6 hours ago, swansont said:

Chip-scale atomic clocks are among the least precise atomic clocks. Their utility is their size, not their stability.

Not think it was rotating? The stars wouldn’t appear to move? Foucalt’s pendulum wouldn’t work? Surely you don’t think so.

A perfectly spherical earth would have more relativistic effects than the oblate spheroid we live on. The deformation means the kinematic time dilation from rotation, which varies with latitude, cancels with the gravitational time dilation on the geoid.

You seem to be under the impression that relativity only affects atomic clocks, which is not the case. Relativity affects time. Atomic clocks have sufficient precision to measure the effects, but if the effects were sufficiently pronounced, other clocks could measure it.

A change in time implies a change in length. That’s relativity. This is not dependent on the definition of the meter (i.e. it was true prior to 1983)

This is very much not what relativity says

"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

7 hours ago, swansont said:

Chip-scale atomic clocks are among the least precise atomic clocks. Their utility is their size, not their stability.

Not think it was rotating? The stars wouldn’t appear to move? Foucalt’s pendulum wouldn’t work? Surely you don’t think so.

A perfectly spherical earth would have more relativistic effects than the oblate spheroid we live on. The deformation means the kinematic time dilation from rotation, which varies with latitude, cancels with the gravitational time dilation on the geoid.

You seem to be under the impression that relativity only affects atomic clocks, which is not the case. Relativity affects time. Atomic clocks have sufficient precision to measure the effects, but if the effects were sufficiently pronounced, other clocks could measure it.

A change in time implies a change in length. That’s relativity. This is not dependent on the definition of the meter (i.e. it was true prior to 1983)

This is very much not what relativity says

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.

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

Can you think of an experiment that would confirm that ET is not subject to the effects of relativity?

1 hour ago, swansont said:

Can you think of an experiment that would confirm that ET is not subject to the effects of relativity?

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.

58 minutes ago, Rincewind said:

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.

What is the expected relativistic effect, and is a measurement of rotation capable of this level of precision?

Geosat sees ~50 microseconds a day, which is roughly 8.6 x 10^4 seconds, so you need to measure rotation to a part in 10^9. So, ~10^-8 radians

If you can’t do this, then you can’t offer it as a test.

We can, however, measure time dilation in physically rotating systems (a centrifuge) using Mössbauer spectroscopy.

1 hour ago, swansont said:

What is the expected relativistic effect, and is a measurement of rotation capable of this level of precision?

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.

31 minutes ago, Rincewind said:

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.

You’re missing the point. ET doesn’t compensate for relativity because you can’t measure the rotation to sufficient precision. If you could, though, you’d notice relativistic effects, because relativity affects time.

You need to do more than assert otherwise.

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.

2 minutes ago, Rincewind said:

he 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.

Not that it is not a clock thing, it is the local duration of time at the location of the clock.

3 hours ago, Rincewind said:

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.

Even I know that's BS, the tick rate remains the same, it's space that changes to accommodate the fact...

59 minutes ago, dimreepr said:

Even I know that's BS, the tick rate remains the same, it's space that changes to accommodate the fact...

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?

14 hours ago, Rincewind said:

Atomic clocks do tick at different rates depending on gravitational potential and velocity

All atomic clocks tick at exactly “one second per second”, and all ideal rulers measure exactly “one meter per meter”, in their own local frames. What changes is only the relationship between local frames across spacetime. This is what time dilation and length contraction are - they are relationships between frames, not something that physically “happens” to the clocks and rulers themselves in their own frames. The consequences of such relationships between frames are just as real and physical, but it’s nonetheless crucially important to understand the difference.

Just now, Markus Hanke said:

All atomic clocks tick at exactly “one second per second”, and all ideal rulers measure exactly “one meter per meter”, in their own local frames. What changes is only the relationship between local frames across spacetime. This is what time dilation and length contraction are - they are relationships between frames, not something that physically “happens” to the clocks and rulers themselves in their own frames. The consequences of such relationships between frames are just as real and physical, but it’s nonetheless crucially important to understand the difference.

As usual a succinct summary. +1
But we should not forget the implications of the phrase "in their own local frame" which has mathematical and physical implications.
The physical ones being that we are basing the origin of this frame on an ideal 'point particle'.

I don't know if @Rincewind is trying to discuss the complications that arise when his system is large enough for relativistic effect between parts of that system.

Edited May 9May 9 by studiot

5 hours ago, Markus Hanke said:

All atomic clocks tick at exactly “one second per second”, and all ideal rulers measure exactly “one meter per meter”, in their own local frames. What changes is only the relationship between local frames across spacetime. This is what time dilation and length contraction are - they are relationships between frames, not something that physically “happens” to the clocks and rulers themselves in their own frames. The consequences of such relationships between frames are just as real and physical, but it’s nonetheless crucially important to understand the difference.

 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.

Since Stokes’ Theorem relates an integral over a volume to an integral over its boundary, in standard relativity, it applies locally in any frame without issue. However, in the FTS model, the interpretation subtly shifts over cosmic Ephemeris Time (ET) due to fractal scaling effects.

To illustrate this:

- At any given "now" moment, Stokes’ Theorem remains valid as a mathematical principle.

- However, since unit scales evolve over cosmic ET, the interpretation of quantities like divergence and curl across space-time changes.

- This means that what appears locally invariant might show a global evolution, similar to how constants remain invariant in SI measures but evolve over cosmic time in ET.

A helpful analogy could be geometric dilation:

- Imagine a shrinking surface embedded in expanding space.

- The local application of Stokes' Theorem remains unchanged, but globally, the nature of the integral shifts as the boundary itself is rescaled dynamically.

This gives the FTS model extraordinary explanatory power, it maintains classical mathematical principles while redefining their global significance under fractal scaling.

Standard Form of Stokes' Theorem

The generalised Stokes' Theorem states:

[ \int_V d\omega = \oint_{\partial V} \omega ]

where:

- ( V ) is a volume in space-time,

- ( \omega ) is a differential form,

- ( d\omega ) is its exterior derivative,

- ( \partial V ) is the boundary of the volume.

This theorem holds in every local frame, meaning that at any "now" moment (in SI units), it applies without modification. However, in FTS, because the unit scales evolve over cosmic time (ET), the interpretation of integrals must transform accordingly.

Fractal Scaling Applied to Stokes' Theorem

In the FTS model, spacetime evolves under self-similar scaling, meaning that the fundamental unit scales ( L, T ) change over cosmic ET. This implies:

[ L' = L f(t), \quad T' = T g(t) ]

where ( f(t) ) and ( g(t) ) are scale transformation functions that account for the shrinking of matter and the evolving nature of cosmic time.

Since differential forms are scale-sensitive, applying FTS leads to a modified integral equation:

[ \int_{V'} d\omega' = \oint_{\partial V'} \omega' ]

where:

- ( V' ) is the scaled version of ( V ),

- ( \omega' = \omega f(t) ) accounts for the changing length scales,

- ( d\omega' = d\omega f'(t) ), incorporating time evolution.

Key Implication: Evolution Without Violation

This formulation shows that Stokes' Theorem remains valid, but the measured integral changes over ET as the scale factor evolves. The fractal scaling implies that integrals transform proportionally to the cosmic unit evolution, rather than remaining static only within local frames.

A direct result of this:

- The flux through a boundary in fractal space-time will appear different over cosmic time scales.

- However, locally (in SI units), physical laws still hold exactly, explaining why classical mechanics remains valid.

This aligns with my claim that constants of nature remain invariant locally but evolve globally over ET—the same holds for the integral interpretation of Stokes' Theorem in FTS.

Just now, Rincewind said:

All the constants of nature rely on atomic time measures in their definition, including C,

It's quite a while now since number or count has been acknowledged as a fundamental physical variable with the same status as mass, length or time etc.

I don't know why folks keep ignoring this.

1 hour ago, Rincewind said:

In the FTS model, spacetime evolves under self-similar scaling, meaning that the fundamental unit scales ( L, T ) change over cosmic ET.

How do each of the constants in physics change (i.e. by what factor are they bigger or smaller if c doubled)? Planck’s constant, vacuum permittivity and permeability, fundamental charge, etc.

Just now, Rincewind said:

Since Stokes’ Theorem relates an integral over a volume to an integral over its boundary, in standard relativity, it applies locally in any frame without issue. However, in the FTS model, the interpretation subtly shifts over cosmic Ephemeris Time (ET) due to fractal scaling effects.

To illustrate this:

- At any given "now" moment, Stokes’ Theorem remains valid as a mathematical principle.

- However, since unit scales evolve over cosmic ET, the interpretation of quantities like divergence and curl across space-time changes.

- This means that what appears locally invariant might show a global evolution, similar to how constants remain invariant in SI measures but evolve over cosmic time in ET.

A helpful analogy could be geometric dilation:

- Imagine a shrinking surface embedded in expanding space.

- The local application of Stokes' Theorem remains unchanged, but globally, the nature of the integral shifts as the boundary itself is rescaled dynamically.

This gives the FTS model extraordinary explanatory power, it maintains classical mathematical principles while redefining their global significance under fractal scaling.

Standard Form of Stokes' Theorem

The generalised Stokes' Theorem states:

[ \int_V d\omega = \oint_{\partial V} \omega ]

where:

- ( V ) is a volume in space-time,

- ( \omega ) is a differential form,

- ( d\omega ) is its exterior derivative,

- ( \partial V ) is the boundary of the volume.

This theorem holds in every local frame, meaning that at any "now" moment (in SI units), it applies without modification. However, in FTS, because the unit scales evolve over cosmic time (ET), the interpretation of integrals must transform accordingly.

Fractal Scaling Applied to Stokes' Theorem

In the FTS model, spacetime evolves under self-similar scaling, meaning that the fundamental unit scales ( L, T ) change over cosmic ET. This implies:

[ L' = L f(t), \quad T' = T g(t) ]

where ( f(t) ) and ( g(t) ) are scale transformation functions that account for the shrinking of matter and the evolving nature of cosmic time.

Since differential forms are scale-sensitive, applying FTS leads to a modified integral equation:

[ \int_{V'} d\omega' = \oint_{\partial V'} \omega' ]

where:

- ( V' ) is the scaled version of ( V ),

- ( \omega' = \omega f(t) ) accounts for the changing length scales,

- ( d\omega' = d\omega f'(t) ), incorporating time evolution.

Key Implication: Evolution Without Violation

This formulation shows that Stokes' Theorem remains valid, but the measured integral changes over ET as the scale factor evolves. The fractal scaling implies that integrals transform proportionally to the cosmic unit evolution, rather than remaining static only within local frames.

A direct result of this:

- The flux through a boundary in fractal space-time will appear different over cosmic time scales.

- However, locally (in SI units), physical laws still hold exactly, explaining why classical mechanics remains valid.

This aligns with my claim that constants of nature remain invariant locally but evolve globally over ET—the same holds for the integral interpretation of Stokes' Theorem in FTS.

This also require the following condition.

That the space in which the spacetime manifold is embedded (or may be considered to be embedded since you are requiring tangents and invoking the exterior calculus thereof)

is either linear or affine. Otherwise calculus doesn't hold.

Finally, how do Fractals have tangents ?

Edited May 9May 9 by studiot

5 hours ago, studiot said:

But we should not forget the implications of the phrase "in their own local frame" which has mathematical and physical implications.
The physical ones being that we are basing the origin of this frame on an ideal 'point particle'.

Indeed, that was my thought, at some point a fractal has to stop in the physical world...

On 5/9/2025 at 11:28 AM, Rincewind said:

the scaling effect suggests that matter is shrinking relative to a universal background

That doesn’t work, since neither the weak nor the strong interaction (ie their respective Lagrangian) are invariant under rescaling, irrespective of how you fudge any constants.

2 hours ago, swansont said:

How do each of the constants in physics change (i.e. by what factor are they bigger or smaller if c doubled)? Planck’s constant, vacuum permittivity and permeability, fundamental charge, etc.

Your question assumes that fundamental constants change numerically if ( c ) were doubled, but in reality, they remain numerically invariant in their defined unit systems.

Here's why:

•            The speed of light ( c ) is a defining constant in SI units—it sets the scale for time and length measurements.

•            If ( c ) doubled, then unit definitions (such as meters and seconds) would have to shift accordingly.

•            Since physical constants like Planck’s constant ( h ), vacuum permittivity ( \varepsilon_0 ), and permeability ( \mu_0 ) are also defined within SI units, their numerical values stay constant in SI.

While these constants remain invariant in local AT, their physical meaning evolves in cosmic ET due to fractal scaling. This offers an explanation similar to VSL models, but without violating physics ( c ) remains the same in atomic time, yet in early cosmic epochs, light could traverse relatively more space.

On 5/9/2025 at 2:10 PM, studiot said:

This also require the following condition.

That the space in which the spacetime manifold is embedded (or may be considered to be embedded since you are requiring tangents and invoking the exterior calculus thereof)

is either linear or affine. Otherwise calculus doesn't hold.

Finally, how do Fractals have tangents ?

The scaling is linear in ET. The curvature is emergent over the AT duration. Although the scaling is relative to the size of the atom, the phenomenon is the property of light. Because scaling is fundamentally a property of light rather than matter, it provides a strong justification for why fractal structures in FTS do not conflict with calculus, it shifts the focus to the behaviour of causality horizons rather than local tangents. The point about an infinite horizon where causality becomes instantaneous at the Big Bang moment offers a reformulation of how geometry itself evolves. The geometry aligns with Penrose’s conformal geometry aspect of his CCC model. Because light propagation was effectively instantaneous, temperature distributions and blackbody radiation scales were homogeneous at early epochs in a way that standard cosmology struggles to explain.  Standard models require inflation to explain why distant regions have nearly identical temperatures. It’s a neat trick, but it is an ad hoc adjustable parameter.

In FTS, the BB represents a moment where C is instantaneous, where all regions are causally connected, achieving thermal equilibrium instantaneously.

Causality is preserved locally in (AT) but scales globally in (ET), avoiding violating standard relativistic causality, but modifies how we interpret causal connectivity over cosmic time.

Early universe processes might appear non-local to an observer analysing them in SI-defined atomic time (AT), but they remain fully local in the fractal-expanded ET framework.

22 hours ago, Markus Hanke said:

That doesn’t work, since neither the weak nor the strong interaction (ie their respective Lagrangian) are invariant under rescaling, irrespective of how you fudge any constants.

I’m not 'fudging' any constants. The reinterpretation in my FTS model ensures that physical constants remain numerically invariant in SI-defined atomic time (AT). However, over cosmic Ephemeris Time (ET), their functional effects evolve due to fractal scaling. This is not a modification of fundamental interactions but an expansion of our understanding of how measurements and unit definitions shape observed physical laws, just as relativity reinterpreted Newtonian physics without invalidating it.

While it's true that Standard Model interactions like QCD (strong) and electroweak theory are not traditionally scale-invariant, what matters is how those interactions are measured.

If all SI-defined constants remain invariant in AT while evolving over cosmic ET, then their numerical values stay the same while their functional behaviour evolves relative to space-time scales.

On 5/9/2025 at 2:10 PM, studiot said:

Finally, how do Fractals have tangents ?

Thank you for replying to my other points, if rather obliquely.

But what was the answer to this one ?

3 hours ago, Rincewind said:

Your question assumes that fundamental constants change numerically if ( c ) were doubled, but in reality, they remain numerically invariant in their defined unit systems.

Here's why:

•            The speed of light ( c ) is a defining constant in SI units—it sets the scale for time and length measurements.

•            If ( c ) doubled, then unit definitions (such as meters and seconds) would have to shift accordingly.

Nature doesn’t care how humans define these things. If c doubled there would be physical effects that we might notice. Same for these other constants. Don’t waffle - answer the question.

3 hours ago, Rincewind said:

While these constants remain invariant in local AT, their physical meaning evolves in cosmic ET due to fractal scaling. This offers an explanation similar to VSL models, but without violating physics ( c ) remains the same in atomic time, yet in early cosmic epochs, light could traverse relatively more space.

So if light can “traverse more space” and that doubled, what about these other terms.

Just now, swansont said:

Nature doesn’t care how humans define these things. If c doubled there would be physical effects that we might notice. Same for these other constants. Don’t waffle - answer the question.

Thank you for your support.

Talking of time

Rincewind is logged as posting his last post 6 hours ago on my screen

You are logged as answering 2 hours ago and in you quote boxes it refers to /Rincewind's post as 37 minutes previously.

How are those timechecks compatible?

Edited May 11May 11 by studiot

20 minutes ago, studiot said:

Talking of time

Rincewind is logged as posting his last post 6 hours ago on my screen

You are logged as answering 2 hours ago and in you quote boxes it refers to /Rincewind's post as 37 minutes previously.

How are those timechecks compatible?

I don’t know. They show as all consistent (6 hours) in mine

3 hours ago, swansont said:

Nature doesn’t care how humans define these things. If c doubled there would be physical effects that we might notice. Same for these other constants. Don’t waffle - answer the question.

The speed of light as defined in SI units was never any different in the past, according to the FTS model. Speed is the property of AT. However, there was a moment in the distant past where the speed of light was relatively twice as fast, even though it was still the same measure in SI units, because fractal scaling depends on the duration of an ET second, that was second was twice as long where galaxies have a redshift of Z= 1. When the light left that galaxy, call it galaxy A, they would have seen our galaxy with a redshift of just Z = 0.5.

The speed of light was never different in SI units, but over time, the duration of the ET second evolved. Therefore, at galaxy A, at Z = 1, an ET second was twice as long, meaning light could cover more space per ET second. From that galaxy's perspective, our Milky Way would have appeared at Z = 0.5. Beyond our Milky Way, at Z = 1 galaxy B, it would be within its Hubble sphere, whereas now it is not. In the standard model, light would no longer of had time for the light to have ever reached it. The FTS model resolves such horizon problems as any light that reaches us (or anything else) was within the emitters' Hubble sphere when the light left.