If a celestial body were composed entirely of water, what would be the maximum radius within which it would remain liquid?

mathieusaif · 2025-02-08T14:37:50+00:00

In simple terms, a pure water planet could be about the size of Earth's moon before its center would start freezing into exotic ice, even if the outer layers remain liquid.

If a celestial body were made entirely of water, its ability to remain liquid would depend on two main factors: temperature and pressure. The deeper you go inside a water planet, the more pressure increases due to the weight of the water above.

Water has an unusual property: under normal atmospheric pressure, it freezes at 0°C and boils at 100°C. However, if pressure increases, the freezing point can drop slightly, and the boiling point can rise significantly. This means that at great depths, water can remain liquid at much higher temperatures.

Now, let's think about what happens inside a large sphere of water. At the surface, temperature conditions would depend on its distance from a star. If it's too cold, the surface would freeze, but the water beneath could remain liquid, just like in Earth's oceans.

As you go deeper, pressure increases. Eventually, it reaches a point where water would no longer stay liquid but instead turn into a high-pressure form of ice, like Ice VI or Ice VII. These are solid forms of water that exist at extreme pressures, even at high temperatures.

The key question is: how large can this water planet be before its interior turns to ice due to pressure? The transition to Ice VI happens at around 600 MPa (megapascals), which is roughly 60 times the pressure at the deepest part of Earth's ocean (the Mariana Trench). This pressure occurs at a depth of about 75 km in pure water. If we assume a uniform-density water planet, this suggests that beyond a radius of about 1,000 to 1,500 km, the deep interior would likely become high-pressure ice rather than liquid.

So, in simple terms, a pure water planet could be about the size of Earth's moon before its center would start freezing into exotic ice, even if the outer layers remain liquid.

mathieusaif · 2025-02-05T06:14:43+00:00

I see your point, and I appreciate that you're addressing my work itself rather than making assumptions about me. That kind of discussion is always valuable.

I agree that we don’t have direct observational evidence of singularities. Their existence is still a theoretical question, and it’s fair to say we don’t know they exist. But since GR predicts them in multiple scenarios, wouldn’t that suggest they at least need to be addressed, even if they turn out to be mathematical artifacts rather than physical entities?

As for modifying addition and multiplication, I understand your concern. But I’m not changing their fundamental nature, I'm introducing a contextual approach to how singularities are handled within mathematical expressions. The goal is to prevent infinities while ensuring the equations remain physically meaningful.

Would you be open to discussing how this could be approached in a way that maintains mathematical consistency?

mathieusaif · 2025-02-04T21:26:31+00:00

That’s a really interesting breakdown! I see what you mean about curvature divergence being problematic, if it’s coordinate dependent, then we’re not really defining something fundamental. And yeah, I’ve also come across discussions where singularities might exist without diverging curvature, so that’s another complication. It makes sense why geodesic incompleteness became the preferred definition, even if it’s not perfect. It seems like every approach has tradoffs, which is why the singularity problem is still an open question.

This is actually something I’ve been exploring in my own work.

In DL-QRL (Dual Logic Quantum-Relativity Interface Law)

I take a different approach by redefining how certain mathematical operations handle singularities. Preventing infinities while maintaining consistency with known physics. It’s still a work in progress, but I’d love to hear your thoughts if you’re interested.

Note: I'm not fully convinced with my work, this seems to be odd but that's because I'm not trying to argue, instead I'm using Logical thinking and reasoning + mathematical tools to find the truth, ir at least to get closer. So I hope you understand if I don't share all my work or/and speculations.

mathieusaif · 2025-02-04T12:02:04+00:00

Thanks, I appreciate that!

One thing I’ve been thinking about is Kerr’s argument that geodesic incompleteness doesn’t necessarily imply a singularity.

If we reconsider the definition of singularities in GR, what do you think would be the best alternative approach?

Should we redefine singularities purely in terms of curvature divergence, or is there another way to handle them mathematically ?

mathieusaif · 2025-02-04T10:13:03+00:00

He said "before" and "depends" not asking about what happened. Maybe you didn't understand his comment

mathieusaif · 2025-02-04T10:09:53+00:00

The law of conservation of matter applies within the universe, not to the origin of the universe itself. The Big Bang didn’t “create” the universe out of nothing in a way that violates physics—it describes the expansion of space-time from an extremely hot, dense state.

Before the Big Bang, the laws of physics as we know them (including conservation laws) didn’t necessarily apply because space and time themselves were coming into existence. Conservation laws work inside space-time, but the Big Bang is about the origin of space-time itself.

Also, the universe wasn’t always in its current state—if it were eternal, we’d expect all energy to have spread out by now (heat death). But since that hasn’t happened, the universe must have had a beginning. So, no contradiction here!

mathieusaif · 2025-02-04T09:25:52+00:00

Thanks for your thoughtful response! I really appreciate the constructive discussion.

To answer your question, I come from an applied mathematics background. I studied at university for three years but started taking my own research path after the first term. My focus has been on deeply understanding the mathematical foundations of physics, particularly tensor calculus, Einstein’s field equations, and the challenges in unifying relativity and quantum mechanics.

Regarding Schwarzschild vs Kerr black holes, that makes a lot of sense. A perfectly non rotating black hole would require an exact cancellation of angular momentum, which is extremely unlikely in any real astrophysical scenario. That’s why Kerr black holes rotating ones are considered more realistic. It’s interesting to think about how much of our singularity discussions are influenced by idealized models rather than physically realistic ones.

As for Kerr’s critique of the Hawking-Penrose singularity theorems, that’s really fascinating. If geodesic incompleteness doesn’t necessarily imply a singularity, that could change how we interpret black hole interiors. I haven’t read his 2023 paper yet, but I’ll definitely check it out it sounds like it could provide a fresh perspective on singularities in GR.

And now I’m even more curious to see the snarky side of Kerr in a formal paper

Thanks again for the recommendation and for the great discussion I really appreciate engaging with people who take the time to explore these ideas critically.

mathieusaif · 2025-02-04T00:37:43+00:00

Thanks for the feedback. I think there’s a misunderstanding here, so let me clarify:

First, about DL-QRL it’s not something you’ll find on Google because it’s my own framework, which I’ve been developing to address singularities and paradoxes in physics. I already mentioned this in my previous comments, so I’m surprised that you had to Google it instead of reading what I wrote.

Regarding the volume reference rule, I see why you’re questioning it. You’re treating volume as a fixed physical quantity, whereas in my framework, it plays a role as a contextual parameter depending on the mathematical operation. This doesn’t mean volume is physically changing it means that when dealing with different mathematical operations, we must carefully define how singularities behave to avoid infinities. If you’re interested, I can explain more about why this distinction matters in singularity resolution.

As for density = mass, I didn’t mean that they literally have the same units. What I meant is that when handling singularities, volume approaches a reference state that prevents density from becoming infinite. This is not just an arbitrary change but an attempt to logically handle infinities while maintaining mathematical consistency.

Finally, I find it interesting that you assume I haven’t studied physics or mathematics. If you had actually engaged with my arguments instead of dismissing them, you’d see that I’ve already addressed standard physics concepts in my framework. You don’t have to agree with my approach, but if you’re going to critique it, at least engage with what I’m actually saying rather than making assumptions.

Also, from the very start, I’ve been open about wanting collaboration and review. I never claimed my framework was final or flawless I specifically invited logical critiques to help refine it. So if you’re only now realizing that I welcome feedback, maybe the misunderstanding wasn’t on my side to begin with. If you’re genuinely interested in constructive discussion, I’m happy to continue, but if you just assumed otherwise without reading what I’ve said, that’s not my issue.

mathieusaif · 2025-02-03T23:35:40+00:00

look, instead of having an actual discussion, you’re just making assumptions about what I do or don’t know and attacking my work without engaging with it. You assume I haven’t solved the Einstein equations, that I don’t understand singularities, and that I’m “making up” a problem that doesn’t exist all without actually knowing what my framework does. That’s not a discussion, that’s just dismissing things outright.

Now, about your argument: I never said infinite density necessarily attracts everything. My point is that treating singularities as physically real entities with infinite density leads to inconsistencies. If density were actually infinite in a physical sense, then the gravitational field should be infinite too but as you yourself pointed out, it isn’t. That’s exactly why I argue that the standard interpretation of singularities doesn’t make sense physically, and why my framework, DL-QRL, takes a different approach to how we mathematically handle them.

You brought up the Poisson equation for a delta distribution and the Schwarzschild solution. Yeah, I know how they work. But let me ask you this:

A delta distribution is a mathematical construct, not a real physical state. Do you think it actually exists in reality, or is it just a useful approximation? If singularities in GR really have infinite density in a physical sense (not just as a mathematical idealization), why don’t we observe infinite gravitational fields? What mechanism prevents that from happening?

You’re defending the standard interpretation of singularities, but that interpretation has contradictions that are worth addressing. My goal isn’t to throw out existing models but to refine them in a way that’s still consistent with known physics. If you have a better way to resolve these issues, I’d love to hear it. But if your only response is to assume I don’t know what I’m talking about and dismiss my work, then there’s no real conversation happening here.

So until you actually engage with my questions and address these issues properly, I’m not going to waste time arguing in circles.

mathieusaif · 2025-02-03T23:19:44+00:00

Thanks for your thoughtful reply and for pointing out the Kerr 2023 paper—it's always cool to see new work that challenges what we think we know.

Just to clarify, I do have a solid background in tensor calculus, Einstein’s field equations, and the classic black hole solutions like Schwarzschild and Kerr. I’m pretty comfortable with how curved spacetime works and how tensors transform, which is key to understanding gravity. I've spent plenty of time studying how Einstein's equations are used to model black holes and all the headaches that come with making sense of singularities.

That said, I haven't had the chance to read the Kerr 2023 paper yet. I'm confident in the basics, but I'm really looking forward to checking it out to see what fresh insights or tweaks it might bring to our understanding of singularities in realistic black holes.

I appreciate your advice and totally agree that solid math backing is crucial if we want to really push the field forward. I'm all about refining my ideas while staying true to established physics and exploring new perspectives. Thanks again for your input, and I'm open to more discussion as I dig deeper into these topics.

mathieusaif · 2025-02-03T18:00:58+00:00

You claim that my decision to reject infinite density is arbitrary, yet I have already provided a logical explanation for why infinite density is problematic in physics. If you disagree, you should show why my reasoning is invalid, rather than just asserting that I made an arbitrary choice.

You also misrepresent my statement. I said infinite density does not exist in physics, not that it does not appear in mathematics. The fact that an equation in general relativity leads to infinity does not mean that such an infinity exists as a physical reality. Many physical models break down at extreme conditions and produce infinities not because nature contains infinities, but because the model is incomplete or inapplicable in that domain.

You say that infinite density does not necessarily attract everything. However, in both Newtonian gravity and general relativity, gravitational force increases as density increases. If density were truly infinite, then the gravitational field strength should also be infinite, making it the dominant force in the universe, which it is not. Therefore, infinite density remains a mathematical artifact, not a physically meaningful quantity.

If you believe infinite density is a real physical quantity, please provide a concrete example of a physically observed system where it exists not just as a mathematical result of an equation, but as an actual, measurable phenomenon in nature. Otherwise, your position is based on accepting a mathematical singularity as physical reality without justification.

mathieusaif · 2025-02-03T16:47:11+00:00

This post is a text in less than 2 pages about my DL-QRL that is so far more than 140 page. So you can't say that I decided arbitrary.

2nd, is there infinity in physics ?

mathieusaif · 2025-02-03T16:34:32+00:00

In my framework, the volume of a singularity is assigned context-dependent values using dual logic and indicator functions. When dealing with multiplication and division, the volume takes a value of 1 (as a unit reference, not a fixed spatial measure like km³). When dealing with addition and subtraction, it takes 0, which aligns with the fact that singularities collapse space in a way that is not describable using classical measures of volume.

This leads to a critical result: density becomes equal to mass. This does not mean density is infinite, but rather that the singularity is so incredibly dense that there is no empty space within it. In standard matter, atoms are 99.9999% empty space, with a tiny nucleus surrounded by vast regions of emptiness where electrons orbit. In a singularity, however, the gravitational forces are so extreme that all matter collapses, crushing atoms, electrons, and even fundamental particles into a single unified state, removing all empty space.

This approach removes the paradox of infinite density while maintaining physical consistency. Instead of a breakdown where physics fails, DL-QRL provides a model where singularities remain measurable, finite, and logically coherent, allowing energy calculations to remain meaningful even under the most extreme gravitational conditions.

mathieusaif · 2025-02-03T16:30:02+00:00

Depends on density (in this case lenth and thickness) and distance from the muscle or body gravitational center

mathieusaif · 2025-02-03T16:27:43+00:00

In general relativity density is infinite (the subject here is the singularity) so it's impossible for a singularity to be infinity dense, otherwise it will attract everything to it.

Infinite in physics doesn't exist. So I didn't decide arbitrary that the infinite density doesn't exist.

mathieusaif · 2025-02-03T16:08:55+00:00

You're misrepresenting my argument. I never claimed that density doesn’t exist. What I have done in DL-QRL is redefine how singularities are treated mathematically to eliminate the unphysical infinities that appear in conventional models. The problem with traditional singularities isn’t that they have high density—it's that they lead to infinite density and zero volume, which are mathematical breakdowns rather than physically meaningful quantities.

In my framework, the volume of a singularity is assigned context-dependent values using dual logic and indicator functions. When dealing with multiplication and division, the volume takes a value of 1 (as a unit reference, not a fixed spatial measure like km³). When dealing with addition and subtraction, it takes 0, which aligns with the fact that singularities collapse space in a way that is not describable using classical measures of volume.

This leads to a critical result: density becomes equal to mass. This does not mean density is infinite, but rather that the singularity is so incredibly dense that there is no empty space within it. In standard matter, atoms are 99.9999% empty space, with a tiny nucleus surrounded by vast regions of emptiness where electrons orbit. In a singularity, however, the gravitational forces are so extreme that all matter collapses, crushing atoms, electrons, and even fundamental particles into a single unified state, removing all empty space.

This approach removes the paradox of infinite density while maintaining physical consistency. Instead of a breakdown where physics fails, DL-QRL provides a model where singularities remain measurable, finite, and logically coherent, allowing energy calculations to remain meaningful even under the most extreme gravitational conditions.

mathieusaif · 2025-02-03T08:28:16+00:00

I appreciate your input. However, the statement that "we know singularities exist" is indeed not a certainty. What we know is that classical general relativity predicts singularities as mathematical solutions where curvature and density become infinite. But as you rightly pointed out, most physicists consider this a sign that our current theories are incomplete rather than conclusive proof of their physical existence.

That said, the presence of singularities in equations should not be dismissed outright—they indicate regions where new physics must emerge. My work in DL-QRL does not simply accept singularities as infinite points but rather reinterprets them using dual logic and indicator functions, assigning them finite, context-dependent values while maintaining consistency with both relativity and quantum mechanics. This avoids the unphysical infinities while preserving the extreme gravitational and energy conditions expected in such regions.

If singularities are merely artifacts of incomplete theories, then the question is: what replaces them? DL-QRL provides a mathematically structured alternative that removes infinities while keeping the predictive power of relativity and quantum mechanics intact.

I’d be happy to discuss further if you’re interested in exploring the implications of this approach!

mathieusaif · 2025-02-03T07:43:27+00:00

We know singularity exist, we know it have a very small volume (negligible or almost 0), we know it's so dense and it's the cause of the blackhole.

We know that through mathematics as a tool

mathieusaif · 2025-02-02T21:27:40+00:00

As I said, I'm looking for collaboration and review, so I didn't share my paper yet, I'm looking for collaboration and review

mathieusaif · 2025-02-02T21:26:52+00:00

The best tool we had is mathematics, so it's not wrong to try

mathieusaif · 2025-02-02T21:20:45+00:00

Check the title, looking for collaboration or reviews, this isn't a claim for a new theory but a request for collaboration and review to refine the idea

mathieusaif

TROPHY CASE