Alternative theories to General Relativity

[trees and plants]

Hey there.Have you read about the alternative theories proposed by other scientists to General Relativity?So far General Relativity still stays the most accurate.But if we could generalise it?Perhaps try with some new maths like complex differentiable manifolds or Lie groups or another topological space that is differentiable?I do not know and I have not tried so much.The Einstein field equations use mostly the metric tensor which is a function like a tensor field and with its derivatives and the stress energy tensor, the ricci tensor and the scalar curvature.An idea would be to put the corresponding elements of other geometric spaces like ricci tensor to make new equations like the Einstein field equations and see what happens. Another idea would be to make equations not corresponding to the Einstein field equations like an analogy I mean and if they have as a special case the Einstein Field Equations it is ok.What do you say?Thank you.

 

[Demystifier]

There are many alternatives to GR. Examples are tensor-scalar gravity (e.g. Brans-Dicke gravity), $f(R)$ gravity, teleparallel gravity, metric-affine gauge gravity (including torsion), Logunov theory, supergravity, emergent gravity (including entropic gravity), ...

 

[trees and plants]

Consequences of Logunov theory show that it is wrong as a theory of gravity I think.But still they have not generalised the theory proposed by Einstein.What are your thoughts on the questions I made in my first post on this thread?

 

[Dale]

There are many generalizations and variations of GR already proposed and examined in the literature. So far they all have less predictive power than GR because they have more free parameters but don’t fit the existing data any better.

 

[trees and plants]

Perhaps a quantum gravity is needed like the case Einstein had with the theories that were inconsistent and then made special relativity.But the proof Einstein made is completely rigorous?I have read about the proof, but two different ways of proving it the one with the gravitational potential and its derivatives and the one with the principle of least action I think, but I do not know if they are completely rigorous.Could someone tell me about it?Thank you.

 

[Dale]

Perhaps a quantum gravity is needed

Yes, that is indeed needed. That is what string theory and its variations are about.

 

[trees and plants]

I thought of something. What if time is more general than the other spatial coordinates in a four-dimensional manifold?I am talking about time that belongs to space,where a spatial coordinate is a special case of this time?Then we have four temporal dimensions which give us a four-dimensional manifold, the three of them vary differently than the fourth one, which has the time dilation. What do you say?We need the right metric tensor for this and the right equations but perhaps it will fit.

 

[Dale]

I thought of something. What if time is more general than the other spatial coordinates in a four-dimensional manifold?I am talking about time that belongs to space,where a spatial coordinate is a special case of this time?Then we have four temporal dimensions which give us a four-dimensional manifold, the three of them vary differently than the fourth one, which has the time dilation. What do you say?We need the right metric tensor for this and the right equations but perhaps it will fit.

This is complete nonsense. Please learn the material first before proposing alternatives. This one is particularly bad since it implies that there is no distinction between timelike and spacelike separations and also that there are no light cones and no causal structure to spacetime.

 

[trees and plants]

This is complete nonsense. Please learn the material first before proposing alternatives. This one is particularly bad since it implies that there is no distinction between timelike and spacelike separations and also that there are no light cones and no causal structure to spacetime.

What if the conditions about the light cone are relaxed in the first three dimensions?

 

[Dale]

What if the conditions about the light cone are relaxed in the first three dimensions?

Then it won’t represent this universe which has light cones. Nor indeed any universe with electromagnetism.

 

[trees and plants]

Then it won’t represent this universe which has light cones.

Do you have any evidence for this that justify it?

 

[Dale]

Do you have any evidence for this that justify it?

Yes Hertz’s experiment, light, radios, WiFi, TV broadcast, cell phones, etc. Anything which satisfies Maxwell’s equations is evidence.

 

[trees and plants]

Yes Hertz’s experiment, light, radios, WiFi, TV broadcast, cell phones, etc. Anything which satisfies Maxwell’s equations is evidence.

What if we consider coordinates that generalise those in Maxwell equations?

 

[Ibix]

What if we consider coordinates that generalise those in Maxwell equations?

Maxwell's equations can be expressed in coordinate free terms. More generally, changing coordinates can't change physics. Otherwise I could get different experimental results by telling my experiments "today, I shall use spherical polars".

 

[trees and plants]

So every theory or model in physics about gravity should have at least three spatial coordinates after Maxwell's era because Maxwell's equations say it and Maxwell's equations are based on experimental results?

 

[PeterDonis]

The OP question has been answered. PF threads are not for random vague speculations. Thread closed.