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

    Experimenting whether the diameter of a pot affects boiling time for water

    Hey guys, I'll try to be as direct as possible. So for school i'm doing an experiment at home trying to find out if the diameter of a pot affects the time it takes to boil water inside the pot as it says in the title. I had three different pots with three different diameters. I got half a liter...
  2. User849483

    Need help finding uncertainty for this equation

    this is the formula v is velocity g= gravity h= height ro= outer radius of cylinder ri = inner radius of cylinder please help
  3. T

    Understanding the Proper Uncertainty Formula to Use

    Good evening, I'm running into a little confusion on the second part of this problem due to finding two different formulas for calculating the uncertainty in multiplied quantities. The way that I was taught was something like this. If ##z = x \cdot y##, then: $$\dfrac{\delta z}{z} =...
  4. srnixo

    Understanding Time Measurement in Physics: Uncertainty and Calculations

    So as you can see in the image, I have noted the time in the [time column (s) ] on the table after conducting the experiment at home using the application phyphox. And now, I have some questions to fill in the remaining gaps: The first question: about ΔH (m) : Should I set it equal to zero...
  5. F

    I Uncertainties accumulate when measuring longer lengths?

    Hello, It is clear that as distance being measured increases, more graduations are needed to represent a unit of measure for such distance. Each graduation in a measuring device is subject to uncertainty and error, and these errors and uncertainties accumulate with the increase in the number of...
  6. J

    I What is the Uncertainty in the Total Weight of a Collection of Similar Items?

    Not a homework assignment. Just what must be a solved problem that I'm embarrassed I don't know how look up or figure out on my own. I want to know the total weight of a collection of N items. They are all similar but of different, unknown weights. My scale has a known accuracy of ±U units. If...
  7. F

    I Reported uncertainties for time and distance in physics experiment

    Hello, I was looking at my physics lab manual... There is a table reporting time and distance data which were both measured and collected (see below). My understanding is that the uncertainty for different and measured time instants should be the same because the time was measured with the same...
  8. Govind

    I What is the correct definition of measurement uncertainty?

    I have some confusion regarding Measurement Uncertainity. In some books/articles it is defined wrt true value as "Uncertainty in the average of measurements is the range in which true value is most likely to fall , when there is no bias or systematic component of error is involved in...
  9. Govind

    I Measurement Error Analysis in Gaussian distribution

    I am new to statistics and recently learned about ISO guidelines for Accuracy & Precision and Uncertainty & Error. But there are some graphs of probability distribution I found on internet which I am not able to grasp. image Source Q. In this graph(above) if...
  10. sunmoonlight

    Uncertainty in Newton's law of cooling

    I'm finding the uncertainty of k, given that each temperature has an uncertainty of +/- 0.5 degress.
  11. S

    B Examples of less popular pairs of physical properties with uncertainty (HUP)

    Position and momentum are the popular pairs of properties with uncertainty we often hear about, for example that we cannot know with precision where an electron is and its momentum at the same time. What are others? Such as an example of an energy and a time that we cannot know both...
  12. C

    Uncertainty: Systematic & Random

    I am thinking that it might could be absolute uncertainty = systematic uncertainty + random uncertainty. Many thanks!
  13. K

    A Measurement uncertainty due to thermal noise

    I have a charged particle in a Penning trap. The particle motion is non-relativistic and the energy is high enough such that we can assume it is not in the quantum regime. For the purpose of the question I am interested only in the axial motion of the particle, so basically this is a classical...
  14. K

    I Monte Carlo for uncertainty estimation

    Hello! This is tangentially also a follow up to this post. I have the following equation: $$A = \frac{0.2\frac{W}{\Delta}}{\left(\frac{W}{\Delta}\right)^2+0.1^2}$$ where ##\Delta## is an experimental parameter, ##A## is obtained by some measurements and it depends on ##\Delta## and the...
  15. C

    Finding Absolute Uncertainty in Data

    For this data, I am trying to find the overall absolute uncertainty of NA, where NA is the numerical aperture: ##\tan \theta_{NA} = \frac{R}{L}## and ##NA = \sin \theta_{NA}## Case R(cm) L(cm) R/L theta_NA[rad] NA error in NA R0,L0 0.5 0.5 1 0.785398163 0.707106781 0 Rmax,Lmax 0.7...
  16. K

    A Uncertainty on an asymmetry signal

    Hello! I have an experiment in which I measure the counts given some experimental parameters, call them ##E## in order to extract some physics parameter of interest, call it ##X##, so I have ##N(E,X)##. This ##N## (the number of counts) will have a statistical error (which goes like...
  17. mfb

    A ATLAS reanalysis of W mass: Lower uncertainty, agrees with SM

    Improved ATLAS result weighs in on the W boson Same dataset, but better analysis methods and some new results from elsewhere that could be used. Money plot from ATLAS: This makes the CDF measurement an even weirder outlier than it was at the time of publication.
  18. X

    A Minimum-variance bound for the extended maximum likelihood estimation

    I am fitting a mass spectrum using pdf(M)=Ns×S(M)+Nb×B(M; a, b) to determine the yield with the extended maximum likelihood fit, where Ns and Nb are the number of signal and background events, S(M) is the function for the signal, B(M;a, b) is the function for the background with parameters a and...
  19. M

    A Extracting the uncertainty on a measured atomic transition

    Hello! I have some measurements of a given transition in an atom, where each event consist of the measurement of this transition and the associated uncertainty (as details, the way it is done, is for each event recorded we measure the laser frequency and Doppler shift it to the frame of the...
  20. uxioq99

    Do Coherent States Imply 0 Energy Uncertainty?

    By considering the power series for ##e^x##, I assert that ##N=e^{-\lambda^2/2}## and that ##a\Psi_\lambda = \lambda \Psi_\lambda##. Because the Hamiltonian may be written ##\hbar \omega(a^\dagger a + 1/2)##, ##\langle E \rangle = \hbar \omega(\langle a \Psi_\lambda, a \Psi_\lambda \rangle +...
  21. uxioq99

    Time Independence of the Momentum Uncertainty for a Free Particle Wave

    Mine is a simple question, so I shall keep development at a minimum. If a particle is moving in the absence of a potential (##V(x) = 0##), then ##\frac{\langle\hat p \rangle}{dt} = \langle -\frac{\partial V}{\partial x}\rangle=0## will require that the momentum expectation value remains...
  22. D

    I How certain is the uncertainty principle?

    How accurate of a measurement can we make on the position of a particle? I heard you need more and more energy to get a measurement more accurate. Would the energy needed to be infinitesimal accurate create a black hole upon. Measurement?
  23. A

    I Why is the minimum energy equal to the energy uncertainty?

    I was watching this video on Youtube, however, I don't get the step at 14:50 where he says that ΔE≥½hf means that E0=½hf. Could someone explain why the minimum energy is equal to the energy uncertainty?
  24. V

    I Uncertainty Principle in QFT & Early Universe Conditions

    I have a question related to the uncertainty principle in QFT and if it is related to the early universe conditions. Do we still have four-vector momentum and position uncertainty relation in relativistic quantum theory? I have been following the argument related to the early universe and the...
  25. Narasoma

    I The clarity of Heisenberg uncertainty

    We know from basic quantum mechanics that the Heisenberg uncertainty states that position and momentum can not be measured simultaneously with arbitrary precision. My question is, is this relation is due to the nature of the quantum system itself, or "merely" unbreachable limitation to our...
  26. B

    Simple overestimate of slope uncertainty in regression

    Hi all, I am a science educator in high school. I have been thinking about how to make a simple estimate that 1st and maybe 2nd year students can follow for the propagation of error to the uncertainty of the slope in linear regression. The problem is typically that they make some measurements...
  27. A

    Uncertainty of the Standard Deviation

    Using this error propagation formula: I expressed the standard deviation (s) and the partial derivatives of s w.r.t. each data point as: This gives me an uncertainty of: , where m is the mean. Does this seem reasonable for the uncertainty of the standard deviation? I also found the thread...
  28. homeworkhelpls

    I I'm confused on which equation gives percentage uncertainty

    im confused about the difference of this equation: and this one: which gives percentage uncertainty, so which one should be used to calculate the uncertainty?
  29. D

    I Time-energy uncertainty relation

    Hi I have just been looking at the derivation of the uncertainty relationship for non-commutating operators. I have come across the following quote in Quantum Mechanics by Mandl regarding the time-energy relationship. "Time is not an operator ; it is an ordinary parameter which commutes with...
  30. pokespriter

    I About the position of electrons (uncertainty)

    Hello guys, I don't know if this is the right place to ask, so please be kind :/ I have a question regarding the location of an electron that belongs to an atom. A teacher told me that the probability of an electron to be found within its orbital is around 99%. When I asked about the remaining...
  31. riballoon

    B Heisenberg's Uncertainty Principle and determinism

    As I understand it the principle states that the more accurately you measure one factor of an object, for example speed, the less you can tell of any other factors, for example position. To me this seems we will every only be able to measure an approximation of reality and thus determinism...
  32. M

    I Time of flight measurement uncertainty

    Hello! I am generating electrons from a 3D gaussian source. The electrons all have the same energy, but the direction is isotropic. The electron source is in between 2 plates that act as a capacitor, and one of them acts as a time of flight (tof) detector. I know the voltage on the plates very...
  33. LCSphysicist

    How Does Quantum Uncertainty Define the Position of a Positron?

    So, let's assumed ##v_i = (v_i \pm \Delta v_i)##. We can say that, for minimum values, $$\Delta X_i \Delta v_i = \hbar / (2m)$$. $$\Delta X_i = \frac{\hbar}{2 m \Delta v_i} \implies V_{min} = \Delta X \Delta Y \Delta Z = \frac{\hbar}{2 \Delta v_x m } \frac{\hbar}{2 \Delta v_y m} \frac{\hbar}{2...
  34. B

    A Uncertainty estimation in pgopher

    Hello! Can someone who used pgopher before (I am fitting a diatomic molecular spectra) help me understand how does it calculate the uncertainty on the parameters when doing a line fit. I found very little online and it is not totally clear to me. Mainly I am not sure how, just by providing the...
  35. M

    A Linear combination of data with uncertainty

    Hello! I have 2 measured data points (they are measurements of different observable, not 2 measurement of the same observable), with quite different errors, say ##x_1 = 100 \pm 1## and ##x_2 = 94 \pm 10##. I want to compute the value (and associated uncertainty) of a linear combination of them...
  36. D

    Why does a free particle in an infinite well have uncertainty bigger than h/2 ?

    So I think I use the right approach and I get uncertainty like this: And it's interval irrelevant(ofc), So what kind of wave function gives us \h_bar / 2 ? I guess a normal curve? if so, why is normal curve could be? if not then what's kind of wave function can reach the lower bound
  37. A

    I Alternate expressions for the uncertainty propagation

    I have seen that there are two different formulas that we can use when calculating the propagation of uncertainty in a measurement. If ##X=f(A, B, C, \ldots)## is the quantity whose uncertainty we want to estimate, which depends on the quantities ##A,B,C,...##, then we could calculate the...
  38. D

    Estimating the Bohr radius from the uncertainty principle

    Soo. I think this problem is too direct and easy so I think I got it in wrong way: p=h/r and then plug in the K and V and then we get E=E(r) and get derivative and we have minimum? What do you think? is there sth I am missing?
  39. dom_quixote

    I Uncertainty in an experiment with an image viewed through a big slit

    This is a simple experiment that demonstrates how it is possible to draw conclusions similar to those of quantum physics, without having to "invade" the microscopic world. A student is led into a windowless room, which has only a slit in the ceiling. The light that passes through the slit is...
  40. H

    I Propagation of uncertainty with some constants

    Hi, I have a value ##100 \pm 0.1## and a function ##\frac{V}{E} = \frac{1}{\sqrt{1 + (\omega r c)^2}}## and I would like to find the uncertainty. Where r = 1000 and c = ##5 \cdot 10^{-8}## are constants. However, I'm not sure to understand how. Here's what I think and did. Since I multiply the...
  41. Yan Campo

    I Robertson uncertainty relation for the angular momentum components

    I'm studying orbital angular momentum in the quantum domain, and I've come up with the Robertson uncertainty relation for the components of orbital angular momentum. Therefore, I read that it is necessary to pay attention to the triviality problem, because in the case where the commutator is...
  42. nuclearsneke

    I Uncertainty in measurements of the thickness of a pile of pellets

    Howdie! We have been playing around with melting and molding HDPE pellets recently. After that, we measured their diameter and thickiness 5 times each to get an uncertainty. In our experiments we put one pellet between gamma-source and detector and measure its attenuation. After that we place...
  43. mopit_011

    Halliday Resnick Krane Example Problem: Uncertainty on Weighing Machine

    In the solution to the example problem, they wrote the following statement. “The least significant digit is the units digit, and so your weight is uncertain by about 1 pound. That is, your scale would read 119 lb for any weight between 118.5 and 119.5 lb.” I don’t understand why the scale...
  44. O

    I Entropic effects of the Uncertainty Principle?

    Per the Heisenberg uncertainty principle, a particle does not have a precisely defined location. Does such uncertainty contribute to the transfer of thermal energy (i.e. entropy)? Is uncertainty the primary means for the transfer of thermal energy at the quantum level?
  45. M

    I Heisenberg Uncertainty Principle Violation?

    Hello, 2 questions please about the Uncertainty Principle and the following scenario: I shoot at each other, 2 electrons each with equal but opposite velocity such that they repel each other? (To me, this indicates that you know the momentum of each electron and you know each position...
  46. M

    The Quantum Uncertainty of a Particle

    Summary:: I'm trying to understand the meaning behind the answer of 2.34... but I haven't taken a quantum class yet so I'm utterly lost. So I took this physics class that's teaching us python and for our final project our teacher assigned random problems to work out, well I got stuck with a...
  47. D

    Uncertainty of pendulum period and pendulum length

    I'm doing a lab report where I manually measure the time taken for a bifilar pendulum to do 10 oscillations. Is there a rule or a method that I should follow to calculate its uncertainty? Or is the uncertainty just an estimation of human reaction time and judgment? I also need to know the...
  48. A

    I Classical electron uncertainty

    In quantum mechanics it is impossible to prepare an electron in a state where both position and momentum are known with arbitrary accuracy. In classical physics such states do exist, but can they be prepared? If we assume that the electron is a classical particle (small ball of charge) can we...
  49. LCSphysicist

    Solving Uncertainty in Data Analysis with Spectrophotometry

    So i have a folder with a lot of data/information. Basically what i have is approximatelly 2k 2upla of x and y, because i need to find the function that describe the behavior of these data. Of course, i can use a program/software to fix/adjust the curve using the concept of OLS... BTW. The...