Minkowski Definition and 206 Threads

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

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...

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...

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...

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...

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

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.

[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.

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...

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...

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...

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...

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...

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...

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...

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...

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)...

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...

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...

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...

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...

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...

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...

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...

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...

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?

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?

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

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

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...

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...

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...

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...

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} =...

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...

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-...

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...

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...

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)...

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...

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...

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...

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...

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...

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?

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

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...

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

Never mind, I just discovered my mistake...

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...