Views of the fourth dimension, stressed space

Contents

Article 1. Imbedded particles, constant and accelerated motion

Article 2. Spacetime stress as the fourth dimension (reprint)

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1. Imbedded particles, constant and accelerated motion

Does mass increase with velocity as special relativity would suggest, or does mass remain constant, and space change in some way to make it appear mass increases (maintaining but reinterpreting the equation)?

Elementary particles have been discussed as gravitational sinks instead of sources, point-like absences of space as illustrated in the one-dimensional schematic in the cover image, where the gaps (for point absences) and one-dimensional line are large enough to be readily seen; these particles are either stationary or moving at constant velocity relative to one another. On the other hand such accelerated particles might move like this,

where in the upper drawing in this figure the particles are accelerated toward one another, and in the lower drawing away from one another.. Note the gathering of space(time) expressed in blue in the direction of accelerated movement and a trailing sparsity, suggesting resistance to this movement in the direction of motion -- as opposed to the more conventional increase in mass or inertia of the particle itself. Accommodation is in the surrounding space rather than in the particle -- a point of non-existence. The sparsity can represent expanded space, and gathering can represent compressed ("curved" in conventional terms) space, so that an extra dimension is added with acceleration/gravity, representing the fourth dimension of space (instead of time), and constant fundamental particle mass at zero. Such amplitude increase and decrease suggests the initiation of a conventional gravitational wave, or stressed space.

It would seem this is a more apt, or auxiliary, description than conventional particle mass increase because conventional particles are not specifically identified, rather indicated as probabilities. Also, spacetime accommodates gravitational waves predicted by general relativity and detected on Earth, where wave initiation is vastly separated from detection. Figure 2 of the following article suggests this, where no adjacent mass is apparent near the gravitational wave.

2. Spacetime stress as the fourth dimension

Clear photoelastic material under stress, where stress is the fourth dimension of space.*

What is "curving" in the space of general relativity?

The curved space of general relativity is not easy to visualize. Formally, there are three dimensions of space and one of time. An intuitive mental image could help grasp the mathematical abstraction.

Curved space is usually illustrated in terms of two dimensions of flat space that are molded into the third space dimension, like this:

Figure 1. Two dimensions of space curved into a third.?B. A New Understanding: Curved Spacetimeuh.edu

where the implication is that the mass is the cause of the curvature of surrounding space, so that another sufficiently close mass will tend to "slide down" into the first mass. But mass is really not immediately necessary to curve space, because of the detection of gravitational waves. In this next picture:

Figure 2.?1640261052027

no mass is apparent, yet there is a two-dimensional surface that curves into a third dimension of space. This situation can be illustrated if a thin rubber sheet is held off the ground by the upper two corners, then shaken in a random manner, so that a pattern like that above is possible -- without the presence of a localized mass. All that's needed is a disturbance, and a wave is transmitted through the sheet.

What would such a wave in four-dimensional space(time) look like? This next picture is of a completely clear thick disc of photoelastic material under compression by the upper and lower horizontal jaws of a vise:

Figure 2.2 Illustration and text from?chegg.com,**

Such clear material exhibits the stress it undergoes when polarized light is shown through it and might help form a mental picture of stress waves through spacetime, such waves representing the fourth space dimension (rather than time).

This is not to say that the mechanism of photoelasticity necessarily relates physically to the various curvatures of spacetime, but at least it might help to mentally grasp a space of four dimensions and add a sense of physical reality to the abstraction.

Yet, the question remains, what is "curving" or more generally, what's going on with familiar three-dimensional space? Whatever it is -- it is?gravity. ***

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* Credit: Science direct: https://www.sciencedirect.com/topics/materials-science/photoelasticity

** https://mediaexp1.licdn.com/dms/image/C4D12AQH34vysVGWeKA/article-inline_image-shrink_1500_2232/0/1640261251031?e=1649289600&v=beta&t=fxd697nqQdosfW0PCDWck4OLKurnGNGnpRiPSUnugZ0

***?i.e., What is gravity? (Part 1 of 3), Letters, December 7, 2021,?What is gravity? | LinkedIn https://www.dhirubhai.net/pulse/what-gravity-warren-frisina/?