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Momentum in the time direction

  1. Mar 27, 2008 #1
    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:

    This gives units of momentum, not of energy. What am I missing?
  2. jcsd
  3. Mar 28, 2008 #2


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  4. Mar 28, 2008 #3


    Staff: Mentor

    You are just missing a conversion factor of c. This is common when using 4-vectors. Remember that the first coordinate of a four-vector is taken to be ct. This is required in order to make it dimensionally consistent, but despite being in units of length it is understood to represent time. Similarly with the four-momentum. 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.
  5. Mar 28, 2008 #4
    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.
    Last edited: Mar 28, 2008
  6. Mar 28, 2008 #5
    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?
    Last edited: Mar 29, 2008
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