the equivalence principle paradox
Discussion
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
ExplorerII said:
This is what I bloody well meant, in relation to this whole thread.
https://www.youtube.com/watch?v=E43-CfukEgs
What an amazing facility. And there's something about that experiment that never fails to stir my sense of wonder.https://www.youtube.com/watch?v=E43-CfukEgs
ExplorerII said:
I understand that the forces of Gravity and acceleration are indistinguishable
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.
ExplorerII said:
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'
Yes, acceleration is the rate of change of velocity with respect to 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
When an object is in orbit around Earth, gravity creates a force that acts on the object accelerating it towards the earth. Hence the object in orbit has weight. You are not weightless in orbit.
http://en.m.wikipedia.org/wiki/Weight
otolith said:
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.
this is the answerExplorerII 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?
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
Edited by RobM77 on Monday 5th January 16:28
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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