# Linked Questions

22 votes
9 answers
10k views

### 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 $$ds^{2} = -(c^{2}dx^{0})^{2} +(dx^{1})^{2} + (dx^{2})^{2} + (dx^{3})^{2}$$ ...
• 1,049
11 votes
3 answers
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
10 votes
4 answers
880 views

### Is velocity an angle?

I am not a physicist. I have only rudimentary notions about the following. I looked for similar questions on SE but I did not find any. I also tried search engines but results relate to angular ...
• 3,236
1 vote
1 answer
163 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 ...
1 vote
1 answer
250 views

### How is a pseudo-Euclidean metric superior to Minkowski's complex metric? [duplicate]

This is my second attempt to get a meaningful response from you guys on this issue. The SR invariance formula makes space-like intervals imaginary (e.g., the distance $x$ in a given frame has ...
1 vote
0 answers
151 views

### Minkowski's model of space-time not extendible to G.R [closed]

My latest comment: Minkowski did not suggest CxR3. He used one (imaginary) dimension for t, & 3 real dims for space. There is no reason to think this is merely a trick. When a math representation ...
0 votes
1 answer
152 views

### How well does the concept or model of imaginary time work? [duplicate]

In order to make the Minkowski metric, in special relativity, equivalent to the Euclidean metric, one idea is to allow time to take imaginary values. As far as I have learned about SR, it does make ...
• 300
0 votes
0 answers
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-...
• 1,171
0 votes
1 answer
62 views

### Minkowski product as Euclidean product plus spatial inversions

In special relativity, we write contravariant and covariant vectors respectively as $$A^\mu=(A^0, A^1, A^2, A^3), \quad A_\mu=(A_0, A_1, A_2, A_3).$$ Since $A_\mu=\eta_{\mu\nu}A^\nu$, we read off the ...
0 votes
0 answers
40 views

### Notation on four-vectors using imaginary spacelike components [duplicate]

Can one just change the notation of four vectors so as instead of having $$X^{\mu} =(X^0, \vec{X})$$we define $$X^{\mu}=(X^0,i\vec{X})?$$ This way we could use the Euclidean metric instead of g^{\...
• 351
-3 votes
1 answer
115 views

### Is time intrinsically complex? Does it have an imaginary component? [duplicate]

In twin paradox, there is an unaccounted area in the unaccelerated frame of its Space-time diagram when one frame's simultaneity is being mapped to the other; ergo period motion of pendulum in one ...
• 1