Universal Definition and 477 Threads

I couldn't get Latex text to render. Sorry if text looks unreadable... [Mentor Update -- OP has updated the below text using LaTeX] Thus, for two perfect spheres with radiuses r and s, densities Pr and Ps, which are positioned in space at distance d between their respective centers, expression...

Please, I have a question about universal enveloping algebra: Let ##U=U(\mathfrak{g})## be the quotient of the free associative algebra ##\mathcal{F}## with generators ##\left\{a_i: i \in I\right\}## by the ideal ##\mathcal{I}## generated by all elements of the form ##a_i a_j-a_j a_i-\sum_{k \in...

Has any of the reversible extensions of the elementary one-dimensional cellular automata described by Wolfram in NKS (e.g. Rule 37R) been shown to be computationally universal (like Rule 110)? If so, please give me links. Otherwise, could this be the case? Or is there a proof that no nR can be...

forget about chronic fatigue, I remembered it has been tracked to gut bacteria! Epstein-Barr virus seems to be associated with many conditions. "Associated" is the operative there because almost everyone is a host for Epstein-Barr. Science News has a somewhat long but quite readable article...

Hello In his book published in 1830, Sadi Carnot expresses doubts as to the universality of his reasoning on gases. It's on page 89. Is it valid for liquids, solids? And he quotes in the text the freezing of water (increase in volume). What experiments or reflections allowed Rudolf Clausius to...

Mostly about free will

Existence of an universal problem solver, a polynomial-time NP-complete algorithm is a $1000000 prize question. But suppose that we were able to know something "simple", e.g. an electron state or electron wave function exactly. Would we be able to solve complex mathematical problems (like...

I need help with understanding this problem. I had initially chosen B, that the two satellites had the same speed because the mass does not effect the velocities of each of the satellites considering they are in orbit. But that answer was marked incorrect by my instructor. What other answer...

Summary:: How to keep the same voltage and change the frequency of a A.C. universal motor. Hello there! I need some help regarding my final project for the university. I have a universal motor, supplied by a single phase, 220V source. I need to make this motor work at the same voltage, but to...

I am not sure of the definition of a total eclipse, but what I am describing as a total eclipse in my question is the kind we on Earth experience; that is to say, an eclipse where only the tiny annular ring of chromosphere is briefly visible. I am guessing that there are many (millions?)...

First, a caveat: this is one component of a project, which is difficult to describe without quite a but of digression. If my descriptions seem illogical, it may be because I haven't described the function of the component in its proper context. I assume it will take a little bit of...

This is a somewhat trivial question, but I never managed to learn much logic back in the day...so: The definition of a subset can be written as: ## A \subset B \Leftrightarrow \forall x (x \in A \Rightarrow x \in B) ## However, over which set is ##\forall## supposed to quantify? It seems to...

I am not getting any ideas to solve this without the universal constants. The method that I want to use invloves the speed of light, which is a universal constant.

A paper in Nature Medicine reports data from a phase I clinical trial of a new flu vaccine strategy that targets the stalk of the influenza virus's HA protein, a region that has much less variation between different flu strains...

If Planck constant h and light speed constant c were (very) different, would we notice it? (I know we can change units and make h and c take any numerical value we like. But let‘s stick with one set of units.) I assume rulers, clocks, coupling constants, all dimensionless constants would...

In the following proof: I didn't understand the following part: Isn't it supposed to be : ## a > s_A - \epsilon >0 ## and ## b > s_B - \epsilon >0 ## Because to prove that ## s ## is a supremum, we need to prove the following: For every ## \epsilon > 0 ## there exists ## m \in M ## such...

Has anyone come across Quine's New Foundations? https://plato.stanford.edu/entries/quine-nf/ https://en.wikipedia.org/wiki/New_Foundations I'm not very knowledgeable about set theory, mathematical logic, or the foundations of mathematics, but I found what I read interesting. The basic idea (as...

For question A, I know that I am supposed to input the numbers given into the Universal Gravitation Equation, but I do not know how to solve for it beyond that. For question B, I know that the astronauts weight depends on the mass and gravity of the new planet but I do not know how to prove it...

Would it make sense to say that the entire evolutionary history of the universal wavefunction could simply be a single, continuous moment of self-measurement? In other words, that the universe exists for no other reason than to be the apparatus that is always in the process of measuring its own...

In the thread is-the-small-world-uncertain-or-is-that-our-perception @mitchell porter said: Can someone explain what "objective universal time" is and what it means for it to conflict with the "spirit of relativity"? Is this an aspect of interpretation where you could describe all events using...

Besides telepathy, what could I use to explain the properties of a device that is a TRUE universal translator, a handheld device that can decipher any language it encounters? I don’t know much about linguistics but I was told that even in a sci-fi setting, this is impossible. Jack Buchanan even...

Hello folks, I am working on Java program just for fun to model an n-body problem using 3-dimension graphics. I'm looking for a way to speed up the model. Suppose for example that I decide to increase the speeds of all objects by a factor of, say, 2. To compensate, I would also increase the...

This sounds interesting to me. I would appreciate the opinions of more knowledgeable and physics oriented forumists. The paper is in Science (I don't think its open access). Here is the abstract:

So while thinking about motors this suddenly struck me, So as the universal series wound motor is spinning there is always some arcing going on around the place where the brushes contact the copper segments that slide past them, I assume this is at least partly because as each coil pair of the...

I have a "262 Lionel Line" O gauge train, from the early 1930's. It has sentimental value, my Father-In-Law (RIP) got it as a gift when he was about age 10. I've set it up each Christmas, a short track around the tree. But it is difficult to control, the gearing is high (it goes fast), so...

Hello, and thank you again to anyone who can confirm if I have the right answer or who can give me some suggestions. This question felt like a bit of a surprise because we have not yet covered one where the mass of a planet was missing. Thus, my confidence in my work is low. Part b felt like a...

In the first question should I remove the delta and put d or that doesn't make a difference and on the second question should I substitute the values of R, K, Cv and Cp or that's not required I'm not really sure how correct is my answer to the second question

Why can't there be a Universal Interpretation of Quantum Mechanics? If you unite Copenhagen and Many Worlds than all other interpretations will fall under the umbrella of a Universal Interpretation of Quantum Mechanics. The main problem with interpretations seems to be the role of the observer...

I didn't use Kepler's 3rd law and this may be the reason I have a wrong answer. However, I want to know: where I make the mistake. ## ma = \frac {G M m} {R^2}## ## R = (\frac {G M} a)^{1/2}## ##a = \frac {v^2} R## ##V^2 = a R = a (\frac {G M} a)^{1/2} = (G a M)^{1/2}## ##V = (G a M)^{1/4}##...

...Or even based on logic? I understand that it is expected that there might be a Universal Speed Limit and that this seems with extremely high probability to coincide with the speed of em transmission in a vacuum. This is borne out by experimentation and observation. Are there any other...

First, I started with F_a = m_aa_a=G \frac{m_am_b}{r^2} and F_b = m_ba_b=G \frac{m_am_b}{r^2} . Solving for their respective accelerations, I got a_a=G \frac{m_b}{r^2} = 100G and a_b=G \frac{m_a}{r^2} = 100G, meaning that the initial acceleration of the two point particles are each 100G ...

Im just asking this general question.

Hi everyone, I'd really appreciate any help with this problem: A helium cylinder for the inflation of party balloons hold s 25.0L of gas and is filled to a pressure of 16500kPa at 15 degrees celsius. How many balloons can be inflated from a single cylinder at 30 degrees celsius if the volume of...

The ideal gas law is given as ##PV=nRT## where ##R## is said to be the universal gas constant equal to ##0.082056\frac{L⋅atm}{mol⋅K}##. ##R## is said to be a constant, and thus cannot change even if we change the values of ##P,V,n,T##. I don't see how this is possible, because the way we found...

A recent paper in Nature describes a new phenomena found in superconducting materials: https://www.nature.com/articles/s41567-018-0334-2 Quanta magazine wrote about it here: https://www.quantamagazine.org/universal-quantum-phenomenon-found-in-superconductors-20181119/

Homework Statement G= 6.67 *10^-11 M= 5.97*10^24 kg m= 430 kg Orbital speed=6800m/s I'm supposed to find radius of satellite orbit. Homework EquationsThe Attempt at a Solution I don't know where to start because in order to find radius, I have to find period as well

As far as I know, the total cross-sections of the following hadron interactions are well described by a single Reggeon trajectory and a single Pomeron (soft Pomeron) trajectory. ##K^-p: (11.93s^{0.0808}+25.33s^{-0.4525})mb## ##K^+p:(11.93s^{0.0808}+7.58s^{-0.4525})mb## ##\bar...

I am reading Tom Leinster's book: "Basic Category Theory" and am focused on Chapter 1: Introduction where Leinster explains the basic idea of universal properties ... I need help in order to fully understand the proof of Lemma 0.7 ... Lemma 0.7 and its proof read as follows:In the above proof...

I’ve been given a food mixer to repair - more sentimental value than monetary. It’s barely been used, if at all - the brushes still have their bedding-in ribs. It would only run if I gave it a spin, but this was just bad contact between brushes and commutator. Solved with switch cleaner. When...

Researchers have demonstrated holonomic quantum gates under zero-magnetic field at room temperature, which could enable the realization of fast and fault-tolerant universal quantum computers. A quantum computer is a theoretical machine with the potential to solve complex problems much faster...

So, this is a bit of an odd question, but something I was curious about. I recently learned in layman's terms that the universe is considered flat because of how we measure triangles in 3D space, in particular the CMB. I've also learned that the cosmological constant that was derived from GR...

Problem: minimize the following using K-Map and implement using universal gates f=sum of m( 2,3,6,7,8,10,11,13,14)My Solution Here is my solution https://prnt.sc/jdyk0k However, my solution is not matching with book solution Book solution https://prnt.sc/jdyj4n I'm confused. which...

Okay, so I was watching this YouTube video: Which says that there is no universal chronological order of events. Different observers may have a different order of events and both would be correct. What I wanted to try and understand (in layman terms), is this purely down to how long it takes...

Articles refer to white holes being associated with dark energy. What if dark energy is a larger version of the following process? Black holes banish matter into cosmic voids Some of the matter falling towards the [supermassive black] holes is converted into energy. This energy is delivered to...

Homework Statement You are on a deep space mission to search for Earth-like planets. Your crew locates a possible planet and with scanners finds the radius to be 7.5 x 106 m. A team lands on the surface. There, they hang a 1.0 kg mass from a spring scale. It reads 8.5 N. Determine the mass of...

Homework Statement earth has a mass of 5.98x10^24 kg and the moon has a mass of 7.35x10^22 kg. The distance from the centre of the moon to the centre of the Earth is 3.84x10^8 m. A rocket with a total mass of 1200 kg is 3.0x10^8 m from the centre of the Earth and directly in between Earth and...

Is there a possibility that we create a wormhole sometime and switch between universes? First of all what is required to make a wormhole? What will happen if we made a wormhole? What proves that there are many universes and that we can switch between them??

Was just curious if there are any holes in the major laws of physics making them not consistent. Or could they change over time? And are they universal, as in, are they the same in all regions of the universe?

Hello Everybody, I am Meaningless and I had this doubt on Newtons laws of gravitation while deriving it. My textbook stated the following derivation 9 for any two masses m1, m2, and radius 'r' It stated that according to the law of product of masses...