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. L

    Questions on multi-worlds interpretation

    Can anybody please answer 3 questions realted to MWI: i)Suppose I measure anything, then I will also be divided into two different universes according to the no. of probable things. But I don't feel any change. I think everything is going continous. But if it really divides where does 'I' go. I...
  2. K

    Feynmann diagrams interpretation and diagramm symmetry order

    I'm trying to understand Feynman diagrams interpretation in terms of virtual particles. What I still can't understand is how this interpretation is compatible with the fact that one should divide each diagram by its symmetry order. As far as I understand, diagram symmetry order means how many...
  3. P

    Question about Copenhagen's interpretation

    I am doing research for a web based science-fiction / physics-fiction novel I am working on. Would anyone here know much about Copenhagen's interpretation and if I am correct or false in assuming the following: The interpretation states that matter can be in a superposition of forms until...
  4. R

    Superposition or Many-worlds interpretation?

    Just wondering what you guys think about the results of the double slit experiment...
  5. E

    Is My Differential Equation Solution in Quantum Mechanics Correct?

    I'm having a problem understanding solutions of differential equation in QM: \psi''(z)+\frac{p}{z}\psi(z)+k^2\psi(z)=0 (1) I usualy use Fourbenious method, and in this case I get a 3 coefficients recursion relation which is really messy. So I do it like this: for really large...
  6. E

    Geometrical interpretation of dot product?

    Does anyone know what the geometrical interpretation of a dot product in 3-D is? I am calculating the dot product between two vectors in 3d and need to use the |a||b|cos(theta) interpretation basically, but that is for 2d. Can I just tack on an additional cos(theta2)? Thanks a lot for your...
  7. R

    Geometric interpretation of Generalized MVT

    Homework Statement I am trying to see the geometric interpretation of the generalized MVT. It is not a homework problem, but would like to know how to interpret the equation Homework Equations [f(b)- f(a)]* g'(x) = [g(b)- g(a)]* f'(x) The Attempt at a Solution On...
  8. mattmns

    What is the correct interpretation of the probability in this scenario?

    I am having some trouble with the interpretation of the following question (specifically, part (a)). Here is the question from the book. ---------------------------------------- Often, news stories that are reported as startling "one-in-a-million'' coincidences are actually, upon closer...
  9. S

    COMSOL Data interpretation problem

    Hey everyone, I have been using COMSOL to study oxygen diffusion through a membrane coupled with a surface reaction at one end of the membrane. It is a 3D cylindrical model and when I want the data values for oxygen concentration at the reaction boundary, it gives me a list of garbled values...
  10. D

    Interpretation of dark energy and gravity as the same thing

    First of all, I don't really know much of physics so it may very well be something silly and laughable... but I just find somewhat interesting, and from the layman's point of view at least, not worse than some ideas that I see from people from the field, such as the hypothesis of darwinian...
  11. M

    Many-worlds interpretation: Worlds joining instead of splitting?

    If two branches of the tree eventually came to be identical would they join or would they continue to exist as separate worlds? If they joined, observers in each would remember a different history. Any connection between this and relativity where people observe the same event happening in...
  12. M

    What is the physical interpretation of enthelpy and entropy?

    Hi guys, I need help on thermodynamics: 1. what is the physical interpretation of enthalpy and entropy? 2. in an open system, change in total energy = change in enthalpy? 3. every reversible process must be adiabatic? 4. what does clausius inequality means? 5. Q-W=U is for closed...
  13. J

    Interpretation of double mutants in signaling pathways

    I found this in my notes, and I memorized it, but I have no idea why this is. Could anyone shed some light: Given: A mutation in A gives repressed reporter expression, while a mutation in B gives constitutive reporter expression. If: A double mutation in A and B gives repressed reporter...
  14. U

    Is Time-Reversed Causality Crucial in Cramer's Transactional Interpretation?

    From the wikipedia entry: "Suppose a particle (such as a photon) emitted from a source could interact with one of two detectors. According to TIQM, the source emits a usual (retarded) wave forward in time, the "offer wave", and when this wave reaches the detectors, each one replies with an...
  15. W

    Geometrical interpretation of Taylor series for sine and cosine?

    I've stumbled upon what might be a geometrical interpretation of Taylor's series for sine and cosine. Instead of deriving the Taylor's series by summing infinite derivatives over factorials, I can derive the same approximation from purely geometrical constructs. I'm wondering if something...
  16. P

    Is the Copenhagen Interpretation a Consequence of the Uncertainty Principle?

    Hi, Can we know the Copenhagen interpretation, a result of uncertainty principle? If you don't agree with that, mention your reasons to see taht will conclude a safe answer or not. Thanks. ------------------------ Formulate realities.
  17. D

    Can the Transactional Interpretation Shed Light on the Double-Slit Experiment?

    I recently heard about the "Transactional Interpretation", and comletely failed to understand it. I then looked it up on Wikipedia, and became even more confused. My main questions are: 1. I gathered that, after receiving a retarded wave, a detector will send out an advanced wave. What is...
  18. U

    Vibrating beam - physical interpretation

    Homework Statement This question arises from partial differential equations work, but concerns introductory-level physics. The interpretation is of solutions representing the displacement (a function, u(x, t), of position and time) of a vibrating bar, fixed but hinged at each end. My...
  19. S

    What is the geometric interpretation of the indefinite integral?

    I would like to know if there is any geometric interpretation of the indefinite integral ? Or perheps to tell me what actually indefinite integral represents?? thnx in return
  20. J

    Exploring the Bohmian Interpretation: Why Study It?

    Why Bohmian interpretation? It's now one and half year after I took my first course on quantum mechanics, and I've already started liking it the way it is. I have trouble seeing any motivation for deterministic theory. Is there any reasons to study the Bohmian interpretation? (I haven't studied...
  21. T

    Torsion tensor: Geometric interpretation

    Can someone pleas explain to me the geometric interpretation of Torsion? Why it is true is more important. Lol i said manifolds instead of torsion!
  22. I

    Hidden variable and the copenhagen interpretation.

    Hi, I just had this argument with this person on another forum and the gist of it was that he was saying collapse is predictable to within a negligible precision if you average out the results a huge number of identical wave-particles that had already collapsed. My contention was that...
  23. X

    Minimalist ensemble interpretation

    im a bit confused about which interpretation is experimentally favored,wave function collapse or the 'minimalist ensemble interpretation (ala L.E Ballentine' (as Doc Al wrote somewhere)?All the older literature talks about 'reduction of wave packet' but reading Ballentine has left me confused.
  24. C

    Geometrical interpretation of vector derivative

    Let f and g be real differentiable functions. Let v be a vectorial function of a real variable t, such that: v(t) = ( f(t), g(t) ) I know that by definition v'(t) = ( f'(t), g'(t) ) In many books they give a geomtrical interpretation of this. They draw the curve (the values of f(t) in...
  25. J

    Photons and physical interpretation of Fourier transform

    When we study physics at the faculty we are told that any non-sinusoidal wave can be regarded as a combination of sinusoidal waves of different frecuencies, with the ‘weight’ of the different frecuencies given by the Fourier transform. On the other hand, if we have an electromagnetic wave, we...
  26. Q

    How Does the Statistical Interpretation Address Quantum Interference Effects?

    I thought Statistical Interpretation of quantum mechanics is a very good alternative besides the orthodox interpretation. But I just can't explain the particle-wave duality from the statistical point. How could the Statistical Interpretation explain the interference effects in the Quantum...
  27. Demystifier

    What is your favored interpretation of quantum mechanics?

    As more than 10 options are not allowed, I was forced to put some different (hopefully similar) interpretations together. After voting for the favored interpretation, you may also indicate what is your second best interpretation, what is the worst interpretation for you, or even make the whole...
  28. E

    Zeilinger interpretation of QM

    I read thesis of Brukner http://www.quantum.at/publications/thesis/cbdiss.pdf and shortened article of Brukner and Zeilinger http://arxiv.org/PS_cache/quant-ph/pdf/0212/0212084.pdf This is new very promising interpretation of quantum mechanics. It also gives Weizs. explanation of 3...
  29. L

    Interpretation of the Lagrangian

    I have showed that if the integrand f in the variational problem \delta (\int f dx ) = 0 does not depend explicitly on the independent variable x, i.e. satisfies f = f(y, \dot{y}), then the Euler equation can be integrated to \dot{y} \frac{\partial f}{\partial \dot{y}} - f = const. How can I...
  30. H

    Geometric and Physical Interpretation of Diagonalization

    I am a second year student in quantum mechanics. I heard in lecture that simultaneous diagonalization of matrices is important in quantum mechanics. I would like to know why is it significant when two matrices can be simultaneous diagonalized, and what is the geometric and physical...
  31. L

    Transactional Interpretation, space and information

    While trying to wrap my head around the Transactional Interpretation, I wondered why we need signals from the future. For the electron about to be ejected, the surrounding space is already filled with information about everything around, and if the momentum conditions assign it to strike beyond...
  32. A

    Interpretation of existing small circuit

    Dear All, Before I lose the link I'll post it up: http://img290.imageshack.us/img290/9122/voltageregulatorlh7.jpg" Can anyone help me identify the unknown component in this picture drawn in blue? I'm trying to come up with an interpretation and circuit diagram of this circuit. It's a...
  33. V

    Commutators and physical interpretation

    An interesting question was posed, and since I have many problems of this type I'll just make the question general: Suppose you have operations A and B, if [A, B] != 0, then what can you conclude about a simultaneous measurement of A and B? For example, if A was momentum in the x direction's...
  34. O

    Simple calculus - interpretation Euler-Lagrange equation

    This is not a homework question but one that is part of the course material and I can't really move on until I understand the basic calculus. I have a problem interpreting "d by dx of partial dF by dy' equals partial d by dy' of dF by dx" in the following question, which I set out and then...
  35. C

    Interpretation of the Bible: Finding a Forum for Religious Discussions

    Is there anywhere that I can post specifically for religious discussions or am I going to have to find a diffrent forum? The topic I'd like to discuss is interpretation of the bible.
  36. P

    Interpretation of matrix multiplication?

    Matrix multiplication is clearly defined but is there a tangible or physical interpretation for it? Or is it just abstract formalism? I am thinking about each column of the matrix as vectors so matrix multiplication with two 2by2 matrices is about multiplying 4 vectors in a certain way. The...
  37. R

    Many Worlds Interpretation Experiment

    I recently learned about the Many Worlds Interpretation of quantum mechanics from another post on this forum. Unfortunately, the post became more of an argument about whether some experiment had or hadn't proven this interpretation to be true, and there wasn't a whole lot of information on what...
  38. T

    Exploring the Relational Interpretation of Quantum Mechanics

    Hi, recently, I have read the paper of Marchildon, http://arxiv.org/abs/quant-ph/0405126" . This encourage me to finally read the Rovelli's paper, but I don't understand what really is the relationnal interpretation. I stopped in the beginning of the paper, and I can't continue until I...
  39. kvantti

    Interpreting GR: Is Spacetime Geometry Necessary?

    Is it justified to state that GR is "just" a geometrical theory to calculate the paths of objects in spacetime? Just because GR states that "gravity is a property of spacetime itself" doesn't necessary mean that spacetime is curved; just that the paths of objects in spacetime are curved in a...
  40. S

    Area Interpretation to Evaluate The Integral

    From 0 to 4. ( I don't know how to make the s sign.) squareroot of (16-x^2) I set it equal to y and squared it to get. y^2 = 16 - x^2 Then I changed it to: Y^2 + X^2 = 16 I know it's a semi circle on the x-axis at 0 to 4. What should my final answer be?
  41. Q

    Copenhagen interpretation of Quantum Theory

    I found a website that says: "The still-dominant "Copenhagen interpretation" of Quantum Theory developed by Niels Bohr, Werner Heisenberg, Wolfgang Pauli, and others says two basic things: 1. Reality is identical with the totality of observed phenomena (which means reality does not exist...
  42. Q

    Many-Worlds Interpretation Issue

    OK, I have a problem with the many-world interpretation, namely the quantum suicide experiment. My problem: How exactly does your consciousness transfer over? When you die in your current "reality," do you just swap randomly to one of the parallel worlds? Or are each of the conscious entities...
  43. A

    Cramer's Transactional Interpretation

    Does anyone have any opinions on the transactional interpretation of Quantum Mechanics? Does anyone really take it seriously. I know criticisms have been levied against it (to do with causal loops) but others have proposed resolutions to this problem without compromising the overall integrety...
  44. marcus

    What Is the Marseille Interpretation of Quantum Mechanics?

    the term "Marseille" is used humorously in part, it could also be called the "Haifa Interpretation" because Asher Peres contributed and he was at the Technion and also David Mermin at Cornell (Ithaca, NY) has written similar stories about how to interpret QM and has called his stories the...
  45. K

    Discussing my explanations and interpretation of quantum mechanics

    I would like to start a thread dedicated to discussing my explanations and interpretation of quantum mechanics. They can be found at http://thisquantumworld.com" . Your questions and comments (critical or otherwise) will be appreciated.
  46. V

    Q: anyone know the formalism of the transactional interpretation of QM ?

    Hello all, I would like to learn more about the formalism of the transactional interpretation in QM. Apparently, the formalism is NOT the same as in unitary QM (but the claim is that the empirical predictions are equivalent). As such, it is not so much an *interpretation* but an equivalent...
  47. P

    Geometric Interpretation Of Schrodinger's

    GEOMETRICAL STUDY OF SCHROEDINGER'S FORMULA If we take a look on previous expression, we could continue with the importance of complex numbers. The complex numbers are very important to represent points or vectors in plane, and can be expressed this way: a = b·x+c·y If we choose...
  48. Loren Booda

    Does Intention or Interpretation Hold More Weight in Communication?

    Which carries a greater weight regarding the outcome of communication? E. g., if I encourage an individual to go out with me, and they respond according to their personal judgment, whose action would be more influential in the general milieu?
  49. Y

    Interpretation of vacuum fluctuation

    to preserve commutation relations in the quantized field operators (basically simple harmonic oscillator raising/lowering operators), a vacuum mode must be introduced in the case of a usual 50-50 beam splitter. thus, one has 4 modes: vacuum incident mode reflected mode transmited...
  50. H

    Interpretation of categorical construction

    The other day, I (once again) decided that I simply don't understand natural transformations. (Or functor valued functors, for that matter... which greatly disturbs me because I'm usually quite comfortable with function valued functions) So, I sat down to try and figure them out, and I...
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