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–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

View More On Wikipedia.org
1. 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. 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. 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. I What is the relationship between honeycombs and Minkowski space?

Anyone know what honeycombs "tile" Minkowski space?
5. 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. I Why Is Minkowski Spacetime Non-Euclidean?

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

50. 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?