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. nomadreid

    Circles in Minkowski space: unknown notation

    I am reading an article about Minkowski space (as a vector space, which is why I am putting my question in this rubric) which is poorly translated from the Russian, and have come across several notational curiosities, most of which I have been able to figure out. However, there is one that I do...
  2. nomadreid

    Units of spacetime in Minkowski metric

    In the equation ds2=dx2+dy2+dz2-c2*dt2 the units on the RHS are units of distance squared. But it would seem that units for a spacetime metric should somehow be in units which incorporate both space and time units. Undoubtedly this is an elementary question, but one has to start somewhere...
  3. R

    Understanding Minkowski Space Compactification

    Hi. I'm reading about the compactification of Minkowski Space, and there is a subject that is keeping me awake. They say that the group of conformal transformations is isomorphic to the group of pseudoorthogonal transformations with determinant equal to 1. I don't know how this happen and it...
  4. C

    What is the Definition of Continuity in Minkowski Space?

    How "continuity" of a map Τ:M→M, where M is a Minkowski space, can be defined? Obviously I cannot use the "metric" induced by the minkowskian product: x\cdoty = -x^{0}y^{0}+x^{i}y^{i} for the definition of coninuity; it is a misinformer about the proximity of points. Should I use the Euclidean...
  5. L

    Hyperbolic path in Minkowski space

    The path described by a constantly accelerating particle is given by: x=c\sqrt{c^2/a'^2+t^2} where a prime denotes an observer traveling with the particle and a letter without a prime a resting observer. If we leave the c^2/a'^2 out it reduces to x=ct, which makes sense. The distance...
  6. SamRoss

    Proof Minkowski metric is invariant under Lorentz transformation

    Ok, this should be an easy one but it's driving me nuts. When we take the Lorentz transformations and apply them to x2-c2t2 we get the exact same expression in another frame. I can do this math easily by letting c=1 and have seen others do it by letting c=1 but I have never seen anyone actually...
  7. Philosophaie

    Schwarzenchild vs Minkowski: 4-Space & EigenValues

    The Schwarzenchild Metric can be the Minkowski Tensor with the correct terms in 4-Space. If not Schwarzenchild Metric must have EigenValues are all real and the Matrix is symmetrical.
  8. marcus

    Stability of Minkowski and deSitter Spaces in GR

    Minkowski space and deSitter space have been shown to be stable in GR under small perturbations. Perturbations do not intensify in higher frequency modes--these solutions don't go haywire and develop black holes all over the place. Piotr Bizon has shown that Anti-deSitter (AdS) space is not...
  9. M

    Minkowski diagram, what does observer see.

    Suppose we have a spacetime diagram like this: Red lines indicating light travel from the moving object to the observer. Object is moving at the speed of 0.8c. At this speed we have: Lorentz factor 1/√(1 - v2/c2)=1/0.6=1.66(6) Relativistic Doppler effect √((1 + β) / (1 - β)) = 3 My question...
  10. ash64449

    Exploring Minkowski Space: Understanding Special Theory of Relativity

    Hello friends, I am reading Einstein's special theory of relativity and came across this subject: Minkowski space. I cannot understand exactly what it is when i read that book and went to Wikipedia for understanding more about it. But i didn't understand much. What i...
  11. shounakbhatta

    Understanding the Minkowski Metric: Explained Step-by-Step for Beginners

    Hello, I don't know whether I have mentioned the subject line properly. Many times while reading over General Relativity I come across the following equation: ds^2=dx1^2+dx2^2+dx3^2+dx4^2 =dx^2+dy^2+dz^2-c^2dt^2. Now, my question from the above equation is: (a) Are we putting...
  12. K

    General and Special Relativity Minkowski spaces

    Homework Statement In attached imageHomework Equations ?The Attempt at a Solution ? A start would be fantastic!
  13. D

    2D Systems and 4D Minkowski Space: Exploring Path Integrals

    The combination of special relativity and quantum mechanics in a single framework makes our understanding of such systems to be true only in 4D, Minkowski space...I have noticed that recent published work concerning 2D systems and I am not sure about this reduction of 4D to only 2D, does it mean...
  14. P

    Rotating Flat Spacetime in Minkowski Metric

    In Minkowski spactime (Flat), if the coordinate system makes a rotation e.g. around y-axis (centred) , for the metric ds^2, how to make the tertad (flat spacetime) as the coordinate system rotats?
  15. 7

    Deriving a Minkowski Force Matrix: Exploring 4-force

    Our professor derived a Minkowski force like this: F^\mu = \left[ \gamma(e\vec{E} + e(\vec{v}\times \vec{B})) , \gamma \frac{e \vec{E} \vec{v}}{c} \right] Does this mean that i can write 4-force like this? F^\mu = \begin{bmatrix} \gamma(e\vec{E} + e(\vec{v_x}\times \vec{B}))\\...
  16. J

    Minkowski Metric: Timelike vs Spacelike

    hello Whic one of these to metric are Minkowski metric ds^2 =-(cdt)^2+(dX)^2 ds^2 =(cdt)^2-(dX)^2 and what about timelike (ds^2<0) and spacelike (ds^2>0) for each metric? With my appreciation to those who answer
  17. 7

    Length contraction and Minkowski diagram

    Hello, in my other topic members on the forum helped me to understand time dilation by using Minkowski spacetime diagram. Now i would also need some assistance with explaining length contraction in Minkowski spacetime diagram. I have observer Žiga in his frame ##x,ct## and observer Ranja...
  18. 7

    Time dilation and Minkowski diagram

    After i figured out how to show length contraction in this topic. I tried to use a similar way to show time dilation in Minkowski diagram. Time dilation means that time interval between two events is the shortest in the frame in which those two events happen in same place. We call this frame its...
  19. A

    Unraveling The Minkowski Metric: Intuitive Explanation

    yeh well, I once understood this, but now looking at it today I can't get it to make sense intuitively. The quantity: dx2+dy2+dy2-c2dt2 is the same for every intertial frame in SR - just like length is the same in all inertial frames in classical mechanics. Now I am not sure that I...
  20. J

    Attempt on Twin Paradox via Minkowski diagrams

    This is an attempt to solve the twin paradox via two Minkowski diagrams with a few questions attached. Note that there might be mistakes in this drawing i will fix in the course of this thread in case someone notices any. First, let me explain the two Minkowski diagrams in the drawing first...
  21. A

    QFT: Solving the integral for the Wightman function in Minkowski spacetime.

    Homework Statement How does one actually solve the integral for the Wightman function for a massless quantum scalar field in 4D Minkowski spacetime? That is, what is the integration technique to go from: \langle \hat{\phi}(x) \hat{\phi}(y) \rangle = \int_c d^4k \, \frac{1}{(2 \pi...
  22. Vorde

    Minkowski Inner Product and General Tensor/Matrix Question

    Hello all. I have a fairly rudimentary knowledge of matrices and broader linear algebra. This gets me in a lot of trouble when I'm following along the math of something fine and then I run into some matrix stuff and get stumped, like this. I'm a little bit confused on taking the inner product...
  23. E

    Minkowski Metric and the Sign of the Fourth Dimension

    Why is the unit vector for time in Minkowski space i.e. the fourth dimension unit vector always opposite in sign to the three other unit vectors? The standard signature for Minkowski spacetime is either (-,+,+,+) or (+,-,-,-). Is there some particular reason or advantage for making time...
  24. S

    Minkowski metric - to sperical coordinates transformation

    I need to transform cartesian coordinates to spherical ones for Minkowski metric. Taking: (x0, x1, x2, x3) = (t, r, α, β) And than write down all Christoffel symbols for it. I really have no clue, but from other examples I've seen i should use chain rule in first and symmetry of...
  25. P

    Minkowski Metric Sign Convention

    Hello, I believe this is a really stupid question but I can't seem to figure it out. So given a Minkowski spacetime one can choose either the convention (-+++) or (+---). Supposedly it's the same. But given the example of the four momentum: Choosing (+---) in a momentarily comoving...
  26. W

    Plane wave in Minkowski space-time

    The classical expression of a plane electromagnetic wave (electric part) \bar{E}(t,\bar{x})=\bar{E}_{0}e^{i(\bar{k}\cdot \bar{x}-\omega t)} looks a lot like the basis function of the Fourier decomposition in Minkowski space-time...
  27. G

    Tachyonic Energies in a Minkowski Metric

    So I'm working on a problem (Hartle problem 6, chapter 6) dealing with tachyons. So far, I have determined the four-velocity and the four-momentum (up to a sign) of a tachyon. I have, with the four-velocity being a unit spacelike four-vector, u^{\alpha}=\frac{\pm...
  28. R

    8-dimensional Minkowski spacetime

    How viable is 8-dimensional Minkowski spacetime with the extra 4 dimensions in the imaginary plane. This is said to give mechanism for quantum entanglement because doing a Pythagorean calculations can make the distances 0. See: http://whyentanglement.com/ reviewed by Ken Renshaw Ken...
  29. C

    Time dilation in minkowski diagrams

    Hey! I'm trying to understand time dilation in terms of minkowski diagrams. Below I've added a diagram showing the two coordinate systems where the primed one moves relative to the unprimed one with a speed v. http://mindseye.no/wp-content/uploads/2012/01/time1.png My reasoning in this...
  30. Demon117

    The Poincaré Group and Geodesics in Minkowski Spacetime

    The poincare' group is the group of isometries of Minkowski spacetime, in a nutshell. In terms of an actual physical definition it is the group of all distance preserving maps between metric-spaces in Minkowski spacetime. What is the difference between this and geodesics?
  31. D

    Up-tunneling is Impossible for Minkowski, DeSitter, or Anti-de Sitter

    http://arxiv.org/PS_cache/arxiv/pdf/1111/1111.0301v1.pdf Hi everyone! I'd like to get a little discussion started on what you guys think about this paper if you have the time to read it. I find it really fascinating that they came to the conclusion that up-tunneling is impossible for...
  32. C

    Quick question on product of Minkowski tensors

    Homework Statement Let's say I have (g^{\nu\alpha}g^{\mu\beta} - g^{\nu\beta}g^{\mu\alpha})F_{\nu} The Attempt at a Solution Would this just equal g^{\mu\beta}F_{\alpha} - g^{\mu\alpha}F_{\beta} = \delta^{\mu}_{\alpha}F_{\alpha} - \delta^{\mu}_{\beta}F_{\beta} = 0?
  33. Z

    Fourier transform in Minkowski space

    Hi, In Fourier analysis, we can decompose a function into sine waves with different wavenumbers that travel at different speeds (i.e., for a given wavenumber k they can have different frequencies ω and therefore different speeds v = ω/k). There is no upper bound on the speed of propagation v...
  34. 3

    Minkowski diagram - the angle between axes

    I was reading through my textbook and it said that the angle between the axes of two inertial frames, one stationary and one moving at velocity v is supposed to be tan^-1(v/c). I assumed this would be easy to show, but after spending a couple of hours on this probably trivial problem, I can't...
  35. D

    Visualizing Minkowski geometry

    Is there a better way of visualizing (flat) spacetime than Minkowski diagrams? In Minkowski diagrams, the distance between events doesn't match the Minkowski norm, and I feel that it may be possible to change this with some other representation of spacetime, maybe involving curved surfaces or...
  36. T

    Geometric shape of Minkowski space

    So, suppose for visualization there are only two dimensions: ct and x. Now if the metric where Euclidean, we could visualize this space is a simple plane. What would be the shape of the "plane" when the metric is +1, -1 (Minkowski)? Is it somehow hyperbolic?
  37. C

    Topology of Minkowski spacetime

    I recently Googled "spacetime topology" and found that the topology of Minkowski spacetime is generally described as that of an R4 manifold. This is not my field, but I'm surprised. Perhaps mathematically the (---+) "Lorentz signature" can be taken as a secondary characteristic of the...
  38. L

    T constant lines in Minkowski Conformal Diagram

    Hi, I've been trying to work out exactly why the t=const and r=const lines look like they do in the Minkowski conformal diagram. I started with the usual Minkowski metric in polar coords (t,r) then go into null coords, then pull in the infinities by using arctan transformations, finally I then...
  39. WannabeNewton

    Killing vectors of minkowski space

    How does one know from the general form of the killing vectors in minkowski space: X^{a} = \omega_a_b(x^{a}) + t^{a} that there are 3 rotational isometries, 3 boosts, 3 spatial translations, and 1 time translation from that general form? It has me very confused >.<
  40. E

    Solving Einstein Field Equations for Minkowski Space with CTC

    For Minkowski spacetime, the metric is: ds^2 = -dt^2 + dx^2 + dy^2 + dz^2 I have read there is a solution when the time dimension is "rolled" into a cylinder forming a closed timelike curve. So the BC is t -> [0,T] with t = 0 identical with t = T. The Field Equation is: Rab - 1/2...
  41. B

    What is the different between Minkowski Space an Semi Riemann Space?

    Last summer I took Semi Riemann Geometry lesson. Almost all the definitions in Semi Riemann geometry are with the same Minkowski geometry. I don't understand what is the different between Minkowski Space an Semi Riemann Space.
  42. C

    Free particle in Minkowski spacetime

    Homework Statement A free particle is moving in the x direction through Minkowski spacetime, and has velocity V as measured by a stationary observer at x = 0; t = 0. Express the particle's world-line parametrically in terms of V , parametrized by the particle's proper time  Homework...
  43. K

    Local Minkowski space and free falling

    Einstein's equivalence principle states that free-falling observers are in local inertial frame, so one can construct a local Minkowski frame everywhere. So my question is whether the logic can be inversed, does every local Minkowski space represent free-falling? because in vierbein...
  44. R

    Prove Minkowski Inequality using Cauchy-Schwartz Inequality

    I expanded (x+y),(x+y) and got x^2+y^2 > 2xy then replaced 2xy with 2|x,y| but now I'm stuck. I need to get it to ||x+y|| <= ||x|| + ||y||. Am I close?
  45. D

    Is Minkowski Space a Metric Space?: Exploring the Requirements and Implications

    is minkowski space a metric space. As best as i can remember a metric space is a set with a metric that defines the open sets. With this intuition is Minkowski space a metric space. I mean i think it should be, but according to one of the requirements for a metric: d(x,y)=0 iff x=y triangle...
  46. P

    Minkowski vacuum: Poincare invariant, quasi-free state

    Minkowski vacuum is Poincare invariant and quasi-free state. I wonder if these two conditions fully define it or there are more states which fulfill these conditions (or maybe Poincare invariance alone is sufficinet). Thanks for answers.
  47. R

    Is Minkowski space the only Poincare invariant space?

    Hi everyone, I was wondering: if a space is invariant under Poincare transformations, does that mean it has to be Minkowski space? Or could it have some further isometries? By the same token, if a space is invariant under the orthogonal transformations, does it have to be Euclidean? I...
  48. S

    Alternative form of Minkowski metric?

    I've tried to find this addressed in other threads without success, so I apologize if it has already been addressed. In Coleman and De Luccia (Gravitational effects on and of vacuum decay), they suggest that by analytic continuation ( \[\xi = i\tau \] ): \[ds^2 = -d\xi ^2 - \rho (\xi...
  49. M

    Orthogonal diretion on the Minkowski diagram

    I have a trivial question: Let assume a world sheet of a time-like spherical shell in Minkowski space-time. On the 2D-Minkowski diagram (R,T), where R is the radius and T is the time, the world line is represented by a time-like curve. Let assume that the shell collapse and its 4-velocity is...
  50. K

    Minkowski Space Basics: Time, Light Speed & Purpose

    Why is the vertical axis time multiplied by the speed of ligth? And, what is the purpose of using Minkowski space?
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