Is there something special about standing on a planet?

[Bob Walance]

Is there anything special that can be attribituted to standing on a planet vs. some other mechanism of generating an upward force?

The only unique attribute that I can assign to this case is that it keeps you in a constant part of the planet's curvature of spacetime.

Maybe I can get my point across with an example:

No matter where I stand on Earth, I'm always in a fixed amount of spacetime curvature. If I strap on my rocket belt (gasses expelled downward), jump off a cliff, and dial in any force OTHER than my weight, I will transition through various magnitudes of spacetime curvature.

So, is one's weight only special because it's the amount of force that will keep you in a fixed amount of curvature? Is there something else I'm missing?

Thank you,
Bob Walance

 

[cesiumfrog]

It's very special: You're accelerated upwards without needing to expend fuel/energy.

Of course, those rotating platforms at kids parks are equally special in the way they accelerate you inward..

 

[pervect]

For a non-rotating body, maintaining constant Schwarzschild coordinates is rather special, because the metric coefficients are all static. IIRC the proper jargon from Wald would be "a time-like orbit of the Killing field, I'm too lazy to look it up right now and I'm not sure anyone really cares :-). (Besides, I recall convicing myself that Wald's description was incomplete).

For a rotating body, because of frame dragging, things get more involved.

 

[D H]

A simple question: What in the world does this have to do with relativity? The upright position is metastable. Someone in a upright posture is not "standing still". The person is instead swaying back and forth and side to side as their musculature constantly adjusts to maintain the upright position. Maintaining an upright position requires constant, semiconscious effort. An immediate consequence of losing consciousness (i.e., fainting) is falling over.

We do not stand upright because we are "maintaining constant Schwarzschild coordinates". We stand upright because it allows us to see more and because it is the starting position for "falling with style" (aka walking).

For a rotating body, because of frame dragging, things get more involved.

Let alone a non-spherical body such as the Earth or Moon. Classical physics is often much more capable of answering simple questions than is modern physics.

The GPS satellites are oft cited as an example of the need for special and general relativity. Crackpots aside, we do indeed need to account for relativistic time dilation to get accurate positions using GPS. However, the future position and velocity of the GPS satellites are predicted using classical and not relativistic physics. (Just try to represent the Earth's non-spherical and time-varying gravitational potential in relativistic terms.) Proper treatment of GPS requires a weird mix of classical and modern physics.

 

[JesseM]

A simple question: What in the world does this have to do with relativity? The upright position is metastable. Someone in a upright posture is not "standing still". The person is instead swaying back and forth and side to side as their musculature constantly adjusts to maintain the upright position. Maintaining an upright position requires constant, semiconscious effort. An immediate consequence of losing consciousness (i.e., fainting) is falling over.

I think you're overemphasizing the word "standing", that wasn't really the focus of the OP, it could have just as easily been "what is special about lying on a planet". The point is that you are feeling a constant G-force when you're on the surface and not in free-fall, the question is whether there is anything "special" about this as distinct from feeling a constant G-force because you're being accelerated in deep space where spacetime is close to flat.

 

[Bob Walance]

A simple question: What in the world does this have to do with relativity? The upright position is metastable. Someone in a upright posture is not "standing still".
[snip]
We do not stand upright because we are "maintaining constant Schwarzschild coordinates". We stand upright because it allows us to see more and because it is the starting position for "falling with style" (aka walking).
[snip]
Let alone a non-spherical body such as the Earth or Moon. Classical physics is often much more capable of answering simple questions than is modern physics.
[snip]

Perhaps it was a poor choice of words for me to use the word "standing". The only issue that I was attempting to get across is the uniqueness of being stationary with respect to a large mass (e.g. the Earth). So sitting, standing, lying, crawling, floating, etc, would have worked, too.

I'm just getting my feet wet (and hands and knees and chin) in GR and I was just trying to get clear in my mind whether one's weight had any special meaning as it applies to GR.

Pervect's mention of static coefficients is the kind of response I was soliciting. Thanks for that, Pervect.

It seems that from a qualitative point of view that the only unique thing is that it keeps one in a constant degree of curvature. This is obvious, and it's probably just as simple as that.

Bob Walance