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# Spacetime Background Independence

Relativity is a theory defined to be background independent.

With that basis,  spacetime cannot be a real thing in the universe.

excerpts from Wikipedia:

'
Background independence is a condition in theoretical physics, that requires the defining equations of a theory to be independent of the actual shape of the spacetime and the value of various fields within the spacetime. In particular this means that it must be possible not to refer to a specific coordinate system—the theory must be coordinate-free. In addition, the different spacetime configurations (or backgrounds) should be obtained as different solutions of the underlying equations.
'

my comment:
This is the appropriate basis for the theory of relativity because relativity describes changes to only the observer's geometry, their 4-D spacetime. Relativity never includes or needs the background for the observer.

The underlying equations are also important because they demonstrate the context on the observer.
The accelerating observer gets the spacetime curvature. Spacetime is a geometry with 4 defined dimensions: ct, x, y, z. This is the Euclidean geometry with a 4th dimension ct allowing time to be introduced as a linear dimension with units compatible with the standard first 3 linear dimensions.
The motion of the accelerating observer is being manipulated by the observer's motion; the combination of change-x, change-y, change-z, change-t are used to calculate the space-time interval for the geometry transformation. This transformation involves only changes in the observer's position and never a reference to a physical location.
The input into the metric tensor are: cdt, dx, dy, dz.

I know this topic is an oversimplification but for now I will proceed.

Relativity does not require a connection to a coordinate system in physical space, when working solely within the context of the observer.

Isaac Newton is said to have worked in a background dependent context with absolute space and absolute time.
In other words, objects could be described by their coordinates in physical space.

A geometry defines the observer's coordinate system, with its dimensions or axes and their scaling.
This geometry is connected to physical space by relating the geometry to a particular point in physical space. A simple example with the Euclidean geometry is defining X0,Y0,Z0 at the lower left corner of one's working space.

In this case the geometry has become background dependent by defining its coordinates in physical space.

This is the context often used by an observer.

To become  background independent the observer could make all measurements of changes in positions without ever needing to define an absolute position of any objects.

In Newtonian physics (i.e., not relativity) the context of either background (in)dependence is never important. There is no behavior in Newtonian physics that will ever be connected to a specific point in the physical space of the universe.
The forces of gravitational fields, electric fields, magnetic fields are all based in movable objects and are never anchored to a point in physical space.

Instead of a Euclidean geometry, a similar technique is used for the celestial coordinate system where the two planes are related to the fixed point at the center of the Earth. Observers around the world can adjust this geometry for their location relative to the center of the earth.
This is a background dependent context for a coordinate system usable by anyone on Earth.

Relativity uses the concept of frame of reference.
Excerpt:

'
The motion of a body can only be described relative to something else—other bodies, observers, or a set of space-time coordinates. These are called frames of reference.

In physics, a frame of reference (or reference frame) consists of an abstract coordinate system and the set of physical reference points that uniquely fix (locate and orient) the coordinate system and standardize measurements.
'

my comment:
This 'abstract coordinate system' can be the observer's context.
Relativity implements its spacetime curvature as changes in the observer's frame of reference.

excerpt:
'
General relativity generalizes special relativity and refines Newton's law of universal gravitation, providing a unified description of gravity as a geometric property of space and time, or spacetime. In particular, the curvature of spacetime is directly related to the energy and momentum of whatever matter and radiation are present. The relation is specified by the Einstein field equations, a system of partial differential equations.
'
my comment:
A statement above is misleading because it omitted critical words. It should be fixed like this with the added text in < > :

In particular, the curvature of < the observer's> spacetime is directly related to the energy and momentum of whatever matter and radiation are present < at the observer >.

This distinction is very important.

Curvature is NOT related to whatever matter and radiation are present ANYWHERE, but the curvature is directly related to the observer. This is just semantics but it should be correct and clear.

Relativistic behaviors affecting the observer's spacetime do not apply to the physical universe when limited to the observer.

However, cosmologists consider spacetime as a real thing, clearly a mistake.

excerpt:
'
The shape of the universe is the local and global geometry of the universe. The local features of the geometry of the universe are primarily described by its curvature, whereas the topology of the universe describes general global properties of its shape as of a continuous object. The shape of the universe is related to general relativity, which describes how spacetime is curved and bent by mass and energy.
'

Spacetime universe is NOT a 'continuous object' with a shape.
Spacetime is defined to be the observer's geometry affected by their proximity to 'mass and energy' but there is no geometry of the universe.
The observer's spacetime geometry is background independent with no link to the physical space. It cannot be a real thing.

Spacetime cannot be anchored to the physical universe other than through the observer whose background independent geometry is affected by local relativistic effects. More abput this is below.

The universe is infinite and everything in it is moving.

It is absolutely impossible to identify a single fixed point in the universe to anchor a proposed global geometry of the universe.

Any attempt at such a geometry must begin with the observer. That means as the observer moves, this geometry of the universe is moving as well, so its respective axis planes could be rotating and their references shifting.

In the big bang cosmology, spacetime (of the universe) was created at the big bang event.

Actually spacetime is limited by relativity to the observer so the big bang cannot create spacetime because only an observer has spacetime.
Despite that inherent restriction this big bang theory proposes an instance of an obsever's spacetime was created and this 'thing' is a continuous object whose shape is described by spacetime.

If this is a real thing then it must have a physical location in the universe.

This location is impossible to assign. The universe has no fixed point to allow a geometry to be defined to describe the location of this continuous object.

Even stranger, cosmologists propose a thing called time in this universal spacetime was created with the big bang. Time is not a real thing; it is an incrementing count. Newton consider time separate from space and he was correct.

The confusion about universal spacetime worsens.

The spacetime curvature resulting from an observer at a mass is sometimes claimed to be observed at great distances from Earth. Examples are black holes and light bending due to curved spacetime caused by a distant large mass like a galaxy.
In each case the observer must be both where they are on Earth and simultaneously adjacent to that distant mass to get the correct curvature defined by relativity for an observer at that adjacent location in the universe. This combination is clearly impossible.

Cosmologists also propose the universe spacetime is expanding. It is impossible to identify the context for this spacetime within the real universe which must include a fixed point reference for its dimensions. This expansion is also not a real thing.

Expansion involves claiming the spacetime geometry is changing so the observer is measuring positions that can change due to the scaling in the observer's geometry.

Excerpt:
'
The expansion of the universe is the increase of the distance between two distant parts of the universe with time. It is an intrinsic expansion whereby the scale of space itself changes. The universe does not expand "into" anything and does not require space to exist "outside" it. Technically, neither space nor objects in space move. Instead it is the metric governing the size and geometry of spacetime itself that changes in scale.

To an observer it appears that space is expanding and all but the nearest galaxies are receding into the distance.
'

my comment:
In this expansion theory, spacetime has its dimensional scaling increasing.

With spacetime being background independent this proposed expansion is difficult to grasp when appied to spacetime after its scope is expanded from only an observer to cover the entire universe.

However there are known problems with this expansion among physicists.

excerpt (several paragraphs):
'
A much slower and gradual expansion of space continued until at around 9.8 billion years after the Big Bang it began to gradually expand more quickly, and is still doing so.

Metric expansion is a key feature of Big Bang cosmology, is modeled mathematically with the Friedmann-Lemaître-Robertson-Walker metric and is a generic property of the universe we inhabit. However, the model is valid only on large scales, because gravitational attraction binds matter together strongly enough that metric expansion cannot be observed at this time, on a smaller scale. As such, the only galaxies receding from one another as a result of metric expansion are those separated by cosmologically relevant scales larger than the length scales associated with the gravitational collapse that are possible in the age of the universe given the matter density and average expansion rate.

Physicists have postulated the existence of dark energy, appearing as a cosmological constant in the simplest gravitational models, as a way to explain the acceleration. According to the simplest extrapolation of the currently-favored cosmological model, the Lambda-CDM model, this acceleration becomes more dominant into the future. In June 2016, NASA and ESA scientists reported that the universe was found to be expanding faster than thought earlier.

While special relativity prohibits objects from moving faster than light with respect to a local reference frame where spacetime can be treated as flat and unchanging, it does not apply to situations where spacetime curvature or evolution in time become important. These situations are described by general relativity, which allows the separation between two distant objects to increase faster than the speed of light, although the definition of "separation" is different from that used in an inertial frame. This can be seen when observing distant galaxies more than the Hubble radius away from us (approximately 14.7 billion light-years); these galaxies have a recession speed that is faster than the speed of light. Light that is emitted today from galaxies beyond the cosmological event horizon, about 16 billion light-years, will never reach us, although we can still see the light that these galaxies emitted in the past. Because of the high rate of expansion, it is also possible for a distance between two objects to be greater than the value calculated by multiplying the speed of light by the age of the universe. These details are a frequent source of confusion among amateurs and even professional physicists.

Due to the non-intuitive nature of the subject and what has been described by some as "careless" choices of wording, certain descriptions of the metric expansion of space and the misconceptions to which such descriptions can lead are an ongoing subject of discussion within education and communication of scientific concepts.
'

my comment:
I fully agree with characterization as 'careless wording'  because we are told to believe that the scaling of galaxy positions within the universe changes over time and now the rate is faster.

We are also told to believe this scaling is changing faster due to dark energy which is defined as:
'
In physical cosmology, dark energy is an unknown form of energy which is hypothesized to permeate all of space, tending to accelerate the expansion of the universe.

my comment:
There is no credibility for 'an unknown form of energy.

This unknown spanning all of space is certainly more than just 'careless wording.' It is not believable.

Conclusion for spacetime:

It is mind boggling to me that an observer's frame of reference as described by relativity is proposed by cosmologists to encompass the entire universe.

This also suggests an observer must created with the big bang to be the basis for the universal spacetime. This is almost a metaphysical problem.

I will continue with another but somewhat related problem, spacetime dimensions.

Some cosmologists mention a mult-dimensional universe. There is no such 'thing' as that simply because a universe is just space and has no built-in dimensions. Dimensions arise with the observer's geometry. Our universe or an imagined universe has no dimensions.

This confusion exists for those that believe spacetime with its 4-D geometry based on the observer is a real thing. With that mistake, one could incorrectly believe our universe has 4 dimensions. It does not.

There is no real spacetime for the universe in cosmology.

Comments are welcome on such a sweeping topic.
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Last updated (10/11/2019)
Here is the list of topics in this Cosmology Topic Group , including my research.

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