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In order to answer your question you must think through the entire measurement. In this case you are measuring the photoelectric effect by placing a photodiode into a circuit. What kind of circuit element is the photodiode? It is a source. And as you have pointed out above, it is a constant voltage source (with voltage determined by the energy of the photons ...


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In contrast to coordinate time, proper time is independent from any geodesics geometry. Any clock is OK as long as it is in the same frame as the object whose proper time is measured. In order to recover the proper time information, the observer must ensure synchronization of his own clock with the clock of the observed object. Thus, your problem might be ...


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My point of view in physics is that, given any concept (in this case, proper time), there are always two notions: (1) the theoretical concept defined in the sense of mathematics, and (2) the experimental concept defined in the sense of experiment. We then hypothesize that these two concepts are equal, and of course, if experiment shows that this is wrong ...


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to solve the problem you need at 4 linear equations (or the two linear ones you have plus another nonlinear one). Otherwise, the solution is undetermined, you have more variables that linear equations and the number of solutions is infinite. Here are the two extra equations that you need. 1) the total force equald the applied force (otherwise it will move ...


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The uncertainty in any particular measurement is $\sigma_E$. Resolution for these devices is almost always stated in relative terms as here, but take it like this because it depends on the energy measured. So just multiply by the energy. That is, express your signal in $\mathrm{GeV}$ and then find $$ \begin{align} \sigma_E = \left(\frac{0.1}{\sqrt{E}} ...


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Use a large and thick copper spoon. Put the spoon in the coffee for 3 seconds. Remove it and insert the spoon in your mouth. (beware it will be hot) Use the tongue and palate to cool spoon pushing hard. When the spoon is close to the temperature of your mouth (feels tepid) remove it and reinsert the spoon in the coffee by another 3 secondos plus 0.5 ...


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well, you could build a faraday cage and go inside it to look at your instruments, no need to transfer information outside - or you could place a recording device inside. if it's a problem for you in your mind that there is a void inside the conductor, that problem would apply on smaller scale as well, your instrument for measuring would still take some ...


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Writing $\mathcal X_C^{n} := \{ \varepsilon_{ C \mathcal X }^1, ~..., \varepsilon_{ C \mathcal X }^n \}$ for any (variable) suitable ordered subset of $n \ge 1$ events in which $C$ took part, and abbreviating $${\! \large \tilde\tau} C_K^P := \! \! \mathop{ \bf \text{ infimum } }_{ \large {\mathcal X_C^{n} } \subseteq \{ \large{ \varepsilon_{C K}, ~... ~ ...


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if there is nothing or no one around to hear it Given that trees/forests don't exist in isolation we would have a very difficult time finding a tree that falls with absolutely no creature capable of perceiving sound within a reasonable distance. Go find a forest completely devoid of birds, rodents, snakes, insects, fish etc. Don't forget a 2+km buffer ...


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Put a microphone & recorder near the falling tree. No one was around to hear the tree fall. Yet you can play the recording and provide evidence of sound.


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It depends on your definition of "a sound". If a sound is not a sound unless it is perceived as a sound (that is, processed in the auditory system of a sentient being), then the answer is "no". If a sound is a coherent disturbance in the pressure distribution of the air, and this disturbance propagates through the medium "at the speed of sound", then the ...


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I see an error in the Lindeburg correction formula presented by you. Instead of 2.1r it should be 2.4r. I found in an article of Smoluchowski, that the coefficient (1+2.4r/R) was proved by Landenburg in the paper: R. Ladenburg, Ann. d. Phys. 23, p.447 (1907). The error is probably responsible for the non-constant value of viscosity.


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A problem formulated in the time domain and its equivalent formulation in the frequency domain contain essentially the same information. They just have different mathematical forms. One is easier to solve than the other, that is why we use transformations. Many problems attempted through the equations of motion obtained from Newton's equations are really ...


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There are no differences. Frequency domain is used as a mathematics transformation tool (Fourier, Laplace) in order to resolve too complex differential equations in time domain spectra.


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A single oscillator will make the rope tied between the two walls, to display standing waves, i.e. any point of the rope will rise and get down according to a law f(t) = Asin(ωt), where A is the maximal amplitude of oscillation at that point. But you have two oscillators. The oscillation of a point in time is (1) f(t) = A_1 sin(ω_1 t) + A_2 sin(ω_2 t). ...


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Within the theory of relativity there exist several different notions of how to characterize a "measuring rod" by a relation between its two "ends"; and correspondingly there are different notions of two distinct participants having been "rigid" to each other. In listing some of those notions it is of course possible at least to discuss the special case ...


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Vernier Constant: it is the ratio of smallest division of main scale to the number of divisions of vernier scale. Least Count: the smallest possible measure that any instrument can do accurately is known as least count.


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I think your understanding is pretty sound. Can you say that a single mode will be excited containing all wavelengths from 1.5 to 3 μm? Yes, absolutely. For analysis, you would decompose the light signal by Fourier decomposition (Fourier integral). You would then impart the phase delay through the fibre appropriate to the lone mode at each different ...


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I think you might consider first special relativity. We can model the problem as being in Minkowski spacetime with cartessian coordinates and put the switch at $(0,0)$ and the lamp in the coordinate $(0,L)$. Where $L$ is the distance from the switch to the lamp. Then the question is what is the state of the lamp at $(120,L)$? Using a spacetime diagram ...


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The smallest length that has been directly measured is about $10^{-18}$m, and the measurement was done at the Large Hadron Collider. In a collider the length scale of the phenomena you are studying is related to the energy of your collision by: $$ \Delta x \approx \frac{h c}{E} $$ where $h$ is Planck's constant, $c$ is the speed of light and $E$ is the ...


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If you count the number of times the switch is flicked, then when the number is even, the lamp is off, and when it's odd, the lamp is on. So we can rephrasing your question: is infinity even or odd? That's one for mathematicians... they will probably say "both". So the short answer is - there is no "real" answer to your question. But most likely the lamp ...


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A measuring rod is an object that has a constant proper length. Start with the simple example of a ruler in Euclidean space. If we place one end of the ruler at the origin then the other end will be at some point $(\Delta x, \Delta y, \Delta z)$, where obviously the position will depend on the length and orientation of the ruler. The length of the rod, $s$, ...


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There is a recent paper in which $G$ has been measured. We obtain the value $G = 6.67191(99) × 10^{−11} m^3 kg^{−1} s^{−2}$ with a relative uncertainty of 150 parts per million (the combined standard uncertainty is given in parentheses). Most measurements of $G$ are based on a torsion pendulum as in the original Cavendish experiment. The paper ...


1

I'm not a fluid mechanics expert, but my mechanical systems knowledge suggests it might be simply a natural oscillatory behavior, which is always present but in this case is more noticeable due to the aggressive initial response (i.e fast influx of air) your chamber experiences. So what is causing this inexplicable pressure drop? Once the chamber has ...


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To answer both parts of your question: In general the flow coefficient will not change with the head height of the system. The head height will only impact on the static pressure and hence the flow rate through the nozzle. This will be true provided the liquid level is not so low that it is influencing the flow pattern near the orifice, in which case the ...


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Nuclear plants (and theoretically fusion plants) work with $e=mc^2$. For example: The mass of 2 Protons and 2 Neutrons is bigger than the mass of Helium, which consists of 2 Protons and 2 Neutrons. The difference is emitted as energy when Helium is made by the fusion of 2 Protons and 2 Neutrons (the actual reaction in the sun are a bit more complicated, ...


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Particle--antiparticle annihilation events are direct evidence of the mass-energy correspondence. Michelson and Morley interferometric results support the absoluteness of the speed of light (or some more esoteric possible results), and building from that and the relativity principle you can arrive at the mass-energy correspondence rather indirectly.


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I believe that the math covering condensed matter physics are very similar to that describing black holes and some high energy physics. So what was seen was an experimental result verifying the maths. Whether the maths really applies to a BH is unknown. In a way, it is more like solving equations experimentally using condensed matter as an analog computer. ...


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First, how do you actually determine the position of the electron without "kicking" it out of the atom? When talking of quantum mechanical entities, as the atom and the electron are, one has to keep clearly in mind that our well validated models that allow us to probe their behavior are probabilistic, the probability given by the square of the wave ...


3

[PDG] quoted something like $(q_p+q_e)/e$ without defining these quantities, That is exactly what you asked for. Recall that the charge on the electron $q_e$ is negative and that on the proton $q_p$ is positive, so the sum there is exactly the difference in their magnitudes. Taking it as a fraction of the defined base charge $e$ makes it a dimensionless ...


0

First, how do you actually determine the position of the electron without "kicking" it out of the atom? This is in the context of non-relativistic quantum mechanics (QM). In QM, an ideal measurement of position requires that, immediately after the measurement, the electron have a definite position. However, a state of definite position is ...


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Bigger problem than what is mentioned in the comments: The picture shows a gap between the water and the side of the "swimming pool straw." (Can't even believe I just typed that.) Anyway, the straw trick only works because there's a pressure difference in the straw above the fluid, and outside the straw, above the fluid. The pressure below the fluid is at ...


1

The speed of light can't be measured anymore (in SI units) because it has had a defined value since 1983. See Why do universal constants have the values they do? Before 1983, the meter was defined in terms of the wavelength of a certain emission line of krypton 86. The second is also defined in terms of an atomic standard (the frequency of a transition in ...


2

The two most common conventions I know are Report the standard deviation of the result: this tells you that a further measurement has 68% probability of falling inside the interval Report the standard error of the measurement (standard deviation / $\sqrt{n}$). This tell you there is a 68% chance that the actual value (the mean of the underlying population) ...


2

Qualitatively: A neutron decays into a proton an electron and a neutrino. Both the proton and the electron are highly ionizing in any medium. After the decay the energy of the charged particles will be absorbed very fast and turned into photons. A gamma ray does not decay, and is not able to ionize the way a charged particle can. It has to interact with ...


2

While I am not familiar with the details of your experiment, I am quite familiar with the methods of maximum likelihood estimation. In the field in which I work, we model the system response as part of our model - so that when we compare the predicted measurements with the actual ones, we find our how close our model is to the underlying truth. It goes ...


1

This is speculation, based on working in material field many, many years ago (before nano scale testing was a Thing). I believe that the smaller scale test can be more faithful to the underlying material properties: in essence, any large scale testing will be affected by the existence of irregularities in the material (grain boundaries, dislocations, ...


0

Say you release the pendulum, then on the other side, there is a period of time where it is motionless where $E_k = 0$. In addition, this is the point where $E_{p,max}$. At the next instant, the pendulum will swing back increasing velocity due to the acceleration of gravity pulling at the weight at the end of the pendulum. Following the Law of Conservation ...


1

@Tom's answer appears absolutely correct, but omits to mention the assumptions behind these formulae: (i) The measured values of $A$ and $B$ follow a normal distribution. (ii) The measurement of $A$ does not depend on $B$ and vice-versa. i.e. the variables are independent. (iii) Over the range $\pm \sigma_A$ and $\pm \sigma_B$; $Z(A)$ and $Z(B)$ are ...


3

One of the formulae in your question is not quite correct (as pointed out by Nikos M) but it should be ${\sigma_Z}^2 = ({\delta Z \over \delta A})^2 {\sigma_A}^2 + ({\delta Z \over \delta B})^2 {\sigma_B}^2$ This is the basic equation for propagating uncertainties. The version you have in your question without the squared terms is a simplification of ...


2

The whole artillery of Quantum Mechanics, operators and all, is a mathematical description of the result of measurements. The contact of the mathematics with measurements comes from the postulates: 1) To every observable there corresponds an operator 2) The square of the wave function for the specific system gives the probability of finding the system ...


1

Just one more look at this... given the numbers, you could fit a curve through the data. If you decided to include one additional point on either side of the missing value (4 points total) you could fit an exact cubic, and the interpolated value would be 1.100; if instead you did an (inexact) quadratic fit through the four points you would get 1.093. A ...


1

I agree with @WetSavannaAnimal as far as interpolating to get the correction factor goes. Alternatively you could go and find out what the correction factor for 7 values actually is. However, the formulae you originally quoted for the unbiased sample variance and the sample standard deviation were incorrect. The formula for unbiased variance is $$s^2 = ...


1

The reason behind the hissing sound is that the temperature of the water droplet is much lower than the hot surface. As soon as the water droplet's base touches the hot surface it quickly evaporates but still the top part of the droplet is in liquid state and there is an opposition to th water-vapour coming from below. As the water-vapour couldn't vertically ...


3

Perhaps I misunderstand your question but I would like to make clear that operating on a state with say, the momentum operator is not meant to be the equivalent of measuring the momentum of the system in that state. Consider, for example, a state that is a superposition of two momentum eigenstates: $$|\psi\rangle = \frac{1}{\sqrt{2}}\left(\,|p_1\rangle + ...


2

You are trying to estimate the mean of population that your data come from, and you are assuming a normal distribution for the data. However, you do not know the true variance of the population, and you need to use the data to estimate the variance as well as the mean. Therefore, you don't get quite as much "information" out of your experiment as you would ...


3

If the data are normally distributed, then the variance of the variance is given by $$ Var(s^2) = \frac{2 \sigma^4}{n-1},$$ where $\sigma$ is the standard deviation. $$\sigma^2 = \frac{1}{n} \Sigma_i (x_i - \bar{x})^2 $$ And $s^2$ is the unbiased sample variance, calculated from the data, where $s^2 = n \sigma^2/(n-1)$. Formulae found here Hence the ...


0

Here are two examples where these things are measured in practice. Energy In photoelectron spectroscopy, electrons are knocked out of atoms or molecules by ultraviolet radiation - photons with 10 or more eV of energy. The energy of the electrons emitted $E_e$ is given by $E_e = h\nu - \text{binding energy of electron}$, where $h\nu$ is the energy of the ...


2

Particle physics up to now has come up with the Standard Model as a mathematical theory that fitted most experimental data up to the LHC and was successful in predicting the results of experiments, including many analysis of LHC data. The standard model has one Higgs, that became necessary because just the groups structure that the data implied ( ...



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