[jeffreyH (OP)]

We have vectors for velocity and momentum. Can there be such a thing as a kinetic energy vector?

[wolfekeeper]

You could doubtless define some vector operator, but what for? The point of the scalar we call 'energy' is that you can show that it's a conserved quantity in Newtonian mechanics.

[alancalverd]

dimensionally, velocity = LT^-1 and momentum = MLT^-1. M and T are scalars, so the vector properties of L are reflected in velocity and momentum. But we define energy as the scalar product ML²T^-2.

Whilst a moving object, or an object in a gravitational field, has kinetic or potential energy that clearly derives from a vector quantity, that energy can be converted conservatively e.g. to heat which has no such connection, even though the conversion necessarily invokes conservation of the momentum vector of the system.

[jeffreyH (OP)]

I know that you have the dot product of velocity which gives a scalar. That said speed is a scalar and that is made into a vector. Why would vector kinetic energy work against energy conservation? The magnitude would still give the same value.

[jeffreyH (OP)]

Just an extra point. In this scenario the only valid vector operations would be addition an subtraction.

[saspinski]

In the 4-vectors of relativity, energy is a component of the momentum vector while not a vector by itself.
For a moving observer momentum changes and energy changes, but E² - P² keeps constant.

[sceptic-eng]

In a mechanical sense energy is scalar but when we are dealing with heat and electricity the energy is absorbed by a volume [ not a length or area] of matter or even magnetised space in the case of electromagnetic 3D light energy surely?

[Colin2B]

In a mechanical sense energy is scalar but when we are dealing with heat and electricity the energy is absorbed by a volume [ not a length or area] of matter or even magnetised space in the case of electromagnetic 3D light energy surely?

Are you suggesting this makes it a non-scalar?