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When I posed the questions I certainly didn't expect an answer. What you have described has nothing at all to do with what I am attempting so is irrelevant. I didn't understand most of it as it made no sense anyway.

Quote from: jeffreyH on 19/01/2016 18:27:33When I posed the questions I certainly didn't expect an answer. What you have described has nothing at all to do with what I am attempting so is irrelevant. I didn't understand most of it as it made no sense anyway.Not sure if this relevant to you Jeff, but when I read your question my first though was a bow and arrow.

Quote from: Thebox on 19/01/2016 19:34:19Quote from: jeffreyH on 19/01/2016 18:27:33When I posed the questions I certainly didn't expect an answer. What you have described has nothing at all to do with what I am attempting so is irrelevant. I didn't understand most of it as it made no sense anyway.Not sure if this relevant to you Jeff, but when I read your question my first though was a bow and arrow.If you were to fire one arrow directly upwards and another at an angle then you would start to see the issues. If you are using exactly the same force to launch all arrows then you can propel an arrow the furthest distance by launching it at a 45 degree angle with respect to the ground. If you consider how fast and therefore how much energy an arrow would need to be able to sustain an orbit or escape the earth altogether then you can reach some interesting conclusions.

Quote from: jeffreyH on 19/01/2016 19:49:44Quote from: Thebox on 19/01/2016 19:34:19Quote from: jeffreyH on 19/01/2016 18:27:33When I posed the questions I certainly didn't expect an answer. What you have described has nothing at all to do with what I am attempting so is irrelevant. I didn't understand most of it as it made no sense anyway.Not sure if this relevant to you Jeff, but when I read your question my first though was a bow and arrow.If you were to fire one arrow directly upwards and another at an angle then you would start to see the issues. If you are using exactly the same force to launch all arrows then you can propel an arrow the furthest distance by launching it at a 45 degree angle with respect to the ground. If you consider how fast and therefore how much energy an arrow would need to be able to sustain an orbit or escape the earth altogether then you can reach some interesting conclusions.A bit like the Cannon ball idea and escape velocity. I should hope the one at 45 degrees would travel further, the arrow fired vertically up will eventually slow , then turn, then travel back down vertically , excluding weather and air of course.added - i drew it for you Jeff , It may help you [ Invalid Attachment ] I added atmosphere to it [ Invalid Attachment ]

Thebox's diagrams are suitable for the purpose and I will come back to them. For now what is needed is a linearly independent solution to the equation Ax = 0 for the energy space. That is that the only solution is the trivial solution where all scalars are zero. Once we have a span and basis for the set of vectors then maybe something interesting will reveal itself.However there has been no definition yet of the format of the space equations.

Jef this just came to me while I was sleeping, don't ask. 0+0=00=xare you working on something like this?https://www.sciencenews.org/article/quantum-histories-get-all-tangled [Links inactive - To make links active and clickable, login or click here to register]

The velocity components increase and decrease. Gravity stratifies matter like any other centrifuge.

We can write out the scalar matrix as such:Only if all the lambda values, when multiplied by the energy matrix, scale each energy value proportionally will we have a vector space. I will show that this is only the case for escape and orbital energy as would be expected. I will also show why relativistic mass is an issue and the problems it brings with it.EDIT: The above assumes we are considering lambda_1 = lambda_2 = lambda_3. Which will not be the case for all 3 energy values.

I guess you have no idea about linear algebra either.

: WikiVector spaces are the subject of linear algebra and are well characterized by their dimension, which, roughly speaking, specifies the number of independent directions in the space. Infinite-dimensional vector spaces arise naturally in mathematical analysis, as function spaces, whose vectors are functions. These vector spaces are generally endowed with additional structure, which may be a topology, allowing the consideration of issues of proximity and continuity. Among these topologies, those that are defined by a norm or inner product are more commonly used, as having a notion of distance between two vectors. This is particularly the case of Banach spacesand Hilbert spaces, which are fundamental in mathematical analysis.

: 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. In the same vein, but in a more geometric sense, vectors representing displacements in the plane or in three-dimensional space also form vector spaces.

I can't answer your OP question Jeff, but I am curious as to this concept of vector spaces and can at least stay 'near' topic...Quote : WikiVector spaces are the subject of linear algebra and are well characterized by their dimension, which, roughly speaking, specifies the number of independent directions in the space. Infinite-dimensional vector spaces arise naturally in mathematical analysis, as function spaces, whose vectors are functions. These vector spaces are generally endowed with additional structure, which may be a topology, allowing the consideration of issues of proximity and continuity. Among these topologies, those that are defined by a norm or inner product are more commonly used, as having a notion of distance between two vectors. This is particularly the case of Banach spacesand Hilbert spaces, which are fundamental in mathematical analysis....andQuote : 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. In the same vein, but in a more geometric sense, vectors representing displacements in the plane or in three-dimensional space also form vector spaces.Could g (gravity) and a (acceleration) be described as force vectors of the same type?Or is a (acceleration) a 'real multiplier'?

: 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

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

http://www.einstein-online.info/spotlights/gravity_of_gravity [Links inactive - To make links active and clickable, login or click here to register]This 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?