Maximum efficiency when doing work over a distance
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Maximum efficiency when doing work over a distance
Suppose you want to impart some energy into an object. If you're very close to the object, you will need to expend X energy to give the object Y energy.
However, what if the object is located far away? Intuitively you will need to expend more than X energy because more energy will be lost in "transit". However, is there a theoretical limit to how much more energy you must expend?
For example, if I'm standing next to a ball, I can kick it. However, if I'm 500 meters away, I can't make the ball move by simply draining the same amount of energy from my body.*
Likewise, if we can hit a particle with a particular beam of light at point blank, we must use a higher intensity light to produce the same effect from farther away (because the light beam's energy disperses across space).
Is there a physical law or constraint that dictates the minimum amount of energy that must be lost (per unit distance) to "transport" a given amount of energy across space?
*I actually started thinking about this when wondering about possible telekinesis that doesn't violate energy conservation. If there is no minimum "transport" energy, then a hypothetical telekinetic can do some crazy stuff (like push an orbiting satellite while standing on earth or punching someone on the other side of the world).
However, what if the object is located far away? Intuitively you will need to expend more than X energy because more energy will be lost in "transit". However, is there a theoretical limit to how much more energy you must expend?
For example, if I'm standing next to a ball, I can kick it. However, if I'm 500 meters away, I can't make the ball move by simply draining the same amount of energy from my body.*
Likewise, if we can hit a particle with a particular beam of light at point blank, we must use a higher intensity light to produce the same effect from farther away (because the light beam's energy disperses across space).
Is there a physical law or constraint that dictates the minimum amount of energy that must be lost (per unit distance) to "transport" a given amount of energy across space?
*I actually started thinking about this when wondering about possible telekinesis that doesn't violate energy conservation. If there is no minimum "transport" energy, then a hypothetical telekinetic can do some crazy stuff (like push an orbiting satellite while standing on earth or punching someone on the other side of the world).
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Re: Maximum efficiency when doing work over a distance
Ignoring gravity, just to keep things simple, there's no need for energy to actually be lost in transit.
Consider the following scenario, somewhere in space.
A cannon fires a cannonball, giving it some amount of kinetic energy and momentum. The cannonball travels through empty space some distance. Nothing slows it down. There is no friction. It's not losing any kinetic energy. It's momentum isn't changing. It eventually hits another cannonball of equal mass in an elastic collision (no energy is lost in total from the colliding cannonballs), headon, imparting all its kinetic energy who that other cannonball, which then continues along the original cannonball's path.
Note that you don't need to know the distance between the cannon and the second cannonball to know that all the kinetic energy the cannon gave to the first cannonball ends up given to the second cannonball.
It used to be thought that moving objects, such as cannonballs, lost impetus as they moved, and that when they ran out of impetus, they stopped (or dropped). Eventually, this concept was improved upon, and now we have the modern concept of momentum, in both Newtonian mechanics and General Relativity. An inertial object, which means, whether it's moving or not, it has no forces acting on it, keeps all its momentum as long as it remains inertial. No momentum, or energy, is used up for it to carry on moving.
So, no additional energy is needed to send energy over an additional distance.
Consider the following scenario, somewhere in space.
A cannon fires a cannonball, giving it some amount of kinetic energy and momentum. The cannonball travels through empty space some distance. Nothing slows it down. There is no friction. It's not losing any kinetic energy. It's momentum isn't changing. It eventually hits another cannonball of equal mass in an elastic collision (no energy is lost in total from the colliding cannonballs), headon, imparting all its kinetic energy who that other cannonball, which then continues along the original cannonball's path.
Note that you don't need to know the distance between the cannon and the second cannonball to know that all the kinetic energy the cannon gave to the first cannonball ends up given to the second cannonball.
It used to be thought that moving objects, such as cannonballs, lost impetus as they moved, and that when they ran out of impetus, they stopped (or dropped). Eventually, this concept was improved upon, and now we have the modern concept of momentum, in both Newtonian mechanics and General Relativity. An inertial object, which means, whether it's moving or not, it has no forces acting on it, keeps all its momentum as long as it remains inertial. No momentum, or energy, is used up for it to carry on moving.
So, no additional energy is needed to send energy over an additional distance.
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Re: Maximum efficiency when doing work over a distance
How do you guarantee the original cannonball will transfer all of its momentum to the one it hits?
Energy technically isn't lost, but you end up having to expend more energy than you would have if you directly fired the target cannonball to get the same result.
Energy technically isn't lost, but you end up having to expend more energy than you would have if you directly fired the target cannonball to get the same result.
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 Xanthir
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Re: Maximum efficiency when doing work over a distance
You guarantee it the same way you have a perfect vacuum  by assuming it as a simplifying assumption in the problem. In reality, no collision is entirely elastic or inelastic, and some energy will be lost to inelastic effects, such as compression of each cannonball.
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Re: Maximum efficiency when doing work over a distance
Cradarc wrote:Energy technically isn't lost, but you end up having to expend more energy than you would have if you directly fired the target cannonball to get the same result.
Well, your question was about doing work over a distance, so I set up an illustrative scenario where the distance could be varied without varying anything else. If you fire the target cannonball itself, that's a different scenario where you're not just changing the distance, but also going from giving energy (which, I should be clear, isn't the same as momentum) to the target cannonball by hitting it with a cannonball, to giving it energy by firing it directly out of the cannon.
If you keep everything but the distance between the cannon and the target cannonball the same, so you only vary the distance, you can consider the work done, if any, to transfer energy over an extra distance. So, compare variations where the distance between the cannon and the target cannonball are 100 m, 200 m, 300 m, ..., 1 km. Each time, the first cannonball hits the target cannonball headon, and transfers all its kinetic energy to the target cannonball.
Let's consider the 100 m case. Whatever the kinetic energy, KE, of the first cannonball is when it reaches 100 m from the cannon, that's the amount it has at that distance (obviously), and that's how much it gives to the target. The target cannonball gets KE kinetic energy.
Let's consider the 100n+100 m cases together, where n is a positive integer from the set {1, 2, ..., 9} (giving the 200 m, 300 m, ..., 1 km distances). At 100 m, the first cannonball has kinetic energy KE, because, so far, everything's identical to the 100 m case. But then it travels another 100n m. Nothing happens to it for it to lose any of that kinetic energy. So, when it's at 200 m, it's still got KE kinetic energy. At 300 m, it's still KE. In general, at 100n+100 m from the cannon, that first cannonball (unless it's already hit the target) has KE kinetic energy.
In each case, it then hits the target cannonball, at a distance from the cannon where that first cannonball still has KE kinetic energy. So that's what the target cannonball gets, KE, no matter what the extra distance was from the cannon.
In practice, like Xanthir says, things aren't quite so simple, neat and tidy. For example, the target cannonball won't actually be hit absolutely headon, and this means slightly different amounts of kinetic energy being given to the target cannonball at different distances. But that's a distraction from the real issue.
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Re: Maximum efficiency when doing work over a distance
I think I wasn't very clear about my question. I'm going to use the cannonball example to better illustrate it.
Suppose your goal is to accelerate a cannonball ( floating in empty space in a vacuum) to some velocity.
One way to do it would be simply push it with your hand. That would achieve some efficiency E. Now suppose you found a method, M, that is the most efficient way to do the work. Is method M distance dependent?
Firing another cannonball is distance independent, but it is extremely inefficient to begin with. You have to use energy to create the second cannonball and fire it as well as deal with collision losses. It's pretty obvious that almost any method of doing work from afar can also do work from up close. However, there may exist more efficient methods of doing work up close than doing work from afar.
This cannonball example is rather simplistic. What if you had to accelerate it in a direction directly opposite to your the line of sight? At point blank this change in direction is trivial, simply push it the other way.
Suppose your goal is to accelerate a cannonball ( floating in empty space in a vacuum) to some velocity.
One way to do it would be simply push it with your hand. That would achieve some efficiency E. Now suppose you found a method, M, that is the most efficient way to do the work. Is method M distance dependent?
Firing another cannonball is distance independent, but it is extremely inefficient to begin with. You have to use energy to create the second cannonball and fire it as well as deal with collision losses. It's pretty obvious that almost any method of doing work from afar can also do work from up close. However, there may exist more efficient methods of doing work up close than doing work from afar.
This cannonball example is rather simplistic. What if you had to accelerate it in a direction directly opposite to your the line of sight? At point blank this change in direction is trivial, simply push it the other way.
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Re: Maximum efficiency when doing work over a distance
How is pushing the ball different than poking it with a stick from 5m away?
Re: Maximum efficiency when doing work over a distance
Is it possible that some intuitions about these scenarios are off because of the inefficiencies in how human muscles operate? That is, holding your arms straight out with some mass will feel like you're doing a bunch of work, despite doing no work in the physics sense (as the mass will move no distance). Similarly, pushing a rock some distance will feel like less than half the work of pushing it twice the distance, even though considering only the work done on the rock would make the difference exactly a factor of 2. The issue here being your muscles are 'wasting' a bunch of energy via the mechanisms they work, as well as internal frictions and heat generated and so forth.
I don't think there's any reason why perfect efficiency in moving something over an arbitrary distance couldn't be achieved though. Your hypothetical telekinetic might have speed of light limitations to be concerned with, and looking too hard at the 'how' would probably cause problems given telekinesis isn't something that exists in actual physics, but most of the 'work' in the layperson sense doesn't need to actually be done in the physics force*distance sense thanks to inertia. That is, one only needs to apply a force for a short time to give that initial acceleration, and then in the absence of other forces (as in a frictionless vacuum) the object will have no additional energy costs regardless of distance.
I don't think there's any reason why perfect efficiency in moving something over an arbitrary distance couldn't be achieved though. Your hypothetical telekinetic might have speed of light limitations to be concerned with, and looking too hard at the 'how' would probably cause problems given telekinesis isn't something that exists in actual physics, but most of the 'work' in the layperson sense doesn't need to actually be done in the physics force*distance sense thanks to inertia. That is, one only needs to apply a force for a short time to give that initial acceleration, and then in the absence of other forces (as in a frictionless vacuum) the object will have no additional energy costs regardless of distance.
Re: Maximum efficiency when doing work over a distance
Dopefish wrote:I don't think there's any reason why perfect efficiency in moving something over an arbitrary distance couldn't be achieved though.
Looks like I'm still struggling to make myself clear. Let me try again...
I'm not talking about perfect efficiency, I'm talking about relative efficiency between performing an action from location A compared to performing the exact same action from location B. The location of the object you are performing the action on has not changed, but the location of your energy source has (or vice versa due to relativity).
I think screen317's comment highlights my point.
Instead of 5 meters away, let's say 1 km away. How much energy would it take to push a ball with a 1 km long stick compared to pushing the ball from 5 m away?
Suppose instead of a stick we used an electric/gravitational field. If the ball were located closer, you would require a far smaller field constant to achieve the same effect since the field strength decreases over distance. (Equivalently, if the ball was closer to the field source, and the field source remains unchanged, it would gain more energy than you intended to give it.)
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Re: Maximum efficiency when doing work over a distance
I think there might be at least two issues mixed together here.
One is the issue of what difference, if any, varying the distance makes. Cannonball billiards is about that.
The other seems to be about converting energy, or otherwise processing it, so as to then send it from the source to the target (whatever the distance), possibly converting it or processing it there, and doing work, where the question is what the maximum efficiency limits are for such processes at the source and target.
Is this really about the latter issue?
One is the issue of what difference, if any, varying the distance makes. Cannonball billiards is about that.
The other seems to be about converting energy, or otherwise processing it, so as to then send it from the source to the target (whatever the distance), possibly converting it or processing it there, and doing work, where the question is what the maximum efficiency limits are for such processes at the source and target.
Is this really about the latter issue?
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Re: Maximum efficiency when doing work over a distance
My point with perfect efficiency was that in your previous post you talked about achieving some efficiency E with one method and a method M with the best possible efficiency, and I'm suggesting that method M would have an efficiency of 1, and it would not be distance dependent. The efficiency E of pushing with your hand would be less than one, but that's because human muscles are inefficient.
The difference between pushing something 1km away with a 1km long perfectly rigid stick and pushing with a 5m stick is that there's a lot more stick you're also exerting energy to move in the former case, but the work done by the stick on the ball would be the same in either case. Given perfectly rigid sticks of equal mass, then the situations would be the same in terms of energy expenditure.
The key thing is the difference between conservative forces and nonconservative forces. If your method involves only conservative forces, then pretty much by definition there's no energy losses due to physical separation. In the real world there's almost always nonconservative forces sneaking into play (e.g. friction and material stresses), but I'm not aware of any theoretical reasons why their influence couldn't be made arbitrarily small in a real world scenario. (Thermodynamics says some things about what kinds of efficiencies you can get turning one sort of energy into another sort, but I don't think it imposes any restrictions on what amounts to moving the 'same' energy from A to B.)
The difference between pushing something 1km away with a 1km long perfectly rigid stick and pushing with a 5m stick is that there's a lot more stick you're also exerting energy to move in the former case, but the work done by the stick on the ball would be the same in either case. Given perfectly rigid sticks of equal mass, then the situations would be the same in terms of energy expenditure.
The key thing is the difference between conservative forces and nonconservative forces. If your method involves only conservative forces, then pretty much by definition there's no energy losses due to physical separation. In the real world there's almost always nonconservative forces sneaking into play (e.g. friction and material stresses), but I'm not aware of any theoretical reasons why their influence couldn't be made arbitrarily small in a real world scenario. (Thermodynamics says some things about what kinds of efficiencies you can get turning one sort of energy into another sort, but I don't think it imposes any restrictions on what amounts to moving the 'same' energy from A to B.)

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Re: Maximum efficiency when doing work over a distance
Cradarc wrote:I think screen317's comment highlights my point.
Instead of 5 meters away, let's say 1 km away. How much energy would it take to push a ball with a 1 km long stick compared to pushing the ball from 5 m away?
If the work done on the ball is the same then the energy is the same.
If the sticks are not ideal devices then there will be transmission losses.
If a real 1km long stick were made the difference in losses will be a function of the engineering tech. used; is the stick moved on maglev or log rollers? Is it made of nanotubes or concrete? etc.
There is no fundamental reason a real 1km stick could not transfer energy to the ball more efficiently than the 5m stick. It's an exercise in engineering.
Re: Maximum efficiency when doing work over a distance
FancyHat wrote:One is the issue of what difference, if any, varying the distance makes. Cannonball billiards is about that.
The other seems to be about converting energy, or otherwise processing it, so as to then send it from the source to the target (whatever the distance), possibly converting it or processing it there, and doing work, where the question is what the maximum efficiency limits are for such processes at the source and target.
Is this really about the latter issue?
Yes, the latter sounds about right. The idea is you can't do the same process from afar as you can at close range. You must convert it in some form, send it, then convert it back with the exact same properties.
With the billiard balls technique you can add energy to the target, but at the cost of having to produce another perfectly identical ball (to ensure proper energy transfer occurs). You also lose some control over what direction you can propel the target ball.
Dopefish wrote:The difference between pushing something 1km away with a 1km long perfectly rigid stick and pushing with a 5m stick is that there's a lot more stick you're also exerting energy to move in the former case
Exactly. So you are actually doing work on the stickball system instead of just the ball. The stickball system has more mass, so it will require more work to move compared to If you only had to move the ball. I'm wondering if there's a limit to how small you can make that difference.
I just thought of a better example :
Consider a battery operated toy car. Take the batteries out and put them far away. You must then set up a system to transfer the energy stored in the batteries back to the car. Assume you have the magical ability to convert the battery's energy into any form you want without any work or loss.
Is there a way to get the car working without doing any extra work?
Even though you have all the energy to power the car and the ability to change it into any form required by the car, you must to do additional work to make the energy accessible to the car.
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Re: Maximum efficiency when doing work over a distance
Cradarc wrote:Consider a battery operated toy car. Take the batteries out and put them far away. You must then set up a system to transfer the energy stored in the batteries back to the car. Assume you have the magical ability to convert the battery's energy into any form you want without any work or loss.
Is there a way to get the car working without doing any extra work?
Even though you have all the energy to power the car and the ability to change it into any form required by the car, you must to do additional work to make the energy accessible to the car.
If I nudge the batteries to get them moving towards the car, I can get them to the car with that initial nudge. I'm assuming that there's no friction on the batteries' way to the car, so even with a tiny nudge they'll start moving there, and get there, with no more energy required. The tinier the nudge, the longer it takes the batteries to get there, but the tinier the amount of energy required to give them that nudge. There's no lower limit above zero for the size of the nudge (the impulse, I suppose), and no lower limit above zero for how much energy is required to give it that nudge. So, I'd say, that's still a maximum efficiency of 100%.
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 sevenperforce
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Re: Maximum efficiency when doing work over a distance
In the case of "beaming" light or a field of some kind hither/thither, you run into the inversesquare law, which says that anything emanating uniformly from a point source* will lose intensity as it spreads out into space. Now, this doesn't mean it loses energy  the energy is still there  but the intensity (and thus the usable energy or usable force, depending on what you're dealing with) drops off...proportional to 1/r^{2}. For example, if you're floating in space and you want to use a flashlight to push a floating solar sail 30 meters away, you'll have to use four times as much power as if it were only 15 meters away, if you want to exert the same amount of force.
On the other hand, if you use a laser that won't (significantly) spread out, it won't really matter at all how far away your target is  if you're going through a vacuum, the laser won't have any scattering losses and will be able to exert the same radiation pressure at a distance of 1 foot or 100 miles.
If you're using a field of some kind, you'll probably be restricted to the inversesquare law unless you have some way of confining the field within a cylindrical path to whatever you're aiming at.
I've actually thought about this from the point of view of telekinesis, too. It makes sense that a telekinetic would have to exert greater energy at a greater distance. You could explain this in one of two ways: either the "beam" used to exert force is lossy and loses force with distance traveled, or the "field" used to exert force spreads out over distance geometrically. Depending on your needs, you can make it drop off according to 1/r or 1/r^{2} or 1/r^{3} or however else you want it. Of course, anything like that implies infinite telekinetic force as r goes to 0, so the equation will probably be a bit more complex.
What's trickier to manage with telekinesis is conservation of momentum.
_{*By arranging reflectors or lenses, it is possible to initially direct all of the light in one particular direction, but it will immediately begin to spread out in space just the same.}
On the other hand, if you use a laser that won't (significantly) spread out, it won't really matter at all how far away your target is  if you're going through a vacuum, the laser won't have any scattering losses and will be able to exert the same radiation pressure at a distance of 1 foot or 100 miles.
If you're using a field of some kind, you'll probably be restricted to the inversesquare law unless you have some way of confining the field within a cylindrical path to whatever you're aiming at.
I've actually thought about this from the point of view of telekinesis, too. It makes sense that a telekinetic would have to exert greater energy at a greater distance. You could explain this in one of two ways: either the "beam" used to exert force is lossy and loses force with distance traveled, or the "field" used to exert force spreads out over distance geometrically. Depending on your needs, you can make it drop off according to 1/r or 1/r^{2} or 1/r^{3} or however else you want it. Of course, anything like that implies infinite telekinetic force as r goes to 0, so the equation will probably be a bit more complex.
What's trickier to manage with telekinesis is conservation of momentum.
_{*By arranging reflectors or lenses, it is possible to initially direct all of the light in one particular direction, but it will immediately begin to spread out in space just the same.}
Re: Maximum efficiency when doing work over a distance
FancyHat wrote:If I nudge the batteries to get them moving towards the car, I can get them to the car with that initial nudge.
True, but having the battery collide elastically with the car is not the same as having the battery powering the car directly (as in before you removed it).
In your scenario you successfully managed to send the battery traveling towards the car by turning some of the battery's chemical energy into kinetic energy. However, what will happen is the battery will collide with the car and give it the same amount of kinetic energy you used to transport the battery. You can choose to convert all of the battery's chemical energy into kinetic energy but then you only succeeded in causing the car to gain kinetic energy in a particular direction.
The battery could also power a speaker on the car, or make it blink some lights, or simply make the car go in a circle. You can't do that by transferring the energy via collision, yet it is trivial when the battery is not removed from the car.
sevenperforce wrote:I've actually thought about this from the point of view of telekinesis, too. It makes sense that a telekinetic would have to exert greater energy at a greater distance. You could explain this in one of two ways: either the "beam" used to exert force is lossy and loses force with distance traveled, or the "field" used to exert force spreads out over distance geometrically. Depending on your needs, you can make it drop off according to 1/r or 1/r2 or 1/r3 or however else you want it. Of course, anything like that implies infinite telekinetic force as r goes to 0, so the equation will probably be a bit more complex.
What's trickier to manage with telekinesis is conservation of momentum.
Well, I thought conservation of momentum is the easy part. From the telekinetic's perspective, it would be as if they are directly in contact with the object being moved. So if they were pushing a heavy object, it would be necessary to dig into the ground to prevent sliding.
What bugs me is a telekinetic would be able to manipulate an object in ways that feel like violations of energy conservation. They can just as easily push a molecule as they can push a box. They can adjust the orbits of satellites with the effort it takes to push a heavy cart. If something is located in another room, they can bring it directly instead of having to walk over to get it. In fact, if everyone were a telekinetic, transportation would be near obsolete. You merely need to see what you're doing, and you would be able to do it without getting out of your chair.
I feel like there should be some physical law that says this sort of thing isn't possible.
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Re: Maximum efficiency when doing work over a distance
Cradarc wrote:True, but having the battery collide elastically with the car is not the same as having the battery powering the car directly (as in before you removed it).
I didn't say it would "collide elastically with the car". Nudging it to send it to the car was just to get it to the car. Once at the car, it would be inserted, as normal, and so on.
What bugs me is a telekinetic would be able to manipulate an object in ways that feel like violations of energy conservation.
I don't think it's a good idea to rely on what things "feel like", since physics can be quite counterintuitive anyway. Conservation of momentum, relative motion, Special Relativity, and, of course, all that quantum stuff, have been found, by many people, to be counterintuitive, and plenty of people have been (and still are) bugged by such things.
Edited to add:
Actually, I don't even know what you mean by "ways that feel like violations of energy conservation", since there's no violation of energy conservation if the total energy remains constant from before the act of telekinesis, all the way through that act, until after that act is completed. Conservation of energy doesn't itself require less than 100% efficiency.
In Newtonian mechanics, we could model telekinesis as the use of light, rigid rods and inelastic strings to exert forces at a distance. The rods and strings have no mass, so can be used to perfectly transmit forces and energy with nothing less than 100% efficiency, no matter how long they are. (Perhaps this is a bit like extreme puppetry?)
Last edited by FancyHat on Tue Mar 10, 2015 5:15 am UTC, edited 1 time in total.
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Re: Maximum efficiency when doing work over a distance
Telekinesis is in fact impossible, so there's not much to worry about there. But if it were real, there'd be nothing conservationviolating about a telekinetic pushing a satellite into a different orbit, just as there's nothing conservationviolating about magnets pulling things around. Well, as long as the the telekinetic had to expend the appropriate amount of energy to do so (whether from metabolic stores or some other source is up to the worldbuilder). If there were mandatory energy loss due to distance, beyond the usual culprits like friction, where would that energy go?
Telekinesis is impossible not because it couldn't conserve energy, but rather because there are no forces that actually work that way. If it were real, yeah, it would be an incredibly useful ability.
Telekinesis is impossible not because it couldn't conserve energy, but rather because there are no forces that actually work that way. If it were real, yeah, it would be an incredibly useful ability.
No, even in theory, you cannot build a rocket more massive than the visible universe.
Re: Maximum efficiency when doing work over a distance
Fancyhat,
The battery can't insert itself. Every energy source required to get the car running has been moved to a new location. This includes the energy you need to insert the battery. Normally, it is inside your body, but you are given the magical ability to convert it into any form you want. Despite this, there's no way for you to use that energy the same way across a distance. To make use of that energy you must use additional energy (like moving your entire body over to the car).
Also notice, by giving the battery a small nudge, you must give it some kinetic energy. That energy must be taken from elsewhere if you want to preserve the initial energy of the battery. Even though it can be infinitesimally small, it cannot be zero by definition.
Yes, but why? We have entropy to explain why some processes are spontaneous and others are not. What is the explanation for this restriction? After all, gravity and electromagnetism seems to work fine over distance.
I'm not that familiar with strong and weak force, but EMF and gravity both have infinite range but weakened strength over distance. This implies you need a stronger field source to exert the same amount of force on an object located farther away as an object located closer. Doesn't it require more energy to create a stronger field source?
The battery can't insert itself. Every energy source required to get the car running has been moved to a new location. This includes the energy you need to insert the battery. Normally, it is inside your body, but you are given the magical ability to convert it into any form you want. Despite this, there's no way for you to use that energy the same way across a distance. To make use of that energy you must use additional energy (like moving your entire body over to the car).
Also notice, by giving the battery a small nudge, you must give it some kinetic energy. That energy must be taken from elsewhere if you want to preserve the initial energy of the battery. Even though it can be infinitesimally small, it cannot be zero by definition.
Meteoric wrote:Telekinesis is impossible not because it couldn't conserve energy, but rather because there are no forces that actually work that way.
Yes, but why? We have entropy to explain why some processes are spontaneous and others are not. What is the explanation for this restriction? After all, gravity and electromagnetism seems to work fine over distance.
I'm not that familiar with strong and weak force, but EMF and gravity both have infinite range but weakened strength over distance. This implies you need a stronger field source to exert the same amount of force on an object located farther away as an object located closer. Doesn't it require more energy to create a stronger field source?
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Re: Maximum efficiency when doing work over a distance
Cradarc wrote:The battery can't insert itself.
Why not? To ensure accuracy, why couldn't there be magnets on the battery and car to ensure it arrives and locks into the right location? Heck, with sufficiently strong magnets and sufficiently insulated from outside forces, why couldn't the magnetic attraction cause the battery to begin approaching the car to begin with without any need for a nudge? Heck, if we could set up the situation with arbitrary precision, maybe they could approach each other through gravity alone...
To make use of that energy you must use additional energy (like moving your entire body over to the car).
Also notice, by giving the battery a small nudge, you must give it some kinetic energy. That energy must be taken from elsewhere if you want to preserve the initial energy of the battery. Even though it can be infinitesimally small, it cannot be zero by definition.
But the point is that it can be made arbitrarily small  even if the energy source we're talking about is magnetic potential energy or gravitational potential energy  which means the efficiency can approach arbitrarily close to 100%.
To put it another way, if the answer isn't 100% what is it? If you name any number under 100% you're wrong  since the 'true answer' is closer to 100% than that...
Re: Maximum efficiency when doing work over a distance
Cradarc wrote:The battery can't insert itself.
That's a detail of your example, not some kind of fundamental limit. That you can come up with examples which have such details doesn't mean such things are inevitable in all cases.
Also notice, by giving the battery a small nudge, you must give it some kinetic energy. That energy must be taken from elsewhere if you want to preserve the initial energy of the battery. Even though it can be infinitesimally small, it cannot be zero by definition.
As elasto said, you can get arbitrarily close to zero, so zero is the limit. While that might mean you can't actually have 100% efficiency in such a case, you can be closer to it than anything less than 100%, so 100% is the maximum limit, even if not achievable itself.
I'm not that familiar with strong and weak force, but EMF and gravity both have infinite range but weakened strength over distance. This implies you need a stronger field source to exert the same amount of force on an object located farther away as an object located closer. Doesn't it require more energy to create a stronger field source?
But since this is about telekinesis, which is a fictional ability, we're free to invent details. That's why I ended up suggesting modelling it, at least in Newtonian mechanics, with rigid rods and inelastic strings that are massless. It gets all the irrelevant details out of the way, leaving us able to focus on the key issue you asked about which was maximum possible efficiency. And the maximum possible efficiency is 100%.
It really doesn't make sense to keep trying to rely on unspecified details of this fictional ability, as if there must be some reason why the efficiency limit has to be less than 100%, because it's a fictional ability which doesn't, therefore, have any known, efficiencylimiting details. Being fictional, and considering the most general case where the details could be more or less anything, so that we're trying to answer the question you asked, we're free to just assume the details are such that they won't reduce efficiency. So, for your question to even be a (nonfictional) science question, rather than a fantasy makebelieve magic question, we really do have to focus on the actual science part  conservation of energy and momentum and real stuff like that  rather than wasting time trying to discover some 'fundamental' limit that relies on arbitrary, unspecified, fictional details of a fictional ability.
So, you've already had your question answered: 100% efficiency is the maximum efficiency possible. There is no reason in science why it would be anything less.
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 sevenperforce
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Re: Maximum efficiency when doing work over a distance
FancyHat wrote:Cradarc wrote:What bugs me is a telekinetic would be able to manipulate an object in ways that feel like violations of energy conservation.
I don't think it's a good idea to rely on what things "feel like", since physics can be quite counterintuitive anyway. Conservation of momentum, relative motion, Special Relativity, and, of course, all that quantum stuff, have been found, by many people, to be counterintuitive, and plenty of people have been (and still are) bugged by such things.
Suppose we specify that, for the sake of energy conservation, our hypothetical telekinetic must expend metabolic stores in order to produce an effect on the target object. If that's the case, then we run into a slightly tricky intersection of conservation of energy and conservation of momentum.
A lot of people trying to build perpetual motion machines will assume they can somehow extract energy from the Earth's gravitational field, because it's an uninterrupted source of force, right? But as we all know, force is not the same as energy. Energy is the product of force and distance, not something arising from the presence of force alone.
In the case of our telekinetic, then, perhaps he can exert force without motion of his own (for example, holding an object in place against gravity), but I don't think he would be able to transfer kinetic energy to an object without some motion of his own. If we go with your extremely helpful conceptualization of rigid massless rods and inelastic massless strings, then you could imagine holding an object up by exerting force without moving, but it would be impossible to actually move the target object without actually pulling the rope or pushing the rod a given distance. Otherwise you're exerting force, but force without distance produces zero change in kinetic energy.
Suppose our telekinetic wanted to keep a car from moving. He could exert a lot of telekinetic force against the car as the engine was revved, etc., and thus keep it stationary, and he wouldn't have to physically move in order to do so. But if the car was turned off and put in neutral, and he wanted to telekinetically move the car, then he would have to actually move through the same distance that he pushed the car in order for the "force x distance = energy" relationship to be preserved.
We could imagine him being able to have massless frictionless rigid inelastic pulleys, in which case he would be able to only move his hands across a very small distance and push an object a very large distance (albeit with the exertion of multiplicatively greater force). But if he has an infinite number of massless frictionless rigid inelastic pulleys, he could exert infinite force on a stationary object, which probably isn't going to work too well for any reasonable approach.
FancyHat wrote:It really doesn't make sense to keep trying to rely on unspecified details of this fictional ability, as if there must be some reason why the efficiency limit has to be less than 100%, because it's a fictional ability which doesn't, therefore, have any known, efficiencylimiting details. Being fictional, and considering the most general case where the details could be more or less anything, so that we're trying to answer the question you asked, we're free to just assume the details are such that they won't reduce efficiency.
Of course, for the sake of a fictional universe, it's probably a good idea to add some sort of functional limitations...like, the means of operation of telekinesis requires line of sight and drops off with distance according to some smooth equation.
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Re: Maximum efficiency when doing work over a distance
I think that Energy may be a red herring. Every gram of matter has ridiculous amounts of "Energy" in it (E=MC^2)  the problem is telling that Energy what to do.
Entropy is the game of telling stuff what to do: LowEntropy Energy is 'available' Energy  a cannonball where the atoms are all going (mostly) in the same direction is a cannonball with a bunch of Energy in a lowentropy kinetic "bundle". The KE of the atoms of a roomtemperature cannonball rivals that of the directed KE of a fired cannonball. The KE of heat is just mostly useless for hitting things.
This is sort of like Maxwell's demon  it requires no energy to pump heat from the cold to the warm side, but it requires emitting Entropy!
In order to get the cannonball moving in a particular direction, we have to generate a bunch of waste Entropy at the launch site. This can be by taking a lowentropy chemical state and burning it (gunpowder) to generate a lowEntropy pressure wave to propel the cannonball down a cannon bore, as a classic way of doing it. Energy wasn't expended, it was transferred: but the hard part wasn't "the Energy" it was the lowEntropy Energy sitting on a cliff next to a potential well which we used to propel the cannon ball.
Now, suppose the "good hit" radius of the target+ball is 1 meter square. We can describe how many bits of information it requires to aim the cannon ball at the target given its range, and it goes up as the target gets further away. In short, specifying where you want the energy to go (aiming) could have an Entropy cost floor. Even if it takes 0 Energy to aim, it will still require Entropy, assuming we want to aim the gun at more than one target (if the gun "just happens" to be aiming directly at our target, it is free: in practice, we have to aim at our target.)
The surface of a sphere is 4 pi r^2. So it requires log_2 (1 m^2 / 4 pi r^2) bits of information to distinguish a "good shot" from a "miss" at the point of firing, or ~ 2 lg(r)  3.6507 bits (where r is in meters).
At a 1 billion light year range this comes out to 80 bits of Entropy (in a flat universe) per shot.
Do we need to multiply that by the number of particles we are aiming at the target or something? Unsure.
Entropy is the game of telling stuff what to do: LowEntropy Energy is 'available' Energy  a cannonball where the atoms are all going (mostly) in the same direction is a cannonball with a bunch of Energy in a lowentropy kinetic "bundle". The KE of the atoms of a roomtemperature cannonball rivals that of the directed KE of a fired cannonball. The KE of heat is just mostly useless for hitting things.
This is sort of like Maxwell's demon  it requires no energy to pump heat from the cold to the warm side, but it requires emitting Entropy!
In order to get the cannonball moving in a particular direction, we have to generate a bunch of waste Entropy at the launch site. This can be by taking a lowentropy chemical state and burning it (gunpowder) to generate a lowEntropy pressure wave to propel the cannonball down a cannon bore, as a classic way of doing it. Energy wasn't expended, it was transferred: but the hard part wasn't "the Energy" it was the lowEntropy Energy sitting on a cliff next to a potential well which we used to propel the cannon ball.
Now, suppose the "good hit" radius of the target+ball is 1 meter square. We can describe how many bits of information it requires to aim the cannon ball at the target given its range, and it goes up as the target gets further away. In short, specifying where you want the energy to go (aiming) could have an Entropy cost floor. Even if it takes 0 Energy to aim, it will still require Entropy, assuming we want to aim the gun at more than one target (if the gun "just happens" to be aiming directly at our target, it is free: in practice, we have to aim at our target.)
The surface of a sphere is 4 pi r^2. So it requires log_2 (1 m^2 / 4 pi r^2) bits of information to distinguish a "good shot" from a "miss" at the point of firing, or ~ 2 lg(r)  3.6507 bits (where r is in meters).
At a 1 billion light year range this comes out to 80 bits of Entropy (in a flat universe) per shot.
Do we need to multiply that by the number of particles we are aiming at the target or something? Unsure.
One of the painful things about our time is that those who feel certainty are stupid, and those with any imagination and understanding are filled with doubt and indecision  BR
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 gmalivuk
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Re: Maximum efficiency when doing work over a distance
Moving to fictional science because it's already been established that there are no hardandfast laws of nature that set a limit lower than 100% efficiency, so it becomes a question of what limits on telekinesis work well for fiction.
This makes a pretty reasonable set of limits on TK for story purposes, I think. You couldn't easily move a satellite because of the amount of torque such a massless rod would exert on you if you were sticking it hundreds of miles up into space.FancyHat wrote:In Newtonian mechanics, we could model telekinesis as the use of light, rigid rods and inelastic strings to exert forces at a distance. The rods and strings have no mass, so can be used to perfectly transmit forces and energy with nothing less than 100% efficiency, no matter how long they are. (Perhaps this is a bit like extreme puppetry?)
Re: Maximum efficiency when doing work over a distance
I can argue 100% efficiency is also fictional, since it's impossible to achieve in reality. How come that is considered "science" but my speculation about the extension of energy over distance isn't? Are Einstein's thought experiments science fiction as well? Just because a scenario unrealistic doesn't mean it doesn't have scientific value.
Two identical particles are at rest: One at location A, another at location B. You cannot get the particles to exist in the same location without doing work. So there is some sort of potential between the particles, even in the absence of any fields.
Symmetry/relativity dictates a force acting on each would yield the same result, but there is an implicit assumption that the applied force is always at the location of the particle being acted on. In reality, forces can't magically appear anywhere, they have to have a source. No matter where you place that source, the distance between A to B can be made significant compared to the distance from A or B to the source.
In such a scenario, can the source act equally well on A as it can on B?
As far as I know, everything in the current model of physics supports "no". A point source's "influence" on a particle dies off over distance. It is possible for the source to do the same work on A as on B, but to do that it will have to increase its overall "strength". I quantified this source "strength" as energy (perhaps mistakenly) because it seemed intuitive that more energy is required to give a force source more strength*.
*Fields store energy, proportional (not necessarily linearly) to the field strength. If you increase the overall magnitude of field strength, the total stored energy increases. Thus, energy must be added to increase the overall field strength.
Two identical particles are at rest: One at location A, another at location B. You cannot get the particles to exist in the same location without doing work. So there is some sort of potential between the particles, even in the absence of any fields.
Symmetry/relativity dictates a force acting on each would yield the same result, but there is an implicit assumption that the applied force is always at the location of the particle being acted on. In reality, forces can't magically appear anywhere, they have to have a source. No matter where you place that source, the distance between A to B can be made significant compared to the distance from A or B to the source.
In such a scenario, can the source act equally well on A as it can on B?
As far as I know, everything in the current model of physics supports "no". A point source's "influence" on a particle dies off over distance. It is possible for the source to do the same work on A as on B, but to do that it will have to increase its overall "strength". I quantified this source "strength" as energy (perhaps mistakenly) because it seemed intuitive that more energy is required to give a force source more strength*.
*Fields store energy, proportional (not necessarily linearly) to the field strength. If you increase the overall magnitude of field strength, the total stored energy increases. Thus, energy must be added to increase the overall field strength.
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 gmalivuk
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Re: Maximum efficiency when doing work over a distance
You're talking about the mechanics of fictional telekinesis. I never said it didn't have scientific value.Cradarc wrote:I can argue 100% efficiency is also fictional, since it's impossible to achieve in reality. How come that is considered "science" but my speculation about the extension of energy over distance isn't? Are Einstein's thought experiments science fiction as well? Just because a scenario unrealistic doesn't mean it doesn't have scientific value.
(And yes, 100% efficiency is impossible, but no number less than 100% is the maximum, so 100% is still the limit, as has been explained.)
Re: Maximum efficiency when doing work over a distance
Cradarc wrote:A point source's "influence" on a particle dies off over distance. It is possible for the source to do the same work on A as on B, but to do that it will have to increase its overall "strength". I quantified this source "strength" as energy (perhaps mistakenly) because it seemed intuitive that more energy is required to give a force source more strength*.
Sure; All forces weaken over distance (except for dark energy, but that isn't really a 'force').
But that's nothing to do with how 'efficient' a force is: The Sun's gravity attracts Pluto just as 'efficiently' as it attracts, say, Mars... There are no 'efficiency losses' that have anything to do with the distances involved...
Re: Maximum efficiency when doing work over a distance
Cradarc wrote:I can argue 100% efficiency is also fictional, since it's impossible to achieve in reality.
You can have a limit that can't be achieved without it failing to be a limit. For example: there's no largest real number less than one, but that doesn't stop one being the limit of 11/x as x tends towards infinity, even though there's no finite x for which 11/x = 1. (Please don't discover that 0=1.)
I quantified this source "strength" as energy (perhaps mistakenly) because it seemed intuitive that more energy is required to give a force source more strength*.
Well, if you're not even clear on such concepts as force, energy, field strength, potential, and so on, and what they are, how they relate, and so on, then you're not really going to be able to understand what you asked about. And intuition isn't a good substitute for actually learning basic physics; it's a really bad substitute. But learning physics is good!
*Fields store energy, proportional (not necessarily linearly) to the field strength.
You can't have one quantity proportional to another without that being linear (but you can have linearity without proportionality).
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 sevenperforce
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Re: Maximum efficiency when doing work over a distance
FancyHat wrote:Cradarc wrote:I can argue 100% efficiency is also fictional, since it's impossible to achieve in reality.
You can have a limit that can't be achieved without it failing to be a limit.
Indeed. And it is possible to achieve 100% efficiency in some cases, depending on what sort of efficiency you're talking about. For example, I'm pretty sure there are orientations of masses which would result in gravitational forces being exerted with no gravitational waves being produced.
Re: Maximum efficiency when doing work over a distance
Why do I get the feeling I'm still being misunderstood?
1. I know what efficiency is: (useful quantity)/(total quantity consumed), where quantity can be total energy, power, etc. Essentially it measures the useful output in relation to the input.
2. I am not talking about the efficiency of a source acting over a distance in an absolute sense. I'm talking about the total "ability to do work" (since you people are touchy about the use of "energy") of a source acting over a long distance compared to that of an identical source acting over a short distance.
The "efficiency" measures this difference.
I don't claim there must be a difference, but I intuitive think there should be a difference.
So far, I haven't gotten many responses that are construct towards this topic. That may be my fault for using analogies to make up for my inability to explain my thoughts coherently. I just ask that you guys be more patient instead of trying to prove me wrong based on certain phrases uttered.
1. I know what efficiency is: (useful quantity)/(total quantity consumed), where quantity can be total energy, power, etc. Essentially it measures the useful output in relation to the input.
2. I am not talking about the efficiency of a source acting over a distance in an absolute sense. I'm talking about the total "ability to do work" (since you people are touchy about the use of "energy") of a source acting over a long distance compared to that of an identical source acting over a short distance.
The "efficiency" measures this difference.
I don't claim there must be a difference, but I intuitive think there should be a difference.
So far, I haven't gotten many responses that are construct towards this topic. That may be my fault for using analogies to make up for my inability to explain my thoughts coherently. I just ask that you guys be more patient instead of trying to prove me wrong based on certain phrases uttered.
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 gmalivuk
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Re: Maximum efficiency when doing work over a distance
Cradarc wrote:I don't claim there must be a difference, but I intuitive think there should be a difference.
Short answer: your intuition is wrong.
With your different use of the word "efficiency" all the basic same points still stand. The most important one being, even if 100% isn't achievable, any number less than 100% can be beaten in principle with an appropriate setup. Therefore, the limit is 100%.
Re: Maximum efficiency when doing work over a distance
Does acting at a distance make a difference? Yes. For example, as gmalivuk said: torque.
Is there an absolute maximum efficiency limit that always applies, no matter what, because of the distance? No.
Is there anything that limits the efficiency of telekinesis itself to a maximum limit that's less than 100%? No.
Now, how about the following scenarios.
I'm floating in space, initially at rest, in a spacesuit, holding a cricket ball, and, aiming at a target, I throw it directly away from my centre of mass so that there's no torque acting on me. My spacesuit and I have a total mass of 100 kg. My cricket ball has a mass of 0.16 kg. I throw it so that it moves at a speed of 10 m s^{1}. I've given it 8 J of kinetic energy, and a momentum of 1.6 kg m s^{1}. I've now got a momentum of 1.6 kg m s^{1}, in keeping with conservation of momentum (which is why it's negative (it's a vector quantity)). So, my speed (a scalar quantity) is 16 mm s^{1}, and I have 12.8 mJ of kinetic energy. (Actually, these numbers don't really matter, but I worked them out (hopefully correctly) anyway.)
I'm floating in space, initially at rest, in a spacesuit, with a cricket ball, also initially at rest, 100 m away from me. There is a target I wish to throw the cricket ball at, but I will have to use telekinesis to do it. This will result in the cricket ball moving in a direction perpendicular to the line initially running through the cricket ball and me. (If you imagine the cricket ball is somewhere on a 100 m radius circle with me at the centre, I'm going to throw it along a tangent to that circle.) My spacesuit and I have a total mass of 100 kg, the cricket ball has a mass of 0.16 kg, and I'm going to throw it so that it moves at 10 m s^{1}. It will end up with 8 J of kinetic energy, and will have a momentum of 1.6 kg m s^{1}. Conservation of momentum means that I will have to move in the opposite direction at a speed of 16 mm s^{1}, and with a momentum of 1.6 kg m s^{1}. But conservation of angular momentum means either I, or the cricket ball, or both, will have to be spinning at least some of the time. If neither I nor the cricket ball are initially spinning, then extra energy will be needed to get one or both spinning. And the larger the distance between the cricket ball and me, the more such extra energy will be needed.
Would that illustrate the kind of need for extra energy involving the extra distance that you were asking about? It's not a field strength, inverse square law kind of thing, but it's something that: involves the extra distance making a difference, and in relation to energy requirements as well; is entirely within current, accepted science; and doesn't depend on any details of telekinesis itself.
It also involves the telekinesis itself being 100% efficient, no matter what the distance. Any extra energy I have to expend to make the same difference to the cricket ball is because of torque and conservation of angular momentum, which does involve distance, and would apply whether using telekinesis or things like massless rigid rods.
Is there an absolute maximum efficiency limit that always applies, no matter what, because of the distance? No.
Is there anything that limits the efficiency of telekinesis itself to a maximum limit that's less than 100%? No.
Now, how about the following scenarios.
I'm floating in space, initially at rest, in a spacesuit, holding a cricket ball, and, aiming at a target, I throw it directly away from my centre of mass so that there's no torque acting on me. My spacesuit and I have a total mass of 100 kg. My cricket ball has a mass of 0.16 kg. I throw it so that it moves at a speed of 10 m s^{1}. I've given it 8 J of kinetic energy, and a momentum of 1.6 kg m s^{1}. I've now got a momentum of 1.6 kg m s^{1}, in keeping with conservation of momentum (which is why it's negative (it's a vector quantity)). So, my speed (a scalar quantity) is 16 mm s^{1}, and I have 12.8 mJ of kinetic energy. (Actually, these numbers don't really matter, but I worked them out (hopefully correctly) anyway.)
I'm floating in space, initially at rest, in a spacesuit, with a cricket ball, also initially at rest, 100 m away from me. There is a target I wish to throw the cricket ball at, but I will have to use telekinesis to do it. This will result in the cricket ball moving in a direction perpendicular to the line initially running through the cricket ball and me. (If you imagine the cricket ball is somewhere on a 100 m radius circle with me at the centre, I'm going to throw it along a tangent to that circle.) My spacesuit and I have a total mass of 100 kg, the cricket ball has a mass of 0.16 kg, and I'm going to throw it so that it moves at 10 m s^{1}. It will end up with 8 J of kinetic energy, and will have a momentum of 1.6 kg m s^{1}. Conservation of momentum means that I will have to move in the opposite direction at a speed of 16 mm s^{1}, and with a momentum of 1.6 kg m s^{1}. But conservation of angular momentum means either I, or the cricket ball, or both, will have to be spinning at least some of the time. If neither I nor the cricket ball are initially spinning, then extra energy will be needed to get one or both spinning. And the larger the distance between the cricket ball and me, the more such extra energy will be needed.
Would that illustrate the kind of need for extra energy involving the extra distance that you were asking about? It's not a field strength, inverse square law kind of thing, but it's something that: involves the extra distance making a difference, and in relation to energy requirements as well; is entirely within current, accepted science; and doesn't depend on any details of telekinesis itself.
It also involves the telekinesis itself being 100% efficient, no matter what the distance. Any extra energy I have to expend to make the same difference to the cricket ball is because of torque and conservation of angular momentum, which does involve distance, and would apply whether using telekinesis or things like massless rigid rods.
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Re: Maximum efficiency when doing work over a distance
Another way of looking at it: Where does the energy go if the efficiency of the telekinesis is not 100%?
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Re: Maximum efficiency when doing work over a distance
Fancyhat,
I'm not quite sure where the torque comes from. The ball moves linearly so wouldn't the telekinetic move linearly as well? In ideality land, the rod would would make an infinitesimal small change in angle with respect to your center of mass. As both the object and you move away from each other linearly, the center of mass remains fixed at the midpoint of the rod.
In your massless rods model, does it take energy to extend and contract rods? If not, then wouldn't it take no energy to push a ball directly away from you?
Another thought experiment:
Suppose a telekinetic needs to move a ball trapped inside a metal chamber. The metal chamber is fixed in place and immovable, but has an opening at the top so the ball inside is accessible. The ball is a neutrally charged insulator, but the chamber has a large positive charge. The telekinetic has a slight positive charge.
There are two trials. In the first trial, the telekinetic performs the action from afar. For the second trial, telekinesis is banned. In both trials, the telekinetic starts in the same location with respect to the ball/chamber. In both trials, the telekinetic delivered the same amount of energy to the ball. In both trials, the telekinetic accomplished the task with 100% efficiency.
Did the total energy expended by the telekinetic differ between the trials?
Efficiency is kind of like the shortest path between two points on a spherical surface. Taking the path along the great arc is indeed the "most efficient" path if you're restricted to the surface, but you can just as easily tunnel through the surface of the sphere in a straightline trajectory, which is "most efficient" in a 3D context. What about higher dimensions?
I'm not quite sure where the torque comes from. The ball moves linearly so wouldn't the telekinetic move linearly as well? In ideality land, the rod would would make an infinitesimal small change in angle with respect to your center of mass. As both the object and you move away from each other linearly, the center of mass remains fixed at the midpoint of the rod.
In your massless rods model, does it take energy to extend and contract rods? If not, then wouldn't it take no energy to push a ball directly away from you?
Another thought experiment:
Suppose a telekinetic needs to move a ball trapped inside a metal chamber. The metal chamber is fixed in place and immovable, but has an opening at the top so the ball inside is accessible. The ball is a neutrally charged insulator, but the chamber has a large positive charge. The telekinetic has a slight positive charge.
There are two trials. In the first trial, the telekinetic performs the action from afar. For the second trial, telekinesis is banned. In both trials, the telekinetic starts in the same location with respect to the ball/chamber. In both trials, the telekinetic delivered the same amount of energy to the ball. In both trials, the telekinetic accomplished the task with 100% efficiency.
Did the total energy expended by the telekinetic differ between the trials?
Efficiency is kind of like the shortest path between two points on a spherical surface. Taking the path along the great arc is indeed the "most efficient" path if you're restricted to the surface, but you can just as easily tunnel through the surface of the sphere in a straightline trajectory, which is "most efficient" in a 3D context. What about higher dimensions?
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Re: Maximum efficiency when doing work over a distance
FancyHat wrote:I'm floating in space, initially at rest, in a spacesuit, with a cricket ball, also initially at rest, 100 m away from me. There is a target I wish to throw the cricket ball at, but I will have to use telekinesis to do it. This will result in the cricket ball moving in a direction perpendicular to the line initially running through the cricket ball and me. (If you imagine the cricket ball is somewhere on a 100 m radius circle with me at the centre, I'm going to throw it along a tangent to that circle.) My spacesuit and I have a total mass of 100 kg, the cricket ball has a mass of 0.16 kg, and I'm going to throw it so that it moves at 10 m s^{1}. It will end up with 8 J of kinetic energy, and will have a momentum of 1.6 kg m s^{1}. Conservation of momentum means that I will have to move in the opposite direction at a speed of 16 mm s^{1}, and with a momentum of 1.6 kg m s^{1}. But conservation of angular momentum means either I, or the cricket ball, or both, will have to be spinning at least some of the time. If neither I nor the cricket ball are initially spinning, then extra energy will be needed to get one or both spinning. And the larger the distance between the cricket ball and me, the more such extra energy will be needed.
Maybe my intuition is failing me but I'm not seeing where energy will be lost to spinning?
If we imagine the massless rigid rods that make up telekinesis extend from the spaceman's centre of gravity to the cricket ball's, why wouldn't a push of infinitesimal duration from the spaceman to the cricket ball simply result in both moving in opposite directions? And if no spin is imparted why would it matter how far apart the two objects are? Surely 'efficiency' would be 100% in all instances?
Let's imagine that instead of massless rods 'telekinesis' works as if the spaceman pushes an unseen rocket device towards the cricket ball which attaches itself at the appropriate point and fires the cricket ball towards the target.
There might be some inefficiencies involved here depending on how you want to measure things (does the fact that the rocket device has to eject mass backwards to push the cricket ball forwards count as an 'inefficiency'? In which case the spaceman pushing himself backwards to push the cricket ball forwards via a massless rod is equally so) but my point is that whatever the inefficiency is it is independent of distance: The cricket ball could be 1m away or 1km away and the efficiency of 'pushing a rocket which attaches itself to the cricket ball and propels it in a given direction' would be identical.
Also, this model of telekinesis definitely wouldn't cause either spaceman or cricket ball to spin, right?
 sevenperforce
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Re: Maximum efficiency when doing work over a distance
elasto wrote:Let's imagine that instead of massless rods 'telekinesis' works as if the spaceman pushes an unseen rocket device towards the cricket ball which attaches itself at the appropriate point and fires the cricket ball towards the target.
There might be some inefficiencies involved here depending on how you want to measure things (does the fact that the rocket device has to eject mass backwards to push the cricket ball forwards count as an 'inefficiency'?
If you used a rocket device, then the balance of conservation of momentum would be between the rocket exhaust (moving away from the target) and the cricket ball (moving toward the target). But since the telekinetic approach involves no actual rocket exhaust, there will be net torque somewhere on the system.
It's a good point, and one that I hadn't considered  except in cases of pure linear pushing or pulling, there is a torquing aspect required for conservation of momentum to be maintained during telekinesis, and this will make it more difficult (not really an efficiency thing, but a difficulty thing nonetheless) than it would otherwise be. The greater the distance, the more that torque will affect the moments of the system, and the more difficult it will become for the telekinetic to stay balanced while he does whatever he's trying to do.
Consider the case of a 2.04 kg weight sitting on a table. The coefficient of friction between the table and the weight is 0.5. It's trivial to show, then, that it will take exactly 10 Newtons of force to overcome friction and move the weight.
If I'm a telekinetic and I merely want to push the weight away from me or pull it toward me, then I will need to exert 10 N of force on it. According to the Second Law of Motion, I will also have to exert 10 N of force on the ground at my feet to keep from falling over (forward if I want to pull the weight toward me; backward if I want to push the weight away from me). No matter how close or far from the table I am, those values won't change. It will be as if there is a rigid massless rod connecting me and the weight and I'm merely pushing or pulling on the rod; the effect will be the same regardless of how long the rod is.
However, suppose that instead of pushing or pulling the weight linearly, I want to move the weight sideways. The weight still requires 10 N of force to be moved, but the rigid rod has now become a lever. In order for the far end of the lever to exert 10 N on the weight, I will need to exert greater force on the near end of the rod, and exert equivalent torque (albeit rotationally opposite) on the ground with my feet in order to maintain balance. Unlike our prior case, the length of the lever now makes this more effect more and more significant:
Now, I don't actually expend more energy as the length of the rod increases, but I am required to produce greater force. Since my telekinetic abilities are (presumably) limited by my physical strength, this will cause my effective left/right telekinetic strength to decrease with distance even though my ability to push and pull remains constant.
For example, suppose I am physically fit and can exert about 1000 Newtons of force when physically pushing or pulling on a heavy object. If I am a telekinetic, I will be able to exert that same 1000 N of linear pushing or pulling force on any object at any distance. However, moving an object sideways at a distance is a different story; at 2 meters I will only be able to exert 500 N of sideways force, at 3 meters 333 N, at 4 M 250 N, and so forth with increasing distance.
This might explain why telekinetics in science fiction or fantasy are always able to blast an enemy away or pull a heavy object toward them much more easily than they are able to exert force on objects they aren't aligned with.
Make sense?
Re: Maximum efficiency when doing work over a distance
This is a long post, so I'll spoiler the two replies it contains.
In Reply to Cradarc
In Reply to elasto
In Reply to Cradarc
Spoiler:
In Reply to elasto
Spoiler:
I am male, I am 'him'.
Re: Maximum efficiency when doing work over a distance
Sevenperforce's diagram really clarified the torque problem. Thanks!
The rigid rod model assumes that the energy source is acting on an intermediate object (the rod) to transfer energy to the target.
In my model, telekinesis is akin to "spooky action from a distance". The transfer of energy is direct. From the telekinetic's perspective, the object is being directly manipulated (ie. if they were blind, they wouldn't be able to tell the difference by the forces felt on their body). The torque felt would be equivalent to the case if the object was arbitrarily close.
Effectively, I allowed the fulcrum to be somewhere along your massless rod, instead of at the telekinetic's arm. After all, there's also no reason why the telekinetic would have to move the arm in the first place. The arm is just another object that can be controlled. The only forces felt would arise directly from the conservation of momentum and energy.
If the object moves linearly, only linear momentum needs to be conserved.
FancyHat,
I would respond to all your points, but that may lead us on another tangent.
It's about distinguishing #1 from #2, and determining whether #3 is true or not. Crossing an intervening distance is not trivial. When a telekinetic acts from a distance, would physical laws take the distance into account?
How I imagined telekinesis, distance doesn't matter. In your model with massless rods, distance does matter. Intuitively I feel like distance should matter, but there apparently isn't a physical law that says so.
If distance doesn't matter, then all transportation is effectively wasted work. If humans were 100% efficient at performing an action, it wouldn't require moving at all. Some form of energy would leave our body, and the desired action will be completed spontaneously while the entropy around our body increases.
In reality, there is always a mechanism of energy transfer (eg. massless rods). Even if those mechanisms are 100% efficient, the mere usage of them leads to extra energy expenditure. I think a telekinetic has the ideal mechanism, one that minimizes the total required work to perform any action.
Because efficiency is the ratio of required work to work put in, a normal person's 100% efficient mechanism is not 100% efficient in the telekinetic's perspective.
This is what I was talking about in the spherical surface analogy. A telekinetic's abilities gives them better "paths" to solving a problem. The conundrum is telekinesis does not have to violate physical laws (at least to my knowledge), which means these better paths are theoretically possible.
The rigid rod model assumes that the energy source is acting on an intermediate object (the rod) to transfer energy to the target.
In my model, telekinesis is akin to "spooky action from a distance". The transfer of energy is direct. From the telekinetic's perspective, the object is being directly manipulated (ie. if they were blind, they wouldn't be able to tell the difference by the forces felt on their body). The torque felt would be equivalent to the case if the object was arbitrarily close.
Effectively, I allowed the fulcrum to be somewhere along your massless rod, instead of at the telekinetic's arm. After all, there's also no reason why the telekinetic would have to move the arm in the first place. The arm is just another object that can be controlled. The only forces felt would arise directly from the conservation of momentum and energy.
If the object moves linearly, only linear momentum needs to be conserved.
FancyHat,
I would respond to all your points, but that may lead us on another tangent.
FancyHat wrote:So, I think that's three options:
1. It's about using telekinesis to act over an intervening distance compared with acting with no such intervening distance.
2. It's about using telekinesis to act over an intervening distance compared with first crossing that intervening distance and then acting.
3. Telekinesis is equivalent to crossing an intervening distance and then acting.
4. None of the above.
5. Not only is it none of the above, but it's like elasto's rocket device model instead.
It's about distinguishing #1 from #2, and determining whether #3 is true or not. Crossing an intervening distance is not trivial. When a telekinetic acts from a distance, would physical laws take the distance into account?
How I imagined telekinesis, distance doesn't matter. In your model with massless rods, distance does matter. Intuitively I feel like distance should matter, but there apparently isn't a physical law that says so.
If distance doesn't matter, then all transportation is effectively wasted work. If humans were 100% efficient at performing an action, it wouldn't require moving at all. Some form of energy would leave our body, and the desired action will be completed spontaneously while the entropy around our body increases.
In reality, there is always a mechanism of energy transfer (eg. massless rods). Even if those mechanisms are 100% efficient, the mere usage of them leads to extra energy expenditure. I think a telekinetic has the ideal mechanism, one that minimizes the total required work to perform any action.
Because efficiency is the ratio of required work to work put in, a normal person's 100% efficient mechanism is not 100% efficient in the telekinetic's perspective.
This is what I was talking about in the spherical surface analogy. A telekinetic's abilities gives them better "paths" to solving a problem. The conundrum is telekinesis does not have to violate physical laws (at least to my knowledge), which means these better paths are theoretically possible.
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 gmalivuk
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Re: Maximum efficiency when doing work over a distance
Given a particular task and a particular efficiency E < 100%, what we've argued is that no physical law prevents us from coming up with some method of doing the task with efficiency E' > E.Cradarc wrote:Intuitively I feel like distance should matter, but there apparently isn't a physical law that says so.
But in a fictional world with TK, presumably the TK always works by the same method, and no one has argued that a particular method can always do a task at arbitrarily high efficiency. You yourself pointed out that the cannonball method works for transferring energy to something you want to move directly away from you, but doesn't do any good if you want to pull it toward you or set it moving laterally. There's always some other way of doing those things efficiently, but if TK works like cannonballs then it won't be good at those other tasks.
You do know that conservation laws are not the only physical laws, right?The conundrum is telekinesis does not have to violate physical laws (at least to my knowledge)
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Re: Maximum efficiency when doing work over a distance
So, energy is conserved. It is never lost. The only "inefficiency" is energy that is used to do something that isn't what your goal was.
The claims that there is no way to bound it away from 100% efficiency seem wrong, as there is going to be an entropic cost to aiming at the target (picking that target, and not others, to apply your energy to), no? And that cost increases with the distance of the target (given a fixed size), as your aim has to be more precise?
This cost (on first approximation) doesn't seem high, but it seems to be nonzero.
The claims that there is no way to bound it away from 100% efficiency seem wrong, as there is going to be an entropic cost to aiming at the target (picking that target, and not others, to apply your energy to), no? And that cost increases with the distance of the target (given a fixed size), as your aim has to be more precise?
This cost (on first approximation) doesn't seem high, but it seems to be nonzero.
One of the painful things about our time is that those who feel certainty are stupid, and those with any imagination and understanding are filled with doubt and indecision  BR
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