The Question
The bothersome question is: how and where is time embedded within Brunelleschi’s centuries old concept that allows for the scientifically precise projection of space onto a plane?
Mathematician Hermann Minkowski, first proposed in 1908, that space was not a stand alone concept. Instead, he determined that it was part of a union of space and time. That single concept was his reformulation of Albert Einstein’s Theory of Relativity published in 1905.
Over the years, I’ve tried hard to visualize a fabric of invisible things. After all, both time and space are invisible. However, fabrics are visible and tangible. Accordingly, my continued inability to see something tangible has bothered me. Some video documentaries show the fabric as a mesh, web, network or woven pattern of interlocking equidistant spaced lines that are often portrayed as bending under the influence of gravity.
Visual assessment, a sub-specialty of landscape architecture, depends upon many disciplines, some quite clearly outside the expertise of traditional designers. It is a multidisciplinary specialty, practiced by professionals with visual and aesthetic skills. Although there happens to be a relationship between time and aesthetics, aesthetics plays no role in this discussion, but certain aspects of space do. Nobody’s understanding of the kind of mathematics and physics behind this specialty is more basic than mine, but it was good enough during my career to determine the visibility of anything positioned in any landscape, no matter how complex or irregular the place was.
But, disciplinary interaction, no matter how tenuous, has inspired me to try to answer that nasty, persistent question. Some might read this paper and immediately be dismissive of any visual modeling of time, especially one based upon ancient graphics. So be it; that doesn’t bother me, nor should it discourage any interdisciplinary “trespass” by anyone.
By the way, this journey is a two way street, meaning physicists and mathematicians should be able to offer designers new ways to think of spacial design. This exchange of ideas would be reciprocal, since visual assessment is, hereby, offering a potentially new way for the other disciplines to “see” time.
Furthering this discussion, another derived question may be instructive: can the physics of time be made more understandable, when literally pictured using Renaissance era architectural graphics and science? Can Renaissance era graphics be an adaptive substitute for contemporary math?
To find out, time might better be thought of as either streaming virtual particles or a wave positioned within those imaginary lines. Is this consistent with Minkowski’s notion of flat space time, where trajectories of particles are straight lines? I’m not sure but, if so, does this hypothetical construct help alleviate the invisibility of time? Hopefully, it should not bother anyone, since all graphics (visual abstractions) should be expressible in some suitable mathematical way. I just don’t have a clue how, nor the math background necessary to accomplish this feat.
Perhaps others, who experience this same difficulty, may understand that visual assessors may be particularly troubled because projecting space onto a plane is both routine and highly visual for them. Through such projections they more completely perceive space, though its measurable emptiness is only revealed by the objects positioned within (note object “A” in model 2).
But what about time?
Because the projection technique is well established, and because time is part of space, can we rightly conclude that we are somehow simultaneously projecting time onto a plane without seeing or realizing it? I think so.
But if so, what might be revealed? Though I am generally ignorant of the science behind this subject, I have not found any discussion of anything like this anywhere. Why? Does it mean I’m wrong in assuming time must be included in spacial projection?
But, rightly or wrongly, using virtual particles makes that elusive space/time fabric now more perceptible. At least it is for me. So I’d like to share that vision for those still patient enough to maintain an interest.
The Answer
A vanishing point, as depicted in scientific perspective, is identical to a physicist’s singularity.
The spot defined in scientific perspective where, in illusory fashion, parallel lines theoretically converge and “meet” at the horizon line is known as a “vanishing point”. If one were to traverse towards this hypothetical spot, the vanishing point would appear to retreat further and further away from the oncoming observer at the same speed as the observer moves toward the horizon line and, accordingly, the parallel lines would, hypothetically, never meet, nor cross each other. However, instead of rotating with the curvature of the earth’s surface, if one were to extend the line of sight on a straight trajectory out into outer space, ultimately, the vanishing point ahead would merge with, the singularity. In fact, vanishing point is an excellent definition of singularity.
In the temporal sense, the trajectory shows the path of time from the present (the observer’s eyes) to the past (the singularity). Conversely, reversing an observer’s temporal path from the singularity (the ultimate location of a vanishing point) the said path would travel from the past to the present.
A singularity is located in space/time at the time and place of the beginning of the universe. Said differently, two hypothetical particles emerging from a vanishing point (in parallel fashion) would appear to continually separate from each other and, measurably, and finally, rest at a calculable distance along the observer’s plane. (Train track rails appear and behave exactly this way on a flat surface extending outward towards an observer).
Model 1
Model 1 depicts how a vanishing point evolves into the same location and temporal construct as a singularity. The depiction shows how a vanishing point simply extends out into space in a straight path rather than following the traditional path atop the curvature of the Earth. With this assumption, one can picture that a vanishing point is an ultimate fitting and identical substitute for a singularity at the beginning of space time. And, using it, a multidimensional fabric of space time becomes evident and may at last be revealed.
Some readers may assert that this vision of the connection between scientific perspective and space time’s singularity is flawed. Maybe it is. But, to invalidate the next modeled vision, physicists and or mathematicians among others, must not only first refute model 1, but confront the fact that at least one aspect of model 2 may simply be irrefutable.
What may not be refuted is the graphic procedure of projecting space onto a plane. Someone may convincingly demonstrate that within this centuries old graphic procedure time has no business being part of space. But if so, we should all be disappointed to learn that, in at least one way, both the old masters Brunelleschi and Minkowski were demonstrably wrong.
Both were perhaps, among of the brightest human beings of all time, and thus, we should refuse to accept that sad premise. So my conjecture is that time must be embedded in the accurate procedure in some hidden way. If so, can it be exposed? The model 2 shows how time may be an integral part of spacial projection.
Model 2
The graphic mechanism, sometimes referred to as scientific perspective or vanishing point perspective, simplifies and enables a variety of visual determinations. For example, the maximum height that something must be limited to that prevent that object from being seen from any selected visually sensitive location can be graphically depicted and scaled by using the procedure.
Furthering the discussion of model 2, can we agree, by definition, that we are all “locked” within the “now” time/space plane or “fabric layer” if you will? For example, we cannot somehow step out of the present and, thereby, measure, experience, or see the future, nor can any object in our future be projected with certainty backwards onto our time space plane. And because it takes time for the image of all viewed objects to reach our eyes (even at the speed of light), we only can view history and not the present even when projected onto our time plane.
However, there is an irony here. As it turns out, we cannot actually “see” anything in our “now” time/space (present plane) because of the time it takes for light to reach our eyes. So, instead we only actually and literally see images from our past, even though, as per the technique we perceive (and accurately measure) things projected onto our time and plane.
With the relabeling, time can be portrayed as linear elements (virtual particles) radiating out from the big bang. (They would radiate throughout space if the full array were depicted). This fully articulated pattern could then be perceived as a coating as is partly shown by the two dimensional fabric in the altered projection. Each path represents a strand of Minkowski’s and Einstein’s fabric, if you will.
Object “A” in the model is simply a placeholder for the viewer to better perceive the space surrounding it. Using the configuration of model 2, I think I now know where (actually when!) dark matter (and dark energy) resides. According to the model, they reside within the “future” fabric of time space colored in blue. It is the future from the observers perspective, but is the present of object “A”.
The vastly expanded angle of “true present/observer’s future” was devised by selecting a hypothetical location for Object A that aids in labeling as well as enhanced comprehension of the theory. The actual angle is minuscule because compensating for the immense speed of light over a short distance makes it too tiny to see at the scale of the model.
In addition, not shown is the full array of projections which would appear as a sphere with future cones emanating into outer space allowing for ample room to accommodate vast amounts of dark matter and dark energy. A mathematician could calculate this area and make a pretty good estimate of the amount of dark matter in the universe.
An interesting observation is that object “A” appears larger in the future than what is correctly sized in the present.
One can assign a “moving” rate of one second per second to these vast series of virtual particles streaming out into the future cosmos. The emanating lines in the redefined model now become the visible historic paths of those virtual particles. But like railroad tracks receding off to a vanishing point they converge (even though they are actually parallel lines that never converge). Or, do they cross in a manifestation of another mirror image universe?
Nonetheless, what they leave behind is called history, what they travel towards is called the future and what they create at the moment of their interception with our plane is called the present, or that tiny and continually elusive moment of time we all refer to as “now”.
This model confirms that dark matter can never be visible but, as per this construct, it is probably not “exotic” material. It is most likely made of exactly the same stuff as visible matter.
This model suggests the exotic particles of dark matter scientists currently seek (and continually fail to detect) will never be found because they don’t exist. Furthermore, this visual theory of time can and does solve one important dilemma. It accounts for “hidden” dark energy. I’ve read physicists have no satisfactory theoretical explanation for this. But, under this construct, it, in identical fashion, resides in our future along with dark matter.
In conclusion, time, can be construed as a series of virtual linear elements, and is actually best graphically depicted as a two dimensional coating or fabric covering all spacial dimensions in every direction and location from the big bang past, to the present and emanating out to the future. This is what can be perceived as the space/time fabric. Only when when time is thought of as a series of streaming virtual particles can this fabric be clearly pictured.
Conclusion
By updating scientific perspective’s capability to project space onto a plane to include time, one can, in identical fashion, project time onto a plane, and thereby reveal a space/time fabric.
This visual assessment of time reveals that the age old question of “what” dark matter is may be more appropriately revised to ask the question “when” does dark matter (and energy) reside.
Dark matter does, in fact, reside in the present, but in a time “zone” that lies within the observer’s future. This 360 degree pattern radiates from the observer position throughout the universe.
It seems likely that dark matter is just normal matter and not made of exotic particles.
Much like the optical illusion of diverging railroad tracks, model 2 depicts the existence of a “temporal” illusion.
Does that illusion account for a wrongly perceived “expansion” of space in every direction?
In conclusion, time can be seen and expressed using Brunellechi’s Renaissance era graphics.
Rick Benas
Comments and suggestions are welcome.