- #1

sweet springs

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is defined or not? Thanks.

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In summary, a particle's world line may have a null tangent vector, which cannot be normalized. However, for a timelike 4-momentum, the 4-velocity can be expressed as the 4-momentum normalized to one, and for a null 4-momentum, this is not possible.

- #1

sweet springs

- 1,223

- 75

is defined or not? Thanks.

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- #2

- 22,104

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- #3

sweet springs

- 1,223

- 75

Thanks a lot.

- #4

sweet springs

- 1,223

- 75

So 4-velocity vector as 4-momentum vector divided by m may be able to exist even in the limit of m to be zero. Normalizable to one but both time and space componebts are infinit. How do you think of that ? Best.

- #5

PeterDonis

Mentor

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sweet springs said:We may regard 4-momentum vector as 4-velocity vector multiplied by mass m.

For a timelike 4-momentum, yes, because the mass m is just the norm of the 4-momentum, so expressing 4-momentum as 4-velocity times m is just another way of saying that the 4-velocity is the 4-momentum normalized to one.

For a null 4-momentum, you can't do that, because, as Orodruin said, you can't normalize a null 4-vector.

- #6

sweet springs

- 1,223

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Thanks. Now I know better.

The four-velocity of a massless particle is defined as a vector in four-dimensional spacetime that represents the particle's rate of change in space and time. It is denoted by the symbol u and has a magnitude of c, the speed of light.

The four-velocity of a massless particle is different from a massive particle because it has a constant magnitude of c and is always directed along the null geodesic (path of light) in spacetime. In contrast, the four-velocity of a massive particle can vary in magnitude and direction depending on its velocity through space.

No, a massless particle cannot have a rest frame because it always travels at the speed of light and does not experience time. In other words, it is always in motion and cannot be at rest.

The four-velocity of a massless particle plays a crucial role in special relativity as it is a fundamental concept that allows us to understand the behavior of light and other massless particles. It is also used in the derivation of important equations, such as the Lorentz transformation and the energy-momentum relationship.

The four-velocity of a massless particle is used in various practical applications, such as in the study of cosmology, where it helps us understand the expansion of the universe and the properties of the cosmic microwave background radiation. It is also used in high-energy physics, where it is used to describe the behavior of particles that travel at or near the speed of light, such as photons and neutrinos.

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