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Why doesn't energy have direction?

  1. Mar 7, 2012 #1
    Hi, I try to understand why energy can not have a direction. For instance, kinetic energy of a particle could be considered to have the direction of its velocity. Potential energy of a body in a gravitational field also can be considered to have direction (at least in the two-body case). The same for a mass and a spring. Of course, there are cases where forces balance and the potential energy has no associated direction anymore (as with a central body that is being pulled by two springs in opposite directions), still the separate components of potential energy of the central body can be associated with a direction and so can the potential energies of the two bodies at the other sites of the springs. I realize there are some complications and questions, but conceptually I do not see why energy does not have direction.

    Any references on this subject?

  2. jcsd
  3. Mar 7, 2012 #2
    It's just not defined that way...but as a scalar, a non directional entity.

    Energy is the ability to do work. Work is defined as a force acting over a distance: W = Fd.
    more precisely: W = F[cos] d, a scalar, a dot product, and the work can be either positive or negative. For example when you lower an object to the floor, the work done on the object by the upward force of a hand is negative....you are opposing the 'force' of gravity....and a 'direction' or such energies may not be obvious in the general situation.

    For things like partical motion, or throwing a ball, giving a direction to 'energy' does have some intutitive appeal. But many forms of energy like thermal energy, radioactivity,zero point energy, chemistry, etc. don't have an easily defined direction. Some 'work' in many directions simultaneously.

    Also energy a scalar energy has some attributes not so readily apparent:

    Last edited: Mar 7, 2012
  4. Mar 8, 2012 #3


    Staff: Mentor

    If energy had a direction then it would not be conserved. Think about a circular orbit, you would have a continually changing KE with no change in PE. Or simple harmonic motion, each time it passes through equilibrium there is no PE and the KE is reversed.
  5. Mar 8, 2012 #4


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    In a sense, energy does have a direction. In the 4-dimensional geometry of space-time, energy is the time component of the momentum vector. Thus, the momentum 4-vector of a particle is p=(E/c, px,py,pz), analogous to its position 4-vector (t/c,x,y,z). So energy points in the time direction. When we do a Lorentz transformation, energy and momentum mix in the same way that space and time mix.

    For ordinary situations, where the velocities involved are much less than the speed of light, the velocity in the time direction is very much greater than any of the spatial velocities. In this case, the energy can be treated essentially as a scalar.
  6. Mar 8, 2012 #5

    Does your description hold inside the Schwarszchild radius of a black hole? ...where 'time becomes an inward radial direction' ??

    Your post seems inconsistent with Dalespams...but I am not sure I understand the consequences of his post...

    When posting above, I was wondering myself about the consequences of the OP question regarding conservation of energy...and implications wrsp Noether's Theorem. If anyone can comment regarding those implications I'd appreciate it.
  7. Mar 8, 2012 #6
    Did you forget Energy-Momentum Tensor and Energy flux? in electromagnetic field description there is kind of different rates of energy flaw in different directions, and this can be thought as a kind of "energy direction", anyway this flaw should be transformed in a tricky way (i.e Lorentz transformations) that will keep the "total flux" conserved.
  8. Mar 8, 2012 #7


    Staff: Mentor

    His post is inconsistent with mine, but his is correct. I was giving a non-relativistic answer, his was relativistic. I assumed that the OP was specifically referring to a spatial direction, not time.
    Last edited: Mar 8, 2012
  9. Mar 8, 2012 #8


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    Conservation of energy is a consequence of Noether's theorem and the Lagrangian being invariant with respect to time translation.
  10. Mar 9, 2012 #9
    I thought the first sentence might be the case as I was initially posting...but I can't figure out how your remaining statements follow. Oh, good grief!!!!.... :approve:
    The lightbulb finally lit....I've been misreading your post: You are assuming a direction and properly noting as a consequence that therefore the KE [direction] would be continually changing. DUH!!!!
    I am definitely getting too old for this stuff................

    I shall now return to installing a new vanity countertop for my wife. THAT I can handle.
  11. Mar 9, 2012 #10


    Staff: Mentor

    Exactly. Sorry about the lack of clarity. It was a rather brief post.
  12. Mar 9, 2012 #11
    If you derive the definition of energy from the work done by a force its value will only be meaningful if the force is in the same direction of the displacement. Thus if you equate energy with ability to perform work it would be unecessary to specify a direction since the force will always be parallel to the dispacement it causes.
  13. Mar 31, 2013 #12
    Hello all .
    Suppose we have a source of energy ( like potential energy ) that can cause moving an object .
    My questions are :

    1 - Is this source a pure potential energy or a momentum-energy ?
    Because if we want to move a object we must give it momentum . or i am wrong ? we must give it energy ?

    2 - If energy has no direction how can get direction to object ?
    Last edited: Mar 31, 2013
  14. Mar 31, 2013 #13
    Doesn't a force contain energy but with force you have given a vector to that energy?
  15. Mar 31, 2013 #14
    It's quite hard to understand what is meant by some of these questions.

    Energy is a scalar, whether it's potential energy or kinetic. Force is a vector. One does not contain the other.
  16. Mar 31, 2013 #15


    Staff: Mentor

    Both momentum and energy are conserved.

    Energy has no direction, but the gradient of a potential does.
  17. Mar 31, 2013 #16


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    And one doesn't cause the other.
  18. Apr 1, 2013 #17
    I am a new collegian and didn't read any about gradient .
    So let's talk about particles .

    Suppose there are two single electron , one of them is in motion and another is at rest .
    Electron in motion possess kinetic energy and momentum and when it collide with electron at rest cause electron at rest start to motion in certain direction . Since energy doesn't have direction so this direction comes from momentum ( momentum is vector ) . am i right ?

    Now suppose we have an electron at rest and a source of energy ( like potential energy ) .
    My questions are :
    Potential energy can "directly" cause to motion the electron ? or it must change form to such as electromagnetism radiation and then cause to motion it ?
    Does the momentum for motion this electron come from potential energy ?
    If yes , is the source of energy really "pure energy" ? or include another quantity like momentum ?

    And in last , for motion which is more fundamental ? energy or momentum ?
    May be you'll say force but this force comes from what ? momentum or energy ?

    Thanks for your answer .
    Last edited: Apr 1, 2013
  19. Apr 6, 2013 #18
    Anyone can answer these questions ?
  20. Apr 6, 2013 #19


    Staff: Mentor


    I am not sure that this question makes sense. An electromagnetic potential is just a different way to represent an electromagnetic field. They are two different descriptions of the same phenomena. There is no sensible way that I can think of to change a potential into a field, they are always both present.


    Neither. They are on equal footing. Conservation of energy comes from time invariance of the Lagrangian and conservation of momentum comes from spatial invariance of the Lagrangian.
  21. Apr 6, 2013 #20
    Are you sure? [itex] F= -\frac{dU}{dx} [/itex] if I remember correctly.
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