Measure Definition and 1000 Threads

Hello PF. I'm currently tackling a problem at work that I could use some input on. I am trying to gather data regarding the force applied by a swelling material against the ID of a pipe. The purpose is to determine how the force increases with swell before leveling off, as well as to see how...

Assuming that the expectation that all matter and energy are quantized is correct, I'm making a further assumption that "random" means something like, "hypothetically predictable, but only by means at least possibly impractical on any permanent or general basis whatsoever, such as enumeration...

I know there is a problem with measuring the one way speed of light, but why can we not use just one clock. If somebody could explain the problems with this method, then it might help me to understand. Can we measure the one way speed of light the following way:- Have a long sealed tube with a...

From what I understand in laymans terms (Since I am a beginner). In quantum mechanics, particles don’t have classical properties like “position” or “momentum”; rather, there is a wave function that assigns a (complex) number, called the “amplitude,” to each possible measurement outcome. The...

I'm trying to read Brian Hall's book "Quantum Theory for Mathematicians". While (I think) I have a basic grasp of most of the prerequisites, I don't know any measure theory. According to the appendix, presumed knowledge includes "the basic notions of measure theory, including the concepts of...

HI all, I think I have to use some combination of waveplates on the signal, but I am not sure, does anybody know this? Thanks for help

Has there been any recent changes in the G constant value?

When I learned the concept of specific heat capacity, I knew that 1J/(K*kg) means that it takes 1 Joule of energy to increase the temperature of a kilogram of matter by one Kelvin, but what does J/K, the unit of entropy, mean?

Hi, I have a motor with no information, not even a label, just the connectors, I was wondering if there was a way to measure its power and if there was a way to control it without affecting it's velocity, I possesses simple elements, some sensors (inductive) and a manometer, my brain is now dry...

I understand that fluorescence intensity time trace is constantly monitor the fluorescence intensity and plot it over time. But the question is at which excitation wavelength? Also, what is the emitted wavelength that is being measured? I suppose it should be two particular wavelengths, but how...

Standard quantum mechanics text-books discusses Born rule, which states that the probability of finding a particle in a certain region in space is given by $$ |\Psi ({\bf r},t)|^2d^3r $$ Thing is, I never have seen a discussion about how you can actually measure the particle position in a...

So, there's a project I'm working on (no, it's not school related), where I'm trying to figure out how to measure thermal conductivity of a material using laminar flow. The idea is to integrate this into a larger system, and it's a measurement I'd like to take in the process. I know the...

Assuming the spatially flat FRW metric for simplicity: $$ds^2=c^2dt^2-a(t)^2(dx^2+dy^2+dz^2)$$ where ##t## is cosmological time, ##a(t)## is the scaling factor and ##x,y,z## are co-moving Cartesian co-ordinates. Light freely propagating along the ##x##-direction follows the null geodesic, with...

Homework Statement I've uploaded a diagram showing a two beam interferometer that can be used to monitor changes of refractive index in a gas cell. it is illuminated with monochromatic light of wavelength λ. The light is linearly horizontally polarised. The two polarizing beam splitters (PBS)...

I know that temperature is used to measure the average internal kinetic energy of an object, but how do we go about measuring thermal energy? It seems as though temperature could only compare the thermal energy of objects with the same mass and volume. But for objects with different mass and...

In mathematics, what does it mean for two things to be the same? The equal sign first appeared in 1557 in Robert Recorde's work "The whetstone of Witte". The principle of indiscernity of identicals says that equal things have the same properties. If two things were literally exactly the same...

Hi guys and gals. I have a constant current welder. 150 Amps DC/ 230 Amps AC output. There is no provision for measuring output current when the machine is welding. I'm thinking of adding a shunt to either the work lead or the return lead. I don't know what size and rating I need. The input...

Homework Statement How many bits would an ADC require to measure the output of the preamp? What minimum frequency would the ADC need to sample at to measure the 4KHz signal accurately? What would the data rate from the ADC need to be at the minimum sample rate? Given a hydrophone with the...

Does a completely regular space imply the Dirac measure. From wikipedia we have the definition: X is a completely regular space if given any closed set F and any point x that does not belong to F, then there is a continuous function, f, from X to the real line R such that f(x) is 0 and, for...

I am little confused as to why temperature is a measure of thermal energy. Thermal energy is defined as the total internal kinetic energy of an object. Temperature, on the other hand, is defined as the measure of the average kinetic energy of an object, or the thermal energy per particle. If...

Hi i am performing a multiphysics simulation in which i am importing results of Electric-Thermal domain into Transient Structural domain in Ansys Workbench 14.5. As the simulation time is 5 hrs and given that i have to perform 20 case studies , so i want to know is their a way around in Ansys...

Hi Guys I am using a mobile phone to collect some accelerometer data for my walking experiments. I know this topic is done to death but a specific answer that I have never got is what does mobile phone accelerometers actually measure? Do they give the acceleration due to all the forces acting...

Let us assume that an observer is stationary at the origin in expanding space. We assume the FRW metric near the origin is given by: $$ds^2=-dt^2+a(t)^2dr^2$$ Let us assume that the observer measures time by bouncing a light beam at a mirror that is at a constant proper unit distance away from...

For a system consisting of multiple components, say, a spin chain consisting ofN≥3spins, people sometimes use the so-called geometric measure of entanglement. It is related to the inner product between the wave function and a simple tensor product wave function. But it seems that none used this...

In Principle, gravitational constant is measured very precise, but the problem is that it is measured together with mass of sun, Earth or moon, G M_s or G M_e; or G M_m. But, is it possible to measure mass of the moon without use of G? Maybe the principle, where the rocket was accelerated when...

In Tom Leister’s book “Basic Category Theory”, he starts by talking about equality of elements, isomorphisms of functors, equivalence of categories, and at each stage, he acts like you have an object, and that object can change, and then, lo and behold, the “change” itself could be viewed as...

Is there any portable/small device that will allow me to measure the strength of the electron field emanating from the Earth's surface, i.e., the ground at a given location? Thanks!

If a plasma is created at one end of a solenoid and heads down towards a target with a density and temperature too high for Langmuir probes, what other instruments can measure the density with a strong signal that is easy to interpret?

Considering the interval [0,1], say for each number (binary) on the interval you form the sequence of numbers: number of zeros up to the nth place/number of ones up to the nth place. Then as n goes to infinity the sequence of numbers (for the given binary number) will go to somewhere in...

Suppose ##\mu:\mathcal{F}\rightarrow[0,\infty)## be a countable additive measure on a ##\sigma##-algebra ##\mathcal{F}## over a set ##\Omega##. Take any ##E\subseteq \Omega##. Let ##\mathcal{F}_{E}:=\sigma(\mathcal{F}\cup\{E\})##. Then, PROVE there is a countable additive measure...

If you have a two-qubit system |x>[(|0>-|1>)/√2], whereby x∈{0,1}, and you want to just know x, do you (a) assume that this means that |x> belongs to one particle, (|0>-|1>)/√2 to another particle, so you just measure the first particle? or (b) if you can't tell the particles apart, pass this...

Hi All, This is my fist post here! Recently, I came across the elusive problem of one-way speed of light which has not yet been measured in any agreeable way. So far, all the speed of light experiments have involved clock synchronization or cyclical path problem and hence provided only...

Firstly, I'd be happy to be corrected if I'm not using the right wording or just plain incorrect with my approach. Is it practical to suggest that units of one measurement system could possibly represent the measurement of things not only at the macro level, but represent particles with and...

Is there a way to measure the light frequencies of brainwaves outside of the brain.

Is there any law that prevents us from accurately measuring the momentum of a particle , just like the energy time uncertainty principle makes us observe the system for an infinite amount of time before we can be certain about its energy? I got this doubt because if we can do it, we will...

Hey I'm curious if it would be possible to measure if a particle's spin is in a superstate similar to how the double slit experiment can show whether or not an electron's location is in a superstate. Wouldn't such a machine allow for FTL communications, since if we measure one of two entangled...

Homework Statement Homework EquationsThe Attempt at a Solution I have managed to solve it for the finite case, where the masure is less than infinity. But how do I solve it if the ,measure if the measure of E is infinite?

Hi, Let's say I consider the real numbers and some function real function f, nowhere zero, and positive. My question is, what are the conditions on f for dx/f(x) to be a valid measure on this space? (I have to consider a Hilbert space L^2(R, dx/f(x)) with scalar product a.b = \int a^*(x)...

I have this question on outer measure from Richard Bass' book, supposed to be an introductory but I am lost: Prove that ##\mu^*## is an outer measure, given a measure space ##(X, \mathcal A, \mu)## and define ##\mu^*(A) = \inf \{\mu(B) \mid A \subset B, B \in \mathcal A\}## for all subsets...

< Mentor Note -- thread moved to HH from the technical physics forums, so no HH Template is shown. Also, thread title edited to make it more descriptive. > The question is asking me to draw a diagram to show how, in the laboratory you would use two rectangular blocks of wood and a metre rule...

Homework Statement i want to measure temperature distribution of a heated cylinder. it become my final project, and now, i feel confuse, how to measure it. i think on put LM 35 DZ on every point at the cylinder, heat the cylinder, and read the output. but that should take a lot of cost...

Hello! :o Let $(X, \mathcal{A}, \mu)$ a space of measure and $A_n$ a sequence of measurable sets such that each point of the space belongs to at most $M$ sets $A_n$. Show that $$\sum_{n=1}^{+\infty} \mu (A_n) \leq M \mu \left ( \cup_{n=1}^{+\infty} A_n \right )$$ Could you give me some...

How is 3-sphere curvature measured? If a 2-D being living "in" the surface of a sphere tried to measure the 3-D curvature of the sphere, how would they go about it? They couldn't detect the curvature by looking for curvature in the paths of signals, because if the surface of their sphere was as...

In classical physics, the definition of a unit of measure involves a deterministic process (e.g. "the amount of force necessary to give a kilogram mass the acceleration of 1 meter per second square"). How are such units defined in Quantum Mechanics? ( Do we replace references to quantities...

Hey! :o What book would you recommend me to read about measure theory and especially the following: Measure and outer meansure, Borel sets, the outer Lebesgue measure. The Cantor set. Properties of Lebesgue measure (translation invariance, completeness, regularity, uniqueness). Steinhaus...

Homework Statement I have been struggling, for over a month now, to find a way to measure instantaneous torque from a servo motor. Here's a servo that look similar to the one I'm using: https://www.servocity.com/html/spg805a-bm_standard_rotation.html I need to find a way to measure the torque...

Hi there, Does anyone know if there is any method to measure the out-of-plane thermal conductivity of a suspended thin film? As the conventional way of measuring the out-of-plane thermal conductivity is to deposit the thin film on a thick substrate, but we want it suspended. Thanks in advance.

So I read that in a motoring test (to test the engine power), the engine is run to the desired speed by its own power. The power is absorbed by an electric dynamometer. Then, the fuel supply is cut-off and the dynamometer is converted to work as a motor to drive the engine at the same speed...

I'm working through an article called "Cosmic abundances of stable particles -- improved analysis" (link -- viewable only in Firefox afaik), the result of which, equation (3.8), is cited quite a lot. I'm more interested in how they arrived there. Particularly, how come momentum space measure...

Hi, everyone. I am researching on a variety of different Physics topics to conduct my Extended Essay on. I was thinking, what if I made a spectrograph to measure the sun's light? Surely I'd be able to get emission and absorption lines which will more or less portray something about the sun's...