Physics as Analog Finite Precision Computation vs Physics as Statistics

I am exploring an approach to physics as "analog finite precision computation" to be be compared with classical physics as "analog infinite precision physics" and modern physics as "physics of dice games" or "statistical physics".

The step from classical to modern physics was forced upon physicists starting in the mid 19th century when it became clear that the 2nd law of thermodynamics could not be found in classical infinite precision physics of irreversible systems. The way to achieve irreversibility was to assume that atoms play dice games with the outcome of a throw of a dice inherently irreversible: To "unthrow" a dice was (correctly) understood to be impossible and thus irreversibility was introduced and the paralysis of reversible classical physics was broken. So far so good.

But the fix came with severe side effects as real physics independent of human observation was replaced by statistical physics representing "human understanding", as if the world goes around just because some physicist  is making observations and claim them to be understandable. Einstein and Schrödinger could never be convinced that atoms play dice, despite major pressure from the physics community.

The unfortunate result of this collapse of rationality of deterministic physics, has led modern physics into wildly speculative physics of strings and multiverse, which nobody can understand.

But there is a milder way of introducing irreversibility into classical reversible physics, and that is to view physics as analog computation with finite precision instead of infinite precision.

This connects directly to a computer operating with finite decimal expansion of real numbers as a necessary restriction of infinite decimal expansion, in order to allow computations to be performed in finite time: In order to make the world go around, and it does go around, and thus not come into a halt, physical processes cannot be realised with infinite precision and thus finite precision computation is a must in a world that goes around. It is thus necessary, but it is also sufficient to introduce irreversibility into classical reversible physics.

Finite precision computation thus solves the main problem which motivated the introduction of statistical physics, but in a much more gentle way and without the severe side effects of full-blown statistics based on dice games.

Finite precision computational physics is represented by the modern computer, while statistical physics would correspond to a "dice computer" throwing a dice in every step of decision, just like the "dice man" created by the pseudonym Luke Rhinehart. The life of the "dice man" turned into misery, which can be compared with (reasonably) successful ordinary (reasonably controlled) life under finite precision, without a dice but with constant pressure to go onto the next day.

So if you want to compare finite precision analog physics to modern statistical physics, make the thought experiment of comparing your usual finite precision computer, which you use to your advantage, to a "dice computer" which would be completely unpredicatable. This is the comparison between an experienced computer wiz often getting reliable results, to a totally inexperienced user pushing the keys randomely and getting garbage.

Or make the comparison of getting married to a person which follows a principle of "finite precision" to a person like the "dice man" who is completely unpredictable. What would you prefer?

Few ideas can change your view in the same way as "physics as analog finite precision computation". Try it!

Physical Quantum Mechanics: Time Dependent Schrödinger Equation

We consider a Schrödinger equation for an atom with $N$ electrons of the normalized form: Find a wave function

• $\psi (x,t) = \sum_{j=1}^N\psi_j(x,t)$

as a sum of $N$ electronic complex-valued wave functions $\psi_j(x,t)$, depending on a common 3d space coordinate $x$ and time coordinate $t$ with non-overlapping spatial supports $\Omega_1(t)$,...,$\Omega_N(t)$, filling 3d space, satisfying

• $i\dot\psi (x,t) + H\psi (x,t) = 0$ for all $(x,t)$,       (1)

where the (normalised) Hamiltonian $H$ is given by

• $H(x) = -\frac{1}{2}\Delta - \frac{N}{\vert x\vert}+\sum_{k\neq j}\int\frac{\vert\psi_k(y,t)\vert^2}{2\vert x-y\vert}dy$  for $x\in\Omega_j(t)$,

and the electronic wave functions are normalised to unit charge:

• $\int_{\Omega_j}\vert\psi_j(x,t)\vert^2 =1$ for all $t$ for $j=1,..,N$.

The total wave function $\psi (x,t)$ is thus assumed to be continuously differentiable and the electronic potential of the Hamiltonian acting in $\Omega_j(t)$ is given as the attractive kernel potential together with the repulsive kernel potential resulting from the combined electronic charge distributions $\vert\psi_k\vert^2$ for $k\neq j$.

The Schrödinger equation in the form (1) is a free-boundary problem where the supports $\Omega_j(t)$ of the electronic wave functions may change over time.

We solve (1) by time-stepping the system

• $\dot u + Hv = 0$, $\dot v - Hu = 0$       (2)

obtained by splitting the complex-valued wave function $\psi = u+iv$ into real-valued real and imaginary parts $u$ and $v$ (and with $\vert\psi\vert^2 =u^2+v^2$.) 

This is a free-boundary electron (or charge) density formulation keeping the individuality of the electrons, which can be viewed as a "smoothed $N$-particle problem" of interacting non-overlapping "electron clouds" under Laplacian smoothing. The model (1) connects to the study in Quantum Contradictions showing a surprisingly good agreement with observations.

In particular, the time-dependent form (2) is now readily computable as a system of wave functions depending on a common 3d space variable and time, to be compared to the standard wave equation in $3N$ space dimensions which is uncomputable.

I am now testing this model for the atoms in the second row of the periodic table, from Helium (N=2) to Neon (N=10), and the results are encouraging: It seems that time dependent N-electron quantum mechanics indeed is computable in this formulation and the model appears to be in reasonable agreement with observations.  This gives promise to exploration of atoms interacting with external fields, which has been hindered by uncomputability with standard multi-d wave functions.

PS The formulation readily extends to electrodynamics with the Laplacian term of the Hamiltonian replaced by

•  $\frac{1}{2}(i\nabla + A)^2$

and the potential augmented by $\phi$, where $A=A(x,t)$ is a vector potential, $\phi =\phi (x,t)$ is a scalar potential with $E = -\nabla\phi -\dot A$ and $B=\nabla\times A$ given electric and magnetic fields $E=E(x,t)$ and $B=B(x,t)$ depending on space and time. 

"Back Radiation" as Violation of the 2nd Law of Thermodynamics

A new article by Martin Herzberg in Energy&Environment reviews & summarizes the NIPCC Report Climate Change Reconsidered -Physical Science. In particular, Herzberg gives the following devastating review of the phenomenon of "back radiation" supposedly being the "heating mechanism" of the "greenhouse effect:

• The most prevalent definition or heating mechanism involves what is referred to as “back radiation”. Greenhouse gases absorb some of the IR radiation that the Earth’s surface radiates toward free space after it is heated by solar radiation. According to the Environmental Protection Agency, ”reradiated energy in the IR portion of the spectrum is trapped within the atmosphere keeping the surface temperature warm.” 
• This mechanism has the colder atmosphere blithely and spontaneously emitting radiant energy toward the warmer surface. 
• That energy is supposed to be absorbed by the Earth’s surface and heat it further. 
• Thus the warmer surface should get even warmer by absorbing energy from a colder source: in direct violation of the Second Law of Thermodynamics.

Advocates of CO2 alarmism work hard to meet this argument claiming that the violation of the 2nd Law is only apparent: "Back radiation" always comes along with "forward radiation" and the net radiation is always from warm to cold and so the 2nd law is not violated. The trouble with this way of handling the objection expressed by Herzberg (and myself), is that "back radiation" and "forward radiation" are supposed to be independent physical processes as "two-way flow of infrared photons",  and at the same dependent coupled processes guaranteeing the the 2nd laws is not violated. 

But independent processes which are dependent, is a contradiction and so the effort to save "back radiation" from joining phlogistons in the wardrobe of unphysical processes, comes to nil and so the "greenhouse effect" is "hanging in the air" without scientific basis.       

Does an Undetectable "Greenhouse Effect" Exist?

Vincent Gray seeks to clarify the physics of the "greenhouse effect" in a new blog post at 

The Australian Climate Sceptics - Exposing the flaws in the greatest hoax inflicted on the human race:

1. Greenhouse gases, predominantly water vapour, do absorb infra red radiation from the earth, radiate the additional energy in all directions, including downwards and so warm the earth. 
2. So the greenhouse effect does exist. 
3. This effect must be very small as it has not been detected, despite the enormous effort that has been applied to try and find it.

We read that Vincent here puts forward the idea that the atmosphere by radiating heat energy downwards causes warming of the Earth surface in a process of two-way radiative heat transfer between the atmosphere and surface including "back radiation" from a cold atmosphere to a warm surface. Vincent thus accepts the picture painted by CO2 alarmism based on a "greenhouse effect" and thereby gives it a free ride. Vincent shares this view with many "skeptics".

At the same time as Vincents claims that "the greenhouse effect exists", he informs us that it has not been detected, presumably then because "it must be very small". 

All this is unfortunate because the two-way heat transfer including back radiation which Vincent describes, is not true physics but fake physics, as I have argued in extended writing. 

Vincent defends his position with a direct attack on my position with the following argument (in bold):

• Radiation energy is converted to heat if it is absorbed by any suitable object. 
• The temperature of that object is quite irrelevant. 
• The speculation by some that radiation cannot be absorbed by an object whose temperature is bigger than that of the radiant emitter requires the absurd assumption that radiation, is capable of detecting the temperature of distant objects before deciding whether they are fit to receive absorption. 
• Such an assumption restores the need for a belief in the existence of an ether.

But is it absurd that an absorber can detect if the temperature of an emitter is bigger than its own temperature? Not at all! That information is encoded in the spectrum of the emission as the high-frequency cut-off described in Wien's displacement law with the cut-off increasing linearly with temperature. The result is that emission from a certain temperature cannot be re-emitted by an absorber at lower temperature and thus must be absorbed and turned into heat causing warming. 

A stone put in the sun light, can thus very well detect that the sun light falling upon itself was emitted at a temperature higher than its own, because sun light contains frequencies above the cut-off frequency of the stone.  The stone detects this by finding itself being unable to re-emit these frequencies and thus cannot prevent getting heated by the Sun. This is nothing the absorber "decides" to do in Vincent's vocabulary, because atoms have no free will "to decide",  but simply something the absorber is unable to do, which involves no "decision" and thus can be physics.

 So in conclusion I pose the following question to Vincent (and other "skeptics"):  Since the "greenhouse effect" cannot be detected experimentally and your theoretical argument in support of its existence has shown to be incorrect, wouldn't it be more rational to give up arguing that the "greenhouse effect exists" because there is "back radiation",  thus giving support to CO2 alarmism?

I have asked Vincent to respond to this post, but it may well be be that Vincent, like some other "skeptics", simply hides (and warms up) after making an attack on a skeptic position of a frequency above his own cut-off.

PS Vincent's claim of existence of a phenomenon that is not detectable, connects to an (unfortunate) aspect of modern physics, as opposed to classical physics, rooted in the Bohr Copenhagen interpretation of quantum mechanics, where the wave function is not viewed to represent real physics independent of human observation, but instead represents human understanding in statistical terms limited to what can be observed by humans. Modern physicists following Bohr are thus allowed to speak about only physics which is observable and then in statistical terms. But this is too narrow, and has opened the possibility of a vast physical landscape beyond observation, which physicists are now eagerly exploring in the extreme forms of string theory and multiversa. The (unfortunate) result is that speaking about phenomena of physics which cannot be detected, which in the view of classical physics is nonsense,  has now become mainstream modern physics. 

Two-way Heat Transfer and 2nd Law: Contradiction!

The discussion with edX in the previous post exhibits a "greenhouse effect" connected to "back radiation" or "Downwelling Longwave Radiation DLR" from a cold atmosphere to a warmer Earth surface, as a part of two-way radiative heat transfer between two bodies each supposed to emit independently of the other according to a Stefan-Boltzmann law of the form $Q=\sigma T^4$ with $T$ body temperature and $\sigma$ a positive constant.

As the discussion shows, advocating two-way heat transfer requires an argument showing that  what appears to be a violation of the 2nd law of thermodynamics with the colder body transfering heat to the warmer, is only apparent. The argument is then that the heat transfer is always bigger from the warmer and so the net transfer is always from warm to cold.

However, this argument is contradictory: Each body is supposed to emit independently of the other, yet at the same time the two transfer processes must somehow be linked to guarantee that the net transfer always comes out right, even if they are nearly equal. The transfer processes are thus assumed to be both independent and dependent, which is a contradiction. And contradictory physics can only be non-physical illusion.

Unfortunately, in modern physics contradictions such as wave-particle contradiction, have come to be accepted by Bohr sophistery as "complementarity" or "duality". A "round square" is thus in modern physics not a contradiction, but just expresses "complementary" or "dual" properties of some higher physical existence incomprehensible to human understanding but still physics. But sophistery is not science and contradictory physics is non-physics.

In this context, recall that the idea of two-way heat transfer was used by Schwarzschild in 1906 to set up a simple model for radiative heat transfer allowing a simple analytical solution as a linear function. The unphysical aspect of Schwarzschild'd model is exposed in the recent post Unphysical Schwarzschild vs Physical Model for Radiative Heat transfer. What was unphysical in 1906 is still unphysical today.

edX: "Back Radiation" as the Physics of the "Greenhouse Effect"

I started my journey as climate skeptic in 2009 in an attempt to understand the physics of the so called "greenhouse effect" threatening human civilisation by global warming from human emission of CO2 as a powerful "greenhouse gas".

I then discovered that the "greenhouse effect"was (and still is) is very vaguely identified in the scientific literature which poses a severe difficulty to skepticism of CO2 alarmism.

The ongoing edX course Denial101x Making Sense of Climate Science Denial is an attack on skepticism to CO2 alarmism, referred to as "denialism", introduced by:

• In this first week you will be introduced to some of the terminology we will use in the course in order to begin building your understanding of scientific consensus, the psychology of denial and the spread of denial. 

The course shows which skeptics arguments are the most effective and thus requires special effort to kill. In this sense the course offers valuable insight. In a video lecture in week 3 on the "Greenhouse Effect", we are informed that:

• The glow from the Earth surface goes upwards, greenhouse gasses absorb some of this heat and they then glow in every direction including down towards us. 
• This is how the greenhouse effect works. We measure it every day here at Reading Atmospheric Obervatory by a pyrgeometer...it has a special window only allowing infrared light through to be measured. Even during a cloudless night it measures the constant greenhouse glow. 
• Even though the greenhouse effect is an observed fact, there is a myth that it does not exist. This myth misinterprets a law of physics called the second law of thermodynamics. The 2nd law says that even though heat moves in all directions, overall heat moves from hot to cold, and not from cold to hot. 
• The myth says that the greenhouse effect does not exist because it means heat moving from a cooler sky to warmer surface. But this is a misrepresentation: The greenhouse effect obeys the law: A square meter of Earth surface send about 500 Watts upwards, so it works like a 500 W heater. The greenhouse effect sends down about 330 Watts of heat, so in total about 170 Watts goes from the warmer surface to the cooler sky. Heat overall goes from hot to cold  but the greenhouse effect sends som back to warm us up.
• The myth misrepresents the 2nd law. Meanwhile observatories measures the greenhouse effect every day all over the globe.

We understand that the "greenhouse effect" is based on "back radiation" from the atmosphere, which is measured by pyrgeometers. 

From the beginning of my skeptics journey I understood, from a new proof of Planck's radiation I had constructed as part of a larger effort to describe physics as analog computation,  that "back radiation" is an illusion without physical reality, and so that a pyrgeometer is constructed to sell this illusion to a market in need of "instrumental evidence".  

This insight has made me into a "denier" in the view of not only alarmists but strangely enough also in the view of leading skeptics such as Singer and Spencer and many others.  As a "denier of back radiation" based on a view of physics as computation,  I have met many strong reactions often including direct censorship of this my view. 

The edX course gives me more courage to not give up this view including a new proof of Planck's law leading to the conclusion that "back radiation" is non-physical illusion. The edX course shows that if "back radiation" is illusion, then so is the "greenhouse effect". Unfortunately, leading skeptics have fallen into the trap of "How to fool yourself with a pyrgeometer".

You find more material under the categories "myth of back radiation" and "pyrgeometer". To get rid of illusions may get very quickly, once you meet the right argument. Notice in particular the recent post on the unphysical aspect of Schwarzschild's radiation model introducing the unfortunate unphysical idea of "back radiation" or "downwelling longwave radiation DLR" as the warming element of the "greenhouse effect".

Take a special look at the argument presented: The 2nd law says that even though heat moves in all directions, overall heat moves from hot to cold.  If anything, this is a false version of the 2nd law: It is not true that "heat moves in all directions".

I asked edX to give the scientific justification of this statement, and report the answer. If you go through the response from edX below, you will find that after an exchange of nearly 100 comments back and forth, we are still far from getting an answer from edX. The tactic used by edX is to meet any question from me as a student following the course, by a battery of counter-questions with the objective of keeping me busy and so avoiding to answer my question. Clever, but tiresome both for edX and me.

Here is a copy of the edX Discussion with teacher Gavin Cawley:

Gavin: The physical mechanism is very straightforward. I would happily go through the physics with you, step-by-step, starting with back body radiation, to see where we agree and where we disagree. Do you agree that a spherical black body object, in a vacuum, will radiate energy in all directions in the form of photons, according to the fourth power of its temperature (i.e. the Stefan-Boltzman law), with the spectrum of radiation governed by Plank's law? If you answer my questions directly, I am sure we will soon reach agreement.

Claes: Yes, if you by a vacuum mean a surrounding environment at 0 K. Is that so? And if you by "photons" mean electromagnetic waves. Is that so?

Gavin: By vacuum, I did indeed mean that the surrounding environment is at 0K. By "photon" I was referring to "an elementary particle, the quantum of light and all other forms of electromagnetic radiation". Do you still agree, given those clarifications?

Claes: Yes, go on.

Gavin: Thank you. A second black-body object (lets call it "B" and the first "A") is then introduced. For convenience make B spherical, with the same radius as A, and placed a short distance from, but not touching A. Would you agree that B also radiates photons in all directions according to the fourth power of its temperature (Stefan Boltzmann) with a spectrum given by Plank's law?

Claes: No, since with A present, the environment of B is not a vacuum at 0 K. And then?

Gavin: The intensity and spectrum of black body radiation depends only on its temperature, as given by the Stefan-Boltzmann and Plank laws, which is why black-body objects are a useful idealization. Can you provide a reference to a derivation for black-body radiation that explicitly states the dependence on environmental temperature?

The thought experiment we are conducting doesn't depend on this point, but we appear to have identified a point of divergence, so it would be useful to understand the source of the disagreement.

Claes: It is certainly very natural to expect that the state of the environment is of importance. We just agreed that a body emits according to Planck's law into a vacuum at 0 K. Don't you remember that? If you claim that the environment is of no importance, then you have to back that with strong evidence, since it is such a strange utterly surprising statement. So what is your evidence? Planck's proof of his law only counts degrees of freedom in a cavity and says nothing about independence of surrounding environment, and thus cannot be used as positive evidence of your claim about independence. Right?

Gavin:Regarding the equivalence between cavity radiation and black body radiation, there is a nice explanation here by Prof. Alan Guth of MIT (it is from an excellent course on the early universe that is well worth watching). Essentially the radiation within a cavity is described by Plank's law, but if you were to put a black body into that cavity and wait for it to reach thermal equilibrium, then it must radiate according to Plank's law as well in order for the incoming energy from the cavity radiation to match the outbound black-body radiation, and like cavity radiation, only depends on temperature. Note in this case, the derivation definitely doesn't depend on the environment being at 0K. Prof. Guth also specifically states that its radiation wouldn't change if you took it out of the cavity (at least until it cooled, but then its radiation would be according to SB and P laws at the lower temperature). Prof. Guth is a leading expert in cosmology, where black-body radiation is an important concept (e.g. cosmic background radiation), so I suspect his understanding of this topic is reliable. However, if you have a reference to a derivation of the Plank and Stefan-Boltzmann laws that detail the sensitivity to the environment, then I would happily read them. Can you supply me with such a reference?

Now the environment is certainly important in determining the warming or cooling of the black body objects, which is why I made the simplifying assumption of a vacuum at 0K. However, whether the bodies warm or cool does not depend solely on their intrinsic radiation, as we shall see later in the thought experiment, so I see nothing unnatural about the intensity and spectrum of radiation depending only on temperature.

Let us assume that object B is a little cooler than object A, would you agree that it (B) radiates photons equally in all directions (being a spherical black body object)?

Claes:The version of SB you find in engineering texts, which is relevant to atmospheric radiation, states that the heat transfer between a body A at temperature T_A and a body B at temp T_B is given by Q = sigma (T_A^4 - T_B^4) with A warmer than B and transfer of Q from A to B. The dependence of the environment is here obvious, right? Do you accept this version of Stefan-Boltzmann?

Gavin:That equation is for heat transfer, not for the radiation of photons from a black-body object, we will get on to transfer later. For the moment, I am trying to establish your position on the intensity and spectrum of photons radiated from B as that is important in explaining the transfer.

Let us assume that object B is a little cooler than object A, would you agree that it (B) radiates photons equally in all directions (being a spherical black body object)?

Claes:No, as I have said, the presence of A will influence the radiation from B, since A is part of the environment of B. And yes, we are speaking about heat transfer by radiation, and nothing else, right? And it is better to leave out cosmology, inflation, Big Bang and multiverse, since it is is of little importance concerning atmospheric radiation, right?

Gavin: As I have asked ClaesJohnson twice for a reference giving derivations of the Plank and Stefan-Boltzman law that detail the sensitivity to the environment, and none has been provided, I will have to leave that issue to one side for the moment.

Claes, my previous question referred only to the direction of photons emitted by object B, do you agree, that being a spherical black body object, B will emit photons equally in all directions?

BTW, I should have said more explicitly that I do agree with the formula "Q = sigma (T_A^4 - T_B^4)" for radiative transfer; I certainly do.

Claes: If we do agree about SB as stated, then we are on speaking terms. The presence and dependence of the environment is clear in this formula, right? In particular, we have our previous agreement in the special case with T_B = 0 K, right? What I have asked you about is reference to a statement of independence of environment. What is your evidence? We have agreed on dependence and now it is up to you to deliver contradictory evidence of independence. What is it?

Gavin: "The presence and dependence of the environment is clear in this formula, right?" no, as I said, that equation is about radiative transfer between objects, not the radiation from the objects themselves.

"What I have asked you about is reference to a statement of independence of environment. " I have already provided two, the second being the lecture by Prof. Guth, whom most would regard as being well qualified on the subject.

"We have agreed on dependence and now it is up to you to deliver contradictory evidence of independence" I have already clearly stated that the environment is relevant to transfer, but not to the intrinsic radiation of the object (indeed the transfer equation can be derived from intrinsic radiation being independent of environment).

Now this is the fourth time I have asked this question without a direct answer, I repeat:

Claes, my previous question referred only to the direction of photons emitted by object B, do you agree, that being a spherical black body object, B will emit photons equally in all directions?

Claes: Again, are we discussing heat transfer by radiation, or something else? What, if so?

Gavin: ClaesJohnson we are discussing the radiation of photons from a black body object, with the intention of explaining the nature of radiative transfer from one black body to another in due course.

Claes, my previous question referred only to the direction of photons emitted by object B, do you agree, that being a spherical black body object, B will emit photons equally in all directions?

Claes: No, the environment of B will influence the heat energy radiated by B.

Gavin: ClaesJohnson, O.K. so does B emit any photons that strike (and are absorbed) by A?

Claes: What does that have to do with the heat transfer by radiation between A which we are discussing? Or are you discussing something else? If so, what?

Gavin: In order to explain my argument to you, I need to properly understand your objection. The best way to do this is to ask questions that allow you to unambiguously state your position in a way that I will understand. You may not understand the relevance of these questions, but I suspect it will be clear to most readers with a background in physics, but the fastest way to reach agreement is simply to give a concise and direct answer to the question. So, please give a direct answer to the question: does B emit any photons that strike (and are absorbed) by A?

Claes: I cannot answer because I do not understand the physics of "photons that strike and are absorbed by A". Again, are we discussing heat transfer by electromagnetic waves? If not, what is it you are discussing?

Gavin: A black body is an idealized physical body that absorbs all incident electromagnetic radiation, regardless of frequency or angle of incidence (source).

Radiation and absorption of photons is the basic mechanism by which radiative transfer occurs. Absorption simply means that the photon no longer exists and the energy that it carried has been transferred to the body that absorbed it. So does B emit any photons that strike (and are absorbed) by A?

Claes: Gavin, if we agree about SB as stated in engineering literature, why is this not enough to describe atmospheric radiative heat transfer? What more do you want? My analysis of blackbody radiation is exposed at https://computationalblackbody.wordpress.com/

Gavin: Claes, as I have pointed out to you before, that equation is for radiative transfer. In order to answer your question about the second law of thermodynamics and the back-radiation, you need to understand how that transfer arises from an exchange of energy in either direction. It is a shame that you have been so unwilling to give direct answers to straightforward questions, so I will explain it to you.

So, the conventional interpretation of thermodynamics would indicate that the warmer of the two bodies would radiate energy (in the form of photons) at a rate given by the Stefan-Boltzmann law, i.e.

Ja = sigma*Ta^4,

where Ja is the power radiated from A, Ta is the temperature of A in Kelvin and sigma is the Stefan-Boltzmann constant. Now, A being a spherical black-body will radiate photons evenly in every direction, however a proportion of these, which we will call c, will be traveling in the right direction to intersect with B, which being a black body will absorb them. The rate at which energy is received at B due to this flow of photons from A is

c*Ja = c*sigma*Ta^4

Similarly, B will radiate energy at a rate given by the Stefan-Boltzman law, such that

Jb = sigma*Tb^4,

where Jb is the power of the radiation from B and Tb is the temperature of B. Now by symmetry (as I have made the two objects spheres of identical radius), the proportion of the radiated photons from B that intersect with A is the same as the proportion of photons emitted by A that intersect with B, i.e. c. Thus the rate at which energy is received at A due to this flow of photons from B is

c*Jb = c*sigma*Tb^4

Now let's consider the gain of energy by the cooler body, B. It has gained energy from A at a rate c*sigma*Ta^4, but has lost energy to A at a rate c*sigma*Tb^4. The transfer of heat between the two, is just the difference of these quantities, i.e.

Q = c*sigma*Ta^4 - c*sigma*Tb^4

or in other words

Q = c*sigma*(Ta^4 - Tb^4)

which is the usual "engineering" representation of the Stephan-Boltzmann law of radiative transfer. The important thing to note is that this arises perfectly naturally from the intensity of black-body radiation depending solely on its absolute temperature. There is no need for some unspecified physical mechanism that influences the direction in which a black body radiates; it just radiates in all directions, and the net flow of energy conforms precisely to the second law of thermodynamics. This is what the footnote in Clausius' book describes, and the basic idea has been well understood for a long time.

So, if a spherical black body does not radiate photons equally in every direction, but is affected by its environment, please explain the physical mechanism by which this is achieved.

Footnote, I am assuming that the constant c has been aggregated with the Stefan-Boltzmann constant in ClaesJohnsons' equation. The constant c depends on the size of the objects, their shape and how much of the radiation from one object is able to fall on another. I have made the scenario in the thought experiment symmetrical so it is easy to see that c is the same for both bodies, although this is true without the exact symmetry.

Claes: I have asked you if an engineering version of SB (or Planck) is enough to describe atmospheric radiation, and if not, what is missing. If you agree that it is basically enough, then we have a common standpoint and we can go on to specific questions concerning the physics of the so called "greenhouse effect". If you insist that it is not enough, then I want to see your arguments supporting this view.

There are endless questions that can take a lifetime or more to answer, such as: What is an "infrared photon"? What physical laws does it follow? How does it travel through space? In straight lines? What is the process of "absorption/emission of an "infrared photon". In which direction is it emitted? Is an "infrared photon" particle or wave? What is its lifetime? How does it interact with other "infrared photons". Are "infrared photons" like bullets traveling through space? If so, what happens when two "infrared photons" meet? Is heat transfer between two bodies carried by two opposite streams of "infrared photons" back and forth between the bodies? If so, what is the mechanism that guarantees that the net heat transfer is from warm to cold? What is the wave function of the multiverse? Et cet, et cet...

But all these questions are irrelevant as concerns the physics of the "greenhouse effect", if the engineering version of SB/Planck (which we have agreed is valid) is enough to describe atmospheric radiative heat transfer.

So I ask you again if we can take this version as a common ground and then proceed to the real questions of importance concerning the physics of the "greenhouse effect", with a basic question being climate sensitivity as the amount of global warming from doubled CO2.

Is this OK to you? Or do you insist that questions of the type I have listed above, have to be answered (by me) before we can can come to the point? And in particular before you will give an answer to my original question about the statement in the video of week 3 that "although heat moves in all directions.." (Is this statement connected to an idea of opposite streams of photons between bodies?)

I expect to get a clear answer to my clearly stated questions, and not just more questions from you to me, which I cannot answer (and probably nobody else).

To meet a question by a battery of counter-questions is a way to avoid answering the original question. I am sure you would not like to resort to this form of discussion trickery, right?

I also ask you if you have looked at the web site on Computational Blackbody Radiation I referred to and if you have read and understood the arguments there presented, and if you have some comments or questions concerning the material?

In short: If net heat transfer from warm-to-cold is what matters, why insist on net heat transfer as the difference of two opposite heat transfers warm-to-cold and cold-to-warm, where the latter appears to violate the 2nd law?

I have given my argument for net transfer as a property of stability (connected to the 2nd law). Transfer as the difference of two opposite gross transfers is an unstable process, since small differences in gross transfers can shift the sign of the net transfer, and thus violate the 2nd law. The only way the 2nd law can be upheld with transfer as difference of opposite gross transfers, is that the opposite transfers somehow are linked, but that contradicts your idea that the opposite transfers are independent of each other. Do you see this?

Gavin: ClaesJohnson wrote

"I have asked you if an engineering version of SB (or Planck) is enough to describe atmospheric radiation, and if not, what is missing. If you agree that it is basically enough, then we have a common standpoint and we can go on to specific questions concerning the physics of the so called "greenhouse effect"."

I have already explained why more is required, when I wrote in the previous message:

"Claes, as I have pointed out to you before, that equation is for radiative transfer. In order to answer your question about the second law of thermodynamics and the back-radiation, you need to understand how that transfer arises from an exchange of energy in either direction."

When we reach agreement on that point, then we will have a common standpoint to discuss the greenhouse effect (and specifically why there is no violation of the second law of thermodynamics).

So, do you accept that the engineering version of SB can be derived (as shown in my previous comment) as the net result of a bi-directional transfer of energy from A to B and from B to A, where the radiation from A is determined solely by is absolute temperature Ta (according to SB), and the radiation from B determined solely by its absolute temperature Tb (according to SB)?

To meet a question by a battery of counter-questions is a way to avoid answering the original question. I am sure you would not like to resort to this form of discussion trickery, right?

Please lets leave rhetoric out of this discussion. I have asked one question in this comment, and one only, please give a direct answer.

Claes: What is your question to me again? I will certainly try to answer if I only understand what you ask. Your answer to my question is that the engineering version of SB/Planck is not enough to (mathematically) model atmospheric radiative heat transfer. But you did not answer my follow-up question to your answer, namely, what more you then need to (mathematically) model atmospheric radiative heat transfer? What additional physical law do you need for this purpose?

You did not either answer if you have looked at the web site I gave. Have you? If so any reaction? And what about my original question?

You say that there are certain things I need to understand in order for you to answer my questions. I don't see that my understanding, whatever it means, is necessary in order for you to answer my questions? Would it not be possible for you to simply answer my clearly stated questions, regardless of my state of mind?

Is it necessary for me to give a complete account of my inner status and thoughts in order for you to answer my questions in my role as student in a course that you are giving on edX?

Isn't the role of a teacher to answer questions from students concerning the material presented by the teacher, rather than subjecting the students to interrogation to see if they carry ideas which the teacher does not like?

And again, what more than the engineering version of SB/Planck do you need to model atmospheric radiative heat transfer??? My view on this question is presented as Unphysical Schwarzschild vs Physical Model for Radiative Transfer at http://claesjohnson.blogspot.se/2015/04/unphysical-schwarzschild-vs-physical.html


Gavin: ClaesJohnson, you seem to have asked multiple questions in your comment, I am happy to answer them one at a time. Please select the technical/scientific question you would like me to answer.

In an earlier comment, I derived the engineering form of the SB equation for heat transfer as being the net result of a bi-directional transfer of energy due to the radiation from each body. This is not a new idea, in his book "The Theory of Heat Radiation", Max Plank (c.f. Plank's law) states:


A body A at 100C emits toward a body B at 0C exactly the same amount of radiation as toward an equally large and similarly situated body B' at 1000C. The fact that the body A is cooled by B and heated by B' is due entirely to the fact that B is a weaker, B' a stronger emitter than A.

This makes it very clear that Plank's conception of heat transfer is of a bidirectional transfer of radiation, both from warmer to cooler and from cooler to warmer, with the transfer of heat depending on the net difference in the two flows. Note Plank also specifically states that the radiation from A is not dependent on the temperature of the body on which the radiation will fall.

So to repeat my question:

...do you accept that the engineering version of SB can be derived (as shown in my previous comment) as the net result of a bi-directional transfer of energy from A to B and from B to A, where the radiation from A is determined solely by is absolute temperature Ta (according to SB), and the radiation from B determined solely by its absolute temperature Tb (according to SB)?

Claes: Of course the one-directional SB can be derived from a two-directional version by trivially taking the difference. But that does not say that the two-directional is correct, right?. The one-directional version may be the correct physical law, while the two-directional may still be non-physical. Confirming an assumption by observing a consequence is one of the logical fallacies, right?

So I have answered your question, and now to my question: What more than the engineering version of SB/Planck do you need to mathematically model atmospheric radiative heat transfer? What additional physical do you need for that purpose? The question is clearly stated and I expect a clear answer.

Gavin: Claes, again you have asked multiple questions (note there are three question marks in your comment). However I will address them in turn, on this occasion (I assume the second was rhetorical):

"Of course the one-directional SB can be derived from a two-directional version by trivially taking the difference. But that does not say that the two-directional is correct, right?."

No, no in itself. However the quote I gave from Plank clearly shows that Plank's conception of heat transfer was the net result of a bi-directional flow of energy. Similarly Clausius' book clearly indicates that a bi-directional flow of heat is completely consistent with the second law of thermodynamics, provided the net flow is from hot to cold. More importantly, I would argue that there is no plausible physical mechanism that can explain how a body can modify its radiation to avoid its radiation being absorbed by a warmer body. My derivation requires no such assumption as the radiation of a body depends only on its local state (specifically its absolute temperature). So my question for this message is: "What physical mechanism allows a body to alter its radiation to avoid emitting photons that reach a (possibly moving) warmer body?"

"What more than the engineering version of SB/Planck do you need to mathematically model atmospheric radiative heat transfer?"

I have answered this question several times already. The net transfer of heat is depends on the difference in the energy exchanged between two bodies (in this case the atmosphere and the surface). Thus it is necessary to consider the amounts of energy radiated by each component and absorbed by each component separately. The greenhouse effect does not violate the second law of thermodynamics because the energy transferred by back radiation from the atmosphere to the surface is "compensated" (as Clausius, in translation, would say) by a larger transfer of energy in the other direction, in the form of IR radiation from the surface.

The key point is that if you accept that a bi-directional exchange of radiation doesn't violate the second law of thermodynamics, provided the net flow is from hot to cold, then the greenhouse effect doesn't violate it either. If you do not accept this, then you need to show that the engineering form of the SB law is inconsistent with the interpretation as the net result of a bi-directional exchange of radiation. However you appear already to have conceded this point

"Of course the one-directional SB can be derived from a two-directional version by trivially taking the difference".

Claes: I asked you: What additional physical law, in addition to the one-directional engineering SB/Planck law we have agreed on, do you need to mathematically model atmospheric radiative heat transfer? What is your answer?

Gavin: Claes, I have already answered that question. We must use the physical laws governing the radiation of black-body objects (at least to begin with), which is the Stefan-Boltzmann law for radiation, i.e. j* = sigma*T^4. From this we can straight-forwardsly derive the "one-directional engineering SB/Planck law" as the net result of an exchange of radiation between two bodies. Under this interpretation of the "engineering SB law", the greenhouse effect does not violate the second law of thermodynamics as the radiation from the warmer surface to the cooler atmosphere is greater than from the atmosphere to the surface. Therefore the "one-directional" net heat transfer of the "engineering" SB law is from warmer to cooler, as required by the second law of thermodynamics.

This question ought to have a yes or no answer, and will help me to understand your position if you give an unequivocal answer. Plank writes:

A body A at 100C emits toward a body B at 0C exactly the same amount of radiation as toward an equally large and similarly situated body B' at 1000C. The fact that the body A is cooled by B and heated by B' is due entirely to the fact that B is a weaker, B' a stronger emitter than A.

My one question for this comment is: Is any of the radiation emitted by B (at 0C) absorbed by A (at 100C), "yes" or "no"?

Claes: This statement of Planck lacks physical reality. Nature does not play with opposite equally large quantities, which are independent, yet always keeping one bigger than the other to not violate the 2nd law. You cannot accept anything that Planck says without yourself judging if that is correct or not? Science is not parrot science where you simply repeat what is written in book or stated by some since long dead scientist.

Again: what additional law is required to mathematically model atmospheric radiative heat transfer, beyond the one-directional SB/Planck law we have agreed on? Is it two-way heat transfer? If so, what equation does that effectively bring into the mathematical model? Have you read my post about Schwarzschild's (unphysical) equations based on two-way transfer? If not, do that and give your view on the necessity of Schwarzschild's model. OK?

Gavin: Claes, I have already answered your question repeatedly. The additional physical law that is required is the Stefan-Boltzmann law of radiation: j* = sigma*T^4. For the reasons, see my previous answers.

Now please give a direct answer to my previous question, I repeat:

Plank writes:A body A at 100C emits toward a body B at 0C exactly the same amount of radiation as toward an equally large and similarly situated body B' at 1000C. The fact that the body A is cooled by B and heated by B' is due entirely to the fact that B is a weaker, B' a stronger emitter than A.

My one question for this comment is: Is any of the radiation emitted by B (at 0C) absorbed by A (at 100C), "yes" or "no"?

You earlier wrote:

To meet a question by a battery of counter-questions is a way to avoid answering the original question. I am sure you would not like to resort to this form of discussion trickery, right?

Note that in my previous comment I asked precisely one question (only one question mark), but in your reply, you did not give an answer, but you asked multiple questions (I count six question marks!).

Claes: My answer is no.

Gavin: Thank you, that is interesting. Consider a third body B'' at 50C, which is of a similar size to B and again similarly situated. I am assuming that since B'' is also cooler than A, you would say that no radiation from B'' is absorbed by A either. Feel free to correct me if this assumption is incorrect. My question is, does A emit a different amount of radiation towards B than it emits towards B''?

Claes: Radiative heat transfer between bodies is described by the one-directional SB law we have agreed is valid.

Gavin: That is not a direct answer to the question, A either does emit a different amount of energy towards B than it emits towards B'', or it does not. Which is it?

Claes: SB gives the answer to your question. This is an exercise you can do yourself. After all you are the teacher and should know.

Gavin: The reason that I am asking for an unequivocal answer is that I intend to demonstrate a contradiction and do not want to leave room for equivocation after it has been established. If you are confident of your position, you ought to be eager to state your position in completely unequivocal terms. So I ask again:

"does A emit a different amount of radiation towards B than it emits towards B''?"

"yes" or "no".

Claes: A as warmer transfers heat to B and B" according to SB. If B" is warmer than B, then less heat energy transfers from A to B" than to B.

Claes: You claim that in addition to SB in the form Q = sigma (T_A^4 - T_B^4) with T_A > T_B, you need an SB of the form Q = sigma T_A^4. But the latter is included in the former if you set T_B = 0. So why is the extra SB needed?

Claes: Gavin: While you are thinking, I hope you also remember to answer my original question about the meaning of the statement "although heat moves in all directions..." in a video of week 3.
Gavin: I have now asked ClaesJohnson a straight-forward "yes"/"no" question three times, and each time have recieved an evasive response. As I have already explained why an indirect answer would be indicative of evasion, I think it is reasonable to conclude that the evasion was deliberate.

ClaesJohnson subsequently attempted to divert the discussion away from a line of inquiry that will demonstrate a contradiction in his position by repeating a question from earlier in the discussion that has already been answered (repeatedly). Again this is evasion.

Socratic method (a form of enquiry based on asking and answering questions) is an excellent means of resolving scientific disagreements, provided that both parties engage in the exercise in good faith. This cross-examination allows misunderstandings to be resolved and exposes the weaknesses in either argument. Evading direct questions is a clear indication that someone is unwilling to change their views, regardless of the evidence or opposing arguments presented. In this case, there is little point in continuing the discussion, and the observers can draw their own conclusion from the evasion.

Ulimately, if ClaesJohnson refuses to look at anything other than the "one-direction" SB law for radiative heat transfer, and is unable to understand that this arises as the net result of a bi-directional transfer of energy (as illustrated by Planck's example), he will be unable to understand why the greenhouse effect doesn't violate the second law of thermodynamics. However, he can't say that this has not been explained to him.

Claes: Gavin, I think we have come to the end of our discussion. Yes, it is true that only the uni-directional SB makes sense to me and to physics. You have not been able to give any scientific support to a "greenhouse effect" based on two-directional heat transfer including "back radiation" with heat transfer from cold to warm, and neither have you been able to explain the obvious violation of the 2nd law in such a process. This means that a "greenhouse effect" based on "back radiation" is nonphysical illusion. The result is that the course lacks sufficient scientific basis and should be closed.

Gavin: ClaesJohnson If only the uni-directional SB makes sense to you, then perhaps you should not obstruct attempts to explain the bi-directional energy transfer required for an understanding of back radiation by the sort of evasive behaviour you have demonstrated during this discussion.

Claes: I have declared my standpoint very clearly. The evasiveness is yours. I am surprised that edX offers a platform for the kind of propagandistic disinformation the course presents. In any case the "denial" will not be affected by the course.

Tragedy of Modern Physics: Schrödinger and Einstein, or Quantum Mechanics as Dice Game?

The story of modern physics is commonly told as a tragedy in which the fathers of the new physics of atomistic quantum mechanics Einstein and Schrödinger, were brutally killed by their descendents Bohr, Heisenberg and Born. This story is told again in a new book by Paul Halpern with the descriptive title:

• Einstein's Dice and Schrödinger's Cat, How Two Great Minds Battled Quantum Randomness to Create a Unified Theory of Physics. 

In this story, it is Einstein and Schrödinger who represent the tragedy in their stubborn opposition to the probabilistic Copenhagen interpretation interpretation of the wave function of Schrödinger's equation and their fruitless search for a unified physical field theory free from dice games, which ended in tragical defeat under ridicule from the physics community controled from Copenhagen by Bohr.  

But it is possible that Einstein's and Schrödinger's dream of a unified physical field theory will come true one day, and then the tragedy will instead be modern physics based on dice games. In all modesty this is the working hypothesis I have adopted in my search for a version of Schrödinger's equation allowing a realistic physical interpretation without "quantum randomness". Stay tuned for an update of recent advances in this direction...

In short, one may say that Einstein and Schrödinger seek a mathematical model of physical reality as a question of ontological realism or existence or  what "is",  while Bohr is only interested in what we can "say" (based on what we can "see") as a question of epistemological idealism. In the quest between realism and idealism in physics, one may argue that idealism is failed realism.

The book describes Einstein's and Schrödinger's positions as follows: 

• As originally construed, the Schrödinger equation was designed to model the continuous behavior of tangible matter waves, representing electrons in and out of atoms. Much as Maxwell constructed deterministic equations describing light as electro­magnetic waves traveling through space, Schrödinger wanted to create an equation that would detail the steady flow of matter waves. 
• He thereby hoped to offer a comprehensive accounting of all of the physical properties of electrons. 
• Born shattered the exactitude of Schrödinger’s description, replacing matter waves with probability waves. Instead of physical properties being assessed directly, they needed to be calculated through mathematical manipulations of the probability waves’ values. 
• In doing so, he brought the Schrödinger equation in line with Heisenberg’s ideas about indeterminacy. In Heisenberg’s view, certain pairs of physical quantities, such as position and momentum (mass times velocity) could not be measured simultaneously with high precision. 
• Aspiring to model the actual substance of electrons and other particles, not just their likelihoods, Schrödinger criticized the intangible elements of the Heisenberg-Born approach.
• He similarly eschewed Bohr’s quantum philosophy, called “complementarity,” in which either wavelike or particlelike properties reared their heads, depending on the experimenter’s choice of measuring apparatus. Nature should be visualizable. 
• Starting in the late 1920s, one of his primary goals was a deterministic alternative to probabilistic quantum theory, as developed by Niels Bohr, Werner Heisenberg, Max Born, and others. 
• Although he (Einstein) realized that quantum theory was experimentally successful, he judged it incomplete. In his heart he felt that “God did not play dice,” as he put it, couching the issue in terms of what an ideal mechanistic creation would be like. 
• Agreeing with Spinoza, Einstein sought the invariant rules governing nature’s mechanisms. He was absolutely determined to prove that the world was absolutely determined.
• Einstein, who had been a colleague and dear friend in Berlin, stuck by Schrödinger all along and was delighted to correspond with him about their mutual interests in physics and philosophy. 
• Together they battled a common villain: sheer randomness, the opposite of natural order. Schooled in the writings of Spinoza, Schopenhauer— for whom the unifying principle was the force of will, connecting all things in nature— and other philosophers, Einstein and Schrödinger shared a dislike for including ambiguities and subjectivity in any fundamental description of the universe. 
• While each played a seminal role in the development of quantum mechanics, both were convinced that the theory was incomplete. Though recognizing the theory’s experimental successes, they believed that further theoretical work would reveal a timeless, objective reality.
• As Born’s, Heisenberg’s, and Bohr’s ideas became widely accepted among the physics community, melded into what became known as the “Copenhagen interpretation” or orthodox quantum view, Einstein and Schrödinger became natural allies. 
• In their later years, each hoped to find a unified field theory that would fill in the gaps of quantum physics and unite the forces of nature. By extending general relativity to include all of the natural forces, such a theory would replace matter with pure geometry— fulfilling the dream of the Pythagoreans, who believed that “all is number.”
• The crux of Schrödinger’s rebuttal was to declare that random quantum jumps simply weren’t physical. He argued for a continuous, deterministic explanation instead. continuous, deterministic equation to defend.
• .....by late 1926 mutual opposition to the notion of random quantum jumps forced the two of them into the same anti-Copenhagen camp. The alliance would be forged once they realized that they were among the few vocal critics of Born’s reinterpretation of the wave equation.
• After returning to Zurich from Copenhagen, Schrödinger continued to defend his disdain for quantum jumps on the basis that atomic physics should be visualizable and logically consistent. 
• By the end of 1926, Einstein had drawn a stark line of demarcation between himself and quantum theory. 
• Einstein appealed to Born, trying to convince him that quantum physics required deterministic equations, not probabilistic rules. “Quantum mechanics yields much that is very worthy of regard,” Einstein wrote to Born. “But an inner voice tells me that it is not yet the right track.
• The theory . . . hardly brings us closer to the Old One’s secrets. I, in any case, am convinced that He does not play dice.
• That was not the last time Einstein would make that point. For the rest of his life, in his explanations of why he didn’t believe in quantum uncertainty, he would reiterate again and again, like a mantra, that God does not roll dice.
• In 1927, Einstein delivered a talk at the Prussian Academy purporting to prove that Schrödinger’s wave equation implied definitive particle behavior, not just dice- rolling. 
• Despite his prominence, Einstein’s entreaties had little impact on the quantum faithful. 
• Einstein returned to Berlin a far more isolated figure in the scientific community. While his world fame continued to grow, his reputation among the younger generation of physicists began to sour, as they derided his objections to quantum mechanics. 
• With experimental findings continuing to support the unified quantum picture advocated by Bohr, Heisenberg, Born, Dirac, and others, Einstein’s dismissal of their views seemed petty and illogical. 
• Schrödinger was one of the few who sympathized with Einstein’s doubts. They kept up a conversation about ways to extend quantum mechanics to make it more complete. 
• Einstein complained to him about the dogmatism of the mainstream quantum community. 
• For example, he wrote to Schrödinger in May 1928, “The Heisenberg- Born tranquilizing philosophy— or religion?— is so deliberately contrived that, for the time being, it provides a gentle pillow for the true believer from which he cannot very easily be aroused. So let him lie there. But this religion has . . . damned little effect on me.” 
• Although the physics community relocated to the realm of probabilistic quantum reality, leaving Einstein the lonely occupant of an isolated castle of determinism, the press still bathed him in glory. He was the wild-haired genius, the celebrity scientist, the miracle worker who had predicted the bending of starlight. He was something like a ceremonial king who had long lost his influence over the course of events; the media were more interested in him than in the lesser- known workers actually changing science. His every proclamation continued to be reported by the press, if largely ignored by his peers. 
• the mainstream physics community, who increasingly viewed him as a relic, he remained the darling of the international media...