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. mrspeedybob

    The limit of the observable universe

    I have heard it said that galaxies exist which are beyond the observable universe because the expansion causes them to be receding at super-luminal velocity. How can this be? We can see all the way back to the surface of last scattering, when the universe was just dense plasma. The limit to the...
  2. N

    Going from system & observable to hilbert space & operator?

    Hello, Given a system and an observable that one wants to measure in it, how does on get the (or a?) relevant hilbert space and the suitable operator in it? The examples I've come across so far seem to rely on... well, I'd call it "vague reasoning", but the word 'reasoning' seems too much. It...
  3. N

    Is the current black hole horizon observable?

    I am wondering which black hole horizons might be observed experimentally. a comment in another thread...(PAllen) Kip Thorne in BLACK HOLES AND TIME WARPS has a nice spacetime diagram for what he calls the absolute (current) and apparent horizons of a black hole. The apparent or...
  4. jfy4

    Electromagnetic Potential as an Observable

    Hi, I suppose I'm a little late to start here, but I just got hung up on the following: The field quanta in E&M is the photon and it comes from the gauge potential in QED A(x) A(x)=\int \frac{d^3 p}{(2\pi)^3 \sqrt{2\omega_p}}\sum_{\lambda=1,2}\left[...
  5. S

    Red shift and observable light

    Since light emitted farther away from our point in the universe is more and more red shifted, would this mean that at a certain time we wouldn't be able to observe light further than a fixed distance since it's been red shifted beyond the electromagnetic spectrum?
  6. T

    Mass Dispersion of Observable Universe

    Does anyone know of any data regarding mass dispersion around Earth? That is to ask (more toward my interest), if the observable universe was broken into equal 3-D sections like "North to Northeast" "NE to E" "E to SE" and so on... would the mass of each section observed from Earth be equal...
  7. T

    When people talk about the current size of the observable universe

    Could I just quickly derail this thread and ask that frequently asked question? When people talk about the current size of the observable universe, are they talking about how far away the furthest objects were when they emitted their light? Or how far away the furthest objects will be now?
  8. bcrowell

    Size of observable universe in two simple cases - this this right?

    size of observable universe in two simple cases -- this this right? One of the most frequently asked questions in the cosmology subforum is about how the radius of the observable universe in units of light-years can be greater than the age of the universe in years. The figures are 46 billion...
  9. F

    How Do We Measure the Size of the Galaxy with Limited Telescope Scans?

    Homework Statement It is said that telescopes have found that our galaxy is about a hundred thousand light years across. It is also said that our telescopes have only scanned a hundred light years of the galaxy. I am just quoting from this video: So my question is, how can we know...
  10. A. Neumaier

    What is observable in a relativistic quantum field theory?

    Steven Weinberg wrote: ''In its mature form, the idea of quantum field theory is that quantum fields are the basic ingredients of the universe, and particles are just bundles of energy and momentum of the fields.'' (see p.2 of his essay, ''What is Quantum Field Theory, and What Did We Think It...
  11. D

    Measuring photon polarization and finding observable operator

    An apparatus has these properties when measuring a polarized photon: -whenever a linearly polarized photon at angle \vartheta enters apparatus, it displays "2" -whenever a linearly polarized photon at angle \frac{pi}{2}+\vartheta enters apparatus, it displays "3" -for all other polarizations...
  12. M

    What Is the Diameter of the Observable Universe?

    What is the diameter of observable universe?
  13. rpt

    Why time is not an observable in quantum theory?

    Why "time" is not an observable in quantum theory? Why "time" is not considered as an observable as any other quantity in quantum theory? Is it because we cannot imagine anything in the absence of time?
  14. K

    Is LHC pushing the limits of naturally observable phenomena in the Universe?

    Are collisions with the energy levels of LHC happening in our modern day Universe? Like at the core of stars or at the event horizon of black holes where a lot of high energy stuff is going on? Sorry for the naive question, I'm extremely interested in physics but I'm just not proficient...
  15. R

    Beyond the Observable Universe

    Hi all, I realize that things beyond our horizon are not causally connected to us and so from a scientific standpoint it is correct to say that nothing exists beyond our observable universe, but my question is more related to inflation. First, I'll explain my understanding of current...
  16. J

    Is action truly an observable in physics?

    I ran across one of Christoph Schiller's physics posts, and this one got me scratching my head: http://www.motionmountain.net/wiki/index.php/Teach_clearly!#On_action_as_an_observable "On action as an observable Numerous physicists finish their university studies without knowing that action is...
  17. H

    Quantum Field is Observable, Not State Property

    I think I've cleared up a fundamental misunderstanding I've had for a while, and want to get confirmation I'm right. Is the following statement true? In QFT, a quantum field is not part of the state of a quantum system, and is not an aspect of reality that needs to be measured to be known...
  18. B

    Is position not an observable of a photon?

    Is position not an observable of a photon?
  19. F

    Question about observable universe.

    If the unobservable universe is defined by the region in which light originated in it is incapable of reaching Earth due to having the expansion of space rate faster than c, the speed of light, thus causing light unable to travel to earth, than under this definition would not our observable...
  20. T

    Observable Boundary of Expanding Universe: Is There a Limit?

    If space is expanding then at at some point we must reach the point where it's expansion is faster than C. Do we know where that is? Is the expansion uniform or is it dependent on something like Dark Matter clusters? Is the expansion accelerating or decelerating at two fixed points? In...
  21. A

    Newbish questions (shape of the observable universe, blueshift, etc.)

    Hello! I've juggled these questions around my mind for a few days now and so far haven't been able to google any useful information: 1. What is the approximate 3D shape of the observable universe? The Wikipedia article on this subject talks about weird stuff, like a "flat universe" and...
  22. C

    Observable [tex]G_{z}= -(xL_x+yL_y)[/tex]

    Homework Statement Consider the space of the states of a particle with no spin under an isotropic harmonic oscillator potential and the observable G_{z}= -(xL_x+yL_y) Obtain the spectrum of Gz. Will be ever he particle in a normalisable state where Gz is defined? Can you interpret...
  23. Z

    Why are people saying that the radius of the observable universe is 46.5 ly

    We can only see 13.7 billion years away from us in all directions. The edge of the observable universe may now be 46.5 billion light years away, but we still can't see that far currently. I thought the observable universe was only as far the light as traveled and that is only 13.7 billion years...
  24. sweet springs

    Is Every Hermitian Operator Observable?

    Hi. I know that operator of observable is Hermitian. Reciprocally, any Hermitian is observable? If not, showing some examples are appreciated. Regards.
  25. sweet springs

    Is energy of a free particle observable?

    Is Hamiltonian of a particle in free space H=P^2/2m OBSERVABLE ? -Yes, we can surely observe energy in some manner. -No, ∫de|e><e| is not identical operator I, thus |e>s does not form a complete set. As an example, energy eigenstate |e> degenerates, as |e=p^2/2m> = α|p> + β|-p>, according to...
  26. B

    Does any model predict the mass (or total energy) of the observable Universe?

    During the (recently departed) matter-dominated era, the total mass of the Universe, including dark matter, is believed to have been fairly constant at around 1055 kg. This was the case in a time period from at least the CMB last scattering surface to nearly the present. Mass content is...
  27. marcus

    Observable QG effects in Chern-Simons gravity-Stephon Alexander

    Observable QG effects in Chern-Simons gravity--Stephon Alexander Important talk, http://pirsa.org/09110132/
  28. N

    Observable universe: expansion and light speed

    a. Is it known if there are actually regions of space which would be far enough and expanding at a rate enough that light will never be able to reach us? Or, is it possible to say that a boundary may exist in a way that, beyond it we can be sure that light will certainly not reach us? b. Also...
  29. S

    Heart shaped observable universe?

    In another forum there was a discussion of the observable universe being heart shaped because of the expansion of space (unless I misinterpreted the drawing). Info that I have found says it to be spherical. Have you seen any drawings of anything heart shaped for anything cosmological?
  30. T

    How can I tell if the night sky is observable from here?

    Firstly, sorry if this is a stupid question but I was just wondering if there's a way I can tell if the night sky is observable where I'm living, Dubai. I really want to get a telescope but it'll be a waste if I can't even use it here. Where I live, I wouldn't say that there's too much...
  31. marcus

    Size of the *observable* universe (noob questions about)

    Size of the *observable* universe Everybody should know that General Relativity allows distances to expand faster than the speed of light, and indeed it predicts that in many circumstances they will do so. This is hardly news, Friedman figured out the standard expansion cosmology model in...
  32. C

    Expected value of observable over time

    Homework Statement We have a linear combination of eigenstates of observable A \Phi_+ and \Phi_- with eigenstates a and -a. The expected value of the energy for both states is 0, while (\Phi_+,H\Phi_-)=E, with E real. Calculate the expected value of A for eigenstates \Phi_+ and \Phi_- over...
  33. L

    Astronomy: Estimate the age of the observable universe

    Homework Statement How does the speed of light's finiteness limit the size of our observable universe? Using the speed of light (c = 3 x 10^8 m/s), estimate the age of the observable Universe in years given its estimated size of about 10^26 m. Homework Equations The Attempt at a...
  34. A

    Standard deviation for a determinate state of observable Q

    There are two things I don't understand here: Firstly, why in the standard deviation expression we use the Q operator instead of the Q value itself? Writting Q seemed more natural and then in the next expression I would just stick the corresponding operator. Which would lead to the same result...
  35. C

    Olbers' Paradox, the CMB and the observable universe

    From Olbers' paradox, the night sky is dark because the universe is finite in age, so some stars' light hasn't had time to reach us. BUT, we see the CMB which occurred some 13 billion years ago (14 billion maybe?) So, if light from the cmb has had time to reach us, shouldn't every object's light...
  36. B

    Observable physical quantity in relativity

    Please let me know when do we say that a physical quantity is observable. Is the answer related to clock synchronization?. If possible do not involve quantum physics.
  37. thenewmans

    Is the Observable Universe Really Limited to 13.7 Billion Light-Years?

    Am I needlessly annoyed or is this an incorrect interpretation of the term observable universe? It’s not the first time I’ve seen this from space.com. I can understand using “Light Travel Time” as the distance but the only reason 13.7 billion light years is a limit is because you can’t see...
  38. D

    Observable Universe and Beyond

    I was just reading a bit about our universe and the observable universe which stirred up a few questions. I am mostly a student of mathematics, so I apologies if I am assuming things that are incorrect or if I am not using proper terminology. Maybe some of the quotes from my readings are...
  39. D

    Is probability a Quantum Observable ?

    Is probability a quantum observable ? I'd like to obtain an observable operator (self-adjoint, hermitian) with correct eignevalues (the probability). Have anyone heard of such an operator in QM ? And what about QFT ? Why is there no such operator in classical textbook ?
  40. 8

    Forces Outside Our Observable Universe?

    Krauss, in his article in the Feb 2008 SciAm magazine stated: " Two different groups of astronomers traced the expansion of the universe over the past five billion years and found that it appears to be speeding up. The source of this cosmic antigravity is thought to be some new form of “dark...
  41. C

    Does every observable commute with the hamiltonian?

    I would guess that they would as every observable is a function of the q's and p's and as those commute with the hamiltonian I couldn't imagine an observable that wouldn't commute, however are there any other cases where an observable won't commute with the hamiltonian?
  42. Fra

    Paper: Rovelli's What is observable in classical and quantum gravity?

    Paper: Rovelli's "What is observable in classical and quantum gravity?" I'm reading Rovelli's QG book and found a reference to his own article: "What is observable in classical and quantum gravity?" I fail to find it on arxiv - anyone know if this is available or do you have to buy it from...
  43. Loren Booda

    How Much of the Universe is Directly Observable?

    How much of the universe would you say is directly observable?
  44. A

    Is the whole Universe expanding, or just the Observable Universe?

    I know the Observable Universe (OU) is Expanding, and I think this is (by now) beyond dispute. However, there is no evidence at all to show that every part of the Universe is expanding. Perhaps the Universe as a Whole (UAW) is not expanding at all. What if it was contracting? What if...
  45. P

    Can everything be observed and measured in our universe?

    Science works on the simple principle of observation, experimentation and conclusion. But, is everything observable and mesurable in this universe. What about those things that might be beyond our senses.(Say if we lack a sixth sense.) The question came to my mind when I asked myself a question...
  46. M

    Expectation value of an observable

    Homework Statement We have an observable A, that has eigen vectors l a1 > and l a2 > , with eigenvalues a1 and a2 respectively. A second observable B has eigenvectors l b1 > and l b2 > with eigenvalues b1 and b2 respectively. The eigenstates of B can be written in terms of the eigenstates...
  47. P

    Mathematica Observable mathematical phenomena

    Lets share some mathematical phenomena that are just cool (for math people) if you multiply any number of integers whose digits are only 1, the product will always be palandromic. Grab a calculator and see for your self. I would be really interested to see a proof for this phenomena...
  48. V

    Expectation value of the square of the observable

    Homework Statement I know how to compute the expectation value of an observable. But how does one compute the expectation value of an observable's square? Homework Equations \langle Q \rangle = \int_{-\infty}^{\infty} \Psi^* \hat{Q} \Psi \; dx \langle Q^2 \rangle = \int_{-\infty}^{\infty}...
  49. V

    Expectation value of an operator (not its corresponding observable value)

    1. Problem statement This isn't a homework question itself, but is related to one. More specifically, I'm computing the time-derivative of \langle x \rangle using the correspondence principle. One side simplifies to \left\langle \frac{\hat{p}}{m} \right\rangle, but what is the physical meaning...
  50. B

    Capturing Light with a Theoretical Mirror Sphere: Observable? Possible?

    What would happen if: I had a sphere produced from a theoretical perfectly reflective one-way-mirror(reflective on the inside) and a shone a light into it? Would the light accumulate inside the sphere for a noticeable period of time? Would it be observable? Could light be captured this way...
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