## Gravity-temperature musings by Toffo

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Toffo
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### Gravity-temperature musings by Toffo

So here are some basics:

Temperature of radiation is its energy/information ratio.

Energy is conserved.

Radiation's information is constant ... except when it isn't ... well we consider radiation with constant information now.

Radiation free falling down gains energy, so its temperature increases.

Radiation free falling up loses energy, so its temperature decreases.

Radiation lowered down in a mirror lined bag loses energy, so it's temperature decreases.

Temperature of matter lowered down must follow temperature of radiation lowered down, so temperature of matter lowered down decreases.

Radiation winched up in a mirror lined bag gains energy, so it's temperature increases.

Temperature of matter winched up must follow temperature of radiation winched up, so temperature of matter winched up increases.

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### Re: Gravity-temperature musings by Toffo

Stream of consciousness is not a terribly productive way to do science.

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### Re: Gravity-temperature musings by Toffo

Energy is only conserved locally, unless you can pump the energy the light has gained back up to the place the light is emitted, you haven't broken anything to do with energy conservation.
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Toffo
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### Re: Gravity-temperature musings by Toffo

When does object lose or gain energy? It would be good if we understood that.

A clock attached to an object runs slower - object lost energy.

A clock attached to an object runs faster - object gained energy.

An example case:
A spacecraft falls into a neutron star - spacecraft loses energy, neutron star loses energy, some empty space somewhere gains energy.

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### Re: Gravity-temperature musings by Toffo

Why does the neutron star lose energy when it gets hit by a spacecraft?
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Toffo
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### Re: Gravity-temperature musings by Toffo

Clocks on the neutron star slow down as extra mass arrives nearby them. We postulate that clocks slowing down is a sign of energy loss.

Maybe I forgot something: Before the crash there is a neutron star and a spacecraft. After the crash there is a neutron star, a spacecraft, and some heat. Hmm.. neutron star and spacecraft create heat, that's why they lose energy. We do not count the heat as a part of the spacecraft or neutron star. The heat might well be radiated into space, which would increase energy of space, if we count the radiation in space as part of the space.

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### Re: Gravity-temperature musings by Toffo

Toffo wrote:Clocks on the neutron star slow down as extra mass arrives nearby them. We postulate that clocks slowing down is a sign of energy loss.

I have a clock at rest wrt to me. I give it energy (boost it into a frame moving wrt to me) and I see it slow down. Your postulation is wrong.
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### Re: Gravity-temperature musings by Toffo

Toffo wrote:When does object lose or gain energy? It would be good if we understood that.

A clock attached to an object runs slower - object lost energy.

A clock attached to an object runs faster - object gained energy.

This is unfortunately straight wrong. You seem to be thinking about it like a clock just physically going slower or faster than normal. Relatively-induced time dilation is time itself flowing faster or slower relative to something else. The clock is slow because it's experiencing less time than us, not because it's got less energy to turn its gears with. As eSOANEM points out, things "run slow" mostly because they're experiencing acceleration, which means they're gaining energy. (Though they can also run slow from being dropped into a gravity well, where they've *lost* gravitational potential energy. It varies.)
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Toffo
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### Re: Gravity-temperature musings by Toffo

eSOANEM wrote:I have a clock at rest wrt to me. I give it energy (boost it into a frame moving wrt to me) and I see it slow down. Your postulation is wrong.

I have a plastic bag which has energy 20 KJ, and a hamburger that has energy 300 KJ. Now I put the hamburger in the bag. The bag still has energy 20KJ. Because we do not count the energy of the contents of the bag as energy of the bag.

Likewise we do not count a kinetic energy in a clock as an energy of the clock.

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### Re: Gravity-temperature musings by Toffo

Toffo wrote:I have a plastic bag which has energy 20 KJ, and a hamburger that has energy 300 KJ. Now I put the hamburger in the bag. The bag still has energy 20KJ. Because we do not count the energy of the contents of the bag as energy of the bag.

Likewise we do not count a kinetic energy in a clock as an energy of the clock.

Really?

If I have a cup of water and heat it up, we say the cup of water has gained energy, don't we? If we don't say that - where do we say the energy has gone?

But heat is just disorganised kinetic energy.

Toffo
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### Re: Gravity-temperature musings by Toffo

We are doing science now. We say things as we say them. It does not matter how things are said in everyday language ... except when everyday language happens to fit our purposes.

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### Re: Gravity-temperature musings by Toffo

I'm not talking 'everyday language' - I'm talking science. I'm querying your claim that science doesn't include energy input in the form of heat as part of the energy of an object.

Sure, the total energy of an object can be divided into many kinds - kinetic energy, gravitational potential energy, electromagnetic potential energy and so on. But that doesn't mean they don't all belong to the object. This is trivially demonstrated by the fact that one form of energy can be turned into another via reversible physical laws or simply by changing your frame of reference.

Your example of putting one object inside another where both objects remain distinct is spurious in this regard: In no frame of reference does a bag containing a burger stop being a bag containing a burger. The same is not true for, say, kinetic energy: The kinetic energy of an object can be changed simply by altering your frame of reference. Indeed, without a frame of reference, asking what the kinetic energy of an object is is a meaningless question.

Toffo
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### Re: Gravity-temperature musings by Toffo

elasto wrote:I'm not talking 'everyday language' - I'm talking science. I'm querying your claim that science doesn't include energy input in the form of heat as part of the energy of an object.

You want to argue about science, while I want to ponder some interesting inanimate objects.

Oh yes, I said "we are doing science now". What did I mean by that? Well definitely not "we are talking about science now" ... I guess I thought that pondering inanimate object is doing science. If it isn't, then I misspoke.
Last edited by Toffo on Fri Nov 13, 2015 6:05 pm UTC, edited 1 time in total.

Toffo
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### Re: Gravity-temperature musings by Toffo

Let's consider black holes and Hawking radiation, and let's assume the radiation comes from the event horizon.

As a photon climbs up from the gravity well it gives 99.9999999...% of its energy to the black hole. This happens mostly during first millimeters of the climb.

And that is why you get fried if you go very close to any black hole. The photons are still very energetic there.

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### Re: Gravity-temperature musings by Toffo

Toffo wrote:Let's consider black holes and Hawking radiation, and let's assume the radiation comes from the event horizon.

As a photon climbs up from the gravity well it gives 99.9999999...% of its energy to the black hole. This happens mostly during first millimeters of the climb.

And that is why you get fried if you go very close to any black hole. The photons are still very energetic there.
If you want the rest of us to do science now, then you should join us yourself. As you've already been told by someone who knows more than you about quantum mechanics in curved space, that this isn't as simple as you want to make it.

If you want to naively do GR on photons emitted right at the event horizon, then you have to conclude that they lose all of their energy to the black hole (i.e. they don't ever escape the black hole), because time dilation is infinite there. That would preclude Hawking radiation entirely, though, so must not be the correct way to think about how hot Hawking radiation gets as you hover closer and closer to the event horizon.
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### Re: Gravity-temperature musings by Toffo

Toffo wrote:
elasto wrote:I'm not talking 'everyday language' - I'm talking science. I'm querying your claim that science doesn't include energy input in the form of heat as part of the energy of an object.

You want to argue about science, while I want to ponder some interesting inanimate objects.

Oh yes, I said "we are doing science now". What did I mean by that? Well definitely not "we are talking about science now" ... I guess I thought that pondering inanimate object is doing science. If it isn't, then I misspoke.

Nah, musing is fine. You don't have to be "doing science." But musing doesn't prevent you from being incorrect about interesting inanimate objects.
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Toffo
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### Re: Gravity-temperature musings by Toffo

What happens if we capture one Hawking radiation photon right where it's born, and give it a ride up?

Well, the box into which we put the photon becomes very heavy, then we have to use lot of energy lifting the box, and people opening the box will be fried.

At some point we should also ponder the question: Does catching very energetic Hawking radiation in a very sturdy box cause a black hole being formed?

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### Re: Gravity-temperature musings by Toffo

If you're still doing simple GR and assuming "right where it's born" is the event horizon, then the photon cannot ever come up from there, whether it's "given a ride" or not.

The box wouldn't become "very heavy", it would become infinitely heavy.
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### Re: Gravity-temperature musings by Toffo

Thanks for the details.

Now let's contemplate heat flow between black holes.

A small black hole is deep in the gravity well of a large black hole. What happens?

Somehow I feel the small black hole cannot suck energy from the large black hole, because thermodynamics forbids that somehow. OTOH small black hole is very time dilated, while large black hole is almost not time dilated at all.

Let's say a small black hole and an observer are lowered down towards event horizon of a large black hole. What does the observer observe?

The small hot black hole does not change, its temperature and expected life time stay the same.

The large cool black hole does change, its temperature increases and its expected life time decreases.

See, the two black holes are becoming more alike according to our observer.

Shall we conclude that a large black hole and a small black hole very close to the large black hole are very close to being in thermal equilibrium?

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### Re: Gravity-temperature musings by Toffo

The black hole doesn't heat up when you add energy to it. It is not doing normal thermodynamics. T_hawking ~ 1/M, so if you add mass to a black hole (like a merger, or by holding something radiating up next to it) it will gain mass and decrease temperature. It doesn't heat up. Its temperature is not really quite like normal temperatures.
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### Re: Gravity-temperature musings by Toffo

Toffo wrote:small black hole is very time dilated, while large black hole is almost not time dilated at all.
How do you figure?

At a given distance above the event horizon, there's more time dilation for a large black hole than a small one, because that distance is a smaller fraction of the Schwarzschild radius.

We are as time dilated as you would be one Earth-radius above an Earth-mass black hole, which is not very time dilated at all. (GPS satellites have to account for the difference, but if you visited one of them in a space ship you wouldn't have to adjust your wristwatch at all.) But one Earth-radius above a solar-mass black hole means a discrepancy of about 1 part in 4000 with respect to distant observers, or 20 seconds per day. And one Earth-radius above a supermassive black hole is extremely deep in its gravity well, with a time dilation factor of about 30 for a couple million solar masses.

And of course, time dilation approaches infinity as you get to the event horizon itself, of any size of black hole.
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### Re: Gravity-temperature musings by Toffo

eSOANEM wrote:Energy is only conserved locally, unless you can pump the energy the light has gained back up to the place the light is emitted, you haven't broken anything to do with energy conservation.

Oh yes. Let's say I lift up an object that has been hanging near a large black hole for a long time. Some people say that object is cold. So now I use that object as a heat sink of a engine whose hot side is at temperature T2.

My engine's efficiency is (T2 - T1) / T2

where T1 is temperature of the black hole

Now I lower my heat sink back to from where I lifted it. And I get more work out of the heat energy!

If I can pump coldness up and lower heat down, laws of thermodynamics are violated.

Hmm ... is there something wrong with the above ... I better postulate that the heat sink is always at same temperature. It's a phase changing heat sink.

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### Re: Gravity-temperature musings by Toffo

I noticed one erroneous idea of mine: The black hole facing side of an object hanging near a black hole is scorched.

If it was so, then we could convert Hawking radiation to electricity, but that's not allowed as Hawking radiation is super entropic.

So therefore: All sides of an object hanging near a black hole are scorched equally.

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### Re: Gravity-temperature musings by Toffo

Well, it was correct of you to notice that you were wrong, but you're much wronger than you thought.
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### Re: Gravity-temperature musings by Toffo

When I lift an object that is hanging near a black hole, what am I lifting up? If the lifting is done with a long rope, energy is traveling _down_ along the rope. Also the black hole is moving _down_, it emits less energetic Hawking radiation as the energy arriving through the rope causes time dilation of the black hole.

So the problem is: What am I lifting up? I feel that something should go up, if lifting is being done.

Let's not consider the later stages of lifting, where things become more normal.

And I don't want to hear that the object moved up, I know that. Is there something in the object that weighs a lot, so that it can serve as a counter-weight for all that energy that is going down in our lifting process?

And I don't necessarily buy a claim that there is a lot of energy in the object, because ... well objects hanging near black holes don't have much energy ... they have much less energy than similar objects that are falling at great speed.

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### Re: Gravity-temperature musings by Toffo

What do you mean, energy is going down? You are moving the mass up, said so yourself.
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### Re: Gravity-temperature musings by Toffo

The object, that is at low position, gains energy. The lifter, that is at high position, loses energy. So energy went from lifter to object, so energy went from high position to low position, so potential energy of the energy decreased, so we have an interesting question: Where did the potential energy go?

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### Re: Gravity-temperature musings by Toffo

Toffo wrote:If it was so, then we could convert Hawking radiation to electricity, but that's not allowed as Hawking radiation is super entropic.
All heat is entropic. That doesn't prevent us from using it for electricity.
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### Re: Gravity-temperature musings by Toffo

Toffo wrote: potential energy of the energy

This is not a thing, ever.
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### Re: Gravity-temperature musings by Toffo

Energy has no potential energy when at high position? That sounds very odd to me.

Let's pretend for a while that energy has potential energy, and let's try to solve this problem of lots of energy moving down when an object hanging near a black hole is winched a few millimeters upwards.

The winch loses energy as it winches, that energy ends in the object - that's a lower position than the original position of the energy.

Black hole loses energy as it helps to lift the object, that energy ends in the object - that's a higher position than the the original position of the energy. (I don't actually know the original position of the energy - maybe it's the event horizon - the lowest possible position)

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### Re: Gravity-temperature musings by Toffo

Why would we pretend something that is absolutely wrong? It would not help you understand energy, gravity, black holes, anything.

Energy does not have potential energy. Energy is a quality, not a thing. Things have energy.
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### Re: Gravity-temperature musings by Toffo

This old post may help with understanding energy.
viewtopic.php?p=1794223#p1794223

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### Re: Gravity-temperature musings by Toffo

gmalivuk wrote:
Toffo wrote:If it was so, then we could convert Hawking radiation to electricity, but that's not allowed as Hawking radiation is super entropic.
All heat is entropic. That doesn't prevent us from using it for electricity.

Hey yet another argument why Hawking radiation is scorching near event horizon:

Let's say we have a black hole with temperature 3 K, and cosmic background radiation with temperature 3 K. The black hole and the cosmic background radiation are in thermal equilibrium. What is the situation like near the event horizon? Well cosmic background radiation is scorching there, so therefore Hawking radiation must be scorching there, if the black hole and the cosmic background radiation are in thermal equilibrium there.

(This is somewhat related to electricity production, as thermal equilibrium and heat engines don't go together very well)

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### Re: Gravity-temperature musings by Toffo

Okay, so objects may get the same temperature on both sides for a black hole the same temperature as the CMB, but what about larger or smaller black holes? Nothing about the Schwarzschild metric or Hawking radiation requires any CMB at all, as far as I know.

Also, you still haven't actually demonstrated that Hawking radiation would be "scorching" from close up. The event horizon is infinitely time-dilated compared to hovering at any finite distance above it, after all.
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### Re: Gravity-temperature musings by Toffo

And I want to do a little pill check like they have in hospitals with ornery patients. Can you confirm for me that you have swallowed what we've said about energy? If you don't understand energy, your prospects for saying anything even partially correct about black hole thermodynamics are doomed.
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### Re: Gravity-temperature musings by Toffo

Doogly, I am able to understand sentence "energy is not a thing", if that was what you guys we telling me

Now I would like to think energy as a dog. So I have a dog, I want my dog to bite a jogger, so I tell the dog to bite a jogger, the dog is sitting next to me, as I give the order, the dog catches the jogger and bites his leg, but the jogger does not stop. Ok so my dog/my energy had to accelerate itself to the frame of the jogger, which decreased the energy available for biting.

What was my idea here again ... well energy has kinetic energy when it moves. Energy's energy, not including kinetic energy, decreases if energy accelerates itself to high speed.

Now here's a question: Does energy lose some of its energy if the energy climbs up in a gravity field?

Well, at least Hawking radiation that scorches near event horizon does not scorch at higher altitudes.

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### Re: Gravity-temperature musings by Toffo

Toffo wrote:Doogly, I am able to understand sentence "energy is not a thing", if that was what you guys we telling me :D

Your following text then continues to assume energy is a "thing" which itself has energy and gets accelerated, so no, you don't understand the sentence.
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### Re: Gravity-temperature musings by Toffo

Let's consider using a black hole to heat a pizza, and the effect of the position of the pizza in the Hawking radiation field - if radiation field is an appropriate term to use, I mean the position of the pizza in the stream of Hawking radiation.

It takes 10 minutes to heat the pizza at position p, where the time dilation factor is f.

If we somehow increased the energy of each photon that was absorbed by the pizza by 100%, then the heating time would become 5 minutes. Well we can achieve just that if we lower the pizza down to a position where the time dilation factor is f*2.

Viewed from the position p it looks like half the number of Hawking radiation photons are used in the 5-minute pizza heating, as compared to the 10-minute pizza heating.

We do not want there to be two different energy consumptions resulting with the same energy increase. So we conclude that in the faster case 50% of the energy dumped into the pizza came from the Hawking radiation, while the other 50% came from lowering the pizza down and lifting a slightly heavier pizza up.

Hmmm... the pizza absorbs less information in the faster case. That's why we can tell apart two pizzas heated up by the two methods.
Last edited by Toffo on Thu Dec 03, 2015 1:45 pm UTC, edited 1 time in total.

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### Re: Gravity-temperature musings by Toffo

Toffo wrote:Viewed from the position p it looks like half the number of Hawking radiation photons are used in the 5-minute pizza heating, as compared to the 10-minute pizza heating.

Viewed from position p, it takes the same amount of time to heat the pizza according to your own argument (you just said the pizza spends 5 minutes where time dilation is 2, which works out to looking like 10 minutes from position p).

Also, the number of photons you think you see depends on where you are in curved space and how you're moving. That's, like, the entire thing about Hawking and Unruh radiation.
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### Re: Gravity-temperature musings by Toffo

gmalivuk wrote:Viewed from position p, it takes the same amount of time to heat the pizza according to your own argument (you just said the pizza spends 5 minutes where time dilation is 2, which works out to looking like 10 minutes from position p).

Nothing was viewed from the point of view of the pizza ... the 5 minutes heating time is 2.5 minutes heating time according to the time dilated pizza.

There was a pizza cook who made one pizza in 10 minutes, according to his clock, and another pizza in 5 minutes, according to his clock.

Hey let's lower the pizza down, and then let's reflect some Hawking radiation on it from the high position. Does the radiation not gain energy on it's way down, and does that not decrease the time to heat the pizza to appropriate temperature?