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  4. Does energy have to be a scalar?
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Does energy have to be a scalar?

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Offline jeffreyH (OP)

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Does energy have to be a scalar?
« on: 21/02/2018 22:36:44 »
We have vectors for velocity and momentum. Can there be such a thing as a kinetic energy vector?
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Offline wolfekeeper

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Re: Does energy have to be a scalar?
« Reply #1 on: 21/02/2018 23:27:02 »
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.
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Re: Does energy have to be a scalar?
« Reply #2 on: 22/02/2018 00:17:09 »
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.
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Re: Does energy have to be a scalar?
« Reply #3 on: 22/02/2018 07:58:23 »
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.
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Re: Does energy have to be a scalar?
« Reply #4 on: 22/02/2018 08:02:20 »
Just an extra point. In this scenario the only valid vector operations would be addition an subtraction.
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Offline saspinski

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Re: Does energy have to be a scalar?
« Reply #5 on: 22/02/2018 18:07:05 »
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.
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Re: Does energy have to be a scalar?
« Reply #6 on: 02/03/2018 07:23:57 »
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?
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Re: Does energy have to be a scalar?
« Reply #7 on: 03/03/2018 09:49:55 »
Quote from: sceptic-eng on 02/03/2018 07:23:57
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?
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