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. H

    A Translation-invariant systems and binary functions of spatial variables

    My question is about a statement in the book, Many-Body Quantum Theory in Condensed Matter Physics: An Introduction, by Henrik Bruus, Karsten Flensberg in appendix A: In a translation invariant system, any physical observable ##f(\vec r,\vec r')## of two spatial variables ##\vec r## and ##\vec...
  2. T

    I Diameter of the observable Universe

    Cosmologists say that the observable universe has a diameter of 93 billion light years. Does this mean the universe has a center?
  3. D

    I What is an observable exactly?

    What is an observable exactly? I hear terms that are used in physics books like an observable or a detection. What types of equipment do physicists use to make all these quantum measurements that are used in books so frequently? How small of a region of space does the wave function "collapse"...
  4. D

    B Would light travel in a circle at the edge of the observable Universe?

    Is there sufficient mass within the observable universe’s volume to form a black hole event horizon around the observable universe and, if yes would light fired tangentially at the edge of our observable universe ever loop back around in a circle or spiral inwards?
  5. K

    I Gravitational Field with Dark Energy: Observable Effects?

    since the cosmological constant observed is that there is a small amount of energy in empty space, and in general relativity anytime there is energy there is curvature and therefore gravity, how to calculate gravitational field with dark energy and does it have any observable effects on matter...
  6. Yan Campo

    I Probability when measuring a local observable

    I have information that $$\rho_{ab}=\sum_{j}p_{j}\ket{\Psi_{j}^{ab}}\bra{\Psi_{j}^{ab}}$$ and $$Pr(o_{j}^{(a)}|\Psi_{ab})=Tr_{ab}(\ket{\Psi_{ab}}\bra{\Psi_{ab}}(\ket{o_{j}^{(a)}}\bra{o_{j}^{(a)}}\otimes \mathbb{I}_{2})) \text{.}$$ I started by representing the density operator for pure states...
  7. P

    Engineering Why Are Some System States Indistinguishable in Observability Analysis?

    https://en.wikipedia.org/wiki/Observability I am studying observability and I try to get some intuition on the topic. Given the observable matrix, we can find the null space. However, the vectors of the null space are states but this differs from the definition of what a state vector of a...
  8. Killtech

    I Can Dirac Delta Functional Observables Be Regarded as True Quantum Observables?

    I ran into an issue of expressing certain types of operators and after a little thinking managed to do it by decomposing them with the help of a weird class of functionals: $$|Φ⟩\rightarrowδ_{\{|Ψ⟩\}}(|Φ⟩)$$ for any state ##|\Psi\rangle##. And yes, it's a Dirac delta acting on the the Hilbert...
  9. J

    I Is the supply of the observable CMB radiation limited?

    About 0.38 Myr after the Big Bang, the universe cooled to about 3,000 K and went through the recombination era. Electrons and protons combined to form neutral hydrogen atoms and the photons became free to travel through space. The freed photons can be considered as photon sources of a small...
  10. nomadreid

    I Confused about the spectrum of an observable

    This is a very elementary question, from the beginnings of quantum mechanics. For simplicity, I refer to a finite case with pure states. If I understand correctly, the spectrum of an observable is the collection of eigenvalues formed by the inner product of states and hence equal to...
  11. Ghost Quartz

    I Simultaneous measurements of 1 observable

    Hi. I'm new to the forum and and I am currently studying quantum mechanics. According Sakurai, page 24, "When the measurement is performed, the system is" thrown into" one of eigenstates of observable". This raised some questions for me: Is possible two measurements simultaneous of one...
  12. PainterGuy

    Why is it giving me different observable canonical form?

    Hi, I found the above observable canonical form using this source: https://www.mathworks.com/help/control/ug/canonical-state-space-realizations.html#mw_a76b9bac-e8fd-4d0e-8c86-e31e657471cc I'm almost certain that I did do it correctly. But the code below gives me different values for B, C...
  13. Cerenkov

    B How can the Observable Universe be a closed system?

    https://www.physicsforums.com/threads/is-the-universe-a-closed-system.620503/ Hello. I was looking back at this thread from 2012 and, to be honest, I'm a bit confused. Quoting Drakkith... To our knowledge it is. At minimum you could count the observable universe as a closed system because...
  14. allisrelative

    B How does the observable Universe have meaning?

    Why does the term observerable universe have any meaning outside of observers on earth? From earth, the observable universe is the universe 13.8 billion light years away in every direction which is large but a finite distance. Say there's a galaxy near the edge of our observable universe...
  15. K

    B Is the Big Bang only about the observable Universe?

    I was watching a video where Lawrence Krauss describes the big bang in terms of the observable universe. He says regions outside the observable universe need not have come from the big bang. Starts At minute 3.
  16. C

    A The Cosmological Principle means infinite Observable Universes

    I am posting to ask for any comments about a couple things. I will post a link to a thread on another forum about this. and would love to hear any and all thoughts about it. the thread begins asking about 2 things. the first one is about how fast we are moving. I,402,00 mph relative to the CMB...
  17. Replusz

    I Mathematical Truth of Physically Observable Quantities

    I assume this is true because using a passive coordinate transformation of the coordinate system should not effect how we measure something. I don't know if this is enough, hence if my original statement is just trivial, or if there is some deeper underlying thing lurking. Is the statement true...
  18. forkosh

    I Von Neumann entropy for "similar" pvm observables

    The von Neumann entropy for an observable can be written ##s=-\sum\lambda\log\lambda##, where the ##\lambda##'s are its eigenvalues. So suppose you have two different pvm observables, say ##A## and ##B##, that both represent the same resolution of the identity, but simply have different...
  19. Z

    Writing a squared observable in Dirac notation

    Edited after post below: Hi, I need to show that the square of the expectation value of an observable takes a certain form in Dirac notation. I know in wave notation that the expectation value is a sandwich integral which looks like this: ##<A>=\int_{-\infty}^\infty \Psi^*(x) \hat A \Psi (x)...
  20. PainterGuy

    B The observable and non-observable parts of the Universe

    Hi, I'm only trying to understand the basic concept. Did the big bang give rise to both observable and non-observable universe? I have been through quite a few source and it seems like that the big bang was the cause of only observable universe and not of unobservable universe. Below I have...
  21. N

    I Dark Matter and quantum observable

    Are there any research about Dark Matter missing some Hilbert space bases or observable? Are bases or observables like spin, momentum, energy, position the basic quantum ingredients of any matter, what is the apriori explanation?
  22. C

    I Is the total energy of the observable universe constant?

    If so, do we have estimates of what that is. Also, if we have estimates of that, what will the final entropy of the universe be, in J/K?
  23. H

    B What is the size of the observable Universe?

    Summary: What is the size of the observable universe and a bit of a rant. I've only recently jumped down the rabbit hole of physics. A social media post on time dilation four months ago got me hooked. Not only has it been a great way to exercise my brain, some of its discovery has been...
  24. P

    I Measurement with respect to the observable Y

    Hello, I would like to start with an assumption. Suppose a system is in the state: $$|\psi\rangle=\frac{1}{\sqrt{6}}|0\rangle+\sqrt{\frac{5}{6}}|1\rangle$$ The question is now: A measurement is made with respect to the observable Y. The expectation or average value is to calculate. My first...
  25. QuasarBoy543298

    I Applying an observable operator on the current state

    hey :) assume I have an operator A with |ai> eigenstates and matching ai eigenvalues, and assume my system is in state |Ψ> = Σci|ai> I know that applying the measurement that corresponds to A will collapse the system into one of the |ai>'s with probability |<Ψ|ai>|2. with that being...
  26. Danny Boy

    A Query about an article on quantum synchronization

    I am currently studying this paper on quantum synchronization. The first page gives an introduction to synchronization and the basic setup of the ensembles in the cavity. My query is on the second page where the following statements are made. Can anyone see why the implication is that all...
  27. C

    Is there an uncertainty in energy measurement in quantum mechanics?

    Let's say I have a system whose time evolution looks something like this: This equation tells me that if I measure energy on it, I will get either energy reading ## E_0 ## or energy reading ## E_1 ## , when I do that, the system will "collapse" into one of the energy eigenstates, ## \psi_0 ##...
  28. nomadreid

    I Time is not an observable, but....

    It is one of the most repeated responses whenever the subject of time comes up. OK, point taken. But a time interval is (represented by) a unitary matrix, and therefore can be written as exp(iK) for K being Hermitian. So it sounds like although a time (interval) is not directly measurable, it is...
  29. nomadreid

    Coherent definition of observable supernatural event?

    I do not want to get into a religious discussion. The question is an abstract one, not directed at any belief system. With that prologue: is it theoretically possible to give a rigorous and coherent definition of "supernatural" that would allow an observable event to be supernatural, independent...
  30. Marrrrrrr

    I QM: I as an Observable & Its Eigenvectors & Eigenvalue

    So, hermitian linear operators represent observables in QM. I (a matrix whose elements are all 1) is certainly a hermitian linear operator. Does this mean that I represent a measurable property? If so, what do we call that property? Identity? Moreover, for any state-vector A, A would be an...
  31. Paul Colby

    B Closed Time-Like Curves: Principles & Observations

    Hi, If I understand correctly, closed time like curves (CTC) are world lines that close upon themselves. What would an observer measure to demonstrate a CTC?
  32. platosuniverse

    B Doesn't there have to be more than one observable universe?

    I was just curious because if space can expand faster than light, doesn't that mean there will be a lot of space that we just can't see? Do objects just vanish because we can't see them? For instance, if a hypothetical alien lived in MACS0647-JD galaxy which is 13.3 billion light years away...
  33. tomdodd4598

    I Do the SU(n) generators represent any observables?

    Hey there, I've recently been trying to get my head around Yang-Mills gauge theory and was just wandering: do the Pauli matrices for su(2), Gell-Mann matrices for su(3), etc. represent any important observable quantities? After all, they are Hermitian operators and act on the doublets and...
  34. T

    B The Universe vs Observable Universe

    After reading the wikipedia article and looking at many other threads on this forum I am still having a hard time understanding the difference between the Observable universe and the entire universe... Why is the entire universe not observable to us? The Big Bang happened 13.8 billion years...
  35. Arman777

    I Observable Universe Tempature and CMB

    It may sound stupid but something bothers me and I want to ask This question come to my mind due to another thread, https://www.physicsforums.com/threads/entropy-and-derivations-is-my-logic-faulty.935533/page-2#post-5910474 In Friedmann Equation we are assuming that universe is homogeneous and...
  36. Urs Schreiber

    Mathematical Quantum Field Theory - Observables - Comments

    Greg Bernhardt submitted a new PF Insights post Mathematical Quantum Field Theory - Observables Continue reading the Original PF Insights Post.
  37. A

    I Exact value for every observable in QM?

    Folks - I'm asking a lot of questions lately (hopefully useful not just for me). By chance, reading about quantum states, I referenced Wikipedia (dubious I know), and came across the following phrase (with a citation, that I will check): "Even in quantum theory, however, for every observable...
  38. A

    A Observable particles as asymptotic states....

    I've read Arnold Neumaier's excellent Insight article on virtual particles, but I'm very confused about one thing: Observable particles are considered to be on-shell, and as 'asymptotic states' at time +- infinity. Now, in a scattering experiment, I may produce a new particle, which will travel...
  39. Chris Miller

    B Simultaneity in Non-Observable Universe: Is it Possible?

    Is there any method/model for determining simultaneity of events farther apart than light can ever travel? I'm guessing not. Would it be wrong to say that the non-observable universe exists only in our past (or future)?
  40. Arman777

    I Observable Universe Size in Different Perspectives

    I am reading The Essential Cosmic Perspective and there says "We cannot observe light coming from anything more then 14 billion-light-years away". ( In my opinion this statement is wrong cause observable universe diameter is 46.5 billion light years. I guess authors meant something else, or...
  41. O

    B Age of the universe: observable or entire universe?

    I was wondering if we are only aware of the observable universe, and the actual universe could be infinite, what do we mean when we say the age of the universe is 14 billion years? Are we talking about the age of only the observable universe or the whole universe?
  42. F

    I Does a field operator always commute with itself?

    In quantum field theory (QFT), the requirement that physics is always causal is implemented by the microcausality condition on commutators of observables ##\mathcal{O}(x)## and ##\mathcal{O}'(y)##, $$\left[\mathcal{O}(x),\mathcal{O}'(y)\right]=0$$ for spacelike separations. Intuitively, I've...
  43. R

    I Centre of mass of the observable universe

    Ok so I have read several of the threads regarding the impossibility of determining the centre of the universe based on observations of expansion of the universe. That one seems to have been beaten to death. So this is a slightly different question. When we look at all the matter that we can...
  44. Grinkle

    B What is meant by the size of the early observable universe?

    As a reference I will make the vague statement that others have posted the below on these forums: As one rolls back the clock, the size of the observable universe becomes smaller than it is today. Does this mean that all of what we observe today was more densely packed yesterday than it is...
  45. Demystifier

    A Value of observable in statistical ensemble interpretation

    The statistical ensemble interpretation (SEI) is supposed to be a minimal interpretation of QM with the smallest amount of philosophy, vagueness and controversy. Yet it turns out not to be the case. For instance Ballentine, the inventor of SEI, interprets Bell theorem as a strong evidence of...
  46. digogalvao

    Proof of expectation value for a dynamic observable

    Homework Statement Show that: d<A(q,p)>/dt=<{A,H}>, where {A,H} is a Poisson Bracket Homework Equations Liouville theorem The Attempt at a Solution <A>=Tr(Aρ)⇒d<A>/dt=Tr(Adρ/dt)=Tr(A{H,ρ}) So, in order to get the correct result, Tr(A{H,ρ}) must be equal to Tr({A,H}ρ), but I don't think I can...
  47. M

    I Are superposition states observable?

    The way I am coming to understand it, the allowed states that an observable can be "observed/measured" in are defined by the eigenvectors (and associated eigenvalues) of the observable's operator. Since those eigenvectors form a basis and span the space of vectors defined by the operator, a...
  48. G

    A Is the matter-antimatter annihilation observable in priciple

    The youngest epoch of the universe we can observe so far is the CMB. It is theorized that systematic and accurate measurement of gravitational waves could allow us to "see" events from even earlier cosmic epochs. If we go to even earlier cosmic epochs we have what must have been a very singular...
  49. T

    Rapidly changing Hamiltonian and an observable

    Homework Statement Consider an experiment on a system that can be described using two basis functions. We begin in the ground state of a Hamiltonian H0 at a time t1, then rapidly change the hamiltonian to H1 at the time t1. At a later time tD>t1 you preform a measurement of an observable D...
  50. U

    Hamiltonian operator affecting observable

    I'm working on this problem "Consider an experiment on a system that can be described using two basis functions. In this experiment, you begin in the ground state of Hamiltonian H0 at time t1. You have an apparatus that can change the Hamiltonian suddenly from H0 to H1. You turn this apparatus...
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