Black-body radiation

Black-body radiation is a concept you will need to grapple with when looking at cosmic background radiation, (should you choose to do so – and I would implore you to, how can a human not be interested in background radiation from the “big bang”?). I use the punctuation because the title in itself is its greatest strength and its biggest downfall. It is a strength because it seems logical and helps to popularize the term, however it is a downfall due to the wildly misleading nature of the term; it seems to imply some big explosion which comes from one point in space and time – which isn’t the accepted view. Indeed it is cosmic background radiation that makes it so clear the big bang is not some explosion about a fixed point; it was in Wilson and Penzias’s laboratories that a large horn concluded (after much fretting over experimental error) there was a background radiation which was isotropic in nature – and that is the scene for today’s discussion.

So let us rewind just a little and consider what black-body radiation actually is.

With a lot of things, particularly in Physics there are layers of understanding. For example, let us consider a a large person running into a small person. Most humans above a certain age can tell you that (assuming the two bodies are running at equal speed) the smaller body will be more hurt. Taking it up a level, someone might be able to tell you that a person who is large has more momentum, meaning they are harder to stop. Someone with a rich understanding of the subject can say that if speed is equal, the total momentum in the system before the collision is simply a function of the mass; so if body 1 has mass 2 and body 2 has mass 1 I have 3v before the collisions. Now, clearly the larger body has twice the momentum of the smaller body – which means either the motion of the larger body will not be reversed and it will run through the larger body – ouch, or it will be reversed but by the conservation laws the larger body must have a lower speed – and hence the smaller one must have a higher speed which again means a very painful rebound. The three viewpoints here all understand the same physical concepts just with varying richness in terms of the processes taking place. The same is true when we talk about issues like we do today – I cannot speak with more knowledge than I have, which caps these discussions at degree level (often lower when I have not formally studied). There is a whole world of detail if a subject inspires you, we are going to try to understand the topic so we are better equip to go into the detail.

Let’s be clear about one thing – black-body radiation falls under the umbrella of electromagnetic radiation so it isn’t something totally new and spooky – rather a special case of something more familiar. Thermal equilibrium is an important concept here – and it is important to just come away from the idea that we are talking about just heat in a hot/cold sense. The idea is this – when thermal radiation hits an object that radiation may be absorbed or reflected in part or in full and subsequently re-emitted again in part or in whole. When we are looking at black-body radiation we are looking at an object that is in equilibrium with its surroundings – i.e. if it goes in it comes out. The radiation spectrum we get when a body is in this equilibrium is a specific spectrum which is known as the black-body. There is a little more to it that this – a black-body should be an opaque object which absorbs all light and does not reflect any; therefore if there were a black-body sitting on my desk right now it should be 100% perfectly black. There are no such objects sitting on my desk.

The idea is the black-body emits thermal radiation – so they will be visible when say, like the sun the temperature is raised and there is a keen glow of thermal radiation. Hopefully you are feeling slightly confused – because you should be it’s a weird idea that plagued many classical physicists. We can only talk about it with such ease thanks to the work of many brilliant minds – Max Planck being one. Everything in the universe above absolute zero emits radiation (which is why thermal imaging works to catch criminals)  but not everything is a perfect emitter – i.e. some objects absorb/emit light and heat better than others. Fortunately you can create an almost perfect black-body by taking a box made out of a thermal insulator and allowing light to enter but not escape a cavity within it.

This is what they did – and they found that black-body radiation looks a little bit like this. The different curves are for different temperatures with the emission spectrum for visible light indicated.


The really really really important takeaway from this is the idea of how the curves have a peak and then they drop off getting ever closer to the x-axis (i.e. higher wavelengths). Before this was discovered conventional physics would have said that the graph just keeps trending up and up and never coming down, which would mean the object become gives of some totally crazy UV radiation that is totally invisible with tiny wavelengths as the object gets hotter – which is clearly not what happens in everyday life. This was the “ultra-violet catastrophe” and it was Planck and others who were able to show that due to the quantized nature of energy – in fact there is a point where the excitation of the radiation beyond a certain point is improbable – that point is the peak which gives us our smooth functions changing with time. In  many ways this is the birthplace of quantum mechanics – but you may have noticed I have carefully sidestepped this area and I do so again.

This all links into the “big bang” as discussed earlier due to the idea that there is a very low energy radiation that fills the entire universe that embodies a black-body emission curve as shown above; but rather than the curve being in the thousands of Kelvin, it is in fact 2.76K which unsurprisingly does not make it peak in the visible light spectrum – but rather in the much longer wavelength domain of microwaves. So when you sometimes hear the background microwave radiation, this is what we mean – the universe is not cooking. The startling thing about this background radiation is – as I started out by saying – the isotropic nature of the stuff. You may see pictures of the cosmic background radiation which appear to show one half in what seems like shorter wavelengths and one half in longer wavelengths – this is illustrating the fact that the Earth moves relative to the cosmic background radiation and therefore there is a Doppler effect present. In fact when you smooth out this background radiation the difference in the background radiation are so small. This created the interesting issue for the big bang theory in the sense that it suggested that the overall universe at the start must have been almost totally uniform – there is no speed known that could of traversed the distance from one edge to the next to communicate.

Hopefully you have found this little tour of black-body radiation interesting – it is a very deep and exciting area which really marks the turning point between more classical ideas in physics and what I would call modern physics – although that is a subjective point open to debate.


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