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. henry wang

    How to calculate uncertainty of gradient of straight line?

    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...
  2. B

    B Uncertainty Principle and a photon

    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...
  3. Kara386

    I Uncertainty Principle: Energy of Unstable Particle?

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

    Uncertainty in Wavelength Calculation from Wave Crests on a Pier

    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...
  5. F

    A Minimum uncertainty in electron position

    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...
  6. M

    What is the uncertainty in 5.00mm measured by analog device?

    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...
  7. S

    What is the uncertainty in the activity of Cesium 137 over time?

    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...
  8. M

    Setting up an Uncertainty Problem

    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]...
  9. dccd286

    B Does the Uncertainty Principle work through barriers?

    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...
  10. Ryan Hardt

    Calculating Uncertainty for a Chain of Trig Functions

    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...
  11. AdrianMachin

    Measurement Uncertainty Problem in MIT OCW 8.01x

    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...
  12. E

    I Uncertainty of electron energy based on confinement radius?

    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...
  13. eow

    I Are Superposition, the Uncertainty Principle, and Duality the same?

    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...
  14. C

    Finding uncertainty of a measurement

    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...
  15. victorhugo

    I What causes Heisenberg's uncertainty principle?

    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.
  16. H

    B Uncertainty Principle - uncertainty in mass.

    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...
  17. adamaero

    Calculating Wavelength Using Diffraction Grating

    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...
  18. G

    Propagation of Uncertainty - Hollow Cylinder

    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...
  19. terryds

    Difference between uncertainty and precision?

    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
  20. Titan97

    Uncertainty in single slit diffraction

    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...
  21. K

    Relative uncertainty (negative exponent)

    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...
  22. majormuss

    I Understanding the Uncertainty Principle

    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."...
  23. C

    B Heisenberg's uncertainty principle and photons

    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...
  24. Chris Frisella

    B Help Understanding the Uncertainty Principle

    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...
  25. R

    A Calculating GPS Uncertainty for a Bicycle Trip

    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...
  26. C

    I Heisenberg Uncertainty Principle

    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...
  27. JustynSC

    What is the area, and approximate uncertainty in a circle....

    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...
  28. C

    B Accuracy in speed of photon - uncertainty?

    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...
  29. Y

    B An application of the uncertainty principle

    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...
  30. weezy

    I What is the reason behind uncertainty principle?

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

    I Uncertainty Principle.... Intent Behind It?

    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...
  32. nomadreid

    I What is the angle in the action-angle uncertainty principle?

    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...
  33. hideelo

    I Understanding ΔEΔt uncertainty

    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?
  34. H

    I Radioactive decay, falling pencils and the uncertainty principle

    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...
  35. H

    I Is the uncertainty principle an ontological statement?

    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...
  36. facenian

    I Uncertainty Principle: Theorem or Principle?

    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...
  37. M

    Using a set square to reduce parallax error

    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...
  38. M

    A question on percentage uncertainty

    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...
  39. S

    B Calculating Uncertainty of Mean Values for Enthalpy Change Measurements

    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.
  40. I

    I Semi ln plot- uncertainty estimation

    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...
  41. J

    I Why don't we use the Schrodinger Uncertainty Principle?

    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!
  42. psycho_physicist

    Errors/ Uncertainty in measurement problem

    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...
  43. J

    I Question about Uncertainty Principle

    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...
  44. A

    I Exact meaning of the Uncertainty Relations

    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
  45. N

    I Uncertainty about relative atomic mass

    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
  46. maxhersch

    SigFigs in Volume and Uncertainty?

    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...
  47. S

    Estimate the uncertainty in electron's position.

    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...
  48. L

    Uncertainty -- particle through single slit

    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...
  49. S

    I Heisenberg Uncertainty Principle & Wave Function

    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...
  50. U

    A Resolution in single molecule localisation

    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...
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