What is Uncertainty: Definition and 1000 Discussions

Uncertainty refers to epistemic situations involving imperfect or unknown information. It applies to predictions of future events, to physical measurements that are already made, or to the unknown. Uncertainty arises in partially observable or stochastic environments, as well as due to ignorance, indolence, or both. It arises in any number of fields, including insurance, philosophy, physics, statistics, economics, finance, psychology, sociology, engineering, metrology, meteorology, ecology and information science.

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  1. S

    Rejecting the Semiclassical Bohr Model: Examining the Uncertainty Relation

    "Show that the uncertainty relation forces us to reject the semiclassical Bohr [...]" Homework Statement The problem along with the solution is attached as TheProblemAndSolution.jpg. Homework Equations Uncertainty principle/relation. The Attempt at a Solution Why is it the consideration of...
  2. H

    Find Volume, SF & Uncertainty of Iron Sphere

    A copper cylinder has a mass of 56.09g with an uncertainty of +/- 0.01g, how do I find the absolute uncertainty and the relative uncertainty? An iron sphere has measurements: Height = 2.3cm +/- 0.05 Diameter = 2.3cm +/- 0.05 Mass = 66.69g +/- 0.01 Find the volume with the correct unit...
  3. Z

    Writing Uncertainty in terms of dA, dB, dC

    Homework Statement Write down formulae for dX in terms of dA, dB, dC if: X = [(A) (B^2)] / C Homework Equations I'm using the formula below as this corresponds to this relationship. (dX/X)^2 = (dA/A)^2 + (dB/B)^2 The Attempt at a Solution For the first line, not the...
  4. Z

    Propogation of uncertainty in a data set (finger-math at most)

    Homework Statement I have conducted a simple lab, that involves getting the distance traveled by a vertically falling weight at certain time intervals. Velocity is calculated for every time interval (distance traveled per time interval). Then I graph velocity versus time to get acceleration...
  5. J

    How do you find the uncertainty in a function of two variables?

    I'm trying to make up an automatic spreadsheet for my Physics students so they can enter the data and see everything calculated for them, but I ran into a snag. I have two random variables, h and t with uncertainties Δh, and Δt, respectively. The uncertainty in h is simply estimated, based...
  6. K

    SU(2) generators in j=1, and pauli uncertainty

    Hello! I have two questions regarding QM. First, I tried to rotate J_z into J_y for the j=1 representation by the transformation rule for matrices.. I took my rotationvector to be (1,0,0) and rotated about 3/4 pi radians which I thought would give me S_y. Instead I got S_z again! Wolfram...
  7. I

    Radius of the electron and uncertainty

    i thought that electrons are merely abstract thing or statistical entities, so i mitigated every attempt to visualize them as something that has a shape like a sphere, has a radius, internal structure, i thought that any attempt to measure a radius (if any) could result in uncertainty in...
  8. N

    Multiple choice question on the absolute uncertainty?

    An experiment is performed to determine a physical quantity and 10 trials are made. The absolute uncertainty in the quantity can be given by a. the mean of the data b. the standard error of the data c. None of the above I'm leaning more towards b because absolute uncertainty has to deal with...
  9. D

    Conservation of momentum and uncertainty.

    In situations where the momentum of particles is only known to some degree of certainty, what can you say about the total momentum of the system? Is it only conserved to an extent that it always falls in a certain range?
  10. L

    What is the uncertainty in a squared quantity?

    Homework Statement D= A +/-ΔA D= 5.160 +/- 0.01 cm D^2= 26.6 +/- 0.1 cm^2 Homework Equations for the power rule uncertainty : A ((ΔA/A) + (ΔA/A) ) So then its (5.160)( (0.01/5.16)(2)) = 0.004 The Attempt at a Solution im getting 0.004 as the absolute uncertainty but the...
  11. H

    How to choose between two uncertainty calculation method?

    Hello, I have made an experimental work and I am ask to provide a formal experimental error analysis. I have a difficulty to choose the appropriate analysis way and would like to have some advices or explanations. I have measured a temperatures at the intlet (Ti) and outlet (To) of a heat...
  12. N

    I wanted to know how it is determined uncertainty

    Hi everyone! I wanted to know how it is determined uncertainty ? i watched some lesson but i didn't understand if it is a variable chosen from who is making the measure of that depends on the tool that i use for the measure ?
  13. J

    How can I get the LINEST function in Excel to return more than just slope?

    I figured there ought to be some Excel savvy people here. Anyway I can't seem to get the LINEST function in Excel to return anything other than slope. I provide it with y-values, x-values, and say true to constant and stats. All it gives me back is a slope. Maybe I'm being vague, just ask if you...
  14. Z

    Calculating the uncertainty in an A4 page

    Homework Statement Calculate the uncertainty in the area of an A4 page using a 30cm ruler with mm divisions. Homework Equations The Attempt at a Solution Page is measured as: Height H = 297mm Width W = 210mm H x W = 62370 mm^2 I'm using this formula to...
  15. R

    Quantum Mechanics (position uncertainty)

    Homework Statement I need some help with the following problem: http://img827.imageshack.us/img827/4061/prob1y.jpg Homework Equations For some particle in state Ψ the expectation value of x is given by: \left\langle x \right\rangle = \int^{+\infty}_{-\infty} x |\Psi(x, t)|^2 \ dx The...
  16. P

    Uncertainty Relations & Wave Packets

    PROBLEM: Laser pulses of femptosecond duration can be produced, but for such brief pulses it makes no sense to speak of the ‘color’ of the laser. To demonstrate this, compute the time duration of a laser pulse whose range of frequencies covers the entire visible spectrum (4.0*10^14 Hz to...
  17. A

    Calculating measurement uncertainty

    Hi, I've been studying uncertainty in measurement. I'm not sure how to decide if the uncertainty of a given measurement should be ±.01 or ±.02 or ±.03, and so forth. I understand that the number of decimal places in the uncertainty calculation should correspond to the number of decimal places...
  18. O

    Mass Flow Rate Uncertainty: A simple problem gone horribly, horribly wrong

    The Mass Flow Rate in a water flow system determined by collecting the discharge over a timed interval is 0.2 kg/s. The scales used can be read to the nearest 0.05kg and stop watch is accurate to 0.2 s. Estimate the precision with which the flow rate can be calculated for time intervals of a.)...
  19. P

    Uncertainty of Average Acceleration

    Homework Statement You have determined the acceleration a_{i} of an object in free fall for i = 1 to n different time intervals. What is the algebraic expression for the uncertainty σ_{a,avg} in a_{avg}? (Use any variable or symbol stated above as necessary.) The answer box is formatted as...
  20. G

    2 scientists think they have defeated the uncertainty principle

    How sound do you think the following research is? http://phys.org/news/2012-09-scientists-renowned-uncertainty-principle.html
  21. B

    Spherical Percent Uncertainty and Violent Storm Question

    Q1: What is the percent uncertainty in the volume of a spherical beach ball whose radius is r = 3.85 plus or minus 0.06 m? I found the volume of the original sphere, as well as one with a radius of 3.91. I then subtracted the volumes to find the difference between the two, divided that by the...
  22. C

    Question about uncertainty principle

    Should relativity be factored into the uncertainty principle. I can't move faster than c so should that affect the measurement process? Should time dilation and length contraction be considered or maybe some of these factors cancel when 2 effects are considered.
  23. H

    How to evaluate an uncertainty involving an experimental correlation?

    hello, Thank you to understand that this is not a homework! I have to evaluate the uncertainty of a measurement but the baseline is also with uncertainty (correlation). I would like to have some ideas or suggestions on the best way to evaluate the uncertainty. Here is the problem: We...
  24. G

    Is the unpredictability of clouds due to QM uncertainty?

    As I see it the unpredictability of clouds can have two causes: 1. quantum indeterminacy or 2. Clouds are classical objects but they are so complicated that they cannot in practice be predicted I'm inclined to think 1 is correct. Correct me if I'm wrong but I'm pretty sure protons'...
  25. M

    Finding Propagation of Uncertainty?

    You measure the mass of the cylinder to be m = 584.9 +- 0.5 grams, and you measure the length of the cylinder to be L = 18.195 +- 0.003 cm. Just like in the lab you performed, you now measure the diameter in eight different places and obtain the following results. Diameter (cm) 2.125 2.090...
  26. J

    Uncertainty principle problem.

    This is problem 25 in chapter 4 of Modern Physics 2nd edition by Serway, Moses, and Moyer. I have changed the wording, but not the meaning I hope. Homework Statement A person drops an object of mass m from a height H. Show that the miss distance must be at least \Delta x =...
  27. F

    Uncertainty Relation between Lx and Ly

    There is an uncertainty relation between the x component and the y component of the angular momentum L of a particle, because [Lx, Ly] = i\hbarLz which is not 0. But what happens when Lz does equal 0? Would we in principle be able to measure both the x and y components of the angular...
  28. S

    Gaussian wavepacket and position-momentum uncertainty

    We know that momentum is proportional to k so by adding more waves to localise our particle we are adding more waves with independent momentum values Upon measurement, the gaussian wavepacket must collapse into one eigenstate of momentum, but if we have a very localised packet there will be...
  29. D

    Math of the uncertainty principle

    How can one operate the deltas of the uncertainty relation? I know they're supposed to be the standard dev, but how are they operated in physical reality? Is there some sort of function to make them have a physical meaning?
  30. A

    Timelike Curves leads to violation of heisenberg uncertainty Relation

    General Relatitivity predicts Timelike curves and there are nonlinear extensions of mechanics which resolve the paradoxical aspects of CTC's *i.e. Time Travel, on the other hand Hawking proposed a conjeture to rule out CTCs, the Chronology Protection Conjecture* there are a class of Timelike...
  31. M

    Write the density and its associated uncertainty of a cylinder

    Homework Statement Need to find the volume and density of a cylinder with measurements, height=0.03378m diameter=0.01876m and mass=7.99g +/- 0.01 kg And also its associated uncertainties. Homework Equations V=L*Pi*R^2 =0.00000933716m^3 p=M/V =0.0000008288 The Attempt at a...
  32. Mk

    Why is the Uncertainty of Counting Phenomena Equal to the Square Root of N?

    My physics teacher told me once about Arthur Eddington's famous observation that the ratio of scaling factors of the electromagnetic and gravitational forces was the same order as the uncertainty of N where N is the number of particles in the universe. From then on, I wondered what "uncertainty"...
  33. E

    Uncertainty in group of measurements, given single measurement uncertainty.

    Hello! I have a question regarding measurement uncertainties. This is not a homework problem. Let's say that I want to measure some quantity, and I want to measure it multiple times using multiple identical but separate instruments. That is, -First measurement taken using equipment 'A'...
  34. L

    High energy particles and uncertainty

    Say we have a linear accelerator, that accelerates particles with 1 TeV along direction x. That means we know that the momentum of the particle in direction x is almost exactly 1 TeV. But high-momentum particles have also a very short Broglie wavelength! The spread in x position is small for a...
  35. S

    Explanation for uncertainty principal?

    Although the uncertainty principal can be written without quantum harmonic oscillators, it still happens when you consider them. Can the reason for the uncertainty principal be explained in terms of changing the equation? If I have a completely undetermined momentum, I should have something...
  36. M

    Position vector r and uncertainty principle

    Hi physicists, How can two atomic-scale particles interact through gravitation (Gm1m2/r^2) or any other force that is a function of r if r isn't know with complete certainty. Is it that the force itself also comprises uncertainty in its value? Thanks
  37. C

    Kinetic Energy and the Heisenberg Uncertainty Principle

    Homework Statement This is not a problem as such. Just a derivation for which I've been given a solution which I cannot seem to find. Homework Equations Ke = 1/2 mv2 = ρ2/2m hbar << 2ΔxΔp Δp≈p as the average magnitude of p is small. The Attempt at a Solution p >> hbar/2Δx p2...
  38. N

    How is percentage uncertainty different from standard deviation

    How is percentage uncertainty different from standard deviation ? I have five measurements and l calculated the average, standard deviation and variance. Do l need to calculate the percentage uncertainty ? Does percentage uncertainty give me any more information which the other values l...
  39. P

    Exploring Uncertainty in Time Series Analysis

    Hello all, I am new to this forum and was wondering if any of you could help me out. I have this interview scheduled for next week for which I have to prepare a 10 min presentation on Uncertainty and how to determine it in a time series. Now, there is a wealth of information of the net...
  40. P

    Why Does the Time/Energy Uncertainty Principle Suggest a Lower Bound in Δt?

    I don't know much about brackets and Hamiltonians, but there is a much simpler aspect of the time / energy uncertainty discussion that confuses me. It has to do with the sign of the uncertainty. [Disclaimer: Purists, please bear with me for a moment as I hash out my point heuristically.]...
  41. H

    Exploring the Exclusion Principle: Understanding the Boson Paradox

    We are often told one reason why an electron does not fall to the centre of atoms is because it would then have a well-defined position. Any two particle which comes into contact define each others positions and so their momentum becomes very large. How then is it, according to the Exclusion...
  42. L

    Uncertainty Principle with time and frequency

    ΔxΔp ≥ \frac{h}{4\pi} Since Δx=ct for a photon and Δp=(mv_{f}-mv_{i}) Then ct(mv_{f}-mv_{i}) ≥ \frac{h}{4\pi} Since mv=\frac{h}{\lambda} You have ct(\Delta\lambda)^{-1}h ≥ \frac{h}{4\pi} Planck's constant cancels, move the c over \lambda, \frac{c}{\lambda}=f This leaves you...
  43. M

    Finding Uncertainty of Average Values

    Let's I have three values, 3.30±0.1, 3.32±0.1, and 3.31±0.1. How would I find the uncertainty of the average of these values?
  44. K

    Uncertainty principle accuracy

    Hi, could anyone try to explain one thing about the Heisenberg Uncertainty Principle I don't understand? The principle says is impossible to measure the position and momentum of a small particle with absolute accuracy. But this doesn't mean the particle doesn't have a definite position and...
  45. S

    Energy/particle number uncertainty in a laser beam

    If I understand things correctly, the coherent state of a laser beam implies that the photon quantum field is a superposition of states with different particle numbers. This also implies that a laser beam is not in an energy eigenstate. To get energy conservation, I assume that this...
  46. L

    Finding the Correct Equation for Heisenberg's Uncertainty Principle

    I'm given a form of Heisenberg's uncertainty principle in the form of: \Delta E\Delta t\geq h I need to determine a time interval which would allow a laser to cover the whole visible spectrum, from 400 to 700nm. Now given the relationship is on on a relative scale I used the approximation...
  47. R

    Hiesenberg uncertainty principle, h or hbar?

    i've seen both: ΔxΔp >= h/2 and ΔxΔp >= hbar/ 2 used, and I'm not sure which is correct. my physics textbook uses h/2, but wiki and other online rescources seem to use hbar/2 do they apply to different situations? (if so, where do you use hbar and where do you use h?) or is one...
  48. M

    WHat is the uncertainty in a metre rule?

    WHat is the uncertainty in a metre rule?? For a single value is it 1 mm or is it 1/2mm(half the smallest division) ? And what about measuring something like a length of a stick (we need to take 2 readings, and deduct them like 15-0=15), then is the uncertainty 1+1=2mm or is it .5+.5=1mm ?
  49. K

    Heisenberg's uncertainty principle question

    Homework Statement The position and momentum of a 1.00 KeV electron are simultaneously determined. If the position is located to within 0.100 nm, what is the percentage of uncertainty in its momentum? (Arthur Beiser - Concepts of modern Physics, 3rd Part exercise 33)Homework Equations...
  50. U

    Expected time of arrival with uncertainty

    Hi, This is actually related to my research work. Let say a location (x1,y1) is given with uncertainty in location is given by co-variance matrix P1. A vehicle is moving towards (x1,y1) from a location (x2,y2) with velocity (x2dot, y2dot). The uncertainty of the vehicle location is given by...
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