Once again, my "assertion" was not "the elevator is not accelerating". Here's what I said:
Mender's replies are, of course, correct: in free fall with no air drag you will experience no acceleration forces, regardless of your distance from the earth.
Michael, my apologies. I'm afraid I may well have mixed up your statements about the situation with those of others. I read your last post and intended to reply, but this has been my first opportunity to do so. I regret that this might have ended up looking like a criticism of your point of view (I guess it was, since I may have mistaken what that was), then, when others gave replies before you had time that were clearly from the GR POV, I did get rather irritated about that shift from classical mechanics, as I have probably said enough times to bore the pants off everyone by now. So the whole thing has got very complicated. I agree with Clive that we can describe the happenings of the universe according to different theories, and I just find the m.c. version perfectly adequate for the purposes. I would have to go back and read your stuff again, or discuss it more to be sure, but it seems you are doing just that.
A great deal of these discussions of forces and motion and acceleration suffer because of our human language and interpretation of things, as I think I intimated earlier. We say things like "There is a force, and that causes acceleration of a body according to its mass", which puts a causal relationship between force (as Clive said, after wikipedia, "real") and the effect, the acceleration of a body. As we see from the following:
You will indeed experience no forces. The people inside the
zero-g flight don't feel any force on themselves when they are in the free fall part of the flight. In fact they are accelerating towards the earth, but if they close their eyes they have no way of telling in which direction they are accelerating: they don't feel the acceleration.
I agree with that (now I've read what you're saying more carefully!), but it points to that problem of words. Here we are focusing on what someone feels and what they can deduce from it. It makes sense to say that we feel our weight only because of the resistance of the ground, the normal force, and hence when we fall, we don't feel our weight, we don't feel the force of gravity. However, in many mechanics explanations of situations, we talk about balanced forces, gravity and the normal force, for instance, resulting in a body not experiencing or feeling any force, and, when we take the ground away, the body now accelerates because it experiences or feels the force of gravity. Which of these linguistic descriptions we wish to put on the giddy, sick feeling is up to us. You start that by saying you won't feel the gravitational force, and end it by saying you won't feel the acceleration. That's a bit odd. You could say (as humber has argued above perhaps) that our guts slopping about and the liquid in our ear canals slopping about is our body experiencing acceleration, feeling acceleration. And going back to the schoolboy physics again, our guts and every part of us is accelerating because it "experiences" an unbalanced force.
I don't pretend to understand GR, but I think there is a hint of what it's saying in the way we neutralize these ideas against each other. In the fixed lift (British-English for elevator), I can say that I feel gravity. When it falls, I can say that I don't feel gravity, because I'm kind of "giving in to it", going with it, allowing myself to be accelerated by it. Hence the equivalence of acceleration and gravity. I'm not sure how far the equivalence goes in reality, or what reality is (shall we describe all this in terms of string theory and QM, I don't know), but it all makes perfect sense to say that we read our accelerometers and adjust for gravity, because they can't tell that they are not accelerating, and just know that there's a force on their springs or whatever.
To go back to the original question, imagine putting an accelerometer
such as described here in the following situations:
a) orbiting around the Earth
b) orbiting around the Moon
c) orbiting around Jupiter
d) in free fall in a vacuum at the surface of the Earth
e) in free fall near the surface of the Moon
f) floating in outer space light years away from any stars
For extra precision this time, I'll add the information that the accelerometer is not spinning.
In all the above situations, the accelerometer will measure zero acceleration.
Yes, but the original point I made, backed up from several sources is that (certainly from a Newtonian perspective) when they measure zero acceleration, that may be because they are
not accelerating, or it may be because they are in a gravitational field
and "giving in to it", accelerating. Hence, as I said all along, mender's replies were correct, as far as I can see, but - in the words of the accelerometer manual linked to earlier "problematic". {ETA: Bold bits added to correct and clarify}
Someone observered earlier, from c.m. perspective, that when something is changing its velocity by changing direction, as we do in orbit, it is changing its velocity. Hence, in orbit, like in freefall (the two are mathematically and physically identical), we are accelerating. The acceleromter reads 0 because the force of gravity balances the
centripetal centrifugal force corresponding to that eliptical motion. {ETA: I know, that's problematic too!} The velocity of an orbiting body, IIRC, describes a path that sweeps equal areas between it and the body it is orbiting over time, which means that Earth/Sun-orbiting comets race past us at great speeds because they are near, and go much slower out in space. They do that by accelerating. I realise you know that, or
I {ETA: whoops, that could have sounded bad!} imagine you do, and that you don't dispute that they, like a falling lift, are accelerating.
So, here again we see the problem. Do we not feel the force of gravity when we're accelerating, because the acceleration causes a force that balances it? Or do we accelerate because we feel a force of gravity that is unbalanced? Since they seem to happen at the same time, it's just another description of the same events.
g) Place it on the surface of the earth and it will read 9.8 M/S2 upwards
h) Place it on the surface of the Moon and it will read 1.6 M/S2 upwards
Does anyone (apart from Humber) dispute this?
I do have to correct myself on saying that we 'calibrate' them. They are calibrated for zero net force, or zero acceleration for those who see gravity as an acceleration. I got that completely wrong. In a sense, the 'calibration', the adjustment we do is after the fact, since we usually want to know how much we are increasingly falling or rising in our airplane, and we learn that 1 g up is fine, and zero is not level flight. Hopefully.
I hope it is also clear that if you are in zero g out in space, and can see the stars out the window, and your accelerometer reads zero, the passage of the stars (or not) will remain constant, i.e. you will have no kinetic, linear acceleration. If you then gradually drift into a gravitational field (or as I said, someone magically materialises a planet nearby), and your meter still says zero, the passage of the stars outside will not be constant. You will be accelerating linearly, like a plummeting lift.
So, to not be able to detect the difference between acceleration and gravity, it seems we need to be inside a sphere, not only to make the acceleration-and/or-gravity zero, but so we can't see the stars. As Clive notes, we could also imagine a very large mass, such that the lines of force approach parallel and then we can remain in a +ve g field. We could observe the stars, then, and we could still tell if we're falling or not.
Or could we - maybe that's a bit of a cheat, or only true in Newtonian-sized problems. Einstein was a clever chap, they say, and I'm sure he has some reason for this weird equivalence! The above "correct answers" are "ideal" answers anyway - orbiting round Jupiter, etc., or indeed stationary on Earth, the accelerometer will constantly change, I think, due to the gravitational field strength changing from all the other celestial bodies. And since light also is affected, at cosmic scales, perhaps we can't tell. The position of the stars are no longer fixed, nor their apparent positions.
