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A Walk Through the Fourth Dimension

May 30, 2014

Doing all this thinking and research on the Five Points has me wishing I could see the area not just in one time, but several times.
If I could go back, or maybe restore parts of the past, which would I choose? Perhaps the 1890’s in the last days of the 24 Baxter distillery building. Or maybe before the bowling alley was added, like in Riis’ photo, and then we could pick up from there and fix the whole area up. (I could picture a Fairway looking good in the building, and why not go far enough back so the main Old Brewery would be apart of it as well). Maybe even earlier, when it was all the little gable houses, or maybe leave the Collect Pond in place and build around it. Lower Manhattan would then resemble a Florida city like Orlando, with the downtown lakes.
But it would also be nice in the last days of the neighborhood, like that last new Mission building photo, when it probably resembled the Village across town with all the turn of the century larger tenements (including the ones that replaced the distillery).

Don’t even get me started on Norfolk. Downtown looks nice now with the Tide, MacArthur Mall, and Waterside Dr., the suburban looking new Huntersville, but old Main St. looked interesting as well, and the old Huntersville could have been fixed up into a nice looking old neighborhood.

With the actual timeline laid out as the fourth space dimension, we could have them all, at the same time!
(Remember, “time” and “space” are both media of displacement of objects and events; just that time is the direction of entropy, where one event causes the next, while space is a random access connection between objects relative to one another in multiple dimensions; i.e. you can go back and forth between points and measure the displacement with a fixed ruler).

So it has me thinking what it would be like if we could walk back through passed time as the fourth dimension.

When we talk about the “fourth” dimension, first, we number specifically the other three. Whichever dimension you are in, you must start with “back and forth”. You have to be able to look “ahead” into your dimension. So what we call “depth” is actually the first dimension.
The next fixed dimension for those anchored to a gravitational body is “up/down” or height.
So “left/right” or width is the “third” dimension; a sort of “extra” degree of freedom we have.

So if a Flatlander on a board could rotate to look out into our dimension, only his “depth” direction would change. (It would match ours, as we look at him at a perpendicular angle to his entire space).
Up and down would still be the same.

So likewise, if we could rotate into the fourth dimension, only our back and forth would change, and both up and down and left and right would be the same. (Rotation about a plane rather than just a line). If we didn’t move off of the hyperplane, one 2D slice of us would still be in the same slot, and one 2D slice of the rest of the universe to the right, left, above and below us (looking like a 1D line in each of these directions), would still be in those same positions from our perspective. By themselves, they wouldn’t be visible, because we would see them as having no thickness.

Now, if we were to lay out the timelike world line of the universe as a fourth spatial dimension we could walk through to reach other times, then as we look through the new dimension (“ahead” or “forth” of depth becomes the past), the 2D slice of the universe would smear out into the distance. Sort of like the older versions of Windows, when a window or application hangs, and you try to move it, its borders (or graphics, even text, etc) sweep out this 2D field of endless copies of itself.
Each “copy” of the image piled onto the next represents each instance of time.

Perhaps now it would be visible, though it would still be hard to make out what you’re looking at, since it’s just a smeared out 1D image for each direction. You would just see smeared out colors.
If you were in a room, it would become an endless tunnel. If you were outside between two walls or other large objects, it would look like you were in an endless ditch, with the sky above you, and whatever clouds were right overhead stretched out.
You would lose the ability to see into 3D objects (as you would have if you were looking at them from hyperspace and they had no hyperthickness) because the swept out surfaces would cut off your vision just as if you were still in 3D. The extended boundaries would now be able to enclose 4-space, at least in the immediate area.

If you then began walking into the direction representing the past, you would eventually see the smeared out surfaces around you end; when you reach the distance representing the time they were formed or at least moved there.
That would be the only place where you could look around the surface and see inside of the objects.

All of this is assuming we are still 3D, with 3D vision projected onto 2D retinas. If we were 4D, with 3D retinas, then each 2D slice of the universe stacked into the distance would still have the third dimension attached to it. This would be aligned in the new dimension.
So of the four dimensions visible, height and width would still be the same, depth would still be “past”, and now the fourth dimension would be what was originally depth; meaning the direction you rotated out of to turn toward the past.
As you walked, you would still pass each 2D slice for each instant of time, and for each one, you would also see the distance that was in “front” of you in this space regress. It wouldn’t be directly approaching or receding; you’d only be “passing” it, like the other dimensions.

Also think what it must be like to be in the act of rotating. As only your “forward” is changing, you see objects appear to get further away, as you’re looking at them further along the new dimension (past or future). They appear to reach the horizon, and then you see the other two dimensions form the “tunnel” or “trench” as mentioned, as you’re looking only at their history, totally parallel 0° in the new dimension.

So this is what 4D existence would be like. I use time, because it gives us something familiar to “fill” the new dimension with, so we could get the idea of what vision and motion through it is like.

The remaining problem with experiencing free motion through time as 4D like that is that 3D would not look the same. It would become an infinitely “thin” membrane in the new visual matrix, so we would always see the hyperspace “around” it. And then, the near impossibility of aligning ourselves perfectly with one particular “brane” of an instant; let alone staying there.
(I always say it’s just as difficult to visualize true 2D vision as it is for 4D!)
The eyes would have to have some mechanism to shut out the extra dimension, and the both the body and the fabric of space would have to have something to anchor one to a particular instant.

  1. On my regular space, I had come up with an idea that the inertial frame of reference for the speed of light generates an additional dimension, as the dimension you’re heading in collapses to zero. In that “proper time”, light would still not be at rest, but rather still pass you at the same speed. So whatever direction that is, must be something beyond our dimensions.

    It seems the consensus in math was that this was undefined. Now, on these sites:

    Time is not frozen from light’s perspective, because light does not have a perspective.
    In the limit that its speed approaches the speed of light in vacuum, its space shortens completely down to zero width and its time slows down to a dead stop. Some people interpret this mathematical limit to mean that light, which obviously moves at the speed of light, experiences no time because time is frozen. But this interpretation is wrong. This limiting behavior simply tells us that there is no valid reference frame at the speed of light. A reference frame that has exactly zero spatial width and exactly zero time elapsing is simply a reference frame that does not exist. If an entity is zero in every way we try to describe it, how can we possibly say that the entity exists in any meaningful way? We can’t. Space and time simply don’t exist at and beyond the speed of light in vacuum.

    A photon cannot be said to have its own inertial reference frame, because inertial reference are defined to be a family of coordinate systems that satisfy the two fundamental postulates of SR, one of which is that light moves at c in all frames. [the other, that The laws of physics are the same in all inertial reference frames]. You could construct a coordinate system where the photon was at rest, but since this coordinate system wouldn’t be an inertial frame there’d be no reason to expect equations that are specific to inertial frames, like the time dilation equation, would still give correct predictions in this frame.

    Another point is that if I’m moving at some very large fraction of c relative to the galaxy, not only do I measure the galaxy to be highly compressed in the direction I’m going, but I also see clocks on either end of the galaxy as wildly out-of-sync due to the relativity of simultaneity…if the galaxy is 100,000 light years long in its own frame, and I’m moving at speed v relative to it, then two clocks at either end of the galaxy which are synchronized in the galaxy’s frame will be out of sync by (100,000 ly)*(v)/c^2 in my frame. So, in the limit as v approaches c, clocks on either end of the galaxy are out-of-sync by 100,000 years, so at the same moment that it’s 2014 A.D. on the leading edge, it’s 102,014 A.D. on the trailing edge. And yet in the limit as v approaches c, the distance between clocks along the direction of motion is compressed to zero. So in the limit, perhaps you could say that the photon’s entire history is traversed instantly, since it’s going zero distance and all the different clock-readings it passes are squashed together on this zero-length path.

    However, I think there would be aspects of this limit that wouldn’t really be well-defined, in that they would depend on the details of what are the series of cases that you are using to construct the limit. For example, consider a particle A moving at some v < c, and a photon B moving at c. In the limit as v approaches c, both A and B are moving at c, and B is still moving at c in the frame of A. On the other hand, consider two particles moving at the same speed v, at rest relative to one another. In the limit as v approaches c, both A and B are moving at c, and B is at rest in the frame of A. So, the question of what velocity A would measure B to have "in the limit" would depend on which type of limit you used, even though in both cases they both have a velocity of c in the limit.

    “This answer hits upon the facet I like: That a photon never moves. From its perspective there was no spatial distance along its path, and it took no time to get from one end to the other. Like it is a point in a higher dimension.”

    What if a system of interacting, massless particles was conscious, and could make observations? The argument given in the preceding paragraph proves that this isn’t possible, but let’s be more explicit. There are two possibilities. The velocity V of the system’s center of mass either moves at c, or it doesn’t. If V=c, then all the particles are moving along parallel lines, and therefore they aren’t interacting, can’t perform computations, and can’t be conscious. (This is also consistent with the fact that the proper time s of a particle moving at c is constant, ds=0.) If V is less than c, then the observer’s frame of reference isn’t moving at c. Either way, we don’t get an observer moving at c.

    In the special relativity, as explained by Einstein, there are two possibilities. Either the speed of any particle is limited at all or not. Now if the speed is not limited, the Galilean theory pops out. But as we already know, that does not properly explain the transformation of velocities from one to another reference frame accurately when dealing with high velocities. So only other case is that the velocity is limited, if so what is it?? It comes out that this velocity is precisely the velocity of light.

    So, any particle which is mass less travels at the speed c, which is why the speed of light is also c.

    “The speed of light c which we are talking about is not a property unique to light. It’s just that the velocity c is the speed of causality as explained in the YouTube channel PBS space-time(By the way, it’s a cool channel, do check it out). So anything with no mass travels with the speed of causality which is c.”

    There is no way to explain this without explaining relativity first. In Galilean universe (the “classical” physics, which is what most people intuitively assume and think about), light speed cannot be explained. Indeed, the Maxwell equations which is describe how light works, were the first clue that our understanding of space-time was flawed.

    Velocity (as in, distance traveled, divided by time taken, measured both by the same person) is limited because the nature of our universe is such, that space and time are geometrically connected, similar to saying “why the largest possible angle in triangle is 180 degrees” or “why there’s no north at the north pole”. Forces cause acceleration and change momentum, but at large velocities, increasing momentum doesn’t change the velocity all that much anymore.

    how come the light speed isn’t infinite? Because if it were, our universe would be much different in ways you’d most certainly notice. For wave equation to make sense, the wave speed has to be finite, so the fact that electromagnetic waves exist (Maxwell equations hold) proves it must be finite. If not, we’d have no induction, no radio, no interference…. it’s quite natural for us to assume that changes in the environment take time to get noticed somewhere else, so much, that people struggled for a long time how gravity and such work (forces at a distance were problematic, and only resolved when we realized there are fields that carry this information through space). In that respect, finite speed of light made some things easier to understand. Instantaneous action at a distance would break a lot of physics.

    “c in our universe happens to be finite and has to be measured to see how much is it in our universe… although, quite a lot of phenomena would severely break down if it were infinite. For one, there would be no wave optics. No Maxwell equations. There is a large gap between large but finite, and truly infinite.”

    The basic question is, “how do we measure that something is this fast at all?” which is, “we measure the distance something goes, we measure the time it took to travel there, we divide the two.”

    How do we know how far it traveled? Well, we use these things called “rulers.” But how do we know that those rulers maintain a constant length, rather than getting larger or smaller? At some point in practice we normal experimenters just trust them…
    So the questions stop being about why the speed of light is what it is, and start being about us: why are we 1-2 meters high and why is our reaction time 0.1-0.2 seconds long? The ratios of these numbers then dictate how fast the speed of light is relative to the speeds we’re prepared for. We chose our units based on these speeds and times that we’re prepared for, and the speed of light doesn’t care about that, but we do.

    So it turns out that when we get down to it we cannot detect these unit variations in isolation but only by combining them all together into unit-less numbers that we call “dimensionless.” (The study of units and how they interact with physical quantities is called “dimensional analysis”, doesn’t have anything to do with the “dimensions” of our 4D-spacetime or “other dimensions” in sci-fi.)

    The important dimensionless constant for how big we are is called the “fine-structure constant.” It is a smidge less than 1/137.036, and essentially says how strong the electromagnetic force is. And if you ask me, “why is it the way it is, so that atoms are possible and molecules have the size that they have and we are the relative size we are compared to light over the time-frames that atoms vibrate?” and all of those questions, I can firmly tell you nobody knows. People have been trying to find a mystical understanding of this number ever since they discovered that it was approximately 1/137, and were not stopped when they discovered that it was actually closer to 1/137.036, but those mystical understandings have never led to scientific theories with testable predictions which we could then confirm with actual evidence. We simply don’t know.

    This one asks “would an object moving with the speed of light not be at the same time at every place if all distances become zero? If so, why is ‘light’ not everywhere, but still has a definite velocity and direction?”

    I likewise also wondered then how if the frame of reference doesn’t exist, then how could the wave be able to vibrate in space, and also change direction and even speed if refracted, reflected, or passing through different mediums. A photon going from the sun to the end of the universe, and another one bouncing off of the moon, or arriving on earth, and bouncing around through the sky, and off a mirror and several walls before entering our eye all experience the same zero time and space! But this was essentially treating light as a particle only.
    This site makes a point I alluded to on the other page, about how waves transmit through different things (like the image of something moving across a pixel screen, where the elements are not actually moving, but simply transmitting across a medium).

    The mechanism of energy transport through a medium involves the absorption and reemission of the wave energy by the atoms of the material. When an electromagnetic wave impinges upon the atoms of a material, the energy of that wave is absorbed. The absorption of energy causes the electrons within the atoms to undergo vibrations. After a short period of vibrational motion, the vibrating electrons create a new electromagnetic wave with the same frequency as the first electromagnetic wave. While these vibrations occur for only a very short time, they delay the motion of the wave through the medium. Once the energy of the electromagnetic wave is reemitted by an atom, it travels through a small region of space between atoms. Once it reaches the next atom, the electromagnetic wave is absorbed, transformed into electron vibrations and then reemitted as an electromagnetic wave. While the electromagnetic wave will travel at a speed of c (3 x 108 m/s) through the vacuum of interatomic space, the absorption and reemission process causes the net speed of the electromagnetic wave to be less than c.

    Were there an infinite value for the speed of light, light itself would not exist at all. Mathematically, the wave equation that describes light as an electromagnetic wave would lose its time-dependence.
    In physical terms, an electromagnetic wave arises due to the finite time it takes for news of the change of location of an accelerated charge to arrive at a distant point
    . Think of an electric charge as being like a hedgehog with flexible rubber spikes going out to infinity in all directions. These spikes represent the electric field lines, the lines along which a test charge would move.
    If the charge is jerked, the segments of the spikes close to the charge will move, but those farther out will still point in their original directions. The result is that each spike will get a kink that moves out to infinity. This kink relays the news that the charge has moved to the distant parts of the spikes and corresponds to an electromagnetic wave. If the wave moves infinitely fast, it is as if it were not there at all; the spikes are infinitely stiff and the news gets out to everywhere without any seeming kinks. In other words, there would be no electromagnetic wave, and thus no light.

    I think this may answer the question for me, of why “infinite speed” as the technical “proper time” of light doesn’t match up with an infinite speed in coordinate time, and what has made 186,282 miles per second the top speed, which is incredibly slow given the size of the universe.
    “One should think of the speed of light as ‘infinite speed’. A common misconception is thinking the speed of light is just like any other finite speed. The speed of light is only finite from the perspective of the outside observer; from the perspective of a photon, it’s infinite. If you move at exactly the speed of light you could go anywhere, no matter how far, in exactly zero seconds.”

    There are some things that behave differently when investigated from an “approaching light speed” way of thinking and the “being at light speed” way of thinking. In this case there’s no difference. When something travels at the speed of light it really doesn’t experience any time.

    On the flip side of that coin, it also doesn’t experience any distance. The time and location of its emission and the time and location of its absorption are the same from a photon’s perspective.

    This may not make sense, and it’s a little mind bending, but consider this:

    Movement isn’t dependent on the time experienced by the moving thing, it’s dependent on your time.

    Here on Earth we feel like there’s such a thing as “non-relative movement”, since we all agree (very naturally) on the same reference frame: the (local) surface of the Earth. That is, you probably frequently refer to yourself as moving, while you rarely think of the Earth as moving.

    The point is: everything always thinks of itself as stationary (you don’t move with respect to yourself), and movement is a property assigned to other things based on each observer’s reference frame. So light may not experience either time or distance itself, but to move, all it needs to do is get from one point in your spacetime to another point in your spacetime.

    If light can be slowed down by passing through matter, matter consists of strings in a particular vibrational pattern, according to string theory. But then spacetime consists of strings also. We’re accustomed to thinking of space as “nothing” (especially given terms like “vacuum” and “void”), but it really is “something”. In other words, a “vacuum” is not totally a vacuum; space itself is a kind of “fabric” (after all) according to this theory! Perhaps it’s simply the spacetime strings themselves that limit how fast anything can be propagated/transmitted through them, just like the strings comprising matter reduce the speed further.

    “Infinite speed” would only be possible in the hypothetical “primeval realm” the strings are imbedded in, which is not even space, but has been compared to “matrices”. A matrix, if I’m understanding it correctly, would be like a game of chess written out move by move, where you identify the piece you’re moving, it’s direction and thus the square it will land on (which all have names/numbers), without actually moving pieces across a board. That eliminates the spatial aspect of it. Now, if you also write the chess steps out of sequential order (and perhaps organize them another way, like alphabetically), that would undo the time element.
    Already, this would match what I described for the hypothetical photon perspective above, where every photon emitted travels different distances and trajectories but since [coordinate] space and time for them are zero, then it’s like all that could be done in their perspective is define a coordinate representing their path, and then it’s instantaneously there. Think of the sun or any other light source with every point at every instance of time marked with a space-time coordinate the light emitted from that point in space and time will end up (which is pretty much already predetermined from that perspective), and it instantly is there. That is basically the “frame of reference” of light. (And also represents the hypothetical “lightlike infinity” marking the diagonal borders of the Penrose diagram).

    The speed of light is not an inherent property of light (especially since it can slow down and even stop!) but rather of the spacetime strings themselves. As mentioned above, it’s the maximum speed of causality, which is basically the effect one string’s energetic (vibrational) state can have on another. As the PBS “Space Time” video “The Speed of Light is NOT About Light” puts it, it’s the fastest speed any two parts of the universe can “talk to each other“. Seen this way, it now makes sense why this would be finite (limited in how fast information can be propagated across these elemental nodes of spacetime. There’s also this notion string theorists talk about, regarding particles far away being “connected” somehow, so that instantaneous events occur between them. I never yet fully understood this, but it obviously is not describing information transmitted across regular space).

    So I came up with a hypothetical (not practical) idea of what must happen to the environment around an observer at the speed of light. I did say there that it essentially is zero, from our perspective. But for one thing, since coordinate time also collapses to zero from the light perspective, you would also need another dimension of time this is occurring in (which I had forgotten about).

    It seems like the only “frame of reference” for a photon would be the direction and the final end point and time, not as an actual distance or duration (since that’s all collapsed into nothingness at that speed), but rather simply plotted in the form of a matrix. It seem the fundamental constant is itself a form of this “primeval realm”. (And it’s the same thing as there being a cosmic limit to size, beyond which, space breaks down into the primeval realm).

  2. Thinking about this more; here’s how I think the speed of c works:

    I liked how the video I referenced above put it in terms of, that locations in spacetime “communicate with each other” (communication is “instant” [and all locations compacted into one point] in “c” proper time, but not coordinate time. So spacetime “addressing” is itself not determined by proper space and time, and is probably more “matrix”-like, like the sub-Planck “primeval realm”).

    So we should then go all the way down to the fundamental units of space and time; the lengths below which reality breaks down:

    Planck length=10-35m
    Planck time=10-43s
    c=10-35m per 10-43s

    Each superstring represents one point in space and time. You may have heard that “we can’t ‘drop anchor’ in the universe” and define a definite point in space”; but that’s when plotting by the three coordinates of space only, and leaving time variable. That’s what you can’t do. That then is what you have to take into account relativity, and ask which frame of reference you’re looking at.

    A string has no “world line”; it only can be plotted in one “instance” of Planck time. When one instance passes, then it is essentially “replaced” by another string. The location of that string in space of course is determined by the relative frame of reference of the one observing it.

    “Speed” is only a determinant of relative change of position in space between two observers. So if you could take all of space, in one instant of time for a particular frame of reference, then two objects will have a definite number of stings between them. If they’re a meter apart, then there will be 100 decillion strings between them, which is 1035. Motion is determined when if in the next instant of time, that number increases or decreases. You can’t determine which object is at “rest” or not, and you may even have differing views of the measured “distance” between them, but there will be a different number of strings, representing a changing distance, as each instant of time passes.

    Matter and force “particles” may simply be vibrations passing from one string to the next. Each passing instance of time represents a “move” (think chess/checkers) which could be to an adjacent string in time, or in space, but with a limitation.

    So c is perhaps created by two rules:
    1) Motion (change of relative string position) can only occur over time (a vibration can only occupy one string per vertical row i.e. space dimension). If time (vertical on the Minkowski diagram) is not traversed, the object is frozen in time and can’t move.
    2) Strings in cannot be jumped over. Motion of vibrations must always pass through adjacent strings.

    Either case would then make any trajectory of y<x impossible. That would mean all FTL travel (even if more than 0° to the horizontal on the diagram) would actually have a segment of technical infinite speed; being more than one point of space at a time. For a vertical line, you can move through time without moving through space (that is, in your own frame of reference), but then this again is not defined, as other frames of reference will see you as moving.

    So the universe having a "maximum [finite] speed" is tied to it having a minimum [nonzero] length and a minimum duration.
    Of course, this is in coordinate time, which is simply a frame of reference where a number of observers all relatively agree on a common frame of reference. Proper time, you can accelerate faster than 186,000 miles per second, and then you’ll also find that you can have lengths and time smaller than the Planck units, as both space and time shrink toward zero. C then would be the hypothetical “infinite speed”, in which you would travel any length in no time. This would also make all lengths basically infinitesimal.

    On our graph, if for every “move” you must always advance at least one instance of time and stop at every point in space you cross, then the y=x trajectory of coordinate time basically amounts to y=0x in proper time. One string over and one “up” is for all purposes the next one “over” as if you weren’t going up. More than one string over is something that doesn’t exist in your frame of reference for to communicate with that point would amount to being two places at the same time.

    So really, outside of the light cone; the so-called “elsewhere” really doesn’t exist to us. We can think of the sun “right now”; eight minutes before the light it emits at that time reaches us, but that is really assuming that it’s still there, and nothing has happened to it since the rays we are receiving now left it. What we’re calling “right now” on the sun or anywhere else in “elsewhere” is really future to us. Then, after the eight minutes pass and we see the light from it still coming to us, we can then think back to eight minutes in [what has then become] our past, when we know the emission occurred, and project this back as what was “right then”. Our “light cone” at that time has expanded past that distance, and the information received is now present. This is why Rudy Rucker says “elsewhere” is really like a “smeared out ‘now'” (Fourth Dimension, p. 157).

    Every point in space-time; every string, can be thought of as existing in its own universe, where it’s the only thing that exists. The other strings in space (which are all outside of the light cone) don’t exist. Even within the light cone, the past array of strings is gone, and the future array of strings hasn’t occurred yet. Each string has an expanding field of strings it can influence in the future, and a contracting field that could have influenced it.
    To move along that boundary is to remain in a frame of reference where you’re always “next to” coordinates that do not exist from the vantage point of the starting string. So there’s no “ahead” of you in space (it appears as if you’ve reached infinity), and therefore, since you’re moving also no ahead of you in time (since it takes infinite time to travel infinite space).

    Also, we can see by comparing frame of reference grids how the translation back to coordinate time (where both the observer and the relativistic traveler agree that all spacetime coordinates have been passed by the traveler; nothing skipped over, or no different path seen by either) is what compressed the dimensions of an increasingly accelerated proper time. At c, the length and time collapses onto the world line itself, which is the 45° hypotenuse of the triangles formed by the coordinate time bisected square representing one Planck length. So the proper Planck length and time fold down to ½√2 and thus not zero itself, but the parallel coordinates have all collapsed onto the world line as well

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