Hello, I'm new to this forum and eager to discuss a preprint paper I recently uploaded to ResearchGate. The paper, titled Fractal Topology of Spacetime, explores a scalar cyclic model and is approximately 17 pages long with a word count of around 7,000. Since it has not yet undergone peer review, I would appreciate any insights or constructive feedback.

Would it be appropriate to share the full text here, or would posting a link to the paper be preferable?

Can you give us a summary of the concept? Or the mathematical model you're using? If the summary sounds solid, we may ask for a link at a later time.

Thank you for your quick response. here is the abstract...

This paper proposes a novel cosmological model that challenges conventional interpretations of time, space, and cosmic expansion. By combining two distinct time scales—Atomic Time [17](AT) and Ephemeris Time [16](ET)—we explore their inverse relationship and implications for understanding the universe. Our model suggests that AT is analogous to Einstein's light clock [1], measuring duration and rates of processes, while ET [2] corresponds to Newton's absolute time [3], measuring time displacement and positional ordinality.

We hypothesise that as matter travels through ET, it undergoes a diminishing isomorphic transformation (matter shrinkage) over cosmic time. This dynamic scale change affects a redshift-to-distance relationship and the causal nature of the apparent accelerating expansion of the universe, providing an alternative explanation for the observed phenomena attributed to the expansion of space and dark energy [18]. Our thought experiments demonstrate the nuanced interplay between local and cosmic scales, including the descent from a geostationary satellite and the impact of gravitational potential on AT and ET. This concept aligns with Oliveira's "matter evanescence", which independently explores related ideas [4].

Furthermore, we extend our model to an infinite, positionally background-dependent universe, represented diagrammatically as a horn torus [18] with infinitely many aeons [5] of time connected by a central Big Bang. Each aeon is causally connected but instantaneously separated, with opposing loops for matter and antimatter [18]. This cyclic model aligns with the principles of a conformal cyclic cosmology and offers a coherent framework for understanding the universe's infinite cycles  [5].

Our findings suggest that this scaling effect mitigates gravitational influences and provides a causal explanation for phase transitions into subsequent Big Bangs, resulting in an eternal, self-renewing universe. This model challenges traditional views and opens new avenues for exploring the dynamic nature of space-time and cosmic evolution.

7 hours ago, Rincewind said:

Hello, I'm new to this forum and eager to discuss a preprint paper I recently uploaded to ResearchGate. The paper, titled Fractal Topology of Spacetime, explores a scalar cyclic model and is approximately 17 pages long with a word count of around 7,000. Since it has not yet undergone peer review, I would appreciate any insights or constructive feedback.

Would it be appropriate to share the full text here, or would posting a link to the paper be preferable?

Its pretty solid, nice work.

19 hours ago, Rincewind said:

Thank you for your quick response. here is the abstract...

This paper proposes a novel cosmological model that challenges conventional interpretations of time, space, and cosmic expansion. By combining two distinct time scales—Atomic Time [17](AT) and Ephemeris Time [16](ET)—we explore their inverse relationship and implications for understanding the universe. Our model suggests that AT is analogous to Einstein's light clock [1], measuring duration and rates of processes, while ET [2] corresponds to Newton's absolute time [3], measuring time displacement and positional ordinality.

We hypothesise that as matter travels through ET, it undergoes a diminishing isomorphic transformation (matter shrinkage) over cosmic time. This dynamic scale change affects a redshift-to-distance relationship and the causal nature of the apparent accelerating expansion of the universe, providing an alternative explanation for the observed phenomena attributed to the expansion of space and dark energy [18]. Our thought experiments demonstrate the nuanced interplay between local and cosmic scales, including the descent from a geostationary satellite and the impact of gravitational potential on AT and ET. This concept aligns with Oliveira's "matter evanescence", which independently explores related ideas [4].

Furthermore, we extend our model to an infinite, positionally background-dependent universe, represented diagrammatically as a horn torus [18] with infinitely many aeons [5] of time connected by a central Big Bang. Each aeon is causally connected but instantaneously separated, with opposing loops for matter and antimatter [18]. This cyclic model aligns with the principles of a conformal cyclic cosmology and offers a coherent framework for understanding the universe's infinite cycles  [5].

Our findings suggest that this scaling effect mitigates gravitational influences and provides a causal explanation for phase transitions into subsequent Big Bangs, resulting in an eternal, self-renewing universe. This model challenges traditional views and opens new avenues for exploring the dynamic nature of space-time and cosmic evolution.

I'm no expert, but this looks like an argument for the universe to have an eternal soul.

So you are proposing time 'scales' differently at different separations ?

This vastly complicates matters, and seems to introduce many more problems than it clears up, such as what happens at the 'transition' between the different time scaling, and why are no effects observed. Or is your claim that 'dark' matter/energy ARE the observed transitional anomalies.
Does sound interesting, but I'm not convinced I want to read 17 pages of text/math yet.

As a matter of fact, why not have distances 'scale' differently at differing separations, and remove one layer of complexity ?
Also not sure how variable time, or two time dimensions, would compromise GR ( hopefully that is in the 17 page manuscript ), which works exceedingly well, other than requiring the 'dark' matter/energy fudge factors.

Please elaborate further.

Eternal nature for sure, but then I’m no theologian.

4 hours ago, dimreepr said:

I'm no expert, but this looks like an argument for the universe to have an eternal soul.

Eternal nature for sure, but then I’m no theologian.

4 hours ago, dimreepr said:

I'm no expert, but this looks like an argument for the universe to have an eternal soul.

Eternal nature for sure, but then I’m no theologian.

4 hours ago, dimreepr said:

I'm no expert, but this looks like an argument for the universe to have an eternal soul.

Eternal nature for sure, but I'm no theologian.

1 hour ago, MigL said:

So you are proposing time 'scales' differently at different separations ?

This vastly complicates matters, and seems to introduce many more problems than it clears up, such as what happens at the 'transition' between the different time scaling, and why are no effects observed. Or is your claim that 'dark' matter/energy ARE the observed transitional anomalies.
Does sound interesting, but I'm not convinced I want to read 17 pages of text/math yet.

As a matter of fact, why not have distances 'scale' differently at differing separations, and remove one layer of complexity ?
Also not sure how variable time, or two time dimensions, would compromise GR ( hopefully that is in the 17 page manuscript ), which works exceedingly well, other than requiring the 'dark' matter/energy fudge factors.

Please elaborate further.

The time dimensions are coterminous; a day on Earth is an absolute rotational transformation relative to the Sun. It is an absolute time displacement that can be measured accurately in the same way that we used to define the second in Ephemeris time.. It differs from what a clock reads in that it is universal; it is the same day upstairs as it is downstairs or orbiting in a GEO satellite. It is the aspect of time that depicts the temporal and positional ordinality of events. However, it is not a duration, for that we need a clock. The same day is longer on the GEO satellite than it is directly below on the Earth; a clock ticks faster on the satellite, making the duration of that day longer.

42 minutes ago, Rincewind said:

The time dimensions are coterminous; a day on Earth is an absolute rotational transformation relative to the Sun. It is an absolute time displacement that can be measured accurately in the same way that we used to define the second in Ephemeris time.. It differs from what a clock reads in that it is universal; it is the same day upstairs as it is downstairs or orbiting in a GEO satellite. It is the aspect of time that depicts the temporal and positional ordinality of events. However, it is not a duration, for that we need a clock. The same day is longer on the GEO satellite than it is directly below on the Earth; a clock ticks faster on the satellite, making the duration of that day longer.

The length of a day of an earth rotation isn’t constant, and ET is defined in terms of the revolution about the sun. I have no idea why you think it’s not a clock. I can measure durations measured in days with earth rotation.

Atomic time is used because it can be measured more accurately and precisely than any method based on earth rotation/revolution.

Just now, Rincewind said:

The time dimensions are coterminous; a day on Earth is an absolute rotational transformation relative to the Sun.

Really ?

And there was me thinking that the Earth moves approximately 1 degree relative to the Sun in the time it takes to revolve once on its own axis.

That is why we have leap years.

14 hours ago, swansont said:

The length of a day of an earth rotation isn’t constant, and ET is defined in terms of the revolution about the sun. I have no idea why you think it’s not a clock. I can measure durations measured in days with earth rotation.

Atomic time is used because it can be measured more accurately and precisely than any method based on earth rotation/revolution.

You are absolutely rite, the length of the day is not constant, and that ET was based upon the tropical year to mitigate the variability of the periodicity of the Earth's rotation. But I think you have missed the point of my argument, it does not matter that last Monday was not the same as next Friday. The point is that, according to two exactly similar clocks, one on the satellite and one directly below on Earth, last Monday was longer for the satellite clock than it was for the Earth clock. The absolute day was the same, but the duration of that day was divergent.

You make a good point about the accuracy of the atomic clock, and I would add that it is far more convenient, but it is not measuring the same aspect of time.

14 hours ago, studiot said:

Really ?

And there was me thinking that the Earth moves approximately 1 degree relative to the Sun in the time it takes to revolve once on its own axis.

That is why we have leap years.

Using a sidereal day instead of a solar day would not change my argument. It is generally more practical for us earthlings to use the solar day, or else midnight would be around high noon by the summer. We use an extra day in a leap year to keep our calendars from drifting out of sync with our seasons because it takes about 365.242 days for the Earth to orbit the Sun.

A sidereal day is relative to the fixed stars and is often favoured by astronomers.

2 hours ago, Rincewind said:

You are absolutely rite, the length of the day is not constant, and that ET was based upon the tropical year to mitigate the variability of the periodicity of the Earth's rotation. But I think you have missed the point of my argument, it does not matter that last Monday was not the same as next Friday. The point is that, according to two exactly similar clocks, one on the satellite and one directly below on Earth, last Monday was longer for the satellite clock than it was for the Earth clock. The absolute day was the same, but the duration of that day was divergent.

That’s why we adopt a common standard. It’s not that there is an absolute time, “absolute” having a particular meaning in the context of relativity, since we are free to choose another standard, and it’s dictated by convenience rather than physics. There’s nothing special about the rotation of the earth, or its revolution about the sun.

2 hours ago, Rincewind said:

You make a good point about the accuracy of the atomic clock, and I would add that it is far more convenient, but it is not measuring the same aspect of time.

Clocks measure time. Saying otherwise requires changing what is meant by one or the other.

20 hours ago, Rincewind said:

Eternal nature for sure, but then I’m no theologian.

Eternal nature for sure, but then I’m no theologian.

Eternal nature for sure, but then I’m no theologian.

Does that make you a physicist?

31 minutes ago, swansont said:

That’s why we adopt a common standard. It’s not that there is an absolute time, “absolute” having a particular meaning in the context of relativity, since we are free to choose another standard, and it’s dictated by convenience rather than physics.

Clocks measure time. Saying otherwise requires changing what is meant by one or the other.

Atomic time (AT) is chosen for consistency and precision, it is how we age and understand physical laws. It does not mean that other time standards, such as ET lack physical significance. My argument directly challenges the assumption that time measurement only follows convenience. Physics still dictates how different clocks experience time, and that has real effects, such as the gravitational time dilation being clear in my example.

The slower clock on Earth makes the day there faster, thereby drawing attention to the conflation that slower clocks mean slower time. By exploring the distinct aspects of AT and ET, we can see that they are not mutually exclusive. Instead, they offer complementary perspectives on the nature of time, enriching our understanding of the universe. Unlike AT, where relativistic effects can influence the speed of changes, ET provides a consistent and reliable measure of time displacement. Therefore, while AT offers unparalleled practicality and duration precision, ET's stability and resistance to relativistic influences remain an essential and complementary time scale measuring temporal and positional ordinality, a separate and distinct aspect of time from the measured duration of such changes in AT. Note that when the base unit “second” was officially changed from ET to AT in 1967, they changed the fundamental meaning of time. We propose that both properties are needed to understand the whole ontology of time.

ET and AT are inversely proportionate in their rate of change, and this has profound effects on our understanding. In a thought experiment involving a Tsiolkovsky-type space elevator descending from a geostationary satellite (GEO), we observe that AT slows down due to changes in gravitational potential while ET remains invariant. Or rather, ET seconds remain invariant, making its seconds appear to speed relative to AT seconds. This relationship underscores the necessity of preserving both AT and ET as distinct but complementary frameworks for studying temporal order and duration precision, essential tools for both observational astronomy and relativistic physics.

2 hours ago, Rincewind said:

Atomic time (AT) is chosen for consistency and precision, it is how we age and understand physical laws. It does not mean that other time standards, such as ET lack physical significance. My argument directly challenges the assumption that time measurement only follows convenience. Physics still dictates how different clocks experience time, and that has real effects, such as the gravitational time dilation being clear in my example.

All clocks experience time dilation. But it’s not measurable unless you have sufficient precision. (All clocks are affected by mundane environmental effects, too that are not effects on time) Earth rotation is one form of clock.

2 hours ago, Rincewind said:

The slower clock on Earth makes the day there faster, thereby drawing attention to the conflation that slower clocks mean slower time.

As I pointed out above, not all things that affect clock rate are effects on time. Things that affect time affect all clocks.

A slower clock on earth does not “make the day faster” - nothing would, unless time itself is affected. If a clock runs slow, it needs to be recalibrated against a standard.

2 hours ago, Rincewind said:

By exploring the distinct aspects of AT and ET, we can see that they are not mutually exclusive. Instead, they offer complementary perspectives on the nature of time, enriching our understanding of the universe.

I’m not sure who you think claims they are mutually exclusive, but I don’t see how they say anything about the nature of time. They do definitely tell us about the nature of timekeeping.

2 hours ago, Rincewind said:

Unlike AT, where relativistic effects can influence the speed of changes, ET provides a consistent and reliable measure of time displacement.

Earth rotation is not consistent and is of limited precision. But it is most definitely be affected by relativity, but owing to the limited precision, it’s not noticeable at a level it could measure

2 hours ago, Rincewind said:

Therefore, while AT offers unparalleled practicality and duration precision, ET's stability and resistance to relativistic influences remain an essential and complementary time scale measuring temporal and positional ordinality, a separate and distinct aspect of time from the measured duration of such changes in AT. Note that when the base unit “second” was officially changed from ET to AT in 1967, they changed the fundamental meaning of time. We propose that both properties are needed to understand the whole ontology of time.

This is based on a false notion. You might calculate the level of relativist effects on earth - how the speed changes over the course of a year and the variation in gravitational potential, to see what the relativistic effects are. Then compare it to the precision of earth time.

Until you do that, your claim has no factual basis.

2 hours ago, Rincewind said:

ET and AT are inversely proportionate in their rate of change, and this has profound effects on our understanding. In a thought experiment involving a Tsiolkovsky-type space elevator descending from a geostationary satellite (GEO), we observe that AT slows down due to changes in gravitational potential while ET remains invariant. Or rather, ET seconds remain invariant, making its seconds appear to speed relative to AT seconds. This relationship underscores the necessity of preserving both AT and ET as distinct but complementary frameworks for studying temporal order and duration precision, essential tools for both observational astronomy and relativistic physics.

ET is not invariant, period. The epoch for defining the second was based on the tropical year 1900, but the earth rotation rate varies on the order of ms per day, with an overall decrease over time, though we’ve seen periods where it’s sped up. We went away from using earth rotation because the earth is a comparatively crappy clock.

On 5/3/2025 at 5:06 PM, Rincewind said:

Eternal nature for sure, but then I’m no theologian.

Only 'nothing' can live forever, but why would you need a god for that?

Gaia is the origin god, so in this context, yes you are.

Edited May 5May 5 by dimreepr

19 hours ago, swansont said:

19 hours ago, swansont said:

All clocks experience time dilation. But it’s not measurable unless you have sufficient precision. (All clocks are affected by mundane environmental effects, too that are not effects on time) Earth rotation is one form of clock.

If you are using the Earth as a clock, the Earth and a GEO satellite can be seen as the same clock; draw an imaginary line between them to make the clock hand that will simultaneously display the same degree of rotation moment by moment. How fast the hand is turning depends on where on the hand you measure the duration. The Earth and satellite clock is not a clock that measures duration from which we can determine speed because the actual duration between each degree of rotation is not consistent; the faster "ticking" atomic clock at the satellite end of the hand will indicate that it is rotating slower than the slower ticking clock at the Earth surface end of the hand (less "ticks" per degree, therefore faster). This type of Earth clock does not display relativistic time dilation, even though different parts experience it.

8 minutes ago, Rincewind said:

If you are using the Earth as a clock, the Earth and a GEO satellite can be seen as the same clock; draw an imaginary line between them to make the clock hand that will simultaneously display the same degree of rotation moment by moment. How fast the hand is turning depends on where on the hand you measure the duration. The Earth and satellite clock is not a clock that measures duration from which we can determine speed because the actual duration between each degree of rotation is not consistent; the faster "ticking" atomic clock at the satellite end of the hand will indicate that it is rotating slower than the slower ticking clock at the Earth surface end of the hand (less "ticks" per degree, therefore faster). This type of Earth clock does not display relativistic time dilation, even though different parts experience it.

The tick remains the same, it's the clock that changed... 😉

1 hour ago, Rincewind said:

If you are using the Earth as a clock, the Earth and a GEO satellite can be seen as the same clock; draw an imaginary line between them to make the clock hand that will simultaneously display the same degree of rotation moment by moment. How fast the hand is turning depends on where on the hand you measure the duration. The Earth and satellite clock is not a clock that measures duration from which we can determine speed because the actual duration between each degree of rotation is not consistent;

That makes it a poor clock, but it’s still a clock.

1 hour ago, Rincewind said:

the faster "ticking" atomic clock at the satellite end of the hand will indicate that it is rotating slower than the slower ticking clock at the Earth surface end of the hand (less "ticks" per degree, therefore faster). This type of Earth clock does not display relativistic time dilation, even though different parts experience it.

It doesn’t show any measurable time dilation, but that’s only because it’s not previse enough. The effect is still there. Much like how people don’t diffract when going through a door, or look like waves. The QM effect is way too small.

If you did the calculation I described earlier you could show this.

On 5/3/2025 at 9:06 AM, Rincewind said:

Eternal nature for sure, but then I’m no theologian.

Eternal nature for sure, but then I’m no theologian.

Eternal nature for sure, but then I’m no theologian.

Eternal nature for sure, but I'm no theologian.

You spammed the same sentence 4 times, why?

Two things, first off, Earth Time (ET), based on Earth's rotation or orbit, is not stable and is affected by many irregularities (e.g., tidal friction, earthquakes), making it a poor standard .Atomic Time (AT) is more precise and repeatable, which is why it became the standard in 1967.

2 hours ago, swansont said:

That makes it a poor clock, but it’s still a clock.

It doesn’t show any measurable time dilation, but that’s only because it’s not previse enough. The effect is still there. Much like how people don’t diffract when going through a door, or look like waves. The QM effect is way too small.

If you did the calculation I described earlier you could show this.

As this is a thought experiment, we can imagine an Earth-mass planet rotating in a similar way to Earth, orbiting its star in a perfectly circular orbit, thereby making the planet + GEO satellite clock very accurately depict time displacement. While the different parts of the system would experience relativistic time dilation, so that an atomic clock on the planet set at 86,400 seconds per day and an exactly similar clock on the satellite would then measure 86,400 seconds + 50 microseconds a day, demonstrating the asymmetry in the two distinct aspects of time. While the two atomic clocks measure an asymmetric duration for the day, a distant observer perpendicular to the rotational axis of the planet would measure the duration of the two clocks' day with no asymmetry with their atomic clock. Thereby demonstrating that the speed of events is peculiar to the clock of the observer. The ordinality of events is better described by a universal time displacement for which Ephemeris Time is a close approximation.

5 minutes ago, Rincewind said:

As this is a thought experiment, we can imagine an Earth-mass planet rotating in a similar way to Earth, orbiting its star in a perfectly circular orbit, thereby making the planet + GEO satellite clock very accurately depict time displacement. While the different parts of the system would experience relativistic time dilation, so that an atomic clock on the planet set at 86,400 seconds per day and an exactly similar clock on the satellite would then measure 86,400 seconds + 50 microseconds a day, demonstrating the asymmetry in the two distinct aspects of time. While the two atomic clocks measure an asymmetric duration for the day, a distant observer perpendicular to the rotational axis of the planet would measure the duration of the two clocks' day with no asymmetry with their atomic clock. Thereby demonstrating that the speed of events is peculiar to the clock of the observer. The ordinality of events is better described by a universal time displacement for which Ephemeris Time is a close approximation.

The rotation rate would still vary, owing to varying mass distribution on the planet (precipitation, rotation of weather systems, tectonic activity, etc.) and you’d expect it to slow from tidal friction.

And the precision of the measurement of the rotation would still be significantly worse than atomic clocks.

We use the rotational period of the earth because we live here. It’s convenient and what we’re used to, so change isn’t likely. Kinda like how the US resists the metric system. There’s nothing special about it when it comes to physics. It’s not “universal” by any stretch.

2 hours ago, Sohan Lalwani said:

You spammed the same sentence 4 times, why?

Two things, first off, Earth Time (ET), based on Earth's rotation or orbit, is not stable and is affected by many irregularities (e.g., tidal friction, earthquakes), making it a poor standard .Atomic Time (AT) is more precise and repeatable, which is why it became the standard in 1967.

That was the first time I used the quote system, and I got it wrong. I hope you can forgive me for that.

Regarding ET, in my posts, ET stands for Ephemeris Time, not Earth Time. Ephemeris Time became the standard in 1960 and was highly accurate for defining time relative to celestial mechanics. While modern time standards like Atomic Time (AT) offer superior precision for scientific applications, ET is more than sufficient for this thought experiment because it provides a stable framework for event ordinality, unlike Earth Rotation Time, which is subject to irregularities such as tidal friction and earthquakes.

The key idea of this thought experiment isn't about debating which time standard is superior; it's about exploring the relationship between time measurement, relativistic effects, and event order in a synchronised planetary system. I would love to continue engaging with this fascinating subject, and I appreciate the discussion so far!

Just now, Rincewind said:

That was the first time I used the quote system, and I got it wrong. I hope you can forgive me for that.

As a fellow member who has also suffered the difficulties of the input editor you are fully absolved and forgiven. +1

Just an innocent question, before I become acquainted with the finer points of the discussion: How is this thing 'fractal'?