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. R

    Problem with randomness and uncertainty

    I was reading the book "the grand design" by stephen hawking and I reached the part about randomness and Heisenberg's uncertainty that I didn't understand. The book seems to suggest that "Probabilities in quantum theories reflect a fundamental randomness in nature". The thing seems right to me...
  2. I

    Temporaly uncertainty principle

    Hi, I am currently having problems solving a an exercise: Let's make the assumption of the existence of an operator H such as [T,H]=i \hbar I. by examining the state: |\psi\rangle}=He^{i \alpha T}|E\rangle} with H|E\rangle}=E|E\rangle} show that the spetrum of H is not bounded below.
  3. I

    Quantum Uncertainty in the Holographic Principle

    Hi all, A question about the Holographic Principle. I've recently started reading up about this, and watched Bousso's neat introductory video . I thought, "Ah, this is so refreshingly simple!", and proceeded to write down my own notes. However here things revealed themselves to be not...
  4. E

    PIC Code Uncertainty: Why Does Placement Matter?

    Hi, I have just managed to make a PIC light blink. My question has to do with the syntax. In my code, I use a Delay subroutine that is called in between turning the LED on and turning it off. I tried two codes. The first had my Delay subroutine being placed before my main code. The second had...
  5. P

    Bevington and uncertainty of a weighted mean

    I'm trying to decide on a method for calculating a weighted mean for my data. In Bevington's Data Reduction and Error Analysis for the Physical Sciences 2nd Ed. Equation 4.19, the variance of the weighted mean is: However, Bevington also suggests the use of Equation 4.22 substituted...
  6. Z

    Question about the uncertainty principle?

    Okay I actually have 2 questions. 1) ΔxΔp >= h / 2π Is x one dimensional? Say if I wanted to locate the certainty of an electron in a hydrogen atom with a diameter of 10e-10 m. The electron is confined to the volume of the atom, not just the diameter, so could I say Δx = 10e-10 or...
  7. S

    No uncertainty principle for scalar particles?

    hi, I do wonder if the Higgs boson is a quantum object because since it is the (only) particle with spin 0, then it should not behave like a wave(since the wave aspect is connected to the fact that it is spinning) and therefore not experience the uncertainty principle. Or am I wrong?
  8. B

    Exploring the Uncertainty Principle: Solving Homework Problems

    Homework Statement See q attached Homework Equations The Attempt at a Solution Am i right in thinking that the answer to both questions is yes? Neither of the commutators [p, V(x)] nor [x, H = + or - ih.. therefore is the answer to both a and b yes?
  9. A

    Uncertainty relation demonstration

    HI, I will not used the template provided since this is not a textbook problem. It's a problem I have with a demonstration in Quantum Mechanics Vol 1, Cohen-Tannoudji " Complement C III [Q,P] = i \hbar Consider the ket: |\phi \rangle = (Q +i\lambda P)|\psi \rangle where \lambda is an...
  10. J

    Heisenberg uncertainty principle derivation and canonically conjugate vairables?

    Hi, I've just worked through a derivation of the H.U.P. that uses the Cauchy Schwarz inequality to come up with the expression (\Delta A)^2(\Delta B)^2 \geq \frac{1}{4}|<[A,B]>|^2 . This much I am happy with, but then it seems that when dealing with two "canonically conjugate observables" you...
  11. L

    Cause of the Heisenberg Uncertainty Principle

    Hi! So I know what the Uncertainty principle states and everything, but I can't find anywhere the "causes" of the uncertainty. Like, what is it exactly that "causes" the uncertainty. If it's not the measurement tools/technology, then what is it?? Please explain in terms of physical phenomena...
  12. P

    Calculating with Uncertainty

    Homework Statement A metal bar has a length measured to a precision of +-1%, a mass measured to +-2% and a radius masured to +-3%. What would be the % error in the value of the density of the metal in the bar calculated from these? Homework Equations V=(pi)r^2h D=m/v The Attempt at...
  13. A

    General Uncertainty Principle

    Homework Statement http://img219.imageshack.us/img219/306/prblem.png (oops, that line should end with "just before measurement? (Express your answer in terms of the variances of the two operators)" ) The Attempt at a Solution...
  14. U

    How do I add percentage uncertainty when calculating an average?

    Homework Statement I currently want to add 2 percent each with a relative uncertainty together: \frac{53.3\% +/- 1\% + 65.8\% +/- 1\%}{2} I'm not sure how I can add the percentage uncertainty. Homework Equations The Attempt at a Solution I've concluded that the average is...
  15. Seanskahn

    Uncertainty Operators in Nouredine Zettili's Book

    Hello community. My second stupid question. In the book by Nouredine Zettili , the uncertaintie operators are defined as \DeltaA = A - <A>, where A is an operator, and <A> = <\psi|A|\psi> , with repect to a normalized state vector |\psi> i was wondering, why is not the uncertainty...
  16. T

    Why is the hidden variable theory wrong?

    In the Messenger Lectures (http://research.microsoft.com/apps/tools/tuva/index.html) Feynman says that the theory of "hidden variables" tells us that the cause of uncertainty in nature (the cause that nature works with probabilities) is that we don't have enough information to predict the...
  17. U

    Uncertainty principle and angular momentum

    \Delta{x}\Delta{p}, \Delta{E}\Delta{t} and particle spin all have units of angular momentum and have ability to be quit uncertain... Any idea if they have something in common (except the units of measurement)?
  18. R

    Position-Momentum Uncertainty Principle

    hi, in the position momentum uncertainty principe , should we believe there is an uncertainty about the mass and not only about the velocity? thank you very much for your reply!
  19. A

    Uncertainty error calculations

    After measurements, the following values and their uncertainties were recorded: x = 8.3 ± 0.1 and y = 2.72 ± 0.07 Find the following values of Z a) Z = x + y b) Z = x - y c) Z = xy d) Z = x/y e) Z = y/[(x)^0.5] (this is y divided by the square root of x) f) Z = exp(y)...
  20. N

    Is the Uncertainty Principle Statistical? And if so

    Hello, I'm (only) receiving an introduction to Quantum Physics atm, and today our professor argued that the uncertainty principle doesn't have a definite form: the right hand side of the inequality is dependent on the confidence measure/certainty you choose, in other words 95%, 99% certainty...
  21. J

    Heisenberg Uncertainty Principle question

    given 2 unnormalized wave functions: Y1(x)=e^i(x/m) Y2(x)=1/2*[e^2i(x/m) + e^3i(x/m) + e^-2i(x/m) + e^-3i(x/m)] if the positions of the particles were measured, which would be found to be more localized in space? (that is, which has a position known more precisely?) to my...
  22. E

    Space-Time — Momentum-Energy uncertainty relations

    From the wikipedia page on http://en.wikipedia.org/wiki/Complementarity_(physics)" : As I recently noticed in the double-slit experiment there is a lot of time-uncertainty, not only position-momentum uncertainty. That is shown in the fact that the probability wave does not reach the screen...
  23. W

    Is it possible to have a measurement with no uncertainty?

    Homework Statement If you were to measure ten identical measurements, would that imply that your measurement of the wavelength had no uncertainty? what would the uncertainty of the measurement be in that case? Homework Equations n/a The Attempt at a Solution I am thinking no...
  24. R

    Scale of uncertainty principle

    in what scale can we consider the uncertainty principle?can it be considered in the non atomic scale?
  25. S

    Uncertainty principle free particle

    Show that for a free particle the uncertainty relation can be written as (Delta lambda) (Delta x) >= lambda^2 / 4pi Firstly I am sorry not writing this in latex but I gave up after trying to write it in latex for half an hour. Would be great if anyone can show me how to do it. Using...
  26. T

    Determining the Uncertainty of a Unit Vector using Error Propagation

    Homework Statement Consider the points (x, y) = (0,0) and (100,10). Calculate the unit vector u pointing from the first to second. If each coordinate has an uncertainty of +/-2, calculate the uncertainty in u using propagation of error, but making reasonable approximations based on the values...
  27. J

    What does the Uncertainty Principle say about the location of photons?

    Since we know the precise velocity of any photon, does that mean it's location is always undeterminable?
  28. J

    Calculating uncertainty of local gravity

    Homework Statement My first lab report in physics requires me to calculate the value of local gravity. I did this using latitude and longitude. I must also state the uncertainty of my local gravity value. I have no clue how to do this. What am I basing my uncertainty on, and is there an...
  29. D

    Uncertainty Help: Solving Homework on Speedometer & Measured Speed

    Homework Statement Imagine that you are driving down a stretch of freeway with a posted speed limit of 65 miles per hour. You aren’t sure whether to trust your speedometer, so you check your speed against a series of distance markers along the interstate. You notice that, in the time it takes...
  30. 3

    Absolute and Relatiave Uncertainty (partial derivatives)

    Homework Statement Calculate the following, expressing all results with uncertainties both in absolute and relative (percentage) form: a) A + B b) A x B c) Asin(theta) d) A^2 / Bcos(theta) The relevant formula for the absolute uncertainty is below, but i have no idea how to...
  31. S

    Uncertainty Principle - nature or human nature?

    Hi, I have taken an introductory undergraduate QM course, solving for different boundary conditions like particle in a box, but the physical interpretations of some of the tenets was not well explained. I was surprised to find this paragraph on Wikipedia: "Published by Werner Heisenberg in...
  32. Z

    Uncertainty in area of a circle

    Homework Statement The radius of a circle is measured to be 14.3+-0.3cm. Find the circle's area and the uncertainty in the area. I don't understand how to correctly apply uncertainty equations with sigma and partial derivatives to these types of problems. Homework Equations...
  33. F

    Uncertainty relation: minimum value

    Homework Statement Show that the smallest possible uncertainty in the position of an electron whose speed is given by \beta = v/c is \Delta x_{min} = \frac{h}{4 \pi m_0 c}\sqrt{1-\beta^2} The Attempt at a Solution Since \Delta x \Delta p \geq \frac{\hbar}{2} , we see that \Delta x_{min}...
  34. L

    Heisenberg Uncertainty Principle

    Does the uncertainty principle apply only to electrons or other particles as well?
  35. A

    Uncertainty about Uncertainty Redux

    Hello everyone. I need your help. I am not a physicist or a physics student, so I am not familiar with the subtleties of quantum mechanics. I do have a good general education, though, and I am eager to learn new things. I have long had a problem with quantum mechanics, specifically the...
  36. T

    Heisenberg uncertainty derivation

    Hi, I am trying to teach myself some quantum mechanics and here is something I am stuck on. Various derivations of Heisenberg uncertainty start out with two Hermitian operators, usually called A and B to represent position and momentum. Then they define another two operators ∆A and ∆B as...
  37. A

    How do you count Uncertainty Measurement using Precision Error and Bias Error?

    Homework Statement Find the Uncertainty Measurement using Precision Error and Bias Error? The Length of line is 5.625 in. Precision Error is 0.13 in. Bias Error is -0.115 in. What is the UNCERTAINTY measurement? Homework Equations None. The Attempt at a Solution Please help! I...
  38. N

    Is the Uncertainty Principle a Limitation of Current Technology?

    Hi people. I am a bit confused about the uncertainty principle. According to Heisenberg, we cannot exactly determine the position and momentum of an electron at the same time because the minimum energy we have to give out (say light energy) is absorbed by the electron and one of the quantities...
  39. C

    Solving the Uncertainty Principle: Kinetic Energy & Position

    I am a little confused by something by something in my physical chemistry textbook. If two measurable quantities do not commute, then an uncertainty relation exists for them. Kinetic energy and position do not commute, and the expectation value for linear momentum in a 1-D particle in a box...
  40. V

    Particle in a box momentum uncertainty

    1. this is for a particle in a box (infinite potential well): For the wave functions calculate (as a function of n) \Deltax \Deltap \Deltax\Deltap Homework Equations h = h bar below u+n(x)=(1/\sqrt{a} )cos((n-1/2)(pi)x/a) u-n(x)=(1/sqrt{a})sin(n(pi)x/a) E-n=h2/(2m)(n(pi)/a)2...
  41. D

    How Does the Uncertainty Principle Apply to a Particle in a Femtometer Sphere?

    A particle is confined within a spherical radius of one femtometer(10^-15 m)? Its momentum can be expected to be about- 1. 20 keV/c 2. 200 keV/c 3. 200 MeV/c 4. 2 GeV/c How should I go about using HUP on a problem like this one? I tried substituting x=10^-15 meters in px=h/4 pi but the answer...
  42. M

    Percent difference and uncertainty

    Homework Statement How do we solve this problem? % Difference = (l 0.282 +/- 0.0019 - 0.288 +/- 0.04 l) / 0.285 +/- 0.02 Homework Equations Percent Difference = (l value - average value l)...
  43. rubenvb

    General Relativity and Heisenberg Uncertainty

    First, I'm not sure where this fits (here or Quantum Mechanics), because it's completely in-between the two... Is there a way to account for the fundamental uncertainty in quantum mechanics through a modification of general relativity? I have very limited experience in Quantum mechanics, and...
  44. Z

    Uncertainty Principle: How Does Position Depend on Photon Wavelength?

    I have a quite simple doubt. One of the practical applications of Heisenberg's uncertainty principle is given by Heisenberg's microscope. In this thought expt. Heisenberg imagines of a hypothetical microscope in which an observer attempts to measure the position and momentum of an electron...
  45. G

    Help with uncertainty percentage

    Homework Statement Determine the percent uncertainty in theta and in sin theta when theta equals 20.0 + or - 0.5 degrees? delta theta/theta = ? delta sin theta/ sin theta = ? Homework Equations Percent uncertainty is a ratio of the uncertainty to the measured value. %uncertainty =...
  46. N

    Finding Uncertainty in a coefficient with a Chi Squared Test

    Hello, I have done a chi squared test on the measurements from a neutron flux experiment to get the best parameters for a function of the form Ysim=Acos(B*X). I used Solver in Excel to find the minimum parameters. The test takes the form chi^2 / dof = SUM(Ysim-Yi)^2/(sigma i)^2 Where...
  47. R

    Uncertainty principle and electromagnetic field

    hi, I have a question about the uncertainty principle. if an electron is in attractive OR repulsive electromagnetic field, is its uncertainty about its position lower than if it is a free electron? I believe particles are more random, with a higher entropy when there is less...
  48. M

    Uncertainty in Algebraic Substitution: Is X=0?

    Homework Statement [PLAIN]http://img137.imageshack.us/img137/4242/probhr.jpg Well ,my problem is why after substitution for the first time the result os uncertainity (0/0) Is X=0? and I don't understand the step no 2
  49. V

    Absolute/Percent Uncertainty Help

    Homework Statement In case A on the left the ball is on a string. The ball is measured at 3.3 inches In case B on the right the ball is on a very sensitive spring. The ball keeps bouncing up and down, reaching the extremes. The low extreme is about 3 inches, the middle is 3.5 inches, and upper...
  50. M

    Uncertainty for a ratio ( help)

    Uncertainty for a ratio (urgent help!) Question: As you eat your way through a bag of chocolate chip cookies, you observe that each cookie is a circular disk with a diameter of d = 8.32 cm +/-1×10−2 cm and a thickness of h = 9.3×10−2 cm +/-1×10−3 cm. Find the uncertainty in this ratio of the...
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