- $R(f ,T) =\gamma Tf^2$ for $f\le T$
- $R(f,T) = 0$ for $f > T$

where $R(f ,T)$ is the radiance of frequency $f$ from a blackbody of temperature $T$, $\sigma$ is a constant and a simplified high-frequency cut-off is used (as compared to Planck's exponential cut-off).

The total radiative transfer $R_{True}$ to a blackbody 1 of temperature $T_1$ from a blackbody 2 of temperature $T_2>T_1$ is given by integration over frequencies as follows:

- $R_{True} =\int_{T_1}^{T_2}\gamma T_2 f^2 df + \int_0^{T_1}\gamma (T_2 - T_1) f^2df \equiv I_1 + I_2$,

where the first integral $I_1$ is the heating effect from 2 above the cut-off of 1 and the second integral the net heating from 2 below cut-off.

We see that $R_{True}$ expressing True-SB is the sum of two integrals with positive integrands, that is, $R_{True}$ is the sum of many small positive contributions all with transfer of heat from 2 to 1.

We shall now see that False-SB arises by rewriting $I_1$ as follows:

- $I_1 = \int_0^{T_2}\gamma T_2f^2df - \int_0^{T_1}\gamma T_2f^2df =\sigma T_2^4 - \sigma T_2T_1^3$

where $\sigma =\frac{\gamma}{3}$, which since $I_2 = \sigma (T_2-T_1)T_1^3$ gives False-SB on the form

- $R_{False} = \sigma T_2^4 - \sigma T_1^4$

expressing the transfer of energy from 2 to 1 as the difference of two gross flows with different signs. We see that False-SB arises by rewriting an integral with positive integrand as the difference of two integrals of different signs as follows:

- $\int_{T_1}^{T_2} f^2 df = \int_0^{T_2}f^2df - \int_0^{T_1}f^2df$,

where the lower integration limit $0$ could be replaced by any positive number smaller than $T_1$. False-SB arises when giving this formal mathematical manipulation a physical meaning stating that one-way net flow is the difference of two-way gross flows, with the flow from 1 to 2 violating the 2nd law of thermodynamics and involving an arbitrary constant.

False-SB thus arises by an ad hoc translation to physics of a mathematical operation which results in a violation of the 2nd law of thermodynamics.

Accordingly False-SB is not found in physics literature, but has appeared outside physics as an ad hoc free invention by climate scientists for the purpose of selling CO2 alarm.

"a simplified high-frequency cut-off is used" - that contradicts all available observational data. Show me a black body spectrum that has a high frequency cut-off, and then please explain why all the black body spectra that have ever been measured that don't show such a thing are somehow wrong.

SvaraRaderaCome on, Wiens displacement law is the high-frequency cut-off. Read Planck and look at the curves and see the high frequency cut-off avoiding the ultra-violet catastrophy.

SvaraRaderaNo, that is not what Wien's displacement law is. There is no cut-off in a black body spectrum. According to your equations, a black body spectrum should contain a discontinuity where the flux suddenly drops to zero. Show me the spectrum that contains such a thing.

SvaraRaderaRead Plank's law and see that it has an exponential term with cut-off of high frequency. Just read!

SvaraRaderaNo, it doesn't. There is no f for which R=0, in Planck's law. As usual you can't bring yourself to answer simple questions so I will repeat it: according to your equations, a black body spectrum should contain a discontinuity where the flux suddenly drops to zero. Show me the spectrum that contains such a thing.

SvaraRaderaIt is just a simplification of an exponential drop to zero, nothing to get upset about.

SvaraRaderaBut doesn't R_true turn out to be the same as R_false? Isn't this just a complicated way of saying what you have already said.

SvaraRaderaKarl Popper, after having had fruitless conversations with his father, concluded that you should never argue about the definition of concepts (such as "backradiation"), it is the scope of a theory's predictive power that should be evaluated. I'm afraid that you are on a very fruitless track at the moment.

It is fruitless if nobody is capable of listening and thinking.

SvaraRadera"It is just a simplification of an exponential drop to zero, nothing to get upset about."

SvaraRaderaStarting with something incorrect renders everything that follows invalid. You are incapable of providing a black body spectrum with a discontinuity in it, so why are you using equations that predict one?

As I said, it is only a simplification of the exponential cut-off in Planck's law. The essence is the same: cut-off of high frequencies.

SvaraRaderaPlanck's law does not cut off high frequencies.

SvaraRaderaYes it does, this is how the ultraviolet catastrophe is avoided and why Planck got the Nobel Prize, and not Rayleigh-Jeans for their radiation law without cut-off.

SvaraRaderaDo you speak English? A decline is not the same as a cut-off. Planck's law does not cut off high frequencies. There is no value of $\nu$ for which I=0.

SvaraRaderaNo, but is very small, practically and physically zero compared to the contributions below cut-off.

SvaraRaderaAnyone who

SvaraRaderathinksabout these points will realise there is no greenhouse effect ...(1) The direction of net radiative energy flow can be the opposite of the direction of heat transfer.If you have a warmer object (say 310 K) with low emissivity (say 0.2) and a cooler object (say 300 K) with much higher emissivity (say 0.9) then net radiative energy flow is from the cooler to the warmer object. Yet the Second Law says heat transfer is from hot to cold. So, there is no warming of the warmer body by any of the (net) radiative energy going into it.(2) Any warming of a warmer surface by radiation from a cooler atmosphere violates the Second Law of Thermodynamics.Consider the situation when the surface is being warmed by the Sun at 11am somewhere. Its temperature is rising and net radiative energy flow is into the surface. How could additional thermal energy transfer from the cooler atmosphere to make the surface warm at a faster rate?Clearly radiation from a cooler atmosphere cannot add thermal energy to a warmer surface. The surface molecules scatter radiation which has a peak frequency lower than the peak frequency of their own emission, and so no radiative energy is converted to thermal energy. (This was proved in Johnson's

Computational Blackbody Radiation.), Sothe atmospheric radiative greenhouse effect is a physical impossibility.Oh Doug, you know you are referring to the The Imaginary Second Law of Thermodynamics now don't you?

SvaraRaderaJust out of curiosity,

SvaraRaderaClaes, do you agree with the comment by mr Cotton?

Yes

SvaraRaderaGood, then I want you to show that radiation exchange between a hotter and a colder body results in a decrease in entropy and hence violates the second law.

SvaraRaderaTo say that it violate Clausius weak formulation does not suffice since it's to weak, so please show us the calculation using a stronger statement that proves your statement that the second law is violated.

Are you capable of showing this violation?

SvaraRaderaYou do claim that there is a violation, and from that I see two options.

Either you have shown this, or you are guessing.

If you are guessing or can't show it, please say so.

Radiation was not understood when Clausius formulated his statement so it's ambiguous in relation to radiation, therefore use another equivalent formulation that is better suited.

Nobody knows what entropy is so forget it. But nobody has ever observed a cold body heating a hot body without extra work, and so there is no reason to believe that this can happen. It is the same with ghosts.

SvaraRaderaNobody has ever seen a real ghost, and thus there is no reason to believe that there are ghosts. To directly prove that there are no ghosts is impossible and is a non-issue.

Do you call

SvaraRaderathisanswering a scientific question in a serious way?How on earth am I gonna take you serious if you do not want to give a serious answer?

Are you a man of double standards? You demand a serious answer from

others but refuse to act such yourself. Judging from you post regarding your discussion with Roy Spencer.

Frankly I feel a bit offended by this.

What do you want me to answer?

SvaraRaderaOf course I want a scientific answer to why (2).

SvaraRaderaHave you calculated it or not?

If not, are you guessing? Since the Clausius statement is ambiguous when it comes to radiation you should not use it. So how, scientifically speaking, is the second law violated? You can not know, and not know, that is very unscientific.

It is also very strange that you say that nobody knows what entropy is.

SvaraRaderaIt's very clearly defined in statistical physics.

If you find the meaning of this abstruse shouldn't be anybody else's problem, that is far from being scientific.

You are trying to answer a question by not answer the question.

I think you should clarify what you mean with warming to.

SvaraRaderaWhat 2nd law are you referring to?

SvaraRaderaIn an isolated system, DS.ge.0

SvaraRaderaFor state x,

S = k log V, V is the sub-volume of the phase space that contains x and is a sub set of the total coarse grained phase space. Preferably the coarse graining is done using quantum states to avoid ambiguity.

Considering how much time you seem to have spent on the subject I feel surprised that I should tell you this.

Does (2) violate this 2nd law?

It is impossible to relate this statistical 2nd law to anything physically meaningful, and so I cannot tell if it is vilolated or not. If you read what I say you should be able to decide yourself, since you are so well informed.

SvaraRaderaSo what is your answer to your question?

Why do say that it isn't meaningful, you need to specify why then.

SvaraRaderaWith this kind of attitude I don't see the point in discussing.

SvaraRaderaYou act very unscientific since it seems you made up your mind and adapt what is acceptable from this a priori idealization of "your version" of science.

How do you think anybody will take your ideas serious?? (Unless others who seem to have made up their minds).

I have now read the conversation between you and one Tomas Milanovic at Judith Curry's blog. From that discussion I get the impression that you go so far as acting directly disrespectful of your fellow scientists that has thought long and hard on these topics. How will that help you spreading your ideas in a serious manner??

It makes me wonder what your motivation for doing science is in the first place. What is it that you want to accomplish. Now it only looks like you are only out quarrel and spread sophistry.

Because it is statistics. Physics is not statistics.

SvaraRaderaYou don't understand my arguments. These are scientific arguments and has nothing to do with disrespectfulness. Science is about scientific truth, not about respect or disrespect. As you say yourself, our discussion is not meaningful and I think we should stop here. Best regards, Claes.

SvaraRaderaPhysics is the science of

SvaraRaderastudyanddescribenature.Do you mean that one can not use statistics to study and describe nature?

Maybe it is possible to use statistics to describe anything, including physics. But I am interested in physics as systems interacting according to some form of deterministic laws in some form of analog computation of finite precision as in digital computation with finite number of decimals. The indeterminancy thus comes from chopping decimals and not by throwing dice. In particular, I cannot see that real physics computes ensemble mean values and thus has little to do with statistics. I am interested in understanding how Nature works without human observers, rather than understanding human observers using statistics when studying Nature which to me is more like psychology.

SvaraRaderaWhat do you think that physics is?

SvaraRaderaHow do you define physics?

I just said that. Read the comment.

SvaraRaderaI just did, and it seems as if you identify physics with nature.

SvaraRaderaThat is just plain strange.

Do you really mean that physics isn't the science of studying and describing nature?

Yes it is describing physical nature but nature does not compute ensembles mean values, while human beings in the form of statisticians compute ensemble mean values as statistics. So I do not see statistics as basic physics, rather as an activity of human beings. Is that so strange?

SvaraRaderaYes, that is strange.

SvaraRaderaYou mix up reality (nature or what you want to call it) with models of reality.

Science is about reality.

SvaraRaderaI think that the modern interpretation of science is to accumulate knowledge and formulate testable hypotheses that you test with experiments in accordance with the

SvaraRaderascientific method.From this view science is connected with reality but it is not the same as the reality.

Physics is a scientific discipline, it is the discipline of observing and hypothesize about energy and matter.

What is your thoughts about analog computation that makes you think that it would be deeper than standard physics?

I do have a faint memory that analog computations is equivalent with a standard Turing machine since it can never be noise free.

Never the less, you are perfectly allowed to view your computations as extra deep and meaningful, but then you must remember that when discussing these things with others they probably will not see it in the same light, and they will probably be discussing from completely different premises than you concerning what physics is.

Sure, I don't view my thoughts as standard and this is why I am pursuing this line of thought.

SvaraRaderaMy view is closer to the view of physicists in the late 19th century, before the deceptions of relativity and statistics, than that of modern string theorists.

Well I applaud your bravery, it's not a really a minor successful science you are competing against.

SvaraRaderaBut what has string theory to do with the current discussion? The people who are working with string theory are a minute minority of all physicists, and they are working within a highly speculative branch of physics called mathematical physics. It's implicitly understood that their endeavor is a playground for more or less crazy ideas, that what Kuhn called extraordinary science. The ordinary scientific method doesn't apply in that realm.

Most physicist works in more applied fields, the dominant I think is condensed matter physics. Interestingly enough that is a field where you really need both statistical mechanics and quantum physics.

Never the less, what is it about analog computing that you think is so revolutionizing? Shouldn't there be the same need of verification and validation that you need for instance when writing an ordinary CFD code for example? It sounds as if you are aiming more at engineering applications than fundamental physics.

Are your hypothesis that the physical world is a simulation done with analog computing?

SvaraRaderaThe physical world is the real thing, not a simulation, except cameleonts.

SvaraRaderaSo, what so special about your type of simulations?

SvaraRaderaAre you aiming at revolutionize the knowledge about Chamaeleo Calyptratus?

No, but seriously. You seem to avoid the question by dragging red herrings all over the place.

What so special about your type of simulation?

The special thing is that a concept of finite precision computation replaces the statistics of statistical mechanics and quantum mechanics. Atoms don't throw dice but they chop decimals in their analog computation which is the world. Think about and you will understand that this opens new possibilities of simulation and understanding.

SvaraRadera"Atoms don't throw dice but they chop decimals in their analog computation which is the world."

SvaraRaderaHow do you prove this?

Atoms do not have the capacity of throwing dice because that requires microscopic games of dice and thus microscopics upon microscopics. So dice throwing is impossible, unphysical. Likewise atoms do not have the capacity of infinite precision, and so the only possibility left is finite precision computation similar to chopping decimals.

SvaraRaderaMaybe you didn't understand my question so I give it again.

SvaraRaderaHow do you prove this?

Now you are defining qualities that an atom should have according to your belief.

It is not a belief, it is rational thinking based on Schrodingers wave mechanics, which has shown to describe atomistic mechanics. The ultimate nature of atoms is beyond human understanding, because we consist of atoms and atoms cannot fully understand atoms. I notice that your just seeking objections without constructive aspects and I am getting tired of explaining.

SvaraRaderaTry to see it from my viewpoint.

SvaraRaderaYou say that there are rational arguments for introducing this ontological status to the atom; based on wave mechanics.

But, the ontological status of the wave function in the Schrödinger equation is far from settled so I don't see how this natural would lead to rational thinking.

If you have some rational deduction that proves your position it is up to this point so abstruse or fully implicit so I don't see it. You need to be much clearer why this is so rational.

I also wonder why you get so defensive when asking for an explanation from you? Isn't it in your full interest that these arguments should be fully lucid?

I also have one other issue with this reasoning of yours, but maybe it's good to take one thing at the time.

I wonder where my comment went? Did you misplace it?

SvaraRaderaAnd also I must say that it feels strange that you write that you are getting tired of explaining, when nothing really has been explained. It is far from obvious that it is possible to draw such fundamental conclusions as you seem to wish from the Schrödinger equation, since it isn't that fundamental in nature.

So, if I miss the obvious, please inform me! I do wish to understand if you have a deeper point concerning this matter.