seem I didn't know anything about fusion. I do know a lot about fusion. The questions I asked were theories I had. I wanted to bounce the ideas off of very smart minds to help me figure it out and work through it. It's kind of a I think I know but I'm not sure kind of moment. So I needed feedback from some other minds that aren't mine. To help give me a push. Lets just say this month has been way too long and very stressful, And I had doubts.
@KyleKanos I've been thinking that the weight is fine for net positively-scored posts, but that net negatively-scored posts simply shouldn't yield any reputation gain. This avoids making downvotes more costly on highly scored answers with a few downvotes, but solves the problem of negatively-scored posts still yielding a positive amount of rep.
> **Needs more focus** > Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. Avoid asking multiple distinct questions at once. See the How to Ask page for help clarifying this question
Que!? Not Too Broad but Needs more focus!?
and "Needs details or clarity instead of unclear what you're asking
@PM2Ring Sometimes I get in such a smart mindset that I start asking to many questions about what if's and possibilities, that I get over whelmed and start I doubting. I needed a reaffirming push from a clear mind.
What if I made a synthetic finger and operate it into my hand, connect the finger with neuron fiber to the motor cortex, wait for the brain to adapt and learn to control the new input and boom, sixth finger?
It's an interesting field. Is anyone doing any progress there? I mean, what are the challenges? I don't have to create the finger nor the neural fiber, I'll just cut it of a dead person. What's the hard part?
@JMac Why wouldn't it? After all, it's just electrical stimulus. Stick it in the motor cortex (close to the areas of the other fingers) and I'm sure it'll find a way?
@NovaliumCompany I'd be more worried about your body not being able to easily add foreign connections on to it's nervous system; and how antibodies would react if you tried.
@NovaliumCompany 1. Random bits of bodies of other people are likely to be rejected by your body (consider the lengths surgeons go to to find "compatible" donors for organs!) 2. Connecting nerves artificially is complicated and hasn't been routinely successfully performed yet. 3. Just connecting a nerve doesn't do it - you need to ensure blood flow to the additional finger, etc, otherwise all the nerve is going to do is make you feel pain from the finger rotting away.
4. It's not clear that you will learn to usefully interpret this finger's signals at all. The brain is plastic, but I don't see any reason why it should necessarily "accept" these signals as anything other than noise it isn't trained for.
@NovaliumCompany Who said it wasn't possible? My point, (and presumably ACM's) is that it's not currently known how to do it. It doesn't make it theoretically impossible; but I doubt anyone is currently capable of doing it with the knowledge and technology they have access to.
The basic principle certainly works, there are several spectacularly gruesome experiments with dogs that show that attaching parts from one body to another in principle works. The difficult part is to make the transplant last without killing the recipient.
@NovaliumCompany That seems to be untrue. When we put our mind to some things, we are able to determine that some things are actually impossible, as far as we possibly understand.
@NovaliumCompany Very likely not - as I said, the mapping between genes and traits/phenotypes is complex and probably depends on many more interactions than we can usefully simulate. What probably is possible already today is specify an edit to a DNA sequence of e.g. a bacterium and then create the bacterium with that edited DNA.
Everyone thinks something is impossible until it's invented. I feel sorry for people who can't dream. I'm not here to discuss that so I won't say anything.
There's a difference between things that are impossible given our current technology, and those that are in principle impossible. All the things you've mentioned here are far beyond our current technology, but not forbidden by any principle. But this doesn't imply that it is possible for us to invent feasible ways to achieve them, either.
to pick a contemporary example, it's the difference between being Steve Jobs (have a vision, convince people to invest, and prove that it could be accomplished) and Elizabeth Holes (have a vision, convince people to invest, and utterly fail to overcome the many practical problems)
Obviously that is a very broad gloss on the Theranos saga. But the whole vision there was predicated on blood-testing becoming "table-top" when that was simply not a viable goal
Some things are complicated in a way that's simply irreducible.
@NovaliumCompany "according to our current knowledge and we might be wrong" is implicit in every human claim. If you insist that "we can't really know anything" because of that, you're only correct because you use a different meaning of the word "know" than anyone else, and that's bad for communication. E.g. given the track record of the principle of conservation of energy, I know that free energy is in principle impossible.
If you think that second sentence wrong, you're either actively disbelieving the foundations of modern physics, or you're just playing word games about what "know" means.
ur right, we don't really know anything and we don't know what it means to know.
world's a messed up place.
we can sit here and pretend to be smart and philosophical and use complicated words but in the end, we don't "know" anything, or even that claim could be "wrong"
many people here are trying to use complicated words and twist their sentences because it gives them the feeling they are smart. That's sad
Many people do and have done that I don't know why.
@NovaliumCompany Things aren't good or bad because others do them. Just doing something different isn't either. Thoughtless non-conformism is just as bad as thoughtless conformism.
I am not able to figure out the physical system as well as the meaning of Euler Lagrange equation is not differential (just algebraic).
