# Why doesn't energy have direction?

by Vincentius
Tags: direction of energy
 P: 18 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!
PF Patron
P: 5,501
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:

 In classical physics energy is considered a scalar quantity, the canonical conjugate to time. In special relativity energy is also a scalar (although not a Lorentz scalar but a time component of the energy-momentum 4-vector).[14] In other words, energy is invariant with respect to rotations of space, but not invariant with respect to rotations of space-time (= boosts).
http://en.wikipedia.org/wiki/Energy
 Mentor P: 15,595 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.
P: 1,958

## Why doesn't energy have direction?

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.
PF Patron
P: 5,501
phyzguy:

 energy and momentum mix in the same way that space and time mix.
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.
 P: 53 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.
Mentor
P: 15,595
 Quote by Naty1 Your post seems inconsistent with Dalespams...but I am not sure I understand the consequences of his post...
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.
P: 1,958
 Quote by Naty1 phyzguy: 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.
Conservation of energy is a consequence of Noether's theorem and the Lagrangian being invariant with respect to time translation.
PF Patron
P: 5,501
Dalespam:
 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
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.
Mentor
P: 15,595
 Quote by Naty1 You are assuming a direction and properly noting as a consequence that therefore the KE [direction] would be continually changing.
Exactly. Sorry about the lack of clarity. It was a rather brief post.
 P: 32 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.
 P: 82 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 ?
 P: 15 Doesn't a force contain energy but with force you have given a vector to that energy?
 P: 1,171 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.
Mentor
P: 15,595
 Quote by 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 ?
Both momentum and energy are conserved.

 Quote by big_bounce 2 - If energy has no direction how can get direction to object ?
Energy has no direction, but the gradient of a potential does.
P: 3,178
 Quote by MikeyW Energy is a scalar, whether it's potential energy or kinetic. Force is a vector. One does not contain the other.
And one doesn't cause the other.
P: 82
 Quote by DaleSpam Both momentum and energy are conserved. Energy has no direction, but the gradient of a potential does.
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 ?