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.

[KJW]

On 1/8/2025 at 1:43 AM, Halc said:

I said that size was a classical concept.

What you said (to which I replied) was that size doesn't apply to fundamental things like an electron, whereas the classical electron radius is a size that does apply to the electron. That it was derived using classical electrodynamics is beside the point. It is not being suggested that the classical electron radius is the actual radius of the electron, but in some sense, it is an "effective" radius of the electron and a physical constant that appears in theories where the size of the electron is relevant.

Another size associated with the electron is the Bohr radius. Even though this was derived using an obsolete model, it remains as a physical constant that appears in modern theories regarding the size of an atom.
 

 

On 1/8/2025 at 1:40 AM, swansont said:

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”

See above. I didn't actually say that the classical electron radius is the actual size of the electron. I referred to a Wikipedia article that describes the classical electron radius as "a combination of fundamental physical quantities that define a length scale for problems involving an electron interacting with electromagnetic radiation".

 

Edited Thursday at 11:51 PM by KJW

[swansont]

21 minutes ago, KJW said:

Another size associated with the electron is the Bohr radius. Even though this was derived using an obsolete theory, it remains as a physical constant that appears in modern theories regarding the size of the hydrogen atom.

That has some physical significance, as it’s the most probable distance an electron would be from the proton in the S state of hydrogen. It gives you the scale of the size of the hydrogen atom. The classical electron radius doesn’t have an analogous role.

 

Quote

I didn't actually say that the classical electron radius is the actual size of the electron

By not saying much of anything other than citing the number, you didn’t do much to dissuade this notion.

[KJW]

On 1/10/2025 at 9:57 AM, swansont said:

By not saying much of anything other than citing the number, you didn’t do much to dissuade this notion.

I'll concede that point. On the other hand, you did say that "a clue should be the use of 'classical' in the name", indicating that it is obvious that the classical electron radius is not the actual size of the electron, and that it was not necessary to explicitly state this. However, I do think that the classical electron radius is in some sense an effective radius or size scale of a dressed electron.

 

 

On 1/10/2025 at 9:57 AM, swansont said:

That has some physical significance, as it’s the most probable distance an electron would be from the proton in the S state of hydrogen. It gives you the scale of the size of the hydrogen atom. The classical electron radius doesn’t have an analogous role.

Where would one expect the size of an electron to appear in physics, anyway? It isn't as though the Bohr radius is used in physics that isn't about the size of atoms. The classical electron radius appears in non-relativistic Thomson scattering and the relativistic Klein–Nishina formula.

 

 

[studiot]

On 11/8/2024 at 10:37 PM, externo said:

Is it conceivable that there is a fundamental flaw in GR like this:

 

 

I suppose it rather depends what you mean by fundamental flaw.

 

GR is just a model.
Reality is under no obligation to follow it exactly.
In fact no model is exact.
But so far as we know there is no self inconsitency.
There are also several 'solutions' to the equations of GR.

So in this respect the GR model has no flaw.

 

As regards your proposal, I think you have the idea a little mixed up.

On 11/8/2024 at 10:37 PM, externo said:

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.

What meaning do you attach to this claim and what (mathematical) proof do you have of its veracity ?

Mathematically we have learned to handle the 'impossible' division by zero.

For instance the point scalar density has a definite and measurable value which coincides with the scalar limit of Mass / volume as the volume approaches 0.

Similarly, but in a more complicated fashion, vector flux reduces to a limit of flux over area as area approaches 0.
This applies to pressure at a point (force over area), magnetic, gravitic or electric field density etc.

 

Mass has zero dimension, force has one dimension, area has two dimensions and volume has three dimensions.

If time is involved it adds at least one more dimension.

When we set a quantity in a multidimensional universe of greater dimensionality, eg force divided by area we introduce at least one extra degree of freedom.

With force over area the area has two dimensions  curvature or rotation has one of these.

But we are setting this ratio in a three dimensional universe so we immediately introduce a second degree of freedom and a second direction for the curvature.

If we want to go to a GR universe we enter a four dimensional mathematical space.

How many ways can curvature operate in this space ?

 

 

 

 

 

[AbstractDreamer]

The most obvious "flaw" in GR is that its model of reality is premised on a differentiable manifold. 

Calculus assumes and necessarily requires the logical leap-of-faith that if you break a curve into infinitesimally small parts, then each part is a straight line.  An infinitesimal change in y with respect to an infinitesimal change in x.   Calculus claims it knows the value of both x and y, at infinitesimality.

Quantum uncertainty principle claims that at infinitesimality, observables are in superposition.  You cannot know fully and simultaneously both the values of y and x.

[studiot]

Just now, AbstractDreamer said:

The most obvious "flaw" in GR is that its model of reality is premised on a differentiable manifold. 

Calculus assumes and necessarily requires the logical leap-of-faith that if you break a curve into infinitesimally small parts, then each part is a straight line.  An infinitesimal change in y with respect to an infinitesimal change in x.   Calculus claims it knows the value of both x and y, at infinitesimality.

Quantum uncertainty principle claims that at infinitesimality, observables are in superposition.  You cannot know fully and simultaneously both the values of y and x.

I don't call that a flaw for the reasons I have already outlined.

Yes it limits the applicability of the model, as does any form of linearisation of non linear equations.

[AbstractDreamer]

OP is talking about fundamental flaws in GR.   Calculus is in direct contradiction with Uncertainty Principle.  This is not just some trivial dichotomy.   Its both a limitation and a flaw.   I don't accept the argument that because its a limitation, we shouldn't discuss it as a flaw.

[swansont]

1 hour ago, AbstractDreamer said:

Quantum uncertainty principle claims that at infinitesimality, observables are in superposition.  You cannot know fully and simultaneously both the values of y and x.

That’s not superposition. The uncertainty principle applies to conjugate variables (x an p are, x and y are not), which are fourier transforms of each other, and you find that transform using…calculus.

[AbstractDreamer]

Conjugate or not depends on what the axes represent in observables.   You cannot make a blanket statement at x and y are not conjugate before you apply units to them.  Well you can, but you'd be wrong.  What if x was position and y was momentum?   Would you then agree x and y are conjugate?

[swansont]

15 minutes ago, AbstractDreamer said:

Conjugate or not depends on what the axes represent in observables.   You cannot make a blanket statement at x and y are not conjugate before you apply units to them.  Well you can, but you'd be wrong.  What if x was position and y was momentum?   Would you then agree x and y are conjugate?

Momentum is p. 

If you want to discuss physics and be understood you need to speak the language. Otherwise nobody knows what you mean.

The larger point is that only a very limited set of variables are constrained in this way. It doesn’t apply to most. And calculus itself isn’t the limitation (but it describes the limitation)

[AbstractDreamer]

1 minute ago, swansont said:

Momentum is p. 

If you want to discuss physics and be understood you need to speak the language. Otherwise nobody knows what you mean.

The larger point is that only a very limited set of variables are constrained in this way. It doesn’t apply to most. And calculus isn’t the limitation.

Nah.   Y can be anything I choose the axes to be.  This is basic algebra, where symbols replace variables - INCLUDING momentum, and IRRESPECTIVE of whether momentum is p. 

So in this case I'm calling my y-axis Momentum.   Is that ok with you?  Do I get your approval?  You said nobody would understand me, do you think they would understand this?  Shall we waste more time arguing over irrelevances? 

Lets talk about the "very limited set of variables" then.  Calculus of course is independent of what its variables are, that goes without saying. But if calculus is used on conjugate variables, then it contradicts Uncertainty Principle.  So instead of blanket claiming Calculus isn't the limitation, SHOW ME!

Show me that Calculus is not performed on conjugate variables in General Relativity



 

[exchemist]

2 hours ago, AbstractDreamer said:

The most obvious "flaw" in GR is that its model of reality is premised on a differentiable manifold. 

Calculus assumes and necessarily requires the logical leap-of-faith that if you break a curve into infinitesimally small parts, then each part is a straight line.  An infinitesimal change in y with respect to an infinitesimal change in x.   Calculus claims it knows the value of both x and y, at infinitesimality.

Quantum uncertainty principle claims that at infinitesimality, observables are in superposition.  You cannot know fully and simultaneously both the values of y and x.

I think you may be confusing abstract mathematics with physics. Calculus is used all the time in QM. The uncertainty principle arises from pairs of non-commuting operators for certain observable properties. This concept is quite compatible with calculus. In fact some of the operators concerned contain things like derivatives.