Interpretation Definition and 834 Threads

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. Fra

    I Newtonian "schema/paradigm" != Newton's mechanics

    As this has been a key point, in several threads in particular the last close one https://www.physicsforums.com/threads/local-mechanism-for-nonlocal-anticorrelations-inside-spin-theory.1066463/ I though I would clarify what this means becuase it is a pity to confuse it with classical (newtons)...
  2. gentzen

    I Can I take the transactional interpretation seriously?

    My first "active" encounter with the transactional interpretation happened when I tried to react to Ruth Kastner's criticism of consistent histories. My next encounter happened when I was fighting with reciprocity occuring for crystal effects in electron scattering, and hoped for help from time...
  3. S

    Find the values of a and b to get max/min of certain expression

    I don't think I understand what the question is asking. Find ##a## and ##b## so that the maximum takes the minimum values? If ##a## and ##b## are real numbers, the maximum values of ##3a^2+2b## and ##3b^2+2a## are infinity. How can infinity take minimum value? I have calculated the values of...
  4. B

    I Experiment distinguishes Standard QM vs Bohm: Asymmetric beam splitter

    Background I was reading a paper, Delayed Choice Experiments and the Bohm Approach by Basil Hiley and Robert Callaghan. The Wheeler's Delayed Choice experiment was explained in a way that was very easy to understand. An interesting point in this paper is that when a Mach–Zehnder interferometer...
  5. PeterDonis

    A Gravity in the Thermal Interpretation

    This question is mainly for @A. Neumaier, but I post it in public in case others are interested. The usual reason given for needing to quantize gravity is, heuristically, that, in the presence of quantized stress-energy where there can be a superposition of different stress-energy tensors...
  6. G

    A Critique of Everett's "Many Wolds" interpretation

    Without proof many folks in the Physics community give the "many worlds" interpretation of the measurement/decoherence problem a level of regard that I believe is wholly unwarranted. To quote Carlo Rovelli ".. is it really worth giving credence to the real and concrete existence of infinite...
  7. K

    I What is the true nature of worlds in the Many-Worlds Interpretation?

    The "worlds" of MWI do not actually appear in the theory behind it. They are, so to speak, an interpretation of the interpretation. But what exactly are worlds? The picture begins with an interaction. In general this results in an entanglement. If we decompose it into product terms, each of...
  8. U

    How to interpret thermal shift experiment's work for binding?

    Hello, PF I’m new here. Can someone please help me explain how to interpret thermal shift experiments work for binding? Apparently the data you receive from such experiment is a derivative dF/dT where F=fluorescence and T=temperature; and I’m very confused because isn’t the experiment supposed...
  9. P

    Quantum spin superposition interpretation

    Here is my workings out: $$$$ If a particle's spin of magnitude ##\frac {\hbar}{2}## is prepared along direction ##\vec r_1## and subsequently its spin is measured along direction ##\vec r_2 ## at an angle ##\vec \theta ## to ##\vec r_1##, the probability of its being found "spin up" along is...
  10. S

    I Many worlds interpretation with unequal probabilities

    Let's pay a visit to one of Schrodinger's cats. In the classical statement of the case, we have to decide if the cat is alive or dead when the probability of the radio-active decay mechanism has a 50/50 chance of releasing the cyanide, most often posed as 60 minutes. If I understand the MW...
  11. dextercioby

    I Interpretation of temperature in liquids/solids

    Usually, the mental image of temperature is: an internal property of a bulk of matter, which typically describes the average kinetic plus rotation/vibration energy of molecules, so we imagine a gas in which temperature is a measure of how quick molecules are, and how frequently they collide one...
  12. T

    B Is Time Dilation About Particle Motion Rather Than Time Itself?

    Hi, i am not a physicist but i have the intuition that time dilation is just slow in the movement of particle's and causality instead of slow in time itself and that this does not affect photons. I understand that there is no way to distinguish between a slow in time and a slow in movement and...
  13. S

    Engineering FEA Results interpretation for these 3 simulations

    Hi Im slightly stuck not sure what i put is ok. FEA was used to carry out analysis on 3 structures and diagram results obtain (no data) Explain where the first point of failure is likely to originate, and why. An analysis of the studies, do you think that they will be an accurate...
  14. P

    A Problems with the interpretation of the Torsion tensor and the Lie Bracket

    Hi, I've been doing a course on Tensor calculus by Eigenchris and I've come across this problem where depending on the way I compute/expand the Lie bracket the Torsion tensor always goes to zero. If you have any suggestions please reply, I've had this problem for months and I'm desperate to...
  15. W

    I Mainstream interpretation of Newton's bucket argument?

    What is the current mainstream interpretation of Newton's bucket argument in regards to "absolute space" or similar concepts? Wikipedia asserts both that Newton's intention may either have been (1) to prove the "metaphysical" existence of something we'd call "absolute space" (i.e. some some...
  16. E

    I Meaning of "Static Electricity" and Physical Interpretation

    If a balloon and a sweater are rubbed together, high-school science teachers like to say "the electrons transferred to the balloon in the form of static electricity." Then, it is often charming to show that two such balloons repel one another "because they have more electrons." Can we unpack...
  17. E

    I Confusion about the interpretation of specific volume

    So I'm reading through Cengel's thermodynamics textbook, and came across this solved example: Firstly, pressure in this context I'm assuming is vapour pressure? Since we're dealing with pure substances in this chapter. But what's confusing me is, here's the diagram I have: They've not...
  18. A

    I Does this tweet have any physical interpretation?

    I read this tweet (I omit the author for privacy), and my curiosity led me to ask questions:: Any optimization problem is equivalent to a convex (linear) one (but infinite dimensional…). The key do perform global optimization using Lasserre’s relaxation via the problem of moment (aka...
  19. Shreya

    Phase of a wave - My interpretation

    Let's begin my interpretation: (please refer the image below). There I have considered a point in the disturbance/wave (let's call it ##P##),(not a particle of the medium) and I follow it as the wave progresses. The solid curve is a Pic of the wave at ##t=0## and the dotted one is its Pic at...
  20. .Scott

    B Is there another workable interpretation of the Bell Inequality?

    I just read an article in Quantum Magazine about "unitary" results and how this is tied to looking at the reversibility of quantum events. It provided an easy-to-understand mechanism for tracking the effects of adding information to a fictional universe. The example they gave for detecting a...
  21. gentzen

    I Incompleteness of Griffiths' consistent histories interpretation

    Robert Griffiths version of consistent histories can be presented as a quantum logic, which is "intentionally" incomplete as an interpretation of QM. The advantage is that one can just require the exact decoherence condition ##D(\alpha,\beta)=0## for all ##\alpha\neq \beta## (with the...
  22. Spathi

    I Elitzur–Vaidman bomb tester in multi-world interpretation

    https://en.wikipedia.org/wiki/Elitzur–Vaidman_bomb_tester In the Elitztur-Weidman experiment there are bombs that are triggered by a single photon hitting their detector, and with some probability you can find out that the bomb is working, despite the fact that it did not explode. I'm trying...
  23. joneall

    I Krauss's interpretation of gauge theory

    Lawrence Krauss, "The greatest story ever told ... so far", pp. 108-109. "Gauge symmetry in electromagnetism says that I can actually change my definition of what a positive charge is locally at each point of space without changing the fundamental laws associated with electric charge, as long...
  24. Killtech

    I The interpretation of probability

    I am looking for a way to compare the handling of probability in QT with how it's done in classic PT (probability theory) - and their interpretations. QT does have it's own formalism that works, so there isn't much motivation to bring it into a usual representation which makes it hard to find...
  25. D

    I Quantum interpretation and classical-quantum distinction

    Are/were there any quantum interpretation according to which quantum mechanics COMPLETELY cease to apply at the macroscopic scale? If YES, please name it. I am interested to learn about such interpretation, even if it is inadequate and not widely supported. Of course, the big question remains...
  26. Jacob Peters

    B Copenhagen Interpretation - Superposition - confirmed?

    Hi, From what I read here, they did a double slit experiment test with neutrons that seemed to confirm superposition that the particle was in both places at once. Thoughts?
  27. M

    The correct interpretation of QM.... according to a "language model" AI

    In the last few years, many of us have heard of GPT-3, a "language model" trained on terabytes of Internet prose, with a remarkable ability to generate essays, dialogues, and other original works. There is a similar but less powerful model called GPT-J which can be accessed freely at the...
  28. K

    I Realistic interpretation of QM

    If it looks like a duck, swims like a duck, and quacks like a duck, then it probably is a duck. Why is there not a standard quantum mechanics interpretation that represents the most straight forward interpretation of what we see in experiments? By this, I mean: 1. Particles are real and...
  29. H

    A 't Hooft cellular automaton interpretation

    Hi Pfs, I am not sure that understand what the ontological state in the r' Hooft interpretation: Is this correct: A particle is never in a superposition of ontological properties. it is not here> + there> there is no free will . if it is here> Bob will choose to measure its position , not its...
  30. A

    Can AI Technologies Interpret and Convert Musical Notes into Audio?

    Musical notes Can AI, Machine learning, Data science, Computer vision, image processing technologies assist in interpreting musical notes ? Input dataset : Musical notes Output : Sound (Audio file) played. A python program which can assist in interpreting or converting text to speech ?. The...
  31. elElegido

    A misconception I have about impulse formula interpretation

    The misconception came up from the following problem: "A 0.50-kg cart (#1) is pulled with a 1.0-N force for 1 second; another 0.50 kg cart (#2) is pulled with a 2.0 N-force for 0.50 seconds. Which cart (#1 or #2) has the greatest acceleration? " I know the answer is the following (I looked it...
  32. K

    I What does the equation dΩ32 = dr2 + r2dΩ22 mean in terms of flat space?

    A 1-sphere exists in 2D space. It is a circle in flat space. A 2-sphere is a 1-sphere embedded in 3D space. Its surface is non flat and 2 dimensional. A 3-sphere is a 2-sphere embedded in 4D space. Its surface is non flat and 3 dimensional. What does this last sentence mean in...
  33. Killtech

    I What is the Interpretation of Observable Operators in Quantum Theory?

    So generally in most literature observables are represented via self-adjont (or equivalently real-valued) linear operators in QT. But that definition leaves it open for a wide variety of operators that can be view as observables. I was always a bit uncertain how to understand this freedom, so i...
  34. M

    I Informational Interpretation of quantum mechanics?

    I heard something today about the "informational interpretation" of quantum mechanics and a phrase used was "it from bit." Is there actually such a thing? What does it mean, and how is it distinguished from other interpretations like MWI or Copenhagen?
  35. G

    I Geometric Interpretation of Turbulence

    I would like to give a geometric interpretation to turbulence. Let's take into consideration for example a Poiseuille flow. The velocity profile resembles a parabolic bullet. As the particles are pushed by other layers of particles, then it must be that in addition to their translation, they...
  36. DaveC426913

    B Periodic spiral graph interpretation

    Could someone explain the geometry of this graph? Why does the radial distance vary non-uniformly? To-wit: Distance from origin to Nov 2020 is much larger than Nov 2020 to Nov 2021 Why are there two areas - one above and one below - the centre line...
  37. ergospherical

    I Physical interpretation of this coherent state

    Given the usual raising & lowering operators ##A^{\dagger}## & ##A## for a quantum harmonic oscillator, consider a coherent state ##|\alpha\rangle \equiv e^{\alpha A^{\dagger} - \bar{\alpha} A} |0\rangle##. I first check that ##|\alpha\rangle## is an eigenvector of ##A##. I already proved that...
  38. B

    B Alternative elastic collision formula / physical interpretation

    Standard formula for final velocities ##v_1##, ##v_2## in elastic collision with masses ##m_1##, ##m_2## and initial velocities ##u_1##, ##u_2## is given by $$v_1 = \frac{m_1-m_2}{m_1+m_2}u_1+\frac{2m_2}{m_1+m_2}u_2$$$$v_2 = \frac{2m_1}{m_1+m_2}u_1+\frac{m_2-m_1}{m_1+m_2}u_2$$. By rearranging...
  39. M

    I Visual Interpretation of Advanced Electrodynamics

    Hello! I am a junior undergraduate physics major and I am very confused on how to visualize things in my electrodynamics class. Specifically, I am having issues with dielectrics and spheres with constant potentials etc. I usually notice that I am lost in a class when I can no longer draw out a...
  40. entropy1

    I MWI and interpretation of measurements

    I was wondering, if we have a measurement of, say, spin of an electron, which can yield spin-up and spin-down in the context of MWI, then the electron gets entangled with the measurement device, yielding the wave function ##|Measurement_{spin-up}, Value_{spin-up} \rangle +...
  41. ergospherical

    A Prove Fermi-Walker Transport of Gyroscope's Spin Vector w/No Applied Moment

    With no applied moments, it is asked to prove that a gyroscope Fermi-Walker transports its spin vector ##S_{\alpha} = - \dfrac{1}{2} \epsilon_{\alpha \beta \gamma \delta} J^{\beta \gamma} u^{\delta}##. In a local inertial frame ##u^{\alpha} = (1, \mathbf{0}) = \delta^{\alpha}_0## and...
  42. Jarvis323

    I Why do we use the word interpretation?

    I've always struggled with the use of the word interpretation in the context of QM. Most so called interpretations do not seem like interpretations at all. Despite what might seem obvious, the conflation between the normal use of the word interpretation and the use of the word interpretation in...
  43. Buckethead

    B Paradox in the block universe interpretation

    Consider two observers, Alice and Bob, standing on the Earth together with synchronized clocks. Bob asks Alice, “Is this now?” to which Alice replies, “Yes, it is”. They are clearly both in the present moment. Bob climbs a mountain and some time later, due to the lower gravitational field...
  44. M

    I David Deutsch's Many Worlds Interpretation and the Double Slit Experiment

    David Deutsch is a well known proponent of the Many Worlds Interpretation. His argument seems to be that a single photon in the double slit experiment must be interfering with one from another world. It is commonly held by physicists that the the photon, as a wave going through double slits, can...
  45. M

    A Interpretation of Lagrangian solution (complex numbers)

    Hi Guys Finally after a great struggle I have managed to develop and solve my Lagrangian system. I have checked it numerous times over and over and I believe that everything is correct. I have attached a PDF which has the derivation of the system. Please ignore all the forcing functions and...
  46. D

    I Physical interpretation of phase in solutions to Schrodinger's Eqn?

    Hello all, So I've been working through the solutions to some simple introductory problems for the Schrodinger Equation like the infinite square well, and I'm trying to make sense of how to think about the phase component. For simplicity's sake, let's start off by assuming we've measured an...
  47. M

    MATLAB FFT interpretation of time vector (simple)

    I have video data that shows an object moving up and down. I'd like to extract the frequency the object moves. Following the given example here (scroll down to "Examples"), am I correct in assuming Fs would be camera frame rate and L would be the total number of frames? Thanks so much!
  48. R

    Interpretation of Net Peak Area in Gamma Spectroscopy

    Hello, My question relates to gamma spectroscopy. I understand how the net peak area is calculated for any photopeak. Fortunately, gamma-spec software (e.g., Genie-2000 from Canberra) provides Net peak area and associated uncertainty (for Cs-137 661.7 keV peak, as an example). My question: are...
  49. Killtech

    A Schrödinger's original interpretation

    I wasn't sure if i should call it an "interpretation" and post it in this forum or not as it isn't entirely clear if it makes any different predictions within its region of it validity. Anyhow, the original idea of Schrödinger that made him come up with his equations is very different from the...
  50. G

    Need help with the interpretation of this v(t) graph

    Summary:: Please tell me an example Determine the distance traveled by the object between 0-7 s. Determine the acceleration of the piece in the range of 0-4 s Determine the acceleration of the piece in the range of 4-7 s.I've tried, but something I'm doing wrong. Could you clarify?
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