Fundamental Definition and 907 Threads

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...

"a charge smaller than e has not been found. if one determines the amount of charge on any charged body like a charged sphere or charged drop) or any charged particle (like positron, a-particle) or any ion, then its charge is always found to be an integral multiple of e, i.e., e,3e; 4e,... No...

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...

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...

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...

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.

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...

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...

I found this video showing an elementary proof of the FTA.

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...

Paul Dirac proposed a hypothesis called "Large Numbers Hypothesis" (https://en.wikipedia.org/wiki/Dirac_large_numbers_hypothesis), where he basically stated that, if he was correct, laws of physics would change with time. But what about fundamental laws and constants? (Not only 'effective'...

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...

The Hubble tension or Hubble discrepancy is a contradiction between the Hubble constant as measured today, and the Hubble constant as measured in the early universe and extrapolated to today. @mfb recently listed the relevant measurements. There are some threads about this in the Cosmology...

is there a rigorous version of this proof of fundamental theorem of calculus?if yes,what is it?and who came up with it? i sort of knew this short proof of the fundamental theorem of calculus since a long while...but never actually saw it anywhere in books or any name associated with it. i know...

In Smolin peer reviewed papers, he proposed time was fundamental. The ideas were summarized briefly in his new book "Einstein's Unfinished Revolution. He wrote that "If time is more fundamental than space, then during the primordial stage, in which space is dissolved into a network of relations...

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...

I'm troubled by what I think the 'community' considers them to be, but I'm not sure if I'm correct. It appears as though finite is thought to have both an end and a beginning, but is it true that infinite (infinity) is thought to only have no end? Is this accurate? If so, then it would seem like...

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

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...

determine their general solution and give a system of fundamental solutions. use the different techniques of diagonal, diagonalizedable, or triangular. $\begin{cases} y'_1 & =3y_1 \\ y'_2 & =2y_2\end{cases}$ set matrix $A= \begin{pmatrix}0 &3\\0 &2\end{pmatrix}$ then find...

(A)My textbook states the following : (1) The example explaining the italicised statement is rather confusing. My understanding of the statement is that we need to include one extra significant figure than what the relevant rule requires us to round off to, for intermediate...

A monic polynomial of degree N has N number of coefficients. The product of N number of linear factors has N number of free terms. A complex number has 2 DOF. Therefore, both a monic polynomial and the product of free terms have 2N number of DOF of real values. Thus, it must be possible to...

Sorry for the misspelling, but this forum doesn't allow enough characters for the title. The title should be: For the topological proof of the Fundamental Theorem of Algebra, what is the deal when the roots are at the same magnitude, either at different complex angles, or repeated roots? I...

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...

I know the textbook definitions and descriptions of the phenomenon, but I'm hoping for a fundamental WHY. I can see that when a water wave passes an obstacle, the wave spreads out into that object's shadow because the wave's energy is not constrained to any direction and so it will move out in...

Does the understanding and application of physics and fundamental chemistry is only required to be physicist? Or you have to be be equally apt in chemistry??

Given that absolute zero is the lowest temperature possible, were all particles have zero vibration. And given that the speed of light is the highest speed any object, particle, sub atomic or not can travel. Using 2 of the most fundamental laws of physics thermodynamics and general relativity...

Is it possible to change a fundamental property of a particle? If that can be done, will it's twin particle's state also be altered accordingly?

Hi. Pascal's law states that static pressure in a confined incompressible fluid without gravity is the same everywhere. Is this law derivable from more fundamental laws? Some thoughts: Is Pascal's law part of the definition of the liquid state? If the liquid operates between two hydraulic...

Homework Statement An ac voltage, comprises of a fundamental voltage of 100 Vrms at a frequency of 120 Hz, a 3rd harmonic which is 20% of the fundamental, a 5th harmonic which is 10% of the fundamental and at a phase angle of 1.2 radians lagging. (i) Write down an expression for the voltage...

For a wave A sin ( kx - ωt) and a wave A sin ( kx + ωt) traveling opposite to each other, on evaluating by applying superposition principle , the resultant displacement function is 2A sin ( kx ) cos (ωt) . For different Node Anti-node configurations we calculate natural frequencies of the...

Homework Statement The current section I'm working on has to do with arc length of a curve and surface area. These all eventually end up with having to take the anti-derivative of a radical. At each instance, I get stuck by using u-substitution because when I take the derivative of ##u##, my...

Is there a fundamental equation in string theory and can it be derived from a variational principle?

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...

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

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... ?

This thread is a direct shoot-off of this post from the thread Atiyah's arithmetic physics. Manasson V. 2008, Are Particles Self-Organized Systems? The author convincingly demonstrates that practically everything known about particle physics, including the SM itself, can be derived from first...

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...

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?

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

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...

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...

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...

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...

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...

When finding the fundamental for thin bars, the approximate equation (http://hyperphysics.phy-astr.gsu.edu/hbase/Music/barres.html) only refers to the length and thickness when calculating. I'm trying to figure out the frequency and node location along the length and width of the fundamental...

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...

I believe it is the CEO of Amazon that would like to establish a large colony on Mars, making the safe assumption that some extinction event on Earth will get us anyway. While there are numerous difficulties to this, there is one, I did not see mentioned, which makes this impossible. The...

This may be an overly-broad question, but is there any reason to think we will ever have the technical mastery over gravity, the strong force, and the weak force, that we have over electromagnetism? Example: turn on a switch, gravity; turn off a switch, no gravity.

Mesons and baryons have both a ground state and excited states involving the same valence quarks but a higher mass (which can in principle be calculated from QCD). Fundamental fermions and bosons, however, do not appear to display this behavior. They have a ground state, and while there are...