Observable Definition and 215 Threads

In physics, an observable is a physical quantity that can be measured. Examples include position and momentum. In systems governed by classical mechanics, it is a real-valued "function" on the set of all possible system states. In quantum physics, it is an operator, or gauge, where the property of the quantum state can be determined by some sequence of operations. For example, these operations might involve submitting the system to various electromagnetic fields and eventually reading a value.
Physically meaningful observables must also satisfy transformation laws which relate observations performed by different observers in different frames of reference. These transformation laws are automorphisms of the state space, that is bijective transformations which preserve certain mathematical properties of the space in question.

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  1. nomadreid

    I Predicted sizes of (observable) universe

    I have read the advice of Nugatory and Jorrie in order to get me started on understanding cosmology; I have played around with the cited calculators (except http://www.einsteins-theory-of-relativity-4engineers.com/CosmoLean_A20.html doesn't open for me), without mastering them, and read for a...
  2. M

    I Object moving out of the Observable Universe due to Expansion

    With the LDCM, cosmological constant, model I understand that the scale factor of the Universe grows more rapidly than the Horizon. I believe the correct horizon I need to be considering is the Hubble Horizon and the point when objects recessional velocity hits the speed of light they disappear...
  3. MassNerd

    Question About Moving Observers and Observable Universes

    [Mentor's Note: Post moved into its own thread from this one] Hello, I have another newbie relativity question which is somewhat related to this topic. Here it is: There are 3 observers on 3 different planets each in a different galaxy. Observer 1 stands on the north pole of their planet...
  4. F

    I Expectation of an operator (observable) how to calculate it

    Hello Forum, I understand that in order to calculate the average of a certain operator (observable), whatever that observable may be that we are interested in, we need to prepare many many many identical copies of the same state and apply the operator of interest to those identical state. By...
  5. Kara386

    I Is Observable A Invariant Under Symmetry Generators G_i?

    How do I know if an observable is invariant, specifically under some set of transformations described via the generators ##G_i##? Which conditions would this observable have to fulfil?
  6. O

    I What can this observable represent?

    ## \hat{A}= \begin{pmatrix} 1 &- 1 \\ -1&1 \end{pmatrix} ## this is written in a basis ##\left ( |1>,|2> \right )## So, i know this is an Hermitian operator, so it can represent an observable. Can this operator represent an electric dipole moment? A momentum? A component of the orbital angular...
  7. K

    I Eigenstate of two observable operators

    Let's say you have two operators A and B such that when they act on an eigenstate they yield a measurement of an observable quantity (so they're Hermitian). A and B do not commute, so they can't be measured simultaneously. My question is this: You have a matrix representation of A and B and...
  8. Tspirit

    I Can the expectation of an operator be imaginary?

    Assume ##\varPsi## is an arbitrary quantum state, and ##\hat{O}## is an arbitrary quantum operator, can the expectation $$\int\varPsi^{*}\hat{O}\varPsi$$ be imaginary?
  9. F

    B Can Measuring Momentum Make a Marble's Position Vanish?

    Can we say a piece of marble is in an eigenstate of the observable position? If you try to measure other observable like momentum, the other eigenstate of position is supposed to be erased. So how come we can't cause a marble to vanish by measuring momentum. Would you know other objects...
  10. R

    I If the observable universe was visible to the naked eye....

    What would the Earth's night sky look like? Would our eyes see any dark spots? Is there are way to calculate such a probability? This hypothetical is about the observable universe only. 93 billion light-years diameter, isotropic, visible light. Not sure what's the most appropriate tag for this...
  11. entropy1

    B What is the origin of Observables?

    Why does an Observable have to be Hermitian, and why do the eigenstates and eigenvalues have to respresent the possible measured values? Is is by definition? What is the origin of this convention?
  12. V

    Bohr frequency of an expectation value?

    Homework Statement Consider a two-state system with a Hamiltonian defined as \begin{bmatrix} E_1 &0 \\ 0 & E_2 \end{bmatrix} Another observable, ##A##, is given (in the same basis) by \begin{bmatrix} 0 &a \\ a & 0 \end{bmatrix} where ##a\in\mathbb{R}^+##. The initial state of the system...
  13. P

    I What is the size of the observable universe relative to CMBR

    Reading the Wikipedia article makes my head spin! Somehow the figure https://en.m.wikipedia.org/wiki/File:Observable_universe_logarithmic_illustration.png doesn't seem quite right. I don't understand how the CMBR doesn't define the edge of the universe. If we can see the CMBR that happened near...
  14. B

    A Collapse and projection-valued measures

    Let suppose I have an observable ##A## with associated projection-valued measure ##\mu_A## $$A = \int_{a \in \mathbb{R}} a \cdot \textrm{d}\mu_A(a)$$ for a system in the (possibly mixed) state ##\rho##. Let ##S \subset \mathbb{R}## be a measurable subset and let ##Z = \mu_A(S)## be the...
  15. Barely_Conscious

    I How would one know whether a star would be observable?

    I'd like to answer this yes or no question for a number of objects: "Is this star, at any point between these two times, going to be above the local horizon?". Say, I'm at the prime meridian at a latitude of 50 degrees, and I want to know whether, between the sidereal times of 11:00:00 and...
  16. R

    I The observable Universe and its shape

    Laymen here. 1. From my understanding the universe is like the surface of a balloon. The universe is expanding as a balloon grows when air in being placed inside of it. Just like a surface of a balloon if you go in any direction in a straight line you will come back to the original point. Is...
  17. T

    B Binary Stars Observable with Binoculars: Periodicity

    Are there any binary stars that can be seen with binoculars which have orbital periods you can observe from week to week or month to month? tex
  18. entropy1

    B Question: Can State Only Be Formulated Relating to Observable?

    Can a state only be formulated with respect to an observable in consideration? That is to say, does the formulation of the state depend on the particular observable in consideration? Thanks.
  19. K

    A Time correlation of an observable in the Schrödinger picture

    This has come up in a number of threads, so I made this thread to talk about it. I think that an interpretation of this in the Schrödinger picture should be possible at least in the style of Feynman. This would go something like this. ##\begin{eqnarray*} \langle A(s)A(t)\rangle_\psi &=&...
  20. Chiclayo guy

    Distinction between observable and unobservable universe

    I know that when we talk about ‘the universe’ we’re normally referring to the observable universe. It is my understanding that the universe is 'one thing’, the only distinction being that part is visible and part is not, yet occasionally when the subjects of size and inflation are discussed...
  21. Harley Cabral

    Help finding some info about the movement of the observable universe

    Hello all! Recently I watched a TV Series episode, but I didn't catch it from the beginning and I need some help to find which one was it, or any clue about it. The part that I want is about the Scientist guy explaining that things on the observable universe (big picture) seems to be moving...
  22. bcrowell

    Do non-black hole singularities have observable properties?

    I hope the topic of this post is not too philosophical to be appropriate here. Some recent discussions on PF have helped to crystallize my view of how classical GR treats singularities, and black hole singularities in particular. However, I'm not sure to what extent these ideas generalize to...
  23. M

    Expectation value of observable in Bell State

    Homework Statement Consider the bipartite observable O_AB = (sigma_A · n) ⊗ (sigma_B · m) Where n and m are three vectors and sigma_i = (sigma_1_i, sigma_2_i, sigma_3_i) with i = [A,B] are the Pauli vectors. Compute using abstract and matrix representation the expectation value of O_AB...
  24. M

    Observable System L Matrix, can a value be negative?

    Homework Statement An error matrix is in the form, has a characteristic equation: ## CE: s^2 + 120s + 7200 = 0 ## A state variable feedback system is described by: ## A_F = \begin{bmatrix}0 & 1 \\-616.8 & -40 \end{bmatrix} ## ## B = \begin{bmatrix}0 \\ 1 \end{bmatrix} ## ## C =...
  25. wolram

    B Proving Quantum Gravity: Observable or Formula?

    How would one prove quantum gravity, would there be some thing observable or would it just be a mathematical formula.
  26. A

    Requirements for an observable pattern in young's experiment

    Homework Statement It's not in fact a question of homework but something I have been wondering but cannot get answers about the requirements for an observable pattern in young's experiment: 1. Polarisation: In my study, the book derived the intensity function of light assuming the light beams...
  27. Buzz Bloom

    Derivation of Gott's formula for size of observable universe

    I understand that Gott derived a formula for calculating the size of the observable universe, and the value of the diameter based on current obsrvations is 93 Gly. Can someone please show the mathematical derivation of Gott's formula, or give a reference to a source which shows this derivation?
  28. G

    Age of the observable Universe?

    Forgive my ignorance?.. If we can see 13.8-ish billion light years away how can the universe be the same age? Matter cannot travel at the speed of light, so how are we as far away (in light years) as the universe is old?
  29. Rupert Young

    How can the observable universe be 46 billion lyrs in size?

    I watched a BBC documentary that said that the observable universe is about 46 billion light years in size. How can this be if the age of the universe is 13.7 billion years (and nothing travels faster than the speed of light)?
  30. R

    Newbie question.... The Big Bang & The Observable Universe (and time)

    I am trying to understand some things but I seem to be confused a little... I was watching a video and it said when you look with hubbles telescope you see the past universe but I seem to have trouble understanding this, does that mean we could see the future if we knew which direction to point...
  31. K

    What Does the Observable Universe Look Like?

    The entire observable universe is contained rather graciously in this wonderful picture, for your admiration.
  32. P

    Relationship between commutators and observables

    Homework Statement Suppose A^ and B^ are linear quantum operators representing two observables A and B of a physical system. What must be true of the commutator [A^,B^] so that the system can have definite values of A and B simultaneously? Homework Equations I will use the bra-ket notation for...
  33. Dain Ironfoot

    How to calculate distance required for observable difference

    Me and my grandfather got into a "debate" (more like one-sided argument) on whether objects fall at the same rate on Earth independent of air resistance or not. He claims that "If you drop 2 objects from an airplane -- like a car and a marble, both objects would hit the ground at the same...
  34. Stephanus

    Farthest Object in Universe & Multiverse | Steven

    Dear PF Forum, After searching many links in Google and threads in PF, I can't find the farthest object in the universe. I have some questions here, perhaps someone can give me quick and simple answer. A. What is the farthest object in the universe? How far away? B. The radius of the...
  35. Alex299792458

    How many cubic planck lengths are in the observable universe?

    If you take the size of the observable universe can you find out how many cubic plank lengths can fit in the observable universe and it doesn't have to be exact just approximation.Also the math and formulas would be helpful too.
  36. S

    Size of observable vs UN-observable Universe, etc

    I understand that these distances are speculative, but I am given to understand that, at the end of inflation, the diameter of the OBSERVABLE Universe was approximately 10 centimeters. However, the diameter of the UN-OBSERVABLE Universe was a good deal larger, with a diameter of approximately...
  37. Safinaz

    Exploring Sigma Regions for Observable R(D) in Theoretical Models | 1206.2634v2

    Hi all, I'd like to understand what does it mean by allowed 1 or 2 ## \sigma ## regions for some observable, like R(D) in Fig. 1 left [ 1206.2634v2] ? And how can I calculate or plot this value or region according to any theoritical model .. Bests.
  38. L

    How wide is the observable horizon, at sea level?

    I'm quite aware of how to compute how FAR you are from the horizon, but my question is, how WIDE is the observable horizon at sea level (like, from left to right, how many kilometers is this): http://www.jeicentral.com/wp-content/uploads/2014/10/far_sunset_in_te_ocean_horizon-wide.jpg Thanks!
  39. L

    From observable to operators in QFT

    from the relativity forum https://www.physicsforums.com/threads/spacetime-in-qm-or-qft.802721/ Sonderval stated (transferred here so not off topic): http://scienceblogs.de/hier-wohnen-drachen/artikelserien/[/QUOTE'][/PLAIN] So the standard Schroedinger Equation can be used for both particles...
  40. T

    Motivations for the C*-algebra of observables?

    As far as I understand, the Hilbert space formalism can be derived using functional analysis and representation theory (not familiar with those) from the requirement that observables (their mathematical models) form a C*-algebra and the possible states of a system map the members of the algebra...
  41. W

    Finding Possible Measurement Results of an Observable

    Homework Statement I am trying to find the possible measurement results if a measurement of a given observable ##Q=I-\left|u\right\rangle\left\langle u\right|## is made on a system described by the density operator ##\rho={1 \over 4}\left|u\right\rangle\left\langle u\right|+{3 \over...
  42. W

    How is Degeneracy Resolved by Building a CSCO?

    When finding a complete set of commuting observables, the goal, as I understand it, is to specify enough observables in the set such that, when given an eigenvalue of a state from each observable's matrix, these eigenvalues uniquely identify a corresponding eigenvector. It seems that every...
  43. P

    Are observables like position emergent properties?

    Title basically says it all. I'm a physics undergrad trying to wrap my head around quantum physics, and I was hoping people here could help. My question comes from something in one of my textbooks. It tries to explain particle-wave duality through a piece of string, which I'll quickly go over as...
  44. Drakkith

    Size of the Observable universe at the Big Bang Singularity

    Just a quick question. How big was the current observable universe at the point in time where we reach 'singularity conditions' in the early universe? I'm assuming it can't be a single point, as there is no way that I know of to make a zero-dimensional point into a 3-dimensional object or space.
  45. F

    Why is there an observable universe?

    If we can only see things that traveled 14 billion light years away (I think) or less, then why is there a so called observable universe? If everything started at a singularity, wouldn't we have already seen everything? It's hard to put this question into words. How can something be farther away...
  46. B

    Observable universe as a black hole

    A substance of arbitrarily low density can form a black hole if there is enough of it. So I took the mean density of the universe and calculated how big it would have to be to form a black hole. It's a surprising coincidence that the swartzchild radius in light years is the exact age of the...
  47. A

    How Do Compatible Observable Properties Transform Between Equations?

    Homework Statement I have problem with properties of compatible observable Homework Equations [AB,CD]=AB CD – CD AB ………. (1) ABCD+ACBD-ACBD-ACDB+ACDB+CADB-CADB-CDAB ………. (2) A{C,B}D-AC{D,B}+{C,A}DB-C{D,A}B ... (3) The Attempt at a Solution How can the equation (1) become (2), and eq (2)...
  48. liometopum

    Constants linked to the observable universe, not whole

    A common equation (attributable to Fred Hoyle) for the mass of the observable universe is: c3/(2GH0). Despite that the whole universe is vastly larger than the observable universe, we can create an equation to calculate the mass of the observable universe, using the standard constants of...
  49. A

    Exploring the Homogeneity of the Hot Observable Universe

    From what I understand, the observable universe began as homogeneous and very hot. if the universe was very hot, doesn't that mean that particles are vibrating at very fast speeds? after all, isn't heat simply kinetic energy of particles? if this is the case, then how could the universe be...
  50. D

    Diffrraction of electron experiment to be observable

    in my textbook , it states that for the diffrraction of electron experiment to be observable, the De Broglie's wavelength of the particles is of the same order as the interatomic spacing... i have a doubt here... what is the meaning of same order here?
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