What is Existence: Definition and 570 Discussions

Existence is the ability of an entity to interact with physical or mental reality. In philosophy, it refers to the ontological property of being.

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  1. C

    I If we had a TOE, would we be able to explain why there is something rather than nothing?

    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?

    I Determination of error in interpolating polynomial

    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]...
  3. chwala

    Find the supremum of ##Y## if it exists. Justify your answer.

    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...
  4. whistle blower

    Absolute Open Mind Holds No Bounds

    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...
  5. S

    I Measure of existence? (Stanford Encyclopedia of Philosophy)

    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...
  6. S

    Existence of directional derivative

    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]...
  7. Graempz

    Exploring the Origins and Diversity of Life in the Universe

    Flipboard, Big Think URL, Astro-Physics interest.
  8. T

    I Integrity of matter / space and time

    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...
  9. Revolucien

    I Biphoton: Existence of layered or multiple entanglements

    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...
  10. E

    I Proof of Lorentz Gauge Existence: Help Understanding Schutz 8.3

    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...
  11. S

    A Extended Wigner’s Friend Scenario and the existence of the reality

    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...
  12. J

    I Existence and Uniqueness of Inverses

    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...
  13. brotherbobby

    Proving that the inverse of a rational number exists

    Problem statement : I cope and paste the problem as it appears in the text below. 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 right, we see ##ab =...
  14. T

    B Proof of the existence of atoms

    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?
  15. J

    A Does the existence of a POVM require an ancilla?

    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...
  16. T

    A Existence of unique solutions to a first order ODE on this interval

    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...
  17. mcastillo356

    B Another proof of the existence of extreme values on open intervals

    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...
  18. C

    DP: proving existence of optimal substructure for "Sherlock and Cost"

    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...
  19. Zeeshan Ahmad

    I Evidence for existence of a 9th Planet in the solar system

    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? The evidence for Planet 9 comes from its gravitational pull on other bodies. If the planet exists, its gravity will affect the orbits of...
  20. H

    I Is the existence of a Dyson Sphere impossible?

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

    MHB Diagonalizable transformation - Existence of basis

    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...
  22. H

    Confirm Limit Existence for Function f w/o Piecewise Def.

    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...
  23. C

    Showing existence of an Edge s.t. Graphs T1' , T2' are Trees

    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 \})...
  24. Eclair_de_XII

    B Proving the Existence and Value of a Derivative at a Point

    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...
  25. P

    Proving the existence of a real exponential function

    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##...
  26. C

    Existence of isomorphism ϕ:V→V s.t. ϕ(ϕ(v))=−v for all v∈V

    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 ##...
  27. MathematicalPhysicist

    A A thought on the existence of an odd perfect number

    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...
  28. V

    Existence and Uniqueness For ODE

    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...
  29. R

    B Can physics deal with the existence of Pi?

    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
  30. R

    What is everything really? All of it?

    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
  31. tomdodd4598

    I Argument for Existence of Normal Coordinates at a Point

    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...
  32. P

    B Consequences of the Existence of Gravitational Waves?

    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...
  33. evinda

    MHB Show Existence of $a,b$: Proof for $f'(\xi) \neq 0$

    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...
  34. Adesh

    Why the existence of the potential function ##U## is not sufficient?

    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...
  35. T

    I The existence of negative gravitational plus positive inertial mass?

    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...
  36. M

    MHB Check existence of limit with definition

    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...
  37. L

    B Existence of parallels in axiomatic plane geometries

    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...
  38. Math Amateur

    I Riemann Integration ... Existence Result .... Browder, Theorem 5.12 ....

    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...
  39. Math Amateur

    MHB Riemann Integration ... Existence Result .... Browder, Theorem 5.12 ....

    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...
  40. A

    B Unraveling the Tachyon and Photon Debate: Exploring Faster-Than-Light Particles

    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...
  41. T

    I On what plane of existence do quantum computations occur?

    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...
  42. Suppaman

    B What parameters of physics are most important to the existence of life?

    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...
  43. Physics lover

    Chemistry Calculating Hybridisation and Existence of a Compound with Boron

    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.
  44. F

    A Exploring the Existence of Baryons with Positive Strangeness

    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...
  45. S

    A Does Bohmian Mechanics yield the existence of a multiverse?

    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...
  46. nomadreid

    I Are existence proofs outlawed in multi-valued logics?

    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...
  47. P

    A Why the fine-tuning argument for improbable existence is a fallacy

    "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...
  48. G

    I Conserved Stress-Energy in Gravitational Theories

    My post https://www.physicsforums.com/threads/indirectly-coupling-gravitational-field-wei-tou-ni-stress-energy.969033/ got no replies. So I formulated those statements on the stress-energy tensor (SET) which are of most interest to me. I would be very grateful if you either confirmed them or...
  49. A

    I Invariant symbol implies existence of singlet representation

    I don't understand what the last paragraph of the attached page means. Why does the Kronecker delta being an invariant symbol mean that the product of a representation R and its complex conjugate representation has the singlet representation with all matrices being zero? Doesn't the number...