# Isn't energy actually a vector?

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Energy has always been defined as a scalar quantity since it measures magnitude but, of course has no direction. (E.g. temperature)

And as we know vectors have magnitude and direction. (E.g: Velocity)

However, there are 4 dimensions. Our three spacial dimensions and then the fourth: Time. Now as I understand it, everything in the universe is travelling through the fourth dimension at lightspeed. So while energy has no typical direction it has a forwards direction in time. So energy in one place, 3 seconds later, will have traveled forwards (4 dimensionally) by "3 seconds"

So isn't energy technically a vector?

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You are on to something here. In spacetime physics, mass, energy, and momentum are combined into a single four-dimensional vector called "momenergy". Since this vector is in spacetime, it has a time component, and three space components. Energy is the time component, and momentum is the space component (actually three space momentum components for x, y, and z).

And mass is the magnitude of this 4-vector. The magnitude or mass is given by: Mass2 = energy2 - momentum2

And the beauty of this construcnt is that the mass is invariant with uniform motion (just like the spacetime interval). So the energy component and momentum component of the momenergy vector change with relative motion, but the mass stays the same. This means that if you are moving with respect to me, you measure a different value for the energy and momntum of a certain paticle than I do. But we both measure the same mass for the particle.

For example, if we choose a new reference frame where the particle’s motion through space is increased, then the particle’s energy will increase due to more energy of motion. The particle’s momentum will increase as well. But the difference between the squares of the energy and momentum will remain the same as in the original frame of reference. The square root of this difference is the particle’s mass.

An excellent description of momenergy is given in Spacetime Physics by Taylor and Wheeler. It is a wonderful book, and you don't need a PhD in physics to understand it.

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Energy is a component of the four-vector, but this is different from saying that energy itself is a vector.

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... and also different from saying that it was a scalar, btw.

Edited by timo

Wonderful!

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Energy has always been defined as a scalar quantity since it measures magnitude but, of course has no direction. (E.g. temperature)

And as we know vectors have magnitude and direction. (E.g: Velocity)

However, there are 4 dimensions. Our three spacial dimensions and then the fourth: Time. Now as I understand it, everything in the universe is travelling through the fourth dimension at lightspeed. So while energy has no typical direction it has a forwards direction in time. So energy in one place, 3 seconds later, will have traveled forwards (4 dimensionally) by "3 seconds"

So isn't energy technically a vector?

Emphasis mine.

Travelling in time? Of course, I agree.

Note: the same question about time being a vector here

Edited by michel123456

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