Infinity - by David Cornberg - Article review

This document is an article review "Infinity" by David Cornberg written in 2023
To order to read the article select: https://www.academia.edu/s/86c2e501bb#comment_1304176
This document by itself is also an article review and contains additional reviews.

Contents

Reflection

Infinity

In response to Tom Golding’s academia.edu discussion paper “In Defense of a Past that Never Began, part 1” I first wrote:

1.
Well...I am neither a monotheistic creationist nor a physics big banger...both the contradictions and the lack of empirical evidence leave me unconvinced of either...however, your conclusion, Tom, seems to me to go directly to the point: the word "infinite" in English is a privative term; that is, the prefix denies the stem without suggesting or implying, one way or another, that reality is only finite or only infinite...
When we use the word finite, the meaning is clear.
We use that to describe an object a volume or a space which is surrounded or enclosed with a clear boundary. For example a house is finite, the earth is finite, the sun is finite and our solar system is finite. But we can enlarge this definition. The space occupied by our galaxy, the milky way, is finite. Also the galaxies and galaxy clusters in our neighbourhood define a finite space. You can even go a step further and define that the space occupied by everything that we humans can observe is finite.
The most important observation is that all what exists in this space is constantly changing as a result of other changes or events. A second observation is that the further away from our observation point the earlier.
A whole different discussion is what is the situation outside our visible horizon?
The most probable answer is that our visible horizon has nothing to do with what is happening in all of space or the universe, enlarge. To claim that we are in someway at the center of something is misleading.
2.
After a couple of weeks during which I received no response from Tom or anyone else, my quiet, unconscious reflection continued and then one day, in fact the day before the discussion ended, I wrote:
3.
Perhaps you are all way beyond my thoughts, or perhaps I can contribute something to this discussion. First, does the English word “infinity” refer to anything in nature that can be observed? If so, what observations of it have been made and how have they been made?
Only physical objects can be observed. All objects are finite.
Second, if “infinity” does not refer to anything that can be observed in nature, then how can it be used in theories in the natural sciences all of which require replicable observations for both verification and falsification?
That is the reason why the word infinity should not be used as part of any physical description (or theory or law)
Moreover, if “infinity” refers to nothing observable in nature, then is it only a mathematical concept that is an artifact of the mathematics that humans have developed for many well-known purposes? If it is only a mathematical concept, then the question of whether or not infinity exists can be answered in the affirmative with reference to mathematics but not to nature.
The meaning of the words finite & infinity, considering mathematics, is a new ball game.
In a pure mathematical sense the concept of infinity can not used to describe something that exist.
In mathematics, when we calculate we use numbers. We can divide the numbers 10 by 2 and the result is the number 5. We can also divide de numbers 1 and 0 and the result is infinity. You can raise the question if 0 is a number, but anyway the concept infinity is not.
In physics we can divide 10 apples by 2. The result are 2 piles of 5 apples each. To divide 10 apples by 0 is a mind twist.
In phycics, Newton's Law is partly described as F= m1*a1 and also by F=G*m1*m2/r^2. r is the distance between the center of the objects. When both objects are moving towards each other, this distance becomes smaller and smaller. But never zero. When the objects collide, there after, Newton's Law is not valid anymore, because the two ojects either merge or explode in many small objects and grains. That means, from a physical point of view, there is no need for concepts like infinity or singularity.
4.
Again no response from Golding but an interesting exchange with an Indian intellectual that was short, enjoyable, and gave me some motivation to consider writing my own paper about infinity.
5.
A few years ago, I got interested in infinity and bought two recent books written about it. I was disappointed that the only coherent notion either author could form about it was mathematical. Almost needless to say, I did not finish reading either of the two books I bought but I did scan them for something other than mathematical concepts. I found none.
That is not very hopefull.
6.
To be recognized as something that exists, the thing must differ in some way or ways from other existing things around or near it. Since the thing differs, it has boundaries. Since it has boundaries, it is finite.
That is correct
7.
Why do I revert to nature? Well, the Dalai Lama promoted, sponsored and led a series of exchanges between well-respected Western scientists and well-respected Buddhist thinkers, himself included.
The physicist, the Dalai Lama had invited, responded to his question about the current view of astrophysics as to the state of the universe by sharing that there are currently enough mathematical calculations and observable evidence to support three different hypotheses: the universe is expanding; the universe is in a steady state; and, the universe is contracting.
I note in passing that the physicist did not add another logical possibility which is that the universe is in a steady state of both expanding and contracting.
The only vissible evidence exists that probably the universe (observable space) is expanding. All the other 2 hypotheses are mathematical possible, including the idea that the universe is in a continuous sequence of expanding,contraction,expanding contraction etc
Be that as it may, this diversion to nature is relevant because astrophysicists use the term infinity both as a word and as a mathematical symbol, in their discussions of the universe. One of the participants in the Golding discussion commented that when a physicist makes a statement such as that the interior of a black hole is infinitely dense, the use of “infinitely” is actually short-hand for the fact that, not only has no one ever observed the interior of a black hole to see whether or not it is infinitely dense, but also the standard definition of a black hole as an object whose gravity is too strong for even a photon to escape implies that no observable signal can come from its interior.
Concepts like intinitely dense are misleading and should not be used.
What should be mentioned is that all objects in the universe influence each other i.e, blackholes, stars and planets. That we humans can not observe blackholes directly does not invalidate the interactions between all these objects.
8.
Two recent experiments also bring the issue of the observation of space and time to the forefront. The results of the gravity probe B experiment are interesting up to the limit of their margins of error, which for some of the quantities is large enough to ask whether another kind of measurement or another kind of measuring apparatus or both could be use. But the gist of the results, along with the previous findings by Cifuolini and Pavlis, overall suggests that space and time maintain some kind of relationship under various kinds of transformation.
For more detail see this link: https://www.science.org/content/article/long-last-gravity-probe-b-satellite-proves-einstein-right
The fact that the earth just keeps spinning and turning about its own axis, around the shape of our solar system and in the solar system as a stable configuration in a moving galaxy, cluster, etc. does not seem to support any particular version of what we call the universe in preference to any other version. Infinite variability of versions? That, I think, would be overstating the situation we’re in because I, at least, cannot state that I have seen all possible transformations of space and of time.
Part of the text is not clear. Transformations are a mathematical concept and don't explain any process that is evolving in the universe.
Put in that way, the locutions space time, space-time, and spacetime can be seen as three transformations, which can be connected historically with Newton, Minkowski and Einstein, in which the nature of the transformations and the relationship(s) denoted by the different spellings remain opaque.
9.
Besides Tom Golding’s very interesting paper and discussion session, this opacity also motivates this paper in two different aspects. First, the evidence that something around the earth can be measured as changing in a determinable relationship to the rotation of the earth seems to me to reopen the question of the nature of whatever the earth floats in.
The earth, nor any of the objects in the universe at large floats in something. The only thing you can state that is that space is not empty and that there exists no vacuum in the universe. The fact that we can observe star light from all directions implies that there are photons, i.e., that there is radiation, travelling through space, in all directions.
The attempts to eliminate the aether on behalf of a space so empty of any kind of material existence that it cannot provide resistance to the motion of any physical object, including photons, seems, with the results noted above, to have failed. Since the very word "aether" has became anathema (something that one dislikes n.v.) to so many physicists, Einstein included, there is no point in insisting on that word.
The problem is that the starting point what we humans want to understand should be vissible. The problem is that there exist no quarantee that all what exists is actual vissual. Large objects like black holes are invissible. At small scale, the atmosphere in which we live is also invissible. That means that all concepts like aether, vacuum and empty space should be handled with great care.
However, and this is the second aspect: according to NASA’s Executive Summary of the Gravity Probe B experiment, “Any change in spin-axis orientation of each of the gyros, as they traveled through the warped and twisted spacetime around the Earth, was measured against this guide star reference to distant spacetime.” https://www.nasa.gov/pdf/168808main_gpb_pfar_cvr-pref-execsum.pdf p10 The fact that the amount of earthgenerated magnetic field was decreased to the lowest ever achieved in space (Ibid. pp7, 9-10 and 21) suggests that the surrounding floatation medium is both non-reactive to earth planetary magnetism and is itself unaffected in its configuration in the same ways that the medium without the magnetism is affected.
Okay
However, a popular report of the success of Gravity Probe B contains an interesting image: “’Imagine the Earth as if it were immersed in honey. As the planet rotates, the honey around it would swirl, and it's the same with space and time,’ said Francis Everitt, GP-B principal investigator at Stanford University.” https://www.nasa.gov/mission_pages/gpb/gpb_results.html . So, space and time, space time and spacetime can be compared with honey but their own natures cannot be directly described.
It is not very wise to compare space and time, space time and spacetime with honey. This gives an impression that these three are physical concepts. But they are not.
Each should be explained separately, within its own context.
For example, space in our vincinity is a physical concept. When you multiply a speed with duration it becomes a distance. The same, when you multiply the speed of light with a duration.
The absence of direct observational data describing the nature of space and time clearly complicates the question of the nature of infinity, especially when infinity is used either mathematically or conceptually, to characterize space and time.
It should be understood that there can be a conflict between a mathematical description and a physical description.
A mathematical description (part of a simulation) is often a simplification of the reality. A physical description is based on actual events. It is very important that the way used to measure (to calculate) the time of all the events should be uniform. This implies that all the clocks used should be identical and fixed in one coordinate system.
From a physical point of view there is a difference between distances measured at same moment in time and at different moments. The first are distances part of the same object. The second are distances between points of different moving objects.
10.
However, I am not only not a mathematician, etc
11.
When I try to find a way into an old and complex topic of human thought, I usually identify key terms and then study their etymology.
12.
When I look at the face of a small clock on a shelf in my living room, I see a circle of numbers and two hands, one shorter/longer than the other. When I read the clock face, I may say to myself that it is twenty minutes to two or that it is one-forty and I may add that it is am or pm, in the morning or in the afternoon. This action has connected me with a consensual system of measuring something that is also consensually called "time".
There are two definitions of the concept time.
  1. The first definition is what we call universal time. This time reflects the age of the universe and is the same everywhere in the Universe. This time increases constantly This is the time we humans feel. All what happens at present we can call events. All these events are happening simultaneous. We can define all the events that have happened: as events in the past. We can also define all the events that will happen: as events in the future. Universal time is neither visible nor invisible.
  2. The second definition is what we call clock time. Clock time is defined by using a physical clock. A clock is an oscillator, which is often a device with a dial, which rotates around a common point. One revolution of the dial is called a tick, which represents a certain duration.
    A problem with every clock is its accuracy. Moving a clock de influences the duration of a tick. Gravity also influences the duration.
But now something very interesting happens. Suppose that I want to buy a new rug for an area of the floor of the living room. With a tape measure, also marked in numbers, and also part of a consensual system called variously “distance”, “length”, “extension”, etc., I take four measurements and write them down in inches to take with me to the store where I will look for a suitable rug. What I measure, though, is not invisible. It is the visible surface of the floor. Also by consensus, I have made a measurement in space.
You have performed is a mathematical operation. You have measured is the surface area of a rug, width is defined as length times width. This has nothing to do with (measuring) space, which is a 3D concept
Space, however, is not the surface of the floor. Space, like time, is invisible.
See also Reflection 1 - WorldView
13.
I live in a sub-arctic area of Interior Alaska. Etc.
However, since both time and space are invisible, communication about them must be done in words and numbers.
14.
Much older means of keeping track of the relations among the sun, earth and moon etc.
15.
The Oxford English Dictionary (Compact Edition) does a very thought provoking thing with both the words space and time.
This is a very confusing paragraph. 3D space and time have nothing in common.
For its first entry under “Space”, it states: “I. Denoting time or duration. 1. Without article, lapse of extent of time between two definite points, events, etc. Chiefly with adjs., as little, long, short, small.” (Ibid. p2936).
For its first entry under “Time”, it states “I. = A space or extent of time. 1. A limited stretch or space of continued existence….” (Ibid. p3324). “Space “ is defined with time and “time” is defined with space.

Additionally, the etymological references for “space” are an adaptation from Latin “spacium” which appears in Mediaeval Latin as “spatium” (Ibid. 2936).
And, in the etymology of “time”, with references to similar terms in other Northern European languages, the root of “time” is postulated to derive from a verb meaning “to stretch, extend” (Ibid.p3324) which root some etymologists think “time” may share with the English word “tide” (Ibid.p3318).

The problem with space, time and spacetime is
  • That space is a 3D concept. Space defines an area or the content of an enclosed area.
  • Time also comes in 2 flavours.
    • If can be defined as universal time, which is an absolute concept.
    • It can be defined as a duration.
  • Spacetime is defined by first multiplying a duration with the speed of light. This gives ct, which is a distance The combination of 3D space in x,y,z and ct defines spacetime. Spacetime is a mathematical concept
16.
An answer to the question of what the numbers on the clock and tape measure are measuring could be, then, in one English word: “duration”. But for there to be duration there must be difference of some kind between things that can be recognized as existing with some degree of independence from each other.
How, then, could such difference be described with relevance to time and space?
The most important is the difference between time and contents of objects
Such a description would have to include, minimally, some kind of passage from one to the other. A passage from one thing—point, place, object, location, area, position, etc.—to another cannot be carried out with invisibles, that is, with things that cannot be observed, such as space and time. A passage from one thing to another, such as the measuring tape along the floor to determine and record the dimensions of the new rug, requires one physical thing—the tape—interacting with another physical thing—the floor—in an action that has a finite duration. The finite duration of the action can be described in both temporal terms and spatial terms. But these terms are not what are interacting; these terms are necessary only to communicate characteristics of the action. These terms move the action into a register of language that removes local contingencies, such as the color of the floor or the tape, the speed of the measuring, the smoothness or jerkiness of the measuring action, the textures of the floor and the tape, etc. The linguistic register of space and time deliberately abstracts everything from the situation that cannot be expressed in numbers and/or quantitative language. At this point, the inquiry reengages the worlds of the mathematician, the physicist and the theologian. -->
17.
In these worlds and the registers of language and number appropriate to them, much thought has gone into the question of the nature of space and time.
In a letter written by Einstein on the occasion of the death of a friend to the friend’s family, he states: “Now he has again preceded me a little in parting from this strange world. This has no importance. For people like us who believe in physics, the separation between past, present and future has only the importance of an admittedly tenacious illusion”. (Quoted from Moon, Tim, “The Conservation of Simultaneity: a Critique of Einstein’s 1905 Reasoning about Time” p9). The contradictions in this brief passage are noteworthy. First, the phrase “has again preceded me” uses a past tense verbal construction to refer to an event that has already happened. If “the separation of past, present and future” is an illusion, then does Einstein think that, in reality, not in illusion, his friend is still alive, or is dying as Einstein writes, or is not going to die at all because death is an event that involves change that can be measured both temporally and spatially? In the phrase “people like us who believe in physics” Einstein uses a present tense verb form which includes words that he has learned during his life. To use those words, he must remember them.
That is correct, humans have brains
Memory is expressed in language through past verb forms; attention is expressed through present verb forms; and, anticipation is expressed through future verb forms. So, does Einstein believe that memory, attention and anticipation are also illusions?
It is tricky to compare these three words by one concept: illusions.
Anyway this requires a clear defition of what illusions are.
Such a belief would certainly put someone considered by many as one of the greatest geniuses of the 20thc thoroughly out of touch with what every predatory organism, such as a human being, must do to survive and reproduce—remember the difference between predator and prey, attend to the signs of the presence and absence of predator and prey, and anticipate the appearance or non-appearance of predator and prey. His belief that “the separation between past, present and future has only the importance of an admittedly tenacious illusion” would also seem to go hard on his own physical theories; for example, in his attempted refutation of the conservation of simultaneity, the movements of the rays of light between observers and reflectors are described with tensed verb forms.
The concept of simultaneity requires a certain worldview.
Einstein cannot carry out his arguments using only present tense verbs because doing so would, at least linguistically, make all the events in his thought experiments simultaneous. His language would refute the very thing he is trying to prove. -->
18.
This biographical lens on Einstein’s thought reasonably leads to the issue of absolute and relative time.
The adjective “absolute” seems to have been used to position time as a flow of something through the universe in complete independence of any component of the universe, including space.
The same adjective used with “space” seems to have been used to position space likewise as completely independent in its existence and in all of its characteristics from any existing thing. The utility of these designations of time and space are well-known in the history of modern mechanics and kinematics from Galileo to the present. In fact, when asked which physics was used to land the first human on the moon, Newtonian or Einsteinian, the scientific director of the NASA moonshot responded “Newtonian”.
If you want to predict the future, specific the position of the the planets, you must perform all the observation in a mutual agreed reference system and using a time system based on clocks which are at rest or fixed to this reference system showing universal time. This time has nothing to do with a flow. When you use this definition the concepts absolute and relative disappear.
19.
In the history of experiments to show whether or not Einstein’s theories of special and general relativity are valid, one of the tested predictions of the theory, that time moves more slowly the closer it is measured to a source of gravitation, such as clocks at the surface of the earth and in orbit around the earth in near outer space, have been affirmative. However, these experiments seem to me to have nothing obvious to do with time.
That is correct. Most probably what that these experiments show is that physical clocks tick slower, but that does not mean that time flows slower.
What they prove seems unexceptional: the function of a physical device, whether an ordinary clock or watch, or an atomic clock with extraordinary precision of measurement, is affected by gravity.
Exactly
The closer the device is to the source of gravity the greater the influence of gravity on the moving parts of the device and so the slower the moving parts can move. However, no measuring device is time. The movements of the parts of the device, whether hands of a clock or atoms in motion, are physical things under the influence of a relationship to another physical thing, earth. It is clear, from multiple images of astronauts in space stations, that human bodies encounter much less resistance to motion in outer space than on the surface of the earth. Why, then, would clocks, regardless of the nature of their components, not show the same effect? But where, in the experimental clock configuration, has anyone observed time or, for that matter, space?
20.
There is also a much easier way to show the conservation of simultaneity.
There is also a much easier way to demonstrate the universality of simultaneity
Sometimes when I walk to the top of my driveway I feel a steady north wind blowing. As I am standing there in the wind, the earth is rotating on its axis and the earth is revolving around the sun. What does it mean to state that they are all happening at once? It means that they are simultaneous.
It means that all these events are simultaneously.
Closer to living home, in order for a human being to survive, its heart, lungs and brain all have to be functioning at the same time. Homeostasis is nature’s conservation of simultaneity.
At any moment all these processes are all happening simultaneously
21.
The issue of absolute and relative time thus becomes relevant to an inquiry into infinity when time is treated as something that exists.
The issue of time becomes irrelevant to an inquiry of infinity, because tiem is not something that exists.
The concept of infinity is relevant because we exist, that there exist a universe of dust, gas and stellar objects.
It seems clear from his writings that Newton regarded time as something that existed in that it flowed through the universe.
This requires more detail where Newton wrote this.
The concept of time is mainly a human experience.
In my reading, I have never gotten the impression that Einstein considered time to be an existing thing. The compounding of spacetime in his relativity theories seems to have resulted from his deliberations on the possibilities of measuring high speed objects such as photons.
i.e. to measure the speed of light, which he declared as constant.
Spacetime in his thought seems to be the core structure of measurement rather than a thing that exists independently of other things.
Spacetime is typical a mathematical concept and not a physical concept.
I am happy to be corrected on this issue but I do not find anything in Einstein’s work that bears directly on the issue of infinity. An exception to such a broad generalization could be found in the notion that gravity transforms spacetime and therefore poses a significant obstacle to a conceptualization of the time of spacetime as a linear, independent flow of something through the universe. With so many powerful centers of gravitation in the universe, spacetime appears to be a combination of large, smooth areas that are frequently punctuated by transformations around stars, nebulae, black holes, galaxies and clusters of galaxies. If the open question of whether the universe is expanding, steady or contracting is brought into focus, then Newton’s ideas of absolute space and time as physical realities, rather than as conceptual computational contexts, seem untenable. In a universe of unknown size, shape and fluctuation, in which spacetime transforms relative to sources of gravitation, no independently existing flows of any kind seem reasonable hypotheses.
22.
Another bit of Einstein memorabilia, however, sheds a different kind of light on the issue of infinity in this man’s complex mind. it is certainly of interest that the man who first brought the big bang into the technical terms of astrophysics, George Lemaitre, was a French astrophysicist who was also a Catholic priest. “In January 1933, both Lemaitre and Einstein traveled to California for a series of seminars. After the Belgian detailed his theory, Einstein stood up, applauded, and said, ‘This is the most beautiful and satisfactory explanation of creation to which I have ever listened.’ The very word 'religion' is a study in locating the first cause, namely the Creator. At this ubiquitous moment of time, the dogma of science and religion intersect.” ( http://www.searchet.com/lemaitre.html ). It seems reasonable to suppose that the creation to which Einstein refers is in Genesis. If so, then the end of that creation is in Revelations. The universe is not infinite. Rather, infinity becomes the province of theology as both eternity and immortality, neither of which, according to current Roman Catholic and Judaic dogma, as far as I understand them, the human mind is capable of understanding much less of subjecting to scientific experiments.
23.
So, what has become of infinity? Perhaps it is just another imaginative human construction that goes nowhere. Or, perhaps a new door has recently been opened to this issue with the images from the James Webb Space telescope. This year, Ruud Loeffen, a Netherlands academic, posted a short paper to the academia.edu website. The title of the paper is “DOES JWST INDICATE A STEADY STATE OF CREATION”. Loeffen calls attention to an apparently unexpected feature of the recently released images taken of the universe through the newly launched and operationalized James Webb Space telescope. This telescope was designed, as I understand its original scientific intent, to magnify time-depths of energy from the Big Bang to show physically describable stages of evolution of the universe from the singularity that is at the beginning of the universe in the Big Bang theory. However, much to his surprise, Loeffen states “We see about the same pictures in any time period, be it 1, 2, 3, ….13 billion years ago. To me, it seems that every period is about the same. Even more important: Every period contains young, middle-aged, and old star systems. It means that the universe could be a kind of ‘steady state’ universe. A continuous process of creation”. (p1) A steady state universe is of course an old option in theorizing the persistent and comprehensive behavior of the universe. However, these images are not mathematical theories or indirect empirical conjectures. They are photographs of the existing universe. Loeffen continues: “ A continuous process of creation? Yes. Every period shows a range of different ages of the celestial bodies. They absorb gasses, dust, grains, and meteorites. They range from just baby born, to adult, grownup, and elderly, and even violently dying novae”. (Ibid p2).
Interesting
He then elaborates with an interesting comparison: “The important thing to realize is that this process of growing is seen in every time period. Every period shows the whole range from infancy, youth, the middle years and old age. It’s like the stages of life of a human being. Every time period in the evolution of humanity shows people of different ages, from newborn babies to dying elderly. All over the world. It does not matter how far we are looking back in time. The images are about the same each billion years of time, putting a big question mark on the images of the Big Bang…”. (Ibid pp2-3)
Yes, If this observation is correct it raises hugh issues.
24.
Does the now newly empirically supported hypothesis of the universe as a continuous creation of matter/energy in all states of growth have any bearing on the issue of infinity? Well, this depends on the reference of the word “continuous”. Is something that is continuous necessarily infinite? Both Hindu and Buddhist cosmologies would respond in the affirmative and elaborate by asserting that there is no beginning and no end to the process of creation and destruction of existing things that constitute our universe. However, west of the Caucasus Mountains, the holy books insist that there are not only beginnings and ends to the universe but that there is also another realm of eternity and immortality that either comes into being once the current universe destructs or exists in some sense parallel and coexistent with the current observable universe. There does not seem to me to be any reliable empirical approach, acceptable to interested parties on both sides of the Caucasus, to resolve this difference of views

Index

absolute time 17., 20.,
inertial reference frame par 4, par 5, par 6,
relativity par 4

Reflection 1 - WorldView

My understanding is, if you want to do proper science you should start with a certain WorldView about the Universe. The purpose is to start with a set of definitions which we all agree about, however they can be adapted.

Starting point is that there exists a universe in time, which exists of objects (stars) which each, at any moment in time have a certain position.
Everything in the universe outside the objects is called space. Space is not empty but consists of gas and dust.
Each of these positions at each moment is called an event. This can also be described that the existance of any object in time, can be considered as a sequence of events. This can also be seen that the positions of all the objects, at a certain moment, can be considered as the state of the universe. All the events, at a certain moment, throughout the whole of the universe are happening simultaneous.

Specific related to this document it is important that events at this moment are happening now. Compared to these events, other events have happened in the past and different events will happen in the future. It is important that the occurence of these events (In general) have nothing to do with any human activity.

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Created: 14 February 2023

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