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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 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.
    Last edited by a moderator: May 3, 2017
  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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