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Let $u^\mu=\frac{dx^\mu}{d\lambda}$ be particle's "4-velocity" where $\lambda$ is affine parameter. If I am not mistaken, we have, for the different cases:

• timelike (massive particles): $u_{\nu}u^{\nu} = g_{\mu \nu}u^{\mu}u^{\nu} = -c^2$
• lightlike (massless particles): $u_{\nu}u^{\nu} = g_{\mu \nu}u^{\mu}u^{\nu} = 0$
• spacelike (hypothetical tachyons?): $u_{\nu}u^{\nu} = g_{\mu \nu}u^{\mu}u^{\nu} = +c^2$

Here the metric signature is $(-,+,+,+)$. I have found in the literature that this is called a normalization condition. Does that mean that other normalization are possible? Where does this normalization even come from?

Questions:

• Can you confirm the formula are correct?
• Are other normalization possible?
• Can these normalization conditions taken as axioms or they can be derived?
• Would you have a good reference that would discuss where these normalization are coming from and derive them from first principles?

Let $u^\mu=\frac{dx^\mu}{d\lambda}$ be particle's "4-velocity" where $\lambda$ is affine parameter. If I am not mistaken, we have, for the different cases:

• timelike (massive particles): $u_{\nu}u^{\nu} = g_{\mu \nu}u^{\mu}u^{\nu} = -c^2$
• lightlike (massless particles): $u_{\nu}u^{\nu} = g_{\mu \nu}u^{\mu}u^{\nu} = 0$
• spacelike (hypothetical tachyons?): $u_{\nu}u^{\nu} = g_{\mu \nu}u^{\mu}u^{\nu} = +c^2$

Here the metric signature is $(-,+,+,+)$. I have found in the literature that this is called a normalization condition. Does that mean that other normalization are possible? Where does this normalization even come from?

Questions:

• Can you confirm the formula are correct?
• Are other normalization possible?
• Can these normalization conditions taken as axioms or they can be derived?
• Could you discuss where these normalization are coming from and derive them from first principles?

Let $u^\mu=\frac{dx^\mu}{d\lambda}$ be particle's "4-velocity" where $\lambda$ is affine parameter. If I am not mistaken, we have, for the different cases:

• timelike (massive particles): $u_{\nu}u^{\nu} = g_{\mu \nu}u^{\mu}u^{\nu} = -c^2$
• lightlike (massless particles): $u_{\nu}u^{\nu} = g_{\mu \nu}u^{\mu}u^{\nu} = 0$
• spacelike (hypothetical tachyons?): $u_{\nu}u^{\nu} = g_{\mu \nu}u^{\mu}u^{\nu} = +c^2$

I have found in the literature that this is called a normalization condition. Does that mean that other normalization are possible? Where does this normalization even come from?

Questions:

• Can you confirm the formula are correct?
• Are other normalization possible?
• Can these normalization conditions taken as axioms or they can be derived?
• Would you have a good reference that would discuss where these normalization are coming from and derive them from first principles?

Let $u^\mu=\frac{dx^\mu}{d\lambda}$ be particle's "4-velocity" where $\lambda$ is affine parameter. If I am not mistaken, we have, for the different cases:

• timelike (massive particles): $u_{\nu}u^{\nu} = g_{\mu \nu}u^{\mu}u^{\nu} = -c^2$
• lightlike (massless particles): $u_{\nu}u^{\nu} = g_{\mu \nu}u^{\mu}u^{\nu} = 0$
• spacelike (hypothetical tachyons?): $u_{\nu}u^{\nu} = g_{\mu \nu}u^{\mu}u^{\nu} = +c^2$

Here the metric signature is $(-,+,+,+)$. I have found in the literature that this is called a normalization condition. Does that mean that other normalization are possible? Where does this normalization even come from?

Questions:

• Can you confirm the formula are correct?
• Are other normalization possible?
• Can these normalization conditions taken as axioms or they can be derived?
• Would you have a good reference that would discuss where these normalization are coming from and derive them from first principles?

If I am not mistaken, we have, for the different cases:

• timelike (massive particles): $ds^2 = g_{\mu \nu}u^{\mu}u^{\nu} = u_{\nu}u^{\nu} = -c^2$
• lightlike (massless particles): $ds^2 = g_{\mu \nu}u^{\mu}u^{\nu} = u_{\nu}u^{\nu} = 0$
• spacelike (hypothetical tachyons?): $ds^2 = g_{\mu \nu}u^{\mu}u^{\nu} = u_{\nu}u^{\nu} = +c^2$

I have found in the literature that this is called a normalization condition. Does that mean that other normalization are possible? Where does this normalization even come from?

Questions:

• Can you confirm the formula are correct?
• Are other normalization possible?
• Can these normalization conditions taken as axioms or they can be derived?
• Would you have a good reference that would discuss where these normalization are coming from and derive them from first principles?

Let $u^\mu=\frac{dx^\mu}{d\lambda}$ be particle's "4-velocity" where $\lambda$ is affine parameter. If I am not mistaken, we have, for the different cases:

• timelike (massive particles): $u_{\nu}u^{\nu} = g_{\mu \nu}u^{\mu}u^{\nu} = -c^2$
• lightlike (massless particles): $u_{\nu}u^{\nu} = g_{\mu \nu}u^{\mu}u^{\nu} = 0$
• spacelike (hypothetical tachyons?): $u_{\nu}u^{\nu} = g_{\mu \nu}u^{\mu}u^{\nu} = +c^2$

I have found in the literature that this is called a normalization condition. Does that mean that other normalization are possible? Where does this normalization even come from?

Questions:

• Can you confirm the formula are correct?
• Are other normalization possible?
• Can these normalization conditions taken as axioms or they can be derived?
• Would you have a good reference that would discuss where these normalization are coming from and derive them from first principles?