tisdag 26 mars 2024

Man-Made Universality of Blackbody Radiation

Pierre-Marie Robitaille is one of few physicists still concerned with the physics of blackbody radiation supposed to be the first expression of modern physics as presented by Max Planck in 1900, as expressed in this article and this article and  this talk.

Robitaille points to the fact that a blackbody is a cavity/box $B$ with interior walls covered with carbon sooth or graphite. Experiments show that the spectrum of the radiation $B_r$ from a little hole of such a cavity only depends on frequency $\nu$ and temperature $T$ according to Planck's Law:

  • $B_r=\gamma T\nu^2$   if $\nu <\frac{T}{h}$  and $B_r=0$ else,       (P)     
where $\gamma$ and $h$ are universal constants, and we refer to $\nu <\frac{T}{h}$ as high-frequency cut-off. 

Experiments show that putting any material body $\bar B$  inside the cavity will not change (P), which is seen as evidence that the spectrum of $\bar B$ is the same as that of $B$  independent of the nature of $\bar B$ as an expression of universality. 

This is questioned by Robitaille, but not by main-stream physicists. Robitaille insists that the spectrum depends on the nature of the body. 

Let us see what we can say from our analysis in Computational Blackbody Radiation. We there identify a perfect blackbody to have a spectrum given by (P) with $\gamma$ maximal and $h$ minimal, thus by maximal radiation and maximal cut-off. By experiment we determine that graphite is a good example of a perfect blackbody. By maximality a blackbody spectrum dominates all greybody spectra.

Let then a greybody $\bar B$ be characterised by different constants $\bar\gamma (\nu)=\epsilon (\nu)\gamma$ with $0<\epsilon (\nu) <1$ a coefficient of emissivity = absorptivity possibly depending on $\nu$, and $\bar h >h$. The radiation spectrum of $\bar B$ is given by 

  • $\bar B_r=\epsilon (\nu)\gamma T\nu^2$  if $\nu <\frac{T}{\bar h}$ and $\bar B_r=0$ else.

This is not universality since $\epsilon (\nu)$ and $\bar h$ depend on the nature of $\bar B$. 

But let us now put $\bar B$ at temperature $\bar T$ inside the cavity $B$ with graphite walls acting as a blackbody and let $B$ take on the the same temperature (assuming $\bar B$ has much bigger heat capacity than $B$) with thus

  • $\bar B_r=\epsilon (\nu)B_r$ for $\nu<\frac{\bar T}{\bar h}$ and $\bar B_r=0$ else.
We then measure the spectrum of the radiation from the hole, which is the blackbody spectrum of $B_r$:
  • $B_r=\gamma\nu^2$ for $\nu<\frac{\bar T}{h}$ and $B_r=0$ else.
If we then insist  that this is the spectrum of $\bar B$, which it is not, we get a false impression of universality of radiation. By maximality with $h<\bar h$ the cavity spectrum $B_r$ dominates $\bar B_r$.
 
We conclude that the universality of blackbody radiation is a fiction reflecting a dream of physicists to capture existential essence in universal terms. It comes from using the cavity as a transformer of radiation from a greybody to a blackbody pretending that the strange procedure of putting objects into cavity with graphite walls to measure their spectrum, is not strange at all. 

We may compare with US claiming that the dollar $D$ represents a universal currency backing that by imposing an exchange rates $\epsilon <1$ for all other currencies $\bar D$, thus imposing the dollar as the universal currency for the the whole World forgetting that all currencies have different characteristics. This gives the FED a man-made maximal universally dominating role, which is now challenged... 

PS1 To meet criticism that painting the walls of the cavity with graphite may be seen as a rigging of the measurement of radiation through the hole, physicists recall that removing the graphite and letting the walls be covered with perfect reflectors, will give the same result, if only a piece of graphite is left inside the cavity. This shows to be true, but the piece of graphite is necessary and its effect can be understood from the maximality of blackbody radiation independent of object size. 

PS2 Recall radiation spectra of solid state is continuous while gasses have discrete spectra. Also recall that measuring spectra typically is done with instruments like bolometer or pyrgeometer, which effectively measure temperature from which radiation is computed according to some Planck law which may but usually does not represent  reality. Atmospheric radiation spectra play an important role in climate modelling, and it is important to take them with a grain of salt, since what is de facto measured is temperature with radiation being computed according to some convenient formula serving man-made climate alarmism.  

PS3 The Sun has a continuous spectrum and so probably consists of liquid metallic hydrogen. Main-stream physics tells that it has a gaseous plasma state.

Thermodynamics of Friction

Everything goes around in construction-deconstruction-construction...

In the previous post we considered viscosity in laminar and turbulent flow and friction between solid bodies as mechanisms for irreversible transformation of large scale kinetic motion/energy into small scale kinetic motion/energy in the form of heat energy, noting that the transformation cannot be reversed since the required very high precision cannot be realised, everything captured in a 2nd Law of Thermodynamics.  

Let us consider the generation of heat energy in friction when rubbing your hands or sliding an object over a floor or pulling the handbrakes of your bicycle. We understand that the heat energy is created from the work done by force times displacement (in the direction of the force), like pressing/pushing a sandpaper over the surface of a piece of wood to smoothen the surface by destroying its granular micro-structure. Work is thus done to destroy more or less ordered micro-structure and the work shows up as internal heat energy as unordered micro-scale kinetic energy. 

The key is here destruction of micro-structure into heat energy in a process which cannot be reversed since the required precision cannot me met.

Skin friction between a fluid and solid acts like friction between solids. 

Turbulent flow transforms large scale ordered kinetic energy into small-scale unordered kinetic energy as heat energy under the action of viscous forces. Laminar flow also generates heat energy from friction between layers of fluid of different velocity.

In all these cases heat energy is generated from destruction/mixing of order/structure in exothermic irreversible processes. This destruction is balanced by constructive processes like synchronisation of atomic oscillations into radiation and emergence of ordered structures like vortices in fluid flow and endothermic processes of unmixing/separation. 

We thus see exothermic processes of destruction followed by endothermic construction, which is not reversed deconstruction, with different time scales where deconstruction is fast and brutal without precision and construction is slow with precision. This is elaborated in The Clock and the Arrow in popular form. Take a look.

 

måndag 25 mars 2024

Norman Wildberger: Insights into Mathematics


Mathematician Norman Wildberger presents an educational program for a wide audience as Insights into Mathematics connecting to the principles I have followed in Body and Soul and Leibniz World of Math.

A basic concern of Wildberger is how to cope with real numbers underlying analysis or calculus, geometry, algebra and topology, since they appear to require working with aspects of infinities coming with difficulties, which have never been properly resolved, like computing with decimal expansions with infinitely many decimals and no last decimal to start a multiplication. Or the idea of an infinity of real numbers beyond countability.

I share the critique of Wildberger but I take a step further towards a resolution in terms of finite precision computation, which can be seen to be the view of an applied mathematician or engineer. In practice decimal expansions with a finite number of decimals are enough to represent the world and every representation can be supplied with a measure of quality as a certain number of decimals as a certain finite precision. This offers a foundation of mathematics without infinities in the spirit of Aristotle with infinities as never attained  potentials representing "modes of speaking" rather than effective realities. 

In particular the central concept of "continuum" takes the form of a computational mesh of certain mesh size or finite precision. With this view a "continuum" has no smallest scale yet is finite and there is a hierarchy of continua with variable mesh size.    

The difficulty of infinities comes from an idea of exact physical laws and exact solutions to mathematical equations like $x^2=2$ expressed in terms of symbols like $\sqrt{2}$ and $\pi$. But this can be asking for too much, even if it is tempting, and so lead to complications which have to be hidden under the rug creating confusion for students.

A more down-to-earth approach is then to give up exactness and be happy with finite precision not asking for infinities.  

How to Generate Heat Energy


We recall from a previous post:

  • Heat energy can be generated from large scale kinetic energy by compression. 
  • Kinetic energy can be generated from heat energy by expansion.

More precisely, we saw in the previous saw that heat energy at high temperature can generate useful mechanical work. Heat energy at high temperature can be created by nuclear/chemical reactions. 

Heat energy typically at lower temperatures also appears as losses from electrical currents subject to resistance, fluid motion subject to turbulent/laminar viscosity and friction between solid bodies. These losses appear as substantial, unavoidable and irreversible as expressions of a 2nd Law.

We have seen that heat energy $\sim T\nu^2$ of frequency $\nu$ carried by an atomic lattice of temperature $T$ subject to high-frequency cut-off $\nu <\frac{T}{h}$ expressing ordered synchronised atomic oscillation or kinetic motion, can be radiated. Here $h$ is a constant. 

We can view turbulent dissipation in fluid flow as a form of high-frequency forcing above present cut-off which cannot be reradiated and so is absorbed as internal energy in the form of unordered small scale kinetic energy. We can similarly view viscosity and friction as forms of high-frequency forcing supplying internal energy. 

The contribution to internal energy increases the temperature and so allows unordered small scale motion to be synchronised to higher frequency and then radiated.  

The key is thus that turbulent, viscous and frictional dissipation all represent high-frequency forcing above   present cut-off, which cannot be represented and reradiated and so shows up as internal energy as small scale kinetic energy. 

Rubbing hands is one way to transform large scale kinetic motion into small scale kinetic motion as heat energy. The brakes on your car work the same way. 

söndag 24 mars 2024

Exergy as Energy Quality


Kinetic energy, electrical energy, chemical and nuclear energy can all be converted fully into heat energy, while heat energy can only be partially converted back again. This is captured in the 2nd Law of Thermodynamics. We can thus say that heat energy is of lower quality compared with the other forms. More generally, the term exergy is used as a measure of quality of energy of fundamental importance for all forms of life and society as ability to do work.

We can make this more precise by recalling that the quality of heat energy comes to expression in radiative and conductive heat transfer from a body B1 of temperature $T_1$ to a neighbouring body B2 of lower  temperature $T_2<T_1$ in basic cases according to Stefan-Boltzmann's Law or Fourier's Law:

  • $Q = (T_1^4-T_2^4)$            (SB)
  • $Q = (T_1-T_2)$                    (F)
with $Q$ heat energy per time unit. Heat energy of higher temperature thus can be considered to have higher quality than heat energy of lower temperature, which of course also plays role in conversion of heat energy to other forms of energy. The maximal efficiency of a heat engine operating between $T_1$ and $T_2$ and transforming heat energy to mechanical work, is equal to $\frac{T_1-T_2}{T_1}$ displaying the higher quality of $T_1$.

Heat energy at high temperature is the major source for useful mechanical work supporting human civilisation, while heat energy at lower temperatures appears as a useless loss e g in the cooling of a gasoline engine.

But what is the real physics behind (SB) and (F)? This question was addressed in a previous post viewing (F) to be a special case of (SB) with the physics behind (SB) displayed in the analysis of Computational Blackbody Radiation

The essence of this analysis is a high-frequency cut-off $\frac{T}{h}$ allowing a body of temperature $T$ to only emit frequencies $\nu <\frac{T}{h}$, where $h$ is a constant. This allows a body B1 of temperature $T_1$ to transfer heat energy to a body B2 of lower temperature $T_2$ via frequencies $\frac{T_2}{h}<\nu <\frac{T_1}{h}$, which cannot be balanced by emission from B2.  

High frequency cut-off increasing linearly with temperature represents Wien's displacement law (W), giving improved exergy with increasing temperature.

The high-frequency cut-off can be seen as an expression of finite precision limiting the frequency being carried and emitted by an oscillating atomic lattice in coordinated motion, with frequencies above cut-off being carried internally as heat energy as uncoordinated motion

Higher temperature thus connects to higher quality heat energy or better exergy. The standard explanation of this basic fact is based on statistical mechanics, which is not physical mechanics. 

PS Radiative heat transfer without high-frequency cut-off would boil down to (F), while (SB) is what is observed, which gives support to (W).


fredag 22 mars 2024

Thermodynamics of War and Peace


Opposing ordered armies at the moment before turbulent destruction. 

The recent posts on 2nd law of thermodynamics describe a process where increasing spatial gradients eventually reach a level (from convection and opposing flow) where further increase is no longer possible because it would bring the process to brutal stop, and so some form of equilibration of spatial differences must set in where 

  • each particle tends to take on the mean-value of neighbouring particles.   (M)

This is the process in turbulent fluid flow transforming ordered large scale kinetic energy into small scale disordered kinetic energy taking the form internal heat energy in a turbulent cascade of turbulent dissipation. Here (M) is necessary to avoid break-down into a stop. The flow or show must go on.

(M) is also the essence of the diffusion process of heat conduction seeking to decrease gradients, even if not absolutely necessary as in turbulent fluid flow.

It is natural to connect turbulence to the violent break-down of large scale ordred structures into rubble in a war necessarily resulting from escalation of opposing military forces in direct confrontation which at some level cannot be further escalated and so have to be dissipated in a war. 

It is then natural to connect the equilibration (M) in heat conduction to a geopolitical/parliamentary process in peace time, where each country/party takes on the mean value of neighbouring countries/parties keeping gradients small. 

While (M) is necessary in turbulence to let the flow go on, one may ask what the physics of (M) in the case of heat conduction, and find answer in this post. 

The mathematics is elaborated in: 

The geopolitical/parliamentary situation today evolves towards sharpened gradients, while politicians refuse to follow (M) and so there is a steady march towards break-down... 


onsdag 20 mars 2024

Secret of Conductive and Radiative Heat Transfer

This is a continuation of the previous post on Heat Conduction in Solids as Radiative Heat Transfer with  clarifying analysis from Mathematical Physics of Blackbody Radiation and Computational Blackbody Radiation.

The key aspect of both conductive and radiative heat transfer is interaction in a coupled system of weakly damped oscillators of different frequencies tending to an equilibrium with all oscillators having the same temperature as the system temperature. The damping can be frictional (1st order time derivative) or radiative (3rd order time derivative) 

There are two main questions: (i) Why do different systems take on the same temperature? (ii) Why do oscillators with different frequencies in a system take on the same temperature?  

The answer is hidden in the interaction between incoming radiation, oscillator and outgoing radiation in a weakly radiatively damped oscillator analysed in detail in the above texts. The essence is that under near resonance between incoming frequency and oscillator frequency,  

  • incoming radiation is balanced by outgoing radiation plus internal heating. 
This is a non-trivial basic fact reflecting that the forcing and oscillator are out-of-phase with a shift of half a period as a consequence of small radiative damping and near resonance. 

Two coupled oscillators thus interact with outgoing from one oscillator acting as incoming for the other and vice versa and so are led to take on the same temperature, which is then spread over the oscillators of a system and also over systems. 

The essential components in this equilibration process are thus
  • weakly damped oscillators generating outgoing radiation and internal heating 
  • out-of-phase balance between forcing and damping from near resonance
  • high-frequency cut-off increasing with temperature from finite precision computation.  
This analysis connects to Planck's derivation of his law of radiation with statistics replaced by finite precision thus replacing non-physics by physics. 

tisdag 19 mars 2024

Sverige Måste Vinna Kriget mot Ryssland?

Sverige besegrar Ryssland i slaget vid Narva 1701 under ledning av Karl XII.  

Idag skriver ett antal svenska ambassadörer och militärer på SvD Debatt:

  • Regeringen bör skyndsamt hitta formerna för att mångfalt öka det militära biståndet till Ukraina. 
  • Inför den ryska aggressionen befinner sig de västliga demokratierna som de befann sig inför Hitler.
  • Kriget kommer inte att sluta så länge Putin sitter vid makten. 
  • Enda sättet att avsluta kriget är alltså att Putin förlorar makten.
  • Det kan ske om han lider ett så svidande nederlag...
  • Putins avlägsnande är bara ett nödvändigt...kännbart ryskt nederlag i Ukraina.
  • Ett sådant nederlag har den västliga demokratiska alliansen i sina händer. Hos den finns de vapen och de resurser med vilka Ukraina kan vända kriget och tillfoga Ryssland ett nederlag.
  • Ukraina måste segra och Ryssland måste förlora.
  • Vi vädjar till regeringen att tänka utanför den ärvda boxen – det gäller att skyndsamt hitta formerna för att mångfalt öka det militära biståndet till Ukraina.

Vi ser här att segern i Narva 1701 är i kärt minne i den "ärvda boxen", medan förlusten i Poltava 1711 och förlusten av Finland 1809 är bortglömda. Tanken är alltså att vi kan besegra Ryssland, som är den starkaste kärnvapenmakten i världen med nyvunnen konventionell militär styrka om mer än en million tränade soldater vida överlägsen den som västliga demokratier kan skrapa ihop, där Sverige kan bidra med kanske 3000 otränade pojkar och flickor, och därmed genomföra den erövring av Ryssland som Karl XII, Napoleon och Hitler misslyckades med.  

Speglar detta stämningarna hos det ledande skiktet av svenska politiker, ämbetsmän, militärer och företagare och svenska folket? Alla partier verkar vara inställda på krig även V och Mp. Fredsrörelsen har somnat. 

USA är på väg att dra sig ur, vilket ger Sverige en ledande roll som krigförande, naturligtvis tillsammans med Finland som är bra på krigföring i snö.

Påven ber Ukraina hissa vit flagg och gå till förhandlingsbordet där Putin väntar. Fortsatt krig gör bara saken värre för Ukraina och Väst. Ett mångfalt ökat militärt bistånd till Ukraina leder till WW3. 

Hur kan någon tro att Sverige kan vinna krig mot Ryssland idag? Eller tänker man att eftersom WW2 var bra för Sverige, så kan WW3 också vara det? I så fall bör man tänka en gång till.

En stark kärnvapenmakt kan inte besegras på hemmaplan. Det bästa resultat som kan uppnås är oavgjort som MAD Mutual Assured Destruction.


Heat Conduction in Solids as Radiative Heat Transfer


What is the physics of heat conduction in a solid like a metal? The trivial story is that "heat flows from warm to cold" or "there is a flux of heat from warm to cold" which scales with the temperature difference or gradient. 

But heat is not a substance like water in a river flowing from high-altitude/warm to low-altitude/cold, which connects to the caloric theory and also to phlogiston theory presenting fire as form of substance, both debunked at the end of the 18th century. 

In any case there is a law of physics named Fourier's Law:

  • $q =- \nabla u$          (F)
which combined with a law of conservation 
  • $\nabla\cdot q = f$
leads to the following heat equation (here in stationary state for simplicity) in the form of Poisson's equation
  • $-\Delta u = f$.                    (H)
where $u(x)$ is temperature and $f(x)$ heat source depending on a space variable $x$, and $q(x)$ is named "heat flux" although it has no physical meaning; heat is not any substance which flows or is in a state of flux. 

Let us now seek the physics of (F) in the case of metallic body as a lattice of atoms, and so seek an explanation of the observation that the temperature distribution $u(x)$ of the body tends to an equilibrium state with $u(x)=U$ with $U$ a constant (assuming no interaction with the surrounding and no internal heating for simplicity). 

We thus ask: 
  • What is the physics of the process towards equilibrium with constant temperature?
  • How is heat transferred from warm to cold?
  • Why is (F) valid?
We then recall our analysis of radiative transfer of energy at distance in a system of bodies/parts separated in space which (without external forcing) leads to an equilibrium state with all bodies having the same temperature, based on the following physical model:
  • Each body is a vibrating lattice of atoms described by a wave equation with small radiative damping. 
  • The bodies interact by electromagnetic waves through resonance. 
  • There is a high-frequency cut-off increasing linearly with temperature with the effect that heat transfer mediated by electromagnetic waves between two bodies, is one-way from high temperature to low temperature. 
The key is here the high-frequency cut-off increasing with temperature, which makes heat transfer one-way. The cut-off can be seen as a form of finite precision threshold allowing coordinated lattice vibration only below cut-off, thus allowing a high temperature lattice to carry higher frequencies. It is like a warmed-up opera soprano being able to reach higher frequencies.

We can view metallic body as a system composed of parts/atoms interacting by 
electromagnetic waves at small distance. 

Heat conduction will then come out as a special case of electromagnetic heat transfer 
between atoms of different temperature with high-frequency cut-off guaranteeing one-way transport as expressed by (F) and exposed above. 

Note that the reference text Conduction of Heat in Solids by Carslaw and Jaeger presents (F) as an ad hoc physical law without physics.

Recall that the standard explanation of radiative heat transfer from warm to cold is based on statistics without physics, which if used to explain heat conduction would again invoke statistics without physics thus not very convincing. 

Also note that the standard explanation of heat transfer in a gas involves collisions of molecules of different kinetic energy, which is not applicable to a metal with atoms in a lattice.

PS1 Fluid flow in a river from higher to lower altitude is driven by pressure. "Heat flow" from warm to cold is not driven by pressure and so the physics is different. 

PS2 Also compare with one-way osmotic transport of material driven by pressure. 

söndag 17 mars 2024

Universality of Radiation with Blackbody as Reference


One of the unresolved mysteries of classical physics is why the radiation spectrum of a material body only depends on temperature and frequency and not on the physical nature of the body, as an intriguing example of universality. Why is that? The common answer given by Planck is statistics of energy quanta, an answer however without clear physics based on ad hoc assumptions which cannot be verified experimentally as shown by this common argumentation. 

I have pursued a path without statistics based on clear physics as Computational Blackbody Radiation in the form of near resonance in a wave equation with small radiative damping as outgoing radiation, subject to external forcing  $f_\nu$ depending on frequency $\nu$ , which shows the following radiance spectrum $R(\nu ,T)$ (with more details here) characterised  by a common temperature $T$,  radiative damping parameter $\gamma$, and $h$ defines a high-frequency cut-off.  Radiative equilibrium with incoming = outgoing radiation shows to satisfy:

  • $R(\nu ,T)\equiv\gamma T\nu^2 =\epsilon f_\nu^2$ for $\nu\leq\frac{T}{h}$,
  • $R(\nu ,T) =0$ for $\nu >\frac{T}{h}$,
where $0<\epsilon\le 1$ is a coefficient of absorptivity = emissivity, while frequencies above cut-off $\frac{T}{h}$ cause heating. The radiation can thus be described by the coefficients $\gamma$, $\epsilon$ and $h$ and the temperature scale $T$. 

Here $\epsilon$ and $h$ can be expected to depend on the physical nature of the body, with a blackbody defined by $\epsilon =1$ and $h$ minimal thus with maximal cut-off. 

Let us now consider possible universality of the radiation parameter $\gamma$ and temperature $T$.

Consider then two radiating bodies 1 and 2 with different characteristics $(\gamma_1,\epsilon_1, h_1, T_1)$ and $(\gamma_2,\epsilon_2, h_2, T_2)$, which when brought into radiative equilibrium will satisfy (assuming here for simplicity that $\epsilon_1=\epsilon_2$):
  • $\gamma_1T_1\nu^2 = \gamma_2T_2\nu^2$ for $\nu\leq\frac{T_2}{h_2}$ 
  • assuming $\frac{T_2}{h_2}\leq \frac{T_1}{h_1}$ 
  • and for simplicity that 2 reflects frequencies $\nu > \frac{T_2}{h_2}$.    
If we choose body 1 as reference, to serve as an ideal reference blackbody, defining a reference temperature scale $T_1$, we can then calibrate the temperature scale $T_2$ for body 2 so that 
  • $\gamma_1T_1= \gamma_2T_2$,
thus effectively assign temperature $T_1$ and $\gamma_1$ to body 2 by radiative equilibrium with body 1 acting as a reference thermometer. Body 2 will then mimic the radiation of body 1 in radiative equilibrium and a form of universality with body 1 as reference will be achieved, with independence of $\epsilon_1$ and $\epsilon_2$.

The analysis indicates that the critical quality of the reference blackbody is maximal cut-off (and equal temperature of all frequencies), and not necessarily maximal absorptivity = emissivity = 1. 

Universality of radiation is thus a consequence of radiative equilibrium with a specific reference body in the form of a blackbody acting as reference thermometer.  

Note that the form of the radiation law $R(\nu ,T)= \gamma T\nu^2$ reflects that the radiative damping term in the wave equation is given by $-\gamma\frac{d^3}{dt^3}$ with a third order time derivative as universal expression from oscillating electric charges according to Larmor.

In practice body 1 is represented by a small piece of graphite inside a cavity with reflecting walls represented by body 2 with the effect that the cavity will radiate like graphite independent of its form or wall material. Universality will thus be reached by mimicing of a reference, viewed as an ideal blackbody, which is perfectly understandable, and not by some mysterious deep inherent quality of blackbody radiation. Without the piece of graphite the cavity will possibly radiate with different characteristics and universality may be lost.

We can compare many local currencies calibrated to the dollar as common universal reference.  
  • All dancers which mimic Fred Astaire, dance like Fred Astaire, but all dancers do not dance like Fred Astaire.     
PS1 The common explanation for the high frequency cut-off is that they have low probability, which is not physics, while I suggest that high frequencies cannot be represented because of finite precision, which can be physics.  

PS2 Note that high-frequency cut-off increasing with temperature gives a 2nd Law expressing that energy is radiated from warm to cold and to no degree from cold to warm, thus acting like semi-conductor allowing an electrical current only if a voltage difference is above a certain value.