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To begin with ask yourself two questions: Has the device been re-calibrated in the middle of data taking? Is the calibration known to drift over time similar to the length of the data taking? If both of the answers are "no" then you can reasonably assume that the calibration effect is the same on each and every data point. So the mean is off by that ...


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The method with measuring the instantaneous weight while swinging the arm with a fixed angular velocity sounds rather impractical. You might try to combine data from multiple sources. I assumed that you are talking about the bit of limb from elbow up to and including the hand, with the hand stretched, but it turns out that you wish to exclude the hand. The ...


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Is there an official list of independent units of measurements? – When I say 'independent units', I mean those which cannot be broken down anymore, and simultaneously forms the basis for any more, complex measurements. It depends a bit on what you mean by broken down: You could theoretically define all units on the basis of counting elementary ...


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The concept you are looking for is called "dimensionality," which was a concept first coined in 1822. The simplest way of thinking of dimensionalities is that you cannot add two values unless their dimensionalities are the same. Thus, if we think in terms of units, 1 foot + 1 meter is a valid addition statement. This is because both foot and meter are ...


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Physics is not a bureaucracy, so there are no "official" documents like that. There are people called "metrologists" who think all week long about how to make physical standards more precise and they do have fairly well thought out ideas with what physical effects one should start to make precise measurements. These are not necessarily the standards that one ...


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If you are reasonably confident about the quality of the plate in question (uniform thickness, a well-defined square shape, etc.) you can measure the resistance of the copper square. This would be a non-destructive method for the arrangement in the OP. The specific resistivity of copper is (per google search) $1.68 \div 1.72 \times (10^{-8} \Omega\,m)$ ...


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I calculate that with 30u thickness we have 675mg mass. Use a microbalance and weight the sample.


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Do you have access to a precision balance? Then you could weigh the plate, and using the known dimensions of the plate and the density of copper, compute the thickness. For $5\,{\rm cm} \times 5\,{\rm cm} \times 30\,\mu{\rm m}$ the weight would be $0.672\,{\rm g}$ for example. The precision of that measurement depends on how accurately you can measure the ...


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EDIT updated (improved) description of phase detection circuit There are two principles used in these systems. The first is the time-of-flight principle. As you noted, if you wanted to get down to 3 mm accuracy, you need timing resolution of 20 ps (20, not 10, because you would be timing the round trip of the light). That's challenging - certainly not ...


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Laser is coherent light, so with a technique called interferometry you can actually measure distance with a resolution of less than a micro-meter, regardless of your timing resolution. It should be noted that the measurement produced by interferometry has half-wavelength periodicity (e.g. 200-350nm for visible light). This means that in order to absolutely ...


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Instead of attempting to time the round-trip of individual pulses (which depends on a good way to separate reflected pulses from ambient noise), you can also build a phase-locked loop. Control the sending of outgoing pulses by a voltage-controlled oscillator, sending one pulse at each rising zero crossing. Whenever you see an incoming pulse just before the ...


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You don't have to run a clock that fast, and you don't need any new physical principles either, just some clever electronic design, mixing analog and digital components and making a few critical parts (switches, in essence) very fast. One simple technique, as described here on wikipedia, is a two-slope ramp. At the start of the time to be measured, you ...


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The timing circuit doesn't have to run that fast. It just needs a time-to-digital converter which has a high enough resolution (0.1ns is nearly trivial with off the shelf CMOS technology) and then it can average many pulses (hundreds or thousands) to get the resolution improved by another order of magnitude. These are all fairly standard engineering ...


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Wave function collapse is not global, it is fictional. Let's suppose that the state is $\alpha|X=0\rangle+\beta|X=1\rangle$, where $|\alpha|^2+|\beta|^2=1$. When Alice measures the state, an operation is applied that correlates both Alice and the environment with the value of $X$, like so ...


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The information you are given was actually vague at a mathematical level, but with your resources you have you already have a mostly correct grasp of the physical quantities. The most important variables in a circuit are voltage ($V$) and current ($I$), because you can measure them unlike the charge. As you already stated $I = \frac{Q}{t}$, and its a ...


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Here's how I understand your question: A and B are space-like separated and make a measurement on a single particle that has equal (or just non-vanishing) probabilities of being in A's or B's region. You now ponder how the measurement process works on a deeper level. Could the collapse be a dynamical (i.e. time dependent) process? I think it can not. If ...


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In quantum mechanics all predictions and descriptions of nature come with a probability distribution . A simple example are the orbitals of the hydrogen atom.. The probability for an electron to be found at (x,y,z,t) can be calculated and the result, is called an orbital, because it is not a classical orbit. To compare a probability distribution with the ...


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The surrounding system is in a very large very mixed state, and that washes out the distinction in angular momentum. Trivial Example Consider the trace distances between the following nearly-maximally-mixed density matrices: $$\begin{align} D \left( \frac{1}{2} \begin{bmatrix} 1& & \\ &1& \\ & &0 \end{bmatrix}, \frac{1}{2} ...


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You are right that the magnetic field, or rather the apparatus used to generate it, absorbs some angular momentum from the quantum spin. This apparatus includes, for example, some coils of wire containing more than $10^{23}$ electrons, as well as many other macroscopic components. The upshot is that increasing the angular momentum of this apparatus by an ...



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