# Why doesn't energy have direction?

1. Mar 7, 2012

### Vincentius

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?

Thanks!

2. Mar 7, 2012

### Naty1

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:

http://en.wikipedia.org/wiki/Energy

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

### 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.

4. Mar 8, 2012

### phyzguy

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.

5. Mar 8, 2012

### Naty1

phyzguy:

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.

6. Mar 8, 2012

### TMSxPhyFor

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.

7. Mar 8, 2012

### 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
8. Mar 8, 2012

### phyzguy

Conservation of energy is a consequence of Noether's theorem and the Lagrangian being invariant with respect to time translation.

9. Mar 9, 2012

### Naty1

Dalespam:
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!!!!....
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.

10. Mar 9, 2012

### Staff: Mentor

Exactly. Sorry about the lack of clarity. It was a rather brief post.

11. Mar 9, 2012

### azabak

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.

12. Mar 31, 2013

### big_bounce

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
13. Mar 31, 2013

### ratchettrack

Doesn't a force contain energy but with force you have given a vector to that energy?

14. Mar 31, 2013

### mikeph

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.

15. Mar 31, 2013

### Staff: Mentor

Both momentum and energy are conserved.

Energy has no direction, but the gradient of a potential does.

16. Mar 31, 2013

### A.T.

And one doesn't cause the other.

17. Apr 1, 2013

### big_bounce

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 ?

Last edited: Apr 1, 2013
18. Apr 6, 2013

### big_bounce

Anyone can answer these questions ?

19. Apr 6, 2013

### Staff: Mentor

Yes.

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.

No.

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.

20. Apr 6, 2013

### Infrared

Are you sure? $F= -\frac{dU}{dx}$ if I remember correctly.

21. Apr 9, 2013

### big_bounce

Thank you .

Another question :
If i want moving an object at rest from point A to B , i need energy ?
Does the object during this displacement need momentum ?

Suppose an object is attached to a spring tip .
If i want moving this object from normal position ( point A ) to point B , i need energy . am i right ?
Do i need momentum for this displacement , too ?

Last edited: Apr 9, 2013
22. Apr 9, 2013

### A.T.

That's a quantitative relation. It says nothing about causation.

23. Apr 9, 2013

### Infrared

Ah, perhaps I misunderstood your original quote. What I meant was that a change in one results in a change in the other, assuming that there are no outside forces(so they are not independent of each other).

Last edited: Apr 9, 2013
24. Apr 9, 2013

### phyzguy

Yes to both questions. In order to move it, it must have some velocity. The velocity determines both the energy and momentum. These can be made as small as you like by moving it slowly enough.

25. Apr 9, 2013

### big_bounce

When we do work , we always moving an object from one point to another point .
So can we say for do work we always need momentum , too ?