Measurement Definition and 1000 Threads

The above question is adopted from the exercise of Preskill's quantum information lecture note My attempt: (a) From the condition, ## p(\theta)\propto \sin^{(2N-4)}\theta \cos\theta ##. Normalizing the probability distribution would give the answer. This is because the weight of the phase of...

Hi. This is Annwoy Roy Choudhury. I have just completed my first-year undergraduate studies in Physics. I am new to Quantum Mechanics. There are certain confusions I have regarding Quantum Measurements. It would be really kind of you to help me out. Postulate 3 states, An example is, Let's...

I find the current first, which is 2 A. Then the voltmeter reading would be 10 V - 1 x 2 = 8 V. But the answer is 12 V. I don't understand why it should be 10 + 1 x 2 = 12 V Thanks

Say you have a simplified 1d Gaussian wave function describing location of a particle. Many worlds says that every outcome is a separate branch. Copenhagen says you will get one of those branches. So how many distinct positions, imaginary or real, can you generate from a fixed segment of a...

Hello Everybody I'd like to set up a mechanical or electrical inertiameasurement of a Propellerarm that is in rotation, while the thrust (rpm of propeller) is rising. Maybe with a forcespring, a pendulum, camera (timer)... Not sure how to set it up nicely. Any suggestions? Best George P.

I have a charged particle in a Penning trap. The particle motion is non-relativistic and the energy is high enough such that we can assume it is not in the quantum regime. For the purpose of the question I am interested only in the axial motion of the particle, so basically this is a classical...

1.How is that possible for us to say that a non-interacting microscopic particle can have numerous values of a physical parameter in a given instant? the mixed state of a microscopic particle is simply the probability distribution of the particle having those values of a given physical parameter...

Let be a superposition ##|\psi\rangle=\sum_j a_j|j\rangle## with one amplitude ##a_x## much greater than the others, where ##x## is not known. For example, ##|\psi\rangle## may result from the quantum Fourier transform of a periodic wave function with an unknown period. I expect a measurement of...

Hi Pfs, I am beginning to read this short paper https://arxiv.org/abs/1504.04215 (quantum time) i read things like that on first page: Ht is the space of a system T (we call it the clock system) isomorphic to a Hilbrt space of a particle on a line. this space is equipped with coordinates T and...

Let's say I have ##F=mg \tan \alpha## and want to calculate ##F##. I know ##m=(1.0 \pm 0.5)\,\mathrm{kg}## and ##\alpha=(20.5 \pm 0.5)° ##. How to calculate ##F=( 3.7 \pm ?)\,\mathrm N##? What is the general method of determining a measurement error in these cases?

In short, the Elitzur–Vaidman bomb experiment consists of a Mach–Zehnder interferometer, where a bomb is placed in one of the paths (I used the wikipedia description https://en.wikipedia.org/wiki/Elitzur%E2%80%93Vaidman_bomb_tester, and Sabine Hossenfelder's video: ) The bomb can be live or a...

Hi all, I'd like to make an home-built OD600 sensor for measurement of cell concentration in suspension by Optical Density. There are several spectrophotometers in the market, indeed quite expensive, so I am interested in realizing a cheap device with standard components. Here's an example on...

I have seen this formula $$\sigma=\sqrt{\frac {\sum_{i=1}^{N}{(X_i- \bar{X})^2}}{N(N-1)}}$$ but also this formula $$\sigma =\frac{\sum_{i=1}^{N}{|X_i- \bar {X}|}}{N}.$$ Which of them is correct?

Is the answer 0.748?

I have a zip-tie like structure, which when pulled, squeezes an elastic part. Think of it like a having a zip-tie around your finger. I can measure a force that is related to the squeezing pressure. This relationship between force and pressure is quite linear. I would now need to create a...

Dang this place has a topology and analysis section too, nice. This is probably a graduate level topic, but I am by no means an expert on these subjects, just things I learn from wikipedia and other people. The commutator is an operation on two linear operators (most often matrices) of the form...

Measured proton electromagnetic structure deviates from theoretical predictions https://www.nature.com/articles/s41586-022-05248-1Meanwhile - https://www.jlab.org/human_resources/recruiting/ELECTRON-ION COLLIDER JOB OPPORTUNITIES

I was not able to attempt since I don't know which formula or method can be used to solve the problem

I find the values of the fundamental constants here https://physics.nist.gov/cuu/Constants/ In anticipation of the data of 2022, I want to clarify one point. Planck's constant is related by an exact expression to some other fundamental quantities: $$h = \frac{\alpha^2 m_e с^2}{2R_c}\qquad (1)$$...

When the expectation value of spin in the z direction for one particle is zero and I make measurements for an even number of particles in the same state, do I get exactly half to be spin up and half to be spin down along the z direction? More generally, what does spin expectation value for one...

In describing the Galelian or Lorentz transformations, All books I've read keep talking about clocks and meter sticks, but I don't see how an event happening away from the observer could be instantaneously described by a set of coordinates and a point in time; information conveying the event...

If I want to get the spin angular momentum of a particle using the Stem-Gerlach experiment, I think I will find the spin 1/2 particle either spin up or spin down, but not both. I however want to ask this : Is there a non-zero probability that a particle which is spin-up in the z direction to be...

There are units of measurement smaller than our eyes can see, but that we use in science. But, what is the smallest one that we can see and work with regularly? I mean...on a traditional ruler, it'd be a millimeter, right? But, we can obviously go smaller - even if a ruler doesn't mark it...

Hi to the community! Glad to be able to ask 1-2 questions here so signed up. As an interested layman with some autodidactic efforts, still can’t see how this happened or got to the value: Question: We defined the second and hence the meter by the speed of light in vacuum, but there isn’t...

I didn't remember the Lavoisier died at the guillotine. The world's roundest object helps solve the longest running problem in measurement -- how to define the kilogram. I knew about the Pt the Pt-Ir standard. I didn't realize that the mass of various 'standards' changed in time...

Quantum mechanics is the most successful theory in physics nowadays. The property of non-commuting operators results in a general uncertainty principle of which the Heisenberg Uncertainty Principle is a special case. Non-commuting quantities happily account for things like the two-slits...

Hello! I am generating electrons from a 3D gaussian source. The electrons all have the same energy, but the direction is isotropic. The electron source is in between 2 plates that act as a capacitor, and one of them acts as a time of flight (tof) detector. I know the voltage on the plates very...

It is commonly said that the phase of coherent states can't be measured, just the relative phase between two coherent states. A qubit example: define the states $$|\phi\rangle=[|0\rangle+\exp (\mathrm{i} \phi)|1\rangle] / \sqrt{2}$$ and the measurement operators...

Yesterday Jonte Hance and Sabine Hossenfelder published this preprint on the arXiv: https://arxiv.org/abs/2206.10445 What does it take to solve the measurement problem?

Halves-lives and average lifetimes, when studying nuclear decay, are often expressed in years even though years are not standarized, at least in SI (as far as I know). Borrowing the convention from astronomy and astrophysics, I usually take 1 \mathrm{yr} to be equal to 365.25 days of 86400...

I have the following elementary confusion about how measurement and collapse work in quantum mechanics. Place an unstable particle and a Geiger counter in a sealed box. The particle can be in two states: not decayed (N) or decayed (D). Scale time so that one unit of time after the particle...

I was wondering if there is a method to measure the actual total mass of carbon dioxide (CO2) emitted from a diesel engine used with a generator for power generation (https://www.cat.com/en_US/products/new/power-systems/electric-power/diesel-generator-sets/1000028914.html). Infrared CO2 sensors...

Probably, to satisfy the significant digits rule for division, we should consider ##r = 5.0 \div 2.0##. But I'm unable to come up with a reason why significant digits rule should not apply to ##r= d \div 2##. Also, if we apply significant digits rule to this calculation then we loose accuracy...

Hello, Is there a mirror that will reflect light in parallel trajectories ? If yes, is the reflected light in sync, and will all beams hit a flat surface simultaneously ? Thank you

I am not an expert in quantum theory. I want to carry out some parameter estimation on a set of data I have. I have a model for the data with the parameter(s) of interest as variable(s). The data available is sporadic, meaning non-statistical or techniques involving no prior knowledge on the...

Hi, I'm new to the quantum world, and would like to know why mathematically can we say that for mean value of measurment: <T>=<phi|T|phi> ?

The solution on my textbook is 13000m/s toward Earth as the light is blue-shifted I'm able to calculate the magnitude of velocity (13000m/s), but i don't understand why thus is blue-shifted? Since in the lab, the light's wavelength observed is slightly higher than light from Ursa Majoris. So my...

Hello! My questions is about this paper, aiming to measure the anapole moment in a molecule. In their derivation, starting from equation (1), they assume that the frequency of the field felt by molecules ##\omega## is much bigger than the energy splitting ##\Delta##. That basically implies that...

In Purcell's E&M Section5.3 "Measurement of charge in motion", he said when a charge is in motion, the force on test charges may not be in the direction of radius vector r. And in next paragraph, he defined Q by averaging over all directions. However, he just measured the radial component of...

Hello! My questions are based on this paper talking about King plot non-linearities. Assuming I have 3 isotopes and 2 transitions, I would like to know how well I should measure the transitions (i.e. what uncertainty on the transition value) in order to reach a given sensitivity for the new...

Hello! I have a question about this paper. They claim that the hyperfine and spin-rotational terms can be treated perturbatively (they do perform a full diagonalization, too, but they claim that perturbation theory is good to get an estimate of the effect). I agree with that for most of the...

Suppose Alice and Bob do an experiment with an entangled pair of particles, for instance electron spin with SG magnets. Now suppose Alice her SGM is stationary while Bob his SGM is switching fast between parallel to Alice and perpendicular to Alice. So there are two possibilities: correlation...

for any set of POVM outcomes it is possible to construct a setup with say one incoming photon and possible outcomes that will click differently. so this is not only mathématics. but what is physically an operator valued measurement?

Given what we know about special relativity and its implication for time and the observer, could this in any way be linked to why the isolated processes of QM are exhibiting everything happening at once and then collapsing to classical physics when bigger objects interact - the measurement...

Hi all, I will like to measure the MTF of a lens experimentally. In the set-up, I have my light - target - lens - camera. When my object (target) is at the focus of the lens, I took an image. My question now is, to I move my object across one pixel or few pixels or to move my object across...

What might be better foundational units given the knowledge we now have and disregarding legacy, human-scale units. Perhaps setting some known constants to be the base unit of 1 in that measure. For example, the second, based on the unperturbed ground-state hyperfine transition frequency of the...

Hi, I obtain really high standard deviations in Excitation-Emission Spectra mainly for the phenolic compounds in olive oil (Em: 290-350nm). Method: I weigh 0.05g of olive oil and dilute it up to 25ml with cyclohexane to remain in the range of linearity for absorbance measurements to correct...

I’m trying to understand the measurement problem using the simplest experiment I can think of--passing a particle P through a 50/50 beam splitter S, sending it down “path A” or “path B” with equal probability. Each path has a detector that can tell us if P was in that path. The detectors...

How do we map experimental measurements of quantum fields, such as those seen in accelerators, to the theory's mathematical formalism? When we see images of particle tracks produced in accelerators such as the LHC, I think it's safe to say a measurement (or series of measurements) has been...

I was wondering, if we have a measurement of, say, spin of an electron, which can yield spin-up and spin-down in the context of MWI, then the electron gets entangled with the measurement device, yielding the wave function ##|Measurement_{spin-up}, Value_{spin-up} \rangle +...