# Ultra violet catastrophe and Plank's theory

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Why Plank's quantum theory was accepted in its time as the only solution to the "UV catastrophe"? Why it been accepted for granted that the blackbody radiation does NOT contain infinite amount of energy inside the spectrum? Is it absolutely true that if it would contain an infinite amount of energy it would be sufficient to destroy entire universe? Maybe this "infinite energy" just doesn't manifest itself under regular conditions and larger part of it doesn't play any role in matter heating, melting and evaporation? What is principal difference between "quant" and "photon"? Regard it as a joke assumption, it would be very nice if any radiation contain an infinite amount of energy (as classical theory suggest) and some day we would be able to find a ways to harness larger portion of it. Theoretically, some energy can be hidden and may not manifest itself under regular conditions. Why is it taken for granted that absorption and re-radiation of any kind of energy always have to lead to explosive manifestations?

Edited by Moreno

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6 hours ago, Moreno said:

Why it been accepted for granted that the blackbody radiation does NOT contain infinite amount of energy inside the spectrum?

Simply put, it violates energy conservation. Take an object close to 0 K, now provide it energy to heat it up to 1000K. You know exact amount of energy that went in, and if your calculations show you that it should radiate infinite amount of energy, end don't meet.

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2 hours ago, pavelcherepan said:

Simply put, it violates energy conservation. Take an object close to 0 K, now provide it energy to heat it up to 1000K. You know exact amount of energy that went in, and if your calculations show you that it should radiate infinite amount of energy, end don't meet.

Not sure it could serve as a mathematical prove. Infinity plus something still gives you infinity. Let say a blackbody radiates infinite amount of energy at ambient temperature. Then you use 1000 Joules of electric energy to heat it up to 1000 K. At 1000 K it will still radiate an infinite amount of energy, but this time we are sure it obtained a certain portion of energy which manifests itself in such visible phenomena as melting, boiling and evaporation. In one word something that affects atomic bonds and crystal structure. But still there can be a huge portion of energy which doesn't manifest itself under regular conditions. It simply doesn't affect the state of atomic bonds.

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22 minutes ago, Moreno said:

Let say a blackbody radiates infinite amount of energy at ambient temperature.

Nope. That's why I specified 0 K. There's no black body radiation at this temperature. And we know exactly what amount of energy we put into making an object radiate. Therefore when see infinitely high amount of energy coming off, but we've just put in 1000J, then where did the rest of the energy come from?

That is not to say that the notion of infinite energy is not absurd in its own right.

Edited by pavelcherepan

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32 minutes ago, pavelcherepan said:

Nope. That's why I specified 0 K. There's no black body radiation at this temperature. And we know exactly what amount of energy we put into making an object radiate. Therefore when see infinitely high amount of energy coming off, but we've just put in 1000J, then where did the rest of the energy come from?

That is not to say that the notion of infinite energy is not absurd in its own right.

Sorry, if I make mistake, but according to modern physics 0 K cannot be reached principally, and blackbody will always radiate something. Do you believe that universe is infinite? If yes, than it should contain an infinite amount of energy anyways?

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8 minutes ago, Moreno said:

Sorry, if I make mistake, but according to modern physics 0 K cannot be reached principally, and blackbody will always radiate something. Do you believe that universe is infinite? If yes, than it should contain an infinite amount of energy anyways?

I tend to believe that the Universe is infinite, but what I believe doesn't matter. We can observe only a chunk of the entirety of the universe with large but finite amount of mass and energy.

As for 0 K, yes, it can't be reached in principle, but we can get within some hundred billionths of a degree to it using lasers. You can look at it in other way. For example, we have an object and it radiates "infinite" amount of energy via black body radiation. We heat it up by X Kelvin. The amount of energy radiation is still an infinity. Therefore, where did the energy we just added to the system go?

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12 hours ago, Moreno said:

Why Plank's quantum theory was accepted in its time as the only solution to the "UV catastrophe"?

Because it worked. At the time it was seen, by Planck, as a mathematical "trick" to get rid of the infinities. But the quantisation was later confirmed by Einstein's work on the photoelectric effect.

12 hours ago, Moreno said:

Why it been accepted for granted that the blackbody radiation does NOT contain infinite amount of energy inside the spectrum?

Where would that infinite energy come from? Torch batteries wouldn't last long if the were the case!

12 hours ago, Moreno said:

Maybe this "infinite energy" just doesn't manifest itself under regular conditions and larger part of it doesn't play any role in matter heating, melting and evaporation?

If it doesn't "manifest" how can you say it is there? You seem to be invoking magic as an alternative explanation

12 hours ago, Moreno said:

Theoretically, some energy can be hidden and may not manifest itself under regular conditions.

Theoretically? Please show the maths and evidence that supports this claim.

Otherwise it is not "theoretical," it is just nonsense.

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How can you explain the following paradox: As blackbody temperature never going to drop to the absolute zero, it will radiate some energy infinitely. If you will multiply any smallest value you have on infinity you will still get infinity. Doesn't it mean there is infinite amount of energy any body contains?

Regarding energy manifesting itself or not is a tricky question, but for example: It is known that photons of lower energies are absorbed by electrons and those of higher energies by nuclei. Will the later anyhow influence interatomic bond and provoke melting, boiling and evaporation? Unless they will somehow convert to photons of lower energies and then absorbed by electrons?

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14 minutes ago, Moreno said:

How can you explain the following paradox: As blackbody temperature never going to drop to the absolute zero, it will radiate some energy infinitely

It will lose energy until it is in equilibium with its surroundings. After that there will be no net loss of energy

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8 minutes ago, Strange said:

It will lose energy until it is in equilibium with its surroundings. After that there will be no net loss of energy

Let imaging we originally had the only blackbody in infinite and empty space. Then it will radiate into space infinitely and never reach equilibrium with surroundings.

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Interesting question. I guess, in this case we have to think of quantum effects. As soon as the BB starts radiating, the previously "empty" space is filled with EM fields. I would expect quantum fluctuations to happen, which would result in some amount of energy going back to the BB and then eventually it will reach equilibrium with the surroundings and stop radiating. It will be extremely close to absolute zero, but it won't radiate indefinitely.

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8 minutes ago, pavelcherepan said:

Interesting question. I guess, in this case we have to think of quantum effects. As soon as the BB starts radiating, the previously "empty" space is filled with EM fields. I would expect quantum fluctuations to happen, which would result in some amount of energy going back to the BB and then eventually it will reach equilibrium with the surroundings and stop radiating. It will be extremely close to absolute zero, but it won't radiate indefinitely.

Don't quantum fluctuations happen constantly all the same? Why part of energy will come back to BB? How exactly?

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I'm not sure if completely empty universe would have quantum fluctuations and it's hardly possible to test it since true vacuum is a theoretical construct and is not achievable. Regardless, I'm pretty certain that fluctuations would happen and after some time the background radiation coming from those would bring the BB into equilibrium with surroundings.

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2 hours ago, Moreno said:

Let imaging we originally had the only blackbody in infinite and empty space. Then it will radiate into space infinitely and never reach equilibrium with surroundings.

It will eventually reach the temperature of the surrounding space.

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46 minutes ago, pavelcherepan said:

I'm not sure if completely empty universe would have quantum fluctuations and it's hardly possible to test it since true vacuum is a theoretical construct and is not achievable. Regardless, I'm pretty certain that fluctuations would happen and after some time the background radiation coming from those would bring the BB into equilibrium with surroundings.

But if space was originally empty and infinite why radiation will ever return to BB? Isn't it going travel out of BB infinitely? There suppose to be no reflection or re-radiation in empty space. How quantum fluctuations can play a role here?

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3 minutes ago, Moreno said:

How quantum fluctuations can play a role here?

For example, an electron-positron pair is created due to quantum fluctuations. They instantly annihilate and produce a gamma ray. It would be moving in a random direction, but with infinite space there will be a significant amount of those that will end up hitting the black body.

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1 hour ago, pavelcherepan said:

For example, an electron-positron pair is created due to quantum fluctuations. They instantly annihilate and produce a gamma ray. It would be moving in a random direction, but with infinite space there will be a significant amount of those that will end up hitting the black body.

By the way, is powerful static electric field sufficient by itself to generate positron-electron pairs? If yes, how it doesn't violate energy conservation law?

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The way I see it, the only way you could have infinite energy is if that energy we're coming from a source outside of the universe.

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Posted (edited)
On 2/24/2018 at 6:52 AM, Moreno said:

Let imaging we originally had the only blackbody in infinite and empty space. Then it will radiate into space infinitely and never reach equilibrium with surroundings.

Why not? In this hypothetical scenario empty space would effectively be at a temperature of 0 K. Your blackbody would tend to that.and have no reason to radiate further as it reached it. The reason you can't get anything to 0 K is that there is no 0 K space around to be utilized to allow it...your hypothetical does not exist.

Edited by J.C.MacSwell

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16 minutes ago, J.C.MacSwell said:

Why not? In this hypothetical scenario empty space would effectively be at a temperature of 0 K. Your blackbody would tend to that.and have no reason to radiate further as it reached it. The reason you can't get anything to 0 K is that there is no 0 K space around to be utilized to allow it...your hypothetical does not exist.

Maybe it wouldn't be able to reach absolute zero due to Heisenberg uncertainty principle. There always going to be some quantum fluctuations in any body and maybe it will continue to radiate because of that.

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1 minute ago, Moreno said:

Maybe it wouldn't be able to reach absolute zero due to Heisenberg uncertainty principle.

You can't have it both ways. Either there are quantum effects, in which case Planck was right. Or there aren't, and there is no Heisenberg uncertainty principle.

2 minutes ago, Moreno said:

There always going to be some quantum fluctuations in any body and maybe it will continue to radiate because of that.

It will still reach equilibrium. Quantum fluctuations are the minimum energy level, not a source of energy.

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57 minutes ago, J.C.MacSwell said:

Why not? In this hypothetical scenario empty space would effectively be at a temperature of 0 K. Your blackbody would tend to that.and have no reason to radiate further as it reached it. The reason you can't get anything to 0 K is that there is no 0 K space around to be utilized to allow it...your hypothetical does not exist.

3rd law of thermodynamics prevents it actually reaching 0 K — it would asymptotically approach it — but it also forbids a 0 K temperature bath.

On 2/24/2018 at 10:32 AM, Moreno said:

By the way, is powerful static electric field sufficient by itself to generate positron-electron pairs? If yes, how it doesn't violate energy conservation law?

Electric fields contain energy.

On 2/23/2018 at 2:23 PM, Moreno said:

Theoretically, some energy can be hidden and may not manifest itself under regular conditions.

Under any conditions. That's the problem. You can add an arbitrary amount to energy terms without making a difference, because we are always measuring energy differences. The added amount cancels. You don't often see this because we have already chosen a reference where the energy is zero and done the cancellation ahead of time

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Posted (edited)
37 minutes ago, swansont said:

3rd law of thermodynamics prevents it actually reaching 0 K — it would asymptotically approach it — but it also forbids a 0 K temperature bath.

Thanks. Is this true just classically, or true in any idealized case? (I pictured the last quantum step getting to the goal line)

Edited by J.C.MacSwell

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30 minutes ago, J.C.MacSwell said:

Thanks. Is this true just classically, or true in any idealized case? (I pictured the last quantum step getting to the goal line)

You can't get rid of quantum fluctuations, so there's an issue there, too.

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On 24/02/2018 at 10:52 AM, Moreno said:

Let imaging we originally had the only blackbody in infinite and empty space. Then it will radiate into space infinitely and never reach equilibrium with surroundings.

There is the absorber problem for an empty universe (as well as many popular cosmological models), which has been around for a long time.

There is a strong case for claiming photons have time-reversal symmetry.

As photons have infinite range, this symmetry implies they have to be destroyed (i.e. the time-reverse of created) as well as as created. There is no way to destroy photons in empty space without violating conservation laws.

So it may be the only blackbody in infinite and empty space has no way to lose energy and will forever retain its temperature.