the equivalence principle paradox

[ExplorerII]

I understand that the forces of Gravity and acceleration are indistinguishable, so that being said, myself standing on planet earth is experiencing an acceleration of approx 9m per sec, per sec. My friend, above me, has just jumped off the Empire state building, and therefore no longer feels any force (weightless) so he must be floating in space at this point. So me, because I feel a force, must be accelerating up to meet him, along with the rest of earth. But obviously this is not the case, so what is really happening?

[Simpo Two]

If you were constantly accelerating you would eventually break the speed of light, so something must be wrong!

[ExplorerII]

Good point. I'm sure the term 'freefall' comes into the equation somewhere. What does not make sense is that someone who is weightless cannot be accelerating towards earth, can they?

[ewenm]

ExplorerII said:

I understand that the forces of Gravity and acceleration are indistinguishable, so that being said, myself standing on planet earth is experiencing an acceleration of approx 9m per sec, per sec. My friend, above me, has just jumped off the Empire state building, and therefore no longer feels any force (weightless) so he must be floating in space at this point. So me, because I feel a force, must be accelerating up to meet him, along with the rest of earth. But obviously this is not the case, so what is really happening?

Your friend is experiencing the acceleration, you are not. F=ma. For your friend the forces are gravity (9.8m/s^2) and air resistance which balance out at approximately 120mph relative to the earth for a falling human IIRC. For you the forces are gravity and the repulsion between the atoms of your feet and the earth. These balance giving you a velocity of 0 relative to the earth.

[Laplace]

It appears to me your axioms are a little confused.

Before your friend jumps you and he both share the same interial frame of reference. One he jumps he undergoes acceleration and the symmetry no longer exists, thus he is moving towards you.

[mrmr96]

If you ignore air resistance then your friend who is falling is subject to the same gravitational acceleration as you are. The difference is you feel an equal and opposite force through your feet as they are pushed upwards by the ground.

If you include air resistance then you're still both feeling the force of gravity, but whilst you're feeling the ground pushing up your buddy is only feeling the air resistance pushing him up. So his speed will continue to increase until the force of the air equals the force of gravity.

Basically things accelerate when the forces acting on it are imbalanced. Your gravity being balanced by your shoes, his is balanced by the air (or nothing if you're think in simplified terms). So he will change speed and you won't.

[Zad]

It is a common mistake to make to assume that objects orbiting the Earth (for example, astronauts inside the ISS) are not experiencing gravity, and are not falling down. They are falling, but because they are orbiting, they are effectively continually missing the Earth. If you were to slow down the orbit slightly, the object would fall downwards. If you were to somehow rapidly bring them to a standstill relative to the Earth, the astronauts would accelerate at not much less than 9.8 m/S/S.

It is tempting to think that gravity only goes as far as the top of the atmosphere but, to give a sense of scale to the actual effect of gravity, the Rosetta probe which arrived at comet 67P-C/G on Wednesday (the comet is only around 3km long) started to feel the gravitational effect from between 100 and 200km away.

[ExplorerII]

My friend who is falling is experiencing the exact same effect as a person floating in space away from any source of gravity. He is completely weightless, so how can he be accelerating? This is my argument.

[ewenm]

ExplorerII said:

My friend who is falling is experiencing the exact same effect as a person floating in space away from any source of gravity. He is completely weightless, so how can he be accelerating? This is my argument.

No he isn't. The person in space a long way from any gravity well (so we're talking billions of miles from the sun) is not experiencing any force. The person falling is experiencing the gravitational force which will accelerate him to his terminal velocity when the air resistance matches the gravitational force and he stops accelerating. At no point is he weightless as he is in a gravity well.

Edit: Given our Sun is caught in the gravitational forces of our galaxy, and clusters of galaxies are all intertwined by gravity, it's pretty had to find anywhere for your hypothetical spaceman to be free of gravity. If you mean people in orbit in the space station then they aren't weightless, they are in free fall experiencing angular acceleration along the line between them and the centre of the earth which is keeping them in orbit rather than shooting off at a tangent.

Edited by ewenm on Thursday 7th August 19:52

[Halmyre]

ExplorerII said:

My friend who is falling is experiencing the exact same effect as a person floating in space away from any source of gravity. He is completely weightless, so how can he be accelerating? This is my argument.

Weightless, not massless...

[otolith]

Your perception of gravity is the result of the force it applies distorting your body, because the force applies to all parts of your body, some of which are fixed and some aren't. Specifically, it is distorting bits of your vestibular system and the nerves there are detecting the distortion and your brain is interpreting it. If you aren't attached to anything and thus are able to accelerate freely under gravity, all the bits of your body will be accelerating at the same rate, thus no distortion, thus no sensation.

[AA999]

Frame of reference is the key....
For the guy jumping off the building he views the earth rushing up to meet him.
For the guy on the earth he views the jumper falling downwards towards him.

[ExplorerII]

ewenm said:

No he isn't. The person in space a long way from any gravity well (so we're talking billions of miles from the sun) is not experiencing any force. The person falling is experiencing the gravitational force which will accelerate him to his terminal velocity when the air resistance matches the gravitational force and he stops accelerating. At no point is he weightless as he is in a gravity well.

Edit: Given our Sun is caught in the gravitational forces of our galaxy, and clusters of galaxies are all intertwined by gravity, it's pretty had to find anywhere for your hypothetical spaceman to be free of gravity. If you mean people in orbit in the space station then they aren't weightless, they are in free fall experiencing angular acceleration along the line between them and the centre of the earth which is keeping them in orbit rather than shooting off at a tangent.

Edited by ewenm on Thursday 7th August 19:52

Incorrect, as described below, there is no indistinguishable difference between floating in space and freefalling toward earth.

Weightlessness poses a similar problem. Imagine you're floating freely inside the elevator. Around you, other objects are floating, as well, and you feel totally weightless. Does that mean you are far away from all gravitational influences, far away from all stars, planets and other massive bodies, somewhere in deep space? Again, you cannot be sure. Alternatively, you and the elevator could be in the gravitational field of a mass, for instance that of the earth, as long as the elevator was in free fall. In that case you, everything else within the elevator and the elevator itself would all be accelerated at exactly the same rate so that, inside, no influence of gravity could be detected. Relative to the elevator, all those objects faithfully keep their relative positions (or move at a constant speed), just as they would in a gravity-free region of space. You, as the elevator's passenger, would feel weightless - after all, in an ordinary situation here on earth, you feel your weight as gravity pulls your body down, pressing whatever part of it carries your weight onto the floor. In the falling elevator, both your body and the floor fall in parallel, at the same rate:

[ewenm]

FEELING weightless and BEING weightless are two different things. You cannot BE wieghtless in a gravity well although you can FEEL weightless (as you've described).

Edit: In terms of acceleration (back to the OP), it is in the direction of the force acting, so towards the centre of the earth in these examples. The OP's standing observer cannot be accelerating towards the falling "weightless" person beacuse there is no force acting on the observer in that direction.

Edited by ewenm on Friday 8th August 10:41

[ExplorerII]

ewenm said:

FEELING weightless and BEING weightless are two different things. You cannot BE wieghtless in a gravity well although you can FEEL weightless (as you've described).

Edit: In terms of acceleration (back to the OP), it is in the direction of the force acting, so towards the centre of the earth in these examples. The OP's standing observer cannot be accelerating towards the falling "weightless" person beacuse there is no force acting on the observer in that direction.

Edited by ewenm on Friday 8th August 10:41

Negating the air in the atmosphere my falling friend is indeed weightless, not just feeling it (as explained above, and by Einstein). And my standing observer does indeed have a force acting upon him, just like you do now, as you're sitting in your chair.

Another way to look at it: If you take everything away from sight and just view the two in question you would indeed come to the conclusion that it was the observer on the pavement accelerating up to meet the jumper.

Edited by ExplorerII on Friday 8th August 13:19

[ewenm]

ExplorerII said:

Negating the air in the atmosphere my falling friend is indeed weightless, not just feeling it (as explained above, and by Einstein). And my standing observer does indeed have a force acting upon him, just like you do now, as you're sitting in your chair.

Resultant force of 0 though - gravity minus electromagnetic repulsion from the atoms of the chair. Hence no acceleration. Am I therefore weightless on my chair?

If a mass is in a gravitational field it has weight, regardless of it's movement. Whether a human feels that weight or not does not mean they have no weight, merely that they are not moving relative to their immediate surroundings i.e. all the air in the falling elevator is also moving (and accelerating) at the same rate. They have weight but are not feeling it.

To be truly wieghtless you either need to be massless or not in a gravitational field. This is different to FEELING weightless due to the relative movement of your immediate surroundings.

When you drive fast over a hump-back bridge do you become momentarily weightless? Or does it just feel like that as your momentum is reigned in by gravity?

[otolith]

This is a biology question more than a physics question.

[ewenm]

ExplorerII said:

Another way to look at it: If you take everything away from sight and just view the two in question you would indeed come to the conclusion that it was the observer on the pavement accelerating up to meet the jumper.

You said take everything away - but not including the pavement? I agree, that with just two people in space, no air, no point of reference, then it is impossible to tell which is moving and which isn't. However, that's not the scenario you've outlined.

From the info above I would conclude that we don't know which is accelerating towards the other, not conclude the pavement-stander was accelerating (as I wouldn't be able to see the pavement). If you won't take away the pavement, you can't take away the air either, at which point the air rushing past the faller would indicate that one was moving/accelerating (if not at terminal velocity).

To make a conclusion about acceleration, we would need to look at the forces involved. The one experiencing a resultant force would be the one accelerating.

[Laplace]

I've been thinking about this again in terms of general relativity.

In GR gravity is not a force but the warping of space-time by the presence of matter or energy.

An accelerometer placed on earth would measure 1g with an upwards direction. Therefore someone standing on earth is being accelerated upwards. It is perfectly acceptable to be accelerating without displacement within the framework of GR as you are essentially moving through space-time, but not through space.

If no force is acting upon you then you are not accelerating and you will follow geodesics. If you are prevented from following geodisics this must be due to a force acting upon you i.e the surface of the earth.

The suicidal jumper carrying his accelerometer, in the absence of air resistance, will measure 0 on his accelerometer as no force is acting upon him.

It would then appear that it is actually the earth bound observer who is accelerating and no paradox exists within GR.

[ExplorerII]

Laplace said:

I've been thinking about this again in terms of general relativity.

In GR gravity is not a force but the warping of space-time by the presence of matter or energy.

An accelerometer placed on earth would measure 1g with an upwards direction. Therefore someone standing on earth is being accelerated upwards. It is perfectly acceptable to be accelerating without displacement within the framework of GR as you are essentially moving through space-time, but not through space.

If no force is acting upon you then you are not accelerating and you will follow geodesics. If you are prevented from following geodisics this must be due to a force acting upon you i.e the surface of the earth.

The suicidal jumper carrying his accelerometer, in the absence of air resistance, will measure 0 on his accelerometer as no force is acting upon him.

It would then appear that it is actually the earth bound observer who is accelerating and no paradox exists within GR.

Thank you Laplace. Paradox was the wrong word to use. And what you have mentioned makes perfect sense to me now. The key point here is accelerating without displacement.