Uncertainty Definition and 1000 Threads

For the uncertainty about relative atomic mass. Such as for H-1 there is 1.00794(7)u. what exactly does the "7"means? Is it 1.007947? or 1.00794(+/-)0.000007? or something else? ref: http://www.ciaaw.org/pubs/TSAW-2007.pdf

Homework Statement A car engine moves a piston with a circular cross section of 7.500 ± 0.005cm diameter a distance of 3.250 ± 0.001cm to compress the gas in the cylinder. (a) By what amount is the gas decreased in volume in cubic centimeters? (b) Find the uncertainty in this volume. Homework...

1. Question The speed of an electron is known to be between 6.0×10^6 m/s and 6.7×10^6 m/s . Estimate the uncertainty in its position. Homework Equations ΔpΔx ≥ h/2π (mΔv) Δx ≥ h/2π (Since Δp= mΔv) Δx≥ h/2π(mΔv) h= 6.63*10-34 J*s c= 3.0*108 mass of electron= 9.11*10-31 The Attempt at a...

Homework Statement Some particles pass through a single slit of width W = 0.17 mm. After the particles pass through the slit they spread out over a range of angles. The de Broglie wavelength of each particle is λ = 561 nm. Use the Heisenberg uncertainty principle to determine the minimum range...

Considering how Heisenberg's uncertainty principle is applied to a top-hat wave function: This hyperphysics page shows how you can go about estimating the minimum kinetic energy of a particle in a 1,2,3-D box: http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/uncer2.html You can also...

Hi all, If a camera images a fluorescent molecule gaussian function with diameter roughly 300nm and each image pixel represents 160x160nm how could you say with higher precision where the molecule is located within that pixel. For instance if the localisation precision turns out to be 40nm how...

Problem I would like to determine the combined standard measurement uncertainty for a mean mass ##\bar{m}## computed from a mean volume ##\bar{V}## and a constant density ##\rho## with $$\bar{m} = \bar{V} \, \rho.$$ I know the mean volume ##\bar{V}##, volume standard deviation ##\sigma_V##...

Homework Statement I did an experiment to measure the speed of sound(using two microphones and a hammer). I changed the distance between the two mics and calculated(using a fast timer) the time taken for the sound to reach from the start mic to the end mic. I made a graph(distance on x axis...

Hello, guys! (And girls, but.. you know..) There are several things I do not quite understand, so, can you help me clear my doubts? ^^ 1) How do I know when to multiply the value of calculated data when it comes to determining the uncertainty of the data? 2) When do I multiply the percentage...

Homework Statement This isn't a specific problem. It's more of something that I have encountered before and I have been unable to find an answer to by looking online or through notes. Hopefully this thread might serve others with similar problems in the future. Say for example, you want to...

Hello, my name is Charles and I am experiencing some doubts about my physics career; I am hoping that other people here have felt the same and can give me some advice. I am presently at a crossroads career-wise and am rather lost. I have just accepted an admissions offer with very good funding...

Ok, for the switch-on voltage of a red LED I have the readings as follows, all in volts: 1.45, 1.46, 1.46, 1.44, 1.45. The mean of these readings, in volts, is 1.45 (I rounded up to 2 decimal places as my scale reading uncertainty was +/-0.01V, and my teacher told me to round them up since to...

Homework Statement Consider a particle with mass m oscillates in a simple harmonic potential with frequency ω. The position, x, and momentum operator, p, of the particle can be expressed in terms of the annihilation and creation operator (a and a† respectively): x = (ħ/2mω)^0.5 * (a† + a) p =...

Homework Statement I am trying to use a slide wire potentiometer and a galvanometer to find the electromotive force of an unknown cell. I have heard that the balance point at which the galvanometer needle has zero deflection should be towards the centre of the slide wire as this reduces...

Can anybody give me a simple example of uncertainty principle in both microscopic and microscopic level so that I can recall it every time I read about this topic ?

Having a bit of trouble estimating total scale uncertainty. In this experiment, I used four precision weights (error << scale resolution). Each weight has a known mass and is weighted on a scale 20 different times. Therefore, for each weight, I have a mean scale measurement, a standard...

Homework Statement Given the following wave function valid over -a \le x \le a and which is 0 elsewhere, \psi(x) = 1/\sqrt{2a} Find the uncertainty in \left<\left(\Delta p\right)^2\right> momentum, and the uncertainty product \left<\left(\Delta x\right)^2\right>\left<\left(\Delta...

what can be the uncertainty of the frequency that humans can hear ? I'm aware that there are many ways,but i tried google-ing to find them but i couldnt. if you could help me it would be great.

Hello all, as far as I can see this question is not posted already, my apologies if it is and please provide a link. But I'm watching this video on youtube: And at 22:38 there's an expression given for the uncertainty of an arbitrary operator Q, however I'm concerned the expression is incorrect...

Homework Statement We are told that resistor 1 has a resistance of 4700Ω ± 5% and resistor 2 has a resistance of 6800Ω ± 5% and the equivalent series and parallel resistances are to be calculated with an estimate of uncertainty. Homework Equations RSeries = R1 + R2 RParallel = R1 × R2 / R1 +...

There's something I don't manage to understand in the union between the relativity of simultaneity and the uncertainty of a quantum system's state. Observer A is in a lab on Earth. Observer B is approaching Earth at half the speed of light. On Earth, we build an experiment that gives a result...

Hi, I'm doing a lab report and for every number we need to calculate the uncertainty. I tried to calculate by using the SQRT of the number but i didn't get the same answer as my partner had? could you help me! These are the numbers and the uncertainty of my partner which i could not figure out...

Homework Statement I know this is more of a physics question, but I tried there and wasn't successful. I have done a physics experiment measuring the weight as a function time of the discharge of water from a cylindrical bottle with a pinhole at the bottom. What I ultimately want to get at is...

Are physical constants, such as the elementary charge or the gravitational constant, subject to Heisenberg uncertainty principle, theoretically and empirically? Theoretically in the sense that infinite precision of these constants will directly violate HUP. Empirically in the sense that, for...

Homework Statement I don't understand how the following works:Homework Equations I follow ## \Delta \nu_0 = \frac{\hbar }{2 m \Delta x_0} ## easily, but then ## \Delta x = \frac{\hbar }{2 m \Delta x_0} t ## ;leaves me puzzled - I understand multiplying through by t, but how does ## \nu_0 t =...

1. Homework Statement I have to demonstrate the Uncertainty Principle Starting from the expression of the following ket: |Ψa>=(ax^+ibp^)|Ψ> where a and b are complex numbers and the ^ denotes that x and p are unitary vectors. 2.Relevant equations I must use the bra-ket notation, but I...

Homework Statement What is a more precise way of finding the total mass? Weighing 5 individual quarters or weighing them all together? 2. Relevant equation individual weights n1+n2+n3+n4+n5 = total weight total weighed together N = total weight The Attempt at a Solution I think weighing...

Looking at the literature it appears that the increase in the variance of the wave function over time is proportional to (1+t^2)1/2. Is that right?

Trying to follow some text: Given a Gaussian-like distribution for a wave packet, ie a symmetric distribution of $k_x$ about a mean value $ \bar{k}_x $. Making the change of variable $u=k_x - \bar{k}_x$, they write the Fourier transform as: $\psi(x,0) = \frac{1}{2 \pi} e^{i\bar{k}_x...

What is the relation between "superposition" and "the Heisenberg uncertainty relation"?

Homework Statement So far i know that the uncertainty of the force of friction is +/- 0.1 and the uncertainty of the force normal is +/- 0.1 also. Homework Equations Force of friction=(myoo)(force normal) Myoo= force friction / force normal The Attempt at a Solution My data is Force of...

Homework Statement Please see the attachment for a better picture The energy of an electron in a hydrogen atom is: E = p^2/2m - αe2/r; where p is the momentum, r the orbital radius, me the electron mass, e the electron charge, and α the Coulomb constant. Use the uncertainty principle for...

Say I have a 0-10 lbf load cell that can measure the force it takes to lift an object. The load cell is accurate to 1% of the full scale. I take 5 measurements and get the following readings: 5.2, 5.1, 4.9, 5.0, & 4.8, all in lbf. Now I am asked to give the mean with the associated...

I've uploaded a proof of the Heisenberg uncertainty principle from Konishi's QM. I just don't quite understand one part: what is the significance of the discriminant being less than or equal to 0? Wouldn't this just result in ## \alpha = R \pm iZ ##? Why would this be desired in this proof?

Homework Statement How do I find the overall uncertainty of R when R = (h2+l2)/2h Homework Equations uncertainty in h = ±0.57% uncertainty in h2=±1.14% uncertainty in l2=±7% The Attempt at a Solution √1.142+72+0.572

I understand this topic has been brought up before, however there appears to be "truth" or "lies" and very little in between when it comes to explaining the Heisenberg Uncertainty Principle (HUP) to students of freshman chemistry. I'm teaching university general chemistry to students who've had...

For an electron can I not do the following to determine both the position and momentum? I take a screen with a small hole and I eventually make the hole smaller and smaller. Cathode rays emitted will hence get diffracted after passing through the hole making momentum more and more uncertain...

Observables are paired up in the uncertainty principle such that we can't measure both to a high degree of accuracy. Specifically, ## \sigma_x \sigma_y>\frac{\hbar}{2} ## where ## \sigma_x ## and ## \sigma_y ## are the standard deviations of our measurements. I've got two lines of questions...

1. The problem statement, all variables and given/known dat Show that if you have a signal f and noise σf for a stellar flux measurement, then the uncertainty on the observed magnitude is given by σm = 1.0875 x σf / f Homework Equations (you should use the fact that when ε<<1 then log(1±ε) ≈...

Homework Statement [/B] a=12.26 +/- 0.08 b=0.25 +/- 0.05 e=1.2 +/- 0.2 Evaluate the uncertainty of following calculations Part 1. z= 5(ab/e) Part 2. p= 3e - b The Attempt at a Solution I attempted part 1 like this Δz/z = 5 (Δa/a + Δb/b + Δe/e) ... Calculated Δz to be 20 but the answer is...

Somebody who can explain the question How big a error must there be at the temperature for the error on the pressure measurement is not more than 5 % ? thanks in advance

what will be the scenario if Heisenberg's uncertainty principle is applied at macroscopic level?

Homework Statement I am writing a lab report and I need to calculate the uncertainty error for Gravitational Potential Energy and Kinetic Energy. The Professor told us that the margin of uncertainty for time is +- 0.025 seconds, margin for height is +- 0.001 meters, margin for mass is +-0.001...

Hello, I am working on a lab report and am unsure about how to express the uncertainty of one of my calculations. I am calculating the volume of a cylindrical disk with height = 0.0258 ± 0.0001 m radius = 0.0767 ± 0.0002m Using V=π(r^2)h and the upper/lower bound method, I find: V= 0.000476205...

Hello, I'm working on a lab report and am having a bit of trouble when it comes to figuring out uncertainty. Trial 1 Acceleration: 0.93 ± 0.14 m/s^2 Trial 2 Acceleration: 0.83 ± 0.35 m/s^2 Trial 3 Acceleration: 0.93 ± 0.14 m/s^2 I have three values listed above and and wanted to find the...

I have to derive I did all the way but stuck with the ">=" to "=" sign. what is the logic behind it ? is it safe to write "approximate" while taking the square-root on both side ? or the energy term "V" has gone during the calculation so it has only momentum "p" ?

Firstly, I assume that I'm correct in assuming that since expansion is accelerating it will increase to any arbitrarily large value at some point in the future. If this is true, there must be some point at which particle/antiparticle pairs (due to uncertainty) are carried away from one another...

Upon a measurement of the position, the wavefunction collapses to a spike centered at x0 https://farside.ph.utexas.edu/teaching/315/Waveshtml/img3240.png I encounter similar spike pictures numerous times, but there is an uncertainty in position , it can't be a spike right. First thing I see...

If I flip an old coin with irregularities 100 times and get side a up 55 times and side b 45 times I say that the probability is 55% that side a comes up. But how can I estimate the uncertainties in this experiment? For example can I say something like "with 95% confidence the probability is...

Homework Statement Show that the uncertainty relation can be written as Δλ Δx >= λ^2 /4π Homework EquationsThe Attempt at a Solution Ok the uncertainty relation is ΔpΔx >= h/2π , also p = h/λ , so substituting that I have Δh/λ Δx >= h/2π , then divide both sides by h, and multiply both sides...