What is Minkowski: Definition and 206 Discussions

Minkowski, Mińkowski or Minkovski (Slavic feminine: Minkowska, Mińkowska or Minkovskaya; plural: Minkowscy, Mińkowscy; Hebrew: מינקובסקי‎, Russian: Минковский) is a surname of Polish origin. It may refer to:

Minkowski or Mińkowski, a coat of arms of Polish nobility
Alyona Minkovski (born 1986), Russian-American correspondent and presenter
Eugène Minkowski (1885–1972), French psychiatrist
Hermann Minkowski (1864–1909) Russian-born German mathematician and physicist, known for:
Minkowski addition
Minkowski–Bouligand dimension
Minkowski diagram
Minkowski distance
Minkowski functional
Minkowski inequality
Minkowski space
Null vector (Minkowski space)
Minkowski plane
Minkowski's theorem
Minkowski's question mark function
Abraham–Minkowski controversy
Hasse–Minkowski theorem
Minkowski separation theorem
Smith–Minkowski–Siegel mass formula
Christopher Minkowski (born 1953), American Indologist
Khristian Minkovski (born 1971), Bulgarian swimmer
Marc Minkowski (born 1962), French conductor
Oskar Minkowski (1858–1931), German physician
Peter Minkowski (born 1941), Swiss physicist
Rudolph Minkowski (1895–1976), German-American astronomer

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  1. cianfa72

    I On the physical meaning of Minkowski's spacetime model

    Hi, I was thinking about the following. Suppose we have a geometric mathematical model of spacetime such that there exists a global map ##(t,x_1,x_2,x_3)## in which the metric tensor is in the form $$ds^2 = c^2dt^2 - (dx_1)^2 + (dx_2)^2 + (dx_3)^2$$ i.e. the metric is in Minkowski form...
  2. bobrubino

    B Minkowski Spacetime vs Euclidean Spacetime

    Which one would you use in order to map out a black hole and its connection to a white hole?
  3. PhanthomJay

    B What does the Minkowski spacetime interval represent and how is it determined?

    In the Minkowski space time equation in one dimensional space , ds^2 = dx^2 - (ct)^2, what is the value to use for x and t, and what does the space time interval ds represent? For example, if Alpha Centauri is 4 light years away, what values are. used for x and t, based on speed I guess, and...
  4. C

    I What is the relationship between honeycombs and Minkowski space?

    Anyone know what honeycombs "tile" Minkowski space?
  5. Sagittarius A-Star

    I Only Minkowski or Galilei from Commutative Velocity Composition

    The LT can be derived from the first postulate of SR, assuming linearity an that velocity composition is commutative, and that GT can be excluded: ##t' \neq t##. Definition of the constant velocity ##v##: ##x' = 0 \Rightarrow x-vt=0\ \ \ \ \ \ ##(1) With assumed linearity follows for the...
  6. Trysse

    I Why Is Minkowski Spacetime Non-Euclidean?

    In the meantime: What is your answer to the question: Why Is Minkowski Spacetime Non-Euclidean?
  7. Trysse

    I Searching for "Why Is Minkowski Spacetime Non-Euclidean" by Cronkhite

    I cannot find the paper that is referenced here https://www.nist.gov/publications/why-minkowski-spacetime-non-euclidean Why Is Minkowski Spacetime Non-Euclidean? Author(s) J M. Cronkhite I have looked here https://aapt.scitation.org/action/doSearch?SeriesKey=ajp&AllField=Cronkhite&ConceptID=...
  8. lindberg

    B Orthogonality in Minkowski Spacetime: Meaning & Visualization

    I have read that non-inertial frames are those, where time is not orthogonal on space. Does it just mean that the speed of light is not isotropic there or does it mean anything else? How can I picture more easily this concept (for space orthogonality I just imagine perpendicularity of one axis...
  9. cianfa72

    I Einstein Definition of Simultaneity for Langevin Observers

    Hi, reading this old thread Second postulate of SR quiz question I'd like to ask for a clarification on the following: Here the Einstein definition of simultaneity to a given event on the Langevin observer's worldline locally means take the events on the 3D spacelike orthogonal complement to...
  10. F

    I Gamma - A Minkowski Spacetime Diagram Generator

    Gamma is a Minkowski spacetime diagram generator. I probably started this project in August and have been working on it almost full-time since. It will be a free, open-source application. The program can draw all the usual things: axes, grids events, and worldlines, etc. It's easy to create...
  11. R

    Minkowski diagram, where to put an event

    I drew the Minkowski diagram, but I'm not sure if this is correct. From what I drew the angle between x and ct ##\approx 0## then the event is "inside" the light ray and will eventually reach A.
  12. K

    A Unruh & Minkowski Modes: Analytic Extension Explained

    In Carroll "Spacetime and Geometry" I found the following explanation for why the analytically extended rindler modes share the same vacuum state as the Minkowski vacuum state: I can't quite understand why the fact that the extended modes [\tex]h_k^{(1),(2)}[\tex] are analytic and bounded on...
  13. F

    I Request for Input: 2D Minkowski Spacetime Diagram Generator

    I’m planning to write a 2D Minkowsky spacetime diagram generator tool. At this point, I am looking for help reviewing the specification. I am not looking for help with the implemenation. To be clear, I’ve written a complete specification, but it would be a waste if it was missing features that...
  14. C

    Calculation Involving Projection Tensor in Minkowski Spacetime

    In Minkowski spacetime, calculate ##P^{\gamma}_{\alpha}U^{\beta}\partial_{\beta}U^{\alpha}##. I had calculated previously that ##P^{\gamma}_{\alpha}=\delta^{\gamma}_{\alpha}+U_{\alpha}U^{\gamma}## When I subsitute it back into the expression...
  15. E

    How can Minkowski spacetime be expressed as a U(2) manifold?

    Firstly, since ##\{ \mathbb{I}, \sigma_x, \sigma_y, \sigma_z \}## is a basis of the space of ##2 \times 2## Hermitian matrices, and because ##X = t \mathbb{I} + x\sigma_x - y \sigma_y + z \sigma_z##, the map is one-to-one (because each matrix has unique decomposition). It's also easily checked...
  16. Arman777

    Tensor Calculations given two vectors and a Minkowski metric

    Let us suppose we are given two vectors ##A## and ##B##, their components ##A^{\nu}## and ##B^{\mu}##. We are also given a minkowski metric ##\eta_{\alpha \beta} = \text{diag}(-1,1,1,1)## In this case what are the a) ##A^{\nu}B^{\mu}## b) ##A^{\nu}B_{\mu}## c) ##A^{\nu}B_{\nu}## For part (a)...
  17. LCSphysicist

    I What is the Minkowski metric tensor's trace?

    I am trying to follow the rule, that is, raising an index and the contract it. Be ##g_{\mu v}## the metric tensor in Minkowski space. Raising ##n^{v \mu}g_{\mu v}## and then, we need now to contract it. Now, in this step i smell a rat (i learned this pun today, hope this mean what i think this...
  18. H

    A Exploring Minkowski: A Multi-Dimensional Grid for Studying Other Spaces?

    I understand Minkowski is empty space with no matter. Is there a possibility to consider Minkowski as a multi dimensional grid in the form of a perpendicular 3 dimensional matrix for further study on other spaces. For example to have a matrix mesh to map other solutions onto. I claim ignorance...
  19. W

    I Understanding Pseudo-Angles in Minkowski Space: A Geometric Interpretation

    Does the concept of the angle between two vectors make sense in Minkowski space? Does the concept of orthogonal basis for Minkowski space make sense? If it does, how is it defined? When we start with the usual (time, distance) basis for 2-D Minkowski space, the axes as drawn make a right...
  20. P

    I Penrose Diagram for Minkowski Space-Time: Step-by-Step Guide

    I'm working through Ray d'Inverno's book "Introducing Einstein's Relativity" and I've got to the section that introduces Penrose diagrams. The first example is just Minkowski space-time. The construction goes from Schwarzschild coordinates ##t## and ##r##, to define null coordinates ##v = t +...
  21. nomadreid

    I Hyperbolic Geom of Minkowski Space: Chung et al. 2009

    In "The Geometry of Minkowski Space in Terms of Hyperbolic Angles" by Chung, L'yi, & Chung in the Journal of the Korean Physical Society, Vol. 55, No. 6, December 2009, pp. 2323-2327 , the authors define an angle ϑ between the respective inertial planes of two observers in Minkowski space with...
  22. P

    I Choice of signature important for superluminal 4-velocity? (Minkowski)

    I guess my question boils down to "Is choice of signature important when dealing with superluminal 4-velocities"? I wanted to show for superluminal velocities that ##\tilde{U} = \left( \frac{c}{\sqrt{\frac{u^2}{c^2} - 1}}, \frac{\dot{x}}{\sqrt{\frac{u^2}{c^2} - 1}}...
  23. T

    I Is Minkowski spacetime a solution of the Friedmann Equations?

    The empty FRW-universe with curvature parameter ##k = -1## and expanding linearly is well known. Also that it is mathematically equivalent (after a coordinate transformation) with the Milne universe which also expands linearly. I wonder if the Friedmann Equations have another solution (I...
  24. Q

    I Minkowski Metric: When to Use It

    I am trying to get a few concepts straight in my mind. There is no homework question here. 1) If we lived in Minkowski space and had to work in a rotating frame of reference would the Minkowski metric still be the one to use? I assume yes as even if the frame is non inertial the geometry of...
  25. A

    Coordinate transformations on the Minkowski metric

    The line element given corresponds to the metric: $$g = \begin{bmatrix}a^2t^2-c^2 & at & 0 & 0\\at & 1 & 0 & 0\\0 & 0 & 1 & 0\\0 & 0 & 0 & 1\end{bmatrix}$$ Using the adjugate method: ##g^{-1}=\frac{1}{|g|}\tilde{g}## where ##\tilde{g}## is the adjugate of ##g##. This gives me...
  26. ohwilleke

    I QFT of Gravitons in Minkowski Space vs GR

    A central feature of classical GR that it is background independent and operates via a curvature in space-time. As I understand it, this is not true of the other Standard Model forces which are consistent with special relativity and operate in Minkowski space, in which forces are transmitted via...
  27. nomadreid

    I Tensor calculation, giving|cos A|>1: how to interpret

    On pages 42-43 of the book "Tensors: Mathematics of Differential Geometry and Relativity" by Zafar Ahsan (Delhi, 2018), the calculation for the angle between Ai=(1,0,0,0) (the superscript being tensor, not exponent, notation) and Bi=(√2,0,0,(√3)/c), where c is the speed of light, in the...
  28. Grimble

    Minkowski & Einstein: Hyperbolic Geometry Breakthrough?

    <Moderator’s note: forked from https://www.physicsforums.com/threads/proper-and-coordinate-times-re-the-twin-paradox.915212/page-13#post-6215675 > Thank you, that is very interesting and I can understand much of it. :smile: But can someone tell me if it was the application of hyperbolic...
  29. K

    I Is this the only form of the Minkowski metric?

    The Minkowski metric for inertial observers reads ##ds^2 = -c^2 dt^2 + dx^2 + dy^2 + dz^2##. Is there a way to show that if it had off diagonal terms, the inertial observers would not see light traveling with the same speed?
  30. S

    I I Came Up with a CTC in Minkowski Space: Exploring To What End?

    If you viewed my most recent thread before this one, then you know that I have been studying curves in spacetime (timelike/spacelike/lightlike), and I have especially been looking into the CTCs (closed timelike curves) that the Godel metric is famous for. During my studies I found that I had to...
  31. jk22

    B Should the 'time' axis of a Minkowski diagram be time's imaginary unit?

    Since the metric is euclidean in coordinates ##(ict,x)## it can be drawn in a plane, but if the metric is ##diag(1,-1)##, can both axis still be drawn in a plane ?
  32. PeterDonis

    Insights How to Study Fermi-Walker Transport in Minkowski Spacetime

    Greg Bernhardt submitted a new blog post How to Study Fermi-Walker Transport in Minkowski Spacetime Continue reading the Original Blog Post.
  33. M

    Calculating different "kinds" of variations

    Homework Statement Let ##x## and ##x'## be two points from the Minkowski space connected through a Poincare transformation such that ##x'^\mu =\Lambda_{\nu}^\mu x^\nu+a^\mu## and ##u:\mathcal{M}\to \mathbb{K}=\mathbb{R}## or ##\mathbb{C}##, ##\mathcal{M}## the Minkowski space. We define: $$...
  34. S

    B Minkowski Diagram: Expanding Universe

    Is this how you would draw the Minkowski space diagram with space expanding, (without acceleration or black holes) ?
  35. binbagsss

    Delta written as Minkowski metric ?

    Homework Statement Hi, I am just stuck in why / how we can write minkowski metric where I would usually write delta. I see that the product rule is used in the first term to cancel the terms in the second term since partials commute for a scalar and so we are left with the d rivative acting...
  36. I

    I Hash marks on minkowski diagram

    I'm confused as to how far apart the hash marks should be on a minkowski spacetime diagram that shows the rocket frame overlapped over the lab frame. Should the hash marks that represent space in the rocket frame be spaced apart exactly the same length as the hash marks that represent space in...
  37. J

    B Understanding Minkowski: Einstein, Relativity & Absolute Simultaneity

    Hi all! Sorry for the bad English! =) I'm reading a book about the interpretations of the findings of Einstein and others and i came across a statement that sounded very nice, but since it's its author is more tendentious to the Lorentz interpretation, I'm not sure if it's right. As I...
  38. Demystifier

    A How Does Visser Derive Schwarzschild Geometry from Minkowski Space?

    In https://arxiv.org/abs/gr-qc/0309072 Visser starts from Minkowski metric (5), performs a coordinate transformation (6)-(7) and gets Schwarzschild geometry (12). But this should be impossible. Minowski metric has vanishing Riemann curvature tensor, while Schwarzschild geometry hasn't. What do I...
  39. E

    Casimir effect in 1+1 Minkowski spacetime

    Homework Statement https://i.imgur.com/sI3JiB4.jpg https://i.imgur.com/PLpnPZw.jpg I have no idea how to solve the first question about the vacuum energy. I solved the second and third problems, but I'm hopelessly stuck at the first. 2. Homework Equations The Hamiltonian can be written as...
  40. DuckAmuck

    A When does the Minkowski metric get non-zero off-diagonals?

    I have only seen scenarios so far where the elements are all along the diagonal, but what are some known cases where there are off-diagonal elements? Thank you.
  41. I

    I Vectors in Minkowski Space & Parity: Checking the Effect

    It is known that vectors change them sing under the influence of parity when ##(x,z,y)## change into ##(-x,-z,-y)## $$P: y_{i} \rightarrow -y_{i}$$ where ##i=1,2,3## But what about vectors in Minkowski space? Is it true that $$P: y_{\mu} \rightarrow -y_{\mu}$$ where ##\mu=0,1,2,3##. If yes how...
  42. S

    B Geodesic equation in Minkowski space clarification

    Hi, So the geodesic equation is saying in my frame of reference I may see acceleration and then in your frame of reference you may see gravity? So by just changing coordinates you can create a "force" ? And also is this relevant to the Minkowski space or do I need to be in GR to be able to get...
  43. Orodruin

    Insights Coordinate Dependent Statements in an Expanding Universe - Comments

    Greg Bernhardt submitted a new PF Insights post Coordinate Dependent Statements in an Expanding Universe Continue reading the Original PF Insights Post.
  44. S

    B Metric Tensor and The Minkowski metric

    Hi, I have seen the general form for the metric tensor in general relativity, but I don't understand how that math would create a Minkowski metric with the diagonal matrix {-1 +1 +1 +1}. I assume that using the kronecker delta to create the metric would produce a matrix that has all positive 1s...
  45. J

    I Line Element in Minkowski Space: Geometric Meaning

    Hello, how can you imagine the geometrically meaning of the minus sign in ds2=-dx02+dx12+dx22+dx32, maybe similar to ds2=x12+dx22 is the length in a triangle with the Pythagoras theorem?
  46. D

    I Minkowski metric beyond the event horizon

    My question is regarding how spacetime looks like beyond the event horizon of a black hole, in particular how distances behave. In the Minkowski diagram of a black hole, all paths leads to the singularity. But what is the magnitude of the distances involved here? Let's say a neutron star is...
  47. H

    I Going from Galilei to Minkowski

    Hi, I'm starting a double degree in math and physics and am still a relativity newbie. I'm a bit stuck figuring out what exactly means to drop absolute time and simultaneity when making the transition from Galilean spacetime to Minkowski spacetime. Judging from the purely mathematical...
  48. R

    Minkowski spacetime - Overall Distance

    Hi guys, I'm not exactly sure how to go about doing this problem. The question has no additional information, so I'm stuck. Any help I could get would be appreciated. 1. Homework Statement In four dimensional Minkowski spacetime an event, A, has components labelled Aμ and another event B has...
  49. P

    B Minkowski metric, scalar product, why the minus sign?

    In Schutz's A First Course in General Relativity (second edition, page 45, in the context of special relativity) he gives the scalar product of four basis vectors in a frame as follows: $$\vec{e}_{0}\cdot\vec{e}_{0}=-1,$$...
  50. Pushoam

    Minkowski Diagram and Mathematica

    Homework Statement [/B]Homework Equations Mathematica The Attempt at a Solution I want to plot the diagram using Mathematica. I saw on the net there is some kind of programming needed for this. Do I need to learn programming for doing this? If yes, how to learn it?