Gravity=Conservation

[foodchain]

I think gravity is just conservation of energy really. I mean without conservation of energy what would the universe look like, or what would the universe look like without gravity, would you have any ability to make classifications like space or time? It would seem to me that a particle or body could just arbitrarily gain or lose energy without causality really, or that something could just be here or there or anywhere. I think another nifty aspect of this would be during the big bang, I mean if all the stuff in the universe was undergoing some form of symmetry transformation in such an intense gravitational field, could that be why atoms exist, as it was the universe in such an environment of time and space? Plus it seems that work has to work against gravity, or energy has to be spent to defeat it else it just stays put.

 

So what about it, could conservation of energy be related to gravity or explain gravity? With the dark stuff or dark matter/energy currently its being proposed that the only interaction or way to measure or observe it is via gravity, so with that said would that possibly mean that certain fundamental forces of nature, like the strong or weak only be products of stuff in some form, and that dark stuff or what not obeys something else, but if that conjecture were possibly true why would gravity still be able to interfere with it unless gravity is something truly fundamental which brings me around to the point in which it seems conservation of energy seems constant and that the universe really is not a void but made up of a fabric in which it seems gravity also impacts in terms of form and or development. Giving other theoretical concepts like quantum decoherence which states measurement is an interaction that produces an appearance of wave function collapse, could gravity in sense in closing simply be why we have conservation of energy for any system of subsystem plus environment? Why we have causality, or anything simply because the universe in terms of energy is conserved and gravity is simply just that occurring, the conservation of stuff down to a quantum level?

[swansont]

Conservation of energy stems from the time translation symmetry of the laws of physics.

[ajb]

In general relativity space and time get "mixed up" and as such the notion of energy and its conservation become much more complicated.

 

If I recall correctly, locally one has energy conservation but globally it is much more complicated. A generic space-time may have no killing-vectors at all thus the notion of symmetries becomes obscure.

 

There is several definitions of a energy pseudo-tensor. As a pseudo-tensor it is not a tensor and as such it is coordinate dependent. This should set alarm bells ringing as we have to be very careful in case we have phenomena due to the coordinates and not physics. Basically, it is a frame dependent notion.

 

I would have to do some more reading in order to be more specific. I think energy can be conserved in general relativity, but that will depend somewhat on what you mean by energy and conservation.

 

You are far better off thinking bout energy-momentum conservation. This is conserved in general relativity.

Edited September 9, 2009 by ajb

[foodchain]

In general relativity space and time get "mixed up" and as such the notion of energy and its conservation become much more complicated.

 

If I recall correctly, locally one has energy conservation but globally it is much more complicated. A generic space-time may have no killing-vectors at all thus the notion of symmetries becomes obscure.

 

There is several definitions of a energy pseudo-tensor. As a pseudo-tensor it is not a tensor and as such it is coordinate dependent. This should set alarm bells ringing as we have to be very careful in case we have phenomena due to the coordinates and not physics. Basically, it is a frame dependent notion.

 

I would have to do some more reading in order to be more specific. I think energy can be conserved in general relativity, but that will depend somewhat on what you mean by energy and conservation.

 

You are far better off thinking bout energy-momentum conservation. This is conserved in general relativity.

 

I just wonder if at the big bang or big bounce or whatever it was any physical laws existed, such as if the forces/particles described by the standard model existed, or if via symmetry breaking such things came to be. With that I wonder if gravity might be more fundamental then other forces, and how all of it ties into conservation laws.

 

Without gravity I would think spacetime or the universe to look much different, would you have any regular form to planetary bodies, or blackholes, or any normal astrological phenomena. I know such a question sort of seriously goes outside of physics, but with that I also wonder if gravity itself could simply be viewed in such a context. If conservation of energy is to always hold true, could that in reality be the force of gravity?

 

I mean physics has to develop a theory of quantum gravity, such is string theory or loop quantum gravity. If you did not have conservation of energy I do not think any sort of "form" could come to exist. I should be able to throw a ball and have it do any number of things with no way to predict any sort of outcome, or really everything should be purely quantum in sense, as I would think I could just constantly tunnel. I wonder if the constraint on such chaos really is just conservation of energy, and how that translates in the physical world is via forces/particles, like gravity.

 

I mean if such a conjecture could be remotely true could atomic reality or particulate reality simply be what spacetime looked like at some point in the universes history? Even on a quantum scale with the uncertainty principal I noticed with sound or phonons that you can have something regular, to an extent, as in beating on a drum does not randomly produce some sound like a cat meowing. I mean can simple conservation laws be applied to the universe as a whole to maybe understand what gravity is?

[ajb]

Like I said, generically one does not have energy conservation in general relativity which is the most successful theory of gravity to date. This is easily understood as energy would require one to single out the time coordinate. Recall, any coordinate system is equally valid in general relativity. Thus, in general one cannot trust any result that requires a choice of coordinate to be chosen.

 

As Swanson has stated, energy is related to time invariance. Really in the same way as momentum is related to translational invariance. But what if you cannot really separate space and time?

 

Now in general it is not possible to meaningfully split the space-time into space and time. However, it is meaningful on a globally hyperbolic space-time. Forgetting what this means technically, topologically it means that the space-time can be decomposed as [math]M = I \times \Sigma[/math], where [math]I \subset \mathbb{R}[/math] is the "time" and [math]\Sigma[/math] is a Cauchy surface. Better put, such space-times allow a global fibration. You can think of this as a series of surfaces each parametrised by time. (You should note that the metric itself does not need to respect such a fibration.)

 

Such space-times are very useful in general relativity as this allows an initial problem formulation. That is everything on [math]M[/math] can be described by equations of motion and an initial condition on [math]\Sigma[/math]. Such space-times are fundamental in most approaches to quantum field theory on curved space-times. However, most space-times are not globally hyperbolic.

 

As an aside, algebraic quantum field theory can be formulated on non-hyperbolic space-times. But this is another story.

 

So, generically you do not have energy conservation. Though, you can formulate things so that in certain cases you do have energy conservation.

 

What you do have in general is conservation of energy-momentum. This comes directly from the field equations and is really geometric in origin, it comes from one of the Bianchi identities . So, maybe you could understand general relativity in this way.

 

But is general relativity the only theory to have energy-momentum conservation?

Edited September 10, 2009 by ajb