Linked Questions

0 votes
2 answers

Why is it problematic to regard the Lorentz group as ${\rm SO}(4, \mathbb{C})$? [duplicate]

If the four-vector $x^\mu$ is defined as $x^\mu\equiv(ict,{\bf x})$, instead of $x^\mu\equiv (ct,{\bf x})$, the Lorentz group will be the compact(?) ${\rm SO}(4, \mathbb{C})$ group. But the Lorentz ...
SRS's user avatar
  • 25.7k
1 vote
1 answer

Why the imaginary unit in time axis? [duplicate]

Why time is not like other dimensions is a real amount? In relativity time axis is $i*c*t$, where $i$ is the imaginary unit and $c$ is light speed in free space. Did science or philosophy reached to ...
Ahmed Kamal Kassem's user avatar
0 votes
0 answers

The imaginary time [duplicate]

Some people work with the interpretation that the time basis vector has magnitude sqrt(-1) to justify the negative sign in a -+++ Minkowski metric signature. I came across a Youtube comment that ...
Ken Wang's user avatar
  • 421
0 votes
0 answers

What is the advantage of using imaginary units for time in the Minkowski Space rather than regular euclidian space as Lorentz used? [duplicate]

I do understand that Lorentz transformations became as a rotation of coordinates as of a hyperbolic rotation. But what is its advantage over real vector? What is the new thing that it introduces and ...
Csopso's user avatar
  • 1
0 votes
0 answers

Imaginary velocity components in geodesic [duplicate]

When we try to find the geodesic of a partical at rest, in the second term of the geodesic equation we use dt/dtau = 1. Shouldn’t it be i (for imaginary number), since the time component of the 4-...
Nayeem1's user avatar
  • 773
19 votes
9 answers

Minkowski Metric Signature

When I learned about the Minkowski Space and it's coordinates, it was explained such that the metric turns out to be $$ ds^{2} = -(c^{2}dx^{0})^{2} +(dx^{1})^{2} + (dx^{2})^{2} + (dx^{3})^{2} $$ ...
Doryan Miller's user avatar
31 votes
3 answers

Can quaternion math be used to model spacetime?

Quaternions are commonly used to model 4 dimensional systems where the quaternion consists of a real 3 dimensional vector and an imaginary scalar. So on the surface Quaternions seem well suited to ...
docscience's user avatar
  • 11.6k
12 votes
4 answers

Minkowski spacetime: Is there a signature (+,+,+,+)?

In history there was an attempt to reach (+, +, +, +) by replacing "ct" with "ict", still employed today in form of the "Wick rotation". Wick rotation supposes that time is imaginary. I wonder if ...
Moonraker's user avatar
  • 3,115
15 votes
2 answers

Are basis vectors imaginary in special relativity?

It sounds absurd, but it seems to come naturally: I know that $g_{\mu \nu }=e_\mu \cdot e_\nu $ (source) and that the diagonal elements of $\eta_{\mu \nu}$ are typically $\pm(1, -1, -1, -1)$. This ...
doublefelix's user avatar
  • 6,814
7 votes
4 answers

How many seconds are a meter in the 4th dimension? [closed]

The title really does say it all. I want to know how many seconds elapse between a meter in the 4th dimension? I don't know if this question is naive, or my understand of the dimension is off. I'm ...
Tobi's user avatar
  • 1,809
10 votes
4 answers

Does time dilation mean that faster than light travel is backwards time travel? [duplicate]

Ok. So my question is, I've always heard it that Faster Than Light travel is supposedly backwards time travel. However, the time dilation formula is $$T=\frac{T_0}{\sqrt{1-v^2/c^2}}$$ And while it ...
Guthrie Douglas Prentice's user avatar
2 votes
2 answers

Minkowski's complex Euclidean space vs. the real pseudo-Euclidean version

The SR invariance formula makes space-like intervals imaginary (e.g., the distance $x$ in a given frame has interval $ix$). Yet modern physicists consider it bad form to define the distance itself as $...
murray denofsky's user avatar
3 votes
0 answers

Why is imaginary time "outdated"? [closed]

I was looking at reviews for Sakurai's Quantum Mechanics textbook, and some mentioned it being outdated, specifically mentioning his use of imaginary time. Is this idea deliberately avoided in modern ...
user2264247's user avatar
0 votes
1 answer

Lorentz transformations: new actual notation for a $4$-vector [duplicate]

For the Lorentz trasformations I use this notation \begin{equation*} \left\{\begin{aligned} x&=\gamma (x'+\beta ct')\\ y&=y'\\ z&=z'\\ ct&=\gamma (ct'+\beta x')\\ \end{aligned}\right. ...
Sebastiano's user avatar
  • 2,454
0 votes
0 answers

Does everything move through spacetime at the same speed? [duplicate]

It seems to me that this article ("What’s the real reason you can’t go faster than the speed of light?", Big Think, November 17, 2022) is wrong or misleading in claiming that every object ...
present's user avatar
  • 109