Gravity-temperature musings by Toffo

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Hypnosifl
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Re: Gravity-temperature musings by Toffo

Postby Hypnosifl » Thu Jan 14, 2016 10:11 pm UTC

Toffo wrote:Here's a mechanism, or whatever, of getting energy out of a black hole:

http://www.nature.com/nature/journal/v2 ... 030a0.html

The "explosion" would still just be thermal radiation, so this would be covered by my comments about using some kind of heat engine to exploit temperature differences between the black hole's Hawking radiation and some external system at a different temperature.
Toffo wrote:Oh yes, maybe I should tell what my simulation simulates. We take one of those Hawking radiation reflecting containers, put one small and one large black hole in there and wait ... after some time small black hole has evaporated and big black hole has absorbed the evaporated radiation. As there is a radiation wind there, we can put a radiation wind turbine there and get some electric energy out of that contraption.

Do you mean something like a Crookes radiometer? As explained on the wikipedia page this is really another type of heat engine, and this paper explains further:
Put a radiometer into a cold anddark place, for example, a refrigerator. The black surfaces, being good absorbers of light and heat radiation, are therefore also good radiators (by Kirchhoff’s law). They cool down more rapidly than the white surfaces, and the vanes will spin in the reverse to the usual sense. This spinning will come to a halt as both surfaces of the vane approach a new thermal equilibrium. So, too, a radiometer run by a heater will gradually cease its rotation as the vanes attain the same overall temperature. The radiometer run by sunlight, which is converted to heat by the blacksurface, does not stop since it never comes to equilibriumwith the temperature of the incident radiation, that is, the temperature of the sun’s surface.

If instead of a Crookes radiometer, which depends on interactions with the gas in the chamber, you wanted to use a turbine powered purely by radiation pressure, I am not sure if this would work with purely thermal radiation--certainly it shouldn't work in a reflective box filled with only radiation and a turbine if the whole system were at equilibrium, since you can't get any work from a system at equilibrium. In the case of the black holes, even though they are both emitting thermal radiation they are at different temperatures so there should be a gradient in the temperature of the radiation, if the turbine wasn't at a different temperature than the ambient radiation maybe you could only get the turbine to spin using radiation pressure if it was large enough so there was a significant temperature difference in the radiation hitting different parts of it. Or it may be that even in a small region where there's very little temperature difference between sides, if there is a significant temperature difference on larger length scales, you could measure significant energy flow (as measured by the Poynting vector) in the smaller region, presumably traveling away from the direction of the faraway hot region and towards the direction of the faraway cold region--I'm not really sure if this is the case, I haven't studied the thermodynamics of radiation much.

Anyway, no matter what system you use, the work you can do with the turbine is presumably going to be much smaller than the total energy that gets emitted by the smaller black hole before it evaporates completely. You said "the released energy is only about 1/4 of the total energy of the two black holes", but even if that calculation is correct (I don't know the details of how you arrived at it so I can't judge), most of that energy is not going to be converted into work by the turbine(s), agreed? So how does this relate to your argument about how "you can not fuse entropic stuff and extract lot of energy"? When you said "extract a lot of energy" you were talking about doing work, right? Also note that the entropy does increase when the mass/energy of a smaller black hole is absorbed into a larger one, since the entropy of a black hole is proportional to the square of its mass, so for example if you have two black holes of masses 3/4*M and 1/4*M and they merge into a black hole of mass M, the initial entropy is equal to some constant time (9/16 + 1/16)*M^2 = 10/16 * M^2 and the final entropy is equal to the same constant times M^2. And generally when you have a closed system that starts at a lower entropy and evolves to a higher one, you can do some work along the way.

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Re: Gravity-temperature musings by Toffo

Postby Toffo » Fri Jan 15, 2016 7:27 am UTC

Also note that the entropy does increase when the mass/energy of a smaller black hole is absorbed into a larger one, since the entropy of a black hole is proportional to the square of its mass


No, not in our case. When a good, I mean ideal, engine does what it does, entropy is not produced. And we have a good engine sitting between a black hole heat source and a black hole heat sink, because we are allowed to have a good engine, we of course pick a good engine.

So entropy does not increase. So entropy stays the same. So the total area of the two event horizons is conserved in our case. So what happens to radius? Could somebody do that math.

An ideal engine takes some energy from an entropic place (small black hole), puts a part of it to a very entropic place (big black hole), and the other part is put to a very low entropy place (battery).

Above reversed:
An ideal motor takes some energy from a low entropy place (battery), uses it to move some energy from a very entropic place (big black hole) to an entropic place (small black hole), and the energy taken from the battery ends up in the entropic place (small black hole).

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Re: Gravity-temperature musings by Toffo

Postby Hypnosifl » Fri Jan 15, 2016 12:05 pm UTC

Toffo wrote:No, not in our case. When a good, I mean ideal, engine does what it does, entropy is not produced. And we have a good engine sitting between a black hole heat source and a black hole heat sink, because we are allowed to have a good engine, we of course pick a good engine.

An ideal heat engine (a Carnot engine) is a system that where the three components--the "working fluid", the hot reservoir, and the cold reservoir--each remain at equilibrium internally, with the process of extracting work running in a quasistatic manner so each remains at equilibrium at all times. But if we imagine a box around the larger system that includes the working fluid and the two reservoirs, this whole system is not at equilibrium (not at maximum entropy), because an isolated system at equilibrium can never have any internal temperature differences. Because of this, a perfect heat engine that never experiences any net increase in entropy as it functions is not actually possible, there will always be some "stray" heat transfer between the two reservoirs beyond the controlled cyclic transfer using the working fluid, like radiation transfer due to the thermal radiation from the hotter reservoir reaching the colder one.

So, you could have a heat engine using a working fluid that moves between two black holes at different temperatures, which would act as the reservoirs. But if you have a larger box around the two black holes and the working fluid, this system is not at equilibrium (it must be in a macrostate of maximum entropy for the system), and the basic definition of black hole entropy tells you that two black holes have a lower entropy than a single black hole of the same mass (a macrostate where all the mass in the system is arranged into one black hole has a higher entropy than a macrostate where the mass is arranged into two black holes, so the two-black-hole macrostate is not one of maximum entropy). And as the black holes change size, the entropy of the whole system does increase. If you disagree with any of this, can you tell me what? Do you disagree that the two black holes will have a lower entropy according to the black hole entropy equation? (which says entropy is proportional to area, and area is of course proportional to the square of the radius, and the radius of a black hole is proportional to its mass according to the formula for the Schwarzschild radius) Or do you disagree that if you draw a box around a Carnot heat engine, the system as a whole is not at equilibrium because of the temperature differences, even if each part is at internal equilibrium?

Also, note that if you want to imagine a truly ideal heat engine which uses the two black holes as reservoirs and has no stray heat transfer other than via the working fluid, then just as the two reservoirs in an ideal Carnot engine do not experience any net change in temperature over the course of one cycle, so neither black hole could, and thus they would not experience any net change in size. If you imagine a process in which one black hole continually shrinks over multiple cycles while the other continually grows, then by definition this process is not the one imagined to take place in an ideal heat engine, and thus the point about there being no net change in entropy in an ideal heat engine wouldn't apply to this process. Also, perhaps I'm confused about how the Carnot heat engine works, but I think the claim about no change in entropy relies on the assumption that the hot and cold reservoirs are essentially infinite in size, so they can lose or absorb finite amounts of heat from or to the working fluid without any change in temperature; I think there is a net transfer of heat into the cold reservoir, and a net transfer out of the hot reservoir, on each cycle (rather than heat in being equal to heat out over a complete cycle). So if that's right, then if you realistically model the reservoirs as being finite and experiencing some change in temperature when there is a net heat transfer in or out, then this is different from the ideal case in that entropy does increase on each cycle.

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Re: Gravity-temperature musings by Toffo

Postby Toffo » Fri Jan 15, 2016 7:44 pm UTC

Hypnosifl, the small black hole does not go into the big black hole. It goes into the battery and into the big black hole. There are other ways to think about what happens, but the best way seems to be what I said there.

An example case:

A small black hole is 1% of a big black hole.

When we lower the small black hole into the big black hole 100% of the entropy of the small black hole goes into the big black hole.

And 1% of the energy of the small black hole goes into the big black hole, while 99% of the energy of the small black hole goes into the winch ... or wherever we decide to store the energy. Again there are other ways to think about what happens, but the best way seems to be what I said there.

Edit: The 1% and 99% there are wrong numbers. We can find the correct numbers by: 1) Using Toffo's simulator 2) Noting that the ratio of black holes' areas is 1/10000, so the big black hole's area increases by 1/10000 of its area, so its radius increases by ... 1/100000000 ... which is 1/10000 of the small black hole's radius, so 1/10000 of the small black hole goes to the big black hole while 9999/10000 of the small black hole goes to an electric battery or similar device.

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Re: Gravity-temperature musings by Toffo

Postby gmalivuk » Fri Jan 15, 2016 10:26 pm UTC

You can't just reference your simulator when you haven't even explained what equations it uses.

And your math is all wrong. If the small BH is 1% the mass of the big BH, then the combined radius after dropping it in will be 1.01 times the original, because radius is proportional to mass. Then the area will be 1.0201 times the original.

Any energy you could store in a battery through the process of lowering it down will come from the potential energy of the small BH relative to the big BH, based on their initial separation.

Not only are you mistakenly treating energy and entropy as interchangeable, you're also mistakenly treating mass-energy and gravitational potential energy as interchangeable.
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Re: Gravity-temperature musings by Toffo

Postby Toffo » Sat Jan 16, 2016 3:33 am UTC

I think we need to study gravity some more. So here's a question:

Let's say you are in a tower with a flywheel weighing 10 Newtons. You spin up the flywheel, which causes it to weigh 10.1 Newtons. Flywheel has now some extra potential energy. Shall we say that A) the extra potential energy is the potential energy of the spinning energy, or B) the extra potential energy is the spinning energy, or C) something else?


I have said earlier:
potential energy of the energy

Then Doogly told me:
This is not a thing, ever.

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Re: Gravity-temperature musings by Toffo

Postby gmalivuk » Sat Jan 16, 2016 3:56 am UTC

Toffo wrote:I think we need to study gravity some more.
That's true, but more important to this discussion is that you need to learn the very basics of what you're trying to talk about.
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Re: Gravity-temperature musings by Toffo

Postby doogly » Sat Jan 16, 2016 2:14 pm UTC

Oh, so you want to spin it to a relativistic speed, use the (deprecated, but alright) relativistic mass formula, and then put the value from that mass into the classical gravitational potential energy formula?
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Re: Gravity-temperature musings by Toffo

Postby Toffo » Sat Jan 16, 2016 9:51 pm UTC

doogly wrote:Oh, so you want to spin it to a relativistic speed, use the (deprecated, but alright) relativistic mass formula, and then put the value from that mass into the classical gravitational potential energy formula?


That seems like a reasonable thing to do. Somehow I feel you find it very very dumb. :)

I'm just asking this question: "which forms of energy have potential energy?"

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Re: Gravity-temperature musings by Toffo

Postby doogly » Sat Jan 16, 2016 10:19 pm UTC

I think you can get away with some of this, but it's not recursive. Gravitational potential energy doesn't have potential energy.

And you can't use a potential energy formulation with general relativistic effects at all.
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Re: Gravity-temperature musings by Toffo

Postby Toffo » Sun Jan 17, 2016 9:23 am UTC

doogly wrote:I think you can get away with some of this, but it's not recursive. Gravitational potential energy doesn't have potential energy.


Yes, except when there's one potential energy on the left and one potential energy on the right, and the two independent potential energies attract each other, correction repel each other.

Potential energy is negative, causes a mass defect, so systems with potential energy gravitationally attract each other less than if they had zero potential energy.

So mass defects repel each other, and mass defects are caused by potential energies, and all potential energies have a corresponding mass defect - assuming gravitational potential energy is not fundamentally different than for example nuclear potential energy.

Note: Earlier I may have talked like potential energy is positive energy, and later I may again talk like potential energy is positive energy, here I'm trying to make some kind of point by using the correct formulation - that this stuff needs a reformulation.

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Re: Gravity-temperature musings by Toffo

Postby doogly » Sun Jan 17, 2016 1:03 pm UTC

Don't post "Yes, except I still believe the opposite of what you said." That's not helpful.
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Re: Gravity-temperature musings by Toffo

Postby gmalivuk » Sun Jan 17, 2016 2:48 pm UTC

Toffo, you're forgetting some fairly basic Newtonian stuff here.

Potential energy can be positive or negative depending on where you set your zero. It's kind of like temperature that way. When we talk about the potential energy of a mass we hold only slightly above the surface of a much larger body, m*g*h is a pretty good approximation of that mass's potential relative to the surface.

Sure, the convention is to set zero at infinity when dealing with gravity and celestial mechanics, since that gives us a nice everywhere-negative function to work with, but that's just a convenient convention. An object moving at escape velocity on the surface of Earth has 0 total (kinetic + potential) energy with the zero-at-infinity convention, but it has 62.5 MJ/kg relative to the stationary surface.
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Re: Gravity-temperature musings by Toffo

Postby Toffo » Sun Jan 17, 2016 3:08 pm UTC

gmalivuk wrote:Toffo, you're forgetting some fairly basic Newtonian stuff here.

Potential energy can be positive or negative depending on where you set your zero. It's kind of like temperature that way. When we talk about the potential energy of a mass we hold only slightly above the surface of a much larger body, m*g*h is a pretty good approximation of that mass's potential relative to the surface.

Sure, the convention is to set zero at infinity when dealing with gravity and celestial mechanics, since that gives us a nice everywhere-negative function to work with, but that's just a convenient convention. An object moving at escape velocity on the surface of Earth has 0 total (kinetic + potential) energy with the zero-at-infinity convention, but it has 62.5 MJ/kg relative to the stationary surface.


I see.

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Re: Gravity-temperature musings by Toffo

Postby Toffo » Sun Jan 17, 2016 3:24 pm UTC

doogly wrote:Don't post "Yes, except I still believe the opposite of what you said." That's not helpful.



Let us consider some scenarios inside an accelerating rocket in order to try to see if we can make sense of potential energy.

If we lower down a mass using a winch attached to the rear of the rocket, we note that the weight of the mass stays constant although the potential energy of the mass presumably changes. This suggests that this potential energy of the mass has no mass, or potential energy.

But if the mass gravitationally collapses and radiates the generated heat away, we note that the weight of the mass decreases, suggesting that the internal potential energy of the mass had some mass and potential energy.

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Re: Gravity-temperature musings by Toffo

Postby doogly » Sun Jan 17, 2016 4:38 pm UTC

You're doing thought experiments that just state your wrong ideas over again. These aren't thought experiments.
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Re: Gravity-temperature musings by Toffo

Postby sevenperforce » Mon Jan 18, 2016 3:06 pm UTC

Think about it this way, Toffo: "potential energy" is the amount of work which could be extracted from a system given some transformation of that system. It is not an entity in its own right; it is a mathematical convention arising from the sum of the parts of a system.
Toffo wrote:Let us consider some scenarios inside an accelerating rocket in order to try to see if we can make sense of potential energy.

If we lower down a mass using a winch attached to the rear of the rocket, we note that the weight of the mass stays constant although the potential energy of the mass presumably changes. This suggests that this potential energy of the mass has no mass, or potential energy.

First of all, the scenario isn't entirely clear here. Are you talking about a rocket accelerating in a uniform gravitational field? Or a rocket accelerating in empty space?

Either way, changing the position of your chunk off mass will not change its "internal potential energy". Depending on how you've set up your system, changing its position may serve to change the gravitational potential energy of the system, where the system includes both the mass and some gravitational field, but this potential is external to the mass.

If the mass gravitationally collapses and radiates the generated heat away, we note that the weight of the mass decreases, suggesting that the internal potential energy of the mass had some mass and potential energy.

Sigh.

If the object gravitationally collapsed, this was because some of its mass-energy in the form of chemical bonds was converted into mass-energy in the form of heat/radiation. We can use a fictional convention to model the chemical bonds as having "potential energy" but that's just for convenience; what's really happening is one form of mass-energy being converted into another form of mass-energy. No "potential" involved. And yes, radiating away mass-energy reduces the mass-energy of the object just like ripping out a chunk of it and flinging it away would reduce its mass-energy. In either case, its gravitational potential energy in an external field changes by the same amount...because, again, it's a convention based on the overall system, not an intrinsic quality/quantity.

Since you're fond of thought experiments, here's one. Put your object or system or whatever it is inside a sealed box which cannot exchange energy with the outside in any way. From the outside, you can winch it up or down or left or right or whatever you want; from the inside, you can convert chemical energy into thermal energy into radiation into "potential" or whatever you want. What happens inside cannot effect the measured mass/weight/whatever outside.

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Re: Gravity-temperature musings by Toffo

Postby Toffo » Mon Jan 18, 2016 11:12 pm UTC

sevenperforce - I notice that you did not disagree with the idea that when towing a mass and accelerating, the length of the towing rope does not affect the force on the hitch.

Maybe you might even say I did not make any error in description of the thought experiment? I mean the observations of the observer in the rocket, I got those right?


Let us apply the equivalence principle now: When a mass is winched down in an almost uniform gravity field, the force on the winch is almost constant. Right? Or wrong? We assume a weightless rope.

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Re: Gravity-temperature musings by Toffo

Postby Neil_Boekend » Tue Jan 19, 2016 9:06 am UTC

Toffo wrote: the idea that when towing a mass and accelerating, the length of the towing rope does not affect the force on the hitch.

I can't find the original idea (neither manually nor through search), so I'm just going to reply to that: I agree only when you assume a non stretchable rope and no weird gravity stuff.
With a stretchable rope a longer rope will have more stretch, thus with short jerks the maximum force on the hitch is lower (short jerks tend to happen during towing.)
When you are going towards a black hole (or other object with relevant gravity) a longer rope will have more problems with tidal forces, increasing force.
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Re: Gravity-temperature musings by Toffo

Postby sevenperforce » Tue Jan 19, 2016 2:08 pm UTC

Toffo wrote:sevenperforce - I notice that you did not disagree with the idea that when towing a mass and accelerating, the length of the towing rope does not affect the force on the hitch.

Maybe you might even say I did not make any error in description of the thought experiment? I mean the observations of the observer in the rocket, I got those right?


Let us apply the equivalence principle now: When a mass is winched down in an almost uniform gavity field, the force on the winch is almost constant. Right? Or wrong? We assume a weightless rope.

Are you "winching" the rope out during the acceleration? Because that will change things. But if you're just comparing different systems with different lengths of rope, then no, it doesn't make a difference. For a tall tower near Earth's surface, or for a rocket accelerating at 1 gee, the tower/rocket exerts 9.81 N on a 1-kg test mass whether the (weightless) rope connecting them is an inch, a foot, or a mile long.

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Re: Gravity-temperature musings by Toffo

Postby gmalivuk » Tue Jan 19, 2016 3:38 pm UTC

It does get weirder with relativity and very long ropes, though. The rear has to have greater acceleration than the front in order to maintain the same distance under continued acceleration, which presumably means tension on a tow rope would increase with length.
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Re: Gravity-temperature musings by Toffo

Postby sevenperforce » Tue Jan 19, 2016 4:46 pm UTC

Perhaps Toffo would be interested in reading up on the Nordtvedt effect.

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Re: Gravity-temperature musings by Toffo

Postby Toffo » Tue Jan 19, 2016 6:11 pm UTC

gmalivuk wrote:It does get weirder with relativity and very long ropes, though. The rear has to have greater acceleration than the front in order to maintain the same distance under continued acceleration, which presumably means tension on a tow rope would increase with length.



Actually the force on the hitch stays constant, as I said.

But the force on the bolts that attach the winch to the rocket increases, as the mass of the batteries that store the extracted energy increases. The batteries are bolted on the winch, for the purpose of easy analysis.

Example case:

1 kg mass is lowered, acceleration is 1g, the mass weighs 10 N all the time. When we lower the mass very close to Rindler-horizon, the extra weight on the batteries approaches 10 N.

So it takes twice as much energy to tow a mass with a very very long rope compared to a short rope.

Of course we could get rid of the energy in the batteries, in which case we can tow using the same energy irregardless of the length of the rope.

Of course we could use the energy in the batteries to accelerate the towing vehicle, in which case we can tow with less energy with a rope that extends very very much during the acceleration, compared to a rope that stays short. Saved energy = rest energy of the mass

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Re: Gravity-temperature musings by Toffo

Postby sevenperforce » Tue Jan 19, 2016 6:22 pm UTC

what

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Re: Gravity-temperature musings by Toffo

Postby gmalivuk » Tue Jan 19, 2016 6:52 pm UTC

Toffo wrote:1 kg mass is lowered, acceleration is 1g, the mass weighs 10 N all the time. When we lower the mass very close to Rindler-horizon, the extra weight on the batteries approaches 10 N.

So it takes twice as much energy to tow a mass with a very very long rope compared to a short rope.
How about you do some math for this claim?
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Re: Gravity-temperature musings by Toffo

Postby Toffo » Tue Jan 19, 2016 7:47 pm UTC

gmalivuk wrote:
Toffo wrote:1 kg mass is lowered, acceleration is 1g, the mass weighs 10 N all the time. When we lower the mass very close to Rindler-horizon, the extra weight on the batteries approaches 10 N.

So it takes twice as much energy to tow a mass with a very very long rope compared to a short rope.
How about you do some math for this claim?


Nah, first I should learn some math.

Well ok then, here's some math:

distance to the horizon = 9.18 * 1015m

I found the distance here: http://gregegan.customer.netspace.net.a ... rizon.html


Energy=distance * force = 10 N * 9.18 * 1015 m = 9.18 * 1016J

Is that same as mc2 when m=1kg ... Yes it is.

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Re: Gravity-temperature musings by Toffo

Postby SDK » Tue Jan 19, 2016 8:31 pm UTC

:lol:

Thanks a lot! Now my coworkers are looking at me funny!
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Re: Gravity-temperature musings by Toffo

Postby gmalivuk » Tue Jan 19, 2016 8:34 pm UTC

I was asking about the part that I quoted, where you claim towing it takes twice as much energy. Pointing out something that seems to have as much energy as the rest mass doesn't actually prove anything about the claim you're making.
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If I'm accelerating at about 1g, then the horizon is 1ly behind me. If I'm towing a payload 0.5ly behind me such that it maintains that distance, then it is experiencing 2g of proper acceleration. So in other words your 1kg mass would have to feel 20N on its end of the rope. If I "lowered" it towards the horizon until it came to rest 0.75ly behind me, it would have to experience 4g of proper acceleration to maintain that distance, or a force of 40N.

The difference in acceleration is a straightforward consequence of the accelerating Rindler metric, and the corresponding difference in force is an even more straightforward application of F=ma.

I'm not sure how that translates to tension felt on my end, because there's also time dilation to contend with, but assuming you mean the end connected to the 1kg when you say "hitch", the tension on that end increases proportionately to the ratio of our distances from the horizon. (As in, if I'm twice as far from the horizon as the mass is, it accelerates twice as hard, and if I'm four times as far from the horizon, it accelerates four times as hard. Everything at rest in the accelerating fram accelerates in inverse proportion to its distance from the horizon.)
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Re: Gravity-temperature musings by Toffo

Postby Toffo » Wed Jan 20, 2016 8:38 am UTC

gmalivuk wrote:I was asking about the part that I quoted, where you claim towing it takes twice as much energy. Pointing out something that seems to have as much energy as the rest mass doesn't actually prove anything about the claim you're making.


If we divide that large energy by c2, then we get a mass, 1 kg, which is the mass increase of the battery pack, when the mass-energy is stored there, and then finally the weight increase of the battery pack is the mass increase times acceleration. It's 10 Newtons.

10 Newtons is pulling the hitch and another 'extra' 10 Newtons is pulling the battery pack 'down'. Power is force times speed, so power is doubled after the down winching is completed.



I never gave any reason why 10 Newtons is always pulling the hitch. That's because I don't have a reason that would convince you. I just happen to know that it's like that. But hey, I can postulate it. :)

So I hereby postulate that force F when mass m is pulled by a rope is F=m*a at the upper end of the rope. At the other end of the rope the force is k*m*a , where k is distance to horizon / rope length.

And somehow this does not violate conservation of energy or momentum, although it seems to do so. I'll try to figure out how this is possible.

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Re: Gravity-temperature musings by Toffo

Postby Neil_Boekend » Wed Jan 20, 2016 9:00 am UTC

Toffo wrote:I never gave any reason why 10 Newtons is always pulling the hitch. That's because I don't have a reason that would convince you. I just happen to know that it's like that. But hey, I can postulate it. :)

Since gmalivuk has provided a proof that the force will increase as you lower the object (with basic Newtonian gravity, no less) I think that it is time to reconsider the knowledge that the force will not change.
Unless you postulate it as a preset condition of your thought experiment, of course. You could change the mass to force the force to stay at 10 N, but then energy and momentum need not be conserved. I don't have a clue how such an thought experiment would illuminate anything but you can postulate such things.
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Re: Gravity-temperature musings by Toffo

Postby Toffo » Thu Jan 21, 2016 12:40 am UTC

Neil_Boekend wrote:Since gmalivuk has provided a proof that the force will increase as you lower the object (with basic Newtonian gravity, no less) I think that it is time to reconsider the knowledge that the force will not change.
Unless you postulate it as a preset condition of your thought experiment, of course. You could change the mass to force the force to stay at 10 N, but then energy and momentum need not be conserved. I don't have a clue how such an thought experiment would illuminate anything but you can postulate such things.


Are you trying to fool me. :) There's no gravity in there.


There's just a contracting towing rope. Which is pulling harder on the towed thing than the towing vehicle. Because every microscopic nudge that is delivered by the towed thing spends a long time in the rope before arriving to the towing vehicle. And that time is increasing as the rope's speed is increasing, that's important.

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Re: Gravity-temperature musings by Toffo

Postby gmalivuk » Thu Jan 21, 2016 4:45 am UTC

Relative to the rope itself, the rope's speed isn't increasing and its time dilation isn't changing.

But again, it's a simple fact of Rindler coordinates that something closer to the horizon has to accelerate harder to maintain the same proper distance to something in front of it.

You have yet to offer any account of why you think that doesn't correspond to more force on its end.
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Re: Gravity-temperature musings by Toffo

Postby Toffo » Thu Feb 18, 2016 1:17 pm UTC

Maybe now I finally understand what people have been trying to tell me all the time:

Let's say I have a pizza at temperature 3 K in an universe with 3 K cosmic background radiation. There's a deep gravity well. I start rapidly lowering the pizza to the well, this causes the pizza to cool down, this cooling I can measure using a infrared thermometer which I'm holding on my hand.

When the temperature of the pizza is 0.001 K, I stop the lowering and wait until the pizza has reached thermal equilibrium with the environment, the temperature of the environment is 3 K, which I can measure using the same infrared thermometer as before.

Then I start lifting the pizza up, this causes the pizza to heat up, this rise of temperature can be measured using the same old infrared thermometer again. When the pizza is back up its temperature is 350 K.

Right?

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Re: Gravity-temperature musings by Toffo

Postby doogly » Thu Feb 18, 2016 1:21 pm UTC

Why would lowering it cool it?
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Re: Gravity-temperature musings by Toffo

Postby Toffo » Thu Feb 18, 2016 1:35 pm UTC

I don't know why lowered objects cool down.

I just know that an infrared thermometers will tell us that the temperature of a lowered object is going down.

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Re: Gravity-temperature musings by Toffo

Postby gmalivuk » Thu Feb 18, 2016 1:40 pm UTC

And how do you know that?
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Re: Gravity-temperature musings by Toffo

Postby Neil_Boekend » Thu Feb 18, 2016 2:05 pm UTC

If I interpret it correctly the lowering in the gravity well will not decrease the temperature of the object. The IR thermometer outside the gravity well will register a lower temperature due to redshift from the radiation exiting the gravity well.
It just looks cooler. It is not actually cooler. A thermometer on the pizza itself (lowered with the pizza) will not display a lower temperature.
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Re: Gravity-temperature musings by Toffo

Postby Xanthir » Thu Feb 18, 2016 7:37 pm UTC

If that's the case (I'm not commenting on whether or not it is, I don't know GR well enough), then it won't ever "reach thermal equilibrium" by raising back to an apparent 3K, obviously.
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Re: Gravity-temperature musings by Toffo

Postby Toffo » Fri Feb 19, 2016 11:10 am UTC

Let's say I have an infrared thermometer at the middle of of a large spinning space station. All parts of the space station are in thermal equilibrium. So everything is in equilibrium with the infrared thermometer, which measures the same temperature for everything, let's say 3 K.

Let's say I have a pizza, at temperature 3 K and I start rapidly (rapidly because I don't want any heat transfer between the pizza and the environment) lowering the pizza towards the perimeter of the space station, this causes the pizza to cool down, this cooling I can measure using the infrared thermometer which I'm holding on my hand.

When the temperature of the pizza is 0.001 K, I stop the lowering and wait until the pizza has reached thermal equilibrium with the environment, the temperature of the environment is 3 K, which I can measure using the same infrared thermometer as before.

Then I start lifting the pizza up, this causes the pizza to heat up, this rise of temperature can be measured using the same old infrared thermometer again. When the pizza is back up its temperature is 350 K.

Right?

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Re: Gravity-temperature musings by Toffo

Postby Neil_Boekend » Fri Feb 19, 2016 11:51 am UTC

Toffo wrote:this causes the pizza to cool down

Why?
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