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It's in the Wiki quote:Quote: WikiEuclidean vectors are an example of a vector space. They represent physicalquantities such as forces: any two forces (of the same type) can be added to yield a third, and the multiplication of a force vector by a real multiplier is another force vector

: WikiEuclidean vectors are an example of a vector space. They represent physicalquantities such as forces: any two forces (of the same type) can be added to yield a third, and the multiplication of a force vector by a real multiplier is another force vector

http://www.einstein-online.info/spotlights/gravity_of_gravityThis gives clear indication as to why you might be asking such a question...

Is there a vector space that can be used with linear combinations that is representative of a non-linear space such as that of the gravitational field? If this exists can it be formulated as an energy vector space?

Quote from: jeffreyH on 16/01/2016 18:26:53Is there a vector space that can be used with linear combinations that is representative of a non-linear space such as that of the gravitational field? If this exists can it be formulated as an energy vector space?Jeffrey, gravity fields and curvature of space is only curved relative to ''flat'' space/background being linear.

Quote from: Thebox on 01/04/2017 21:17:53Quote from: jeffreyH on 16/01/2016 18:26:53Is there a vector space that can be used with linear combinations that is representative of a non-linear space such as that of the gravitational field? If this exists can it be formulated as an energy vector space?Jeffrey, gravity fields and curvature of space is only curved relative to ''flat'' space/background being linear. Yes. That is very perceptive.Quote from: jeffreyH on 01/04/2017 21:21:30Quote from: Thebox on 01/04/2017 21:17:53Quote from: jeffreyH on 16/01/2016 18:26:53Is there a vector space that can be used with linear combinations that is representative of a non-linear space such as that of the gravitational field? If this exists can it be formulated as an energy vector space?Jeffrey, gravity fields and curvature of space is only curved relative to ''flat'' space/background being linear. Yes. That is very perceptive.Any fields or waves from (a) to (b) exist in the present.

Quote from: Thebox on 01/04/2017 21:17:53Quote from: jeffreyH on 16/01/2016 18:26:53Is there a vector space that can be used with linear combinations that is representative of a non-linear space such as that of the gravitational field? If this exists can it be formulated as an energy vector space?Jeffrey, gravity fields and curvature of space is only curved relative to ''flat'' space/background being linear. Yes. That is very perceptive.

Am I way off left side with this notion of an energy vector space Jeff?

What do you mean 'No' - clearly that quite simply is not true.If one attributes the acceleration of gravity with a physical cause that describes curvature of space, i.e the path that light travels in space between masses, but describes the extra distance associated with this curve as a flat distance that took extra time to travel in the weaker field, then Einstein's GR equations will describe Newtonian geometry as per the linearity of Newtonian gravity and GR will be able to describe a test particle in relation to more than one mass by summing up the gravity fields.This is indeed a radical simplification, and indeed a much more efficient description of multiple fields - that in being compatible with Newtonian gravity will also be compatible with electrodynamics.

So how would you cater for the gravity of gravity due to changes in energy.