# Momentum in the time direction

## Main Question or Discussion Point

I'm trying to understand the stress-energy tensor and I keep seeing the phrase, "momentum in the time direction is energy". I don't understand this. In the definitions of the momentum four-vector that I've found, the time component is the object's rest mass times the speed of light times gamma.

Here's an example:
http://scienceworld.wolfram.com/physics/MomentumFour-Vector.html

This gives units of momentum, not of energy. What am I missing?

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Dale
Mentor
I'm trying to understand the stress-energy tensor and I keep seeing the phrase, "momentum in the time direction is energy". I don't understand this. In the definitions of the momentum four-vector that I've found, the time component is the object's rest mass times the speed of light times gamma.

Here's an example:
http://scienceworld.wolfram.com/physics/MomentumFour-Vector.html

This gives units of momentum, not of energy. What am I missing?
You are just missing a conversion factor of c. This is common when using 4-vectors. Remember that the first coordinate of a http://en.wikipedia.org/wiki/Four-vector" [Broken]. In this case the timelike component is E/c in order to make it dimensionally consistent with the spacelike momentum components. But E/c is still understood to represent energy in the same way that ct represents time.

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Momentum is energy flux. Classically (pre-Einstein) one thinks of momentum as the result of movement through space. Consider a particle in its rest frame (v = 0). Is it still moving? Absolutely: It's moving from one second to the next (through time). This is momentum in the time direction.

Schutz's book has a great chapter on this very topic.

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Thank you all, especially DaleSpam. I suspected that it was simply a matter of leaving out c (selecting units so that c=1) but wasn't certain.

Up to now I've been confused about how the stress-energy tensor is put together because the components as named (energy density, momentum density, viscosity, etc.) all seem to have different dimensions/units. Are they all actually joules per cubic meter? Are the c's the only invisible constants/variables?

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