Rincewind

The generalised Stokes theorem relates the integral of a differential form over a volume to the integral of its exterior derivative over the boundary of that volume. Your argument that all atomic clocks tick at exactly "one second per second" in their own frame, and all rulers measure "one meter per meter" locally, aligns with the standard relativistic view. The FTS model agrees that this is the case locally but that the scaling effect suggests that matter is shrinking relative to a universal background, which implies a change in the fundamental unit scales, not just a relative effect. Time dilation and length contraction in my model are not just relational effects but intrinsic changes due to the fractal scaling of matter. All the constants of nature rely on atomic time measures in their definition, including C, which means that they remain constant in their SI measures while they evolve over cosmic time (represented by ET) due to the fractal scaling in the FTS model. What this means is that the speed of light remains invariant in AT while being able to transit more space in the past, as it was relatively faster in ET. This gives the model extraordinary explanatory reasoning similar to VSL models without violating the laws of physics.

I appreciate the engagement, but let's clarify the physics here. Atomic clocks do tick at different rates depending on gravitational potential and velocity—this has been experimentally confirmed in relativity tests, including those involving GPS satellites and high-speed particle accelerators. If time dilation did not affect clock rates, we wouldn't need to adjust satellite clocks before launch to ensure they remain synchronised with Earth-based timekeeping. The fact that we do adjust them proves that tick rates change due to relativistic effects. If you’re arguing that space accommodates this rather than the clocks themselves ticking differently, could you clarify what you mean? Are you referring to a coordinate-based interpretation of time dilation rather than a proper-time effect?

ET doesn't need to compensate for relativity because it doesn't measure duration; it measures time displacement and temporal ordinality. The idea that ET should show relativistic effects assumes that all time measures must be affected by relativity, but that's only true for duration-based time scales like Atomic Time (AT), which are tied to local clock rates. To illustrate: If we define an ET second using a pulsar's steady pulse count, all observers—on Earth, HST, and JWST—will agree on the pulse count over time, meaning ET remains invariant across different reference frames. However, if we measure the pulse duration locally, those measurements will differ due to time dilation effects. Relativity affects duration, but ET is a background-dependent measure that tracks ordinality universally, unaffected by local relativistic distortions. The issue is not the precision of rotation measurement but the nature of what ET represents. A good indication of a theory’s validity is its ability to make predictions before the consequences are observed. If the redshift-to-distance relationship is homogeneous, meaning the apparent expansion of the universe is universally observed, then it must be an intrinsic property of the universe. This apparent expansion is measured in km s⁻¹ Mpc⁻¹, where a parsec (pc) defines astronomical distances based on angular measurement relative to an astronomical unit (AU), making it a background-dependent unit linked to ET. The redshift-to-distance relationship determines the rate of apparent expansion, but the speed at which this expansion is measured depends on the observer’s gravitational potential affecting atomic clocks. Since AT governs duration, H₀ measurements will differ across instruments in varying gravitational environments: - JWST (in deep space) will record a slower H₀ due to its faster AT ticking relative to ET. - HST (in LEO) will record a faster H₀ due to its slower AT ticking relative to ET. These discrepancies arise because simultaneity belongs to ET, while duration is an emergent measure of AT (note that AT is unable to determine simultaneity). When I first investigated this, I asked NASA whether WMAP and HST showed different values for H₀. At the time, overlapping error bars made the evidence inconclusive. However, as error bars have now diverged, this effect could be a significant contributor to the ongoing Hubble Tension. Not that it is not a clock thing, it is the local duration of time at the location of the clock.

That's a good question and one that we have demonstrated with the GPS system. GPS systems provide a real-world example of how timekeeping must account for relativistic effects. Satellites experience both special relativistic time dilation (due to their orbital velocity, making clocks tick slower) and general relativistic time dilation (due to weaker gravity, making clocks tick faster). The net effect causes GPS satellite clocks to tick about 40 microseconds faster per day compared to Earth-based clocks. To ensure synchronisation, engineers pre-adjust the satellite clocks before launch so that once in orbit, they match Earth-based timekeeping. This is a practical demonstration of how duration (AT) is affected by gravitational potential and motion, whereas time displacement and ordinality (ET) remain a universal reference. If ET were subject to relativistic effects, then different observers in varying gravitational potentials would measure different temporal ordinalities for a distant periodic source, like pulsar B1937+21. However, all observations of its pulse count over time would remain consistent, independent of relativistic distortions. This reinforces the idea that ET is a reliable background-dependent time scale, while AT is tied to local relativistic effects.

Thank you for following me here. To test whether Ephemeris Time (ET) is unaffected by relativity, we could use a distant celestial object with a stable periodicity, such as pulsar B1937+21, discovered in 1982, which maintains a remarkably consistent rotation period of approximately 1.56 milliseconds. If we define an ET second using its pulse rate and count pulses over time with observations from the HST, JWST, and Earth-based telescopes, all measurements will agree. However, if we measure the pulse rate at these locations, differences will emerge due to time dilation effects. ET provides an invariant measure of time displacement and temporal ordinality, whereas AT is dependent on the observer’s frame of reference. A clock at JWST will register a slower duration of the pulses compared to Earth, while HST, experiencing greater relativistic effects, will measure the fastest pulse rate. Both ET and AT describe real effects, but they measure different aspects of time. ET tracks the sequential passing of events universally, while AT is subject to gravitational and relativistic influences.

Hi everyone, For those new to this thread, we are discussing a recent preprint paper that I uploaded on ResearchGate and now here. Initially posted in Astronomy and Cosmology, it has since been moved to the Speculations section as per the forum guidelines: "You posted this in Astronomy and Cosmology. We expect mainstream physics to be discussed here. Non-mainstream science goes in the Speculations section, where you must comply with its rules." While this change may shift the context of the discussion, it also provides an opportunity to reach a wider audience interested in alternative perspectives on cosmology. I hope that those who engaged in the original thread have followed along and that others seeking fresh approaches to some unresolved questions within the standard ΛCDM model will find value here. I invite you to explore the paper, as its reasoning and implications become clearer through discussion. Looking forward to insightful exchanges. Fractal Topology of Space Time 23 02 2025.pdf

The cosmology I'm trying to discuss depends on the physical framework of the model under consideration.

"This toy model offers a way to examine relativistic effects from a fresh angle, one that may provide insights into scaling transformations beyond conventional interpretations I see where you're coming from, and I really appreciate your perspective on this. My goal with this thought experiment isn’t to challenge established relativistic principles but rather to explore a conceptual model where we examine time dilation and scaling effects in a controlled framework. I think it brings up some interesting implications about how we interpret time as both an absolute and relative measure. I’d love to hear your thoughts on whether you see any interesting takeaways from this setup For the sake of this thought experiment, we assume an idealised system free from real-world irregularities. Note that it is a thought experiment and a toy model. We should assume the clocks are accurate and align with Einstein's ideal light clock. It is an interesting point that you make about the relativistic effects on an oblate spheroid, a shape that works well in this toy model due to the asymmetry of the equator. For the same reason, a geosynchronous GPS satellite experiences an extra 40 microseconds during its two 12-hour orbits and yet a GEO satellite records no more than about 50 microseconds. A Foucault pendulum would indeed be able to indicate if it was rotating, unless it was on the equator. While GR and SR describe relativistic effects through gravitational potential and Lorentz transformations, respectively, FTS provides a broader perspective by examining time as both an absolute and relative measure. While GR and SR account for these effects through gravitational potential and Lorentz transformations, respectively, FTS extends the concept by considering that the atomic clock is implicit in defining the metre along with the constancy of the speed of light. The metre is defined by the elapsed time it takes a photon to traverse the metre. Speed is length divided by time. If time dilates and the speed of light remains constant, then both time and length have to change together. In GR, the coordinate speed of light changes due to gravitational potential, keeping the measure constant, while in SR, length contraction via Lorentz transformations, where the metre shrinks to account for the reduced elapsed time of the moving frame. In the FTS model, it is due to the coordinate speed of light being faster in the past in a relative way, so that it remains constant due to the universal isomorphic transformation of matter. This respects the fundamental principles of relativity, even if it presents an alternative perspective within the framework of relativity.

I appreciate your points about real-world rotation irregularities, but this thought experiment is designed to remove those variables by considering an idealised, perfectly rotating Earth mass planet. One that is so spherical that if it were not for the chip-scale atomic clocks, we would not think it was rotating. The goal is not to argue for Earth's rotation as a fundamental time standard for duration, but rather to explore how relativistic time dilation affects synchronised orbital timekeeping. In this framework, local variations in time measurement exist, yet event ordinality remains intact from a broader perspective. This thought experiment aligns with Einstein's "ether sermon" as he later described it to Lorentz, where he did not deny Lorentz’s ether: " According to the general theory of relativity, space without ether is unthinkable; for in such space there not only would be no propagation of light, but also no possibility of existence for standards of space and time (measuring-rods and clocks), nor therefore any space-time intervals in the physical sense. But this ether may not be thought of as endowed with the quality characteristic of ponderable media, as consisting of parts which may be tracked through time. The idea of motion may not be applied to it." Albert Einstein 5 May 1920 at the University of Leiden. In this framework, local variations in time measurement exist due to relativistic effects, yet event ordinality remains intact from a broader perspective because the structure of space-time itself provides a consistent reference for event sequencing, an idea well-aligned with Einstein’s view on the ether-like framework necessary for measurement." Thank you for another great question. In a thought experiment involving a Tsiolkovsky-type space elevator, descending from a geostationary satellite (GEO), we observe that atomic time (AT) slows down due to changes in gravitational potential while ET remains invariant. This suggests an inverse relationship where ET seconds speed up relative to AT seconds, slowing down. The same absolute rotation is observed more slowly on the satellite due to atomic clocks ticking faster on the equator, highlighting the conflation of faster clocks with faster time and interpreting relative measures as absolute ideals, as the slower Earth clock shows that the same absolute ET day has passed faster in AT. A change in AT implies a change in the meter’s length, since the SI meter is defined by the speed of light in a vacuum. As Henri Bergson’s critique of SR in his 1922 book “ Durée et Simultanéité” pointed out for an extra-terrestrial travelling Relativistically, the measurement of the speed of light would be the same as his stationary measure but only because their units of time were different “I am measuring with a ruler whose length he sees as changing” The SI metre establishes the scale of the universe. In General Relativity, Einstein considered the coordinate speed of light to be faster in a relative way where the gravitational potential is lower, as on the GEO satellite relative to the Earth. Our light-speed rulers shrink as we descend the elevator, indicating a changing scale. This uniform shrinkage is more pronounced in gravity wells or when travelling at relativistic velocities, when considering special relativity (SR) The rotation is absolute and synchronous for the GEO satellite and the Earth. They share the same absolute time displacement, which reflects the absolute and universal temporal nature of ET. AT is a quantitative measure of duration, the property of time that relates to speed. If the scale change is universal, then the gravitational time dilation reflects the local peculiar change in the speed of that change. We consider that the decrease in AT duration offsets the increase in rotational inertia. The shrinking scale in SI distances can be interpreted as expanding space relative to matter while space remains static. This makes the apparent expansion of space relative to matter in the present. If we privilege ET as a close approximation for the universal concept of absolute Newtonian time, descending the elevator speeds up the apparent space expansion as light-speed rulers have less AT in which to shrink and speed up the rotation of the Earth, as AT clocks slow down. As one ascends the elevator, the speed at which the universal light-speed rulers shrink slows down, indicating a slower apparent expansion of space and Earth rotation. Neither of these changes the total energy of the system. Note that at any now moment in time (ET), all light-speed rulers are the same size throughout our universe, shrinking in ET unison at peculiar AT rates. The expanding universe was predicated on the redshift-to-distance relationship, first observed by Vesto Slipher theoretically described by Alexander Freidman, and later established by Edwin Hubble, By privileging ET as the time concept and AT as the peculiar and emergent duration quantity, we can unify SR’s Lorentz transformations, GR’s relative light speed anisotropy, and the redshift-to-distance relationship, as the emergent effects of the universal changing scale resulting in matter shrinkage relative to space in this model. This shrinkage of matter, like Olivera’s matter evanescence, is a fundamental property of the universe with a similar scaling effect, not only revealing the nature of dark energy but for the nature of all the apparent expansion of the universe. This is from Oliveira’s paper "A Self Similar Model of the Universe Unveils the Nature of Dark Energy": With dark energy, cosmic expansion is neither the consequence of a cosmic event, like a Big Bang (although this may contribute), nor of some exotic substance, but of a fundamental property; and as a fundamental property, dark energy has to be embedded in fundamental physical laws. While introducing a parameter to account for it may be appropriate for the mere purpose of fitting selected observations, it is not totally satisfactory from an epistemological point of view." Relative and Absolute Measures: This thought experiment highlights the interplay between relative measures (AT) and absolute ideals (ET). While the scale of the universe appears to change uniformly in ET, it is subject to relativistic and gravitational effects in AT, speeding up or slowing down with relativistic time dilation as the light-speed rulers shrink monotonically over cosmic time ET. Consistency: The consistent shrinkage of light-speed rulers throughout the universe in ET suggests a coherent framework for understanding cosmic scales and distances, regardless of local gravitational influences. In Oliveira’s self-similar model, the H_0 is fixed, whereas in the FTS model AT can vary in differing gravitational potentials and, as such, cannot be a universal parameter. The apparent expansion of the universe is due to the scalar change in duration and distances. The apparent expansion of the universe is measured in km s⁻¹ Mpc⁻¹. A parsec (pc) is a unit of length that measures the distance to astronomical objects outside our solar system. It is defined as the distance at which one astronomical unit (AU) subtends an angle of one arcsecond, a background-dependent unit related to ET. The apparent expansion is determined by the redshift-to-distance relationship—the speed at which the redshift changes and is measured in relative atomic SI units km s⁻¹. The second is an AT measure of duration. How fast the universe expands, like the Earth’s rotational speed, depends on the gravitational potential acting on the measurement instrument. Therefore, the measurement of the H_0 will be slower for JWST, where AT clocks tick faster relative to ET, and measured faster for HST, where AT clocks tick slower in its LEO. Different instruments at different locations with AT clocks ticking simultaneously (simultaneity being the property of ET) at different relative speeds (an AT measure) will measure different values for the H_0, and a contributory factor in the Hubble Tension. I apologise for the length of the reply, but I did not have the time to write a shorter version. In answer to your question, we can imply a Haurssdouff dimension with the concept of a universal isomorphic change of scale that makes it aligns the strength of gravity with the length of the ruler that we measure the coastline of Britain.

That is a very good question, and thank you for your interest. I think it captures the essence of the model, which involves the intricate interplay of infinite time scales and the dynamic, self-similar nature of the universe. The term "fractal" conveys the idea of repeating patterns and self-similarity, while "topology" emphasises the geometric and structural aspects of space-time. This name was chosen to effectively communicate the novel concepts underlying this model and aligns well with the visual representation it describes. It also highlights the unique approach it takes in exploring the universe's infinite cycles and dynamic scaling. I thought it might resonate well with those familiar with cosmology and mathematics and draw attention to the novel ideas presented.

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!

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.

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.

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.

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. 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.

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.

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.

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.

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?

I often use AI to rephrase my work, as it corrects grammatical mistakes and usually flows better. I have to check it carefully as it can sometimes change the meaning when elucidating new ideas. Can I assume that this does not violate the rules?