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. stevmg

    How Do Minkowski Diagrams Illustrate Lorentz Transformations?

    kev - From your prior post you brought in this URL: http://hubpages.com/hub/Minkowski-Diagram which has this diagram (figure 3) Using his v = 0.6c, how do you prove that the (1,1) is the same as the (2,2) I can't make it happen. Also, his Lorentz and Inverse Lorentz...
  2. stevmg

    Minkowski 4-Space Equation: Exploring Symmetric Hyperbola

    The standard Minkowski 4-space equation runs like this (as far as I know); x'2 + y'2 + z'2 - c2t'2= x2 + y2 + z2 - c2t2 For purposes of simplicity, if we drop the y and z components and go to a 2-space, let c = 1 and x measured in units of c (if we express c as 300M m/sec, the 1 unit for...
  3. C

    Understanding Minkowski Space-time: An Explanation of Time as a Dimension

    If you have read my other threads, i am having trouble understanding special relativity. The issue seems to be my understanding of space-time. Space-time infers to me that two events are not separated by only a length in three dimensions, but also time, with time being essentially...
  4. T

    Would an energy diffraction ring in five space form a Minkowski space?

    If you think of a sphereical symmetric diffraction ring, the intensity is constant for each sphereical section (intensity doesn't vary for theta or phi), but it varies kind of like a sine wave in the r dimension from zero to zero with a maximum in the middle of the ring. So that if you think...
  5. TrickyDicky

    What are the properties of Minkowski spacetime geodesics?

    I have some difficulties understanding how Minkowski spacetime is flat and therefore its geodesics should remain parallel, but at the same time I see it described in other sites as hyperbolic and then geodesics should diverge. Any comment on my confusion about this will be welcome. Thanks
  6. X

    Is Minkowski Metric a Constant Riemann Metric in Finsler Geometry?

    If a Minkowski metric is just a constant Riemann metric? I am confused with the concept in the Finsler geometry,there Minkowski metric is defined as g=g_{ij}(y)dx^idx^j.
  7. I

    Help with understanding Minkowski diagrams

    [PLAIN]http://img20.imageshack.us/img20/4083/minkowskidiagram1.jpg B is meant to have occurred before C in the S' frame, but I don't get how it's possible.
  8. M

    Are Einstein and Minkowski's interpretations of special relativity different?

    Regarding the book Einstein, Relativity and Absolute Simultaneity edited by William Lane Craig and Quentin Smith. Routledge 2008. Chapter 1- The metaphysics of special relativity: three views. William Lane Craig. This deals with the Einsteinian interpretation, the Minkowskian...
  9. stevmg

    Minkowski 4-space? Yes or No.

    In Einstein's "Relativity," this equation appears in Appendix I (Lorentz Transformations): x1'2 + y1'2 + z1'2 - c2t1'2 = x12 + y12 + z12 - c2t2 This essentially says that for a given event at a given point and time in space, looking at this event from any frame of reference will give...
  10. A

    Gravity on the Minkowski spacetime

    Would someone please provide me with some papers or sources about the tensor gravitation theories on the Minkowski spacetime? They are field theories wherein the matter is supposed to not affect the geometry of spacetime and thus leaving the background spacetime unchangend with respect to the...
  11. Q

    Null curves vs. straight curves on Minkowski space

    I understand that we could think of a null curve in Minkowski space as being the curve c(s) such that the tangent vector dc(s)/ds = 0 at all s. So suppose that we have a curve c(s) = (t(s), x(s), y(s), z(s)) and we want to ask ourselves what conditions would make c a straight line. I guess...
  12. T

    Geometry of minkowski spacetime

    since the first moment I've started studying the theory of relativity i thought that the minkowski metric represents a flat spacetime (a 4D euclidean space) but while I was surfing the WWW , I arrived to an interactive applet the helps you visualise the idea of spacetime curvature is GR , here...
  13. J

    Minkowski Diagram: Clarifying One-Dimensional Question

    I need a clarification about this diagram On a one dimensional line two objects are riding along on the t and t' axis. One present moment of black's is represented by the red line. Since the green segment defined from the origin to the red line is longer than the black segment defined from...
  14. K

    Minkowski diagram frame scale comparison

    Homework Statement Draw a clearly labelled “Minkowski spacetime” diagram illustrating two events ((1) a farmer firing his laser gun at his cow, which is sitting along his positive x-direction, and (2) the cow dying) as observed by two observers (S at rest in the farmer’s and cow’s frame, and...
  15. K

    Minkowski spacetime diagrams, what does the hyperbola represent?

    Homework Statement Draw a clearly labelled “Minkowski spacetime” diagram illustrating two events ((1) a farmer firing his laser gun at his cow, which is sitting along his positive x-direction, and (2) the cow dying) as observed by two observers (S at rest in the farmer’s and cow’s frame...
  16. Grimble

    Rotation and Minkowski diagrams.

    Roger Penrose is reported to have said: And I understand that, in Minkowski space-time, the relative velocity between two inertial frames of reference is a rotation of the frames, with respect to one another, about a common origin. Now in the description of Minkowski diagrams given...
  17. R

    Why Does Rotating the Minkowski Metric Yield Non-Zero Curvature Components?

    Hi, if you perform this coord. transformation on minkowski metric in cartesian coord. (T,X,Y,Z): T=t , X=x cos(w t)-y sin(w t) , Y=x sin(wt)+y cos(wt) , Z=z (it is a frame rotating with angul. speed w around the Z axis) then you get this metric (I'm using the +,-,-,- convention)...
  18. J

    How is the -(ct)^2 term in Minkowski metric conceived?

    Hi, I am just trying to understand Special Relativity by reading http://en.wikipedia.org/wiki/Introduction_to_special_relativity All is ok except where in "The Minkowski formulation: introduction of spacetime", the introduction of -(ct)^2 term is not clearly justified (or so it seems to...
  19. Rasalhague

    Evaluating T(A,A) and Components of T(A,__) in Minkowski Spacetime

    Excercise Exercise 1.6 of Roger Blandford and Kip Thorne's online textbook Applications of Classical Physics: "In Minkowski spacetime, in some inertial reference frame, the vector A and second rank tensor T have as their only nonzero components A0 = 1, A1 = 2, A2 = A3 = 0. T00 = 3, T01 = T10...
  20. Rasalhague

    Minkowski Norms and Lorentz Metric in Spacetime

    From my reading of introductory texts on special relativity, I've seen this defined in various ways, and I'm curious about whether any of these definitions are preferable to others, for example because they're more convenient, consistent, logical, clearer, more widely used or more easily...
  21. M

    Calculating Distance and Innerproduct in 4-D Minkowski Vector Space

    Homework Statement In the 4-D Minkowski vector space [you can think of this as the locations of events in space-time given by (t, x, y, z)] consider the vectors pointing to the following events: (4ns, -1m, 2, 7) and (2ns, 3m, 1m, 9m) (a) Find the distance between the events. (b) Find the...
  22. N

    Is the Dual Basis in Minkowski Space Affected by the Metric Tensor?

    Normally, if you have an orthonormal basis for a space, you can just apply your metric tensor to get your dual basis, since for an orthonormal basis all the dot products between the base vectors will boil down to a Kronecker delta. However, in Minkowski space, the dot product between a unit...
  23. K

    Special Relativity, Light cones in Minkowski Diagrams

    Homework Statement Show that a point Q outside the "light cone" can occur either before or after a point P inside the light cone (eg: at the origin), depending upon the frame of reference. Show that a point R inside the light cone is always in the future or in the past with respect to P...
  24. Advent

    Minkowski metric tensor computation

    Hi, I'm having problem with understanding tensors and the Einsteins summation convention, so I decided to start doing explicit calculations, and I'm doing it in the wrong way. Hope someone could help me to clarify the concepts. In flat spacetime we have \eta with the signature (-+++). Under...
  25. P

    Compactness of V in Minkowski Space: A Question

    Consider the closed forward light cone V = \left \lbrace x \in M \mid x^{2} \geq 0, x^{0} \geq 0 \right \rbrace and M denotes Minkowski space. My question is whether V is a compact set or not. If it is a compact set, how do I show it? Intuitively I would say it is compact, but I...
  26. nomadreid

    Minkowski in 5-D: what is the fifth?

    In the equation for the Minkowski 5-D space in which deSitter space is embedded, I read the equation t^2 -x^2-y^2-z^2-v^2=-H^-2. What is v?
  27. nomadreid

    Minkowski vs deSitter: hyperbolic vs spherical?

    I am a bit confused over the shape of matterless spacetime:confused:: on one side Minkowski space is described as hyperbolic, and deSitter space is (hyper)spherical. Both are used, yet how can you have spacetime being both hyperbolic and spherical?
  28. T

    Negative time Minkowski metric

    What does it mean physically that the sign on the time component is opposite those of the spatial components of the Minkowski metric?
  29. S

    General Relativity and Minkowski space question

    Is the curved spacetime of General Relativity possible to be described by Minkowskian space which is flat, or do one need some other geometry?
  30. N

    Structure of Minkowski Space

    In another thread Fredrik referenced THE RICH STRUCTURE OF MINKOWSKI SPACE at http://arxiv.org/abs/0802.4345..(The math is NOT simple!) But the introduction got me wondering... around page three is this statement: So what knowledge regarding more exact models of spacetime and the relativity...
  31. P

    Beginner's Minkowski diagram / space-time interval question

    Good morning, We are trying to understand Special Relativity through internet, and we would like to ask a couple of questions about the subject. We plan to post more questions as more doubts arise. Both doubts concern the Minkowski space-time diagram. First doubt: in the temporal dimension...
  32. nicksauce

    FRW vs. Minkowski: Variable Speed of Light?

    We can write the Minkowski metric as ds^2 = -c^2dt^2 + d\mathbf{x}^2 or if we wanted different units for the metric ds^2 = -dt^2 + \frac{d\mathbf{x}^2}{c^2} If we make c a function of time we have ds^2 = -dt^2 + \frac{d\mathbf{x}^2}{c(t)^2} Which looks exactly like the FRW metric where...
  33. L

    Minkowski Diagram for Twin Paradox

    In the twin paradox, if B moves away from A at constant high speed what would the minkwoski diagram look like in the frame of A and in the frame of B. well in the frame of A. if B starts next to A i.e. at O and is moving at close to c to begin with the world line of B will just be a straight...
  34. J

    How can you create a geodesic path using the metric and initial velocity?

    Let's say there is a small object heading towards Earth (it will burn up). It is first observed at: x^{\\mu}=[x^{1},x^{2},x^{2},x^{4}]=[x_{0},y_{0},z_{0},t_{0}] with a velocity: V_{v}=[v_{1},v_{2},v_{3},v_{4}] The metric is: ds^{2} = dx^{2} + dy^{2} + dz^{2} -c^{2}*dt^{2} g_{\\mu\\v} =...
  35. B

    Minkowski Metric: Does it Violate Metric Space Axioms?

    I have just been learning in some of my maths courses that a metric space is a set which has an operation mapping 2 members of the set to the reals, called "distance", which respects certain axioms, one of which is that the distance between two members of the set is greater than or equal to...
  36. M

    Minkowski Space-Time: A Philosopher's Guide

    I'm taking a "Space and Time" 4000 level philosophy course and right now we are desperately trying to wrap our heads around the discrepancies between minkowski and prior space-time diagrams and the philosophical significance of absolute speed of light and of time- and length-...
  37. P

    Spec Rel: Proof concerning IF through Minkowski diag

    Homework Statement This problem is from "Relativity" by Rindler, second edition, problem 3.4: Use a Minkowski diagram to establish the following result: Given two rods of equal length l_1 and l_2 (l_2 < l_1), moving along a common line with relative velocity v, there exists a unique inertial...
  38. S

    Minkowski Spacetime: Exploring General Relativity

    Hello, I've had my first couple of lectures on general relativity. Actually, we started by talking about special relativity. We were taught the SR uses Minkowski spacetime and that the displacement (squared) between any two events is given as follows: ds^2 = (c^2)(dt^2) - dx^2 - dy^2 - dz^2...
  39. F

    Defining Velocity, Momentum, and Energy in Minkowski Space

    I'm not completely sure were this post must be (math or here). But i got a question, I want to define velocity, momentum and energy. These looks like a simple task but let me explain the problem. I'm working in the Minkowski space, and the lorentz transformations (just geometrical one's)...
  40. S

    Newtonian perturbations to Minkowski

    The Newtonian gravity limit of GR is represented by a perturbation to Minkowski metric: ds^2 = - (1+ 2\Phi(x,y,z,t)) dt^2 + (1-2 \Phi(x,y,z,t))(dx^2 + dy^2 + dz^2) The geodesic equations of this metric correctly reproduce the Newtonian equations for acceleration of a test particle in...
  41. T

    Vector Space Algebra of Minkowski Space

    Consider the Minkowski space of 4 dimensions with signature (- + + +). How does the vector space algebra work here? More specifically given 3 space like orthonormal vectors how do we define fourth vector orthogonal to these vectors? I am looking for an appropriate vector product like it is in...
  42. Jorrie

    Is the Loedel Diagram a Special Case of the Minkowski Spacetime Diagram?

    The main attraction of the Loedel spacetime diagram is that it treats the reference frame and the first moving frame symmetrically and hence they have identical scales in geometric units. The Minkowski diagram uses different scales for the orthogonal and the non-orthogonal axes, where the time...
  43. A

    What is the Minkowski Metric and How Does it Relate to Special Relativity?

    hey, i'm just trying to learn about special and general relativity and i figure a good place to start is with minkowski space since that is the basis of special relativity. I have a few questions though, i hope you forgive me because these questions will sound rather ignorant and silly i...
  44. T

    Exploring Minkowski Metric and Tensors in General Relativity

    hello. I'm working on a philosophical summary of general relativity. i have difficulty understanding tensor. i made the following characterization; can any expert minds here tell me if i said it correctly? if anyone can take a peek to see if what i got so far is correct that'd be sooooooo...
  45. A

    Is Light-Like an Appropriate Term in Minkowski Space Terminology?

    Hey friends, When using phrases such as time-like and space-like, is it proper form to use the phrase light-like? Or is there a more professional expression?
  46. B

    Proof of Minkowski Inequality using Cauchy Shwarz

    I tried to expand the [SUM{[X sub k + Y sub k]^2}]^1/2 term but I am stuck there.
  47. M

    Relativity in Minkowski Space and Minkowski Diagram

    hi :smile: I'm working on "Relativity on Minkowski Space and Minkowski Diagrams" as my undergraduate project. I have some references for my project but I want to make it perfect. May you introduce me some cool stuff (references, interestings, topics to work on & etc.) about this topic...
  48. Oxymoron

    Geodesics in Minkowski Spacetime

    What are Jacobi Fields and how can I better understand geodesics in Minkowski spacetime by knowing what they are?
  49. S

    Minkowski metric in spherical coords.

    Never mind, I just discovered my mistake...
  50. F

    Fourier tr. of dirac delta in minkowski space

    Hey everyone, a quick question: what is the Fourier space representation of the dirac delta function in minkowski space? It should be some integral over e^{ikx} (with some normalization with 2*pi's). I'm curious if the "kx" is a dot product in the minkowski or euclidean sense, and how one...
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