Inertial vs accelerating frame

[Rear Naked]

I'm free-falling towards a planet.

Inertial or not?



I suppose this is a postulate of general relativity isn't it?

When I'm studying special relativity I would say Non-inertial, but then if I think about how I cannot really tell if I am accelerating or just traveling a constant velocity, I'm getting confused.


What say you?

 

[Naty1]

yes, er,no...actually depnds on which vision you have:

Newton says: you are accelerating,

Einstein says: no way, you feel no force, therefore you are moving inertially (excluding tidal effects)...

 

[Rear Naked]

So in SR I am non-inertial, but in GR I am inertial?




Do Not Like.

 

[henry_m]

The concept of an inertial frame only really has meaning in flat spacetime.

If you work in special relativity and regard a gravitational field as a fixed potential applying forces to a system of particles, sort of like a static electric field where everything has the same mass/charge ratio, then a falling observer is not inertial. It's then the observation that you can't tell the difference between freefall in gravity and no gravity (if you're looking in a small enough region) that leads to the equivalence principle.

The way the idea of inertial frames carries over into GR is to the weaker idea of local inertial frames, which are sets of coordinates in which spacetime looks locally like flat Minkowski spacetime. So if you're freefalling towards a planet, and you do some experiments in a small enough region near you (much smaller than the length over which the gravitational field changes appreciably), you get the same results as you would with no gravity. This is the same idea that if you're living on a giant sphere, like a perfectly smooth earth, you can't tell it's curved until you start to venture long distances, so if I'm working in a small area I can assume it's flat.

 

[Rear Naked]

Ok.Can I do an experiment while falling over a great distance that tells me that I am accelerating?

The equivalence principle only applies to those instances where change in gravitational forces are negligible?

fishy...

 

[henry_m]

No, you can't tell you're accelerating. But you can tell when things are accelerating relative to one another.

Imagine you're falling towards the planet, but you set it up to begin with so you're surrounded by a sphere of stones, which are also falling freely. From your point of view, what happens?

The stones at the top are slightly further from the planet, so they're in less gravity. You accelerate more rapidly than the stones, so from your point of view, they accelerate upwards away from you. Similarly, the stones below you accelerate down away from you. The stones to the side are getting a slightly different direction of gravitational field, at a small inward angle, so they appear to get accelerated towards you as everything is pulled to the centre of the planet.

So the sphere appears to deform into an ellipsiodal sort of shape. But you are not measuring the acceleration here, but the relative acceleration. The larger the sphere, the more obvious the effect will become. In the limit of a very small sphere, you see no measurable effect and you can't see anything that tells you you aren't in deep space. This is the equivalence principle. What destroys the 'inertialness' is the effect of tidal forces, which are anisotropies in the gravitational field.

Your suspicion over the equivalence principle is well founded. While it has a decent mathematical formulation (spacetime is a Lorentzian manifold) it's physical basis is perhaps a little bit woolly. As I alluded to in my previous post it's the same as the statement that a small enough patch of a sphere is flat, which is a statement of approximation rather than absolute fact.

 

[cosmik debris]

There are many types of acceleration. In Newton's framework we talk of 3-acceleration that is acceleration in 3 dimensions. In Relativity we have 4 dimensions so we talk of 4-acceleration. 4-acceleration has three meanings:

1) co-ordinate acceleration. This corresponds to the Newtonian concept of dv/dt.
2) acceleration 4-vector. This is invariant, has no need of co-ordinates because it is a tensor of rank 1.
3) proper acceleration. This is the 4-vector projected onto a co-moving reference frame.

Each has different properties and it is important to know which you are talking about. If you are in free fall although your v is changing with respect to the co-ordinates (i.e. accelerating in the Newtonian sense), your acceleration 4-vector is zero. To be accelerating in 4-space the angle of the 4-velocity must be changing.

 

[Dale]

So in SR I am non-inertial, but in GR I am inertial?

No. In Newtonian physics you are non-inertial, in GR you are inertial. SR simply doesn't apply.

 

[Passionflower]

I'm free-falling towards a planet.

Inertial or not?

If I assume you are talking about general relativity then you are in a local inertial frame. When you try to extend this frame globally you will be confronted by tidal forces.

 

[ZealScience]

It's about things moving with respect to you, if they are moving with the same accelertion you will not be able to tell. But if you falling towards a planet there would be curvature of space and causes tidal forces.

I am not sure there would be bending of light because of the acceleration. Anyone help?

 

[Rear Naked]

No. In Newtonian physics you are non-inertial, in GR you are inertial. SR simply doesn't apply.

Why doesn't SR apply? Doesn't that assertion rely on the faller having knowledge about the planet and gravitational effects?


If we have Einstein inside of a falling room. The classic elevator perhaps. He is accelerating toward the planet due to gravitational effects. He doesn't know this. Does Einstein accept or reject SR in this elevator?

I guess my question is : At what point does the faller decide that SR doesn't apply?

Do SR experiments fail in this elevator?



Thanks everyone

 

[Dale]

If we have Einstein inside of a falling room. The classic elevator perhaps. He is accelerating toward the planet due to gravitational effects. He doesn't know this. Does Einstein accept or reject SR in this elevator?

I guess my question is : At what point does the faller decide that SR doesn't apply?

At the point that he can measure tidal effects.

 

[Rear Naked]

Ok I got it. Just to be sure, tidal forces are the only reason SR doesn't apply in gravitational situations?

 

[Dale]

Yes. Tidal forces are represented by spacetime curvature in GR, and SR is the limit of GR where spacetime is flat.

 

[grav-universe]

SR applies locally, briefly between observers in the same immediate place in a gravitational field, whether freefalling or accelerating, while GR applies globally.

 

[Rear Naked]

SR applies locally, briefly between observers in the same immediate place in a gravitational field, whether freefalling or accelerating, while GR applies globally.

Saying that SR applies briefly and locally in an accelerating field, is really saying that under those conditions, tidal effects are negligible, and therefore SR applies.


I have very little understanding of GR obviously.