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September 28

Is the following argument sufficient, for logically proving that any material can become energy - without using Einstein's formula?

Here are three accepted assumptions:

1. There are black holes.

2. A given black hole can-theoretically absorb any given material.

3. A given black hole can-theoretically evaporate, by becoming Hawking radiation.

Hence, logically, any given material can-theoretically become energy: Just let this material be absorbed by a black hole, and then let the black hole evaporate and become Hawking radiation.

Apparently, all of this is done without using Einstein's formula $[E=mc^{2}]$ . So, it seems that Einstein's formula is not needed for proving that any given material can-theoretically become energy, right? HOTmag (talk) 18:00, 28 September 2024 (UTC)[reply]

Hawking radiation is not all energy. It contains particles (and anti) too. To theorize about Hawking radiation you (or Hawking) need(ed) Einstein's equation. So you need it, but you need not write about it. 176.0.164.155 (talk) 19:55, 28 September 2024 (UTC)[reply]

1. Re. the particles contained in Hawking radiation: So why does the lead of our article Hawking radiation only describe it as "black body radiation", i.e. "electromagnetic radiation", without mentioning any "particles" contained in Hawking radiation?

2. Are you sure the formula

E=mc^{2}

is needed for concluding that black holes emit Hawking radiation? HOTmag (talk) 22:09, 28 September 2024 (UTC)[reply]

1 See the first paragraph in Emission

2 See the first paragraph in black hole evaporation

In 1 you need to pay special attention to the word "particle". 176.0.164.155 (talk) 23:35, 28 September 2024 (UTC)[reply]

Re. 1: Yes I'd seen this paragraph, but it doesn't answer my previous question, so let me repeat it: Why does the lead of the article only describe Hawking radiation as "black body radiation", i.e. "electromagnetic radiation", without mentioning any "particles" contained in Hawking radiation? Are you claiming that black body radiation can contain particles (besides energy)?

Re. 2: Yes this paragraph really shows how Hawking uses Einstein's formula for concluding that the black hole, not only creates energy, but also becomes energy. However, this article indicates also that "some [authors] find Hawking's original calculation unconvincing" - because it uses an "infinite frequency" as well as "a wavelength much shorter than the Planck length", while these authors use techniques other than Hawking's one, so I still wonder whether Hawking's technique using Einstein's formula is necessary for concluding that the material in the black hole, not only creates energy, but also becomes energy. HOTmag (talk) 01:06, 29 September 2024 (UTC)[reply]

Particles are energy and electromagnetic waves are particles; they are two aspects of the same. It's just that at typical temperatures used for blackbody radiation, the only particles you can make are photons. (There's enough energy too to make neutrinos, but that requires some weak interactions, so it's unlikely to happen.) Once energies go to the MeV scale (temperatures of gigakelvins), your blackbody radiation will contain other particles.

Not sure what you mean by "creates energy" or "becomes energy". Energy cannot be created or destroyed; it's always there. It just changes shape. Mass is equivalent to energy, that's an intergal part of relativity. And "equivalent to" doesn't mean "can be turned into", it means "is an alternative view of". PiusImpavidus (talk) 09:34, 29 September 2024 (UTC)[reply]

The lede indeed says "black-body radiation" and I think that's misleading. It was introduced here. I've changed it to prevent misunderstandings. --Wrongfilter (talk) 11:44, 29 September 2024 (UTC)[reply]

Thank you for this important correction. HOTmag (talk) 17:29, 29 September 2024 (UTC)[reply]

the only particles you can make are photons. (There's enough energy too to make neutrinos, but that requires some weak interactions, so it's unlikely to happen.) Are you claiming, that the "particles" mentioned in the first paragraph of the chapter Emission only mean "photons" (or neutrinos but it's unlikely), for "regular" tempratures?

Not sure what you mean by "creates energy" or "becomes energy". When I wrote "this paragraph really shows how Hawking uses Einstein's formula for concluding that the black hole, not only creates energy, but also becomes energy", I meant that the first paragraph in black hole evaporation really showed how Hawking used Einstein's formula for concluding that the black hole, not only emitted energy, but also lost mass equivalent to the emitted energy.

Mass is equivalent to energy, that's an intergal part of relativity. Who said that that was not? I only said, that without Einstein's formula

E=mc^{2},

[you'd have had no special relativity, so] you couldn't have concluded: "Mass is equivalent to energy".

Energy cannot be created or destroyed; it's always there. Correct, but without Einstein's formula

E=mc^{2},

that paragraph couldn't have concluded that "When particles escape, the black hole loses a small amount of its energy and therefore [loses] some of its mass", because without Einstein's formula - one could imagine a body emitting energy - while the body's mass remains the same as before the emission - while the emitted energy does not disappear but is only released ousdise. HOTmag (talk) 17:29, 29 September 2024 (UTC)[reply]

You also need Einstein's equation to prove that black holes can exist (assumption 1). PiusImpavidus (talk) 20:28, 28 September 2024 (UTC)[reply]

I was referring to Einstein's formula, i.e.

E=mc^{2}.

Are you sure this equation (=formula) is needed for concluding that black holes exist? HOTmag (talk) 22:09, 28 September 2024 (UTC)[reply]

You want to remove special relativity, but maintain General relativity? You can't. The latter relies upon the former. 2A0D:6FC0:767:D900:3439:2201:29C1:1A87 (talk) 08:31, 29 September 2024 (UTC)[reply]

Theoretically, one could consider General relativity without considering Special relativity: Combining both theories, gives us a Pseudo Riemannian manifold - and as a special case - a Lorentz 4D space. But Special relativity alone - would only give us a Pseudo Euclidean 4D space - and as a special case - Minkowsky space, while General relativity alone - would only give us a Riemannian 4D space. To sum up: Theoretically, one could imagine a Generally relativistic 4D space, that ignores Special relativity. The same is true for the issue of mass-energy equivalence you're talking about: Also without Special relativity, one could still consider the Einstein field equations of General relativity, so that the geometry of spacetime would be shaped by the density and flux of momentum and of energy according to these field equations, but without assuming anything about any relation between mass and energy.

But this is a side point. My main question to user:PiusImpavidus was about whether Einstein's formula

E=mc^{2}

is really needed for concluding that black holes exist. So I'm still asking: Is it needed? HOTmag (talk) 17:29, 29 September 2024 (UTC)[reply]

No it's not needed. There was a theory of black holes before Einstein (by Gottfried Wilhelm Leibniz,I think), but they were way bigger than according to Einstein. 176.0.162.8 (talk) 12:47, 30 September 2024 (UTC)[reply]

Since Hawking radiation includes particles, no your asumptions don't logically lead to that any material can become energy. NadVolum (talk) 19:06, 29 September 2024 (UTC)[reply]

Yes.

Due to the current thread, the article Hawking radiation has just been corrected by user:Wrongfilter, so now it explicitly states (in the lede) that Hawking radiation includes also particles. But when I posted my original post, the lede of the article had only mentioned electromagnetic radiation. That's why I posted my original post. HOTmag (talk) 19:33, 29 September 2024 (UTC)[reply]

particles include anti particles too! 176.0.148.153 (talk) 13:24, 13 October 2024 (UTC)[reply]

e-bike = 1000 miles per gallon gasoline?

1 gallon gasoline = 127 megajoule (per the gasoline article) = 35KWH thermal energy
If you can convert that to electricity at 28% efficiency (portable generator), that's 10KWH electric
Ebikes can go around 50 miles on a 500 WH battery charge, so 100 miles per KWH
So that's 1000 miles per gallon if you power the bike from a generator.

Questions: 1) Amirite? I.e. does the math above look ok? 2) Why are motorized bikes/mopeds so much less efficient? They typically get 100 mpg or so.

Thanks. 2601:644:8581:75B0:0:0:0:C813 (talk) 22:20, 28 September 2024 (UTC)[reply]

28% is way high for a generator. Tires, mass, are significantly different. Does your genny meet the emissions regs for a moped? Moped's aren't optimised for economy, bicycles are. Greglocock (talk) 08:03, 29 September 2024 (UTC)[reply]

A Stirling engine with 1200 Kelvin input (and 300 Kelvin output) has an efficiency of 75% (theoretically). And 1200 Kelvin is not outrageously high. So an efficiency of 28% is not high, but rather low. 176.0.162.8 (talk) 12:37, 30 September 2024 (UTC)[reply]

Nonsense, Greglocock (talk) 07:52, 1 October 2024 (UTC)[reply]

Care to elaborate? 176.0.159.38 (talk) 10:00, 1 October 2024 (UTC)[reply]

Sure. The most efficient internal combustion engines are far short of 75% efficient, and the engines used in gennies are fairly basic. Yes I have been an engine design engineer. And as the article on stirlings says "Stirling engines cannot achieve total efficiencies typical of an internal combustion engine, the main constraint being thermal efficiency" Greglocock (talk) 10:35, 1 October 2024 (UTC)[reply]

Did you read the part about why that is too? In short it says that the internal combustion engine does not need to transfer the heat through the wall of the engine thereby losing temperature and therefore efficiency. But you said a "fairly basic" engine. And there you have it. You could get good efficiency from a basic Stirling engine where you need a fancy internal combustion engine for. The trend to direct fuel injections reduces the part of volume where the maximum temperature is achieved, which is good for nitrous gas emissions but bad for efficiency. On the other hand a Stirling engine heats the outer volume which is a larger part of the volume than in an internal combustion engine with a cooled wall. Which leads to another average.

But as you are an engine design engineer, I want to give you a design that is fairly basic of a Stirling engine that should have a good efficiency because there's relatively few steps in generating power. Imagine a torus with a cold half and a hot half. Every half is made from metal, both are connected by ceramic. In the torus two bent cylinders chase each other, keeping distance by means of magnetic repulsion. Now you may ask about eddy currents in the metallic halfs of the torus. So I have to tell you that the metal is not purely metal, but there are many small metallic cylinders in a ceramic matrix. If you want to ask about the Currie temperature I wanted to answer you that the magnetic core in the bent cylinders have to be thermally isolated and that isolation is lifted (by an external magnetic field, which is needed anyhow because the distance between the cylinders has to be modulated in response to the position in the torus) when the (bent) cylinder is in the cold part of the torus. One of the cylinders has the regenerator in it and therefore lets the fluid flow through the center, the other cylinder need to get the work out of the fluid. The result of the chase is a changing magnetic field around the torus and a coil at the ceramic part can get the AC of the device. It may be that more (bent) cylinders (alternating power and regenerator) makes the magnetic interaction easier (and makes it possible to make the cylinders (and therefore the engine) smaller, thereby reducing thermal inertia needed) but that would need more thermal sectors and that would need additionally thermal distribution devices. The trade-off would depend on the reachable efficiency. Part of that efficiency would be a blower to make a hotter flame that needs part of the generated electricity. 2A02:3032:308:A7D3:6020:6890:D467:113B (talk) 20:51, 2 October 2024 (UTC)[reply]

E-bikes (which are basically light electric mopeds; I don't see why the law makes a distinction between those) typically cruise at about 6 m/s (22 km/h). A regular moped cruises at 12.5 m/s (45 km/h), twice as fast. That quadruples drag and energy use. Combine that with the low efficiency of small (but still oversized), two-stroke petrol engines and the much lower rolling resistance of bicycle tyres, in particular when compared to the tyres of motorscooters. PiusImpavidus (talk) 09:08, 29 September 2024 (UTC)[reply]

Yes, aero and higher cruising speeds are the most likely cause. Greglocock (talk) 07:52, 1 October 2024 (UTC)[reply]

If it helps, I am using a gas generator right now because we have no power. It is producing between 4 and 5 KWH per gallon of gas. It is not a bad generator at all. It is a brand new one in the upper price range: Westinhouse WGEN2000C (all the cheaper ones were sold out). I assume that industrial level generators will do better, but I doubt a residential one will get to 10KWH. (I updted the numbers after checking the generator today. After a rough start, it is doing better now.) 12.116.29.106 (talk) 11:01, 1 October 2024 (UTC)[reply]

how hot is the exhaust? 176.0.148.153 (talk) 19:50, 13 October 2024 (UTC)[reply]