What is Equivalence: Definition and 743 Discussions
In mathematics, an equivalence relation is a binary relation that is reflexive, symmetric and transitive. The relation "is equal to" is the canonical example of an equivalence relation.
Each equivalence relation provides a partition of the underlying set into disjoint equivalence classes. Two elements of the given set are equivalent to each other, if and only if they belong to the same equivalence class.
Dear Everybody,
I am working on my homework. I am trying to prove a problem that was written by my professor in an odd way: Prove that when p is true, then q is true. Which proposition statement should I assume? I personally thought that I should assume the first one. But reading my...
So, my approach and solution are as follows:
$$
[x * y] = \{ z \in M : z \sim (x * y) \}
$$
Since we know that ##a * b \sim a^{\prime} * b^{\prime}## we can rewrite ##z## as ## x^{\prime} * y^{\prime} ##. Plugging this in yields:
$$
[x * y] = \{ x^{\prime}, y^{\prime} \in M : x^{\prime} *...
I'd like to do some experiments with flames at different Equivalence Ratios - but I'm confused as to how I can find the Equivalence Ratio for different conditions. Wiki-article
So the stoichiometric balance for Methane + Air is
CH4 + 2(O2 + 3.76N2) -> CO2 + 2H2O + 7.52N2
Referencing equations...
https://arstechnica.com/science/2022/09/einstein-wins-again-space-satellite-confirms-weak-equivalence-principle/
See also http://dx.doi.org/10.1103/PhysRevLett.129.121102 (limited access)
The following passage is from Halliday Resnick Krane in Chapter 3 which is about dynamics in one dimension.
"We can measure frictional forces. By placing the body on a horizontal surface where it experiences a frictional force, we could attach a spring and pull the body with just the right...
Dear All,
I am trying to solve the attached two questions.
In both I need to determine if the relation is an equivalence relation, to prove it if so, and to find the equivalence classes.
In both cases it is an equivalence relation, and I managed to prove both relations are reflexive. Now I...
Many tutorials that explain the weak principle of equivalence (Galileo, Newton) do not clearly state whether the body is affected by the force of inertia during free fall as a result of the gravitational acceleration of the body. In other words, the question is whether, during the free fall of a...
It's assumed that interaction rate between a species of particule m and l is expressed as:
Γm=<nlσv>,
where nl is the density of the species l, σ the cross-section of species m (=probability of interaction) and v the relative velocity between the two particles.
It's also assumed that...
I'd like to share the following competition problem:
My first reaction was that the thermometer will be able to measure heating due to the Unruh effect whilst his lab is accelerating.
Although I am not a physicist, I am interested in physics, and recently I've been reading about special relativity. I have a doubt about it, a difficulty I see in the equivalence of all inertial reference frames which I haven't found solved anywhere, and I've thought perhaps you in this Forum...
It is a theorem that: two propositions implying each other, in the sense that the set of outcomes making one true is the same as the one making the other true) have the same probability. this comes from the fact that if p --> q, the P(p&q) = P(p), we have that if p <-> q, then P(p&q) = P(p)=...
Without suggesting that there actually is a massive spherical shell enclosing the universe, I am trying to explore whether the observed expansion of the universe would be the same if there was a spherical shell with a diameter greater than the universe, with some arbitrary mass producing a...
I am studying the general theory of relativity(GTR). Covariance and the principle of equivalence are foundational pillars for the theory. I can understand the need for covariance but I don't see why the need for the principle of equivalence (POE). What I have seen so far is that the...
Not sure when to use Rindler coordinates to analyze dynamics in a constant accelerating reference system. Rindler coordinates seem messy because they are always changing. Wouldn't it be easier to invoke the principle of equivalence and treat the environment of an accelerating system as a...
Summary:: Searching for Paper by R H Dicke
Good day all.
Does anyone know where I might obtain a copy of the Paper
R. H. Dicke. Gravitation without a principle of equivalence. Review of Modern Physics, 29(3):363–376, 1957
I am prepared to pay for it.
Thanks
Paul
Consider the following theorem:
Theorem: Let ##f## be a concave differentiable function and let ##g## be a concave function. Then: ##y \in argmax_{x} {f(x)+g(x)}## if and only if ##y \in argmax_{x} {f(y)+f'(y)(x-y)+g(x)}.##
The intuition is that local maxima and global maxima coincide for...
Consider the two functions f(x)=(x²+3x+10)+(2x²+2x-17) and g(x)=(4x²+4x+4)-(x²+x+11). If they are equivalent, prove they are; if they are not equivalent, prove they aren't.
Consider the two functions f(x)=(x-1)(x4+x³+x²+x+1) and g(x)=x5-1. If they are equivalent, prove they are; if they are not equivalent, prove they aren't.
I just thought of this. I'm not an expert, so cut me some slack if I get something wrong.
Given:
1) Acceleration is supposed to produce a Rindler horizon.
2) If I understand it correctly, under Relativity and/or the Equivalence Principle, standing on (for example) the Earth is the same as...
I read that the parameters of each these two theories can be obtained from parameters of the other theory and if one event may appear in ads5 with a given probability there is another event in the CFT side which will get the same probability.
But is there a one to one map between the two space...
The equivalence principle states that a person stood on Earth would experience “gravity” the same as if he was in an elevator in space traveling at 1g. I get this. but when Einstein was first exploring this, I read he came to the realisation that a person free falling on Earth (if in a vacuum)...
Sometimes to help describe one expression, another expression is shown that produces identical results. The exact equivalence of expressions is indicated with ‘ ≡’.
For example: rot90 ([1, 2; 3, 4], -1) ≡ rot90 ([1, 2; 3, 4], 3) ≡ rot90 ([1, 2; 3, 4], 7)
What is the meaning of 'rot90;?
What...
a) Can we convert energy to mass (matter) in every day life?
b) When we charge a phone battery, its mass (weight) increases according to E=mc2 . Does it mean we convert energy to matter? If not, how its mass increases?
I am a high-school teacher and a PhD. student. I am looking for ways to introduce my students to GR. In my treatment, I speak about the equivalence principle and later about curvature in general and consequently that of spacetime. I am missing a connection of these two parts that would be...
Hello,
So I read that a person in a rocket accelerating at 9.8m/s^2 would feel the same pull downwards as a person standing on the Earth's surface.
However, I can think of a few instances where you could tell the difference:
- If you measure g (9.8N/kg) on Earth, you will notice that the...
First, in section 20.4, after listing all the things gravitational potential energy does not do, they say the equivalence principle forbids it being localized. I thought I understood the equivalence principle, but maybe I don’t. Any comments explaining that would be appreciated.
Second, they...
I was recommended a paper:
<https://digital.library.adelaide.edu.au/dspace/bitstream/2440/101285/3/hdl_101285.pdf>.
And in the opening sentence read: "The Einstein equivalence principle (EEP) is at the heart of special relativity."
To me this didn't make sense. Firstly because Einstein...
Prove that:
$(A\cap B)\cup(B\cap X')=0$ is equιvalent with
$B\subseteq A'$ and $B\subseteq X\subseteq A'$
0 is for the emty set and $X'$ is for the complement of $X$
In the attached image, there are two quantum circuits that are equivalent. I am trying to understand how. Let's call the top qubit ##q_1## and the bottom one ##q_2##, and the outputs ##q_1'## and ##q_2'##. From what I understand, the C-NOT gate doesn't affect the control qubit. Because Hadamard...
This paper appears to be a major break though in observational evidence of a strong equivalence principle violation, something predicted in MOND and contrary to general relativity. The analysis is model dependent, but it seems to rule out the most plausible conventional GR based alternatives...
Please help me understand all the errors and misunderstandings, contained in the following paragraphs:
1. When a gravitational wave passes through earth, it 'squashes' the form of earth, hence gravity geometry is changed, hence gravity at any given point on Earth change at that moment, be it a...
Hello all,
Apologies if this has already been asked before, but I tried researching this question for a while with no results.
I was reading Grainger's Power System Analysis' derivation of the inductance of a single wire and got confused by his definition of magnetic flux linkage.
He seems to...
We work with Maxwell's equations in the frequency domain.
Let's consider a bounded open domain ## V ## with boundary ## \partial V ##.
1. The equivalence theorem tells me that if the field sources in ## V ## are assigned and if the fields in the points of ## \partial V ## are assigned, then I...
In the first sentence of Chapter 2 in Ben Crowell's "General Relativity" he states:
"The geometrical treatment of space, time, and gravity only requires as its basis the equivalence of inertial and gravitational mass".
This is stated as if it's an obvious fact, but I don't understand why. Why...
Hi.
One of the first things I was told about quantum interpretations was that they are all equivalent, i.e. make the same experimentally testable predictions. This seems reasonable for simple experiments whose mathematical description is straightforward, like preparation – unitary evolution –...
I was finding the energy required to separate tritium into it's component parts, the binding energy when it hit me that how could 1amu= 931.2 MeV and 1.66e-27 kg at the same time?
The near-range magnetic field ##\vec{B}## of a point charge ##q## at distance ##\vec{r}##, moving at a non-relativistic velocity ##\vec{v}##, is given by
$$\vec{B}=\frac{q}{4\pi\epsilon_0c^2}\frac{\vec{v}\times\hat{r}}{r^2}.$$
Faraday's law of induction for the induced EMF ##V_c## in a coil...
Hey! 😊
Question 1: We consider $\frac{2n-1}{n+7}$. For which $n$ is this term an integer? I have done the following:
We set $n+7=m \Rightarrow n=m-7$.
Then we get $$\frac{2n-1}{n+7}=\frac{2(m-7)-1}{(m-7)+7}=\frac{2m-15}{m}$$ So $m$ has to be a divisor of $15$, i.e. $m\in \{1,3,5,15\}$...
The following is an improved version of my previous post https://www.physicsforums.com/threads/falling-electric-dipole-contradicts-the-equivalence-principle.964594/
Consider the following system comprising a particle on the left with charge ##+q## that is a large distance ##d## away from two...
https://en.wikipedia.org/wiki/Riemann_hypothesis#Quasicrystals a quasicrystal as "a distribution with discrete support whose Fourier transform also has discrete support."
https://en.wikipedia.org/wiki/Quasicrystal#Mathematicsdefines a quasicrystal as "a structure that is ordered but not...
If we are in a cabine in a gravitational field and inside, we have a racket and a ball. We put strings in each side of the racket and we connect the racket to the ceiling of the cabine. This strings only allows us to keep the weight of the racket. Then, we drop a ball to the racket.
We do this...
I'm following this video on how to establish an equivalence relation to define the tensor product space of Hilbert spaces:
##\mathcal{H1} \otimes\mathcal{H2}={T}\big/{\sim}##
The definition for the equivalence relation is given in the lecture vidoe as
##(\sum_{j=1}^{J}c_j\psi_j...
According to https://plato.stanford.edu/entries/zermelo-set-theory/ , Zermelo (translated) said:
I don't know if that quote is part of his formal presentation. It does raise the question of whether set theory must formally assume that there exists an equivalence relation on "elements" of...
(a) I present the following counter example for this. Let ##A = \{0,1,2,\ldots \}## and ##B = \{ 2,4,6, \ldots \} ##. Also, let ##C = \{ 1, 2 \} ## and ##D = \{3 \}##. Now, we can form a bijection ##f: A \longrightarrow B## between ##A## and ##B## as follows. If ##f(x) = 2x + 2##, we can see...
Hi all, I have ran into some confusion about the equivalence principle; perhaps I should state what I understand and then proceed to ask questions.
It is my understanding that the equivalence principle states that spacetimes are locally Minkowski, and so the rules of SR apply in that locality...