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. soothsayer

    I Questions about ensemble interpretation of QM

    I've been reading up on the ensemble interpretation (aka statistical interpretation) of QM and it's making a bit more sense to me that it did on the onset, but I still have some questions about how it is consistent with experimental observations of various QM experiments, especially...
  2. N

    I Thermal interpretation and Bell's inequality

    Concerning p.198 of Bell's famous 1964 paper http://cds.cern.ch/record/111654/files/vol1p195-200_001.pdf How does TI explain Bell's move from the first equation to the second equation? Under TI, what is the physical significance of this move? Thank you.
  3. vanhees71

    A The thermal interpretation and measurement

    [Moderator's note: Spin off from previous thread since this is a separate topic from that one.] It's hard to expect that it ever gets a standard interpretation, because it contradicts the very observations which lead to the discovery of modern quantum including Born's probability interpretation...
  4. Buzz Bloom

    I A variation of the Multiple World Interpretation

    The multiple worlds are not real, but instead they are contingent. This mean that each of the various possible combinations of all of the possible future measurements or relevant interactions that change the probabilities, that could possibly happen according the wave function of everything...
  5. Beelzedad

    I Is my interpretation of this three dimensional improper integral correct?

    In Physics/Electrostatics textbook, I am in a situation where we have to find the electric field at a point inside the volume charge distribution. In Cartesian coordinates, we can't do it the usual way because of the integrand singularity. So we use the three dimensional improper integral...
  6. XLAYZ

    A Interpretation of Bi-207 decay spectrum

    I measured the decay spectrum of Bi-207 as a beta source with scintillation detector and now I am trying to interpret the information given by the spectrum. As far as I know, the Bi-207 nuclei decay to the excited states of Pb-207 primarily via EC and a small beta+ branch, emitting beta...
  7. L

    I "Knowledge" in Psi-Epistemic Interpretation Fundamental or Emergent?

    Is "Knowledge" in quantum Psi-Epistemic interpretation fundamental or emergent? And what does it mean? What do you think? https://backreaction.blogspot.com/2019/08/the-problem-with-quantum-measurements.html "One way to deal with the measurement problem is to argue that the wave-function does...
  8. F

    I Likelihood, posterior, prior interpretation and credibility/confidence

    I try to understand the following article : testing general relativity from curvature and energy contents at cosmological scale I don't understand the title of figure 1 : where it is indicated the prior values for ##\omega_{b}, \omega_{\text{cdm}}, \text{h}, ...## : what do authors mean by...
  9. D

    A Soft photons and the ETH interpretation of QM

    As the thread on Jürg Fröhlich's paper on the "ETH interpretation" of QM has been closed, I want to consider here a specific point. Fröhlich points out that this interpretation requires the inclusion of massless particles and I think this is the key to getting a physical understanding...
  10. L

    I The Cellular Automaton Interpretation of Quantum Mechanics

    Why aren't you guys discussing this? http://de.arxiv.org/abs/1405.1548 The paper is 259 pages. And it will take me a year to read it. The Cellular Automaton Interpretation of Quantum Mechanics doesn't use any wave function. Just please tell me. How does it explain for example the double slit...
  11. MichPod

    A How momentum measurement is defined in Pilot Wave interpretation?

    Considering pilot wave interpretation, a singular particle measurements are fully defined (?) by knowing its wave function (a pilot wave) and the position of the "particle" (some hypotetical point particle riding on the wave). This should provide some sort of "realistic" explanation of how a...
  12. S

    A Relation between Bohm's Interpretation and Implicate order?

    What relation exists between Bohm's Implicate-Explicate order and De Broglie-Bohm interpretation? If any relation exists at all...
  13. F

    I Interpretation of QM in the Heisenberg Picture

    This is in reference to a question, never fully resolved, posed here: https://www.physicsforums.com/threads/interpretation-of-the-heisenberg-picture-in-qm.816449/ The von Neumann postulates for Quantum Theory - Evolution (Schrödinger's equation) and Projection (Born's rule) are always framed...
  14. mollwollfumble

    A Bohr's contribution to the Copenhagen interpretation

    I wish to learn about Bohr's contribution to the Copenhagen interpretation by reading his original papers on QM, preferably in English. Which papers are most important?
  15. Lone Wolf

    Static equilibrium -- interpretation of forces

    I solved this question correctly, however I have a question regarding how I should work with the weight of the firefighter climbing the ladder. When drawing the force diagram for this problem, I should only include forces acting on the ladder, right? Which means I would represent the normal...
  16. Celso

    I Partial derivative interpretation

    How do I interpret geometrically the partial derivative in respect to a constant of a function such as ##\frac{ \partial}{\partial c} (acos(x) + be^x + c)^2##?
  17. F

    I QQplot, question about my textbook's interpretation

    Hello everyone. I am currently reading a book on quality control. In the part of experimental design, here, the effect vector, beta, takes the following form: beta=(81.75, 9, 0.75, -4, -0.5, 0.25, 3, -0.25), which corresponds to the effects of lenght, width, type of steel and their interactions...
  18. P

    I Interpretation of Schrodinger's Cat

    [Moderator's note: Discussion spun off from another thread.] I guess you don't get the thought experiment then... Schrodinger devised it precisely because it's the inevitable consequences of the standard model of QM, though not with regards to cats specifically due to decoherence (which wasn't...
  19. A. Neumaier

    I More on the thermal interpretation

    I just finished a 4th part of my series of papers on the thermal interpretation: Foundations of quantum physics IV. More on the thermal interpretation This paper continues the discussion of the thermal interpretation of quantum physics. While Part II and Part III of this series of papers...
  20. A. Neumaier

    I Spectra in the thermal interpretation

    In any quantum system, the differences of the energy levels (the eigenvalues of the Hamiltonian ##H##) are in principle directly observable, since they represent excitable oscillation frequencies of the system and thus can be probed by coupling the system to a harmonic oscillator with adjustable...
  21. A. Neumaier

    I The double slit in the thermal interpretation

    I prefer to discuss in the double-slit experiment light in place of electrons since it makes the underlying principle more clear. Consider the quantum system consisting of the screen and an external (classical) electromagnetic field. This a very good approximation to many experiments, in...
  22. A

    A Interpretation of Decoherence

    My question is about decoherence, specifically in regards to its interpretation in Hilbert space. In every single textbook I've read, decoherence has always been explained by (1) introduce density matrix and (2) explain that interactions with environment cause off-diagonal terms (coherences)...
  23. I

    Physical interpretation of this integral equation involving distance and time?

    I am able to solve the problem however if x was position and t was time how is this problem interpreted? I know, for example that ##\frac{dx}{dt}## tells us how the position of something changes as time changes (or instantaneous change) and an integral gives a net change so to speak.
  24. Demystifier

    A Schrodinger's Cat and the thermal interpretation

    [Moderator's note: spin-off from a previous thread since this discussion is a separate topic.] In this sense, the Schrodinger's famous thought experiment prepares the cat in a superposition of dead and alive. I still don't see how TI can possibly prevent it.
  25. Demystifier

    A Proof that the thermal interpretation of QM is wrong

    Preface After a lengthy discussion of the thermal interpretation of quantum physics in https://www.physicsforums.com/threads/the-thermal-interpretation-of-quantum-physics.967116/ , now I think I can prove that it is wrong, i.e. that it doesn't solve the measurement problem in a way it claims it...
  26. J

    Interpretation of distance mentioned as degrees

    What is the image that comes to mind/meaning behind the above statements where an objects is seen/appears 'to be (angle) diameter of the Earth? My interpretation is that if the given angle is drawn with one object as the vertex then the diameter of the second object subtends the given angle.(?)
  27. Mr Davis 97

    I What are the properties of a plane cut into regions by a set of lines?

    Problem: Let ##L## be a set of ##n## lines in the plane in general position, that is, no three of them containing the same point. The lines of ##L## cut the plane into ##k## regions. Prove by induction on ##n## that this subdivision of the plane has ##\binom{n}{2}## vertices, ##n^2## edges, and...
  28. PeterDonis

    A How does the thermal interpretation explain Stern-Gerlach?

    I am posting this question separately from the ongoing thermal interpretation thread started by @A. Neumaier since it is a question about a specific experiment and how that interpretation explains it. The experiment is the Stern-Gerlach experiment. For concreteness, I will specify that we are...
  29. Celso

    Simple harmonic motion interpretation problem

    I'm in trouble trying to understand the expression ##t= \frac{1}{\omega} cos^{-1}(x/A)## that comes from ##x = Acos(\omega t)##, in which ##A## is the amplitude, ##t## is time and ##x## is displacement. When ##x = 0##, ##t = \frac{\pi}{2\omega} ##, shouldn't it be 0 since there was no movement?
  30. A. Neumaier

    I The thermal interpretation of quantum physics

    A complete description of the thermal interpretation of quantum physics can be found in my just finished papers (for the bare bones, see Section 2.5 of Part II) Foundations of quantum physics I. A critique of the tradition, Foundations of quantum physics II. The thermal interpretation...
  31. Cerenkov

    B General Relativity: Finding Info on Interpretation

    Hello. I have some questions about general relativity that (I hope) will be permitted in this forum. Not long ago I discovered that there is more than one interpretation of GR. Now, I believe that the issue of interpretation is considered to be philosophy and therefore off topic. If that's...
  32. Demystifier

    I Find your ideal quantum interpretation

    Find the interpretation of QM that best suits your personality. You don't need to think much about quantum interpretations to decide which one is the best for you. Just choose one of the offered answers to a couple of questions on the graph. You don't need to think much about the offered...
  33. J

    I What is Stochastic Quantum Mechanics (in simple terms)?

    Could someone, in laymen's terms explain to me what stochastic mechanics is?
  34. L

    A Interpretation of state created by the field in free QFT

    Let us consider QFT in Minkowski spacetime. Let ##\phi## be a Klein-Gordon field with mass ##m##. One way to construct the Hilbert space of this theory is to consider ##L^2(\Omega_m^+,d^3\mathbf{p}/p^0)## where ##\Omega_m^+## is the positive mass shell. This comes from the requirement that there...
  35. entropy1

    B Is the Universe information?

    Is the problem with interpretations of quantum mechanics that one can describe the universe consisting of "stuff" that exists ontologically in different but conflicting ways, so that the universe can really only be described informationally instead of ontologically? That is: does the universe...
  36. S

    I Interpreting SM Lagrangian "differential particle" terms

    The Standard Model Lagrangian contains terms like these: ##-\partial_\mu \phi^+ \partial_\mu\phi^-## ##-\frac{1}{2}\partial_\nu Z^0_\mu\partial_\nu Z^0_\mu## ##-igc_w\partial_\nu Z^0(W^+_\mu W^-_\nu-W^+_\nu W^-_\mu)## How should one interpret the "derivative particle fields" like...
  37. J

    I Energy in Everett's Many-worlds Interpretation

    Hi, Is anybody able to explain how energy is "distributed" in the many-worlds interpretation. I'm using scare quotes as I think this may be the wrong line of thought. It's tempting to imagine energy being distributed amongst subsequent branches as the wave function evolves but I'm not certain...
  38. W

    Thermal Physics: Interpretation of equilibrium constant

    For a reaction defined as such, $$A\rightleftharpoons B$$ the equilibrium constant ##K## is defined by ##K = p_B / p_A##, with ##p## denoting the partial pressure (edit: at equilibrium). However, if ##K<<1##, which implies ##p_A >> p_B##, it is said that the backwards reaction dominates and that...
  39. rpthomps

    I Interpretation of a cross section vs energy graph

    Hello. I am reading DeAngelis - Introduction to particle and astroparticle physics and I have come across a plot showing proton proton cross section vs energy. I am trying to reconcile the statement in the book that says cross section total = cross section elastic whenever there is no available...
  40. Demystifier

    Against "interpretation" - Comments

    Greg Bernhardt submitted a new blog post Against "interpretation" Continue reading the Original Blog Post.
  41. P

    I Grover algorithm geometric interpretation

    Good day everybody, I'm currently working on the Grover algorithm. You can also illustrate this process geometrically and that's exactly what I have a question for. In my literary literature one obtains a uniform superposition by applying the Hadamard transformation to N-qubits. So far that's...
  42. R

    I Physical interpretation of a plasma (Te, Tv, Tr)

    I'm trying to understand the physical implications of electron temperature (Te), vibrational temperature (Tv), rotational temperature (Tr) and translational temperature (To) of a plasma. I am reading often that Te > Tv > Tr ≃To, in terms of what is happening inside the plasma what does this...
  43. C

    I QFT Interpretation of Electron and Attached EM Field

    This is an elementary question on visualizing the interaction of an electron with the surrounding EM field in QFT. I believe in QFT the electron is viewed as an excitation of the Electron matter field with an associated coupling constant between the electron field and EM field (say q) - q...
  44. Math Amateur

    MHB Geometric Interpretation of k-Forms from H&H's Vector Calculus

    I am reading the book: "Vector Calculus, Linear Algebra and Differential Forms" (Fourth Edition) by John H Hubbard and Barbara Burke Hubbard. I am currently focused on Chapter 6: Forms and Vector Calculus ... I need some help in order to understand some notes by H&H following Figure 6.1.6 ...
  45. Math Amateur

    MHB 1-Forms .... Interpretation by Bachman ....

    I am reading David Bachman's book: "A Geometric Approach to Differential Forms" (Second Edition) ... I need some help with some remarks Bachman makes near the start of his section on 1-forms ... The relevant section reads as follows:In the above text from Bachman we read the following: " ...
  46. G

    Synoptic Chart Interpretation

    Hello, I wonder if you might be able to help me understand what's happening on this synoptic chart? What I can see, there appears to be an occluded cyclone in the Atlantic moving North/Eastwards. I'd like to know why there is an extended cold front and warm front merging in the centre of the...
  47. MichPod

    I What has changed since the Copenhagen interpretation?

    If to look at the foundations of QM and if to ignore various not much verifiable alternative interpretations of QM which emerged since the Copenhagen, starting with Bohm and Everett, what are the commonly accepted and recognized changes to the original views of the QM creators? There are planty...
  48. J

    A Hardy's Paradox and lorentz invariant realist interpretation

    Does Hardy's paradox show that all realist interpretations cannot be made lorentz invariant? Or is it just realist hidden variable theories?
  49. J

    I Can the Many Worlds interpretation state the Born Rule as a postulate?

    Every derivation from the MWI of the born rule is circular. http://fmoldove.blogspot.com/search?q=MWI So my question is, can the MWI state the born rule as a postulate (without deriving) and still be a coherent interpretation of probability? The most famous argument against this notion is by...
  50. F

    I Normalized source function: physical interpretation

    Hello, In physical radiative processes, I am studying the solution of the following equation : ##S=(1-\epsilon) J + \epsilon B## with : 1) S the source function 2) J the mean intensity ( ##J=\dfrac{1}{2}\int_{-1}^{1} I_{\nu}\text{d}\tau_{\nu}##) 3) B the Boltzmann distribution 4)...
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