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
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...
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...
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...
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=...
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...
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...
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...
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.
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...
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...
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...
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...
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)...
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...
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...
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...
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 +...
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...
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}}...
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...
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...
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...
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...
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...
<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...
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?
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...
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 ?
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:
$$...
Homework Statement
Hi, I am just stuck in why / how we can write minkowski metric where I would usually write delta.
I see that the product rule is used in the first term to cancel the terms in the second term since partials commute for a scalar and so we are left with the d rivative acting...
I'm confused as to how far apart the hash marks should be on a minkowski spacetime diagram that shows the rocket frame overlapped over the lab frame. Should the hash marks that represent space in the rocket frame be spaced apart exactly the same length as the hash marks that represent space in...
Hi all! Sorry for the bad English! =)
I'm reading a book about the interpretations of the findings of Einstein and others and i came across a statement that sounded very nice, but since it's its author is more tendentious to the Lorentz interpretation, I'm not sure if it's right. As I...
In https://arxiv.org/abs/gr-qc/0309072 Visser starts from Minkowski metric (5), performs a coordinate transformation (6)-(7) and gets Schwarzschild geometry (12). But this should be impossible. Minowski metric has vanishing Riemann curvature tensor, while Schwarzschild geometry hasn't. What do I...
Homework Statement
https://i.imgur.com/sI3JiB4.jpg
https://i.imgur.com/PLpnPZw.jpg
I have no idea how to solve the first question about the vacuum energy. I solved the second and third problems, but I'm hopelessly stuck at the first.
2. Homework Equations
The Hamiltonian can be written as...
I have only seen scenarios so far where the elements are all along the diagonal, but what are some known cases where there are off-diagonal elements?
Thank you.
It is known that vectors change them sing under the influence of parity when ##(x,z,y)## change into ##(-x,-z,-y)##
$$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...
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...
Greg Bernhardt submitted a new PF Insights post
Coordinate Dependent Statements in an Expanding Universe
Continue reading the Original PF Insights Post.
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...
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?
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...
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...
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...
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,$$...
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?