New answers tagged

1

The small number of "conceptually independent types of processes and calculations" is exactly a symptom of the theory's being fundamental! Even in classical physics, all calculations could have been mathematically reduced to the calculation of the final state that evolves from an initial state (or a state that is stationary etc.). In quantum mechanics, this ...


0

You can't just tilt the mirror (for the reasons described in JEB's answer). You can have off-axis parabolic mirrors but they are tricky to make. You either have to machine the surface with a diamond tip CNC machine, or saw an off axis region out of a larger mirror At radio frequencies they are a lot more common. Where you can make the shape from metal ...


1

Aberrations. A parabolic mirror perfectly focuses rays along the optic-axis, while off axis rays are blurred--tilt the mirror and you get more light, but it's out of focus. I would guess that the non-tilted mirror has 2nd order aberrations, while tilted one is 1st order: it's a lot worse.


0

While reading Dicke&Wittke, pp. 274-275, it occured to me that a (maybe more) convincing derivation of the "transition rate formula", as an experimentalist would interpret such a thing, can be given as follows. As usual, we assume that the system is in a pure state $\vert i \rangle$ at $t=0$, when the perturbation (which for simplicity I assume to be ...


2

One indication whether the 'inner' balloons are filled with helium or something heavier is whether the 'outer' balloon still floats in air or not. Whether it floats or not depends on whether its overall density is lower than air's density or not. Its overall density $d$ is simply given by: $$d=\frac{\Sigma m}{V}$$ Where $\Sigma m$ is the sum of all the ...


0

Theoretically there is nothing wrong with your experiment. But I doubt you could succeed. Firstly, how would you prevent air currents from creating water waves that spoil your measurement? A light source at one end of the pool will heat up the water and cause turbulence. This could spoil your measurement because of scintillation of the light beam in the ...


4

Some additional reasons not mentioned in the other answers: Clipping losses: Gaussian beams fall off exponentially, so any finite size tube will cause a small loss in power. Typical design rules when making an optical design of such instruments is that not more than 1 part per million of the light is lost due to the finite size mirrors. Typically, all ...


0

Detecting the emitted photons from a charge accelerating in Earth's gravity looks like a hopeless task, given that the radiated power is tiny (see formula 9 in Anna's answer). But we can try to exploit the fact that the number of emitted photons always diverges no matter how small the acceleration. While very low energy photons (so-called "soft photons") ...


14

This must have been a conscious design consideration, since it means that a much larger volume of vacuum must be maintained While I don't think that it's what motivated LIGO, the volume is not as much a consideration in high-vacuum as the surface area. Once the chamber has been pumped out, the ultimate vacuum level is set by the rate of ...


1

Young's modulus of a material doesn't depend on geometry. It is a mechanical property of material and depend on its structure. But, we cannot determine Young's modulus of a material by its structural properties experimentally. We (in your case) want to determine $E$ (Young's modulus) by using $E=\large{\frac{PL}{A\delta}}$ in a tension test ($P$ is the ...


1

There is some misunderstanding here. whether a freely falling charge radiate photons, how strongly and relative to which frame of reference it does or does not radiate if you mean a charge in free fall. In this calculation:, from the conclusion It is found that the "naive" conclusion from the principle of equivalence - that a freely falling ...


1

It is done all the time in acoustics, ask any musician! However Shen probably was referring to harmonic generation in radio frequencies; with radio is is called a frequency multiplier. The heterodyne technique was invented in 1901. The Kerr effect was first found about 1876. The first footnote in this article provides some historical background: altering ...


34

The LIGO beam is 200 W as generated at the input mode cleaner; the beam is then recycled multiple times in the arms, increasing the power density significantly. This requires large optics with near perfect coatings in order to avoid "hot spot/cold spot" damage from various types of possible defects. But there is an additional reason for the large beam size, ...


0

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 ...


0

Of course it is possible. There is no practical constraint at all. You do not even need $C_2$ in order to convince yourself that it is possible. Just take $C_1$ and turn it upside down so that it is 9:10 instead of 10:9. On the other hand, in terms of human usability it is rational to have the ratios all going the same way ($>1$), so that all vernier ...


2

Comparison of fabrication techniques for hollow retroreflectors describes, in great detail, the two obvious methods: The use of a precision solid prism corner cube as a mandrel to hold the glass plates prior to gluing of the edges. An adjustable set of precision mirror mounts, designed to hold the three plates In both cases interferometric techniques ...


2

The direction of the force due to surface tension depends on whether the liquid wets the the body or not. In the first picture liquid does not wet the body, so the force is directed in such a way as to decrease the contact surface area of the body with the liquid. That is, upwards. In the second picture liquid wets the body, so the force is directed in ...


0

There is no need to calculate the moment of inertia I, which could be quite difficult for an irregular lamina. You can find both I and g from the same experiment. The period T of small amplitude oscillations of a compound pendulum is give by (see Source below) : $(\frac{T}{2\pi})^2 = \frac{k^2+h^2}{gh}$ where k is the radius of gyration (related to ...


0

Well, this will certainly depend of the shape and mass distribution of your pendulum. For instance, for a pendulum made of a rod and a thin cylindrical disk, the moment of inertia of the rod (about its own symmetry axis) would be $\frac{1}{12}M_rL^2$, and the moment of inertia of the disk $\frac{1}{2}M_sR^2$. If you have a solid sphere instead of the disk, ...


2

During the acceleration phase the object's movement can be modeled with the quadratic curve $$x=x_0 + v_0t+\frac{1}{2}at^2 \qquad\text{where } x_0 \text{ is the initial position, and }v_0 \text{ is the initial velocity}$$ During the constant velocity phase, the object's movement can be modeled with the linear equation $$x=x_1 + v_1(t-t_1)$$ where $x_1$, ...


0

The average value of acceleration should just depend on the initial and final velocity and the time interval between them. Since the average value of a function over the interval a to b is the integral of the function from a to b divided by (b-a), and since the integral of acceleration gives you velocity then if the limits are $t_1$ and $t_2$ the average ...


2

In the Geiger region an incoming charged particle produces an avalanche of charged particles which migrate across the tube and produce an easily measurable electric pulse on the electrodes. The tube contains a halogen quenching agent which then stops the production of further charges so that one incoming particle produces one pulse. As the voltage across the ...


1

Let us dive into the light clock thought experiment, Special relativity is based on two postulates, There is no such thing as absolute motion. Phrased another way, all laws of physics should be invariant under changes in inertial frame. The speed of light is measured to be the same value in all inertial reference frames. Let's say you are on the train ...


1

In essence you are trying to decide whether the friction forve is proportional to the velocity or velocity squared. Assume that the period of a swing $T$ stays constant. If $x(t)=A_oe^{-\gamma t}$ then if after $n$ swings the amplitude is $A_n$ $A_n = A_o e^{-\gamma T n} \Rightarrow \ln A_n = -\gamma T n + \ln A_o$, so plot a graph of $\ln A_n$ against ...


4

I did a couple of experiments with a DSLR and a cheap red home improvement laser level. The most revealing factor is that a direct reflection of the laser on the CCD sensor gives a distinct square diffraction pattern. This is pretty much what one would expect from a camera that has square pixels. The reflections have sharp peaks that are spaced fairly far ...


2

It seems like some kind of Newton rings formed. Does your mobile camera has a flat thin sheet covering the lense. If so, the newton rings formed is captured in the sensor. Having said that, I can't explain why there are multiple of them, that too in a lattice formation. May be if the distance between the thin sheet and lense increases we have various newton ...


2

Some other effects that might be at play: 1. Reflections from the end-faces of the fiber causing interference 2. Brillion Scattering 3. Check to see if in fact the fiber you're using has a cut-off wavelength shorter than the wavelength you're actually using.


0

Check the pointing stability of the laser, which, together with mechanical vibrations, would make the coupling efficiency fluctuate. After making the setup as mechanically stable as possible, try to put small diameter tubes everywhere around the beam before the fiber. And/or enclose everything in a box. Air movement has an effect, and it helps to block it.


2

Observation of a single electron in a Penning trap shows the upper limit of the particle's radius is 10^−22 meters Reference.


2

This article appeared in Mother Earth News in olden days (1972!) and discusses ways to build an ice house for cool storage and how to harvest the ice with which to fill the house once its completed: How to Build an Ice House Of course, ice houses work better in some areas due to the local climate. An ice house would be a worthwhile project in Vermont, ...


3

The basis for constructing a working ice house is described in The First Icehouse in America? The fundamentals are: a large mass of ice; good drainage, an environment with constant temperature. Insulation of the ice with saw dust or straw helps to slow the melting, but it must be kept dry, which requires good drainage. You would obtain a better discussion ...


0

Since the charged conductor is present it will create an electric field and corresponding potential but to measure it experimentally you will need another known charge at one position, say A and then move it or allow it to move ( that depends on whether the charged body and our test charge are of same sign or the opposite sign) to a position B and then ...


0

You have to have probe wires in order to bring any charge into the voltmeter so it can be measured. Electrons will flow in a wire because they are attracted or repelled by other nearby charges. For example, if the charge is positive and you place the probe near the charge, electrons in the probe wire will move toward the charge, causing the other end of the ...


0

The measurements are repeated $N$ times for the same physical conditions; there are thus $N$ points for this single datum, which will be reported as the mean of the sample , along with the measured standard deviation. The interval is conventional, based on common usage. This makes it easier to interpret the meaning of the reported measurements. ...


7

It's true that if you know the masses of, e.g. two orbiting stars $M_1$ and $M_2$, their orbital period $T$, and the distance $d$ between them, then you know $G$. And we can measure $T$ pretty well and $d$ fairly well. But how do you think we figure out the masses of the stars? We can't just count the amount of stuff in them; we have to infer the mass from ...


1

If your curve-fitting program allows it, instead of fitting $y=a+bt+ct^2+dt^3$ you could try fitting $y=d(t-a)(t-b)(t-c)$. The output parameters $a$, $b$, $c$ will then be the required roots and the errors (or rather variances and/or co-variances) will be included in the statistics.


3

The experiment certainly does produce a very general complex superposition of momentum eigenstates. The spread is not "small" in any way – virtually all allowed (by conservation laws etc.) final states are represented in the superposition for any initial state. We detect particles of particular momenta in the final states because the detectors (e.g. at the ...


7

My bet is that your fiber is very short (something like one meter or so) and that the fluctuations you see on the output mode are due to cladding modes, i.e. a part of the injected light propagating into the cladding of the fiber instead of the core. The resulting fluctuations are due to external perturbations of the fiber (thermal fluctuations or you ...


4

This sounds as though the aberration in the laser's output could be fluctuating owing to "mode hopping" (where several of the laser's cavity modes are active and playing a time varying role) so that, even at a constant output power, the aberration of the output beam varies with time. Wavefront aberration is roughly the Fourier-dual of Strehl ratio. This ...


1

Judging by your Q1, I think you are asking about error bars for data points in graphs, especially in relation to plotting a line or curve of best fit. Error bars are not often calculated statistically for this purpose. To do so, a sample of N measurements must be made for each chosen value of the independent variable x and a mean and SD calculated. The ...


2

Yes the human body has a gravitational field, and yes it's large enough to be measured experimentally (see the Cavendish experiment).


1

There are often several different methods of synthesizing materials, and in lots of cases they arrive at the same result. Sometimes the experiments you want to do will depend on your growth method, though: for instance, the polycrystalline samples you get from solid state reactions can be good for x-ray or neutron diffraction studies. If you want to ...


0

Robert Griffiths is quite fond of Mach-Zehnder experiments as useful windows into interpreting quantum foundations, and he presents calculations for some toy models of M-Z interferometers in Chapter 13 of his book, Consistent Quantum Theory. As a caution, most of this book is written to parallel the consistent quantum histories formulation of quantum ...


1

It depends on the efficiency of the RO membrane. When the membrane conversion rate was below 20 percent, the answer in general would be yes. However, with the newer type membranes the conversion rates are quite high. In RO sea water desalinization, the normal pressure required to force the the pure water molecules through the membrane is in the range of ...



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