Measure Definition and 1000 Threads

I have some questions about the curvature of space (NB not of spacetime) near a planet like Earth. Unambiguously defining space curvature requires choice of a coordinate system, so I choose the Swarzschild system. Here are my questions: Would constant-time hypersurfaces under the Swarzschild...

I'm trying to figure out how you would actually measure the result of a quantum gate. For example, suppose I build a Hadamard gate by using a beam splitter. The output of this gate creates either |\psi> = \frac{1}{\sqrt{2}} |0> + \frac{1}{\sqrt{2}} |1> or |\psi> = \frac{1}{\sqrt{2}} |0> -...

Hi! Can anyone recommend a good introductory book for measure theory? I've found Terence Tao's online book to be a good start, but would I be asking too much if I wanted something even more introductory? Ultimately I'm working toward Ergodic theory (and probability theory along the way) with...

I have the problem of making "at home" or almost, a measure of a laser's pulse energy for unit area of the target: those kinds lasts for ~ tens of milliseconds, up to some hundreds of ms and I should be able to verify that this energy "density" doesn't go beyond 40 J/cm^2 for a single pulse...

Hello everyone, I am trying to work out how much force is generated when a tyre fails at a certain pressure. The tyre will be inside an OSHA section 1910.177 compliant tyre cage. What calculation would be used to solve the following?: The tyre size is 35 x 11.5-17 with a rated inflation of...

Homework Statement For the state ##(4|00\rangle+3i|11\rangle)\otimes (|0\rangle+i|1\rangle) + (2|01\rangle -i|10\rangle)\otimes(|0\rangle-|1\rangle)## What's the probability of zero being the outcome of measuring the second bit and what is the state of the other two qubits after measurement...

Homework Statement Consider the following circuit where i(t) is sinusoidal and exists across both components. (1) is an inductor and (2) is a capacitor. The ideal voltmeters measure effective value. What is the value measured by V2: [![enter image description here][1]][1] [1]...

Homework Statement The star Betelgeuse is 427 lightyears from earth. Betelgeuse has a diameter 800 times that of the sun, where the diameter of the sun equals ##1.39*10^6 km##. Given that Betelgeuse has an angular resolution given by the Rayleigh Criterion of 58 nRad, is it possible for the...

Hello. I have problem with this integral : \lim_{n \to \infty } \int_{\mathbb{R}^+} \left( 1+ \frac{x}{n} \right) \sin ^n \left( x \right) d\mu_1 where ## \mu_1## is Lebesgue measure.

Homework Statement Given the following Hamiltonian: And the observable: Calculate the probability of measuring any of the possible values of A in the fundamental state. The attempt at a solution I have calculated the eigenvectors and eigenvalues of the Hamiltonian, being the eigenvalues...

I can't read the tons of posts and replies about one-way light speed in this forum. I was criticised once for sustaining light speed should be equal in both outward and return trips and Einstein's method of syncing clocks as the only reasonable one. Then I studied some scientific articles gently...

Does anybody know where i can buy a device with which i can measure the frequency of light from various sources such as bulb light?

Can we experimentally measure the very weak gravitational force between two objects just like we can detect magnetic field lines by a deflecting compass.

aren't you supposed to measure weight in Newtons? And mass in kilograms/grams?

<Moderator's note: Moved from a technical forum and thus no template.> Here’s the question Design a simple expirament that you could carry out in your own home to i) determine coefficient of friction between your object and surface ii) prove that coefficient of static friction is only...

Homework Statement The detector is made of two co-planar layers of silicon two metres apart, and there is a plane of wire chambers halfway between them. The wire chamber can measure a track with precision ##100\mu##m. What is the highest momentum a particle can have for which the detector will...

Hi guys, I am working on a project that involves measuring the phase angle between two sinusoidal voltages. The circuit under examination is an RL type (the resistor was in series with the inductor), where the phase of voltage across the inductor is measured relative to the voltage input of the...

Homework Statement Im doing a project on Emf and internal resistance. I'm just trying to understand what the load would be and where I would put the positive and negative pens on the schematic to find the load. Homework Equations Terminal Voltage would be what I have in the image above...

Hey! :o I want to prove or disprove that for a probability measure $Q$ over a $\sigma$-algebra $\mathcal{B}$ with $A,B\in \mathcal{B}$ the following hold: $Q(A\cup B)=1-Q(\overline{A}\cup \overline{B})$ $1-Q(\overline{A}\cap \overline{B})=Q(\overline{A})+Q(\overline{B})+Q(\overline{A}\cup...

Why are clocks not used to measure gravity waves? Spacetime wriggle and time must also vary. It is possible to measure time very accurately and with a high resolution. Så why not use clocks to detect gravity waves?

Could someone explain how to find the net force of an object based on a diagram. For example a 2 people walking with forces labeled weight force, reactant force, thrust and drag on one image all forces are balanced which I know the net force would be zero however on the second image thrust is...

Hello all First time on the Math side of this great Forum. I need to do a correlation study. There are 3 methods to measure Form Error of a round metal part. The base line is the traditional measuring method that is laborious but of the highest accuracy. A cnc machine measurement machine...

I'm aware that the LIGO system uses interferometry but I'm confused how it works in this case. Do they test both beams of light? Or do they use one beam to test the wavelength of the other and see the difference? Also it is sensitive up to 10 e-18 meters, is that for the change in wavelength or...

Hello, I have a tennis racquet that has a certain weight distribution that makes it play very well. Due to quality control issues from the manufacturer my second racquet of same make and model has a very different weight profile, making matching difficult. I'd like to determine the weight...

In my physics textbook it says that ammeter in circuit C shows higher current than ammeter in circuit A and D. And the voltmeter shows higher voltage in D than in B, and C. It's explained in the book that way: some electric current is passing through the voltmeter in C, thus the ammeter will...

I was wondering how I could measure the rate constant k for chemiluminescence reaction of luminol (when oxidised by H2O2. I was told that I can use a lux meter that measures the intensity of light emitted, but I'm not so sure how this can be done since the equation calculating the rate constant...

Why do EMF meters measure ELF and VLF in flux density units but RF in power density units? Is it because ELF/VLF have low power density and high flux density, and RF has high power density and low flux density? They are all EM waves, right? what's driving the difference in measurement units? thanks

Homework Statement Let ##E## be a nonmeasurable set of finite outer measure. Show that there is a ##G_\delta## set ##G## that contains ##E## for which ##m^*(E)=m^*(G)##, while ##m^*(G-E) > 0##. Homework Equations ##E## is a measurable set if and only if there is a ##G_\delta## set ##G##...

Hi. Is there some kind of measure theory generalized to uncountable unions? Of course one needs to take care how to make sense of sums over an uncountable index set. I was thinking about following formulation of the additivity property of the "measure": $$\mu\left(\bigcup_{i\in\ I}...

Hello! I've made a lot of research about measurement of high magnetic fields - such us 1T - 2T and I can't find sensors for this range. I'm looking for a hall sensor with which I will be able to measure 1T magnetic field with good accuracy - about 0.1 mT. Do you know about anything like that...

Homework Statement If ##\{E_k\}_{k=1}^\infty## is any countable collection of sets, disjoint or not, then ##m^* \left(\bigcup_{k=1}^{\infty} E_k \right) \le \sum_{k=1}^{\infty} m^*(E_k)##. Homework Equations ##m^*(A) = \inf \{ \sum_{k=1}^{\infty} \ell (I_k) ~|~ A \subseteq...

Given a list of values, one calculates the arithmetic mean of those values which are greater than the arithmetic mean of all values. Is there an established name for that quantity?

The title of this thread is the title to this Phys.org article posted today: https://phys.org/news/2017-08-physicists-complementary-properties-quantum-clones.html First, correct me if I'm wrong, but the problem is not that complementary states cannot be both measured, but that the there is a...

Take it slow, polaritons are a new concept for me. Anyways, I'm trying to get some intuition for excitation polaritons having mass. Is this a quantity that we could directly measure, at least in theory if not practically? How would we separate the mass of the polariton itself from the mass of...

At the outset I am a novice in physics. i have constructed a rain water storing tank with a capicity of 1,20,000 litres. I propose to seal the tank so that there is no light penetrating inside the tank. My question now is how do I measure how many feet of water is left inside the tank? Can...

Okay, let me prelude this by saying I only have an -EXTREMELY- limited understanding of classical physics, and zero knowledge of quantum mechanics. This is really just my asking a few questions in regards to an idea I had for an experiment, and what would be a good and accurate way to...

hello, i am trying to calculate the volume of a balloon (which is quite large). It has been filled with helium via a valve connecting helium storage tanks to the balloon. The knowns I have are the volume of the storage tanks, the intital pressure in the tanks, and the final pressure in the tanks...

I'm well aware of the common adage and quantum fact that, until a particle is measured by some sort of instrument, it exists in a state of superposition, can interfere with itself, etc. My questions pertains to the definition of "measurement". In order for something to qualify as a measurement...

Homework Statement m1= 0,05 kg, m2= 0,03 kg, mass of spring is omitted. We look at movement after spring stopped vibrate. How long does the spring measure during the movement if not stretched spring measure 0,1 meter and if we use force 0,1N elongation measures 0,02 meter. (sorry, English isn't...

Something I've always wondered: why do we measure the amount of disorder (entropy) rather than the amount of order? We don't measure brightness by the amount of "dark". Surely order is the thing of interest, so why don't we measure that rather than measuring the absence of it? And in...

Hi, I am a new student and trying to to measure the power and voltage output from B200 SDR device (https://www.ettus.com/content/files/b200-b210_spec_sheet.pdf) using oscilloscope (TDS3000 Series: https://www.atecorp.com/ATECorp/media/pdfs/data-sheets/Tektronix-TDS3000_Series_Manual.pdf)...

I have searched the Internet and I have not found a simple layman's explanation other than this. We observe their decay products of quarks and that is what the mass is reconstructed from. Is this correct? If so I would like to have that confirmed. I am just looking for a simple direct...

Sooooo... I have a Far infrared (FIR) sauna. It has large flat 'carbon' panel heaters. They get warm to the touch and won't burn you if you touch them. My non contact infrared thermometer zapper says that they get to about 70 degrees C. They are meant to be producing lots of FIR. A regular...

Hello, I'm having a question regarding the sensors and the techniques in fluid mechanics. Since my skills are amazing in this field, here I'm asking you questions xD I want to measure the air pressure of this tube/pipe (P1,P2,P3). This pipe will be flushed with water and then with compressed...

Hi all, I'd like to know if there's a reliable tool that can measure UVA and UVB concurrently at regular interval and record it. Or if can't record, then at least can be connected to a computer or network and will send the readings at regular interval. or perhaps anybody can point me to a...

Hello, I need to measure the moment of inertia of a DC motor's rotor. Any suggestion? Thanks

I have 2 rubidium clocks which both are generating 10MHz sine wave. Some reason my system is giving bad data. So, I am deciding to inspect every single part of the system. I am trying to check the rubidium clock and make sure it have to be in nanosecond time variation, because: t=1/f = 1/10e6 =...

I am doing a math project. Our goal is to use Mathematica to design some small wind turbine blades, 3D print them, and then attaching it to a small dc motor. I did something very similar for science Olympiad, where we had been measuring the "power" by measuring the voltage between the two wires...

While the motor is spinning, I measured the voltage (Vrm) across the motor by connecting the two probes from the multimeter to the two terminals of the DC motor via alligator to alligator banana cables. Since the current was fairly constant, I could ignore the inductance. So, no voltage across...

[Moderator's note: posts from several threads on the same topic have been merged into this thread.] When we measure the EM field of a charged particle, what exactly are we measuring? Are we measuring the position of the EM field, the strength of it, what? Does a penning trap measure the EM...