# Uncertainty Definition and 72 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. ### 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?
2. ### 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...

4. ### Finding the Relative Uncertainty for the Standard Error of the Mean

While I will not be showing the graph here, I am trying to dissect what the question even means. While I do understand that relative uncertainty can be found via the equation ##\frac{\sigma_A}{A}##, I do not understand how I can find the "relative uncertainty of SEM". Does anybody here have any...
5. ### Calculating Numerical Uncertainties in an Equation

Background Information: I am working on a pulsed NMR lab project that involves graphing out a semi-log graph of free induction decay amplitude as a function of time. After graphing out the semi-log graph, I am to determine the apparent spin-spin relaxation time (##{T_2}^*##) through the...
6. ### I Understanding the meaning of "uncertainty" in Heisenberg's UP

Hi! I am checking Zettili's explanation on the uncertainty principle and I have this confusion on what the "uncertainty" really means which arises from the following statements: When introducing the uncertainty principle, for the case of position and momentum it states that: if the x-component...
7. ### Asymmetric uncertainty intervals in astrophysical data

My initial guess was to calculate the upper and lower value, and then average those two values, but I don't know whether this is correct to make the uncertainty interval symmetric. After I calculated the average value, I subtracted it form the upper and lower value, and obtained the symmetric...
8. ### Heisenberg and Varying the Velocity

Good Morning When we derive the Euler Lagrange equations using Hamilton's Principle, we make a point of varying the velocity and the position at the same time, (despite the fact that, normally, they are related through a derivative). I do understand that this is allowed: we are trying to find...
9. ### Propagation of uncertainty with tangent function?

For a lab, I needed to calculate the uncertainty of a refractive index that was found using Snell's law. I found an equation online for propagation of error for any general function, which was I thought that since my equation was I could just get rid of the variable y, and have After...
10. ### 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...
11. ### 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...
12. ### 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...
13. ### 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 Equations The Attempt at...
14. ### 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...
15. ### Homework help: Uncertainty with negative power

Question: A distance R is measured to be 3.400 ± 0.007m. What is the absolute uncertainty in R^−2? Attempted solution: Relative uncertainty: 2* (0.007/3.4) = 4.11E-3; R^-2 = 3.4^-2 = 0.0865 m^-2; Absolute uncertainty = R^-2 * relative = 0.0865 * 4.11E-3 = 3E-4 m^-2; Any help would be greatly...
16. ### B Greatest Possible Uncertainty and Sig Figs

There is something I seriously don't understand about uncertainty. Suppose there is an electric balance that reads 5.67g The limit of reading is 0.01g The greatest possible error is half of the limit of reading and is thus 0.005g By this logic, and assuming the very best possible situation, I...
17. ### Fractional uncertainty of g on the surface of the Sun

Homework Statement Homework Equations The Attempt at a Solution it looks like I got too big numbers for the uncertainty
18. ### Static and Kinetic Friction vs Normal Reaction Graphing

How do i suppose to determine the uncertainty for the slope of my Static friction against normal reaction graph? My data for static friction and normal force has the uncertainty of +/- 0.0001 The uncertainty is too small for me to draw airbox/bar in the graph to draw the max and min slope...
19. ### I Uncertainty of coefficients after a least square fit

Fitting data to a linear function (y=a0+a1*x) with least square gives the coefficients a0 and a1. I am having trouble with calculating the uncertainty of a0. I understand that the diagonal elements of the covariance matrix C is the square of the uncertainty of each coefficient if there are no...
20. ### I Measuring Electron spin

Watching an old (2012) youtube video (), the narrator says (time 10:38) that if A measures the y-axis spin of an entangled pair and communicates his finding to B, then B "cannot" measure his x-axis spin, because doing so would give him knowledge of the spins along both axes, which uncertainty...
21. ### A What are the typical uncertainties of data in Astophysics?

Hello, everybody. I'm conducting an investigation in planetary sciences. Specifically in exoplanet detection by the radial velocity method and I'm stuck because I need to know how to defend the data that I'm using. I'm using the data from http://exoplanet.eu/catalog/ and I have found some data...
22. ### I Calculate measurement uncertainty? I made one measurement....

How to calculate measurement uncertainty of m. I understand I should use these formulas to calculate it if I had data of many measurements, but when have only measurement then it becomes undefined, because of 0/0 in standard deviation formula. ##u(m)=\sqrt{u_a^2(m)+u_b^2(m)}##...
23. ### Multiple choice on uncertainty

1. A student measures the density of a metal and calculates answer to be 8543.2kgm^-1 . The result is accurate to +- 1.1% Which of the following states answer to an appropriete number of sig figs? A 8.543x10^3 B 8.5x10^3 C 9x10^3 D 8.54x10^3 2. Relative Uncertainty = Absolute Uncertainty/...
24. ### Time Uncertainty Propagation - Stoke's Law & Average Time

Homework Statement [/B] So basically I am calculating the terminal velocity for a small sphere falling in a measuring cylinder filled with glycerine. The distance traveled is 20 cm (0.20 m), and I have conducted 3 trials for each temperature. I have measured the displacement of the ball using...
25. ### Uncertainty in the intersection of two lines with error bars

The only thing I wish to take from this graph is the intersect of the two lines of best fit. How can I get the uncertainty in this point? While the points appear to have the same uncertainties, they actually each have their own distinct % uncertainty. Would the maximum uncertainty in the X...
26. ### Uncertainty/error of a volume is greater than the normal volume

Homework Statement I have an empty cylinder with an external diameter of (23.0 ± 0.5) mm, an internal diameter of (22.5 ± 0.5) mm and a height of (60.0 ± 0.5) mm. I need to calculate its volume with its uncertainty/error. Homework Equations The Attempt at a Solution I do it like this...
27. ### B Propagation of uncertainty

i have an equation like this: Given m(B-V)= 1.2 +- 0.2 How do you calculate the uncertainty in T? (btw, I solve T using graphs by finding the intersection point) My idea was first to calculate T when m(B-V) =0.2, and I then calculate T when m(B-V)= 1.2 + 0.2(its uncertainty). and then find the...
28. ### Pulse echo technique to find the distance of the Moon

Homework Statement [/B] Over 40 years ago, the Apollo astronauts placed reflectors on the surface of the Moon. These are still used by a number of observatories on Earth to monitor the distance to the Moon by reflecting pulses of laser light from them and detecting the reflected signal...
29. ### B Walter Lewin videos -- why ± 0.5 cm uncertainty why not ± 0.1?

here is the link to walter lewin video lecture please jump to 13:13 8.01x - Lect 2 - 1D Kinematics - Speed, Velocity, Acceleration i thought that all meter ruler/ meter stick use ± 0.1 cm as uncertainty .how did he get ± 0.5 cm?
30. ### I Experimental Data - Error in slope

I have conducted a tensile test on five specimens. I intend to do a linear regression for every set of data and get a value for the slope (modulus of elasticity) and its error by finding the standard deviation (using LINEST function on excel) of the slope. I will now end up with 5 slope values...
31. ### Calculating uncertainty with a set of angles

Homework Statement Hi there, the issue I'm having right now is finding the right way to calculate uncertainties when trigonometric terms come in play. The question goes like this, we're given 2 sets of 5 angles in degrees, the incident angle (10.0, 20.0, 30.0, 40.0, 50.0) and the other is the...
32. ### I Computing uncertainties in histogram bin counts

I am working on astrophysical data and I have a large number of redshift values of quasars. Now, each redshift estimate comes with its estimated standard error naturally. If I plot a histogram of these redshifts, I would expect the bins counts to also have some sort of uncertainty. I am unable...
33. ### 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...
34. ### 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...
35. ### Uncertainty problem

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...
36. ### 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...
37. ### 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...
38. ### 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...
39. ### 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...
40. ### 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...
41. ### 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...
42. ### How to Combine Gradient Uncertainty with other Uncertainty?

Homework Statement I did an experiment to measure the speed of sound(using two microphones and a hammer). I changed the distance between the two mics and calculated(using a fast timer) the time taken for the sound to reach from the start mic to the end mic. I made a graph(distance on x axis...
43. ### What constant p.d. should be used in a potentiometer?

Homework Statement I am trying to use a slide wire potentiometer and a galvanometer to find the electromotive force of an unknown cell. I have heard that the balance point at which the galvanometer needle has zero deflection should be towards the centre of the slide wire as this reduces...
44. ### I Expression for Uncertainty of Arbitrary Operator

Hello all, as far as I can see this question is not posted already, my apologies if it is and please provide a link. But I'm watching this video on youtube: And at 22:38 there's an expression given for the uncertainty of an arbitrary operator Q, however I'm concerned the expression is...
45. ### Uncertainty of Derivatives

Homework Statement I know this is more of a physics question, but I tried there and wasn't successful. I have done a physics experiment measuring the weight as a function time of the discharge of water from a cylindrical bottle with a pinhole at the bottom. What I ultimately want to get at is...
46. ### Tangibly Explaining HUP to General Chemistry Students

I understand this topic has been brought up before, however there appears to be "truth" or "lies" and very little in between when it comes to explaining the Heisenberg Uncertainty Principle (HUP) to students of freshman chemistry. I'm teaching university general chemistry to students who've had...
47. ### Calculation of uncertainty

Homework Statement [/B] a=12.26 +/- 0.08 b=0.25 +/- 0.05 e=1.2 +/- 0.2 Evaluate the uncertainty of following calculations Part 1. z= 5(ab/e) Part 2. p= 3e - b The Attempt at a Solution I attempted part 1 like this Δz/z = 5 (Δa/a + Δb/b + Δe/e) ... Calculated Δz to be 20 but the answer is...
48. ### Calculating Uncertainty Error

Homework Statement I am writing a lab report and I need to calculate the uncertainty error for Gravitational Potential Energy and Kinetic Energy. The Professor told us that the margin of uncertainty for time is +- 0.025 seconds, margin for height is +- 0.001 meters, margin for mass is +-0.001...
49. ### Finding Uncertainty Using Upper/Lower Bound

Hello, I'm working on a lab report and am having a bit of trouble when it comes to figuring out uncertainty. Trial 1 Acceleration: 0.93 ± 0.14 m/s^2 Trial 2 Acceleration: 0.83 ± 0.35 m/s^2 Trial 3 Acceleration: 0.93 ± 0.14 m/s^2 I have three values listed above and and wanted to find the...
50. ### Error propagation with dependent variables

Homework Statement Based on Microdosimetry theory, trying to figure out error propagation for a lot of quantities that are produced from radiation spectra. I am having trouble finding information on how to calculate and propagate errors when the quantities in my equations are not independent...