Uncertainty Definition and 1000 Threads

Are there fundamental limits on the accuracy for measuring both position ##q## at time ##t## and momentum ##p## at time ##t+\Delta t##, with tiny ##\Delta t##? If yes, why? If no, why can't one then measure (in principle) both ##q## and ##p## arbitrarily well at the same time ##p## (which is...

<Moderator note: Thread moved from General Physics hence no formatting template shown> The fractional uncertainty is defined as: uncertainty/measured value. So for 2 cm +/- 1 cm we have 50%. For 9 cm +/- 1 cm we have 11.1%. My question is what if the measured value is 0 cm? How is the...

Homework Statement Hi there, the issue I'm having right now is finding the right way to calculate uncertainties when trigonometric terms come in play. The question goes like this, we're given 2 sets of 5 angles in degrees, the incident angle (10.0, 20.0, 30.0, 40.0, 50.0) and the other is the...

In one of my problems, I have this set of data. I have to create two best fit lines, and find a value of absolute zero for both. The first best fit line is to be made assuming there is NO uncertainty in P. This is rather straightforward, just use the normal linear regression, find a slope...

I am working on astrophysical data and I have a large number of redshift values of quasars. Now, each redshift estimate comes with its estimated standard error naturally. If I plot a histogram of these redshifts, I would expect the bins counts to also have some sort of uncertainty. I am unable...

I have a set of values I got from measurements, and each of these value has an uncertainty associated to it. I compute the average of my values. How can I average the uncertainty associated to my average value ? Do I simply take the average of all uncertainties ?

Mod note: Moved from a technical forum section, so missing the homework template. I am analysing the data from my undergrad experiment, which the aim is to find the Plank's constant by scattering x-ray off NaCl crystal and using Braggs law. The straight-line equation is as follows...

Let a photon of a definite wavelength (hence a definite momentum ) start it's journey at time 0. After 8.3 minutes it hits a detector on earth. So it's position is exactly known (in fact it can be predicted for any time less than 8.3 minutes). So we have particle with definitely known momentum...

For an unstable particle is it reasonable to take the uncertainty in energy as the energy it was created with? If so, why?

Homework Statement Standing in the middle of a 20 m long pier, you notice that at any given instant there are 15 wave crests between the two ends of the pier. Estimate the minimum uncertainty in the wavelength that could be computed from this information. Homework Equations [/B] Uncertainty...

I am wondering about the minimum possible uncertainty (standard deviation) in an electron's position (Δx). How precise can one know the electron's whereabouts without creating other sorts of particles and phenomenons. I know of the localization energy interpretation of the energy uncertainty...

Homework Statement What is the uncertainty in 5.00mm measured by an analog device? Homework Equations No equations, Uncertainty and error analysis question The Attempt at a Solution I know that the uncertainty is half the smallest division but i can't figure out what is the uncertainty and...

Hello, one of my friends came over to get some help on a homework problem, and it went past over my head I am pretty good with stats, just don't know how to approach this to help him out. So a radionuclides' activity (Cesium 137) is measured in the year of 1981, (no date just year), and its...

Homework Statement A proton is known to lie within the nucleus of a gold atom. The radius of a gold nucleus is approximately 6 fm. What is the minimum uncertainty in the proton’s velocity [you may treat the problem as one-dimensional and you should express your answer as a fraction of c]...

I'm currently designing an experiment on Double slits for a high school science fair, but I'm not sure whether it's plausible or not. I'll be spending some of my savings for this, that's why I would like to hear some feedback from more-knowledgeable people first. In this experiment, I am trying...

Homework Statement I have a series of 12 values that I need to calculate the Theoretical Intensity, I, using the formula below. I have found values for all variables and their uncertainties, and have calculated the I value for each set using the formula. Now I need to calculate the...

Homework Statement What's the answer to (0.781±0.002)/(0.551±0.002)? Well, here is the answer (1.417±0.008) that professor Walter Lewin said in one of his videos. I checked this in an online uncertainty calculator and it turned out 1.417±0.006. Homework Equations n/a The Attempt at a...

I am trying to calculate what we'd expect the uncertainty in energy would be for an electron in a hydrogen atom where it was confined to its usual radius (120 pm) versus if we confined it to the width of a proton (.88 fm) to try and make an argument about why the electron does not fall into the...

Are quantum superposition, Heisenberg uncertainty principle, wave/particle duality the same thing? Do they imply each other? They all seem the same to me like the wave-like nature of photons -> superposition, and superposition means there's not definite position -> uncertainty principle. Sorry...

Homework Statement What is your average reaction time? What is the uncertainty? Homework Equations To find time I used the following equation: t=\sqrt{\frac{2(\frac{D}{100})}{9.81}} D is measured in cm, hence the division by 100 (to get meters). 9.81 is acceleration due to gravity (this comes...

I know the equation which explains how it works, but why is it like that? The closest thing I can think as to why is because of the wave-particle duality of matter given by λ=h/mv, which also explains itself. But I don't know exactly why.

Physicists often speak of the uncertainty principle in terms of position and velocity (in momentum). But momentum is Mass X Velocity. Why is it that we can say something like "a particle with a well defined position has high uncertainty in velocity". But I never hear a statement like "a particle...

Homework Statement A common method for finding wavelength is to use diffraction grating. The relationship between wavelength λ and the angle of max intensity θ for first order interference is λ = d*sinθ where d is the spacing between lines on the grating, which is the inverse of the grating...

Hi, I'm having quite a bit of trouble finding the propagation of uncertainty (using partial derivatives) of the volume of a hollow cylinder. The examples in my tutorial only demonstrates how to find the propagation of uncertainty on simple operations such as x + y, x/y, etc... 1. Homework...

Is precision the smallest division in measurement instruments? Is uncertainty one-tenth or a half of the smallest division in measurement instruments? I'm confused some say one-tenth, some say a half... Thanks in advance

Homework Statement An electron is moving in a parallel beam along the x-direction with momentum, p=mv. It encounters a slit of width w. Assuming that the electron gets diffracted somewhere within the central maximum of small angular magnitude Δθ, estimate the uncertainty Δp in its momentum...

Homework Statement A distance R is measured to be 3.400±0.003m. What is the relative uncertainty in R? 9×10-4 What is the relative uncertainty in R^-2? Homework EquationsThe Attempt at a Solution Relative uncertainty of R is 0.003/3.4=8.8e-4 Relative uncertainty of R^-2= -2(8.8e-4)=-1.76e-3...

Hi everybody, I was reading about the Uncertainty principle and I came across the statement: "the position-space wavefunction of a minimum-uncertainty state is a Gaussian. Indeed, because it’s a minimum-uncertainty state, its momentum-space wavefunction is also a Gaussian."...

Hi everyone, Apologies if this is common knowledge or a silly question, I'm just coming back to physics and I've been looking through the double slit experiments ( both double slit and delayed choice quantum eraser ) and it got me thinking about the uncertainty principle. With a photon of...

To check my understanding, imagine this scenario: You have a very small surface rigged as a light detector (the contact surface is let's say a single atom). You then fire off single photons towards it. As soon as you get a read on the detector, you know very precisely where the light is/was, and...

Let's say I have a GPS unit that reports an "accuracy" (this is what the GPS device reports as the uncertainty in the measurement of position) of 15ft. I travel some distance, with the GPS reporting a position every second. At the end of 1000 seconds I arrive at my destination. For the sake...

Hi all, I am 18 years old, and am looking to go into engineering, but I have a strong interest in theoretical physics. As such I have recently written a short research paper into the Heisenberg Uncertainty Principle, and I wondered if anyone would be willing to have a quick read and give me any...

Homework Statement What is the area, and approximate uncertainty in a circle with radius 3.1*10^4 cm (or written: 3.1e4 cm)? Homework Equations Area=Pi*r^2 The Attempt at a Solution My attempt to the solution took some trial and error, and it went as follows: Substitute the circle's radius...

Hi there! I wanted to ask you, we know that light, photons have a certain fixed speed generally. Wouldn't this imply, considering Heisenberg's uncertainty principle, that the uncertainty for the speed (momentum) of the photons, should be infinite? But we know for sure, for example, that...

It is in the IB textbook. Said as an application of the uncertainty principle, consider an electron, which is known to be confined in a region of size L. We know the uncertainty in position of the electron must satisfy Δx<L. Therefore, according to the uncertainty principle, we can work out...

Heisenberg's uncertainty principle: due to experimental limitations or dual nature of matter? Or both?

I've been pre-occupied with Heisenberg's uncertainty principle for around four years now, and I've come to fabricate a lot of questions. The most pressing one, however, is as follows: To me, the uncertainty principle seems to reference our (relatively) poorly controlled methods to measure a...

There are lots of basic explanations on the Internet of the two most famous uncertainty principles, that of momentum-position and Energy-time, but I do not find any basic explanation of the action-angle uncertainty principle. I do not even know what angle (or what operator) is being referred to...

Would it be meaningful to think of it as the 0 component of the 4-vectors x and p? In which case the regular uncertainties between position and momenta are the 1,2,3 components of the 4 vectors and the ΔEΔt is just the 0 component?

Consider an ensemble of identically prepared pencils balanced on its tip. If a pencil is precisely vertical, ##x=0##, and precisely at rest, ##p=0##, then it will never fall. But some pencils in the ensemble would fall, because according to the uncertainty principle, the standard deviation...

From the following definition, it seems that the uncertainty principle is an epistemological statement. "Heisenberg's uncertainty principle, is any of a variety of mathematical inequalities[1] asserting a fundamental limit to the precision with which certain pairs of physical properties of a...

Hello, It's been puzzling for me to try to understand this issue. To begin with it is clear that there are basically two principles, the Position-Momentum uncertainty and the Time-Energy uncertainty. It is also clear that there are at least two different interpretations attached to both. One is...

Homework Statement In one of my revision guides, there is an experiment for calculating the acceleration of free fall using the electromagnet and trap door arrangement. The biggest error is in the measurement of the height over which the ball falls. The guide says: "You could reduce the error...

Homework Statement Say we have the equation D2 = C x N where C = A2. Using a graphical method to find the % uncertainty of C (from graph of D2 against N) which involves working out the gradient which equals C and so forth. This value is 25%. The question is "what is the percentage uncertainty...

I am trying to find the uncertainty of the mean of 3 values. These values were calculated from experiments to calculate the enthalpy change of various alcohols. These values are independent values. −283 ± 11, −175 ± 9, −282 ± 11 How would I calculate the uncertainty of these values? Thank you.

Hello there! There is a problem with calculating the uncertainty from semi- ln plot. The linear fitting gives standard errors as you can see in attached picture. In the Y axis are ln J values, obviously. If the intersection with y-axis, x=0, then we get the point y=b=-33,21, and it's ln J', so...

I have read that the Schrodinger Uncertainty Principle is an extension of Heisenberg's. So, why don't we use the Schrodinger Uncertainty Principle instead of Heisenberg's? Thanks!

Homework Statement [/B] The surface tension (T) is measured by capillary rise formula T = \frac {rh ρg}{2 cos\Theta} . The quantities of ρ, g and θ are taken from the table of constants while the height and diameter are measured as h = (3.00 + 0.01)cm and D = (0.250 ± 0.001)cm Find the...

In the Infinite Square Well problem, an energy eigenstate is in an equal superposition of two momentum eigenstates with eigenvalues that are opposite in sign(like standing waves that are formed by two wavefunctions corresponding to "opposite momentums"). So, for every energy eigenstate, we...

In another thread I quoted a paper Bill pointed me to. It included the statement "It is the measurement results that fluctuate, not the underlying object." Bill indicated that this was a misconception but would need a new thread to discuss it. So please discuss... Thanks Andrew