söndag 17 februari 2019

Approaching relativity - The doppler radar

This is yet another blog post that is seemingly unrelated to the theme of the blog. My interest in the subject of Special Relativity began relatively recently, partly from a curiosity to learn more about it and partly from perhaps being able to bring some clarity over the controversies surrounding it, controversies that I had not been aware of when I first studied the subject as an undergraduate. For the most part, the controversy concerns the question of who was the true originator of the theory of Special Relativity, was it Einstein or perhaps Poincaré or Lorentz? For the rest, the controversy is about the theory itself, whether it is false or true or whether it is even meaningful in a physical sense. Sometimes these discussions get mixed up in a very confusing way. Here we will not touch the priority dispute at all but will only be concerned with the postulate of Special Relativity stating that the speed of light c is constant in every inertial reference frame, together with its consequences in terms of time dilation, length contraction and so on. This demarcation is suitable since "Relativity Theory" is often associated with other postulates such as the formula E = mc², the bending of light in gravity fields, that are only weakly related to, or even unrelated to, the postulate of the constancy of the speed of light. Before we move on to the main arguments we have to warm up with some concepts from classical physics.


Galilean relativity

The theory of relativity formulated by Galileo Galilei is a cornerstone of classical mechanics. It could be stated saying that there does not exist any measurable "absolute" motion in space but only relative motion between interacting bodies. For example, when you sit in an airplane you can still play with your jo-jo as if you were both at rest in your comfy chair at home. This despite of the fact that, according to an observer on the ground, both you and the jo-jo travel at a considerable speed. Another way of putting it is to say that the laws of physics stay the same in all reference frames in uniform motion relative to each other. Newtonian mechanics is a perfect example of a physical theory that obeys Galilean relativity. As we will see further on, it is when Maxwell's equations of classical electrodynamics are confronted with Galilean relativity that the seed of Special relativity is born. If you speak of the "speed of light" being 300 000 km/s the question becomes: in which reference frame?


The classical doppler effect

If we now move our attention instead to sound waves waves the question of Galilean relativity becomes a much simpler matter. Why so? because now we have a medium where the waves travel as our natural reference frame. Sound waves need some medium, such as air or water, in which to travel. Hence, when we speak of the "speed of sound" we mean, naturally, the speed of the sound waves relative to the medium in which they travel. However, for a vehicle traveling in the medium it is still quite possible to approach the crests of the sound wave with a relative speed exceeding the speed of sound relative to the medium. This variability in relative speed gives rise to the doppler effect. When a vehicle approaches the sound wave with a speed v relative to the medium it will reflect the crests of the sound waves at shorter intervals giving rise to an increase in frequency of the reflected wave. We will not go into the detailed theoretical derivation of this phenomena here, but merely point out some main bullet points to take away from this section:

1. In the case of sound waves, the question of Galilean relativity is unproblematic since, in this case, the speed of sound refers to the motion of the waves relative to the medium where they travel.

2. It is possible for a vehicle traveling in the medium to approach (or move away from) a sound wave with a relative speed that is higher than (or lower than) the speed of the sound wave relative to the medium. This gives rise to the doppler effect.

3. In the case of sound waves, the magnitude of the doppler effect depends on whether it is the source or the receiver that moves in the medium.


Maxwell's equations and Galilean relativity

We now come to the important question: Do Maxwell's equations obey Galilean relativity? In other words, do they predict the same measurable phenomena under a Galilean transformation, that is, switching to a reference frame in uniform motion relative to the former. One thought experiment, which is also  mentioned in the introduction to Einstein's 1905 paper, concerns the moving magnet and conductor problem. We will not go into the details of that problem here but only point out that, in this case, the measurable outcome remains the same even after a Galilean transformation, hence, the moving magnet and conductor problem seems to be an example where Maxwell's equations elegantly cope with a change of reference frame. An apparently more difficult problem arises when we consider instead the solution to Maxwell's equations in vacuum, that is, when we are left without any electromagnetic source terms in the form of charged particles or currents. In this case, it can be shown that Maxwell's equations boil down to a wave-equation whose solution is a wave propagating in space with velocity c, and now the Galilean relativity problem arises: The speed c in which reference frame?


Lorentz, the ether theory and the Michelson-Morley experiment

Whether it was considerations of Galilean relativity that led Lorentz to formulate his ether theory will be left unspoken. However, the idea of a motionless light medium, called the "ether", could provide a natural reference frame in which light always travel at the speed c, just like sound waves travel at a constant speed relative to their medium. In order to test this hypothesis, Michelson and Morley conducted an experiment set out to detect the motion of the earth relative to the motionless ether. The result was negative, no ether wind could be detected. Lorentz, nevertheless, continued to pursue his ether theory and attempted to explain the negative result of the Michelson-Morley experiment with notions such as length-contraction and time-dilation, formulas that still remain with us today although with a somewhat different interpretation. The stage was now set for Einstein to enter.


19th century dogma turned into 20th century dogma?

In short, Einsteins solution to the problems discussed in the previous section has been formulated as follows:

The speed of light in a vacuum is the same for all observers, regardless of the motion of the light source.

It could be disputed whether this exact formulation ever occurs explicitly in Einstein's 1905-paper, but that is another story. As mentioned in the introduction, we are not interested here in the contribution of various individuals to the theory of relativity but merely to examine the theory as it stands today.


The doppler radar

I would like the reader to have a look at the following article from Wikipedia explaining the working of the doppler radar, a hand-held equipment used primarily by military och law-enforcement officers to measure the speed of moving vehicles.

https://en.wikipedia.org/wiki/Doppler_radar

 It turns out that, the classical formula for the doppler effect remains valid with the slight modification that we do not make any distinction between whether it is the source or receiver that is moving, only the relative motion comes into play. Curiously enough, the article states explicitly:

There is no need to invoke Einstein's theory of special relativity, because all observations are made in the same frame of reference.


Fair enough, but now we come to the question: How are we to explain this "classical" doppler effect of light if we insist that "The speed of light in a vacuum is the same for all observers, regardless of the motion of the light source." Clearly, when we derive the doppler shift for sound waves we assume that it is possible for the vehicle to approach the sound wave at variable speeds. To add to confusion there does also exist a hypothetical relativistic doppler effect, but the formula for this theoretical effect is different in nature and smaller in magnitude than that which we observe. I will leave to the reader to try to make sense out of all of this, if it is even possible, but until the doppler radar is explained in accordance with relativity theory I will remain doubtful as to the validity of the main postulate of Special Relativity.


The roots of the difficulties


Here we will make some very tentative remarks about the source of all confusion, namely the solution to Maxwell's equations in vacuum. First I would like to point out that light essentially is a force, or at least becomes a force when it comes in contact with charged particles. So, in essence, the solution to Maxwell's equations in vacuum is a solution that contains only forces and no particles. What is wrong with that picture? I would say that such a system is necessarily incomplete, because forces never exist on their own, they are always mediators between particles. If a particle is accelerated by an electric field then, according to Newton's third law, some other particle in the universe needs to take the recoil. However, saying that a reference frame is incomplete is not the same thing as saying that it is useless. For example, often in mechanics the earth is replaced by a constant gravitational force pointing downwards, thus we forget that every time we jump upwards the earth needs to take a recoil downwards. In summary, posing an extremely fundamental question such as that of Galilean relativity so a system that is by necessity incomplete might lead you astray. Very, very astray.

lördag 9 september 2017

Perth Group: HIV - a virus like no other

As a follow-up to a previous post on issues parallel to AGW, I will here bring to your attention a recent paper published online the Perth Group entitled "HIV - a virus like no other". This 83-page article provides a comprehensive review of the many serious flaws in the alleged scientific evidence for the existence of a single retrovirus particle HIV as the causative agent for the ever expanding umbrella of diseses under the acronym AIDS. Indeed, the conclusion reads as follows:

On the basis of the presently available data in the scientific literature, one has no choice but to conclude that whatever “HIV” is, it is not “the virus that causes AIDS”, or even “a real virus”.

At the moment, this analysis stands uncontested as most scientific journals do not even dare to send the paper for review as indicated by the following explanatory note:

On 21st February 2017 the Perth Group emailed this manuscript to Nature, The Lancet, the British Medical Journal, Science, Medical Hypotheses, the Journal of the American Medical Associationand the New England Journal of Medicine. The following covering note was addressed to each editor-in-chief.

My colleagues and I have a somewhat unusual request of your editorial office. The attached document is a detailed re-evaluation of the HIV/AIDS theory. For several decades we have closely followed the evolution of this theory and the data upon which it was based. In our view the theory was formulated on evidence and observations that were not always subjected to the expected strict scientific rigour. Consequently its conclusions and predictions need to be thoroughly questioned and the precise nature of "HIV" redefined.

We are aware that the topic is contentious, especially as some well-publicised challenges to the orthodox view have had deleterious public health implications. Our request to you as guardians of scientific thought and integrity is to assess our critique, and see whether in your considered opinion it is worthy of being brought to the attention of the scientific community. If you decide that it is, we would then like to prepare, under your guidance, a concise version for publication.

Despite repeated requests, three editors did not acknowledge receipt of our email. All responses came from editorial committees. One was “we do not encourage pre-submission enquiries”; another, we “respectfully pass on having the opportunity to publish a paper on this topic at this time. Best of luck publishing your work in another good journal”. A third, “After considering its focus, content, and interest, we made the editorial decision not to consider your proposal further. We are informing you of this decision promptly so that you can submit your manuscript elsewhere”. All replies ignored our request for a private appraisal and/or responded as if the manuscript were a submission for publication (a futile exercise given that no editor would accept a paper of this length).

söndag 18 juni 2017

Repulsive forces as the cause of heat diffusion

Recently some thoughts have crossed my mind about our general understanding of the fundamentals of thermodynamics, especially concerning its alleged foundation in mechanics at the microscopic level. These thoughts are modest in scope but the more papers I read on the subject it seems to me that this particular aspect is rarely mentioned, if it is mentioned at all. Therefore I would like to give it some attention here. The classical formulation of the second law of thermodynamics goes something along the lines

Heat flow spontaneously from higher to lower temperature

This is an empirical observation dating back to the time when the atomic theory of matter was not established science. Hence, at that time, it was a somewhat bold to say that the spread of heat in space from higher to lower temperature could in fact be explained by inter-molecular forces at the microscopic level. One problem, pointed out by Poincaré and others, was the time-reversibility of the standard laws of mechanics. If, at any moment, you were to reverse the velocity vectors of every molecule in the system, then the process would start to run backwards resulting in the opposite process of heat going instead from lower to higher temperture. This might not seem as that great of a difficulty to overcome, since an argument could be put forward that such an event is so unlikely to occur that it is never seen in reality. This probabilistic argument was to become the starting point for statistical thermodynamics and subsequently statistical mechanics, and it has prevailed to this day.

A somewhat more controversial branch of early thermodynamics is the never ending story about the ever increasing entropy. Entropy has its origins in an apparently innocuous looking term arrived at in the analysis of the Carnot cycle

dS = dQ/T

which during the course of an entire Carnot cycle can be shown to increase, assuming the usual form of the second law of thermodynamics. This observation, allied with the probabilistic explanation for heat spread, sparked an intense quest for the microscopic foundation of this mysterious new quantity called entropy. At this stage people were no longer talking simply about the spread of heat in physical space but instead more generally of the increase in entropy in the 6N-dimensional phase space of the molecules taking part in the process. A mechanical explanation for the increase in entropy was never found though, the Gibbs entropy can in fact be shown to be constant under Newtonian dynamics. However, the narrative has prevailed to the present day, and still we here stories of the irreversibility of the smashing of glass and the like as caused by an increase in some entity called entropy.

In any case, I would now like to take some steps back and look at our initial intuitive understanding of the spread of heat and matter in space. 


Imagine an ensmble of atoms and molecules confined to some space as ilustrated above. Thermodynamics tells us that heat should spread from regions with higher temperature to lower, likewise we expect molecules to spread from denser regions to less dense regions. Based on our experience from observing the behaviour of billiard balls in a snooker game it certainly makes sense to envisage these processes as the result of microscopic mechanics, however, I would like you to think carefully about what tacit assumptions you might be making of the molecular interactions taking place. One assumption that comes to my mind is the following:

We assume that there are repulsive forces acting between the molecules

Imagine what the situation would be like if we replaced the repulsive forces by attractive forces, like for example the gravitational force. In that case our intuition would no longer dictate that heat and matter spread in space, but rather the opposite. You agree?

Ok so what?, you might say, it is indeed plausible that there are repulsive forces acting between the electron shells of each atom, that makes sense doesn't it, so what is the problem? Nothing really, except that this simple assumption about the forces being repulsive is hardly ever mentioned. What insights can we gain from this? Well, consider for example the entropy discussion earlier. For many years people tried to explain the increase in entropy from mechanical considerations alone, but if no assumption about the repulsive nature of the forces is injected into the analysis, no wonder why they didn't succeed. If the forces were instead attractive you wouldn't expect any such thing as increase in "disorder".

Furthermore, in atmospheric and cosmological thermodynamics we have seen that the classical picture of thermodynamics probably breaks down at some level. Could that be because we have not properly taken into account the effect of attractive forces such as gravity? Who knows, but I just wanted to make this little point, repulsive forces are the cause of diffusion, remember that. That's all.

Further reading:

Boltzmann’s H-theorem, its limitations, and the birth of (fully) statistical mechanics
https://arxiv.org/pdf/0809.1304.pdf

onsdag 30 april 2014

Good and bad arguments

In connection to a recent post by Roy Spencer: Skeptical arguments that don't hold water, I thought I might take the opportunity to clarify and summarize certain key points that I have argued for on this blog. Roy Spencer is an incredibly valuable source for understanding the reasoning and conceptual twists needed to support the castle of sand upon which modern atmospheric physics is founded. He is also very kind to deliver the standard climatology explanation for the atmospheric lapse rate:


“Without the destabilization provided by the greenhouse effect, convective overturning would slow and quite possible cease altogether. The atmosphere would eventually become isothermal, as the full depth of the atmosphere would achieve the same temperature as the surface through thermal conduction; without IR emission, the middle and upper troposphere would have no way to cool itself in the face of this heating.” 


The same thing can not be said about some other people in Spencer's entourage. For example, in a 2003 issue of Energy & Environment a certain Mr Hans Erren threw a "Cotton-argument" when hypothesizing about the situation in the atmosphere in the absence of so called greenhouse gases:

"...Upper layers would be cooler because the vertical component of the thermal molecular speed
is reduced...."

However, maybe the time log for this statement of his is sufficiently old for him not to get caught in the "Cotton-sock" of Spencer's commentators field.


Another view inconsistent with that of Spencer and the IPCC was put forward by Robert G Brown:

"In nature, the dry adiabatic lapse rate of air in the atmosphere is maintained because the system is differentially heated from below causing parcels of air to constantly move up and down."

This makes no reference to any greenhouse gases. Is it the case that the system is heated from below only when there are greenhouse gases present?


At this point the observant reader should have noticed that the "debate" going on here is not about opposing scientific views but rather some kind of tribal fight for petty prestige. So what is the tactic of Spencer & Co? I think it is to simply ignore good arguments put forward against the GGH and instead focus on rebutting bad ones, because these indeed exist. By this method they hope to impart on the public an illusion that they, enlightened scientists, are winning the battle against the deluded barbarians and, in the fly, save their beloved trademark the Greenhouse Effect for future generations.


An example of a good argument is to point to the non-zero lapse rate in Jupiter's atmosphere in the pressure range from 1000 to 100 mB. This observation refutes the theory of Spencer that GHGs are necessary for the lapse rate and this is probably the reason why he never comments on it. Instead he makes a list of 10 other arguments of mixed quality. I will try to comment on these.


1. THERE IS NO GREENHOUSE EFFECT

Here it seems as if Spencer equates the existence of downwelling IR-radiation (back-radiation) with a physical effect with the name of the "Greenhouse Effect". However, this does not qualify as a thermodynamic effect at this stage, since nothing has been said quantitatively about warming or cooling of any part of the atmosphere. Furthermore, no assumption is made on the function of this downwelling radiation, will it act as radiation pressure or be part of some ordinary diffusive process. Moreover, why this obsessive focus on radiation, why not talk a little more about other quasi-particles such as phonons and direct molecular collisions. Most important perhaps, no effect of this kind has been attributed solely to so called greenhouse gases. If, however, people insist on denying the existence of downwelling IR-radiation, yes, please stop that.


2. THE GREENHOUSE EFFECT VIOLATES THE 2ND LAW OF THERMODYNAMICS

There are ways to argue why Spencer's and IPCC's version of the GE violates the 2nd law, but it must be stated in very precise way. I have done that in an older post. It is not sufficient, however, to simply say that

"The GE cannot work since the 2nd law prohibits heat transfer from the cold atmosphere to the warmer surface." 

Although there might be some sound reasoning behind this, it can easily be obscured and disarmed by pointing to the fact that the walls in your house passively increases the inside temperature under constant radiator-forcing. The statement is problematic since its relevance to the GGH is unclear. Where does the GGH state (explicitly or implicitly) that the cold atmosphere actively (rather than passively) heats the surface. Answer: Nowhere. Finally, the statement expresses a certain ignorance of the basic problem at hand since it doesn't address the fundamental question: Why is the upper atmosphere colder than the surface in the first place?


3. CO2 CAN'T CAUSE WARMING BECAUSE CO2 EMITS IR AS FAST AS IT ABSORBS.  

I think Spencer is right here. Dead herring.


4. CO2 COOLS, NOT WARMS, THE ATMOSPHERE.

You should never make any definitive statements about the warming or cooling effect of CO2 at its present concentrations. Tentative speculations, ok. It could be that CO2 cools slighty by absorbing IR radiation from the sun and warms slighly through the Neanderthal effect. Who knows?

However, here Spencer is kind enough to deliver the following:

"the net effect of greenhouse gases is to cool the upper atmosphere"

Some people simply don't get the meaning of this. They immediately confuse themselves by altering the statement to

"the greenhouse gases in the upper atmosphere has a cooling effect"

A cooling effect on what?? The surface? The upper atmosphere?

Moreover, if a theory predicts a cooling of the upper atmosphere and a warming of the lower, then by default, this implies an increased lapse rate in some part of the atmosphere. 


5. ADDING CO2 TO THE ATMOSPHERE HAS NO EFFECT BECAUSE THE CO2 ABSORPTION BANDS ARE ALREADY 100% OPAQUE.

Dead herring. I would also consider this as a kind of lukewarmist argument since it assumes that the absorption bands of CO2 have some particular importance. 


6. LOWER ATMOSPHERIC WARMTH IS DUE TO THE LAPSE RATE/ADIABATIC COMPRESSION.

I guess that Spencer makes some valid points here. At least, the "adiabatic theory" lacks a coherent physical model to support it. We should, however, be open to arguments of this kind since they might be needed to explain certain parts of the planetary atmospheres. As an extreme example: The interior of the sun. No pressure effect there?

Spencer asks: "If adiabatic compression explains temperature, why is the atmospheric temperature at 100 mb is nearly the same as the temperature at 1 mb, despite 100x as much atmospheric pressure?"

Yes Spencer, if greenhouse gases are needed to support the lapse rate between 1000 and 100 mB, then why does it exist on Jupiter?


7. WARMING CAUSES CO2 TO RISE, NOT THE OTHER WAY AROUND

I have no opinion on this.


8. THE IPCC MODELS ARE FOR A FLAT EARTH

I havn't inspected the IPCC models in that detail, which are not that easy to get access to I presume. However, this seems to be a rather inefficient argument.  
   

9. THERE IS NO SUCH THING AS A GLOBAL AVERAGE TEMPERATURE

This is somewhat similar in nature to the previous one. For now, inefficient. Perhaps it has some relevance when evaluating the statistical trends for small temperature variations, but it seems to be a distraction from more important issues.


10. THE EARTH ISN’T A BLACK BODY

Dead herring. Just as you can write down a heat diffusion equation linear in temperature you can write down a diffusion equation using the temperature to the power of four. Which is the best? Who knows? In any case you would need to adjust the tranport coefficients to match the empirical results. 

lördag 28 september 2013

Reclaiming the Neanderthal Effect

As I have described previously on this blog there appears to be a group of people, here denoted the Lukewarmers, whose mission is to convince people that the Greenhouse Effect is not the Greenhouse Effect. Or perhaps it should be rephrased as follows: The Greenhouse Effect does not refer to the Greenhouse Effect. Why would they do that? Because the Greenhouse Effect™ is now so deeply ingrained into the public consciousness that it would be simply inadmissible to let people know what it actually refers to. What it refers to in the climatology literature is a heat pump composed of so called greenhouse gases that act so as to cool the stratosphere and warm the surface at the same time, and it does so with an astonishing efficiency. The absurdity of this is obvious, especially since it can be so easily disproven by simply looking at the planetary data. For this reason the Lukwarmers have devised at least two strategies to deal with this dilemma, one intended for gullible ordinary citizens and another one for gullible scientists. In short they go as this


1. The Greenhouse Effect is the Tyndall Effect

2. The Greenhouse Effect is the Neanderthal Effect


We will deal with these in the proper order:

1. The strategy to re-define the Greenhouse Effect as the Tyndall Effect is common in many videos available online, often intended for defenseless school children. By shining light from some particular lamp on two different containers of gas one can apparently detect a difference in the heating rate between the two containers. One of the things you could object to is the use of a lamp in the first place. Why can't you do anything unplugged? The answer would probably be: Because in the lab we don't have access to the sun. I could accept that answer if it hadn't been that according to the canonical description of the Greenhouse Effect the greenhouse gases are supposed to let the sunshine through, it is the terrestrial radiation that is supposedly being trapped. Moreover, if we are to believe the radiation intensities used in standard climatology there ought to be an abundance of terrestrial radiation in the lab, hence I do not understand the use of the lamp. 


2. I guess the Lukewarmers have somewhat sensed the above inconsistencies, hence the need for another strategy intended for deniers with scientific training. This one is much more cunning and deceitful, that is probably the reason why so many people have difficulties dealing with the following argument. The argument is: The Greenhouse Effect is the Neanderthal Effect. The Neanderthal Effect is simply the obstruction of radiative cooling caused by blankets, furs, aluminium foil on light bulbs, most probably the atmosphere, in other words a very ordinary effect known even by the Neanderthalians. A common reply by skeptics is something like the following:

-Yes, the obstruction to cooling is real but it is not caused by "back-radiation".

Oh, no no no no no.......

You went into the trap. Now you have, for free, given the Lukewarmers an extra degree of confusion:

3. The Greenhouse Effect is whatever effect is caused by "back-radiation"

The problem is that we don't know exactly what causes the Neanderthal Effect. Hence, you cannot say anything about the role of back-radiation in this case. All we know is that it is very ordinary and is caused by virtually any material, including CO2. And since it is caused by any material there is no justification picking out some particular "greenhouse gases" responsible for some particular "Greenhouse Effect". The latter is simply an illegitimate scientific concept.

In summary:

What the Lukewarmers want you to believe is that:

Radiative heat transfer is special
CO2 is a special gas (as regards thermodynamics)

Whereas the truth reads:

Radiative heat transfer is ordinary
CO2 is an ordinary gas (as regards thermodynamics)

onsdag 18 september 2013

A Discrete Model Atmosphere, UV-updated

I have updated my Discrete Model Atmosphere so that it now includes UV-forcing of the upper layers giving rise to a thermosphere. I have also included a "troposphere" where the heat absorption is uniform leading to a constant lapse rate in that region. I stress that these kind of toy models may very well become superfluous after a more complete simulation using the Navier-Stokes equations. Maybe Claes has some update on this. Anyway, regardless of its usefulness it gives rise to some questions of pure academic interest. Here is what it looks like now:



The thing I wanted to point out is the annoying jump discontinuity at the surface. Numerical experiments suggest that this jump can not be made smaller than F/(2k) regardless of the meshsize and other factors. I would very much like in input from some clever mathematician about the significance of this and how it could perhaps be circumvented in a more developed model. As a side remark, I think that Miskolczi discusses the topic of jump discontinuities at the surface in his paper. The problem is that I don't understand his paper (nor find it on the internet anymore). Input is very welcome.


Updated script:

import numpy as np
import matplotlib.pyplot as plt


interval = 6
trop = 1        ## height of the "troposphere"
meshsize = 0.1

N = int (interval/meshsize)

weight = np.zeros(N)

## Please note that the "weight" is not the actual weight but a positive
## function taking values between 0 and 1 which increases monotonically on the
## actual weight (mass), meant to quantify the "heat-absorption"

weight[0] = 1   ## The surface is given complete heat absoption


for idx in range(1,N):

    if idx*meshsize < trop:
        weight[idx] = 1*meshsize    ## Troposheric weight put to 1 (times meshsize)
    else:
        weight[idx] =  np.exp(-(idx*meshsize - trop))*meshsize
   


A = np.zeros([N,N])
   
for idx1 in range(N):
    for idx2 in range(N):
        if idx1 == idx2:
            if idx1 == 0:
                A[idx1,idx2] = -1
            else:
                A[idx1,idx2] = -2
           
        else:
            A[idx1,idx2] = weight[idx2]

            if idx2>idx1:

                for idx3 in range(idx1+1, idx2):
                    A[idx1,idx2] = A[idx1,idx2]*(1-weight[idx3])

            else:
                for idx3 in range(idx2+1, idx1):
                    A[idx1,idx2] = A[idx1,idx2]*(1-weight[idx3])    
           

k = 1           ## Conductivity
uv = 1          ## UV-factor
screen = 0.5    ## Screening of UV-light (not rigorous, just toy model)

F = np.zeros(N)

F[0] = 1.0    ## Solar radiation incident on surface


for idx in range(N):
    F[idx] = F[idx] + uv*screen**(N-idx)    ## adding UV-forcing

 

temp = np.linalg.solve(A,-F/k)  ## Forcing vector divided by the "conductivity"
                                ## or perhaps more accurately, the diffusion parameter


x = np.arange(0,interval,meshsize)



plt.plot(x, temp)
plt.ylabel('Temperature')
plt.xlabel('Position')

plt.show()

onsdag 7 augusti 2013

(Back-(Radiation)-Therapy)

To cut a long story short:

Whatever the thermodynamic effect of a colder object radiating on a warmer object is, it has already been taken into account by the coefficient of thermal conductivity which, despite its name, measures all kinds of diffusive heat transport including radiation. (How could it not?)

That is the correct solution. I could also mention that I am not alone with this opinion. 

For example, G&T write the following in their first falsification paper:

"A physicist starts his analysis of the problem by pointing his attention to two fundamental thermodynamic properties, namely

the thermal conductivity, a property that determines how much heat per time unit
and temperature difference flows in a medium;"

In their reply to Halpern et al. they write:

"Speculations that consider the conjectured atmospheric CO2 greenhouse effect as an "obstruction to cooling" disregard the fact that in a volume the radiative contributions are already included in the measurable thermodynamical properties, in particular, transport coefficients."

I couldn't agree more.  What I have just stated is very powerful in its simplicity, since, if you want to know the thermodynamic effect of doubling the CO2 concentration you only need to measure the changes in the transport coefficients. These changes will of course be unmeasurable (although there is probably some tiny factual difference). And that's it. No need for any redundant radiative transfer calculations. The Greenhouse Effect is no more, gone like a fart in the wind.

The reason I am mentioning this is that there is a tendency of some people to over-do things. The overall theme of these various claims is that radiation from a colder body cannot be absorbed and/or cannot have any effect on a warmer body. My reaction to that is: Why not? Look at Newton's law of cooling:

The heat tranfer Q from hot (T1) to cold (T2) is given by 

Q = k(T1 - T2)

Since the temperature of the colder object T2 occurs in the formula the colder object must be doing something with the warmer object. If it did nothing we wouldn't feel the difference between 20 and -10 degrees. What is this something? Well, maybe in part it is the absorbtion of radiation. I don't know for sure but some people seem to know a whole lot about those things. And if it isn't radiation it must be something else. Does this "something else" violate the second law?

There is no possibility to discuss all of the excessive staments here, I have already done so to a certain extend previously on this blog. I just want to point out an obvious danger. 

Accepting that a warmer object can indeed absorb radiation from a colder object and that this might slow down the cooling is not the same thing as accepting the Greenhouse Effect.

If you do claim the contrary then the Lukewarmers have won. Then their "trademark" has been saved for future generations and can pop up any time with some new twisted definition. Insisting on this naïve simplification would be a great disservice to society.