Not really. The simplest way to measure would be a mass on a spring. In a gravitational field the spring would stretch slightly more when held lower than when held higher. In your scenario, it would not.
Actually, it would, because of the way the walls you’re comparing the expansion/contraction length of the spring to are accelerating.
That’s exactly what Bryan was saying: they would each fall in a straight line towards the center. As such, their paths would converge.
No. According to him, they would initially fall in a direction that is NOT directly toward the center of the earth, but would over the time of their fall be drawn closer and closer to the center. His scenario would call for a very slightly curved path to the center of the earth. I maintain that a dropped object would drop directly toward the center of the earth‚in a straight line.
If not, I ask again, what force is acting on the objects causing them to fall in a direction that is not directly toward the center of the earth? And in which direction?
I don’t recall mentioning or implying curved paths. The paths would actually resemble the legs of an extrememly tall and thin isosceles triangle, with matched segments that do, in fact, converge.
Although come to think of it, in both experiments wouldn’t the weights exert a minute gravitational pull on each other, so their paths would theoretically be slightly curved as they accelerated towards each other?
My mistake then. I guess I did, in fact misunderstand you. If you agree that the lines would be straight we are in agreement. My apologies.
Interesting. But I think that assumes that the attraction to each other would have a lag or increase in intensity over time. Which, theoretically,it would. I think.
Doesn’t Einstein postulate that, as straight as they seem, they are subtly curved because space is curved?
Except I wouldn’t be comparing them to the walls, I would be comparing them to the built in gauge (seriously, have you never seen a fish scale?). The walls could be doing the hokey pokey, but it would have no relevance because they are not part of my system and I do not need to reference them. They only could be part of my system if they exert a force on me. The only way they could do that is if they are attached to the floor. In which case they would not be accelerating at a different rate.
I’m sorry, I’m not getting it. You’re saying that in your scenario, the walls of our hypothetical elevator car are drifting apart, so that the elevator is slowly, uh, exploding? I think the rest of us were thinking of an elevator car that is bolted together like normal elevator cars.
Well, plus we must consider that the dropped objects might be yo-yos, and thus subject to string theory.
The deviation from parallel would be very small. And the point of it is to duplicate the acceleration felt by the same box here on Earth. If it can withstand the acceleration on Earth, it can withstand the same acceleration in space.
There’s a disconnect between what I’m saying and what you’re understanding. The physical forces don’t matter. The pseudo forces in an accelerating frame of reference are an artifact of the accelerating frame of reference. No physical mechanism is needed.
I’m apparently not explaining it well, but it’s a basic part General Relativity. You can’t avoid it’s effects–if the elevator box in space is accelerating exactly the same as the elevator box on Earth, there’s no classical measurement (there are probably quantum ones) inside the box you can make to distinguish the two cases.
I think I understand what you are getting at, but you are missing something fundamental. To accelerate you need a force. To have a different rate of acceleration on my head than my feet you need to apply a different force to each.
Lets step back a minute. Here is what I am picturing:
I am standing in a box holding two super precision fish scales in my hand. Each has a 1 kg weight attached to it, hanging free.
On earth, the top one weighs 9.8066499 and the bottom one weighs 9.8066500.
What happens in the accelerating box scenario?
The way I, and I believe the others arguing with you see it, the only force causing the acceleration of my body is the normal force of the floor acting on my feet. The only force causing acceleration of the of the scales is the normal force from my hands.
You seem to be saying that my hands will be accelerating at different rates. Explain where the acceleration comes from. You can’t just say “a system of rockets” because the rockets must have a way to cause the acceleration by coupling a force.
You scenario works only if the we hang the scales from a strips on the wall that are connected to different rockets. But if the scales are mounted to the same spot by by a rigid system, they will not accelerate at different rates.
Jonathan
Ah, there’s the problem–this isn’t true. You can also have acceleration due to the effects (called pseudo forces) of an accelerating frame of reference. On Earth, everything is affected by a pseudo force pulling toward the center of the Earth. It’s as if there’s something pulling on each bit of matter separately. But it’s not an actual force, there’s no physical connection, it’s simply an effect of the non-inertial frame of reference we typically use. (Sure, we can approximate the behavior of matter by using Newton’s Law of Gravitation, but it’s an edge case of the actual physics happening.)
The accelerating elevator box in space is no different. You’ll measure a force pulling on each bit of matter separately. Not because there’s anything physical actually pulling on it, but because your accelerating frame of reference makes it appear to be so.
Another note–no fair using perfectly rigid objects. They’re strictly impossible. You can violate Special Relativity as well with rigid systems.
Yes, and the differential tidal force on the bottom and top of the elevator car would be very small, too. But this whole discussion came from a hypothetical about whether it would be possible, in principle, to tell the difference between being in an accelerating box, and a box that’s stationary but subject to gravity. And some of us have pointed out that the differences are small, but in principle there are differences: the different vector directions on opposite sides, and the difference in the force of gravity on top vs. bottom of the box.
You keep saying that we’re mistaken, that those differences don’t exist, but either we’re doing a poor job of understanding what you’re saying or you’re not communicating it very well.
Assuredly, both. 
I’m saying that in principle the small differences can be accounted for. The box in space can experience the same acceleration as the box sitting on Earth. And if it does, no measurement will be able to distinguish the two.
But for the box that’s being accelerated in open space, the acceleration that you measure inside the box will be exactly uniform throughout the box, both in terms of its magnitude and its direction. Right?
But the box sitting on the Earth’s surface, the acceleration measured will slightly point in a different direction on the left side of the box compared to the right, and the acceleration measured at the top will be slightly less than the acceleration you measure at the bottom. Right?
That depends on how it’s being accelerated. A uniform acceleration is certainly possible, but it’s not the only possibility. There’s no physical reason the box could not be accelerated exactly the same way the box on Earth is.
Hey guys, maybe this thread hijack about acceleration should go in a different thread.