Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: rmolnav on 09/11/2017 07:56:38
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Recently I´ve been trying to convey the idea that what we feel in a gravity field isn´t actually gravity itself, but internal stresses originated by both the fraction of gravity somehow not allowed to make each part of our body accelerate (acc. to Newton´s 2nd Law), and the push and/or pull exerted on us by the "obstacle" that avoids our fully free fall (and the subsequent "chain" of reaction forces of each part of our body (acc. to Newton´s 3rd Law).
Whatever the deep nature of gravity, that´s quite clear, as far as I can understand.
But "apparently" (?) this Einstein´s journey first steps (before bringing up the idea of relativity), didn´t keep that in mind. "To be "politically correct", I have to say I must be wrong !! … Please kindly help me "ruminate" it over, in order to try and find where my error could be.
It´s better to go step by step, not to jump the gun (and possible errors …)
From an Einstein specialized site I´ve taken:
"...We, the crew of the spaceship shown on the right, are floating freely in space, far away from all major sources of gravity. Now imagine that there is another observer in a spaceship, shown on the left: The rocket engine of that observer's spaceship is firing and produces an acceleration of 9.8 meters (32 feet) per square second. This accelerated observer feels as heavy as we would feel on earth, since the gravitational acceleration with which an object on earth falls to the ground has that exact same value".
So far, so good. But, any further comments? Or ... any nuances to bring up? (for now, better if only directly about what said above …)
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You are correct that we feel only the force of the ground preventing us from falling towards the Earth's center of mass, not the gravitational pull itself.
Let us compare two cases in which a spaceship is accelerating at 1 G (9.8 m/s2):
1) A spaceship in free fall towards a gravitational body (let's say it's not in a stable orbit, but actually falling towards a very massive body that is very far away, so we don't have to worry about splattering our passengers during this thought experiment, but their path is still just a straight line)
2) A spaceship far from any gravitational fields, in vast empty space, which is firing its powerful rockets to achieve a constant acceleration of 1 G for the duration of this thought short experiment, without worrying about reaching relativistic speeds (for now).
In the first case the passengers feel weightless, while in the second they feel the 1 G acceleration as if they are standing on a surface on earth. Why are these cases different? Because of how the force acts.
Gravity pulls all parts of anything massive with exactly the same acceleration, no matter what (barring extreme cases of tidal forces etc.). The force is proportional to the mass, so the acceleration is constant, and every part of a person gets pulled in the same way at the same rate. A person in case 1 would be falling at the same acceleration whether they were in the spaceship or not.
In case two it would matter very much whether you were in (or attached to) the spaceship or not. Here there is a force that acts only on the spaceship, and if you are pressed against the floor of the spaceship the force will be conveyed to the passenger as well, felt as pushing, or if they are tethered they will feel the force as pulling. It is the fact that the thrust force acts indirectly on the passengers that it is felt, and that the gravitational force acts directly that it is not felt.
So two cases in which the acceleration is the same (passengers would see the same relative motion out their windows), but the apparent acceleration is either 0 or 1 G. Imagine the passengers in the first spaceship see the impending impact, and fire up their thrusters to deliver enough force to accelerate them at 1 G. Now they feel their weight (experiencing the force associated with a 1 G acceleration), because of the indirect force from the thrust, but if they look out their window, they can breath easier knowing that their velocity relative to the objecting pulling on them is now 0. Again, it matters whether they are in or tied to the ship, or if they are not!
Alternatively, they could navigate into a stable orbit, in which they are still accelerating at 1 G, but still in an apparently weightless free fall (because the direct action of the gravitational force is spread evenly through their bodies). And in this case it doesn't matter whether or not they are in the ship.
Does that help?
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Let' say we have one spaceship falling from a point in the gravitational field where the potential is very near to zero. They fall in a straight line path towards a black hole. They are far enough away so that by the time they reach the event horizon their instantaneous velocity will be very near to the speed of light. If we attempted to mimic the same with a spacecraft using fuel then it is said that the energy required will approach an infinite value as the velocity approaches c. So where does gravity get this energy from?
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Let' say we have one spaceship falling from a point in the gravitational field where the potential is very near to zero. They fall in a straight line path towards a black hole. They are far enough away so that by the time they reach the event horizon their instantaneous velocity will be very near to the speed of light. If we attempted to mimic the same with a spacecraft using fuel then it is said that the energy required will approach an infinite value as the velocity approaches c. So where does gravity get this energy from?
The kinetic energy comes from the potential energy of being so far from the black hole (think of it as being really high "above" the black hole). If we define infinitely far away from the black hole as 0 potential energy, then any finite distance away will have negative potential energy. This potential energy becomes increasingly negative as you fall down towards the black hole, so for conservation of energy to be maintained, your kinetic energy (which must be positive) increases such that the sum of potential and kinetic energy doesn't change from the original (assuming there is no other way to dissipate or transfer the energy).
Note that energy is not necessarily conserved between reference frames. (the people on the spaceship falling into the black hole at relativistic speeds may not agree with those in a different frames of reference as to how much kinetic and potential energy they have--but each will observe that the sum of potential and kinetic energies is constant)
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Thank you. Your post does help … but also reinforces my idea that we have to be very careful in our reasoning. I asked for any comments or nuances relative to what quoted, trying to go slowly but as surely as possible … I do appreciate your effort, but I´m afraid you have jump the gun (what doesn´t make the discussion any easier) … and have been not sufficiently accurate, as far as I can understand:
Gravity pulls all parts of anything massive with exactly the same acceleration, no matter what (barring extreme cases of tidal forces etc.). The force is proportional to the mass, so the acceleration is constant, and every part of a person gets pulled in the same way at the same rate.
Perhaps I should have included the link of the site:
http://www.einstein-online.info/spotlights/geometry_force
so that we all could use same examples in our discussion.
If we make a "close up" when looking at what quoted in my initial post, we can say that "The rocket engine of that observer's spaceship is firing and produces an acceleration of 9.8 meters (32 feet) per square second. This accelerated observer feels as heavy as we would feel on earth, since the gravitational acceleration with which an object on earth falls to the ground has that exact same value" is a rather MISLEADING statement, because:
1) "This accelerated observer feels as heavy as he would feel on earth, since the gravitational acceleration …"
He DOESN´T actually FEEL any "heaviness" globally … He feels internal stresses caused both by the spaceship push (N.´s 2nd Law: chosen 9.8 m/s2 times its mass m), and inertial reaction forces on each part of his body kind of trying to keep their velocity constant (Newton´s 3rd Law: a total of 9.8m in opposite direction).
2)"… since the gravitational acceleration with which an object on earth falls to the ground has that exact same value": that is NOT THE HOLE picture. If that object/person were stopped by some obstacle, he would feel internal stresses originated by both the other object push (N.´s 1st and 2nd Law: upward 9.8m), and gravity pull exerted by Earth on each part of its body (universal gravity law: a total of 9.8m downward).
Certainly our sensations would be similar, but just because the artificial acceleration given to us when out of gravity, has been chosen equal to the natural Earth´s gravity g.
And mentioned laws lead us to similar bottom end, but not equal at all. If in our body we had stress gauging devices sufficiently accurate (e.g., as LIGO gauging devices), we would find meaningful differences, because Earth´s pull exerted on each unit of mass is the nearer to our head (standing), the smaller. That counts when the spaceship is still standing on ground, but not when accelerated in space with no gravity …
Do you agree? … If not, don´t exit ate and tell me (but step by step, please ...). If you do, NEXT STEP could be another careful analysis of other quote form linked site:
"Our accelerated observer has a clear notion of "up" and "down" - when he looks up, he sees all freely drifting observers and their space stations "fall downwards", in the direction of his own spaceship's floor. "Upwards" is the direction in which his spaceship is accelerating. But there is no gravity in this situation. All the observers in freely drifting spaceships (rocket engines shut off) are in agreement: The fact that the accelerated observer sees objects "fall" is merely an artefact, brought about by his spaceship's acceleration - it vanishes as soon as you leave the accelerated reference frame and change to a free-falling one".
Any further comments? Or, just any nuances to bring up?
And again, thank you.
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Yes, I will accept that my explanation is entirely qualitative, and I may have used a few terms loosely (however, I tried my best to discuss "perceived weight" to make clear that I was not equating the mechanisms behind those perceptions). My explanation was also purely "Newtonian," and isn't necessarily the best lens to view Einstein's theories with.
Thank you for the link. I have only a cursory understanding of general relativity, but I do understand that many of the open questions about gravity from the Newtonian perspective can be addressed by thinking of gravity as a manifestation of curved spacetime due to high mass (and/or energy) concentrations, rather than an actual attractive force. I invite other, more knowledgeable, folks to take it from here...
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Let' say we have one spaceship falling from a point in the gravitational field where the potential is very near to zero. They fall in a straight line path towards a black hole. They are far enough away so that by the time they reach the event horizon their instantaneous velocity will be very near to the speed of light. If we attempted to mimic the same with a spacecraft using fuel then it is said that the energy required will approach an infinite value as the velocity approaches c. So where does gravity get this energy from?
The kinetic energy comes from the potential energy of being so far from the black hole (think of it as being really high "above" the black hole). If we define infinitely far away from the black hole as 0 potential energy, then any finite distance away will have negative potential energy. This potential energy becomes increasingly negative as you fall down towards the black hole, so for conservation of energy to be maintained, your kinetic energy (which must be positive) increases such that the sum of potential and kinetic energy doesn't change from the original (assuming there is no other way to dissipate or transfer the energy).
Note that energy is not necessarily conserved between reference frames. (the people on the spaceship falling into the black hole at relativistic speeds may not agree with those in a different frames of reference as to how much kinetic and potential energy they have--but each will observe that the sum of potential and kinetic energies is constant)
You missed the point. Where does the gravitational field get the exponentially increasing energy from to accelerate a mass up to light speed? The field surely doesn't have boundless energy. If us accelerating an object to light speed required an exponential increase in energy then how is gravity supposed to sidestep this?
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Let' say we have one spaceship falling from a point in the gravitational field where the potential is very near to zero. They fall in a straight line path towards a black hole. They are far enough away so that by the time they reach the event horizon their instantaneous velocity will be very near to the speed of light. If we attempted to mimic the same with a spacecraft using fuel then it is said that the energy required will approach an infinite value as the velocity approaches c. So where does gravity get this energy from?
The kinetic energy comes from the potential energy of being so far from the black hole (think of it as being really high "above" the black hole). If we define infinitely far away from the black hole as 0 potential energy, then any finite distance away will have negative potential energy. This potential energy becomes increasingly negative as you fall down towards the black hole, so for conservation of energy to be maintained, your kinetic energy (which must be positive) increases such that the sum of potential and kinetic energy doesn't change from the original (assuming there is no other way to dissipate or transfer the energy).
Note that energy is not necessarily conserved between reference frames. (the people on the spaceship falling into the black hole at relativistic speeds may not agree with those in a different frames of reference as to how much kinetic and potential energy they have--but each will observe that the sum of potential and kinetic energies is constant)
You missed the point. Where does the gravitational field get the exponentially increasing energy from to accelerate a mass up to light speed? The field surely doesn't have boundless energy. If us accelerating an object to light speed required an exponential increase in energy then how is gravity supposed to sidestep this?
I don't have the answers, but wikipedia does!
https://en.wikipedia.org/wiki/Surface_gravity#Surface_gravity_of_a_black_hole
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Let' say we have one spaceship falling from a point in the gravitational field where the potential is very near to zero. They fall in a straight line path towards a black hole. They are far enough away so that by the time they reach the event horizon their instantaneous velocity will be very near to the speed of light. If we attempted to mimic the same with a spacecraft using fuel then it is said that the energy required will approach an infinite value as the velocity approaches c. So where does gravity get this energy from?
The kinetic energy comes from the potential energy of being so far from the black hole (think of it as being really high "above" the black hole). If we define infinitely far away from the black hole as 0 potential energy, then any finite distance away will have negative potential energy. This potential energy becomes increasingly negative as you fall down towards the black hole, so for conservation of energy to be maintained, your kinetic energy (which must be positive) increases such that the sum of potential and kinetic energy doesn't change from the original (assuming there is no other way to dissipate or transfer the energy).
Note that energy is not necessarily conserved between reference frames. (the people on the spaceship falling into the black hole at relativistic speeds may not agree with those in a different frames of reference as to how much kinetic and potential energy they have--but each will observe that the sum of potential and kinetic energies is constant)
You missed the point. Where does the gravitational field get the exponentially increasing energy from to accelerate a mass up to light speed? The field surely doesn't have boundless energy. If us accelerating an object to light speed required an exponential increase in energy then how is gravity supposed to sidestep this?
I don't have the answers, but wikipedia does!
https://en.wikipedia.org/wiki/Surface_gravity#Surface_gravity_of_a_black_hole
The Schwarzschild solution of k = 1/4M seems familiar. I have read something on that but can't place it. The undefined nature of the acceleration due to gravity at the event horizon is something I'm looking into.
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I know that in units of c=G=1 the value 2M is the radius of the event horizon. Then 3M is the photon sphere. I wish I could remember why 4M was significant.
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I have only a cursory understanding of general relativity, but I do understand that many of the open questions about gravity from the Newtonian perspective can be addressed by thinking of gravity as a manifestation of curved spacetime due to high mass (and/or energy) concentrations, rather than an actual attractive force. I invite other, more knowledgeable, folks to take it from here...
I´m not a relativity expert either whatsoever ... But the purpose of this thread is to discuss about what it is said triggered Einstein´s leap from Newton´s theories to his.
As far as I can see, reasons given to say those cases (elevator and others) are not explainable within Newton´s Mechanics, are flawed.
And from a careful and correct analysis of them, it can´t necessarily be deduced that another theory is necessary.
We know many facts tell us Einstein was right, and I would´t dare say the opposite. But I guess he "saw" something more, beyond the apparent oddity (within Newton´s Mechanics) of those experiments.
I could be wrong, and that´s why I proposed a careful analysis, step by step, of the considered roots of the equivalence "principle".
You know, there are scientists who go far beyond just "equivalence" (?), when exposing their ideas on the matter. E.g., after explaining the elevator experiment:
1st scientist: "Einstein realized there is no way to tell the difference between sitting in a gravitational field and being accelerated (by the way: that is not exact, as I explained in my last post ...) They are equivalent situations".
2nd: "The fact that these two effects are the same, give the same results, means that gravity is acceleration, NOT JUST LIKE ACCELERATION , IT´S THE SAME THING".
(from a Spanish tv program I saw, "Inside Einstein´s Mind")
Perhaps that is true, but it can´t be deduced from those experiments, as far as I can understand !!
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The force of gravity is dispersed evenly throughout an object. When we apply a force to an object it is via a surface and stresses propagate through the object. That is the ONLY difference. Since there is a gravitational force it has limits just like the force we apply. It may diminish at the event horizon.
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Where does the gravitational field get the exponentially increasing energy from to accelerate a mass up to light speed? The field surely doesn't have boundless energy. If us accelerating an object to light speed required an exponential increase in energy then how is gravity supposed to sidestep this?
Boundless energy would be required only if a massive object were accelerated to "c". This, we are told cannot happen.
If the energy of gravity has its origin in the Big Bang, then enough energy is available to take the entire Universe back to a single point. What more would be needed?
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The force of gravity is dispersed evenly throughout an object
Sorry, but hat would be right only if our object were isotropic, at least as far as density is concerned ...
In your words, if total mass were also dispersed evenly through it !
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I'm not sure what you're talking about rmolnav?
Whatever idea or hypothesis you have you will need something more than what's already there in form of a theory (in this case seeming to be about the equivalence principle?). That means you will need to find whatever you want to replace it with explaining some fact unexplained by the 'older theory'. Newton is in cooperated in Relativity, as a limited case, with Relativity covering more circumstances.
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And yes, the equivalence principle between a 'gravity' and a very specific type of acceleration are accepted to make perfect sense, for over a hundred years now. Here is a good description http://eagle.phys.utk.edu/guidry/astro421/lectures/lecture490_ch6.pdf
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Also, a gravitational acceleration isn't the same as a accelerating rocket. A accelerating rocket expends/transforms 'internal energy' (in)to accelerating. The rocket free falling doesn't. Look up geodesics.
What you might want to argue is the fact that to construct the equivalence to a gravitational 'field' you need to expend energy, and so expect a equivalence to be correct in the case of the free falling rocket? That 'something' needs to expend 'energy' there too? Well, locally measured there is nothing spending energy as far as I know. Neither Earth, nor the rocket. When it comes to 'SpaceTime' you might be able to argue differently though. But we have a problem there, gravity doesn't go from one state to another, it has one sign, there is no such thing as 'negative gravity' and it doesn't transform from state to state.
Although :)
https://www.forbes.com/sites/startswithabang/2017/02/28/is-dark-matter-about-to-be-killed-by-emergent-gravity/#3e7e574c5359
But that's a different kettle of fish
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That means you will need to find whatever you want to replace it with explaining some fact unexplained by the 'older theory'. Newton is in cooperated in Relativity, as a limited case, with Relativity covering more circumstances.
Thank you.
In short: I consider that analogies and differences in cases such as the elevator when still on earth surface, and when far from any gravity field, but artificially given "g" acceleration, can be explained within Newton´s Mechanics. Also when comparing an object free fall (in a gravitational field), and an object really with no gravity (very far from any massive celestial object).
And I was trying to make a detailed analysis of them, to justify my stand. To say things such as "he feel weightless ...", or other similar ones, can hide important clues to the issue. Because we never actually feel our "weight", gravity itself: we feel internal stresses, and only when gravity somehow is not allowed to accomplish its theoretical "duty" of giving us "g" acceleration ...
And applying carefully Newton´s Laws those cases can be fully explained, as far as I can understand.
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The force of gravity is dispersed evenly throughout an object
Sorry, but hat would be right only if our object were isotropic, at least as far as density is concerned ...
In your words, if total mass were also dispersed evenly through it !
If density were a factor then denser objects would fall faster in a gravitational field than those of lower density. This is different to the source of a gravitational field where density variations do matter.
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Where does the gravitational field get the exponentially increasing energy from to accelerate a mass up to light speed? The field surely doesn't have boundless energy. If us accelerating an object to light speed required an exponential increase in energy then how is gravity supposed to sidestep this?
Boundless energy would be required only if a massive object were accelerated to "c". This, we are told cannot happen.
If the energy of gravity has its origin in the Big Bang, then enough energy is available to take the entire Universe back to a single point. What more would be needed?
A single object like a black hole doesn't have the energy of the whole universe at it's disposal.
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If density were a factor then denser objects would fall faster in a gravitational field than those of lower density
But you were talking about a single object, "The force of gravity is dispersed evenly throughout an object".
And on denser parts gravitational exerted forces (per volume unit) are bigger.
If solid object, it´s clear all parts only could move at same speed and acceleration ... That would generate internal stresses, in such a way that total forces exerted on any part (external and internal), divided by its mass, would have to be equal to the common acceleration, the "g" of the gravitational field at that spot.
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There has to be a distinction between the action of the gravitational field external to the source and the source itself. Density variations in the source affect the action upon external objects. I have seen no evidence that density variations in an object affects the action of the field upon said object. If the field was uniform then those density variations have to be irrelevant. Otherwise the feather and hammer experiment on the moon may have been far less mundane.
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I have seen no evidence that density variations in an object affects the action of the field upon said object. If the field was uniform then those density variations have to be irrelevant.
That´s right for relatively small objects. But let us consider our moon, in earth´s gravitational field.
It´s somehow in free falling, because only gravity there affects its movement. But due to its initial speed, it´s rotating around earth (more precisely, around earth/moon barycenter). And it´s tide locked to earth, with two opposite bulges as our planet (but, being all its surface solid, relatively much smaller), one of them towards us.
At last phase of that locking, with very low angular spinning speed, tidal friction was tending to null.
Why did it stop in its current position? My "educated" (?) guess was (long ago) that as it must be anisotropic, in its current position density distribution must be such that some mass concentration happens at farther and nearer parts, corresponding to parts were centrifugal and centripetal forces are bigger, respectively.
It probably even passed a little bit that position, and spinned back afterwards, with a kind of "oscillating" spin stopping.
That was my guess, and later I learnt some facts that seem to agree with it. But I´ll leave it there.
If moon had been fully isotropic, most probably we´d now be seeing a different "semi-moon" ...
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At last phase of that locking, with very low angular spinning speed, tidal friction was tending to null.
Why did it stop in its current position?
I hope nobody is mislead by that: I mean with very little higher angular speed than the final one of 2π radians avery some 29 days.
And when saying "spinned back" I actually mean that it decreased a little its spin, oscillating around current angular speed, less and less every time ...
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A single object like a black hole doesn't have the energy of the whole universe at it's disposal.
Of course not; but would it not be proportional to the energy of the Universe?
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I know I’ve posted this, or similar, in the past, but have not mastered the skill of finding past posts quickly; so please forgive any repetition
Suppose you are in a box and have with you two marbles.
Release your marbles simultaneously from the top of the box. They will fall to the bottom. If you are being accelerated, their trajectories will be parallel, but if you are on the surface of a planet their trajectories will converge on the centre of the planet, because gravity operates as though the entire mass of the gravitating object were at its centre; so the marbles will move towards the centre of the planet; thus they will converge as they fall.
I think this doesn’t challenge the equivalence principle, it just shows that it is, to some extent, an analogy, and as such is open to “nit-picking”
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Oh no. On the contrary, that is challenging the equivalence principle. Since it is stated that there is no way to tell the difference.
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I think this doesn’t challenge the equivalence principle, it just shows that it is, to some extent, an analogy, and as such is open to “nit-picking”
Oh no. On the contrary, that is challenging the equivalence principle. Since it is stated that there is no way to tell the difference.
Thank you. That difference between your opinions is in the "root" of my decision to initiate this thread ...
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Obviously, one would need ridiculously sensitive equipment to test this, but it seems to work, in principle.
Another test would be to drop your marbles, simultaneously, from different heights. They should maintain that difference under acceleration, but move further apart under gravity.
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Obviously, one would need ridiculously sensitive equipment to test this, but it seems to work, in principle.
Thank you.
Another similar case which challenges the equivalence principle:
Also in the box, but with a long bar (very accurately isotropic) in the box, and comparing the two cases when no gravity at all, and with gravity but in free fall.
If we had sufficiently accurate strain devices installed along the bar, we would find that in one of the cases, the bar never stretches. But in the other, the bar stretches slightly, and more or less depending on its orientation in the box …
This later case would be the one with gravity.
I suppose you´ve guessed why. But I´ll leave it there … Kind of a riddle!
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I take your point, but would the bar stretch if it were orientated at right angles to the direction of the gravitational attraction?
Not clear about the "riddle"; possibly because my brain isn't working too well at the moment. I hope it's only temporary. :)
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I take your point, but would the bar stretch if it were orientated at right angles to the direction of the gravitational attraction?
Not clear about the "riddle"; possibly because my brain isn't working too well at the moment. I hope it's only temporary.
Thank you. I do hope the same, if that were the case ... I remember your user´s name from many interesting post!
Perhaps I have the advantage of having been ruminating on similar situations in my very long discussion on tides (and centrifugal forces), where not uniform distribution of gravitational pull per unit of mass is of paramount importance to really understand those phenomena (should I be more politically correct, and add "as far as I can understand"? ... Frankly, I "feel" really sure ...
The bar would be slightly stretched not when you say ... the opposite: the more in line with the actual gravitational pull, the more.
Why? "Lower" bar parts would be slightly closer, to the C.G. of the celestial object causing gravity, than farther ones. But being a solid, all of them have to accelerate the same. The bar would be accelerating an average, what implies that "lower" parts would be exerting an additional pull (though really, really tiny) on "upper" ones ...
As you said, "one would need ridiculously sensitive equipment to test this", but not more sensitive than, e.g., LIGO´s ...
By the way, the bar even would tend to get in line with the field, rather than staying in another orientation ...
And, if the bar were very, very long ... not special equipment would be needed.
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Oh no. On the contrary, that is challenging the equivalence principle. Since it is stated that there is no way to tell the difference.
Jeff
I don’t view it that way. I read Einstein’s model of the equivalence principle to be based on a uniform gravitational field, the grav field of a planet is not uniform so you can tell the difference.
Instead of the iron bar idea think about dropping a handful of marbles high above a planet’s surface they would slowly spread out in the direction of the planet (radially) but draw slightly together tangentially as they fall.
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Instead of the iron bar idea think about dropping a handful of marbles high above a planet’s surface they would slowly spread out in the direction of the planet (radially) but draw slightly together tangentially as they fall.
That´s what Bill S already said in #24 ...
And regarding what you say "I read Einstein’s model of the equivalence principle to be based on a uniform gravitational field, the grav field of a planet is not uniform so you can tell the difference" ... I can´t see your point! As far as I can understand, all gravitational fields would not be uniform, if to consider them "uniform" their "g" ought to be the same whatever the distance to the C.G of the celestial object causing the gravity !!??
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Oh no. On the contrary, that is challenging the equivalence principle. Since it is stated that there is no way to tell the difference.
Jeff
I don’t view it that way. I read Einstein’s model of the equivalence principle to be based on a uniform gravitational field, the grav field of a planet is not uniform so you can tell the difference.
Instead of the iron bar idea think about dropping a handful of marbles high above a planet’s surface they would slowly spread out in the direction of the planet (radially) but draw slightly together tangentially as they fall.
Yes of course that is right. Sorry Bill.
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Thanks for the kind comment.
Why? "Lower" bar parts would be slightly closer, to the C.G. of the celestial object causing gravity, than farther ones.
No problem with that, but what about if the bar were lying perpendicular to the direction to the direction of the gravitational attraction? Some slight thickening of the bar, perhaps?
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No problem with that, but what about if the bar were lying perpendicular to the direction to the direction of the gravitational attraction? Some slight thickening of the bar, perhaps?
Thank you.
Well ... If we are "infinitely" accurate, you are right. If cylindrical, it would get a kind of very, very slightly elliptical section.
But it would be in a quite unstable equilibrium: it should be "perfectly" perpendicular to keep so, and with absolute absence of other affecting factors ... Otherwise, it would slowly tend to get in line with gravity pull direction. Wouldn´t it?
And it could reach that orientation after a little bit oscillating movement, smaller and smaller each time ("∞²" accuracy required now !!)
Well, after all it would be something similar to what happened to our Moon long ago, when it got tidal locked ... Though it continues to oscillate a little bit, due to relatively small "discontinuities" in total dynamic factors that affect our Moon.
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Molnav, Just for interest, has the original question/point in the OP been addressed?
I always feel it's a shame that interesting threads rarely have any sort of "conclusion".
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Just for interest, has the original question/point in the OP been addressed?
I always feel it's a shame that interesting threads rarely have any sort of "conclusion".
You are right: we have mainly been discussing things somehow in relation to the original question, but not always directly ...
I have in mind a kind of conclusive post, but before I was trying to get more readers´s comments about some details kind of "hidden" in the original question, which I mentioned. Please have a look at:
#4 : "… Do you agree? … If not, don´t hesitate and tell me (but step by step, please ...). If you do, NEXT STEP could be another careful analysis of other quote form linked site: …"
#10: "... I could be wrong, and that´s why I proposed a careful analysis, step by step, of the considered roots of the equivalence principle".
#16: "… In short: I consider that analogies and differences, in cases such as the elevator when still on earth surface, and when far from any gravity field but artificially given "g" acceleration, can be explained within Newton´s Mechanics. Also when comparing an object in free fall (in a gravitational field), and an object really with no gravity (very far from any massive celestial object).
And I was trying to make a detailed analysis of them, to justify my stand. To say things such as "he feels weightless …" …"
In any case, we can´t expect a proper "conclusion" ... What supposedly Einstein deduced from the discussed principle seems to have been proven right ... So, I wouldn´t dare say Einstein was wrong ... Perhaps he saw something more I haven´t even been able to imagine so far !!
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Looking through the # Refs you gave, I think I’m a bit out of my depth, so if I can ask any questions that do no more than highlight the naivety of the “hitch-hiker”, I’m happy to do so, and may well learn something along the way.
The following are a couple of examples.
#4. “He DOESN´T actually FEEL any "heaviness" globally … He feels internal stresses caused both by the spaceship push (N.´s 2nd Law: chosen 9.8 m/s2 times its mass m), and inertial reaction forces on each part of his body kind of trying to keep their velocity constant (Newton´s 3rd Law: a total of 9.8m in opposite direction)”.
I’m not clear as to how this impacts on the equivalence principle.
“…since the gravitational acceleration with which an object on earth falls to the ground has that exact same value": that is NOT THE HOLE picture. If that object/person were stopped by some obstacle, he would feel internal stresses originated by both the other object push (N.´s 1st and 2nd Law: upward 9.8m), and gravity pull exerted by Earth on each part of its body (universal gravity law: a total of 9.8m downward)”.
Are you saying that the equivalence principle covers the case where a body in free fall is interrupted by some external influence?
I suspect not, but if you are able to make your points clear to someone with my limited knowledge, I think you are well on the way to achieving the clarity you seem to be seeking.
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#4. “He DOESN´T actually FEEL any "heaviness" globally … He feels internal stresses caused both by the spaceship push (N.´s 2nd Law: chosen 9.8 m/s2 times its mass m), and inertial reaction forces on each part of his body kind of trying to keep their velocity constant (Newton´s 3rd Law: a total of 9.8m in opposite direction)”.
I’m not clear as to how this impacts on the equivalence principle.
If we don´t actually feel gravity directly, but only through a kind of interface (those internal stresses caused by those forces), for me it´s not especially meaningful to say that we feel as weightless when in free fall as when still, but far from any gravitational field (equivalence principle) ... Of course it is so, but simply due to the fact that in the first case the hole gravity attraction is "spent" in moving us with "g" acceleration (no internal stresses in our body), and in the second no force is being exerted on us at all …
“…since the gravitational acceleration with which an object on earth falls to the ground has that exact same value": that is NOT THE HOLE picture. If that object/person were stopped by some obstacle, he would feel internal stresses originated by both the other object push (N.´s 1st and 2nd Law: upward 9.8m), and gravity pull exerted by Earth on each part of its body (universal gravity law: a total of 9.8m downward)”.
Are you saying that the equivalence principle covers the case where a body in free fall is interrupted by some external influence?
Not. But please note the complete quote (from linked site) was:
"The rocket engine of that observer's spaceship is firing and produces an acceleration of 9.8 meters (32 feet) per square second. This accelerated observer feels as heavy as we would feel on earth, since the gravitational acceleration with which an object on earth falls to the ground has that exact same value",
and I was just saying that last sentence "This accelerated ... same value" is NOT THE HOLE picture", that he feels equally "as heavy" only because those internal stresses are caused by equal forces in both cases ...
Not sufficient to deduce that gravity and acceleration are the same thing ! (at least to me ...)
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"This accelerated ... same value" is NOT THE HOLE picture", that he feels equally "as heavy" only because those internal stresses are caused by equal forces in both cases ...
Not sufficient to deduce that gravity and acceleration are the same thing ! (at least to me ...)
I'm not sure that the equivalence principle actually says they are the same thing. My understanding is that it says one is indistinguishable from the other, in specified circumstances.
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I'm not sure that the equivalence principle actually says they are the same thing
You´re right, as far as the principle itself says ... But, as I said in #10:
"You know, there are scientists who go far beyond just "equivalence" (?), when exposing their ideas on the matter. E.g., after explaining the elevator experiment:
1st scientist: "Einstein realized there is no way to tell the difference between sitting in a gravitational field and being accelerated (by the way: that is not exact, as I explained in my last post ...) They are equivalent situations".
2nd: "The fact that these two effects are the same, give the same results, means that gravity is acceleration, NOT JUST LIKE ACCELERATION , IT´S THE SAME THING".
(from a Spanish tv program I saw, "Inside Einstein´s Mind").
I think that program was from NOVA.
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One would then have to ask if acceleration curves spacetime.
Of course, that would be after you asked if gravity curves spacetime, or if that is just a mathematical concept.
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NOT JUST LIKE ACCELERATION , IT´S THE SAME THING".
I believe this is a mistranslation/misunderstanding of the original German which means equivalent to rather than exactly the same as. The same problem occurs with mass/energy equivalence.
To an extent it is similar to extending an analogy beyond its original meaning.
As I said before, Einstein was using a uniform gravitational field in his illustration so certainly didn’t include the grav field of massive bodies.
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Here you have the NOVA page with the TV program I saw.
In some countries, mine included, the video can´t be seen, due to license restrictions. But fortunately one can read the transcription ...
http://www.pbs.org/wgbh/nova/physics/inside-einsteins-mind.html
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The EP seed
A passage based on Einstein's autobiography 1946.
"[a thought experiment that came to him in 1907: nothing less than the definition of the equivalence principle, later developed in his general relativity theory. It occurred to Einstein – thinking first of all in visual terms, as was usual for him – that if a man were falling from the roof of his house and tried to let anything drop, it would only move alongside him, thus indicating the equivalence of acceleration and gravity. In Einstein's words, "the acceleration of free fall with respect to the material is therefore a mighty argument that the postulate of relativity is to be extended to coordinate systems that move nonuniformly relative to one another . . . ."]"
"Einstein's Third Paradise", Daedalus (Fall 2002),
© 2003 by Gerald Holton
source aip.org
Sometimes reading about the person is as interesting as their inventions.
The success of the relativity principle in SR encouraged him to apply it in GR. He did not see a need for a special reference frame, if a general one would work. The results of unification, electric and magnetic, gravitational mass and inertial mass, mass and energy, proved correct.
The elevator example.
The left example is a box accelerating upward at g, with Al (small box) at the bottom center. Al records his weight standing on a scale. A light beam enters a small hole centered on the right wall. As the light moves from the right wall to the left wall, the box moves a tiny distance y upward. Al perceives the light to strike the left wall lower than the point of entry.
The right example is an identical box resting on the ground, with Al standing on a scale, weighing the same as in the left example. If the laws of physics are the same in both frames of reference, Al should see the light beam move in a curved path moving through the box.
The effect of light moving through a g-field was verified in a 1919 solar eclipse. Similar effects are observed today as gravitational lensing.
The equivalence holds for uniform g-fields, or small space and time intervals (to avoid tidal effects).
https://app.box.com/s/0gobsjcp4ukr6kaikvli1gc966ajvztf
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“if a man were falling from the roof of his house and tried to let anything drop, it would only move alongside him, thus indicating the equivalence of acceleration and gravity. In Einstein's words, "the acceleration of free fall with respect to the material is therefore a mighty argument that the postulate of relativity is to be extended to coordinate systems that move nonuniformly relative to one another . . . ."]"
The success of the relativity principle in SR encouraged him to apply it in GR. He did not see a need for a special reference frame, if a general one would work. The results of unification, electric and magnetic, gravitational mass and inertial mass, mass and energy, proved correct.
The elevator example.
The equivalence holds for uniform g-fields, or small space and time intervals (to avoid tidal effects).
I think these quotes are fundamental to understanding the equivalence principle, which is often misquoted.
For an object falling towards the earth surface, this application of reference frame for nonuniform motion does allow us to consider that (relatively) the object is stationary and the surface is accelerating towards it, but only for “uniform g-fields, or small space and time intervals”. To try and apply this in the larger scale is clearly unreasonable, however, as you say this simple thought process led to a very predictive theory.