23 questions linked to/from Minkowski Metric Signature
1k views

### Why did Einstein put a negative sign in the Pythagorean theorem? [duplicate]

In 4-dimensional spacetime, when we study the spacetime interval, why did Einstein put a negative sign in it? $$x_1=x$$ $$x_2=y$$ $$x_3=z$$ $$x_4=ct$$ $$ds^2=dx^2+dy^2+dz^2-(cdt)^2$$
135 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. ...
• 2,547
1 vote
162 views

### 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 ...
182 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 ...
• 431
91 views

### 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 ...
4k views

### 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 ...
• 3,155
3k views

### Special relativity and imaginary coefficient of the time coordinate

I read somewhere that part of Minkowski's inspiration for his formulation of Minkowski space was Poincare's observation that time could be understood as a fourth spatial dimension with an imaginary ...
• 278
1k views

### Is there a geometric interpretation of the spacetime interval?

In Euclidean space, the invariant $s^2 = x^2+ y^2+ z^2$ is equal to the length square of the position vector $r$. This is easily understood and can be represented geometrically in a graph. On the ...
• 93
777 views

### What is the intuition behind the spacetime interval?

In an article that I am currently reading (under the Lorentz Invariants sub-heading), it explains that, just as the distance between two points on a Cartesian plane are obviously invariant of the ...
• 411
1k views

• 3,203
1k views

### Is imaginary time a fifth dimension? [duplicate]

I've read that by introducing the concept of imaginary time, the dimension of time can be treated like a spatial dimension mathematically. Assuming, without imaginary time, one considers the universe ...
• 111
660 views

### Minkowski metric: Why does it look like it does? [duplicate]

I have been searching for why would we even start with Minkowski spacetime metric as being written as: $$ds^2=-dt^2+dx^2+dy^2+dz^2.$$ No really, so why would we have a negative sign for temporal ...
• 1,406
1 vote