Is such a flaw conceivable in GR?

[externo]

Hello,

Is it conceivable that there is a fundamental flaw in GR like this: Could it be that it is as impossible to curve spacetime in GR to the point of reducing the size of objects to 0 as it is for matter in motion to reach the speed of light and be contracted to a length of 0. The curvature would have to be non-linear, and it would be increasingly difficult to curve space to the point that the formation of a black hole is not possible because it would require infinite energy.

This would mean that Einstein's equations would not be good. What is wrong would not be the form of the curvature but the coupling between energy and curvature, which in fact would not be linear. This would be a relic of Newtonian mechanics that was not treated correctly by Einstein. We can't realize it because from the moment we fix by observation the escape velocity or the curvature of light, we deduce a false mass but correct equations of motion. The mass is simply underestimated.

Would this be conceivable or can we show that such an error is impossible?

[Mordred]

We are already aware that GR reaches a singularity condition such as you described above ie ds^2=0.

 However the problem is that GR is incredibly precise at all other velocities where v does not equal c. 

Curvature is non linear any curve is non linear however one can linearize non linear relations to close approximation.

Considering GR high degree of accuracy I wouldn't think of it as flawed but rather has a limit to its accuracy.

 

Edited November 8, 2024 by Mordred

[Markus Hanke]

5 hours ago, externo said:

What is wrong would not be the form of the curvature but the coupling between energy and curvature, which in fact would not be linear.

The equations already are non-linear.

5 hours ago, externo said:

Would this be conceivable or can we show that such an error is impossible?

There are some stringent mathematical constraints as to what form the equations can take in standard GR, they aren’t just randomly invented, but derived from those conditions. It is not possible for them to take a different form without violating some of these conditions.

You can have different equations, but then you’re not doing GR any longer, but some alternative theory of gravity.

[Khanzhoren]

On 11/9/2024 at 1:37 AM, externo said:

Hello,

Is it conceivable that there is a fundamental flaw in GR like this: Could it be that it is as impossible to curve spacetime in GR to the point of reducing the size of objects to 0 as it is for matter in motion to reach the speed of light and be contracted to a length of 0. The curvature would have to be non-linear, and it would be increasingly difficult to curve space to the point that the formation of a black hole is not possible because it would require infinite energy.

This would mean that Einstein's equations would not be good. What is wrong would not be the form of the curvature but the coupling between energy and curvature, which in fact would not be linear. This would be a relic of Newtonian mechanics that was not treated correctly by Einstein. We can't realize it because from the moment we fix by observation the escape velocity or the curvature of light, we deduce a false mass but correct equations of motion. The mass is simply underestimated.

Would this be conceivable or can we show that such an error is impossible?

Hello, in my opinion , "singularity" or "object with size 0" cannot realy exist because of the quantum uncertainty principle.  And as  it is known GR is incomplete because, in particular, it is not a quantum theory. So the real solution to the problem related to singularity should be from quantum description.

[dimreepr]

1 hour ago, Khanzhoren said:

Hello, in my opinion , "singularity" or "object with size 0" cannot realy exist because of the quantum uncertainty principle.  And as  it is known GR is incomplete because, in particular, it is not a quantum theory. So the real solution to the problem related to singularity should be from quantum description.

Probably, not...

[Khanzhoren]

2 minutes ago, dimreepr said:

Probably, not...

Why ?

[Halc]

9 hours ago, Khanzhoren said:

 in my opinion , "singularity" or "object with size 0" cannot realy exist because of the quantum uncertainty principle.

'Singularity' doesn't mean 'object of size zero'. It means conditions under which the equations no longer produce meaningful results. It means a different theory (or different coordinates, or something else) is needed to describe what goes on under said condition. You note this below.

As for zero size object, size is a classical concept and doesn't really apply to quantum things.  The uncertainty principle loosely says you cannot know both momentum and position at the same time. Neither references a size.

 

9 hours ago, Khanzhoren said:

And as  it is known GR is incomplete because, in particular, it is not a quantum theory. So the real solution to the problem related to singularity should be from quantum description.

A quantum description probably doesn't work either since it cannot describe the spacetime curvature. A unified theory would really help.

[Khanzhoren]

On 1/6/2025 at 2:29 AM, Halc said:

'Singularity' doesn't mean 'object of size zero'. It means conditions under which the equations no longer produce meaningful results. It means a different theory (or different coordinates, or something else) is needed to describe what goes on under said condition. You note this below.

I agree with you

On 1/6/2025 at 2:29 AM, Halc said:

As for zero size object, size is a classical concept and doesn't really apply to quantum things.  The uncertainty principle loosely says you cannot know both momentum and position at the same time. Neither references a size.

I don't entirely agree with you because one also talks about the size of an atom, a molecule, or a solid, for example, within the framework of quantum physics (even if it's not exactly the same as the classical concept). These "sizes" moreover depend on the localization, movement, and interactions of the constituents with the environment. These are described by quantum mechanics and are related to the uncertainty principle, among other things.

On 1/6/2025 at 2:29 AM, Halc said:

A quantum description probably doesn't work either since it cannot describe the spacetime curvature. A unified theory would really help.

I agree with you because actually, when I said quantum description, I was referring to a quantum theory of gravity as well.

[Halc]

10 hours ago, Khanzhoren said:

I don't entirely agree with you because one also talks about the size of an atom, a molecule, or a solid

A solid is definitely classical. But what I should have said is that size doesn't apply to fundamental things like an electron.  All such things are quantum, but technically a horse is a quantum thing as well, so not all quantum things are without meaningful size.

[KJW]

9 minutes ago, Halc said:

But what I should have said is that size doesn't apply to fundamental things like an electron.

https://en.wikipedia.org/wiki/Classical_electron_radius

 

[swansont]

31 minutes ago, KJW said:

https://en.wikipedia.org/wiki/Classical_electron_radius

 

The classical electron radius is not the actual size of the electron

A clue should be the use of “classical” in the name, while the electron is a quantum particle. Classical concepts have a habit of failing when QM comes into play

As the article says, “It links the classical electrostatic self-interaction energy of a homogeneous charge distribution to the electron's relativistic mass-energy”

[Halc]

33 minutes ago, KJW said:

https://en.wikipedia.org/wiki/Classical_electron_radius

 

That's a classical radius, and I said that size was a classical concept.  Swonsont beat me to it.

To quote the site:

"The classical electron radius is a combination of fundamental physical quantities that define a length scale for problems involving an electron interacting with electromagnetic radiation. It links the classical electrostatic self-interaction energy of a homogeneous charge distribution to the electron's relativistic mass-energy."

I don't entirely get that, and I certainly don't know how that sort of thing can be measured to 11 significant digits. Nevertheless, defining this size is 'useful', so there it is.

To also quote the same site and show what I was talking about:

"According to modern understanding, the electron is a point particle with a point charge and no spatial extent."

[swansont]

1 hour ago, Halc said:

I don't entirely get that, and I certainly don't know how that sort of thing can be measured to 11 significant digits. Nevertheless, defining this size is 'useful', so there it is.

The radius is not measured, since it doesn’t physically exist. The precision stems from being able to measure the mass.