GBE issue

[Infinite9Luck]

Hi, I was checking this wikis pages and calculation and I think everything is very well done, but I have some concerns regarding a topic, and that topic is the GBE.

I might be wrong of course, so that's why I make the thread, I would like to have an answer or a new solution that can explains my doubts, I'll proceed explaining them now.

I was looking at this thread, which is the thread that banned the use of GBE calculation in regards of the Schwarzschild radius.

However I think the OP is misleading in his claims.

The issue:

The OP claims that the KE formula for FTL and GBE are related, hence it's a double standard allowing one of them, and the other not.

However that is what I find misleading, the 2 formula are NOT related at all, there is NO conceptual connection between the 2, for example the KE formula is NOT used to derive the GBE and the GBE formula is not used to derive the KE formula. It's motion versus gravitational cohesion. They are not mathematically or conceptually linked.

At least as of my current math knowledge, if someone is capable to post me a proof that those 2 formula are indeed connected theoretically and mathematically, It will resolve my doubts.

This to claim, that if FTL KE is banned, then it's not a good reason, to not use GBE for certain situation.

And to make my position clear, I completely agree that FTL KE CAN'T be used, I read explanation from @DontTalkDT, and I agree with him.

However now let's address what the OP suggested on that thread and why I think again it is misleading.

The Culprit:

The Schwarzschild radius.

This is what is written on the GBE page:

Spoiler: GBE page

Gravitational Binding Energy only works as quantification for the destruction of things as long as they are not smaller than their own Schwarzschild radius. In reality objects of such a nature would always be black holes, but in fiction one frequently finds giant celestial objects which have not collapsed into such despite being inside their own Schwarzschild radius.
The trouble with such objects is that, according to proper physics, dispersing them should be impossible. I.e. their gravitational binding energy would be considered either infinite or just simply undefined. Hence quantifying the energy to disperse them becomes more difficult.
In case of actual black holes one would do it as described on the black hole feats in fiction page. In other cases there are several options to go through.

And I completely agree with this, because that's how our universe work! But now let me explain why it is invalid to ban certain calculations based on this, given we established that using FTL KE is completely irrelevant here.

This is the formula we are talking about:

r_s = (2 * G * M) / c^2

The Explanation:

To put it simply, this answer the question: “What is the radius where the escape velocity equals the universal speed limit?”

Someone might have already understood what I mean, but we can clearly see that in the formula there is a "c" why so?

Because that's the speed limit on our universe! You see, the formula isn't an absolute rule, we put c there not as definition, but as rule, what does this mean? again the formula answer on theoretical level “What is the radius where the escape velocity equals the universal speed limit?”, so if we take an hypothetical universe where c, aka the speed of light isn't an established limit that the formula became pure non sense, and would simply adapt to that universe limit. Yes, the formula would literally change in another universe.

For example in the Marvel universe or many other Japanese manga, plethora of character go FTL without creating black hole, or time travel or paradox, this mean that on a theoretical level the speed of light, can indeed be surpassed in that universe, and the universe allow it, in such universe, the Schwarzschild radius formula, can't be applied, and need to be adapted to the speed limit of that universe to be accurate, because that's the definition of the formula.

Another blatant example is that indeed, some being or object bigger than a galaxy EXISTS in fiction, and simple don't turn into black hole at all. The formula must imply that if some character that big exist, they turn into a black hole.

What I want to point out is that, banning the GBE to be used for those objects, is like saying that no characters can be FTL. And yes, it's completely different from FTL KE.
For example if I say that I cant use GBE for that massive object, is like saying Superman can't be FTL due to our universe rule, because the formula simple use c as our rule, not as absolute definition. And the fictional work don't even follow it to begin with.

Well, that's at least my train of thoughts, if someone can solve my doubts it would be awesome, because as for now I find it as a contradiction in the wiki standards to not allow the use of GBE.

My Idea:

My suggestion is simply to allow to use GBE because it works even for those massive result! GBE is not like the KE formula, GBE can be used to calc even those massive things and it works and deliver an accurate result! Because the GBE formula is NOT related to c at all, meanwhile KE yes, it is.

What are you guys thoughts?

 

[ElajRuengies]

This is what I've taken from your OP:

1. You agree that FTL KE can't be used for @DontTalkDT 's reasons listed here.
2. You think the GBE of bodies that are so massive they should absolutely be blackholes should be fine to calcs, because the speed of light could be different in different universes because of different physics, despite how @DontTalkDT 's already addresses why that's not viable to consider.

Explain the double standard please?

Also, changing the speed of light also changes the sizes of atoms, as [copied from somewhere else] the Bohr radius is a quantity that determines the size of an electron's orbit around an atomic nucleus. It is inversely variable with both the speed of light, and the charge of the electron.

You can't just say that bigger planets are possible because "the speed of light is different," as changing constants changes everything. And you can't compensate for the different speed of light by just adjusting the charge of the election in the other direction to fix the atoms, because then the proton and electron's charges are no longer equal in magnitude, ruining chemistry. And you can't fix that by then adjusting the charge of the proton to match, because the energy levels at which molecules form, hold together, and break apart, are now radically different, once again ruining chemistry.

Don't try to justify writers not having a grasp of astronomy with headcanon. Unless the Orthogonal series gets a page on the wiki, we're not considering "different physics."

 

[Infinite9Luck]

This is what I've taken from your OP:

1. You agree that FTL KE can't be used for @DontTalkDT 's reasons listed here.
2. You think the GBE of bodies that are so massive they should absolutely be blackholes should be fine to calcs, because the speed of light could be different in different universes because of different physics, despite how @DontTalkDT 's already addresses why that's not viable to consider.

Explain the double standard please?

Also, changing the speed of light also changes the sizes of atoms, as [copied from somewhere else] the Bohr radius is a quantity that determines the size of an electron's orbit around an atomic nucleus. It is inversely variable with both the speed of light, and the charge of the electron.

You can't just say that bigger planets are possible because "the speed of light is different," as changing constants changes everything. And you can't compensate for the different speed of light by just adjusting the charge of the election in the other direction to fix the atoms, because then the proton and electron's charges are no longer equal in magnitude, ruining chemistry. And you can't fix that by then adjusting the charge of the proton to match, because the energy levels at which molecules form, hold together, and break apart, are now radically different, once again ruining chemistry.

Don't try to justify writers not having a grasp of astronomy with headcanon. Unless the Orthogonal series gets a page on the wiki, we're not considering "different physics."

Let's address point by point, I'm glad you didn't brought up the fact that KE and GBE are related as you did in your first post. That was my main concern and a pretty huge mistake to claim they are conceptually linked. I think that's misleading, and if we are going to ban GBE we need to ban it for other reason than that.

Rebuttal

Regarding all your explanation, yeah I agree with what you said here, of course by changing the speed of light limits lot of things would change, but that is going deep into hyper-technicism, that honestly are not needed in my opinion.

In a fictional universe where FTL is allowed and the speed of light is not a hard limit, the Schwarzschild radius ceases to be a barrier to escape.
The logic that leads to black hole formation in real physics is rooted in the impossibility of exceeding c.

If that impossibility is ignored or routinely broken in the narrative, then so are all consequences that rely on it, including event horizons and the prohibition on using GBE for super-compact objects.

Therefore, in FTL settings, it is entirely internally consistent to use the GBE formula for objects of any size, regardless of what would happen in real-world physics.

Arguments about chemistry or the size of atoms are not relevant unless the fiction explicitly addresses them. What matters is internal consistency with the rules set by the narrative, not adherence to real-universe physics that the story already disregards.

Lastly, let me explain why this is not a double standard. The GBE formula actually works and allows you to calculate the binding energy for extremely massive objects. In reality, such objects would become black holes, but the formula itself allows you to plug in those values.

In contrast, the classical KE formula is outdated and cannot be used for FTL scenarios because it is inherently limited by the speed of light. The GBE formula does not have this limitation.

So there is no double standard: one formula (KE) is outdated and invalid for certain values, while the other (GBE) is a fully functional formula that can be applied to these cases, though the resulting object would theoretically become a black hole due to the Schwarzschild radius which is way different than the formula itself being not valid.

Conclusion

It is important to note that FTL kinetic energy (KE) cannot be applied under any circumstances. What you are actually arguing is not that the GBE formula is inapplicable, but rather that the Schwarzschild radius would come into play, this is an extremely important and subtle distinction.

The GBE formula can still be used; and if, in a fictional universe, an object does not turn into a black hole and FTL speeds exist, then GBE remains an accurate way to calculate its energy.

 

[VanderSalva]

Let's address point by point, I'm glad you didn't brought up the fact that KE and GBE are related as you did in your first post. That was my main concern and a pretty huge mistake to claim they are conceptually linked. I think that's misleading, and if we are going to ban GBE we need to ban it for other reason than that.

GBE absolutely relies on classical mechanics (KE) to get its formula. If escape velocities a) are relativistic or b) beyond the speed of light, of course the formula will give you a) an inacurate result or b) a result that relies on the universe not having a speed limit.

The GBE formula actually works

For non-relativistic, under the speed of light escape velocities.

in a fictional universe, an object does not turn into a black hole and FTL speeds exist,

Then you could use Newtonians mechanics regardless of being relativistic or beyond the speed of light, sure.

then GBE remains an accurate way to calculate its energy.

The meat of GBE is KE. If you can argue for relativistic and beyond m v² / 2, because

If that impossibility is ignored or routinely broken in the narrative, then so are all consequences that rely on it,

and

What matters is internal consistency with the rules set by the narrative, not adherence to real-universe physics that the story already disregards.

alright, but I understand it to be a tall order.