[jeffreyH (OP)]

It's in the Wiki quote:

: Wiki
Euclidean 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 just means multiplying by a real number. Rather than say a complex number.

[jeffreyH (OP)]

http://www.einstein-online.info/spotlights/gravity_of_gravity

This gives clear indication as to why you might be asking such a question...

You are correct.

[guest39538]

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?

Jeffrey, gravity fields and curvature of space is only curved relative to ''flat'' space/background being linear.

[jeffreyH (OP)]

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?

Jeffrey, gravity fields and curvature of space is only curved relative to ''flat'' space/background being linear.

Yes. That is very perceptive.

[guest39538]

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?

Jeffrey, gravity fields and curvature of space is only curved relative to ''flat'' space/background being linear.

Yes. That is very perceptive.

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?

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.

[guest39538]

Jeffrey, will you please go over to my speed of time thread, as to not spoil this thread.  Discuss how 3.24cm is between emit and detect in atomic clock.  The wavelengths/frequencies between points occupy the present.

[timey]

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?

Jeffrey, gravity fields and curvature of space is only curved relative to ''flat'' space/background being linear.

Yes. That is very perceptive.

I too am appreciating that one Box...

So - If gravity fields and curvature of space is only curved relative to ''flat'' space/background being linear, then if we can somehow keep the linear flatness, distance wise, but describe the extra distance associated with describing curvature by an alternative means that corresponds directly to the energy/acceleration involved in the gravity field, then would this suffice to describe an energy vector space using linear combinations that is representative of the non linear space of the gravity field?

[timey]

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

[jeffreyH (OP)]

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

Energy is a scalar but can be expressed as a vector if you modify the mathematics. There has to be a good reason to do this. If you gain no advantage over other methods then it isn't worth the effort.

[timey]

...and what is it that would constitute an 'advantage' in your opinion?

[jeffreyH (OP)]

Efficiency and simplification.

[timey]

If the nonlinearity of curved space can be described linearly via attributing a means that directly relates to the energy of the acceleration caused by the gravity field to describe the extra distance associated with a curved space relative to a flat space, wouldn't this constitute a more simple and efficient means of describing the curvature of space?

[jeffreyH (OP)]

No.

[timey]

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.

[jeffreyH (OP)]

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.

I said no because your first post was incomprehensible and I couldn't be bothered to decipher it. Your second post had much better clarity.

[timey]

In that case I am pretty sure that the answer to your original question in the thread title is:
"Yes, there is."

[jeffreyH (OP)]

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

[guest39538]

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

Jeff , try considering that all gravity is isotropic and linear.    Then consider rotation and orbits are created by the force creating ''linear twist'' (torque). 

Imagine pushing down on a spinning top, where you push the bar down and it causes the base to spin.   Consider that if space was spinning, then the satellites would spin.

ADDED-Imagine pushing two bars/rods tips together at high pressure, the bars/rods will curve.

q+ versus q+  and q- versus q- is  one of the retainer ''rods''.


''Charge'' stops things compressing. A ''spring'' that pushes outwards.

[timey]

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

Well Jeff nobody really understands what gravity is or how it does what it does - but that is ok because this gives us a certain freedom regarding interpretation.

http://www.einstein-online.info/spotlights/gravity_of_gravity

In this link the author explains the difference between Newtonian gravity and GR gravity...
Where Newtonian gravity is concerned: multiple fields can be added for a corresponding sum total...
Where GR gravity is concerned: If you add up two gravitational fields, including their sources, where each field-source-combination obeys Einstein's equations, then the sum will not be another combination of fields and sources compatible with Einstein's laws of gravity...

In GR's case, the gravity of gravity is a consequence of the mass/energy equivalence where energy is a source of gravity.
By attributing the energy of the gravity field itself as being caused by the source body/s M, where this energy causes a time dilation that is the physical cause for observed gravitational acceleration in the field, we now have a scenario where adding up 2 or more gravitational fields and their sources under the remit of Einstein's equation will result in a sum total that will be compatible to Einstein's law of gravity under this remit.

This being because now that we can consider that the energy contained in the distances between masses is causing the test particle to take a longer, or shorter amount of time to travel a metre of this distance dependent on proximity to mass...
Add more gravitational fields and their sources to the equations, the additional energy doesn't alter distance of curvature, it just increases the rate of time in the field itself.
Take away gravitational fields and their sources, the subtraction of energy doesn't alter distance of curvature, it just decreases the rate of time in the field itself.

Where the link starts discussing the binding energy of rejoining the left hemisphere with the right hemisphere is very interesting, and leads me straight to the doorstep of GR time dilation, this being the other half of this scenario that I'm discussing on 'is there a discrepancy with the equivalence principle' thread...
...and a comment that a physicist Kip Thorpe (think I got name right) made in a recent program by physics professor Jim Al-Khalilli called 'gravity and me: the force that shapes our lives', where Kip suggests that the test particle always seeks the location where it is of least energy.

[jeffreyH (OP)]

I am sure Kip Thorne will be thrilled you goy his name right.