What is Interpretation: Definition and 831 Discussions

An interpretation is an assignment of meaning to the symbols of a formal language. Many formal languages used in mathematics, logic, and theoretical computer science are defined in solely syntactic terms, and as such do not have any meaning until they are given some interpretation. The general study of interpretations of formal languages is called formal semantics.
The most commonly studied formal logics are propositional logic, predicate logic and their modal analogs, and for these there are standard ways of presenting an interpretation. In these contexts an interpretation is a function that provides the extension of symbols and strings of symbols of an object language. For example, an interpretation function could take the predicate T (for "tall") and assign it the extension {a} (for "Abraham Lincoln"). Note that all our interpretation does is assign the extension {a} to the non-logical constant T, and does not make a claim about whether T is to stand for tall and 'a' for Abraham Lincoln. Nor does logical interpretation have anything to say about logical connectives like 'and', 'or' and 'not'. Though we may take these symbols to stand for certain things or concepts, this is not determined by the interpretation function.
An interpretation often (but not always) provides a way to determine the truth values of sentences in a language. If a given interpretation assigns the value True to a sentence or theory, the interpretation is called a model of that sentence or theory.

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  1. F

    Interpretation of Cross Section of p,n reaction mb or mb/MeV

    Dear Forum : I'm reading a cross section data of 20MeV proton + 16O reaction from ICRU 63. ( as attachment and link http://ppt.cc/qf-9 ) The total cross setion of (p,n) reaction is 4.372mb However, the cross section of emitting neutron of energy between 0 to 1.5MeV is 0.91 mb / MeV. The...
  2. naima

    Zurek's existential interpretation

    Hi PF I am reading this paper and this one. Zurek insists on the fact that pointer states emerge when the same information is imprinted in a huge number of disjoint subsystems of the environment. Many observers can read those informations and agree with the others. He never tells what this...
  3. L

    Laplace transform interpretation

    Hello, We were introduced to Laplace transforms in my ODE class a few days ago, so naturally I went online to try to figure out what this transform actually is, rather than being satisfied with being able to compute simple Laplace transforms. The Wikipedia page for the transform says it...
  4. T

    Convergence in Uniform and L2 sense, function interpretation

    Let: gn(x) = 1 in [1/4 - 1/n2 to 1/4 + 1/ n2) for n = odd 1 in [3/4-1/n2 to 3/4 + 1/n2) for n = even 0 elsewhere Show the function converges in the L2 sense but not pointwise. My issue is in how I should use the definition of...
  5. atyy

    Gibbs paradox in the Bohmian interpretation

    The Gibbs paradox in statistical mechanics is usually resolved by saying that particles do not have distinct trajectories, and so are truly identical. For example, http://ocw.mit.edu/courses/physics/8-333-statistical-mechanics-i-statistical-mechanics-of-particles-fall-2007/lecture-notes/...
  6. bohm2

    Vaxjo Interpretation of Wave Function

    For those interested in this stuff, what is your opinion of this less well-known Vaxjo interpretation: Vaxjo Interpretation of Wave Function: 2012 http://arxiv.org/pdf/1210.2390.pdf "Einsteins Dream”-Quantum Mechanics as Theory of Classical Random Fields http://arxiv.org/pdf/1204.5172.pdf...
  7. bcrowell

    Exploring the Limits of Dark Matter Detection: Insights from the LUX Experiment

    An article in Nature reports a negative result from the LUX experiment's attempt to directly detect dark matter: http://www.nature.com/news/no-sign-of-dark-matter-in-underground-experiment-1.14057 Can anyone give some context? How does its sensitivity compare with that of previous...
  8. M

    Minimal no collapse interpretation

    Is this a proper summary of a minimal-no-collapse interpretation? (I like to call it the fuzzy world interpretation, but I suppose I'm the only one) When objects entangle, it constrains their degrees of freedom. As they entangle with more and more objects, their degrees of freedom are...
  9. L

    Interpretation of an impulse graph

    Which of the following is true if the mass is at rest at t=0 ? A. Velocity of the mass is decreasing btwn 10 and 20 seconds. B. The accel. of the mass is constant between 0 and 10 seconds C. At 40 seconds the mass is stationary. D. The distance trsveled by the mass bten 0 and 10 seconds is...
  10. MalachiK

    Classical interpretation of the photoelectric effect

    I've been reading through the posts on this forum that deal with the photoelectric effect as evidence for the quantization of the EM field. In all of the introductory texts I've read, the cut off frequency and the dependence of the photoelectron energy on the frequency of the light are...
  11. Z

    Spherical Coordinate System Interpretation

    Homework Statement (a) Starting from a point on the equator of a sphere of radius R, a particle travels through an angle α eastward and then through an angle β along a great circle toward the north pole. If the initial position is taken to correspond to x = R, y = 0, z = 0, show that its...
  12. Z

    What's the physical interpretation of ρ for dipole forbidden channel?

    Consider we have a \Lambda type three level system, the one upper level is denoted by 3, and the two lower levels are denoted by 1 and 2. Assuming that the transitions between 1\leftrightarrow3 and 2\leftrightarrow3 are dipole alowed, while the transition between two lower states 1 and 2 is...
  13. T

    Interpretation for identity with binomial coefficients

    I am looking for a counting interpretation to make the following identity evident: \sum_{k=0}^{n-j}(-1)^k\binom{j-1+k}{j-1}\binom{n}{j+k} = 1 The form of it looks like inclusion-exclusion. The sum is 1, more or less independent of j. So that makes me think it would be something like "how...
  14. T

    Can Quantum Mechanics be studied without the Copenhagen interpretation

    Hello everyone, I'm a doctoral student of particle physics in ETH Zurich, and have a question in fundamental QM. I remember a friend telling me that the professor that taught him Quantum Mechanics in ETH Zurich did not believe in the Copenhagen interpretation, and thus taught the class...
  15. M

    Geometrical integral interpretation

    Hi friends, i have i request for you. For my statics exam i need integrals and i found this page in russian, and can not find rest or even know how it's called because when i translate title i don't get any results. Can you please help me and tell me where can i find the rest...
  16. bohm2

    Does the PBR theorem rule out the 'minimalist' Bohmian interpretation?

    I had trouble understanding this and had brought it up before but I thought I'd start a new thread on it, in case anyone has any further insights. In the original Leifer summary discussing the implications of PBR theorem on the various QM interpretations, Leifer argued that realists should...
  17. tom.stoer

    Question regarding the Many-Worlds interpretation

    Let's prepare and experiment with individual photons moving along the z-axis and polarization in the xy-plane such that a detector registers - polarization along the x-axis with 90% and - polarization along the y-axis with 10% According to the MWI for each registered photon there's a...
  18. M

    Physical Interpretation of Laplace's Transform

    Hi all, I am trying to hard to understand integral's transform. While an interpretation of Fourier transform is relatively easy to furnish in terms of signal decomposition and harmonics, it seems the "meaning" of Laplace transfrom is more subtle (in spite of the similarities between the two)...
  19. SamRoss

    What was Schrodinger's interpretation of his own equation?

    I have heard that Schrodinger's interpretation of his equation is different from the modern interpretation. What was Schrodinger's interpretation of his own equation and what did he think ψ represented?
  20. L

    Flux/ Divergence Theorem interpretation

    Hello, I am approaching the end of my multivariable/ vector analysis "Calc III" class and have a question about flux. My book states that flux, ∫∫ F \bullet N dS measures the fluid flow "across" a surface S per unit time. Now, the divergence theorem ∫∫∫ divF dV measures the "same...
  21. B

    Non-Integrability of a Pfaffian - Geometric Interpretation?

    The question of Solving a Pfaffian ODE can be interpreted as the question of finding the family of surfaces U = c perpendicular to a surface f generated by the vector field $$F(x,y,z) = (P(x,y,z),Q(x,y,z),R(x,y,z))$$ At each point, the gradient of the family of surfaces U = c will either...
  22. Mandelbroth

    Interpretation of the Gradient Vector?

    I've always thought of the gradient of a scalar function (id est, ##\nabla\varphi##) as being a vector field. However, I started thinking about it just now in terms of transformation with respect to coordinate changes, and I noticed that the gradient transforms covariantly. Thus, shouldn't the...
  23. J

    Experiment to test if many worlds is the correct interpretation

    hi there. I studied physics for years, even went as far as getting a PhD. but that was 13 years ago, since then rusty. Anyway something occurred to me and I wondered what you all would think about it. My question is, can anyone think of an experiment you could do to check if the "many...
  24. P

    The Many-Worlds Interpretation: how far does it go?

    The Schrodinger's cat thought experiment provides two possible outcomes in the many worlds interpretation; it is dead in one universe, and alive in the other. There are however many other possibilities of what could happen; there are wave functions concerning the positions which the cat may...
  25. L

    Confidence interval interpretation mistake

    Hi all. I've been thinking about this question a lot for the past few days and it seems to me that I'm committing a mistake somewhere along the way, but certainly can't figure out where. Here's one of the interpretations which I've encountered most frequently and think is the right one (here's...
  26. C

    Interpretation of the functional Z (in Zee).

    In Zee's book at page 12 in both editions he finds that he can write the amplitude $$\langle q_f|e^{-iHT} |q_i\rangle = \int Dq(t) e^{iS} $$ where T is the time between emission at ##q_i## and observation at ##q_f##. He then states that we often define $$Z = \langle 0 | e^{-iHT} |0...
  27. B

    Is LET an Interpretation of SR?

    There has been a narrative that has run through a number of posts on special relativity. It establishes the idea that LET (Lorentz Aether Theory) is an interpretation of SR (Special Relativity). I personally believe this is a false narrative and that there is at least one fact that must be...
  28. marellasunny

    Interpretation of an ideal engine torque,power curves

    Attached you will find the torque vs engine rpm and power vs engine rpm curves for an 'ideal engine' and also for a 'normal SI engine'. 1.(for the 1st ideal engine curve) Is it 'ideal' that the torque curve should decrease as the engine rpm increases? Why? Does this mean that 'ideally' in a...
  29. nomadreid

    Elementary questions about inner product interpretation

    When one says that <\varphi|\psi> is the probability that \psi collapses to \varphi, does this "collapse" necessarily involve a measurement (so that one would have to find the implicit Hamiltonian)? Or does this just exist as part of the evolution of the wave function, perhaps the vacuum energy...
  30. S

    Interpret Relativistic Momentum: Facts & Popular Opinion

    I understood the derivation of relativistic momentum, but I am uncertain of how to exactly interpret it. One could interpret the arrangement of terms to be relativistic mass times velocity, and this appears to be in agreement with data from particle accelerators (or so I have been led to...
  31. B

    Copenhegen interpretation or Many World Interpretation?

    Can there be an experiment (even a thought experiment), which could settle the debate CI vs MWI? Now a days many scientists seem to favour MWI. I find it interesting because it perhaps allows time travel (the possibility of an observer going back to his/her own past) while avoiding the...
  32. C

    Classical interpretation of Wave Motion

    Ive been learning a lot about how similar waves and particles are at the fundamental level, but today i was assaigned to discuss the difference between the CLASSICAL physics of particles vs Classical Physics of waves. Differences and similarities and well as how momentum is/isnt diferent as...
  33. S

    Quantum Bayesian Interpretation of QM

    Any comments (pro-con) on this Quantum Bayesian interpretation of QM by Fuchs & Schack ?: http://arxiv.org/pdf/1301.3274.pdf
  34. C

    Interpretation and relevance of current matrix element

    In reading about the axial anomaly I stumbles across a matrix element on the form $$\langle p,k|j^{\mu 53}|0\rangle. $$ and I have seen similar matrix elements turn up other places. But when matrix elements (correlation functions) of the form $$ \langle 0 |T \phi(x) \phi(y)|0\rangle $$...
  35. N

    Interpretation of QED in the Standard Model

    Three related questions on which I could use some help: a] In another thread, Bill_k posted something like: "Electrons, being charged, could exchange energy by exchanging a virtual photon." ok, yet I thought electrons usually interacted via the EM field ['real' photons]... So how...
  36. C

    Dipole excitation response function - physical interpretation

    Hi everyone, I'm a new member but it's not the first time I look at the forum. Well, I don't know if this is the right section to post my question. I think it is related to quantum mechanics interpretation too. Anyway, let's have a look at my problem. I've computed cross section for photon...
  37. J

    Cosmological redshift interpretation

    Can the cosmological redshift be interpreted as atomic frequencies increasing by the scale factor as the Universe expands? This explanation seems closer to the truth than the popular idea that a photon's wavelength somehow expands while it travels to us from a distant galaxy. Metric expansion...
  38. C

    Question about the Many-Worlds Interpretation

    I get the basics of the interpretation, but I don't understand one specific element. If there are parallel worlds, where is this parallel world? Is it like a stack of newspapers, each page being a different world, where the entire, connected newspaper is the universe? What I'm asking is if this...
  39. C

    Is this 'e' interpretation correct?

    Considering e is the limit->+oo of (1+1/n)^n, then is e "what you get if you wait for the least gain, by waiting for the most amount of time"? Something like "e is the patience number".
  40. A

    [BASIC] Interpretation of multiplication

    Hello, I know this question may be absurd or very basic, but I need to know what it means when two variables with different units are being multiplied. I need to know what multiplication is in physics, in order to make sense of formulas (such as momentum, force, energy formulas) without only...
  41. G

    Understanding the Copenhagen Interpretation

    This is from Wikipedia regarding the first point of the Copenhagen Interpretation: What does it mean to make a measurement? Is this something that only living beings do or can a dead particle make a measurement? Why does measurement collapse the wave function.
  42. Jameson

    MHB How should I interpret this question?

    Tell me how you understand this question. I've removed the details of the calculation to focus on the language and how certain ideas should be expressed. I know it's a weird thing to ask so just try to answer how you can. Calculate __________ for each $v_1, v_2, v_3$ and $p(t)$.
  43. Q

    Born's Interpretation of Wavefunctions

    (The following is a purely qualitative consideration of Quantum Mechanics) In a particular Quantum Mechanics text, I've come across the following quote which I'm having some difficulties interpreting. "We describe the instantaeous state of the system by a quantity \Psi , which satisfies a...
  44. T

    Hilbert Space Interpretation of Fourier Transform

    I've been taught (in the context of Sturm-Liouville problems) that Fourier series can be explained using inner products and the idea of projection onto eigenfunctions in a Hilbert space. In those cases, the eigenvalues are infinite, but discrete. I'm now taking a quantum mechanics course, and...
  45. alyafey22

    MHB Find a closed form interpretation for the integral :

    $\displaystyle \int^{\infty}_0 \, \frac{\log (1+e^{ax})}{1+e^{bx}}\, dx $ I am not sure whether it can be solved :confused:
  46. N

    Interpretation of the fictitious force

    Hello. Before I ask a question I want you to remind that it is my first time to use this page. And I am not even good at speaking english. My question is about the fictitious forces. I have made a long proof for the formula of the force in the non-inertial reference frame with the second law of...
  47. U

    Green's function? Physical interpretation?

    Green's function?? Physical interpretation?? Hi friends.. Can anyone help me to understand the physical interpretation of the green's function with help of some physical application example such as that from electrostatic?? I am unable to understand what is meant by linear operator in green...
  48. Quotidian

    The Many-Worlds Interpretation of QM

    Greetings all. I'm a new poster here but have spent some time on philosophy forums previously. I subscribe to New Scientist and try and stay reasonably current with science, on the popular level at least. This week they have had a feature about physical cosmologies and 'theories of...
  49. kai_sikorski

    Probobalistic interpretation of a PDE

    Consider the following PDE. A lot of this is from "Numerical Analysis of an Elliptic-Parabolic Partial Differential Equation" by J. Franklin and E. Rodemich. \frac{1}{2} \frac{\partial^2 T}{\partial y^2} + y \frac{\partial T}{\partial x} = -1 With |x|<1, |y| < \infty and we require...
  50. Jim Kata

    Can Topos Theory Resolve Quantum Mechanics Paradoxes?

    I'm kind of rambling here since I'm not sure how to formulate what I'm trying to say. Is there an interpretation of quantum mechanics that uses topos theory? As in is there a way to fix some of the logical paradoxes of QM interpretations, by using a many valued logic system?
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