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. T

    Vortex Nucleation Critical velocity using the Uncertainty Principle

    Hi there, I'm very stuck on this problem when approaching it like this. I know I could use the Landau Criterion for rotons but that's not accepted here, it wants the approach to come from the uncertainty principle. My thinking is along these lines: There will be a change in chemical potential...
  2. R

    A question related to de Broglie wavelength and the Uncertainty Principle

    "Now, if an electron has a definite momentum p, (i.e.del p = 0), by the de Broglie relation, it has a definite wavelength.A wave of definite (single) wavelength extends all over space. By Born’s probability interpretation this means that the electron is not localised in any finite region of...
  3. S

    Uncertainty for n using calculus

    i'm thinking of differentiating the inside of both sin functions but I'm not sure what to do with the sin. if anything, I'm new to this sort of uncertainty calculation. I have calculated the uncertainty and values for both Dm and a in advance.
  4. L

    I Momentum-Position vs. Energy-Time Uncertainty Relations

    In a few textbooks in introductory quantum mechanics which I have looked through (e.g. Griffiths), it is heavily emphasized that the momentum-position uncertainty relation has a completely different meaning from the energy-time uncertainty relation, and that they are quite unrelated and only...
  5. S

    I RMS vs. RSS for uncertainty

    Hi, the following statement comes from a document of Keysight spectrum analyzer: The sources of uncertainty can be considered independent variables, so it is likely that some errors will be positive while others will be negative. Therefore, a common practice is to calculate the root sum of...
  6. stephen8686

    Heisenberg's Uncertainty Principle Question

    So with the \gamma=\frac{1}{\sqrt{1-\beta^2}} it seems obvious that relativistic momentum, p=\gamma m_o v is supposed to be used. Then \frac{ dp}{dv}=m_o(1-\beta^2)^{-1/2}+m_o v...
  7. DanishForestCat

    Calculating the uncertainty in a Geiger counter

    Does the absolute uncertainty in A+B-C equal √A+√B+√C? If so, this is larger than the value of A+B-C. Surely that can't be right? For this investigation, I have been working from a lab script from my local uni physics department. This suggested that calculating this actually required a method...
  8. S

    Three quantum mechanics questions (about Uncertainty p. and comp. conjugate)

    Is the last inequality correct? Should it not be ##|A|^2 \cdot 2(1+\cos{(ka)})##? How is the time calculated here? Given ##\Delta v > 10^{-34}##... How come ##mv \Delta v = \Delta (\frac{mv^2}{2})##? Where does the ##(1/2)## come from?
  9. Negatratoron

    I Uncertainty between position and angular frequency - is this correct?

    Motivation: In my thermodynamics + statistical physics class, we derived the equipartition theorem for ideal gasses using Boltzmann factors, dividing the phase space of a gas particle in position+momentum space into units of size x*p=h based on the quantum nature of the space of states that are...
  10. N

    How do I calculate Heisenburg's Uncertainty Principle?

    I know Heisenburg's Uncertainty Principle states that there has to be a minimum amount of uncertainty. Where the minimum uncertainty is hbar/2. My attempt at the solution Uncertainty in x = 28E-12 m (Turn pm into m) h=6.63E-34 (constant) hbar=1.055`19E-34 (constant) hbar/2 = 5.275986363E-35...
  11. B

    Relating Uncertainty in Time to Uncertainty in Wavelength

    I actually have a solution available to me, but I don't understand what it's doing so I'll include my attempt at a solution and briefly describe the correct solution that I don't understand. ΔE Δt ≥ ħ/2 (Uncertainty) ΔE = hΔf (De Broglie) ΔE = hc/Δλ Substituting, (hc/Δλ)Δt ≥ ħ/2 Rearranging...
  12. B

    Sig Figs when the Uncertainty is Larger than the Values

    Hey, so in my lab I took some apparently bad data and when I averaged it and took the standard deviation I got values for the SD that were larger than the average of the data. I'm sure they still want sig figs in the results but I'm not sure how to report it. My average is -0.7101 and my...
  13. jfizzix

    A Is there a quantum uncertainty to the number of atoms in a marble?

    I know precious little about quantum field theory, but want to understand the following. If each Fermion and Boson has its own field.. ..and as an example, the EM field can be in a coherent state, which is a superposition over many photon number states.. .. then can a fermion field, or...
  14. E

    Springs in series affecting the uncertainty

    No idea on this one - I know that the spring constant will divide by 3 but am unsure how this will affect the % and the absolute uncertainties. Completely stuck on the extension...
  15. B

    Index of Refraction Uncertainty Problem

    A is the angle of refraction (~60 degrees) and Dm is the angle of minimum deviation that was different for each of the spectral lines associated to one of the six wavelengths measured. The problem I'm having is when I use equations of propagation of error to find the uncertainty in these...
  16. S

    Bra-ket of uncertainty commutator (Sakurai 1.18)

    It's easy to show that ##[\Delta A, \Delta B] = [A,B]##. I'm specifically having issues with evaluating the bra-ket on the RHS of the uncertainty relation: ##\langle \alpha |[A,B]|\alpha\rangle = \langle \alpha |\Delta A \Delta B - \Delta B \Delta A|\alpha\rangle## The answer is supposed to be...
  17. zzzriprip

    Uncertainty of an oscilloscope frequency, read from the period

    Hi, I am unsure of what uncertainty to get, so here is my full question: I used the CRO for an experiment, and since what I need is frequency, I read the period, so for the uncertainty of the period, it is the smallest division divided by two. So if my uncertainty for period is 0.001s, then what...
  18. K

    Help calculating the uncertainty in the Sun's rotational speed

    Hi everyone, The equation is one we have been given to calculate the rotational speed of the sun for different latitudes. phi = average latitude. This shouldn't be a problem for me, but for some reason I just can't trust my error calcs. We are given : A = 14.713 ± 0.0491◦/d B = −2.396 ±...
  19. usehn

    How to get the Uncertainty of a percentage change

    I have a measurement with uncertainties for two years. Say Year 1 Rain : 100mm(80-120mm) Year 2 Rain : 120mm(103-131mm). Now I get the percentage change in rain in Year 2 w.r.t Year 1 as 20%. Is there a way to get the uncertainty associated with this percentage change?
  20. Ampulla

    B What causes quantum uncertainty?

    What causes quantum uncertainty? My friend who's working for Apknite says that detectors are not the cause of wave collapse, because you are measuring something that isn't remaining in the same state.
  21. T

    Calculating Uncertainty: Where Am I Going Wrong?

    So the only part of this question I am having an issue with is the uncertainty part in part e). I have included the whole question as reference. So to derive the uncertainty in ff I used the uncertainty equation outlined above but the issue is that when I propagate the uncertainty I end up with...
  22. Sasho Andonov

    A Uncertainty vs Randomness in Quantum Physics

    In Quanta Magazine there is article on this link...
  23. W

    I Uncertainty Principle in the context of tracking particle paths

    I have a bit of confusion regarding the application of the uncertainty principle in the context of experiments. If a detector allows you to measure a particle's path through said detector, does that mean that you know a particle's position at all points in time, and are able to work out its...
  24. B

    B Measuring a circle and the Uncertainty principle

    I have been trying to see if my understanding of uncertainty principle is right. So I thought consider a circle. for this augment we will look at its diameter and it circumference. Suppose you get a length of string and make a exact measure of the circles circumference using this length of...
  25. D

    B Heisenberg's uncertainty principle - does it always apply?

    I am not too knowledgeable about QM, so please forgive me if this is a dumb question. I have outlined below an experiment setup for which Heisenberg's uncertainty principle seems not to apply: Imagine a particle for which we wish to collect the exact position and velocity. We have a detector d1...
  26. T

    Why is the final answer for the micrometer measurement 3% instead of 2.9%?

    I thought that since he micrometer is to 2 significant figures (0.35 and 0.01mm) that the final answer should also be to 2 sig.figs, thus answer A. But the final answer is C, 3%. Can someone explain why?
  27. N

    B Molecular Uncertainty: Exploring Position & Momentum

    Apologies in advance if my understandings are simply incorrect. As I understand it, there is a limit to what can be known about both a particle's position and momentum, and in some interpretations this is because there is no position or momentum until measurement only a probability. What I am...
  28. J

    How to calculate n with its uncertainty in the equation Q= kL(h^n)?

    I am thinking of doing the same thing (summing up all the uncertainties that contribute to U(E) in the example) for the task, so summing up all the fractional uncertainties that contribute to U(Q). But the problem is unlike energy in the example, I'm not sure what's the contributors that lead to...
  29. J

    Statistics: How to differentiate Type A and B uncertainty?

    I tried to find examples on the internet but I am still confused.
  30. Bure

    A The uncertainty principle in quantum gravity

    The main role in quantum gravity can be played by the uncertainty principle , where is the gravitational radius, is the radial coordinate, is the Planck length. This uncertainty principle is another form of Heisenberg's uncertainty principle between momentum and coordinate as applied to the...
  31. S

    I Uncertainty Over Sextans Galaxies' Group Membership

    Hi all. Awesome site! Just wondering if anyone can answer my question: If the Sextans galaxies are inside the group's zero velocity surface, why is there uncertainty over whether they're part of the group?
  32. H

    I Divergent vacuum uncertainty of fields in QFT, how to resolve?

    If you calculate the uncertainty of a scalar field in the vacuum state, i.e. ##\langle0\left| \phi^2\right|0\rangle##, you get a divergent integral that comes out to something like $$\frac{1}{4\pi^2}\int_0^\Lambda \frac{k^2 dk}{\sqrt{{m^2}+{k^2}}}$$ Where ##\Lambda## is some momentum cutoff...
  33. D

    I Requesting help with the uncertainty principle equation

    Hi For 2 Hermitian operators A and B using the Cauchy-Schwarz inequality and assuming the expectation values of A and B are zero I get (ΔA)2(ΔB)2 ≥ (1/4)|<(AB+BA)>|2 + (1/4)|<(AB-BA)>|2 Now both terms on the RHS are positive so why is this inequality usually just written with only the...
  34. T

    What are the uncertainty values for my corrected magnitudes?

    Homework Statement I need to work out the errors of my corrected apparent magnitudes. The Colour Excess is 0.36 with uncertainty = 0.01 The star was observed in two wavebands. r-band = 2.285 g-band = 3.303 The 2.285 and 3.303 are the ratios R_V for the SDSS (Sloan digital sky servery) r and...
  35. T

    How do I determine the uncertainty value of the star's absolute magnitude?

    Homework Statement I have a star that has an apparent magnitude of 13.73 with uncertainty of 0.03303 It's distance Modulus is 13.9967 so it's absolute magnitude is -0.26 The distance is 6300 parsecsHomework Equations [/B] The uncertainty on log10(d) is given by Δ(log10)≈0.4343 Δd/d ΔQ) =...
  36. E

    Uncertainty of measurements & significant figures

    Homework Statement This conversion factor 1m = 39.3701 inches was used, when measuring a tape that had inches on it to a full meter. The measuring tape increased by 0.0625 inch increments, so the 1 meter (39.3701) was estimated to be in between the 39.3125 and 39.3750 on the actual measuring...
  37. Zack K

    Importance of uncertainty and probability in research papers

    As someone who is interested in astrophysics, I always get emphasized on the importance of knowing statistics and error analysis in results of a calculation. However when I read about real physics papers, I never see any numerical solutions, just equations that demonstrate phenomena. I know that...
  38. E

    Circumference of Circle with Uncertainty

    Homework Statement Calculate the circumference (including uncertainty) of a circle whose measured radius is r=7.3 ± 0.2cm. 2.Relevant equations & 3.The attempt at a solution - Circumference of circle --> C = 2πr = 2π7.3 = 45.87 cm - Exact constant error propagation --> z =...
  39. E

    Calculating Uncertainty when Converting Time

    Homework Statement The problem asks to convert time in minutes to time in hours, and to also calculate the uncertainty for the time in hours.Specifically 10 minutes +/- 0.2min being converted to hours with uncertainty. 2. Homework Equations & 3.The attempt at a solution conversion of time...
  40. manojr

    I Uncertainty of momentum and position

    I was reading a book which had some comments on EPR paper (Einstein, Podolsky, Rosen - 1935) like following: In Newton's physics, when two identical billiard balls hit each other head-on, bouncing off in opposite direction, knowing one ball's position and speed will also indicate other ball's...
  41. J

    Uncertainty - Reynolds number and the friction factor

    Homework Statement Correctly present the table of information. The values in the table are deliberately in a wrong format. The calculated Re values have been analysed to have an uncertainty of ± 0.4% and the calculated f values an uncertainty of ± 0.1%. Homework EquationsThe Attempt at a...
  42. A

    A Uncertainty principle, removing infinity in the Fourier Transform

    I have come across a paper where it is stated that if the infinity assumption in the FT is removed, the uncertainty doesn't hold. Is this a sensible argument? Thank you.
  43. gmastrogiovanni

    I Do I need energy to measure position without uncertainty?

    I state the following study and then expose my doubt at the end. MY SYSTEM A free particle (absence of forces) on one-dimensional space (X axis). INITIAL STATE At t=0 the wave function is a Gaussian wave packet NOT normalizet centered in ##x_{0}## and with standard deviation ##\sigma##...
  44. Kevin Chieppo

    B Exploring QM: Is Uncertainty a Physical or Measurable Limitation?

    I'm a hobbyist physicist and I just started studying QM through watching Leonard Susskind's lectures on the Stanford Youtube channel. I get the idea of it being impossible to precisely know both a subatomic particle's position and momentum, but is this actually a physical limitation? Or is it...
  45. nomadreid

    I Uncertainty: balance of two aspects?

    There are two aspects of uncertainty (a) how far different from the situation where all possibilities are of equal probability (b) how spread out the values are. In discussions about (Shannon) entropy and information, the first aspect is emphasized, whereas in discussions about the standard...
  46. S

    I The Uncertainty Principle - question within Griffiths' Text

    Hello, In Griffiths (2nd edition) pgs 110-111 - deriving the uncertainty principle I have 2 questions 1) I am stuck on a point ... (h = ^ hat ) <f | g > = < ( Ah - <A>) ψ | ( Bh - <B>) ψ > = <Ψ | ( Ah - <A>) ( Bh - <B>) Ψ> FOIL = <ψ | AhBh ψ> - <B><ψ | Ah ψ> - <A>< ψ | Bh ψ> +...
  47. M

    I Photons and Heisenberg's Uncertainty Principle

    To summarize, my current understanding of how Heisenberg's uncertainty principal works suggests that there would be a contradiction (somewhere down the line) with any way that it applies to (or doesn't apply to) photons, due to the fact that they must always travel the speed of light. I...
  48. Jussi Lundahl

    I Propagation of uncertainty in the slope

    I'm doing a lab report from electronic spectrum of iodine. I did Birge-Sponer plot from my data. Excel gave it to me a slope y = -2,0698x+133,34. From regression analysis I get uncertainties for slope and intercept. Slope: ##-2,069761731 \pm 0,075075941## Intercept: ##133,3385857 \pm...
  49. Another

    I About the Heisenberg uncertainty principle

    heisenberg uncertainty principle ## Δx Δp ≥ ħ## where ##Δx = \sqrt{<\hat{x}^2>-<\hat{x}>^2}## ##Δp = \sqrt{<\hat{p}^2>-<\hat{p}>^2}## I don't know. Why ##Δx## equal to ## \sqrt{<\hat{x}^2>-<\hat{x}>^2} ## and ## Δp ## equal to ## \sqrt{<\hat{p}^2>-<\hat{p}>^2} ## What can I find out about...
  50. N

    Quick question about uncertainty in using a stopwatch

    Homework Statement Watching an object fall, along a ruler, using a stopwatch to take the time from when the object flies passed the upper part of the ruler, and again when it hits the floor (bottom of the ruler) Homework EquationsThe Attempt at a Solution My friend is doing introductory...
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