Planck’s law of radiative heat transfer has held up well under a century of intense testing, but a new analysis has found it fails on the smallest of scales.
Exactly what this means isn’t all that clear yet, but where laws fail, new discoveries can follow. Such a find wouldn’t just affect physics on an atomic scale – it could impact everything from climate models to our understanding of planetary formation.
The foundational law of quantum physics was recently put to the test by researchers from William & Mary in Virginia and the University of Michigan, who were curious about whether the age-old rule could describe the way heat radiation was emitted by nanoscale objects.
Not only does the law fail, the experimental result is 100 times greater than the predicted figure, suggesting nanoscale objects can emit and absorb heat with far greater efficiency than current models can explain.
“That’s the thing with physics,” says William & Mary physicist Mumtaz Qazilbash.
“It’s important to experimentally measure something, but also important to actually understand what is going on.”
Planck is one of the big names in physics. While it’d be misleading to attribute the birth of quantum mechanics to a single individual, his work played a key role in getting the ball rolling.
Humans have known since ancient times that hot things glow with light. We’ve also understood for quite a while that there’s a relationship between the colour of that light and its temperature.
To study this in detail, physicists in the 19th century would measure the colour of light inside a black, heated box, watching through a tiny hole. This ‘black body radiation’ provided a reasonably precise measure of that relationship.
Coming up with simple formulae to describe the wavelengths of colour and their temperatures proved to be rather challenging, and so Planck came at it from a slightly different angle.
His approach was to treat the way light was absorbed and emitted like a pendulum’s swing, with discrete quantities of energy being soaked up and spat out. Not that he really thought this was the case – it was just a convenient way to model light.
As strange as it seemed at first, the model worked perfectly. This ‘quantity’ of energy approach generated decades of debate over the nature of reality, and has come to form the underpinnings of physics as we know it.
Planck’s law of radiative heat transfer informs a theory describing a maximum frequency at which heat energy can be emitted from an object at a given temperature.
This works extremely well for visible objects separated at a visible distance. But what if we push those objects together, so the space between them isn’t quite a single wavelength of the light being emitted? What happens to that ‘pendulum swing’?
Physicists well versed in the dynamics of electromagnetism already know weird things happen here in this area, known as the ‘near field’ region.
For one thing, the relationship between the electrical and magnetic aspects of the electromagnetic field becomes more complex.
Just how this might affect the way heated objects interact has already been the focus of previous research, which has established some big differences in how heat moves in the near field as compared with the far field observed by Planck.
But that’s just if the gap is confined to a distance smaller than the wavelength of emitted radiation. What about the size of the objects themselves?
The researchers had quite a challenge ahead of them. They had to engineer objects smaller than about 10 microns in size – the approximate length of a wave of infrared light.
They settled on two membranes of silicon nitride a mere half micron thick, separated by a distance that put them well into the far field.
Heating one and measuring the second allowed them to test Planck’s law with a fair degree of precision.
“Planck’s radiation law says if you apply the ideas that he formulated to two objects, then you should get a defined rate of energy transfer between the two,” says Qazilbash.
“Well, what we have observed experimentally is that rate is actually 100 times higher than Planck’s law predicts if the objects are very, very small.”
Qazilbash likens it to the plucking of a guitar string at different places along its length. “If you pluck it in those places, it’s going to resonate at certain wavelengths more efficiently.”
The analogy is a useful way to visualise the phenomenon, but understanding the details of the physics behind the discovery could have some big impacts. Not just in nanotechnology, but on a far bigger scale.
This hyper-efficient rate of energy transfer could feasibly change how we understand heat transfer in the atmosphere, or in a cooling body the size of a planet. The extent of this difference is still a mystery, but one with some potentially profound implications.
“Wherever you have radiation playing an important role in physics and science, that’s where this discovery is important,” says Qazilbash.
This research was published in Nature.