Infinity has no geometric. The notion of a “sphere at infinity” contains a “surface” which is a boundary. Actual, real boundlessness in all directions means there is no “shape” which can be assigned to it. But, space is “curved,” it has no “corners,” like a square room. Space is not triangular. In other words, all “boundaries” in space are smooth, not jagged. This is a certain type of “order.” The planet smoothly glides around its star, not chaotically or haphazardly. The star, however, is “fixed” in space even if it may “orbit” the galactic center. In other words, a planet definitely orbits a star, but a star may be embedded in space and thus at least partially space itself is also along with the star “orbiting” the center. Density, elasticity and viscosity.
Two “infinities” are thus “in play.” The immediate infinity, which is space and the mediated infinity, which is time, and, clearly, an “infinity of time” is yet to happen because it is “not over.” The universe is not making “more space” but the universe is always making “more time.” When a process ends, time ends, and when a process begins, time begins, but even if there is an infinity of processes in play at any time this does not mean that this adds up to an infinity of time at any moment because none of even an infinity of processes is “eternal.” There is no process which could traverse infinite space from “one end” to the “other end” because there is no such traverse possible at all!!
In the astronomical vernacular, space is “cosmological” but time is “local.” What happens in one locality does not affect another locality because time itself cannot “flow” from one to the other. Mediacy has limits but not immediacy. Space, thus, is perfectly unaffected by time. No limit can influence limitlessness but this does not mean limitlessness cannot influence itself on an immediate basis.
This is the question of “tachyonic measurement.” The ability to instantaneously measure infinity. If space is dense, viscous and elastic, this should be measurable instantaneously over the entirety of infinite space. But, does a “ground state” of space exist anywhere? Is space “at rest” anywhere? And, the measurement cannot involve time because it all happens instantaneously within the rules of density, viscosity and elasticity. All what moves at a finite “speed” is time dependent, only what moves at infinite speed is totally independent of time. A clock which never “ticks” cannot “tell time.” But this does not mean there cannot be a “thing” which continually moves if the motion is instantaneous. Gravity therefore cannot have a “particle nature” nor a “wave nature” because both are time dependent. Thus, a “gravity wave” is not really a wave made of gravity, rather it is an energy wave caused by a gravitational process.
Supposedly the “graviton” is the “gravity particle.” This is more or less what an H2O molecule is to the ocean here on Earth. The graviton is not a proton and not a photon but supposedly it is the “thing” which “curves” space. The problem is that the graviton is time dependent, it does not act instantaneously. Dominoes are a good visual. After the first domino is triggered it takes “time” for the last domino to fall, this is the visual of how “gravitons” work. Instantaneous action is when upon the first domino falling all fall immediately, instantaneously. In other words, there is no “potential,” there is only “action.” The “potential” is a time dependent notion. The proof of zero potential and thus instantaneous action cannot be obtained with a “time dependent” instrument made of photons and protons.
The Earth is in the Sun’s gravity well. The Sun represents about 98% of all “mass” in the solar system, its well thus dominates the system. So, why does the Earth not “fall” into the Sun? Or, why does the Earth not “fly away” from the Sun? Clearly, because the Sun has a gravity well at any point along this well there is a computable “escape velocity.” It appears the Earth has neither escaped nor fallen in billions of years, meaning “orbits.” Nor have any of the other planets. The motion of the planets in their orbits is “just right,” not too fast and not too slow. And this makes sense: during solar system formation anything that was moving too fast has already “exited” and anything moving too slow has already “fallen.” Only the “just right” celestial bodies remain, there were no “observers” here in the “beginning.”
Therefore there is a “law” which permits a “just right” orbital speed for a given center of gravity which creates a specific gravity well. This is the problem with the notion of “potential.” A gravity field contains no “potential.” It is always “on,” it never “turns” ifself “off.” Were Superman to stop the planet in its “tracks” the planet would start plunging down the gravity well instantaneously. There would be no delay “waiting” for the “potential” to “kick in.” This law for all practical purposes is the “disk effect.” A solar system develops during formation an equitorial plane wherein most of the largest orbiting satellites are found. If a line is drawn between the star’s two poles, is it perpendicular to the equitorial plane? The disk formation law is even more pronounced in galaxies, but especially “spiral” galaxies, they all look like flat disks. What is basically a two dimensional structure is pinwheeling through 3D space. One of the “Ds” is taken away, it is a reduction in the “degrees of freedom.” Arguably, as QM shows, this is the opposite of what happens with the electron as it circles the proton, the electron does not move in a “disk.”
If QM is “fundamental” to all physics why is there this apparent “disk law?” The disk is one of the “observables,” so how does the disk emerge from the “math formalism alone?” And the disk is a simple structure so it cannot be very complicated math. And the disk is ubiquitous, it is observable as far as the eye can see. A telescope may be pointed in any “dark patch” of sky and more and more disks will be found. On the other hand, the “farthest thing,” the CBR, is clearly “spherical,” is not a disk. It is as if all what can be “seen” is inside this “sphere.” No telescope can “be pointed” beyond the sphere’s “walls” and thus the CBR is a type of “boundary.” So, there is an actual, physical boundary but does this mean there is “nothing” beyond this boundary? “We all accept the existence of things that we cannot see but could see if we moved or waited, like ships beyond the horizon.”[1]
And this is the question of the two infinities, of space and time. The horizon is one of time, not of space. We cannot see beyond some finite time and therefore the infinity of space is obscured. Why? Because time is “brought to us” by photons. The CBR is in fact the “oldest” observable thing. There may be even “older” things but these would by definition be “beyond the horizon.” The CBR itself this is this horizon but it is not like the ocean which has a ship beyond the horizon, it is a different type of horizon, it is a time horizon made of photons, quanta of energy.
The CBR is the largest possible sphere and every observer is always a the center of this largest possible sphere. No observer can be anywhere else. So, there is no “elsewhere.” Each observer sees the same CBR even if space is infinite and there is an infinite number of observers because the CBR acts as a finite “bubble,” limiting observations to the space which the CBR “contains.” If, as Tegmark remarks, an observer “moves” then the observer will still see the same CBR but he will also see the space enclosed by his version of the CBR because, again, he will be at the center of the CBR sphere. So what is beyond one observer’s CBR horizon will come into “view” for another observer because he has moved in space. He can changed his actual, physical location, but the sphere must remain the same, every location is the same, there are no “privileged” locations. In other words, it is impossible to do away with the CBR sphere from any location because photon based information is “time sensitive.” Motion in space is not motion in time because the time horizon does not change with a motion in space. This is one reason the “Olbers paradox” is false, meaning, it is not really a paradox. Space is not “static,” only time is “static” and time’s staticity is displayed with the CBR, the finite radius of the sphere which is the same from every observation post even if the distance between the two posts is 100x greater than the radius of the CBR sphere. Time “flows” only a finite “amount” before it “expires.” The CBR is the solution to what Olbers conjectured: “nearly every line of sight would end on the surface of a star, [and] thus one would expect that the whole sky would be as bright as the sun, even at night.”[2] The CBR is the “night.” It does not get any “darker” than the CBR. But this “darkness” is purely “situational,” it is the same from every observation post. There is a point, today, beyond our CBR horizon where the light from our galaxy shall never be seen, even if the observer waits an eternity, not unless he “moves” closer to us. The photon emitted by the Sun starts traveling toward this beyond the CBR horizon observer but the light never “gets there.” This is why his sky is “dark” even as he is looking directly at us along a “line of sight.” Along the way our photonic emanations in essence “peter” out and thus “go dark.” It is merely a temporal presumption Olmers concocted that “every line of sight would end on the surface of a star.” The error is clear, as crystal: that a photon can “travel” an eternity so long as there is a “line of sight.” Because space is infinite and the sky is “dark” this means photons cannot travel an eternity. In other words, it is the photon itself which “creates” the “line of sight,” the “line of sight” is not theoretical, it must be physical and if the photon is not “there physically” there is no line of sight to infinity.
Olbers merely assumes there is a theoretical “line of sight” to infinity. In other words, an actual “straight line” which is obviously projected from the observer’s post here on Earth. Olbers thus is doing no more than imposing linearity on the Cosmos which clearly does not act linearly. Olbers’ mind merely projected a “perfect” Platonic “world” onto the Cosmos and then he assumed this is “true.”
There is zero physical proof that a photon emanating from a star shall propagate an actual infinity of distance through space. Why does a photon propagate through space at all? And why does it have a “speed limit?” At least in Shankar’s opinion “no one tries to explain why c = 3 x 1010 cm/sec.” And why does in 1988 Hawking cite to a “German philosopher,” Olbers, who wrote about his theory in “1823?” Are there no more recent or more contemporary “physicists” who would “second” Olbers? Is what Olbers said on the subject in 1823 the “final word?”
The problem is that Hawking equates a “static universe” with an “infinite” universe but the two are not identical. A “big bang” obviously is “more sexy” than an infinite “steady state” universe. “There is apparently no point in the past at which the expansion [of the fireball] could have been arrested. It follows that the fireball must have been in a state of infinite density a finite time ago. According to the theory of relativity, this event, called a singularity, represents an edge or boundary of time.” The CBR is argued to be the “remnant” of the “fireball.” It is theorized that the CBR was a “one time” event, when the “fireball” cooled to a point where universe went from “opaque” to “transparent.” Surely, this one time event did not create an infinite number of photons, but, it seems, even today the CBR photons are happily streaming to all corners of the Cosmos as if a one time finite event created an infinity of them. Why has the CBR not vanished by now, why is it still observable? Why should not what is the absolute edge of observable space not be PERFECTLY DARK?
The theory is the CBR is a type of “imprint” of how the “early Universe” looked like. It is like a “snapshot.” So, does the CBR have any “video” features? A dedicated telescope could be pointed at a precise spot continually to see if anything changes with “time.” But would this be no more than the “deep sky” survey which eventually detected more galaxies and more objects which were not the CBR? Yet even between these objects the CBR was detected? How big would a telescope have to be to actually “get to” only the CBR, without any intervening objects? And, if this CBR only patch of sky were surveyed for a sufficient amount of time would there be any change in the CBR and then it would be like a “video,” not like a “snapshot?” And this would then indicate there is some sort of “depth” to the CBR and thus minimally indicate the “one time event” took several hours, or days, or billions of years to “play out?” And how would this putative CBR video fluctuate? By frequency?
If space is infinite then minimally the “fireball” did not create space, it is merely an “in space” phenomenon, and, thus, also, there is no “expansion” of space since space is already infinite, there is no more “room” into which space could “expand.” And thus the CBR is not at the “edge” of the expansion of space, it can only be at the edge of the expansion of time. The fireball really did create a new “time bubble.” But then the question is why is this fireball seemingly a “one of?” Stars are uncountable, why not fireballs? No wonder physicists are grabbing at straws and conjuring up things like “parallel universes.” There is no substantive or material difference between an infinity of stars and an infinity of universes. In either case Newton is correct: “an infinite number of stars [or universes], distributed more or less uniformly over infinite space [would not fall together] because there would not be any central points to fall to.” This is the problem of infinity not having a “shape.” There is no geometric depiction of infinity possible. Infinity cannot have a “central point” exactly because it requires some sort of finite “picture” and then one looks a the picture, which is always finite, and then picks a “center.”
Gravity resolves itself into a “steady state” universe because gravity is “distributed more or less uniformly over infinite space” which is beyond “time.” Space has no “time component” nor any “time parameter.” If it did it would not be infinite. Time cannot reverse gravity but gravity can reverse time. All of gravity is always in “the now” and thus the universe as a whole is not “going anywhere.” Only finite objects inside infinite space may or may not have a “destination.” And this includes time because time is subject to gravity, it is not in any way controlling gravity. This is one reason every “light cone” has a point designated as “now.” Inside the “now” there is no time. Were time to penetrate the “now” it would no longer be “the now.” If a proton’s “lifetime” is “at least 3 x 1032 years,” then at “no time” does the proton exit “the now.” There is no “decay” for “at least 3 x 1032 years.” If this is not “steady state” what is? A photon, in contrast, does not exist at all, ever, until and unless it is “emitted” by some quantum process. No photon has ever been observed to “exist” for “at least 3 x 1032 years.” The proton experiments can prove the proton’s longevity, why can’t photon experiments prove the same longevity for the photon? “No one tries to explain why c = 3 x 1010 cm/sec.”
What really is a “quantum of energy?” How many exact quantums did the “fireball” represent even if it was “infinitely dense?” What was the radius of the singularity at “time zero?” If the radius was finite could it have encapsulated an infinite number of “quanta?” This is the essence of QM’s problem: even as it boasts of an infinity of “kets” or “eigenspaces,” in the final analysis there is only a finite number of actual, physical “quanta” unless or when there is proof of “infinite energy” which then is divisible into an infinity of quanta. Then the “fireball” at time zero was contained in a sphere with an infinitesimal diameter where there was infinite temperature and infinite density and infinite energy and all of this physicality was at time zero already “quantized” into an infinity of “quanta” and this means all of QM math formalism already existed. And all this “existed” before the “bang.” The “bang” could not “bang” without all these infinities “pre-existing” the bang. Therefore the “big” had to perform the necessary calculations to produce the “bang.” And, as Hawking indicates “the calculations required to find out whether or not there were any infinities left uncancelled were so long and difficult ... no one was prepared to undertake them. Even with a computer, it was reckoned it would take at least four years.” In other words, the cosmos itself had to eliminate all the “infinities” and the only way to “do it” was to calculate the BANG. But this could have take not only “four years,” this could have taken a literal ETERNITY, so there was some absurdly small probability the “bang” would never happen, but thankfully it did.
Is it not true that the “big bang” fireball cancelled all initial “infinities?” And thus it is only mortal physicists who are having difficulties? Is this why Tegmark needs the “infinitely intelligent mathematician?”
