the equivalence principle paradox
Discussion
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?
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.
Incorrect, as described below, there is no indistinguishable difference between floating in space and freefalling toward earth.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
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 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.
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. 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
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
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. 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.
And also a change of direction is equal to an acceleration, which would explain why you are weightless in an orbit around the Earth. Velocity being the key word.
'Acceleration, in physics, is the rate at which the velocity of an object changes over time'
'Acceleration, in physics, is the rate at which the velocity of an object changes over time'
Edited by ExplorerII on Sunday 10th August 10:29
This is what I bloody well meant, in relation to this whole thread.
https://www.youtube.com/watch?v=E43-CfukEgs
https://www.youtube.com/watch?v=E43-CfukEgs
IsaacNewton said:
Acceleration is not a force.
Acceleration is the rate of change of velocity of an object with respect to time caused by a force (or combinations of forces) acting on that object.
Gravity is a force, which, in the absence of any other forces, will cause an object to accelerate.
No, of course acceleration isn't a force in itself but a force is required to accelerate an object, correct? Acceleration is the rate of change of velocity of an object with respect to time caused by a force (or combinations of forces) acting on that object.
Gravity is a force, which, in the absence of any other forces, will cause an object to accelerate.
RobM77 said:
Firstly, the earth and you are actually accelerating up to meet your friend when he jumps, it's just that the amount they do it by is inconseqentially small compared to the amount he does it by towards the earth. The gravitational attractive force that the earth and your friend feel towards each other is the same, but the earth's mass is so much larger that it barely gets shifted at all by the force, whereas your friend is much lighter and easily accelerated downwards. However, it's worth pointing out that in actual fact the earth is covered in animals and objects that are moving, jumping and falling the entire time, so this little incident involving your friend jumping off the building would be balanced out by all the myriad of other things going on around the planet and you'd never be able to practically detect it. If the earth was a dead object though and your friend jumped from a building then yes, in theory the earth and your friend both move.
Moving on to Einstein's equivalence principle and your main question, your thought experiment has cut to the very core of it, and in fact the very same thought experiment was what led Einstein to develop the principle in the first place. Einstein said, as you correctly quote, that if you're locked in a closed box then you can't distinguish acceleration from gravity. So in your thought experiment, you on the ground in the sealed box would feel 9.81m/s/s and you wouldn't be able to work out whether you were on earth feeling gravity or in empty space away from gravity but accelerating upwards at 9.81m/s/s - the equivalence principle states that you can't tell which it is. As for your friend, if we imagine he's in also in a sealed box (and in a perfect vacuum, more of that later), and as you say he cannot feel any force at all on him (which you call 'weightless', as it is colloquially known), so he doesn't know if he's stationary in empty space or, as is the case, in a gravitational field accelerating at the same rate that the field would cause him to fall at. That is the equivalence principle. The fact that your friend feels no force does not mean that he's not moving, because again, the equivalence principle states that if you're at a constant speed in a closed box you've got no way of knowing that you're moving, so he just knows that he's either stationary in empty space or accelerating in a gravitational field. I promised I'd mention the vacuum: the reason I stated that your friend had to be in a vacuum was that in actual fact, air resistance will be acting on him falling from the building, and that will reduce his acceleration over time, so he could detect that change and work out what was going on and his impending doom, although probably not before he hit the ground!
Finally, a note no the principle of being 'weightess': astronauts in orbit around the earth are weightless, but not because there's no gravity, of course there's gravity, that's why their spaceship stays in orbit. They feel weightless because they are in effect free falling in the gravitational field the entire time, just like your friend in the box falling off the building.
HTH
Many thanks Rob, I enjoyed reading your very plausible explanation. Moving on to Einstein's equivalence principle and your main question, your thought experiment has cut to the very core of it, and in fact the very same thought experiment was what led Einstein to develop the principle in the first place. Einstein said, as you correctly quote, that if you're locked in a closed box then you can't distinguish acceleration from gravity. So in your thought experiment, you on the ground in the sealed box would feel 9.81m/s/s and you wouldn't be able to work out whether you were on earth feeling gravity or in empty space away from gravity but accelerating upwards at 9.81m/s/s - the equivalence principle states that you can't tell which it is. As for your friend, if we imagine he's in also in a sealed box (and in a perfect vacuum, more of that later), and as you say he cannot feel any force at all on him (which you call 'weightless', as it is colloquially known), so he doesn't know if he's stationary in empty space or, as is the case, in a gravitational field accelerating at the same rate that the field would cause him to fall at. That is the equivalence principle. The fact that your friend feels no force does not mean that he's not moving, because again, the equivalence principle states that if you're at a constant speed in a closed box you've got no way of knowing that you're moving, so he just knows that he's either stationary in empty space or accelerating in a gravitational field. I promised I'd mention the vacuum: the reason I stated that your friend had to be in a vacuum was that in actual fact, air resistance will be acting on him falling from the building, and that will reduce his acceleration over time, so he could detect that change and work out what was going on and his impending doom, although probably not before he hit the ground!
Finally, a note no the principle of being 'weightess': astronauts in orbit around the earth are weightless, but not because there's no gravity, of course there's gravity, that's why their spaceship stays in orbit. They feel weightless because they are in effect free falling in the gravitational field the entire time, just like your friend in the box falling off the building.
HTH
Edited by RobM77 on Monday 5th January 16:28
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