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

    How is Uncertainty Propagated in Pendulum Period Measurements?

    Hello. I have measured the period of the pendulum T=2.18 +/- 0.02 which is consistent with the true period 2.19865... so I expect myself to find a consistent value of g if I apply the formula propagating the error in the right way. I get g=9.96 +/- 0.2Why?
  2. J

    Finding uncertainty for varying error bars

    Homework Statement I am currently doing an experiment on Compton scattering and have plotted a linear graph of 1/E' on (1-cos θ), where E' is the scattered gamma ray energy. My goal is to find the value of the gradient and y-intercept with their corresponding uncertainties. Instead of using the...
  3. T

    Uncertainty Principle mechanics

    Can one use uncertainty principle for Classical mechanic wave and still get the same equation for Quantum mechanics, as in (root-mean square uncertainty of position) (" of momentum) > hbar/2? It's just that V(x) [Potential equation] is same for both Classical and Quantum mechanics so I wonder if...
  4. S

    Formula of Heisenberg Uncertainty

    I came across two different forms of Heisenberg uncertainty: \Delta x . \Delta p \geq \frac{h}{2 \pi} and \Delta x . \Delta p \geq \frac{h}{4 \pi} and I read here in PF both forms are correct. I want to know how we apply both forms in solving problem. Here is the example: 1. An electron...
  5. T

    Estimate for root-mean-square uncertainty

    Homework Statement In classical mechanism, the lowest possible energy accessible to any system is the minimum potential energy, in this case 0. However, quantum mechanically, one finds that there is a zero-point energy (where ground state energy > classical minimum). Fundamentally, zero-point...
  6. L

    Heisenberg momentum uncertainty

    Homework Statement An electron is trapped in a one-dimensional well of width 0.132 nm. The electron is in the n = 10 state. a) What is the energy of the electron? b) What is the uncertainty in the momentum? c) What is the uncertainty in the position? Homework Equations En = h2n2/8mL2...
  7. Z

    Propagating uncertainty when calculating acceleration due to gravity?

    Hello, I'm having trouble with a lab report. The experiment conducted was we used an angled air-track and a timer to determine the speed at which an object slid down the track and its acceleration. The final average acceleration we calculated was (61.034 +- 2.227)(cm/s2) We're then given a...
  8. L

    Uncertainty principle for electron inside atom

    Homework Statement Hopefully it is not a faux pas to post two questions relatively close together in time. This is more of a conceptual question than a calculation based question. An electron is confined to a region of space of the size of an atom (0.1 nm). a) What is the uncertainty in the...
  9. C

    Help with Error in gravity due to uncertainty in r.

    Homework Statement Derive an algebraic expression for the error in gravity due to the uncertainty in r. Use limit error formulas and show all steps. Assume that errors in G and M are negligible. Homework Equations g=GM/r^2 The Attempt at a Solution [/B] i use the error formula but not sure...
  10. M

    Uncertainty in Average Intensity Calculation

    Homework Statement I am analysing intensities of some pictures. There are specific regions of higher intensities and so far i have managed to locate those regions automatically in Mathematica and the program returns the average intensity and standard deviation on this regions ("circles"), so I...
  11. F

    Quantum Mechanics / Uncertainty Principle Question

    Homework Statement The square of a wave function gives the probability of finding a particle at a given point. What is the probability of finding an electron in a 1s orbital within a volume of 1pm^3, centred at: a) the nucleus b) 50pm away from the nucleus? Homework Equations...
  12. P

    This long uncertainty viscosity problem where I need to get the error

    Any help with this basic college problem. Homework Statement The following readings were obtained in an experiment to find the coefficient of viscosity of water n by measuring the rate of flow of water through a horizontal capillary tube. Diameter of capillary tube = 1.40 mm Length of...
  13. P

    A simple uncertainty question about height.

    So this is a physics question, that I am trying to solve. The premise seems simply but I am getting caught up on the uncertainty. The questions reads like this: "Something from the top of a platform takes (2.0 ± 0.1)s to fall to the floor, assuming the acceleration due to gravity is 10 m/s2...
  14. R

    Absolute Uncertainty of a Negative Power

    1. Determine the relative and absolute uncertainties of R-2 if R is measured to be 4.5 ± 0.005 m 2. The attempt at a solution So according to what I know so far, multiplication and division of uncertainties requires the addition of relative uncertainties... First I tried to get the...
  15. D

    Percent Uncertainty Shenanigans

    Parts C and D: http://s7.postimg.org/pnq5gry63/image.png Part D of this problem is just like Part C above it. The only difference is the presence of "sin," but that doesn't affect the calculation of percent uncertainty at all. Chapter 1 of my Physics book (Physics: Principles with Applications...
  16. S

    Keeping uncertainty at arm's length

    It seems self-evident that mathematics must keep uncertainty at arms length. For example, to deal with probability mathematics establishes a set of assumptions. The assumptions themselves are not probabilistic - i.e. the "laws" of probability are assumed to be true "all the time", not...
  17. C

    How Does Measuring Voltage Before and After an Experiment Impact Uncertainty?

    How does taking the voltage of a circuit before and after an experiment help with uncertainty in the voltmeter? Our teacher instructed us to do this, and i got that voltage before was 1.516 and voltage after was 1.498. Does this mean the voltmeter became less resistant? How do I turn this...
  18. mishima

    Counting uncertainty in pendulum experiment?

    Hi, I am confused about when the rule for counting uncertainty applies. I know for radioactivity experiments one expresses the uncertainty (error) in the decay count as the square root of the count. So if you counted n decays you would report an average rate of n \pm \sqrt{n} I was...
  19. A

    Programs How to dear with fear and uncertainty regarding switching majors

    I've always been an incredibly indecisive fellow, from decisions ranging from "would you like coke or sprite?" to "what would you like to do with your life?" So ever since junior year of high school (I'm about to start sophomore year in college), I've been debating about what I should major in...
  20. V

    Uncertainty error of resistors in parallel

    Homework Statement Find the Uncertainty of the Total Resistance of two (2) parallel-connected resistors: R1 = 2.2 kΩ ± 5\% \ ;\ R2 = 1.8 kΩ ± 20\%. Homework Equations We know that resistors in parallel are: \frac{1}{R_t}={\frac{1}{R_1±\delta_{R_1}}+\frac{1}{R_2±\delta_{R_2}}} This...
  21. Greg Bernhardt

    How Is the Heisenberg Uncertainty Principle Derived?

    Definition/Summary One of the most asked questions is concerning how to derive the Heisenberg Uncertainty Relation. Starting from almost basic concepts of Quantum Mechanics, a derivation is given here. Some details are left as minor exercises for the interested reader. The derivation...
  22. Greg Bernhardt

    What is the uncertainty principle

    Definition/Summary This is a derivation of the Uncertainty Principle based on the properties of non-commuting Hermitian operators. Equations \langle (\Delta A)^2 \rangle \langle (\Delta B)^2 \rangle \geq \frac{1}{4} |\langle [A,B] \rangle | ^2 \langle (\Delta x_i)^2 \rangle...
  23. F

    What is the norm of an operator?

    In a communication channel there is the time-bandwidth product limiting the amount of information that can pass through the channel. The math for Heisenberg's Uncertainty Principle is very much similar to the math for the time-bandwidth product. I wonder if this allows us to discover by analogy...
  24. H

    Individual Measurement Uncertainty vs. Standard Error of Regression

    Let's say a student does a simple experiment where she conducts 10 trials at each x value (at each value of the independent variable). She collects data over 30 x values, giving her 300 total trials. For each of the 30 x values, she averages the 10 y values and she calculates the standard...
  25. M

    Is the uncertainty consistent?

    Homework Statement I am given a set of x and y values x: (1,2,3,etc.) y: (1.2,2.2,3.1,etc.) with a given uncertainty and am asked a) find the best fit b) at what prob can you rule out a 5% higher slope c) is the stated uncertainty consistent with the data? Homework Equations...
  26. Q

    Heisenberg Uncertainty due to interaction of the inherent reality?

    Coming from a Chemistry background, the Uncertainty Principle always seemed to be described as an inability of precision due to strictly physical and real reasons (i.e. you have to interact with an object to measure something about it, and this certainly will alter the object). It seems as if...
  27. J

    Understanding Electron Movement with Heisenberg's Uncertainty Principle

    I'm trying to work out why electrons don't crash down into the nucleus using HUP. So if we take 10^-10 meters, the diameter of hydrogen, and use 10^-13 meters as our Δx, the HUP should come out unequal. So I get Δp=10^-35*10^13 or Δp=10^-22 and p=mv, so Δv=10^10 This is where I am...
  28. D

    Uncertainty Principle and the Infinite Well

    For the infinite square well in one-dimension the wavefunctions have the form Acos(kx) where k is the wavenumber which is proportional to momentum. Now due to H.U.P. if Δx is fixed as the infinite well size we can't know the exact momentum. I presume this is because the wavefunction exists as a...
  29. O

    Measurement Uncertainty: How do I calculate it?

    Homework Statement Hey guys! I'm new here, so firstly- hello! I've a exercise to from Metrology. Evaluate measurement uncertainty for the following measurement: 1. Measurement quantity: length of a bar L = 500 mm 2. Material of the measuring object: steel 3. Temperature range in the...
  30. T

    Schrödinger's Cat, uncertainty, and observation question

    First of all, from what I've read the descriptions of an observation or measurement in Quantum Mechanics have been quite vague. Since the word measurement is used alternatively I am going to assume that this includes all types of measurements, which brings me to a question. If the box...
  31. N

    Uncertainty principle & simultaneous measurement

    I have been reading and would be interested in feedback to the comments that I make, below. One of the points made in this paper is that the interpretation of the uncertainty relation needs to be re-examined in its relation to the viability of having simultaneous measurements of A & B. For...
  32. C

    Lab- Calculate Relative Uncertainty, How many sig figs?

    Homework Statement Calculate the relative uncertainty in the mass mass (M) = 1.0 grams Homework Equations \frac{\delta M}{M} The Attempt at a Solution \delta M = \pm0.05g \frac {0.05g}{1.0g} = 0.05 or \frac {0.05g}{1.0g} = 0.050 Which one has the appropriate amount of sig figs? thanks...
  33. MrRobotoToo

    Meaning of the Energy-Time Uncertainty Relation

    I'd like to know what exactly it's telling us. Does it mean that the more accurately we measure the energy of a system the less accurately we know for how long the system has been in that range of energies? Or does it mean that the more accurately energy is measured the less accurately we know...
  34. V

    Heisenberg's Uncertainty Principle

    I was watching a YouTube video about Heisenberg's uncertainty principle and was wondering if it only works for position and momentum or does it work for any other two measurable quantities?
  35. R

    Does the uncertainty principle apply at all to photons?

    I know this may sound strange, given that we cannot really work out where in space a photon is because it cannot be completely stopped. But here's a thought. Let us assume that a photon has been emitted in vacuum going in a straight line. At any given moment in time, this photon will have...
  36. B

    Heisenberg's Uncertainty Principle

    Hello, i'm solving some quite simple problems using the uncertainty principle, but I don't have access to the solutions and I really don't have a feel for what a 'sensible' answer is... When finding the minimum uncertainty in velocity, I end up with things greater than the speed of light, so I...
  37. F

    Uncertainty principle - Nature of observer

    Uncertainty principle -- Nature of observer About the fact that electrons have a determined position only after having been observed/measured, I don't understand how they make the difference between being watched by an eye/instrument or any non-measuring object just sitting there.
  38. R

    Calculating Uncertainty, involving a logarithmic quantity

    Essentially I'm asking if the uncertainty in μ = -5 log10 (d/10) is given by Δμ = 5 * ( Δd / d*ln(10) ) 1. The problem, all variables and given/known data I am to calculate the uncertainty in absolute magnitude (M), which is calculated using an equation involving logs. The equation...
  39. S

    How Do You Calculate Uncertainty in Mean Difference?

    Homework Statement Homework Equations Mean difference and SEM The Attempt at a Solution Would the mean difference be 0.16?. I'm not sure about the answer because they give that much working space, Do I have to find the uncertainty of the difference first and then my answer implement that...
  40. B

    How do I find the uncertainty?

    I am currently working on my physics lab report, and my question is "What effect does the mass have on the change of acceleration?" The lab currently consist of two pulleys hanging on each end balancing weighing 100kg, i continuously add 10kg for each turn, i then record the time of the...
  41. J

    Our attempts at certainty (measurements) actually increase uncertainty

    Here is my theory: - The measurement of an observable by an observer is a thermodynamically irreversible process. All thermodynamically irreversible processes increase total system entropy. - Landauer's principle (which was experimentally shown in 2012) says that the minimum amount of energy...
  42. K

    Need some guidance on sensitivity and uncertainty analysis

    Hi, I have a set of results for which I wish to carry out sensitivity analysis. I have already googled it and it always comes up with examples on Microsoft Excel but I don't want to use excel for the sensitivity analysis. So can someone explain to me what sensitivity and uncertainty analysis...
  43. mrspeedybob

    Does uncertainty of position of particles make substances continuous?

    Ever since learning about atoms and molecules as a child I have envisioned substances (air, water, metal, etc) as being composed of discrete individual atoms and molecules. Today it occurred to me that might be an oversimplification, especially for gasses in which molecules are free to move...
  44. Y

    What is the best way to estimate uncertainties in a lab experiment?

    I am asked to indicate the uncertainty on the radius R of rotation of the plumb bob. Please see picture. Basically, there is a vertical shaft, over which is attached a horizontal shaft and a plumb bob is hung over with a thread on the horizontal shaft. The bob is attached with a spring to the...
  45. nomadreid

    No-cloning and uncertainty principle

    In an explanation to distinguish the Heisenberg Uncertainty Principle from the Observer Effect, on p. 89 of "Quantum Computation and Quantum Information", Nielsen and Chuang start by writing: "The correct interpretation of the uncertainty principle is that if we prepare a large number of...
  46. A

    What happens to uncertainty when I divide values by a constant and squ

    The values below are different wire thicknesses measured with a micrometer screw gauge. The uncertainty of it is +/- 0.01mm. Diameter/thickness of wire/mm 0.02 0.10 0.14 0.30 0.42 I need to halve (or divide by two) these values to calculate radius and hence calculate cross...
  47. S

    Uncertainty of Randomness: Exploring a Phenomenon

    maybe this is too basic question but it is not so clear for me. when we refer to a random experiment, can a phenomenon be absolutely random by itself or its all about our uncertainty about the outcome that we call it random?
  48. J

    Experimental Uncertainty and Error

    Hello all, I used the micrometer in my lab that has a resolution of 100 nm. so, my measurement looks something like, 0.2345 mm, with an uncertainty of 0.00005 mm. But I don't want to write, (0.2345 +/- 0.00005)mm in my data table because it just looks a little awkward to have so many...
  49. nomadreid

    A step in derivation of E-t uncertainty not clear

    I am not sure if I should be posting this under QM or under Linear Algebra, since it appears to be an algebraic step that I do not see, and am asking the wonderful people on this forum to spell it out for me. In John Baez's derivation of the Energy-time Uncertainty relation...
  50. J

    Heisenberg's Uncertainty or hidden variable

    Intuitively it seems more plausible that there should be a hidden variable influencing the path of particles when they travel, than having a fundamental mechanism of nature be truly random, but what do I know. I just don't understand how you can ever completely rule out a hidden variable. I know...
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