Another thread here highlighted the need for a solid counterargument to Dingle's objection to Relativity Theory. It seems that previous participants were unable to resolve the issue convincingly. Therefore, we would like to present a straightforward and intuitive solution, providing easier access to understanding the problem.
We apply the theory of segmented spacetime to this problem. If you are not familiar with the theory yet, here is an illustrative paper. Please don’t dismiss it simply because it also addresses singularities - that’s only part of the discussion. The paper is straightforward and engaging to read.
Article Segmented Spacetime and the Natural Boundary of Black Holes:...
Essentially, the segmented spacetime theory proposes that gravitation segments space, slowing down objects, while moving objects are segmented themselves. This concept is expanded upon in a subsequent paper:
Preprint Segmented Spacetime - A New Perspective on Light, Gravity an...
Now, consider two clocks in different gravitational fields. In this scenario, space is segmented differently in each field, meaning these are distinct environments with varying segmentations. If we take a clock from environment A and place it near a clock in environment B, the time difference between them remains observable due to these distinct segmentations.
However, in the example with two clocks, where one moves and the other remains stationary, both exist within the same environment, with the same spatial segmentation. Here, any time difference arises from the moving clock itself: as it accelerates, its internal segmentation increases, causing it to run slower. Upon negative acceleration, these segments are removed, allowing the clock to speed up again.
This is why a clock accelerating and negative accelerating within the same environment will not retain a permanent time difference. It contrasts with moving a clock from environment A to environment B, where the segmentation is tied to the environment, not the clock itself.
We invite you to discuss this concept.
Burada görme duyuları için konum ve zaman, saat ve saate ait olanlar için yerdeğiştirme göz önünde bulundurulmalıdır. Gözlemcinin bu olayda rolü unutulmamalıdır. Şartlar hem gözlemci için hemde saat için geçerlidir. Ama gözlemci için geçerli olan her şart saat için geçerli olmayabilir. Başlangıçtaki konum ile son konum göz önünde bulundurulmalıdır. Bu saat ve gözlemci için de geçerli. Zamanla akrep ve yelkovanın boyunda bile değişmeler meydana gelebilir. Bu yüzden konum ve zaman parametrelerinde değişmeler meydana gelir. Segmentasyon elemanları bu yüzden göz önünde bulundurulmalıdır.
Şükrü Aktaş Thank you for your thoughtful comment and for raising these points. It's important to clarify that the normal clock is a conceptual model specifically designed to illustrate the effects of gravitation, not acceleration.
In our earlier work, we described the normal clock as an idealized clock that 'inflates' and slows down in response to increasing gravitational influence. This was intended as an analogy to help conceptualize how space and time are segmented under gravitational conditions.
Our approach began with the concept of spacetime stretching under gravitational influence, as described in general relativity. This served as the foundation for our thought experiment with the normal clock, which illustrated how gravity could cause time to slow down by influencing the structure of spacetime. Building upon this, we asked a critical question: How is this stretching structured? This led us to the idea of segmentation, a framework that goes beyond continuous deformation by proposing that spacetime is inherently segmented under gravitational conditions. This perspective allowed us to explore not only how spacetime behaves, but also the fundamental mechanisms behind these changes.
However, acceleration behaves differently in our model. While gravitational forces induce a restructuring of spacetime segmentation, acceleration affects the internal dynamics of an object, such as its inertia, rather than altering its interaction with the external segmentation of space. This distinction is crucial: The normal clock expands and segments under gravity as part of the conceptual framework, but in reality, objects do not physically expand under acceleration or gravitation - they experience changes in weight and time perception due to external segmentation.
We hope this clarification helps illustrate the separation between gravitational effects and acceleration in our model. Thank you for the opportunity to expand on this!
It doesn't make sense to raise ``objections" to a theory. What only mattrs is mathematical consistency and experimental relevance. Special relativity has both properties. The confusion just expressed the ignorance of group theory. Special relativity describes invariance of the equations of motion under global Lorentz transformations, that form a group, the Lorentz group, SO(3,1), or SO(1,3), depending on convention. And it's a standard exercise now to show that Maxwell's equations are invariant under such transformations. Experiments can be designed to check this and they're now standard lab exercises. Making these transformations local leads to general relativity, something that was understood after Einstein wrote his equations, but is, now, also, standard course material.
I think that more modern, simpler and, above all, richer explanations are never a mistake.
Carmen Wrede ,
"any time difference arises from the moving clock itself: as it accelerates, its internal segmentation increases, causing it to run slower. Upon negative acceleration, these segments are removed, allowing the clock to speed up again."
To me is clear that an oscillator, which is in an accelerational field like that of gravity, due to its deviated oscilation-path "ticks" slower than without such acceleration-related deviations -> time-dilation.
How must I imagine "segmentation" in this scenario?
"Segmentation" appears to me to be something discrete, while the increase in "ticking"-time (time-dilation) is something continuous.
Are there some "zones", where the spacetime gets finer or coarser, depending on the acceleration field?
What happens at such "zones' " transitions?
Should I map the spiral to the phases of an oscillation, of a wave's propagation? Does it describe redshift of the wave, in the end?
Andreas Schwarz That's a lot of questions for a little person like me! 🐥 I suggest we discuss the questions one by one. What do you think?
How about we start with this question:
"How must I imagine "segmentation" in this scenario?"
You don't even have to imagine it. I can show you. Because nature is designed this way: If something exists, then it is visible! Consequently, the segmentation is also visible.
Fortunately, we can see segmentation very well near massive stars. I am attaching a picture showing the so-called Einstein Cross. Here we see that the space near massive objects actually shows a fourfold segmentation.
Bu örnek, saat örneğinde olduğu gibi 3,9 ve 6,12 rakamlarının saat yüzeyinde zamanı göstermesi gibidir. Bunlar uzayda oluşurken belirli elementler ve atomlarla oluşur. Demir elementi örneğinde olduğu gibi, saatin basit yapısını düşünün. (İcat edildiği günden bugüne).Demir çivi merkeze monte edilir ve akrep ve yelkovan üzerine eklenir. Geçmişten bugüne gelişerek devam eder. Burada yerçekimi ve ivme sabittir. Yerçekimi ve ivme, akrep ve yelkovanın hareket etmesiyle Demir elementinin meydana gelmesine neden olur. Eğer akrep ve yelkovan hareket etmezse Demir elementi oluşmaz. Demir elementinin oluşmaması bu şeklin kaybolmasına neden olur. Bu şekillerin yerine basit halkalar oluşur ve bunları merkezde dengede tutan halkalar oluşur. Bu halkalar için yerdeğiştirme, yerçekimi ve ivme önemlidir. Halkaları çubukların üzerinde tutmak için yerçekimine ihtiyaç vardır. Bunun yeryüzünde insanlara yansıma şekli Demir eksikliği ve buna bağlı hastalıklar olarak ortaya çıkar. Hiçbir şey evrende oluşmadıktan sonra yeryüzünde oluşmaz. Mutlaka bir karşılığı vardır. Bunu insanoğlu ve evren ,kuantum ve doğa yayınlarında okuyabilirsiniz.
Şükrü Aktaş Write englisch. I am not your secretary to translate your stuff first.
Carmen Wrede ,
we can see the deflected images of the quasar, which is not completely exact behind a massive object, seen from us.
Were this massive object a perfect sphere and exactly between us and the quasar, we would see a ring instead of these four attenuated copies of the quasar.
To me is not clear, where the connection to segmentation may be...
Andreas Schwarz The four images of the quasar show that space is not uniform but is segmented by mass. Gravity influences light so that it is deflected along these segmented paths. Without segmentation there would be no different curvature of the light paths and therefore no four images.
Justo Pastor Lambare
"Dingle's objection was formulated in the context of SR, so GR and gravitation are not part of it and are out of context."The statement “gravity is not part of the SR” is technically correct, but it ignores that without gravity the SR does not exist in the larger physical context. The GR extends the SR by showing that gravity affects the geometry of spacetime itself. Gravity plays a fundamental role, even if it is formally “excluded” from SR.
Justo Pastor Lambare
Actually he didn't-he deduced the equations of motion by other arguments and there remained the issue of the status of what would later become known as the Bianchi identities, that neither he or Hilbert could understand whether they were independent equations of motion or not. That, in fact, was the question that Hilbert asked Emmy Noether in 1918, which she answered by formulating her theorems.There's no reason living in 1917, now, of course. Now we know, by applying Noether's theorems, that special relativity describes equations that are invariant under global Lorentz transformations and that general relativity describes equations invariant under local Lorentz transformations; and the latter, in fact, describe diffeomorphisms of the spacetime geometry. What isn't appreciated is the fact that, because the group of diffeomorphisms is noncompact, general relativity is a gauge theory with a noncompact gauge group. And that it is this property that, on the one hand, implies the inevitability of the appearance of spacetime singularities and, on the other hand, implies that gravity can't be ``quantized'' by any of the techniques that apply to gauge theories, with compact gauge group. The problem of quantum gravity amounts to understanding how a noncompact gauge group can emerge in the classical limit.
Stam Nicolis The difference between you and me is the fact that while you are trying to stuff singularities and other holes with stories, I am actually filling them with truth.
Carmen Wrede ,
"Without segmentation there would be no different curvature of the light paths and therefore no four images."
Following this statement, "segmentation" is another word for gravitational action on EM-waves, correct?
But
"Gravity influences light so that it is deflected along these segmented paths."
lacks to me the possibility to map "these segmented path"...
How can I figure out paths of EM-waves to be "segmented"?
Andreas Schwarz "lacks to me the possibility to map "these segmented path"..."
This is a very bold statement. Your concern about mapping 'segmented paths' suggests that these paths might lack a clear mathematical basis. However, in our model of segmented spacetime, these paths are rigorously defined and mathematically quantifiable.
Specifically, segmented paths correspond to the geodesics of curved spacetime, described in terms of segmentation by ϕ and the relationship between frequency, wavelength, and radius. As detailed in our paper, the segmentation increases under gravitational influence, proportional to the wavelength expansion and radius growth. This is mathematically described through:
N=4⋅f
Where N is the number of segments traversed by the wave per period. This approach provides a consistent and scalable framework for understanding how gravity structures spacetime.
The concept of segmented paths is not merely abstract but directly tied to measurable phenomena, as demonstrated through the proportional changes in wavelength, radius, and segmentation due to gravity.
Carmen Wrede ,
"the segmentation increases under gravitational influence, proportional to the wavelength expansion and radius growth."
Thus, as I already mentioned earlier somewhere, "segmentation" is another approach to look at the gravitational redshift?
There, I compared that to the EM-wave's radius, its 1/k, which increases or decreases, depending on the gravitational field's influence...
Is this the correct mapping?
Andreas Schwarz No, 'Segmented Spacetime' is not merely another way to look at gravitational redshift. It is an extension of both General Relativity (GR) and Special Relativity (SR), providing a broader framework that integrates segmentation as a structural property of spacetime itself.
While gravitational redshift can be mapped through the relationship between wavelength (1/k) and the gravitational field, Segmented Spacetime introduces a quantifiable segmentation of space, influencing how light and other phenomena behave under varying gravitational conditions. This goes beyond simply describing redshift. It redefines the structural behavior of spacetime at different scales.
Have you fully understood that 'Segmented Spacetime' addresses the Cosmic Censorship Conjecture directly? The model provides insights into how spacetime is naturally segmented, preventing singularities from being true 'points' and instead redefining them within structured frameworks.
Carmen Wrede ,
"It redefines the structural behavior of spacetime at different scales."
Is this a "physical" change of 3D-space, or completely based on GR's purely mathematics, i.e. "deformed" spacetime?
Carmen Wrede ,
"Cosmic Censorship Conjecture"
This was new for me so far. As far as I understand that up to now, the related "Cauchy Horizon" describes, that differential equations cannot be solved unambiguously, if one gets too near to a (mathematical) singularity.
Do your work "switch" to a controlled discreteness below this horizon to match with reality?
Carmen Wrede ,
"The model provides insights into how spacetime is naturally segmented, preventing singularities from being true 'points' and instead redefining them within structured frameworks."
I try to explain, how I recognize "segmentation":
We start with a smallest possible radius, let's say Planck-length (a photon sphere), which can communicate with its environment.
This 'point' in spacetime is an oscillation. In your work with the first 4 segments: one period. It is a 3D-oscillation, with circling waves on its surface, no preferred plane.
While this oscillation radiates/propagates its (doubled) wavelength all around, it suffers from a constant growth-factor, per wave period (per 4 segments).
At the same time, due to energy conservation, all the wavelength-deltas in energy need to return to the oscillator, to keep it running.
Thus, after lots of periods (segments), this propagation of the Planck-oscillator reaches a wavelength, a size, which corresponds with a resonance....
----
Isn't that very similar to my model? The only difference is that you use a logarithmic spiral, which guides you to an exponential expression, while I used a constant factor K per period to increase the wavelength.
Andreas Schwarz The "Cauchy Horizon" is a philosophical concept without clear mathematical description. It is undefinied. The problem is that the region behind the Cauchy horizon is causally isolated from the outside world. This means that the deterministic nature of Einstein's equations breaks there because no information from outside can enter this area to make predictions.
Our approach of not viewing the interior as a singularity, but rather describing it as a reflection of space with clear segmentation, solves this problem. Instead of getting stuck in the undefined, we offer a way to describe the space behind the Cauchy horizon in a mathematically meaningful way.
This is next level and expands on Einstein's work, offering new perspectives on the structure of spacetime.
Carmen Wrede ,
what me makes wondering is that your growth factor is such large.
Do you expect your model to be valid only WITHIN a back hole, or can you continue it beyond the horizon, into the deep space environment, also?
Andreas Schwarz When it's fully developed it will be a ruler for inside and outside of the black hole, for gravity and segmentation. Later on it will be able to directly say which object moves with which speed through space. And with tensors it will allow to fully map space. That's the plan so far...
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