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### 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 ...
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### 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 ...
167 views

### 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 ...
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### 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 ...
37 views

### 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-...
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### 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 $$ds^{2} = -(c^{2}dx^{0})^{2} +(dx^{1})^{2} + (dx^{2})^{2} + (dx^{3})^{2}$$ ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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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 $... 3 votes 0 answers 468 views ### 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 ... • 141 0 votes 1 answer 127 views ### 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. ...
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