Existence Definition and 543 Threads

So far, I've got that ## g(a)=(c-1)a+\frac{3}{4}a^3\implies g'(a)=c-1+\frac{9}{4}a^2 ##. I know that if the first derivative of a function is positive (greater than ## 0 ##), then that function is always/strictly increasing. However, how should I construct this proof in order to show that...

Are quantum physicists hopeful that a theory of everything can derive neccesity out of quantum fluctuations or whatever is said to have been the most fundamental existence? The reason I ask is because the deepest question in philosophy is why does anything exist at all. But it doesn't seem to...

If we could have one day theory of everything thing, would we be able to explain why there is something rather than nothing and would we be able to know why there are physical laws?

Professor showed this result in the lecture without giving any proof (after proving the existence of the interpolating polynomial in two variables). I've been trying to prove it myself or find a book where is proved but I failed. This is the theorem: Let $$ x_0 < x_1 < \cdots < x_n \in [a, b]...

Refreshing on old university notes...phew, not sure on this... Ok in my take, ##x>0##, and ##\dfrac{dy}{dx} = -3x^2=0, ⇒x=0## therefore, ##(x,y)=(0,\sqrt2)## is a critical point. Further, ##\dfrac{d^2y}{dx^2}(x=0)=-6x=-6⋅0=0, ⇒f(x)## has an inflection at ##(x,y)=(0,\sqrt2)##. The supremum of...

I’m male, my nature has always been to question everything explore possibilities, over my latter years convinced that for the short period of time we existed we gained very little, if we did stay around a little longer we may learn a little more, what we cannot prove to be correct is where we...

I'm reading the article on the Many Worlds Interpretation in the Stanford Encyclopedia of Philosophy. I'm keeping up well, but this excerpt uses things I'm very unfamiliar with: I guess some characters weren't recognized. It's Section 3.6 here. I'm somewhat familiar with Wigner's Friend, but...

My attempt: I have proved (i), it is continuous since ##\lim_{(x,y)\rightarrow (0,0)}=f(0,0)## I also have shown the partial derivative exists for (ii), where ##f_x=0## and ##f_y=0## I have a problem with the directional derivative. Taking u = <a, b> , I got: $$Du =\frac{\sqrt[3] y}{3 \sqrt[3]...

Flipboard, Big Think URL, Astro-Physics interest.

I have probably a basic question from Space, Time and Matter area. My 11 years old daughter asked me once why we exist physically in a stable form if everything is infinite. We had a conversation about it but then it got me thinking about this and it seems I can't find the answer. There is...

I read this recent article describing photon quantum entanglement to produce higher resolution microscope. https://phys.org/news/2023-05-quantum-entanglement-photons-microscope-resolution.html I am curious if quantum entanglement could exist in layers with a third or more entanglement feature...

In Schutz 8.3, while proving that a Lorentz gauge exists, it is stated that $$\bar h^{(new)}_{\mu\nu} = \bar h^{(old)}_{\mu\nu} - \xi_{\mu,\nu} - \xi_{\nu,\mu} + \eta_{\mu\nu}\xi^\alpha_{,\alpha}$$ where ##\bar h## is the trace reverse and ##\xi^\alpha## are the gauge functions. Then it follows...

https://backreaction.blogspot.com/2022/02/has-quantum-mechanics-proved-that.html It is unclear for me, why from these experiments the tabloids made the conclusion that "the reality does not exist"? Does the essence of this experiment lie in the fact that it confirmed the Wigner's friend...

Existence: Ax = b has at least 1 solution x for every b if and only if the columns span Rm. I don't understand why then A has a right inverse C such that AC = I, and why this is only possible if m≤n. Uniqueness: Ax = b has at most 1 solution x for every b if and only if the columns are...

[FONT=georgia]Problem statement : I cope and paste the problem as it appears in the text below. [FONT=georgia]Attempt : Not being a math student, I try and prove the above statement using an "intuitive" way. Let us have a rational number ##b = \frac{n}{m}##. Multiplying with ##a## from the...

It is said that some physicists doubted the existence of atoms in 1900 until Einstein proved their existence a few years later. Did Mendeleev's creation of the periodic table in the 1870s already prove the reality of atoms by giving the known elements atomic masses?

In DeMuynck's paper, POVMs: a small but important step beyond standard quantum mechanics, he describes a "generalized quantum mechanics" in which a generalized observable can be represented by POVM. In contrast, most other references that I have seen discussing this talk about first...

I am trying to find a way to prove that a certain first order ode has a unique solution on the interval (1,infinity). Usually the way to do this is to show that if x' = f(t,x) (derivative with respect to t), then f(t,x) and the partial derivative with respect to f are continuous. However, this...

Hello, PF This is Theorem 8 of Chapter 4 of the ninth edition of Calculus, by Robert A. Adams: "Existence of extreme values on open intervals". I have an alternative and easier proof, based on epsilon-delta arguments, but it's not mine, and I don't understand it completely. The fact is that...

I was attempting to solve the "Sherlock and Cost" problem from HackerRank using DP: But before I went to come up with a recursive relation, I wanted to find if the problem possesses an optimal substructure, and I was following these steps as written at CLRS book: Mentor note: Inline images of...

[FONT=times new roman]Could the existence of the 9th planet of the solar system is possible under these arguments of existence of it some where in the out scurt of solar system[FONT=times new roman]? The evidence for Planet 9 comes from its gravitational pull on other bodies. If the planet...

Specifically a monolithic Dyson Sphere; also, how would a Dyson Swarm work / be a better option?

Hey! :giggle: Let $1\leq n\in \mathbb{N}$ and for $x=\begin{pmatrix}x_1\\ x_2\\ \vdots \\ x_n\end{pmatrix}, \ x=\begin{pmatrix}x_1\\ x_2\\ \vdots \\ x_n\end{pmatrix}\in \mathbb{R}^n$ and let $x\cdot y=\sum_{i=1}^nx_iy_i$ the dot product of $x$ and $y$. Let $S=\{v\in \mathbb{R}^n\mid v\cdot...

If you are told something holds if the limit exists, and given a function f (specifically not piecewise defined), is it enough to show that the limit as x approaches c = the function evaluated at c? With a piecewise defined function, it is easy to check both sides of a potential discontinuity...

Attempt - I am stuck at this problem for hours, couldn't make any progress. Still, here's what I've done : Let ## e_1 \in E_1 \setminus E_2 ## be arbitrary. Suppose for the sake of contradiction that ## \forall ## ## e_2 \in E_2 \setminus E_1 ##, ## T_1' = \langle V,(E_1\setminus \{ e_1 \})...

This proof has three steps and is very similar to (if not the same as) that other proof I posted here.(1) Prove the existence of a ball centered around ##a## with the property that ##f'## evaluated at any point in the ball is positive. (2) Prove that the right end-point of this ball is bounded...

Ok, first I tried to show that ##A = \left \{a^{r}|r\in\mathbb{Q},r<x \right \}## does not have a maximum value. Assume ##\left\{ a^{r}\right\}## has a maximum, ##a^{r_m}##. By this hypothesis, ##r_{m}<x## and ##r_{m}>r\forall r\neq r_{m}\in\mathbb{Q}##. Consider now that ## q\in\mathbb{Q}|q>0##...

Problem: Let ## V ## be a vector space over ## \mathbb{F} ## and suppose its dimension is even, ## dimV=2k ##. Show there exists an isomorphism ## \phi:V→V ## s.t. ## \phi(\phi(v))=−v ## for all ## v \in V ## Generally that way to solve this is to define a basis for the vector space ## V ##...

Well the most obvious approach to prove that such a number doesn't exist is by ad absurdum, or so I think. Assume there exists an odd perfect number ##2n+1##, then by definition ##2n = \sum_{m\ne 1, 2n+1, m|(2n+1)}m##. So, since m is odd (since 2n+1 is odd and it divides it), if you can prove...

I'm new to learning about ODE's and I just want to make sure I am on the right track and understanding everything properly. We have our ODE which is y' = 6x3(y-1)1/6 with y(x0)=y0. I know that existence means that if f is continuous on an open rectangle that contains (x0, y0) then the IVP has...

Hi. I'm not sure if physics/cosmology can deal with my question. I suspect not, but I'll ask it anyway. The answer could be "No" and that would be "end of". Is there any situation, where Pi = 3.142...does not exist as a fact? Thanks. Rich

Are there any references?

You keep asking what caused it and you get to Big Bang.maybe you’re smarter and can go further back.but does it end?and even if it does or doesn’t?why do everything,equations,ideas and physical things exist?what is all this?everything?are you feeling what I’m trying to ask?existence scares me

Hey there, I've been recently been going back over the basics of GR, differential geometry in particular. I was watching one of Susskind's lectures and did not understand the argument made here (26:33 - 35:40). In short, the argument goes as follows (I think): we have some generic metric ##{ g...

I'd like to see some of the consequences of the existence of gravitational waves (both expected and unexpected), in laymen's terms so a simpleton like me can understand and relate to them. A possible consequence that I thought of (and I'm sure someone will correct me if I'm wrong) is that...

Hello! (Wave) Let $I$ an interval and $f: I \to \mathbb{R}$ a differentiable (as many times as we want) function. If $\xi \in I$ with $f''(\xi) \neq 0$, then there are $a,b \in I: a< \xi <b$ and $\frac{f(b)-f(a)}{b-a}=f'(\xi)$. Hint: First suppose that $f'(\xi)=0$ and show that at $\xi$ we...

In Sommerfeld’s Lectures on Theoretical Physics, Vol II, Chapter 2, Section 6, Page 43 we derive an expression for the equilibrium of liquids as $$ grad ~p = \mathbf F$$ Where ##p## is the pressure and ##F## is the exertnal force. Then he writes, [ The equation above ]includes a very remarkable...

The term “negative mass” gets puts forth occasionally, and it’s definitions can sometimes be unclear. the topic I’m interested in is particles which have both positive inertial mass and negative gravitational mass. So far, what theories do physicists have of speculating on the existence of...

Hey! :o I want to check the existence of the limit $\lim_{x\to 0}\frac{x}{x} $ using the definition. For that do we use the epsilon delta definition? If yes, I have done the following: Let $\epsilon>0$. We want to show that there is a $\delta>0$ s.t. if $0<|x-0|<\delta$ then...

Parallels exist in both Euclidean and Hyperbolic geometry. Yet each includes a separate postulate that declares the number of parallels to a line in a plane through a given point. But it seems that if both geometries have parallels then their existence - as opposed to how many of them - should...

I am reading Andrew Browder's book: "Mathematical Analysis: An Introduction" ... ... I am currently reading Chapter 5: The Riemann Integral and am currently focused on Section 5.2 Existence Results ... ... I need some help in understanding the proof of Theorem 5.12 ...Theorem 5.12 and its...

I am reading Andrew Browder's book: "Mathematical Analysis: An Introduction" ... ... I am currently reading Chapter 5: The Riemann Integral and am currently focused on Section 5.2 Existence Results ... ... I need some help in understanding the proof of Theorem 5.12 ...Theorem 5.12 and its...

A tachyon or tachyonic particle is a hypothetical particle that always travels faster than light. Most physicists believe that faster-than-light particles cannot exist because they are not consistent with the known laws of physics. - Tachyon definition The photon is a type of elementary...

I was recommended by another mentor to purchase a good book on MWI, which I think should be a thread or poll of its own. Anyway, I might have debased myself too much in that other topic, as I understand on an abstract level how QM works. In my own words, I feel as though possible worlds are...

The universe after the big event was a lot of lifeless stuff. However, as things settled down the rules behind the curtain were such that life was allowed to develop, they may have even been such that they encouraged the things to happen that were conducive to the process that has resulted in...

One would easily calculate its hybridisation by the above formula which comes out to be sp. But my doubt is that will the compound even exist?As boron will become electron deficient and how we will calculate no. of bond pairs and lone pairs.Please clear my doubt.

Hi all, I read on "Intoduction to Elementary Particle Physics" (A. Bettini) that baryons with positive strangeness cannot exist. I don't know what to conclude from this sentence: sigma-baryons have negative strangeness, since there's a sigma as valence quark. But these baryons have, of course...

David Deutsch, a theoretical physicist, talks about David Bohm in his book "the Fabric of Reality": "[w]orking out what Bohm’s invisible wave will do requires the same computations as working out what trillions of shadow photons will do. Some parts of the wave describe us, the observers...

First, is my assumption that all consistent multi-valued logics obey the principle of explosion from a false proposition correct? If so, how would one prove that? (I assume it is, because if not, then by the definition of intuitionist logic by Wolfram Mathworld...

"In 1961, physicist Robert H. Dicke claimed that certain forces in physics, such as gravity and electromagnetism, must be perfectly fine-tuned for life to exist anywhere in the universe. Fred Hoyle also argued for a fine-tuned universe in his 1984 book Intelligent Universe. Much as been written...