What is Fundamental: Definition and 946 Discussions

Given a topological space and a group acting on it, the images of a single point under the group action form an orbit of the action. A fundamental domain or fundamental region is a subset of the space which contains exactly one point from each of these orbits. It serves as a geometric realization for the abstract set of representatives of the orbits.
There are many ways to choose a fundamental domain. Typically, a fundamental domain is required to be a connected subset with some restrictions on its boundary, for example, smooth or polyhedral. The images of a chosen fundamental domain under the group action then tile the space. One general construction of fundamental domains uses Voronoi cells.

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  1. e2m2a

    I The Fundamental Theorem of Arithmetic and Rational Numbers

    The fundamental theorem of arithmetic applies to prime factorizations of whole numbers. Can this theorem also correctly be invoked for all rational numbers? For example, if we take the number 3.25, it can be expressed as 13/4. This can be expressed as 13/2 x 1/2. This cannot be broken...
  2. R

    B A doubt on the fundamental unit of charge

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  3. S

    A Can Cosmic Inflation and String Theory change fundamental laws?

    Is there any version of string theory or cosmological inflation that allows the most fundamental laws and constants change between universes? String Theory and Cosmological Inflation are two theories or models that allow multiple universes to exist. Laws and constants of physics could change...
  4. S

    A Standard Model and number of fundamental forces

    Just a curious question, is there a limit within the standard model on how many fundamental forces there can be? I have some familiarity with particle physics/QFT(not quite mastery obviously otherwise Id probably be able to answer this myself) and the thought popped in my head when reading about...
  5. Anachronist

    Fundamental frequency of a rectangular-cavity whistle

    I designed a parametric CAD model of a whistle that can be 3D printed. Basically I designed the internal airspaces, put a skin around it, and printed it. Combine two of these in the same enclosing body, with slightly different frequencies, and you get a warbling sound similar to a pea whistle...
  6. N

    I What does it mean to say space and time are fundamental in physics?

    What feature of the equations of classical physics show that space and time are fundamental and how would the equations differ if space and time were not fundamental but emergent? I heard all of this from a previous talk and I would appreciate any help and any further reading recommendations.
  7. EchoRush

    I Questions about the fundamental thoerem of calculus

    As you can see form my previous posts, I am in my first university level calculus class ever. It is going very well, and through the class I am asking good questions and trying to actually make connection with the stuff we arr doing - not just doing the math just for the sake of passing - I am...
  8. Z

    Building a CPU with Si JFETs: Fundamental Challenges?

    Would there be any fundamental reasoning (i.e. excluding cost, energy, and resources) that we could not build a modern day CPU using Si JFETs rather than Si CMOS? I realize the JFET device size would be huge, and the absences of enhancement mode JFETs may impact power consumption, but would...
  9. PeroK

    I Fundamental Theorem of Algebra: Proof

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  10. berkeman

    How were the fundamental improvements in Voice Recognition achieved?

    I remember about 20 years ago a colleague had to start using the Dragon Voice Recognition software on his EE design PC because he had developed really bad carpal tunnel pain, and he had to train the software to recognize his voice and limited phrases. That was the state of the art not too long...
  11. S

    I Could fundamental laws change in Dirac's Large Numbers Hypothesis?

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  12. L

    I "Knowledge" in Psi-Epistemic Interpretation Fundamental or Emergent?

    Is "Knowledge" in quantum Psi-Epistemic interpretation fundamental or emergent? And what does it mean? What do you think? https://backreaction.blogspot.com/2019/08/the-problem-with-quantum-measurements.html "One way to deal with the measurement problem is to argue that the wave-function does...
  13. M

    A Explaining the Hubble tension with fundamental physics

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  14. R

    B A proof of the fundamental theorem of calculus

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  15. J

    I Is Time More Fundamental Than Space? Exploring Smolin's Hypotheses

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  16. J

    I Why are all quarks considered fundamental?

    Summary: If 5 of the quarks can eventually decay into the up (plus other stuff), why are they still considered fundamental? I can't decide if I'm just misinterpreting the word fundamental in this particular usage or if there is something about the non-up quarks that makes them fundamental even...
  17. E

    B Finite & Infinite: Univerally Accepted Definitions?

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  18. bernardoprepmare

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    I do not know how to declare time t and unit steps. The image of problems to get a better understanding as well.
  19. S

    A Is M-Theory more fundamental than String Theory?

    M-Theory is a theory of membranes which are the fundamental objects of the theory (M2 and M5 branes), however these objects are considered solitons, solutions of supergravity. How can membranes be "fundamental" if they are solitonic solutions of supergravity? Or am I missing something? And is...
  20. karush

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  21. J

    B Questions Regarding the Fundamental Rules of Error Analysis

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  22. G

    Ni's Alternative Theory of Gravity: Examining Fundamental Properties

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  23. S

    I Can Fundamental Theorem Algebra be proven by simple DOF?

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  24. S

    I On the topological proof of the Fundamental Theorem of Algebra

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  25. M

    Fundamental solution for unbounded solution

    Homework Statement Find the fundamental solution to the unbounded problem $$t u''(t) - u'(t) = \delta_0.$$ Homework Equations Variation of parameters. The Attempt at a Solution I'm not sure how to use variation of parameters on this since it's an unbounded problem, so I'm not even trying to...
  26. ChrisXenon

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  27. O

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  28. S

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  29. A

    B Is it possible to change a fundamental property of a particle?

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  30. G

    I Pascal's law (fluids): Derivable from fundamental laws?

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  31. Jason-Li

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  32. Nikhil Rajagopalan

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  33. opus

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  34. K

    I Fundamental equation in string theory

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  35. C

    MHB Some fundamental question in combinatorics

    Hey. We started to study all this subject of combinatorics integrated with the subject of functions. 1. I don't actually understand how to integrate between combinatorics and function, those functions which represent our possibilities and etc... And why at all we need to represent our...
  36. Delta2

    Insights A Numerical Insight for the Fundamental Theorem of Calculus - Comments

    Greg Bernhardt submitted a new blog post A Numerical Insight for the Fundamental Theorem of Calculus Continue reading the Original Blog Post.
  37. Fala483

    B Proof: 0.999... Squared = 1

    I am trying to prove that all numbers of the form 0.999... Squared end in a decimal value of 1. For example 0.99sq = 0.9801 0.999sq = 0.998001 Etc. Is it possible to prove for all 0.999... ?
  38. Auto-Didact

    A Quantization isn't fundamental

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  39. P

    A Fundamental definition of extrinsic curvature

    My question is quite simple: what is the fundamental definition of extrinsic curvature of an hypersurface? Let me explain why I have not just copied one definition from the abundant literature. The specific structure on the Lorentzian manifold that I'm considering does not imply that an...
  40. J

    A Does it make sense to break T duality at fundamental level?

    https://arxiv.org/abs/hep-th/0605250 Here is an attempt to make bohmian mechanics compatible with string theory. It posits that T duality breaks at the fundamental level, and that the is no minimal length in the theory. Does this proposal make sense?
  41. J

    Why do Harmonics Decay Faster than the Fundamental?

    When looking at the FFT spectrum of a sonometer, I noticed that the harmonics decayed faster than the fundamental. Why is this?
  42. F

    How scientists ensured this fundamental property of magnets?

    Firstly, please note that I am talking about the period BEFORE electricity and magnetism were unified. So I am NOT seeking for answers based on Ampere atomic current model of magnets. I have read the following statement about the property of magnets at two different places. One from here: and...
  43. K

    I Theories without Fundamental Space and Time

    Can string theory be made without time equations? According to Carlo Rovelli in his latest book "The Order of Time" https://www.amazon.com/dp/073521610X/?tag=pfamazon01-20 : "The equations of loop quantum gravity on which I work are a modern version of the theory of Wheeler and DeWitt. There...
  44. S

    Fundamental confusion about THREE-PHASE electric power setup

    Homework Statement Hello to everyone who's reading. :) I hope I posted this in the right place; while this is not exactly a homework problem, I am trying to improve my understanding of the background information before proceeding with course-style problems. This post is because I'm trying to...
  45. L

    I Particles more fundamental than fields

    In this Nima Arkani-Hamed paper on page 5 I found the sentence: These constraints are an artifact of using fields as auxiliary objects to describe the interactions of the more fundamental particles. In Schwartz's QFT book I also get away with the impression that the Poincaré irreps (i.e...
  46. L

    I Is Energy Fundamental or Derived?

    In the beginning we had Newton's Laws which introduced force as the fundamental entity of nature. Energy was understood as a derived concept, i.e. Energy = force x distance. Later, however, there arose the formulations of LaGrange and Hamilton where energy is the fundamental entity, i.e. Force...
  47. R

    A Free bar fundamental vibration relationship length to width

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  48. cnh1995

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    I am revising some topics in analog electronics and I am currently working on the BJT. I know the applications of these devices (diodes, transistors) and know the necessary formulae to work out problems. But there are a few fundamental things which are still unclear to me and I am not very...
  49. arupel

    I Colonies on Mars -- fundamental problem

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  50. A

    A How to calculate the second fundamental form of a submanifold?

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