Post History
All given metrics are for orthonormal-basis. 2 dimensional spacetime : I saw that Minkowski Metric looks like this : $$\pmatrix{-1 & 0 \\ 0 & 1}$$ or $$\pmatrix{1 & 0 \\ 0 & -1}...
#6: Post edited
- All given metrics are for orthonormal-basis.
- **2 dimensional spacetime :**
- I saw that Minkowski Metric looks like this :
- $$\pmatrix{-1 & 0 \\\\ 0 & 1}$$
- or $$\pmatrix{1 & 0 \\\\ 0 & -1}$$
- I was wondering why it's not written like identity metric. To define a vector in spacetime it's written like this $dS^2 = -(ct)^2+(dx)^2=(ict)^2+(dx)^2$. I know it's same as Minwkowski metric. But in Euclidean metric I was just using identity metric. Is there really any derivation of Minkowski metric? Or he just wrote it curiously. What the negative explains? I know that $ct$ is coordinate. Particle physicist write vector in spacetime (I had read it 3-4 hours ago, I can't find the source again so can't add reference here) like this $ dS^2 = (ct)^2-(dx)^2$.
- **4 dimensional spacetime :**
- The minkowski signature is $\pmatrix{- & + & + & +}$ or negative for space and positive for time. I read in [the question](https://physics.stackexchange.com/questions/107443/minkowski-metric-signature) that, the tensor for spacetime can be written like this : $ds^2=g_{\mu \nu}dx^{\mu}dx^{\nu}$ while $g_{\mu \nu}$ is Minkowski signature and $dx^{\mu}$ and $dx^{\nu}$ represent space coordinate. But in PSE question he wrote that $dx^0=ict$ where $i$ is imaginary number and $dx^0$ is time coordinate. I wonder what's the main reason of taking $ict$ as coordinate. $ct$ looks good to me to be a coordinate. At first I thought, the tensor got a negative sign for time for Minkowski signature. But when I saw $ict$ as coordinate my mind changed again.
- I know the question is too confusing and I am confused about time coordinate, it is $ct$ or $ict$, I don't know. Why Minkowski wrote signature like that?
$g_{xx}=\vec e_x \cdot \vec e_x=1$ That's what we exactly know. But it's different for Minkowski spacetime, when dot product of time basis vector is 1 then dot product of space basis vector is -1 and vice versa, why?
- All given metrics are for orthonormal-basis.
- **2 dimensional spacetime :**
- I saw that Minkowski Metric looks like this :
- $$\pmatrix{-1 & 0 \\\\ 0 & 1}$$
- or $$\pmatrix{1 & 0 \\\\ 0 & -1}$$
- I was wondering why it's not written like identity metric. To define a vector in spacetime it's written like this $dS^2 = -(ct)^2+(dx)^2=(ict)^2+(dx)^2$. I know it's same as Minwkowski metric. But in Euclidean metric I was just using identity metric. Is there really any derivation of Minkowski metric? Or he just wrote it curiously. What the negative explains? I know that $ct$ is coordinate. Particle physicist write vector in spacetime (I had read it 3-4 hours ago, I can't find the source again so can't add reference here) like this $ dS^2 = (ct)^2-(dx)^2$.
- **4 dimensional spacetime :**
- The minkowski signature is $\pmatrix{- & + & + & +}$ or negative for space and positive for time. I read in [the question](https://physics.stackexchange.com/questions/107443/minkowski-metric-signature) that, the tensor for spacetime can be written like this : $ds^2=g_{\mu \nu}dx^{\mu}dx^{\nu}$ while $g_{\mu \nu}$ is Minkowski signature and $dx^{\mu}$ and $dx^{\nu}$ represent space coordinate. But in PSE question he wrote that $dx^0=ict$ where $i$ is imaginary number and $dx^0$ is time coordinate. I wonder what's the main reason of taking $ict$ as coordinate. $ct$ looks good to me to be a coordinate. At first I thought, the tensor got a negative sign for time for Minkowski signature. But when I saw $ict$ as coordinate my mind changed again.
- I know the question is too confusing and I am confused about time coordinate, it is $ct$ or $ict$, I don't know. Why Minkowski wrote signature like that?
- $g_{xx}=\vec e_x \cdot \vec e_x=1$ That's what we exactly know. But it's different for Minkowski spacetime, when dot product of time basis vector is 1 then dot product of space basis vector is -1 and vice versa, why?
- I forgot to mention which actually made me curious to write the question, we know that dot product of any basis vector to itself is $1$ (they always not 1) $\vec e \cdot \vec e = |e| \\ |e| cos\theta$ $\theta=0$ hence $\vec e \cdot \vec e = |e| \\ |e|$. To write $\vec e \cdot \vec e = -|e|^2$, we must make them perpendicular but which is never true. Angle between dot product of vector of itself is $0$ but in Minkowski spacetime diagram, it is something different.
#4: Post edited
- **2 dimensional spacetime :**
- I saw that Minkowski Metric looks like this :
- $$\pmatrix{-1 & 0 \\\\ 0 & 1}$$
- or $$\pmatrix{1 & 0 \\\\ 0 & -1}$$
- I was wondering why it's not written like identity metric. To define a vector in spacetime it's written like this $dS^2 = -(ct)^2+(dx)^2=(ict)^2+(dx)^2$. I know it's same as Minwkowski metric. But in Euclidean metric I was just using identity metric. Is there really any derivation of Minkowski metric? Or he just wrote it curiously. What the negative explains? I know that $ct$ is coordinate. Particle physicist write vector in spacetime (I had read it 3-4 hours ago, I can't find the source again so can't add reference here) like this $ dS^2 = (ct)^2-(dx)^2$.
- **4 dimensional spacetime :**
- The minkowski signature is $\pmatrix{- & + & + & +}$ or negative for space and positive for time. I read in [the question](https://physics.stackexchange.com/questions/107443/minkowski-metric-signature) that, the tensor for spacetime can be written like this : $ds^2=g_{\mu \nu}dx^{\mu}dx^{\nu}$ while $g_{\mu \nu}$ is Minkowski signature and $dx^{\mu}$ and $dx^{\nu}$ represent space coordinate. But in PSE question he wrote that $dx^0=ict$ where $i$ is imaginary number and $dx^0$ is time coordinate. I wonder what's the main reason of taking $ict$ as coordinate. $ct$ looks good to me to be a coordinate. At first I thought, the tensor got a negative sign for time for Minkowski signature. But when I saw $ict$ as coordinate my mind changed again.
- I know the question is too confusing and I am confused about time coordinate, it is $ct$ or $ict$, I don't know. Why Minkowski wrote signature like that?
- $g_{xx}=\vec e_x \cdot \vec e_x=1$ That's what we exactly know. But it's different for Minkowski spacetime, when dot product of time basis vector is 1 then dot product of space basis vector is -1 and vice versa, why?
- All given metrics are for orthonormal-basis.
- **2 dimensional spacetime :**
- I saw that Minkowski Metric looks like this :
- $$\pmatrix{-1 & 0 \\\\ 0 & 1}$$
- or $$\pmatrix{1 & 0 \\\\ 0 & -1}$$
- I was wondering why it's not written like identity metric. To define a vector in spacetime it's written like this $dS^2 = -(ct)^2+(dx)^2=(ict)^2+(dx)^2$. I know it's same as Minwkowski metric. But in Euclidean metric I was just using identity metric. Is there really any derivation of Minkowski metric? Or he just wrote it curiously. What the negative explains? I know that $ct$ is coordinate. Particle physicist write vector in spacetime (I had read it 3-4 hours ago, I can't find the source again so can't add reference here) like this $ dS^2 = (ct)^2-(dx)^2$.
- **4 dimensional spacetime :**
- The minkowski signature is $\pmatrix{- & + & + & +}$ or negative for space and positive for time. I read in [the question](https://physics.stackexchange.com/questions/107443/minkowski-metric-signature) that, the tensor for spacetime can be written like this : $ds^2=g_{\mu \nu}dx^{\mu}dx^{\nu}$ while $g_{\mu \nu}$ is Minkowski signature and $dx^{\mu}$ and $dx^{\nu}$ represent space coordinate. But in PSE question he wrote that $dx^0=ict$ where $i$ is imaginary number and $dx^0$ is time coordinate. I wonder what's the main reason of taking $ict$ as coordinate. $ct$ looks good to me to be a coordinate. At first I thought, the tensor got a negative sign for time for Minkowski signature. But when I saw $ict$ as coordinate my mind changed again.
- I know the question is too confusing and I am confused about time coordinate, it is $ct$ or $ict$, I don't know. Why Minkowski wrote signature like that?
- $g_{xx}=\vec e_x \cdot \vec e_x=1$ That's what we exactly know. But it's different for Minkowski spacetime, when dot product of time basis vector is 1 then dot product of space basis vector is -1 and vice versa, why?
#3: Post edited
- **2 dimensional spacetime :**
- I saw that Minkowski Metric looks like this :
- $$\pmatrix{-1 & 0 \\\\ 0 & 1}$$
- or $$\pmatrix{1 & 0 \\\\ 0 & -1}$$
- I was wondering why it's not written like identity metric. To define a vector in spacetime it's written like this $dS^2 = -(ct)^2+(dx)^2=(ict)^2+(dx)^2$. I know it's same as Minwkowski metric. But in Euclidean metric I was just using identity metric. Is there really any derivation of Minkowski metric? Or he just wrote it curiously. What the negative explains? I know that $ct$ is coordinate. Particle physicist write vector in spacetime (I had read it 3-4 hours ago, I can't find the source again so can't add reference here) like this $ dS^2 = (ct)^2-(dx)^2$.
- **4 dimensional spacetime :**
- The minkowski signature is $\pmatrix{- & + & + & +}$ or negative for space and positive for time. I read in [the question](https://physics.stackexchange.com/questions/107443/minkowski-metric-signature) that, the tensor for spacetime can be written like this : $ds^2=g_{\mu \nu}dx^{\mu}dx^{\nu}$ while $g_{\mu \nu}$ is Minkowski signature and $dx^{\mu}$ and $dx^{\nu}$ represent space coordinate. But in PSE question he wrote that $dx^0=ict$ where $i$ is imaginary number and $dx^0$ is time coordinate. I wonder what's the main reason of taking $ict$ as coordinate. $ct$ looks good to me to be a coordinate. At first I thought, the tensor got a negative sign for time for Minkowski signature. But when I saw $ict$ as coordinate my mind changed again.
- I know the question is too confusing and I am confused about time coordinate, it is $ct$ or $ict$, I don't know. Why Minkowski wrote signature like that?
$g_{xx}=\vec e_x \cdot \vec e_x=1$ That's what we exactly know. But it's different for Minkowski spacetime, when dot product of time basis vector is 1 then dot product of space basis vector is -1, why?
- **2 dimensional spacetime :**
- I saw that Minkowski Metric looks like this :
- $$\pmatrix{-1 & 0 \\\\ 0 & 1}$$
- or $$\pmatrix{1 & 0 \\\\ 0 & -1}$$
- I was wondering why it's not written like identity metric. To define a vector in spacetime it's written like this $dS^2 = -(ct)^2+(dx)^2=(ict)^2+(dx)^2$. I know it's same as Minwkowski metric. But in Euclidean metric I was just using identity metric. Is there really any derivation of Minkowski metric? Or he just wrote it curiously. What the negative explains? I know that $ct$ is coordinate. Particle physicist write vector in spacetime (I had read it 3-4 hours ago, I can't find the source again so can't add reference here) like this $ dS^2 = (ct)^2-(dx)^2$.
- **4 dimensional spacetime :**
- The minkowski signature is $\pmatrix{- & + & + & +}$ or negative for space and positive for time. I read in [the question](https://physics.stackexchange.com/questions/107443/minkowski-metric-signature) that, the tensor for spacetime can be written like this : $ds^2=g_{\mu \nu}dx^{\mu}dx^{\nu}$ while $g_{\mu \nu}$ is Minkowski signature and $dx^{\mu}$ and $dx^{\nu}$ represent space coordinate. But in PSE question he wrote that $dx^0=ict$ where $i$ is imaginary number and $dx^0$ is time coordinate. I wonder what's the main reason of taking $ict$ as coordinate. $ct$ looks good to me to be a coordinate. At first I thought, the tensor got a negative sign for time for Minkowski signature. But when I saw $ict$ as coordinate my mind changed again.
- I know the question is too confusing and I am confused about time coordinate, it is $ct$ or $ict$, I don't know. Why Minkowski wrote signature like that?
- $g_{xx}=\vec e_x \cdot \vec e_x=1$ That's what we exactly know. But it's different for Minkowski spacetime, when dot product of time basis vector is 1 then dot product of space basis vector is -1 and vice versa, why?
#2: Post edited
- **2 dimensional spacetime :**
- I saw that Minkowski Metric looks like this :
- $$\pmatrix{-1 & 0 \\\\ 0 & 1}$$
- or $$\pmatrix{1 & 0 \\\\ 0 & -1}$$
- I was wondering why it's not written like identity metric. To define a vector in spacetime it's written like this $dS^2 = -(ct)^2+(dx)^2=(ict)^2+(dx)^2$. I know it's same as Minwkowski metric. But in Euclidean metric I was just using identity metric. Is there really any derivation of Minkowski metric? Or he just wrote it curiously. What the negative explains? I know that $ct$ is coordinate. Particle physicist write vector in spacetime (I had read it 3-4 hours ago, I can't find the source again so can't add reference here) like this $ dS^2 = (ct)^2-(dx)^2$.
- **4 dimensional spacetime :**
- The minkowski signature is $\pmatrix{- & + & + & +}$ or negative for space and positive for time. I read in [the question](https://physics.stackexchange.com/questions/107443/minkowski-metric-signature) that, the tensor for spacetime can be written like this : $ds^2=g_{\mu \nu}dx^{\mu}dx^{\nu}$ while $g_{\mu \nu}$ is Minkowski signature and $dx^{\mu}$ and $dx^{\nu}$ represent space coordinate. But in PSE question he wrote that $dx^0=ict$ where $i$ is imaginary number and $dx^0$ is time coordinate. I wonder what's the main reason of taking $ict$ as coordinate. $ct$ looks good to me to be a coordinate. At first I thought, the tensor got a negative sign for time for Minkowski signature. But when I saw $ict$ as coordinate my mind changed again.
I know the question is too confusing and I am confused about time coordinate, it is $ct$ or $ict$, I don't know. Why Minkowski wrote signature like that?
- **2 dimensional spacetime :**
- I saw that Minkowski Metric looks like this :
- $$\pmatrix{-1 & 0 \\\\ 0 & 1}$$
- or $$\pmatrix{1 & 0 \\\\ 0 & -1}$$
- I was wondering why it's not written like identity metric. To define a vector in spacetime it's written like this $dS^2 = -(ct)^2+(dx)^2=(ict)^2+(dx)^2$. I know it's same as Minwkowski metric. But in Euclidean metric I was just using identity metric. Is there really any derivation of Minkowski metric? Or he just wrote it curiously. What the negative explains? I know that $ct$ is coordinate. Particle physicist write vector in spacetime (I had read it 3-4 hours ago, I can't find the source again so can't add reference here) like this $ dS^2 = (ct)^2-(dx)^2$.
- **4 dimensional spacetime :**
- The minkowski signature is $\pmatrix{- & + & + & +}$ or negative for space and positive for time. I read in [the question](https://physics.stackexchange.com/questions/107443/minkowski-metric-signature) that, the tensor for spacetime can be written like this : $ds^2=g_{\mu \nu}dx^{\mu}dx^{\nu}$ while $g_{\mu \nu}$ is Minkowski signature and $dx^{\mu}$ and $dx^{\nu}$ represent space coordinate. But in PSE question he wrote that $dx^0=ict$ where $i$ is imaginary number and $dx^0$ is time coordinate. I wonder what's the main reason of taking $ict$ as coordinate. $ct$ looks good to me to be a coordinate. At first I thought, the tensor got a negative sign for time for Minkowski signature. But when I saw $ict$ as coordinate my mind changed again.
- I know the question is too confusing and I am confused about time coordinate, it is $ct$ or $ict$, I don't know. Why Minkowski wrote signature like that?
- $g_{xx}=\vec e_x \cdot \vec e_x=1$ That's what we exactly know. But it's different for Minkowski spacetime, when dot product of time basis vector is 1 then dot product of space basis vector is -1, why?
#1: Initial revision
Confusing on Minkowski signature
**2 dimensional spacetime :**
I saw that Minkowski Metric looks like this :
$$\pmatrix{-1 & 0 \\\\ 0 & 1}$$
or $$\pmatrix{1 & 0 \\\\ 0 & -1}$$
I was wondering why it's not written like identity metric. To define a vector in spacetime it's written like this $dS^2 = -(ct)^2+(dx)^2=(ict)^2+(dx)^2$. I know it's same as Minwkowski metric. But in Euclidean metric I was just using identity metric. Is there really any derivation of Minkowski metric? Or he just wrote it curiously. What the negative explains? I know that $ct$ is coordinate. Particle physicist write vector in spacetime (I had read it 3-4 hours ago, I can't find the source again so can't add reference here) like this $ dS^2 = (ct)^2-(dx)^2$.
**4 dimensional spacetime :**
The minkowski signature is $\pmatrix{- & + & + & +}$ or negative for space and positive for time. I read in [the question](https://physics.stackexchange.com/questions/107443/minkowski-metric-signature) that, the tensor for spacetime can be written like this : $ds^2=g_{\mu \nu}dx^{\mu}dx^{\nu}$ while $g_{\mu \nu}$ is Minkowski signature and $dx^{\mu}$ and $dx^{\nu}$ represent space coordinate. But in PSE question he wrote that $dx^0=ict$ where $i$ is imaginary number and $dx^0$ is time coordinate. I wonder what's the main reason of taking $ict$ as coordinate. $ct$ looks good to me to be a coordinate. At first I thought, the tensor got a negative sign for time for Minkowski signature. But when I saw $ict$ as coordinate my mind changed again.
I know the question is too confusing and I am confused about time coordinate, it is $ct$ or $ict$, I don't know. Why Minkowski wrote signature like that?