Minkowski Definition and 206 Threads

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?

Can anyone please illustrate highlighted part? Can anyone please explain me how invariance of s^2 is useful in characterization of events? I didn't understand the highlighted part i.e. how to determine velocity of S' relative to S?

If Hubble's constant = 160,000 m/sec/million light years and c = 299,792,458 m/sec, then shouldn't any two points in the universe farther than about 1,873,000,000 light years apart be expanding away from each other faster than c? Since light from sources much farther than this has reached us...

Hello, I noticed something peculiar when looking at the Minkowski Diagram and I'm not sure how to interpret this. Let observer A be the reference frame for the diagram and B someone who travels with respect to A. The red line is the displacement of light over time. The blue, yellow and green...

In an inertial coordinate system in two-dimensional Minkowski spacetime, the metric takes the form $$(ds)^{2} = - (dt)^{2} + (dx)^{2},$$ and in an accelerating coordinate system in two-dimensional Minkowski spacetime, the metric takes the form $$(ds)^{2} = - R^{2}(d\eta)^{2} + (dR)^{2}.$$ The...

I set eyes on the next formulas: \begin{align} E_{\alpha \beta \gamma \delta} E_{\rho \sigma \mu \nu} &\equiv g_{\alpha \zeta} g_{\beta \eta} g_{\gamma \theta} g_{\delta \iota} \delta^{\zeta \eta \theta \iota}_{\rho \sigma \mu \nu} \\ E^{\alpha \beta \gamma \delta} E^{\rho \sigma...

I've made a Interative Minkowski Diagram Tool, http://divykjain.github.io/IMD You can add events, connect events and add world lines. Lorentz transformation for moving frames also present. I've added support for frame velocities equal or greater than light speeds(but the animations are a mess...

Forgetting for the moment about curved spacetime, does the relativistic QFT in use today by experimental physicists live in Euclidean spacetime or Minkowski spacetime. Thanks in advance.

Homework Statement A generalized potential suitable for use in a covariant Lagrangian for a single particle. This is Goldstein problem 9 chapter 7. −Aλν(xμ)uλuν where Aλν stands for a symmetric world tensor of the second rank and u^v are the components of the world velocity. If the...

1. Homework Statement In a diagram where I have two observers (one still (A) and one moving with a "v" velocity (B)), where the two parts disagre in the simultaneity of events, how can I prove that the angles of the B person axis that are put in the A person axis are equal. (/alpha=/beta , in...

If our base space, B, is Minkowski spacetime and our fibers are circles S^1 are the following constructions ways to put together B and S^1 and have a total space, T, that is considered a fiber bundle. Remove from Minkowski spacetime, M, a timelike line, L. At the remaining points of Minkowski...

robphy submitted a new PF Insights post Relativity on Rotated Graph Paper Continue reading the Original PF Insights Post.

Something that has been bothering me for a while is this question. As seen from this Minkowski diagram,http://imgur.com/GkBN2HQ , the angle between x and x' is equally big as the angle between ct and ct'. I really can't seem to figure out why this is, although I think it has to do with the...

Hi. I have seen quite a lot of demonstrations of time dilation and length contraction that used standard Minkowski diagrams WITHOUT any scales on the axes at all. If I understand them correctly they seem to directly compare lengths, which would imply (I think) that the scaling on the ##ct/x##...

Hi, When I started learning about GR I wondered if it emerged from SR (which the name suggests) or if the connection between the two is mere technical. GR describes the behaviour of the metric of space-time, which is locally Minkowskian and therefore SR applies. But is a curvature-based theory...

Does the constancy of the speed of light for all observers naturally emerge from the Minkowski spacetime metric? Do Einstein's two postulates of relativity emerge from the Minkowski spacetime metric? Suppose we begin with Minkowski spacetime and the Minkoswki metric...

Homework Statement Consider Minkowski space in the usual Cartesian coordinates ##x^{\mu}=(t,x,y,z)##. The line element is ##ds^{2}=\eta_{\mu\nu}dx^{\mu}dx^{\nu}=-dt^{2}+dx^{2}+dy^{2}+dz^{2}## in these coordinates. Consider a new coordinate system ##x^{\mu'}## which differs from these...

Hello, First of all, I'm sorry since I bet there are quite a few threads about this but I still have a bit of a hard time wrapping the axes of the Minkowski diagram around my head. I understand very well that, to have the speed of light traveling at a 45 degree angle in a space-time diagram...

Wald, General Relativity, p. 411, says that Minkowski space is unstable in semiclassical gravity. He gives a reference to this paper: Horowitz, "Semiclassical relativity: The weak-field limit," Phys. Rev. D 21, 1445, http://journals.aps.org/prd/abstract/10.1103/PhysRevD.21.1445 The Horowitz...

I understand that in order to preserve the inner product of two four vectors under a change of coordinates x^{\mu}\rightarrow x^{\mu^{'}}=\Lambda^{\mu^{'}}_{\,\, \nu}x^{\nu} the Minkowski metric must transform as \eta_{\mu^{'}\nu^{'}}=\Lambda^{\alpha}_{\,\...

I have attached a derivation of the Minkowski norm of the four-momentum but just don't quite see how the writer arrived at ## -m^2 c^2 ## from what was given. How exactly does this quantity follow from ## -\frac {E^2}{c^2} + p^2##? I feel like it might be very obvious, so any explanation would...

The Euclidean classical action ##S_{\text{cl}}[\phi]## for a scalar field ##\phi## is given by \begin{equation} S_{\text{cl}}[\phi]=\int d^{4}x\ \bigg(\frac{1}{2}(\partial_{\mu}\phi)^{2}+U(\phi)\bigg). \end{equation} This can be obtained from the action ##S_{\text{Mn}}[\phi]## in Minkowski...

I'm trying to get an intuitive feel for Minkowski space in the context of Special Relativity. I should mention that I have not studied (but hope to) the mathematics of topology, manifolds, curved spaced etc., but I'm loosely familiar with some of the basic concepts. I understand that spacetime...

Couple of questions as to how to interpret the Minkowski diagram when it comes to intergalactic space. 1) To begin, I'll make some pre-assumptions to the question, which you may correct if I'm wrong: 1a) Within any given galaxy, the distances between it's constituent stars is roughly equal...

Suppose I take 2d Minkowski space ds^2=-dt^2+dx^2 and put a test particle in there. I would expect that since we have a flat space with no matter inside that it should just "sit still" so to speak i.e. not move anywhere. However, there will be an integral of motion (since we have a timelike...

Homework Statement two objects are at rest in an inertial reference frame. Two objects accelerate simultaneously in the same direction until reaching half the velocity of light and then halt simultaneously. The two objects are initially connected by a thread just long enough to cover the...

I had some questions about how to understand the Minkowski diagram better: 1) One thing that I hear characterizes a light ray or a photon is that it "experiences no time." That is, it's time dilation is so extreme that at the "null lines" or light cone lines at the 45 degree mark, the...

Hi, I'm doing a first course in GR and have just found out that \eta_{ab} = g(\vec{e}_{a}, \vec{e}_{b}) = \vec{e}_{a} \cdot \vec{e}_{b} where g is a tensor, here taking the basis vectors of the space as arguments. I haven't seen this written explicitly anywhere but does this mean that...

Hi all, Just doing some hobby physics while I put off working on my research. In one dimension, the function \begin{equation} f(a,b)=[1-\exp(-(a-b)^2)] \end{equation} vanishes when a=b. In Minkowski spacetime though, such a function is not so easy to find (if you require Lorentz invariance). If...

Hello, in this section of the wiki article on Rindler coordinates it is stated that the proper acceleration for an observer undergoing hyperbolic motion is just "the path curvature of the corresponding world line" and thus a nice analogy between the radii of a family of concentric circles and...

So I was wondering, is the variation of the Minkowski Metric zero? As in ##{\delta}{\eta}_{\mu\nu}=0## . I would think this is the case because the components of the Minkowski Metric are just numbers (either +1 or -1), so varying it gives you 0. Is this correct?

Starting from the general expression of the metric in coordinates, what is the time misured by a clock in a non inertial reference sistem?

This is a little toy I put together that I thought might be of interest: http://ibises.org.uk/Minkowski.html It's an interactive Minkowski diagram. You can add events and connect them up with straight-line paths, then Lorentz boost either to a specified velocity or to the rest frame of a...

I have the expression ##g_{ab}=\eta_{ab}+\epsilon h_{ab}##, The indices on ##h^{ab}## are raised with ##\eta^{ab}## to give ##g^{ab}=\eta^{ab}-\epsilon h^{ab}## I am not seeing where the minus sign comes from. So I know ##\eta^{ab}\eta_{bc}=\delta^{a}_{c}## and...

Homework Statement How do you find the killing vectors for Minkowski space(or from any metric as well)? Homework EquationsThe Attempt at a Solution I'm new to GR and I'm going through Carroll's book. I've been alright so far but for some reason I just don't understand what's going on here...

I've never seen a satisfactory explanation of the metrics used in a calculation of distance in Minkowski space. In Euclidean space, the distance is: ds^2 = dx^2 + dy^2 + dz^2 But in Minkowski space, the distance is ds^2 = (dt * c)^2 - dx^2 - dy^2 - dz^2 Why are the signs reversed? This implies...

Consider the lower right plot in this picture (or many similar ones). I interpret the angle of the t' axis with respect to the t axis as: From the point of view of the stationary observer, all progress in time for the moving observer will be accompanied by the latter's spatial progress (to the...

I am attempting to read my first book in QFT, and got stuck. A Lorentz transformation that preserves the Minkowski metric \eta_{\mu \nu} is given by x^{\mu} \rightarrow {x'}^{\mu} = {\Lambda}^\mu_\nu x^\nu . This means \eta_{\mu \nu} x^\mu x^\nu = \eta_{\mu \nu}x'^\mu x'^\nu for all x...

Hello everybody, I'm currently reading the book Special Relativity in General Frames by Gourgoulhon. There, Minkowski Spacetime is introduced as an affine space \mathscr{E} over \mathbb{R} with a bilinear form g on the underlying vector space E that is symmetric, nondegenerate an has signature...

Can two objects have same world line in Minkowski Space, if they are having same speeds ?

I have recently been studying the tensors on the left side of the Einstein field equations, but I have been studying and deriving them in 3-D. I would now like to move on to adding time into the mixture. I have some questions regarding the Minkowski metric \eta\mu\nu. First, I know that...

First of all note that 8-dinensional Finsler space (t,x,y,z,t^*,x^*,y^*,z^*) preserving the metric form \begin{equation} S^2 = tt^*-xx^*-yy^*-zz^*, \end{equation} actually presents doubled of the Minkowski space. Then the solution with one-dimensional feature localized on the world line...

If I am not mistaken, the change of the minkowski metric to: n_{\mu\nu} \rightarrow g_{\mu\nu}(x) will violate the Poincare invariance of (example) the Electromagnetism Action. However it allows us to define a wider set of arbitrary transformations (coordinate transformations). The last...

Hello to everybody, the question seems trivial in my mind, yet, is it legal to say that there is not unique frame of 0 total momentum in the Minkowski spacetime plane? I am thinking of two non-accelerating equal masses on a horizontal plane, one is moving horizontally, the other...

So I have just been introduced to indices, four vectors and tensors in SR and I'm having trouble knowing exactly what I am being asked in some questions. So the first question asks to write explicitly how a covariant two tensor transforms under a lorentz boost. Now I know that it transforms...

What is the difference between the normal in Minkowski spacetime and the normal in Euclidean space?

Hello friends , I have some conceptual problems in understanding the difference between Minkowski spacetime and the spacetime of general relativity. The general spacetime of GR is defined as a smooth manifold which is locally like Minkowski spacetime . What does this statement mean ? Does...

I am currently studying special relativity on my own and I am looking into space time and space time diagrams. While reading through various sources I came across what seemed to be two methods to describe space time. X0, X1, X2, X3 (ct, x,y,z) -> Lorentz Metric X1, X2, X3, X4 (x,y,z,ict)...

Hi, I know these questions must sound ridiculous and I apologize, I'm a newbie. My textbook says that the inner product of the momentum four-vector is P\bulletP=P\bulletP - E^{2}/c^{2}=-m^{2}*c^{2} So my silly questions are: 1) where did the - E^{2}/c^{2} term come from? 2) I know I'm being...