# B Orbits and forces

1. Feb 11, 2017

### mieral

Orbits of electrons around nucleus can never exist because it can lose energy as charges accelerate so there is never orbits of electrons.

Why can't we treat gravity as forces in similar fashion.. as something that doesn't really exist.

My point is. General Relativity and spacetime curvature is our reality just like electrons using Schroedinger Equation is our reality. Hence why should we even treat classical space as valid or legitimate. Can't we treat classical space like same category of orbits of electrons which is fiction? Because if you assume classical space.. you assume force of gravity which never existed at all because for example black holes can't be modeled as gravity being a force. So you can't say space is classical limit of spacetime curvature.. in the same way you can't say the orbits of electrons is a classical limit of schroedinger equation.

2. Feb 11, 2017

### Staff: Mentor

Because it works very well for modeling a wide range of phenomena.

3. Feb 11, 2017

### Staff: Mentor

No, you don't. GR has "classical space" (more precisely, classical spacetime), but gravity is not a force in GR.

4. Feb 11, 2017

### pervect

Staff Emeritus
Some people think that we may need to replace "classical spacetime" with a "quantum foam" to do quantum gravity. However, we don't appear need a "quantum foam" to do General Relativity. I'm not aware of any obstacle that prevents us from using GR in a classical (but curved) space-time. It seems to work just fine. So, since it's not broke (until - perhaps! - one gets into quantum gravity), there's no need to fix it.

I've never seen any published paper treat gravity as a "force" in classical relativity. I'll stop short of saying that it's proven that gravity can't possibly be treated as a force, but I can raise some issues that suggest it does not.

The subset of Christoffel symbols $\Gamma^x{}_{tt}, \Gamma^y{}_tt, \Gamma^z{}_{tt}$ acts rather like a "force" in many regards, but being only pieces of a rank 2 tensor, it's not a force, and doesn't transform as a force in general.

If one could demonstrate that there is no rank 1 tensor that transforms properly tha acts like a force, I think one would have the required proof. Personally, I don't see how any such thing could exist, but that stops short of a formal proof.

Interestingly enough, I believe that if one use an orthonormal basis in a flat space-time, the transformation equations for the 3 Christoffel symbols mentioned make it transform just as a force would - though this procedure does not generalize to a curved space-time. But I've never seen this as a published claim, it's just a personal observation.

The issue arises that this explanation is not very beginner -level friendly, because the whole issue of how things transform under a change of coordinates is just something that people don't think about at the begininner level - and probalby not even the Intermediate level. I could essay an "explanation" at a lower level, perhaps, but it probably wouldn't be terribly rigorous and hence wouldn't be terribly convincing. So, I think I'll stick with the argument that there isn't any suitable , known, rank 1 tensor suitable to be called a "force". To appreciate the argument, one undortunately does need to know what a tensor is, and why it's important, though.

5. Feb 12, 2017

### Mister T

What is the context of this claim? If we use the explanations Newton used we get planets that are bound to suns behaving in a certain way that matches what we see planets doing. For the most part! But as you say that explanation won't work for electrons bound to atomic nuclei because it doesn't match the way we see electrons behaving. Instead we have an explanation that gives us something that is not Newton's orbits.

The loss of energy you mention is indeed one explanation of why Newton's explanation for planets won't work for electrons.

Nevertheless, many people still refer to the electron as orbiting the nucleus. This is not wrong. It's just that the orbit is not the orbit of Newton's explanation. Instead it's the orbit of Schrodinger's explanation. For the most part!

I really can't get understand what you're getting at in the rest of your post. It appears you are mixing up the thing being modeled with the model. The thing being modeled is Nature's behavior. The model is an invention of the human mind. They both exist, and are therefore part of our reality. But our knowledge of Nature's behavior is limited to what we've been able to observe, and our models are based on that limited knowledge. Currently we have no single model that can describe all of the ways in which we observe Nature behaving. And we are developing new tools that will allow us to witness new behaviors. We really do have a lot of uncharted territory in the sense that we are bound to discover new behaviors for which our current explanations won't work. And we already have lots of behaviors we've witnessed that we can't explain.