What is Observable: Definition and 213 Discussions

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. O

    Expectation value of composite observable in singlet state

    Homework Statement I've been reading Leonard Susskind's Theoretical Minimum volume on QM, and enjoying it quite a bit - the book doesn't include exercise solutions at the end though, and if they exist online for this volume I haven't been able to find them. (Perhaps if such solutions...
  2. Q

    Is QM necessary for single observable parameters?

    Forgive the title if improper, the language of QM is not my native tongue. :) All scenarios where QM is invoked that I am used to involve parameters that do not commute, but I suppose I've never truly asked myself if QM is necessary to describe scenarios wherein you are not concerned with this...
  3. J

    How many gravitons are there in the observable universe?

    It is thought that there are approximately 10^80 protons in the observable universe, but there are approximately 10^90 photons in the observable universe. If my googling is correct, there are also approximately 10^90 neutrinos in the observable universe, but their temperature is only 1.9 degrees...
  4. G

    Why is the expectation value of an observable what it is (the formula)

    Homework Statement I really do not understand why the expectation value of an observable such as position is <x> = \int\Psi*(x)\Psi Homework Equations If Q is an operator then <Q> = = \int\Psi*(Q)\Psi cn = <f,\Psi> The Attempt at a Solution What I understand this is saying is...
  5. F

    Neil deGrasse Tyson's Observable Universe

    In Dr. Tyson's first episode of Cosmos he said "...there are parts of the Universe that are too far away. There hasn't been enough time in 13.8 billion year history of the Universe for their light to have reached us." Since the remnants of the Big Bang has a redshift over 1000 and large...
  6. L

    What is the average value of an observable in a quantum system?

    Why we define that average value of some observable ##\hat{A}## in state ##\psi## is ##(\psi,\hat{A}\psi)## Why this isnot perhaps ##26(\psi,\hat{A}\psi)##?
  7. D

    MHB Modes observable and modes controllable

    How do you find observable and controllable modes? \[ \mathcal{L}\Big\{\big(\mathbf{A} - s\mathbf{I}\big)^{-1}\Big\} = \begin{bmatrix}...
  8. Jalo

    (Quantum mec.) Probability of measuring a given value of an observable

    Homework Statement Given the following hamiltonian and the observable \widehat{B} find the possible energy levels (a is a real constant). If the state is in it's fundamental state what's the probability of measuring b_{1}, b_{2} and b_{3}? Homework Equations The Attempt at a...
  9. H

    Comparable size of the observable universe immediately after inflation

    Regarding scale. How big was the region of the universe we now understand to be the observable universe, immediately after early inflation? I'm tyring to understand the scale. I know our sphere of observation is very approximately 45 billion light years or something, I don't know for sure...
  10. E

    Is every observable the generator of a symmetry?

    We know that observables correspond to hermitian operators on the Hilbert space of physical states of the system. We also know, via Wigner theorem, that for each symmetry there is a linear unitary operator (or anti-linear and anti-unitary). In the case of a continuous symmetry, that is in the...
  11. M

    Negative variance of an observable quantity

    Quantum mechanics has a well-known procedure for evaluating the expectation value of an observable quantity in a given quantum state. First one must obtain the quantum operator O that is associated with the observable quantity. Then the rule for computing the expectation value is: Apply O to the...
  12. Nugso

    The Observable Universe ve The Universe

    Hello everyone. As I was reading an article on wiki, I stumbled upon this by chance; If the universe is finite but unbounded, it is also possible that the universe is smaller than the observable universe. In this case, what we take to be very distant galaxies may actually be duplicate images of...
  13. C

    Two-level quantum system observable quantities

    Homework Statement A two-level system is spanned by the orthonormal basis states |a_{1}> and |a_{2}> . The operators representing two particular observable quantities A and B are: \hat{A} = α(|a_{1}> <a_{1}| - |a_{2}> <a_{2}|) and \hat{B} = β(|a_{1}> <a_{2}| + |a_{2}> <a_{1}|) a) The state...
  14. J

    What Lies Beyond the Observable Cosmos?

    If the universe is a 3 dimensional (plus time) space expanding into something, what is that something? Am I correct in stating that the universe is an infinite eternal space in which the Big Bang happened 13.5 billion years ago, and that the observable cosmos is expanding into this space...
  15. B

    Exploring the Observable Universe: Discovering New Stars in the Night Sky

    Hello, i'm reading through a book called "Discovering The Universe" and in the chapter about cosmology the familiar idea of the observable universe is discussed. It speaks of the radius of the cosmic particle horizon being ~15 billion light years, which makes perfect sense as light from...
  16. P

    Can we rewrite Schrodinger equation using observable variable?

    We know that in Schrodinger equation, Ψ is called wave function, which is not observable, while Ψ·Ψ* is the probability, which is observable. can we rewirte the Schrodinger equation to a form without Ψ but only Ψ·Ψ*? because I think, in this way can I figure out all conservations in the...
  17. K

    Charge balance in observable universe

    Hi, I've been wondering about the charge balance in the known universe, factors that might alter it, and the consequences of any small imbalance that might exist. This is a sort of layman's theory. I don't expect it to be right but I'd love to understand how it can be refuted. I am surely...
  18. M

    Question about the Planck spaces and observable universe, .

    From Wikipedia: http://en.wikipedia.org/wiki/Googolplex A Planck space has a volume of a Planck length cubed, which is the smallest measurable volume, at approximately 4.222×10^-105 cubic meters = 4.222×10^-99 cubic cm. Thus 2.5 cubic cm contain about a googol Planck spaces. There are only...
  19. atyy

    Is every state an eigenstate of an observable?

    I started a new thread from a side discussion in https://www.physicsforums.com/showthread.php?t=681625&page=2, since it seems very off topic, but I still had questions. Is there a requirement for an operator that corresponds to an observable to be part of a complete set, ie. its...
  20. V

    Expectation value of non-physical observable

    Homework Statement This may be incredibly obvious, but I just need to check. Of course we all know that physical observables must yield real expectation values. What if you tried to calculate, say, <xV(d/dx)>, where x is the position, d/dx is a first derivative, and V is the potential? This...
  21. C

    The observable universe, the actual uinverse, and CMB

    Hi all. I relish hearing from our great cosmological explainers like Neil DeGrasse Tyson and Brian Greene and watch whenever I find something new on youtube, but one thing that I don't understand and haven't heard anyone specifically address is that, if the part of the universe we are able to...
  22. C

    Uncertainty in some observable A

    Why do we define the uncertainty in some physical quantity ##A## as: $$\delta A = < \sqrt{<A^2> - <A>^2} > .$$ I know that it can be derived by computing the variance of ##A##, but what is the physical meaning? Thanks!
  23. julcab12

    Observable universe and events between vast distances

    Hi Guys. I would like to ask what is the very nature of event in the same moment given a vast distances. Considering Point A (earth)-vast distance-Point B (galaxies). Would be possible that the event we're observing already happened long before it reaches us and may not exist at this very...
  24. S

    Observable Universe and Black Holes

    Hi, my first post here! Galaxies outside the observable universe (that we can't see their light) can affect us with their gravity? If the answer is no, we can say that gravity information travels at the speed of light. So, in a black hole how gravity information from an object inside...
  25. A

    Hermitian operator <=> observable?

    My question is about both sides of the same coin. First, does a hermitian operator always represent a measurable quantity? Meaning, (or conversely) could you cook up an operator which was hermitian but had no physical significance? Second, are all observables always represented by a...
  26. V

    Number of Voids in the (observable) Universe

    Hi, Does maybe someone know if there was ever the attempt to count the number of voids in the (observable) universe? I assume that is not the case, but would be very interested in any work that gives some estimation. Many thanks, Martin
  27. G

    Measuring the size of the observable universe

    The size of the observable universe usually gets put at 93 trillion light years, though some people believe it is infinite, though I'm not sure which camp is in the majority. Those who believe it is 93 trillion light years across are they just assuming that the size of the universe at the first...
  28. A

    Are Observables Only Quantities That Commute with Hamiltonian?

    are observables only those quantities which commute with system's Hamiltonian ?
  29. B

    Tugs from Beyond the Observable Universe

    Dark Flow: Tugs from Beyond the Observable Universe? Is this true ? If true then what lies Beyond the Observable Universe ?
  30. R

    10^80 particles in observable v unobservable universe

    Here is a chart showing the unobservable universe The green lines indicates the part we can see. My question is that figure that gets thrown around, there are 10^80 particles in the universe, is that for observable or the unobservable universe.
  31. R

    The flatness of the observable and unobservable univ

    I was watching this lecture and the professor said that before inflation the universe's shape was spherical or curved and inflation blew it up to the point where the observable universe appears flat but the actual unobservable universe is still a curve or spherical. Did I understand correctly...
  32. W

    Overlapping observable universes

    Here's a puzzle that I have been wondered about. I know the answer, but I do not understand the reasoning for it. Could someone explain it to me in a way that a layman like could understand in an intuitive manner? (The math involved in GR equations is too complex for me to grasp.) General...
  33. S

    When is operator phi(x) an observable in QFT?

    In QFT of a real Klein-Gordon-Field, the field operator \phi(x) is an observable. Mathematically, this is the case because it is a sum (over all k) of a and a^\dagger and this yields a Hermitian operator. Physically, I can understand this because this equation would describe, for example, a...
  34. H

    Is there any gravitationally unbound' galactic clusters in observable universe

    is there any "gravitationally unbound' galactic clusters in observable universe my hunch is that everything in the universe is gravitationally tugged on each other ..we can say moon is connected to andromeda galaxy in a way moon->earth->sun->milkyway->andromeda even the slightest imbalance...
  35. H

    How WMAP satellite surveyed all over observable universe

    what i want to know is how much area of universe (in light years if possible) is surveyed by WMAP .when you say CMB permeates entire universe based on data from these satellites orbiting Earth how much of universe is actually surveyed by WMAP ? if you survey around where we are now in this...
  36. K

    Is this possible? (regarding observable and actual size of universe)

    I think the picture explains it better than I can with words. Is it possible that we can only see a small sphere around our planet (red circle around Earth in the picture), but there could be a 'planet x' on the real edge of the universe that can see light from 14 billion light years away in one...
  37. R

    Probability of an observable

    Hey, How would you compute the probability of measuring a specific value of an observable (resp. range for continuous variables), given a wavefunction with an eigenbasis that is different from the one associated with the observable? An example: Let's consider my wave function is a...
  38. H

    What do i do if my control system is not observable?

    so i made a state space model of a physical system where A matrix is 4 by 4 and B matrix is 4 by 1. I have 2 inputs in the system and 1 output. I used Matlab to create the A,B,C,D matrices and i used the ctrb (controlability matrix), then the rank function. instead of rank 4 (full rank) i...
  39. vmr101

    Observable and Operators - Obtain an expression

    Homework Statement a) Two observables A and B are represented by operators A(hat) and B(hat), which obey the following commutation relation: [A(hat), B(hat)] = iC, where C is the real number. Obtain an expression for the product of the uncertainties ΔAΔB. b) Hadrons, such as protons...
  40. G

    Eigenvalues of 4x4 Hermitian Matrix (Observable)

    Homework Statement Find the allowed energies for a spin-3/2 particle with the given Hamiltonian: \hat{H}=\frac{\epsilon_0}{\hbar}(\hat{S_x^2}-\hat{S_y^2})-\frac{\epsilon_0}{\hbar}\hat{S_z} The Attempt at a Solution The final matrix I get is: \begin{pmatrix} \frac{3}{2} & 0 &...
  41. D

    Larger structure than observable universe?

    Hi all, just like the atomic world is unobservable to our normal optical observation, can it not be that there can be out there some structure too large that we are deluded to believe that there are merely galaxies and all empty beyond.
  42. J

    Critical density and total observable mass

    Assuming a Hubble constant of 74.3 km/sec/Mpc, the critical density is about E-29 gm/cm3. To calculate observable matter based on 5% of this density (the other 95% is dark matter and dark energy), a volume has to be used. But which volume, the one with a 13.7 billion light year radius or the...
  43. B

    From the Planck length to the Observable Universe

    Here is a study in distances based on powers of ten of the meter. It gives easy-to-see graphic examples of relative size, from the Plank length out to the Observable Universe. Imho, a great teaching aid. http://www.newgrounds.com/portal/view/589217
  44. S

    Time derivative of an observable

    According to my book: \frac{d}{dt} \langle Q \rangle = \frac{i}{\hbar} \langle [\hat{H}, \hat{Q}] \rangle + \langle \frac{\partial \hat{Q}}{\partial t} \rangle . No derivation for this is given. How can derive you this?
  45. J

    Critical density and observable mass

    Please comment on my assumptions and results, this has confused me for some time. Thanks The following is an attempt to reconcile the critical density of the universe with the amount of observable matter as represented by number of stars. Assumptions for critical density: Hubble constant...
  46. A

    Potential energy as observable

    In quantum mechanics it seems that the operator for potential energy is U. Therefore, every state is an eigenstate of potential energy and there will never be any uncertainty in potential energy? It seems weird...
  47. N

    What is an invarient observable in GR

    In another thread here, https://www.physicsforums.com/showthr...=548148&page=3 , post #36, Peter Donis posted this: "...But we *can* describe a generic spacetime in GR using a curved geometry (*which* curved geometry depends on the specific spacetime), and we *can* describe any given...
  48. K

    Why is inertial mass not an observable in QM?

    In classical mechanics, I can measure the inertial mass of a particle by measuring force and acceleration: m=F/a. In QM, this equation only holds for expectation values <F> and <a>. Does this lead to the fact that inertial mass is not an observable? Is there a deeper underlying principle which...
  49. P

    Is our entire universe observable?

    In an earlier thread--What is space?--a few people indicated that only a part of our universe is observable: Because space is expanding, photons from distant parts of the of the universe haven't had time to get here yet. So that's my next question. Is our entire universe observable? My...
  50. V

    Different Slices of Now Observable from Earth?

    Different "Slices of Now" Observable from Earth? Brian Greene's excellent series continued last week on PBS with "The Illusion of Time" in which he showed with graphics how different "nows" occur depending on the motion of an observer. Using the example of a space alien 10 billion light years...
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