"If you consider a charged ball, then think about squishing it from a 3D object into a 2D piece of paper. That represents the area-based charge density." What does "squishing" mean hear? Do they mean something like projecting?
(this still refers to the post about the infinite sheet)
I don't say that there are two time-like dimensions, only that two time like dimensions are perceived. I can control the frequency of the light, so at least I can move relatively freely in the frequency dimension. Whether you want to call the frequency dimension timelike or not is not really important. And I said before that I consider electromagnetic radiation, so what. And even if, wouldn't a single downvote have been sufficient? 5 downvotes for a question which to the asker felt just normal?
But I can still look inside a solid body, if I use a frequency which doesn't interact too strongly with the matter. Especially low frequency radiation penetrates through matter without much problem. This is not too different from spatial dimensions, where I can evade an object.
(an object, but I am really thinking of a sort of barrier, which I can evade)
Why do they consider this $A$ then when they proceed to talk about the solid angle occupied by charged material later on anyways?
I find it a big assumption to say that the field strength is determined by the solid angle occupied by charged material times the 2D charge density. That seems to be an explanation of something by simply stating another assumption?
Well I guess it is more general, than the specific case of the infinite sheet
hm, one last try though: can we apply this "solid angle" argument also with a particle? Because in the case of a particle, its area is zero, no? So it never occupies any field of vision. Why do they mention is then? Or did they mention this surface A, such that they could give the particle a finite volume/area?
oh, I think I finally get it. So in the case of the infinite sheet, our solid angle is constant, and the 2D density too, because the sheet already is 2D, so we don't even have to worry about projections.
@dmckee Thanks for the explanation anyway. If you or somebody else here understands my problem and is able to formulate it in a way that other physicians would understand it too (instead of considering it ridiculous and downvote), it would be nice to know.
(My guess for the answer to my question is that achieving a high modulation of an em-wave in time is relatively easy, but high modulation in space leads at best to a change of direction, at worst to evanescent waves. This answer only came to me after I thought about why nobody understands my question...
And independently, what I wrote at the beginning of the question is still true: "In quantum mechanics, it is not obvious (for me) how to deduce the perceived dimensionality of the world from the (mathematical) description by high-dimensional wave functions.")
Yes, this is exactly what I try to understand: "What do I need to do for communicating with the physics community?"
And just assume that I don't want to teach the physics community my ideas, but get help with the points I don't understand. In case of my question, the first sentence described what I don't understand, and then I focused it on a concrete instance of the problem where I hoped that there would be an answer.
> It seems to me that in addition to the 3 spatial dimensions, two dimensions related to time are perceived: the frequency dimension corresponding to the fact that matter only interacts strongly with electromagnetic radiation of its characteristic frequency ranges, and the normal time dimension.
Explain it to me, @ThomasKlimpel - "the frequency dimension corresponding to the fact that matter only interacts strongly with electromagnetic radiation of its characteristic frequency ranges". Why does that make frequency related to time?
@ArtOfCode Because I think of QM a bit in terms of "Fourier-pairs", and here frequency is the "Fourier-pair" of time. And I wondered why the "Fourier-pair" of space was somehow different...
I put it in quotes, because "Fourier pair" is (probably) not really a valid term. If I take the Fourier transform in time, then I end up with frequency as the independent variable instead of time. This is what I mean by "Fourier pair".
@ThomasKlimpel You cannot "deduce" the dimensionality of the world from the wavefunction. The number of spatial dimensions - the number of indepedent position operators - is an input to the theory. I don't understand how you think we somehow perceive both time and frequency as dimensions, but then don't think the same of the "Fourier pair" of position and momentum.
@ACuriousMind The first part ("You cannot "deduce" the dimensionality of the world from the wavefunction.") is something I would really like to understand, I just guess it won't be too easy for me. So I focused on my questions with respect to the "Fourier pairs". I think em-waves ("we") somehow perceive frequency as a dimension, because having the (completely) wrong frequency can prevent the interaction.
I don't think the same of the "Fourier pair" of position and momentum, because I have a hard time coming up with experiments where I would be able to perceive them as a dimension.
@JohnRennie First of all, thanks for the answer, man. So, just to make sure I'm understanding this correctly, my calculations from the spacetime interval were correct (that is: $(\Delta x')^2 = (\Delta x)^2 + c^2(\Delta t')^2$ was correct, and the reason this works isn't because $\Delta x'$ is greater than $\Delta x$, but because $\Delta t$ is negative?
@0celouvskyopoulo7 age. The EXIF data on the file should indicate it was taken a few minutes ago, which lines up with me saying something about university ID. The date of birth on the card lines up with what I'm claiming.
Better proof, though, is the fact that I don't have a good reason to lie :P
@BernardoMeurer better point: if web developers didn't exist, neither would the web. Wikipedia. Google. SE. Social media. <insert other useful or entertaining websites here>.
@0celouvskyopoulo7 go look at my GH profile. Sure, I could just not have any C on it, but the likelihood is that if I knew C I'd have a project or two in it on GH.
