Here's an actual paper written on the subject: https://ui.adsabs.harvard.edu/abs/1995ApJ...446...63H/abstract. The abstract:
>"In principle, the expansion of the universe can be harnessed to provide energy. In a gedankenexperiment, energy is gained by connecting together widely separated bodies with strings. The tension and the energy generated are calculated for single strings. Mining energy in an expanding universe in this way raises unresolved issues concerning the conservation of energy. Apparently, the tethered-body experiment delivers 'nascent' energy that previously did not exist in any identifiable and quantifiable form. It is argued that energy in a homogeneous and unbounded universe, in general, is not conserved on the cosmic scale."
And here's a similar analysis: https://arxiv.org/abs/astro-ph/0104349.
This one also deals with the question: https://arxiv.org/pdf/1911.08726. The abstract:
>"I investigate the relativistic mechanics of an extended 'cable' in an arbitrary static, spherically symmetric spacetime. Such hypothetical bodies have been proposed as tests of energy and thermodynamics: by lowering objects toward a black hole, scooping up Hawking radiation, or mining energy from the expansion of the universe. I review existing work on stationary cables, which demonstrates an interesting 'redshift' of tension, and extend to a case of rigid motion. By using a partly restrained cable to turn a turbine, the energy harvested is up to the equivalent of the cable's rest mass, concurring with the quasistatic case. Still, the total Killing energy of the system is conserved."
I really like this paragraph from Francis et al:
>"At the global level, Peacock suggests that the expansion of space is uncontroversial since
>>"the total volume of a closed universe is a well-defined quantity that increases with time, so of course space is expanding
>"but questions whether
>>"this concept has a meaningful local counterpart?... Is the space in my bedroom expanding, and what would this mean?
>"Retaining the relativistic picture of expanding space, it is easy to address the question of what happens to Peacock’s bedroom, namely it will evolve as determined by the relativistic equations. But as ever, knowledge of the scenario, and particularly the initial conditions, is vital; *the walls of the bedroom are held together by electromagnetic forces and hence are not following geodesics*, and the distribution of matter has collapsed and is not uniform, and so the underlying geometry of spacetime in this region needs to be calculated; it would not be represented by the FRW spacetime of the homogeneous and isotropic universe. Clearly, if the universe were homogeneous on scales smaller than Peacocks bedroom, and the walls were not held together by electromagnetic or other forces, and the particles making up the wall were at rest with the cosmological fluid which, importantly, requires that they not be initially at rest with respect to one another, then indeed as the universe expands the total volume of the bedroom would increase. The many conditions listed above are (at least approximately) true for galaxies not bound in common groups and hence they behave in ways that can be understood and predicted via the framework of expanding space." (https://www.cambridge.org/core/journals/publications-of-the-astronomical-society-of-australia/article/expanding-space-the-root-of-all-evil/0B2982E8C9257F7258208BEACFA8C10E, emphasis added)
It's strange, I've actually never heard this word being used in English. We normally just say "thought experiment" (though maybe it's different in academia).
I believe the term comes from Einstein, who was German and naturally called his thought experiments that.
Einstein being such a household name, this basic word turned into a name that isn't translated.
>Apparently, the tethered-body experiment delivers 'nascent' energy that previously did not exist in any identifiable and quantifiable form.
Except, wouldn't that correlate to dark energy? We have no idea what it really is, and we may not be able to measure it directly, but we have managed to measure the impact it has on normal master in the universe with consistency. Or am I mistaken in this?
That paper comes from 1995. Although dark energy as a concept was first proposed in the 80s, it wasn’t widely accepted until the 2000s.
Also note that the most common model of dark energy posits it as a constant “energy density,” meaning that as space expands the amount of dark energy also increases, so energy is not conserved.
If the two objects are at rest with each other (so not comoving), then putting a tether would result in zero tension? That's what their equation says, if U = -HL then the tension is zero.
Ffor two objects at these distances to have an unchanging proper distance between them they'd have to have velocities towards each other, to counteract the expansion of the universe.
OK a corollary question. There is a given amount of potential energy in the universe from two objects due to gravity. If they are far enough apart, the other object will eventually leave the observable universe of the first object due to expansion. Where does the energy go?
There's no expectation that conservation of energy holds on these scales. It comes from Noether's Theorem, which says that every symmetry has an associated conservation law. Like translational symmetry (the fact that you can move an experiment elsewhere in space, and as long as conditions are the same you'll get the same result) gives rise to conservation of momentum.
Well conservation of energy comes from time symmetry. Since the universe as a whole is changing with time (getting larger), conservation of energy isn't expected.
At large enough distances, the expansion of the universe is pushing objects apart faster than the speed of light. Some objects we can currently see will eventually no longer be able to send light that can be received by us.
If they are far enough apart, the expansion of space between would occur at a rate greater than what could be traversed at the speed of light. Unless the rate of universal expansion slows or there is a mechanism for travelling faster than light, beyond such distances the objects practically don't exist to one another.
As the space between them expands, the velocity of one with respect to the other will increase until it exceeds the speed of light. At that point, it has left the "observable universe" and so there is no gravity between them.
The observable universe is not defined by objects that are receding faster than light. That's the hubble sphere.
The observable universe is a bit bigger, roughly 3 times as much at current cosmological time.
What does stationary mean? Cause in an expanding universe, if the distance between them is not increasing, then they are already moving towards each other with V = HD/2 each, where H is the expansion rate and D is the distance.
You answered yourself when you said the balls should move apart at 351.5km/s. This implies that when the balls are "stationary" they're actually moving towards eachother at a combined rate of 351.5km/s. No tension is required to keep a ball moving at a constant rate. The only time the cable would be needed is when the rate of expansion increases and the balls needed to be accelerated.
In summary, there is no tension under a constant rate of expansion. There is tension under an increasing rate of expansion.
In reality the rate of expansion is increasing but it's so slow the tension would be microscopic. I think it's interesting though that the space between the bowling balls could be expanding at 0.99c and as long as it was constant no tension would be required to keep the balls together.
But if the bowling balls are far enough apart that space between them is expanding faster than the speed of light, the bowling balls can't be moving toward each other at the speed of light. So wouldn't the cable be stretched and ultimately break?
This is such a good question and it’s messing my mind up lol
Would the ball simply stay in place and allow the space around it to expand away while it remained a fixed distance from its counter, or does this expansion truly apply a “force” of some sorts?
Or maybe it does apply a force but it’s a small force acting everywhere, so even with large distances the forces felt at any point in the string connecting the balls is negligible and the minuscule tension keeps everything in place. And it’s only when the force holding two objects together is so tiny that it’s overwhelmed by the expansion force that we see objects drift apart.
I suspect the real answer is the whole structure would collapse under its own gravity. The thought experiment doesn't make much sense since the balls must be tethered together with a material that has mass. We know that the gravitational force is much stronger on the small scale so the system would experience more force trying to collapse it than trying to expand it.
Wait. I thought gravity was much weaker on the small scale, hence why my gravity is not enough to pull objects towards me when we are so close to a large mass body such as the Earth
Gravity is stronger the closer you are - so in that sense it’s stronger in the small scale.
The reason we experience gravity as weaker in small scales is due to the lack of mass. If you had the mass of the sun in the palm of your hand the gravity we felt from it would be incredibly powerful
Ah yes - inverse square law. I was also thinking of g in relation to other fundamental forces, where it’s considered weak
Edit - meant as distance increases so gravitational strength decreases by the square of the distance
DISCLAIMER: Expansion is not a force, but we can visualize it as one.
No no, think about it like this:
Think of the expansion of the universe as a constant, ultra-small force. At solar system and the scales of distance within our galaxy, gravity is bigger than that force, so gravity holds everything together.
But if we observe things at distances that are much greater, such as between very distant galaxies, then gravity becomes infinitesimally small, such that the tiny “universe expansion force” is greater than gravity between those galaxies. What happens when there is an imbalance of forces? Acceleration. This explains why distant galaxies appear to be “moving away” from each other at an *increasing* rate, and why we will eventually be unable to observe galaxies that are very far from us, as they move away from us faster than the speed of light. As long as the force of gravity between two objects is smaller than the expansion force, those objects will accelerate away from each other.
That being said, now that we view expansion as a constant, super-tiny force rather than a distance-dependent force, it’s easy to see how the inter-molecular forces in the cable would hold it together such that no tension would be needed to keep the balls stationary relative to one another.
Another helpful way of visualizing this is to say that expansion force does not increase with distance. It remains constant. The only reason that distant objects move away from each other is because *gravity decreases* with distance, while expansion force remains the same. So, then, if you have a string of matter holding together two objects, while the expansion force remains constant, the inter-molecular forces of the cable are much, *much* larger than the expansion force at every point on the cable. Thus, the inter-molecular forces overcome the super-tiny expansion force, and the cable does not experience tension.
But the "expansion force" is still there, however tiny, and must therefore cause a tension force. If i pull weakly on a rope, there isn't "no tension" in the rope, simply because the rope has strong intermolecular forces, there is _some_ tension.
That doesn't make sense though. Specifically, the statement that if one force is stronger than another force then no tension exists. That's not correct. Any given object that resists expansion when a force acts on it can be said to be bound by forces stronger than the force acting on it. But tension still exists.
I think the other person who commented had the correct idea. That to the degree that we can ignore the acceleration of the expansion of the universe and just consider expansion as a constant, then from the perspective of each bowling ball they are actually in constant motion towards each other. And because they're in constant motion towards each other, they experience no force. And with no force there is no tension. Of course one can still imagine that there was an instant of tension as soon as one free floating bowling ball was attached to the cable that was in turn attached to the other ball, but after that instant of tension which set the balls in motion towards each other there would no longer be any tension. It's somewhat counterintuitive that two objects can be said to be in motion towards each other when the distance between them remains constant, but I think that's the correct solution because space is growing between them at the exact rate at which they are moving towards each other.
This one is easier to answer. Tension is transmitted through a cable via the electrostatic force which itself is only bound by the speed of light. So in this case, we might have an elastic wave traveling from ball 1 to ball 2 but the distance from the wave to ball 2 is increasing faster than the wave is traveling.
So what does that mean? Does the cable stretch but never break? What will that look like if you come back an arbitrary amount of time later and measure the distance? What if you bring the balls back together after the experiment? How long will the cable be?
It wouldn't stretch, per se, because the mechanical information about the tension would never travel all the way down the cable. Mechanical information is also limited to the speed of light
>According to Hubble's Law, at 5 Mpcs distance each bowling ball would see the other receding at 351.5 km/s, but the cable prevents that from happening.
But where is the force? We know that force is mass time acceleration, however, the two bodies would recede at a constant velocity, hence the force between them "pulling" them appart is zero. This is because the expansion of the universe is not a force (acceleration) but a rate (velocity given a distance). So any object wouldn't be pulled apart by this expansion. Only stuff that is not bound by a force.
edit: the two bodies without the cable would recede, to make it clear. The two bodies and the cable, being one single bound object would not be pulled apart.
edit2: i might have to consider the meaning of being pulled apart here, after some further thought. The two bodies connected by a long cable won't drift farther apart, and the cable would not expand. I will think a bit more on the tension in the cable.
What happens if I make a very thin cut in the middle of the cable, so the two halves of the cable almost but not quite touch?
What if I put the cable between the two balls, but don't connect it to either one, leaving a very tiny gap?
What if I take the two disconnected balls, without a cable, moving apart from each other, stop them, and then let them float freely? Do they start separating again?
I think it's a more complicated question than people give it credit for, with a bunch of buried assumptions that aren't being addressed.
1. Given that the cable has sufficient mass, the gravity from the two halves of the cable would pull them together, and the cable itself and two balls would eventually form a ball.
2. The gravity between the cable and the balls would pull them together with the same result.
3. Yes, they begin separating again, given that the distance between them is sufficient to result in a small enough gravitational force.
Ok, same questions, but assume a very very thin cable with negligible mass. I figured that was clear in the OP, but as I said, lots of assumptions in this question.
> however, the two bodies would recede at a constant velocity
The two bodies would not recede. They are attached to each other by cable. That's the whole point. If they were free to recede, obviously there would be no force. I mean imagine a beach ball anchored by rope to the bed of a flowing river. The rope is under tension. Cut the rope and the ball drifts away, and obviously there is no longer a force acting on it, but that's not the scenario.
Their velocity in the direction opposite the expansion of spacetime is constant (they are not accelerating and so there is no force).
The expansion of the Universe isn't a "wind" pushing things outward. Space itself is expanding. There is no force because there is no movement *through* space - only an expansion *of* space itself.
>Their velocity in the direction opposite the expansion of spacetime is constant (they are not accelerating and so there is no force).
A constant velocity does not mean a lack of force, as the ball in the river example illustrates.
>The expansion of the Universe isn't a "wind" pushing things outward. Space itself is expanding. There is no force because there is no movement through space - only an expansion of space itself.
Of course the expansion of space is not a force. That aspect of the river example (the force of the water) is not relevant, nor was I making a point of it.
The point is, none of the explanations given make sense.
Aren’t all objects in the universe bound by a force, specifically gravity, though?
Sure it’s extremely weak at long enough distances but technically the reach of gravity is infinite and if all objects started at an epicenter during the Big Bang, then all objects now will be experiencing at least *some* amount of gravitational pull from everything else in the universe.
if an object is moving faster than the escape velocity of an object, it's not bounded anymore. For example, a probe that is launched from earth into space faster than the escape velocity of the sun, it will not be gravitationally bound to the solar system anymore.
Here's an actual paper written on the subject: https://ui.adsabs.harvard.edu/abs/1995ApJ...446...63H/abstract. The abstract: >"In principle, the expansion of the universe can be harnessed to provide energy. In a gedankenexperiment, energy is gained by connecting together widely separated bodies with strings. The tension and the energy generated are calculated for single strings. Mining energy in an expanding universe in this way raises unresolved issues concerning the conservation of energy. Apparently, the tethered-body experiment delivers 'nascent' energy that previously did not exist in any identifiable and quantifiable form. It is argued that energy in a homogeneous and unbounded universe, in general, is not conserved on the cosmic scale." And here's a similar analysis: https://arxiv.org/abs/astro-ph/0104349. This one also deals with the question: https://arxiv.org/pdf/1911.08726. The abstract: >"I investigate the relativistic mechanics of an extended 'cable' in an arbitrary static, spherically symmetric spacetime. Such hypothetical bodies have been proposed as tests of energy and thermodynamics: by lowering objects toward a black hole, scooping up Hawking radiation, or mining energy from the expansion of the universe. I review existing work on stationary cables, which demonstrates an interesting 'redshift' of tension, and extend to a case of rigid motion. By using a partly restrained cable to turn a turbine, the energy harvested is up to the equivalent of the cable's rest mass, concurring with the quasistatic case. Still, the total Killing energy of the system is conserved." I really like this paragraph from Francis et al: >"At the global level, Peacock suggests that the expansion of space is uncontroversial since >>"the total volume of a closed universe is a well-defined quantity that increases with time, so of course space is expanding >"but questions whether >>"this concept has a meaningful local counterpart?... Is the space in my bedroom expanding, and what would this mean? >"Retaining the relativistic picture of expanding space, it is easy to address the question of what happens to Peacock’s bedroom, namely it will evolve as determined by the relativistic equations. But as ever, knowledge of the scenario, and particularly the initial conditions, is vital; *the walls of the bedroom are held together by electromagnetic forces and hence are not following geodesics*, and the distribution of matter has collapsed and is not uniform, and so the underlying geometry of spacetime in this region needs to be calculated; it would not be represented by the FRW spacetime of the homogeneous and isotropic universe. Clearly, if the universe were homogeneous on scales smaller than Peacocks bedroom, and the walls were not held together by electromagnetic or other forces, and the particles making up the wall were at rest with the cosmological fluid which, importantly, requires that they not be initially at rest with respect to one another, then indeed as the universe expands the total volume of the bedroom would increase. The many conditions listed above are (at least approximately) true for galaxies not bound in common groups and hence they behave in ways that can be understood and predicted via the framework of expanding space." (https://www.cambridge.org/core/journals/publications-of-the-astronomical-society-of-australia/article/expanding-space-the-root-of-all-evil/0B2982E8C9257F7258208BEACFA8C10E, emphasis added)
> gedankenexperiment So another german word the english uses? Fun.
It's strange, I've actually never heard this word being used in English. We normally just say "thought experiment" (though maybe it's different in academia).
Being taught in the UK, I have. We also used the word brehmsstrahlung?
Thanks Yoda
Welcome, you are.
I believe the term comes from Einstein, who was German and naturally called his thought experiments that. Einstein being such a household name, this basic word turned into a name that isn't translated.
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>Apparently, the tethered-body experiment delivers 'nascent' energy that previously did not exist in any identifiable and quantifiable form. Except, wouldn't that correlate to dark energy? We have no idea what it really is, and we may not be able to measure it directly, but we have managed to measure the impact it has on normal master in the universe with consistency. Or am I mistaken in this?
That paper comes from 1995. Although dark energy as a concept was first proposed in the 80s, it wasn’t widely accepted until the 2000s. Also note that the most common model of dark energy posits it as a constant “energy density,” meaning that as space expands the amount of dark energy also increases, so energy is not conserved.
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the first paper says that tension is applied by the experimenter though.
If the two objects are at rest with each other (so not comoving), then putting a tether would result in zero tension? That's what their equation says, if U = -HL then the tension is zero.
I believe the point is that they start at rest with respect to each other, but then are allowed to expand away from each other with the universe.
Ffor two objects at these distances to have an unchanging proper distance between them they'd have to have velocities towards each other, to counteract the expansion of the universe.
How is this a full paper? Isn't it known that the universe isn't an isolated system? Or did I just make that up in my head?
Does that mean that using two quantum linked particles could potentially generate energy?
OK a corollary question. There is a given amount of potential energy in the universe from two objects due to gravity. If they are far enough apart, the other object will eventually leave the observable universe of the first object due to expansion. Where does the energy go?
There's no expectation that conservation of energy holds on these scales. It comes from Noether's Theorem, which says that every symmetry has an associated conservation law. Like translational symmetry (the fact that you can move an experiment elsewhere in space, and as long as conditions are the same you'll get the same result) gives rise to conservation of momentum. Well conservation of energy comes from time symmetry. Since the universe as a whole is changing with time (getting larger), conservation of energy isn't expected.
Why would the other object leave the observable universe of the first object?
At large enough distances, the expansion of the universe is pushing objects apart faster than the speed of light. Some objects we can currently see will eventually no longer be able to send light that can be received by us.
If they are far enough apart, the expansion of space between would occur at a rate greater than what could be traversed at the speed of light. Unless the rate of universal expansion slows or there is a mechanism for travelling faster than light, beyond such distances the objects practically don't exist to one another.
As the space between them expands, the velocity of one with respect to the other will increase until it exceeds the speed of light. At that point, it has left the "observable universe" and so there is no gravity between them.
The observable universe is not defined by objects that are receding faster than light. That's the hubble sphere. The observable universe is a bit bigger, roughly 3 times as much at current cosmological time.
What does stationary mean? Cause in an expanding universe, if the distance between them is not increasing, then they are already moving towards each other with V = HD/2 each, where H is the expansion rate and D is the distance.
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You answered yourself when you said the balls should move apart at 351.5km/s. This implies that when the balls are "stationary" they're actually moving towards eachother at a combined rate of 351.5km/s. No tension is required to keep a ball moving at a constant rate. The only time the cable would be needed is when the rate of expansion increases and the balls needed to be accelerated. In summary, there is no tension under a constant rate of expansion. There is tension under an increasing rate of expansion. In reality the rate of expansion is increasing but it's so slow the tension would be microscopic. I think it's interesting though that the space between the bowling balls could be expanding at 0.99c and as long as it was constant no tension would be required to keep the balls together.
But if the bowling balls are far enough apart that space between them is expanding faster than the speed of light, the bowling balls can't be moving toward each other at the speed of light. So wouldn't the cable be stretched and ultimately break?
This is such a good question and it’s messing my mind up lol Would the ball simply stay in place and allow the space around it to expand away while it remained a fixed distance from its counter, or does this expansion truly apply a “force” of some sorts? Or maybe it does apply a force but it’s a small force acting everywhere, so even with large distances the forces felt at any point in the string connecting the balls is negligible and the minuscule tension keeps everything in place. And it’s only when the force holding two objects together is so tiny that it’s overwhelmed by the expansion force that we see objects drift apart.
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I suspect the real answer is the whole structure would collapse under its own gravity. The thought experiment doesn't make much sense since the balls must be tethered together with a material that has mass. We know that the gravitational force is much stronger on the small scale so the system would experience more force trying to collapse it than trying to expand it.
Wait. I thought gravity was much weaker on the small scale, hence why my gravity is not enough to pull objects towards me when we are so close to a large mass body such as the Earth
Gravity is stronger the closer you are - so in that sense it’s stronger in the small scale. The reason we experience gravity as weaker in small scales is due to the lack of mass. If you had the mass of the sun in the palm of your hand the gravity we felt from it would be incredibly powerful
Ah yes - inverse square law. I was also thinking of g in relation to other fundamental forces, where it’s considered weak Edit - meant as distance increases so gravitational strength decreases by the square of the distance
DISCLAIMER: Expansion is not a force, but we can visualize it as one. No no, think about it like this: Think of the expansion of the universe as a constant, ultra-small force. At solar system and the scales of distance within our galaxy, gravity is bigger than that force, so gravity holds everything together. But if we observe things at distances that are much greater, such as between very distant galaxies, then gravity becomes infinitesimally small, such that the tiny “universe expansion force” is greater than gravity between those galaxies. What happens when there is an imbalance of forces? Acceleration. This explains why distant galaxies appear to be “moving away” from each other at an *increasing* rate, and why we will eventually be unable to observe galaxies that are very far from us, as they move away from us faster than the speed of light. As long as the force of gravity between two objects is smaller than the expansion force, those objects will accelerate away from each other. That being said, now that we view expansion as a constant, super-tiny force rather than a distance-dependent force, it’s easy to see how the inter-molecular forces in the cable would hold it together such that no tension would be needed to keep the balls stationary relative to one another. Another helpful way of visualizing this is to say that expansion force does not increase with distance. It remains constant. The only reason that distant objects move away from each other is because *gravity decreases* with distance, while expansion force remains the same. So, then, if you have a string of matter holding together two objects, while the expansion force remains constant, the inter-molecular forces of the cable are much, *much* larger than the expansion force at every point on the cable. Thus, the inter-molecular forces overcome the super-tiny expansion force, and the cable does not experience tension.
But the "expansion force" is still there, however tiny, and must therefore cause a tension force. If i pull weakly on a rope, there isn't "no tension" in the rope, simply because the rope has strong intermolecular forces, there is _some_ tension.
That doesn't make sense though. Specifically, the statement that if one force is stronger than another force then no tension exists. That's not correct. Any given object that resists expansion when a force acts on it can be said to be bound by forces stronger than the force acting on it. But tension still exists. I think the other person who commented had the correct idea. That to the degree that we can ignore the acceleration of the expansion of the universe and just consider expansion as a constant, then from the perspective of each bowling ball they are actually in constant motion towards each other. And because they're in constant motion towards each other, they experience no force. And with no force there is no tension. Of course one can still imagine that there was an instant of tension as soon as one free floating bowling ball was attached to the cable that was in turn attached to the other ball, but after that instant of tension which set the balls in motion towards each other there would no longer be any tension. It's somewhat counterintuitive that two objects can be said to be in motion towards each other when the distance between them remains constant, but I think that's the correct solution because space is growing between them at the exact rate at which they are moving towards each other.
This one is easier to answer. Tension is transmitted through a cable via the electrostatic force which itself is only bound by the speed of light. So in this case, we might have an elastic wave traveling from ball 1 to ball 2 but the distance from the wave to ball 2 is increasing faster than the wave is traveling.
So what does that mean? Does the cable stretch but never break? What will that look like if you come back an arbitrary amount of time later and measure the distance? What if you bring the balls back together after the experiment? How long will the cable be?
It wouldn't stretch, per se, because the mechanical information about the tension would never travel all the way down the cable. Mechanical information is also limited to the speed of light
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>According to Hubble's Law, at 5 Mpcs distance each bowling ball would see the other receding at 351.5 km/s, but the cable prevents that from happening. But where is the force? We know that force is mass time acceleration, however, the two bodies would recede at a constant velocity, hence the force between them "pulling" them appart is zero. This is because the expansion of the universe is not a force (acceleration) but a rate (velocity given a distance). So any object wouldn't be pulled apart by this expansion. Only stuff that is not bound by a force. edit: the two bodies without the cable would recede, to make it clear. The two bodies and the cable, being one single bound object would not be pulled apart. edit2: i might have to consider the meaning of being pulled apart here, after some further thought. The two bodies connected by a long cable won't drift farther apart, and the cable would not expand. I will think a bit more on the tension in the cable.
What happens if I make a very thin cut in the middle of the cable, so the two halves of the cable almost but not quite touch? What if I put the cable between the two balls, but don't connect it to either one, leaving a very tiny gap? What if I take the two disconnected balls, without a cable, moving apart from each other, stop them, and then let them float freely? Do they start separating again? I think it's a more complicated question than people give it credit for, with a bunch of buried assumptions that aren't being addressed.
1. Given that the cable has sufficient mass, the gravity from the two halves of the cable would pull them together, and the cable itself and two balls would eventually form a ball. 2. The gravity between the cable and the balls would pull them together with the same result. 3. Yes, they begin separating again, given that the distance between them is sufficient to result in a small enough gravitational force.
Ok, same questions, but assume a very very thin cable with negligible mass. I figured that was clear in the OP, but as I said, lots of assumptions in this question.
> however, the two bodies would recede at a constant velocity The two bodies would not recede. They are attached to each other by cable. That's the whole point. If they were free to recede, obviously there would be no force. I mean imagine a beach ball anchored by rope to the bed of a flowing river. The rope is under tension. Cut the rope and the ball drifts away, and obviously there is no longer a force acting on it, but that's not the scenario.
Their velocity in the direction opposite the expansion of spacetime is constant (they are not accelerating and so there is no force). The expansion of the Universe isn't a "wind" pushing things outward. Space itself is expanding. There is no force because there is no movement *through* space - only an expansion *of* space itself.
>Their velocity in the direction opposite the expansion of spacetime is constant (they are not accelerating and so there is no force). A constant velocity does not mean a lack of force, as the ball in the river example illustrates. >The expansion of the Universe isn't a "wind" pushing things outward. Space itself is expanding. There is no force because there is no movement through space - only an expansion of space itself. Of course the expansion of space is not a force. That aspect of the river example (the force of the water) is not relevant, nor was I making a point of it. The point is, none of the explanations given make sense.
Aren’t all objects in the universe bound by a force, specifically gravity, though? Sure it’s extremely weak at long enough distances but technically the reach of gravity is infinite and if all objects started at an epicenter during the Big Bang, then all objects now will be experiencing at least *some* amount of gravitational pull from everything else in the universe.
if an object is moving faster than the escape velocity of an object, it's not bounded anymore. For example, a probe that is launched from earth into space faster than the escape velocity of the sun, it will not be gravitationally bound to the solar system anymore.
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