Why Is Gravity Viewed as Spacetime Distortion Rather Than a Force?

[ndung200790]

Please teach me this:
Why we do not infer the gravity for the force(a type of interaction of fields) but for the distortion of space-time.
Thank you very much in advance.

 

[Bill_K]

a) Because we can. Because thanks to the principle of equivalence, gravity affects all matter the same.

b) Because we must. Because gravity affects light. If gravity were only a force in a flat spacetime, it would not be able to redshift a light beam, or deflect a light beam, unless we modified Maxwell's Equations somehow. Gravity also affects itself, and the precession of Mercury's orbit tests this fact.

 

[ndung200790]

Please teach me more detail: why we must consider Quantum Field Theory in Curved Space-Time,but do not consider the QTF Theory(e.g Quantum Electrodynamics) in flat space-time with ''gravity coupling'' (mass).In this theory normal field interact with gravity field?

 

[ndung200790]

In this case,the electromagnetic field in Maxwell's equations interact with gravity field,so ''in fact'' there is ''not exist'' the free electromagnetic field because the presence of gravity.

 

[atyy]

Why we do not infer the gravity for the force(a type of interaction of fields) but for the distortion of space-time.

Yes, gravity a field. Because gravity causes our rulers to bend and clocks to slow, which is what we "measure" spacetime with, we also say that gravity is a distortion of spacetime.

Please teach me more detail: why we must consider Quantum Field Theory in Curved Space-Time,but do not consider the QTF Theory(e.g Quantum Electrodynamics) in flat space-time with ''gravity coupling'' (mass).In this theory normal field interact with gravity field?

In this case,the electromagnetic field in Maxwell's equations interact with gravity field,so ''in fact'' there is ''not exist'' the free electromagnetic field because the presence of gravity.

These are approximations. The electromagnetic field does couple to gravity in full classical general relativity. The full theory of quantum gravity is yet unknown.

 

[ndung200790]

Why we do not battle with quantum gravity by starting with classical gravity Lagrangian(Einstein equation) then use canonical quantization.I think that the nonrenormalization difficulty is only the technical difficulty,that yielded by Feymann perturbative technique.I think that there are many technique calculations without Feymann technique.

 

[atyy]

Why we do not battle with quantum gravity by starting with classical gravity Lagrangian(Einstein equation) then use canonical quantization.I think that the nonrenormalization difficulty is only the technical difficulty,that yielded by Feymann perturbative technique.I think that there are many technique calculations without Feymann technique.

This approach is called "Asymptotic Safety"
http://www.percacci.it/roberto/physics/as/index.html
http://arxiv.org/abs/0709.3851

A related approach is "Causal Dynamical Triagulations"
http://arxiv.org/abs/1105.5582

 

[ndung200790]

I think that the mass is the result of all quantum processe of ''basic'' fields.Then the gravity can not consider as a ''basic'' field,then it must be an attribute of space-time,so we can not consider gravity as a force but as a distortion of space-time.Is that seem correct?

 

[pervect]

My understanding of the issues goes something like this. The issue fundamentally comes down to how does gravity transform. Electromagnetism is represented, for instance, by a rank-2 tensor, the Faraday tensor, which gives the force on a unit charge given its velocity.

The curvature of space-time, however, transforms differently. The Riemann transforms as a rank 4 tensor.

If you adopt any specific coordinate system, you can think of gravity as a "force" in the sense that there will be differential equations of motion involving the Christoffel symbols for geodesic motion. (I suppose here I am making certain simplifying assumptions, that an object is following geodesic motion, which is usually a good approximation but not always correct).

But the manner in which this "force" transforms when you change coordinates is important. And if you assume that this "force" transforms like the forces you are used to, you won't be able to make it work. So you need a more general model for how the "force" transforms, and the correct model will be the same as the model for how a curved space-time transforms.

If you want something more definite,think about how the different Christoffel symbols transform under the relation t'=at. It's helpful to classify the Cristifoffel symbols up into how many time indexes they have- there are some that have NO time indexes, which gives you a clue to how time scaling affects them.

Compare and contrast this to how the Faraday tensor transforms under t' = at.

 

[atyy]

I think that the mass is the result of all quantum processe of ''basic'' fields.Then the gravity can not consider as a ''basic'' field,then it must be an attribute of space-time,so we can not consider gravity as a force but as a distortion of space-time.Is that seem correct?

Classically, gravity is a basic field and the distortion of spacetime: http://www.youtube.com/watch?v=8MWNs7Wfk84".

Quantum mechanically, gravity is only understood as an http://relativity.livingreviews.org/Articles/lrr-2004-5/" .