# A questiona about equivalence principle

• haisydinh

#### haisydinh

Here are the 2 situations:
Situation A: a person floating in space far away from any mass (i.e. the person is in zero-gravity environment)
Situation B: a person undergoes a free-fall from the top of a roller coaster (assuming that there's no air resistance)

My question is, would the person in situation A feel differently from the person in situation B? In other words, are these two situations equivalent? My guess is that they are the same, because equivalence principle states that: An inertial frame of reference is equivalent to a freely-falling frame of reference that is in a uniform gravitational field (this is basically what I understand about GR). Can you guys tell me whether I'm correct?

That is essentially what the equivalence principle says. The only problem with your analogy is that the Earth's gravitational field is not uniform, and so the roller coaster rider is not in complete free fall.

That's why the word 'locally' (in spacetime) occurs in the EP ;)

thanks very much for your answers. However, I'm still a bit sceptical about this. I mean I have tried traveling in a roller coaster before, and I know that it's a super terrible feeling to fall down freely. But if free-fall is equivalence to floating in zero-gravity, then does that mean that I would have that same terrible feeling if I'm just floating in space far away from any mass? In other words, I am sceptical because this is somewhat against my intuition.

Yes, that is what it means. Sometimes in physics, especially in areas like relativity and quantum mechanics, intuition can lead us astray.

haisydinh
I mean I have tried traveling in a roller coaster before, and I know that it's a super terrible feeling to fall down freely.

That's partly because all the experience of a lifetime tells us that free-fall will end badly when we hit the ground; and partly because changes in acceleration - that stomach-dropping-out feeling you get when the rollercoaster goes over the top and starts down - are very disconcerting. With practice, most people can become comfortable with the feeling (rather as a non-swimmer finds floating in deep water utterly terrifying but experienced swimmers do not).

nitsuj
From a practical viewpoint though, roller coasters almost never have vertical free-falls, most going no more than 50 degrees to the horizontal. From this view, a roller coaster ride is still quite different from "floating free in space". Perhaps the superman ride in six flags is a little bit better at this. :)

thanks very much for your answers. However, I'm still a bit sceptical about this. I mean I have tried traveling in a roller coaster before, and I know that it's a super terrible feeling to fall down freely. But if free-fall is equivalence to floating in zero-gravity, then does that mean that I would have that same terrible feeling if I'm just floating in space far away from any mass? In other words, I am sceptical because this is somewhat against my intuition.

I think the rollercoaster is a poor analogy. For example, imagine:

a) Standing on the ground.

b) Standing on the edge of the roof of a tall building.

Physically, these two situations and equivalent in terms of gravity and forces, but you're going to "feel" a lot different in b).

... a bungee jump might be better, although even then you have significant air resistance and the fear factor.

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if free-fall is equivalence to floating in zero-gravity, then does that mean that I would have that same terrible feeling if I'm just floating in space far away from any mass?

Yes.

I am sceptical because this is somewhat against my intuition.

Your intuition isn't trained to deal with floating in space far away from any mass, so it's not too surprising that it gives the wrong answer for this case. We know the correct answer in this case because astronauts have experienced essentially the same condition--not just in free-fall orbit about the Earth, but also during transits to and from the Moon in the Apollo missions, which were in free fall.

But if free-fall is equivalence to floating in zero-gravity, then does that mean that I would have that same terrible feeling if I'm just floating in space far away from any mass?
I suspect that it's mainly the sudden change in proper acceleration that is unpleasant. It usually means an expected event like falling over, so it triggers avoidance instincts and adrenaline rush. In an elevator you sometimes get a similar feeling when the proper acceleration returns from a higher value back to it's normal value of 1g, hinting that the sensation comes from the quick change, not the actual value of proper acceleration. I also remember from flying gliders that you get used to zero g rather quickly, when at higher altitude and hence not seeing the ground coming closer fast, as you do on a roller coaster.

So if you are in free fall for a while, you don't feel terrible all the time because your proper acceleration is constant at zero. It's just the quick transition to free fall that feels unpleasant. That's why it doesn't make sense to build roller coasters higher and higher, as the dive would just get boring.

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nitsuj
I think the rollercoaster is a poor analogy. For example, imagine:

a) Standing on the ground.

b) Standing on the edge of the roof of a tall building.

Physically, these two situations and equivalent in terms of gravity and forces, but you're going to "feel" a lot different in b).

Yes, the visual impression is a significant part of the "feel". I remember from flying, that dives at high altitude (where visually altitude appears rather static) are far less exiting than diving close to the ground (which feels much more like a roller coaster).

I suspect that it's mainly the sudden change in proper acceleration that is unpleasant. It usually means an expected event like falling over, so it triggers avoidance instincts and adrenaline rush.

The intial moments after jumping out a plane was very very...emotive. I've referred to it as feeling the "full pull" of gravity, of course it's the exact opposit...none the less it's an acceleration. Coordinately, the wind, the ground and other visuals had no impact for my experience with respect to "Oh Lord I'm falling!". It was just that sudden (and exteneded) sense of not feeling that CONSTANT acceleration we're all so familuar with. Once being supported by a cushion of air it was back to normal.

It was just that sudden (and exteneded) sense of not feeling that CONSTANT acceleration we're all so familuar with.
There is more to it in sky diving, for example the complete lack of something to grab onto. After all, we evolved from monkeys, which were jumping from tree to tree catching branches. Failing to grab often meant death. Free fall feels quite different in a cockpit fixed to the seat by the belts.

If zero g was all there is to it, then swinging high on a child swing would be just as exciting as roller coasters and sky diving.

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There is more to it in sky diving, for example the complete lack of something to grab onto. After all, that we evolved from monkeys, which were jumping from tree to tree catching branches. Failing to grab often meant death. Free fall feels quite different in a cockpit fixed to the seat by the belts.

If zero g was all there is to it, then swinging high on a child swing would be just as exciting as roller coasters and sky diving.

I'm not crazy so it was a tandom jump lol. And the guy said if you don't position proper I'll smack your side. Sure enough I basically turtle, he smacks my side I position and within those few seconds we're at "top speed".

You're absolutely right about the whole scene, my hands were sweating like mad on the ride up. Which in itself was a new experience, though not scary. Preparing for the jump, being next to a giant hole in the side of this small plane NOT buckled into a seat I was like a cat on a tightwire above a swimming pool...Not moving a muscle, mentally "beside myself".

You're flippin bright! You mention "something to grab onto". With the parachute open I couldn't help but grab onto the straps above that are attached to the chute's lines. Had to be told twice to not to lol So there I dangled trusting the harness, which is far superior to my hand strength but somehow less assuring.

I mean I have tried traveling in a roller coaster before, and I know that it's a super terrible feeling to fall down freely.
Have you ever jumped on a trampoline? When mid air you are much closer to the free fall that astronauts experience, than on a roller coaster, but it's far less scary and after a few jumps just fun.