Checking out Einstein and going quantum
Quantum and classical physics both have the concept of energy in common. The conservation of energy still applies in quantum physics the same way it does in classical physics. The difference is in the math used to calculate energy and work. In quantum physics it is all about probability – the energy something has is a probability rather than a precise number. It comes down to the concepts of wave functions which is beyond the level of this resource. For advanced students in year 10+ they might be interested in Parth G’s examination of quantum energy in the video below.
For this resource, wave functions are important, but only in the context that at the quantum level, particles have a wave-like behaviour, which we examine at the level of the electron and what happens to the wave function and mass when we change the energy of electrons. And this is where E = mc2 and the other not-so-famous equation come in.
Light exists as a wave and a particle (or a tiny quantized packet of energy called a photon). Light’s energy is described in that not-so-famous equation E=hf that together with the definitely famous E = mc2 underpin our understanding all forms of energy and indeed how the universe works.
For E = hf
E = energy
h is Planck’s constant (= 6.6 × 10-34)
f is the frequency of the light.
Similar to a water wave, a light wave has a momentum (movement) in a particular direction, but it is the energy that propagates forwards rather than anything physical. The energy in light can change the properties of materials. Indeed, FLEET exploits this ability to shift materials between a conductive and insulative state, something they hope will be useful to help develop the next generation of low-energy electronics. The energy in photons (ie light behaving as a particle) is also responsible for the production of electrical energy in solar panels.
Find out more about light in our FLEET Schools unit on light.
In Activity 10, students can do a hands-on activity that demonstrates the results of a recent experiment that showed for the first time, how energy affects the mass of an atom. The experiment has implications for greater precision in how we measure the effects of energy that could help unravel big mysteries of our universe such as dark matter.
The content and support material in Activity 10, Quantum energy: Mass, energy and the oscillating ruler, are adapted from a unit developed by Einstein First and presented in the paper, Shachar Boublil and David Blair 2023 Phys. Educ. 58 015003.
E = mc2 indicates the proportional relationship between energy and mass. This is evident even at the quantum scale, a phenomenon recently demonstrated by researchers at the Max Planck Institute (Germany) who showed that photons, even though considered massless can, when absorbed by an atom, add mass to that atom. The atom will lose that mass when the photon is later emitted (Schüssler R X et al 2020).
The experiment in Activity 10 is a classroom version of the experiment that the Max Plank researchers conducted to determine this. In the real experiment, the researchers used light (photon) of a specific energy (determined by E = hf) and detected the change in an atom’s vibration frequency when it absorbed or emitted the photon. This change in frequency was a demonstration of E = mc2 because it showed that energy (in this instance, the energy of a photon) will affect mass (in this instance, the mass of an atom). This was a multi-million dollar experiment using highly sensitive equipment. We will use plastic rulers and a small weight to demonstrate how energy affects mass.
How did they do it: In short, the researchers had to cool their atoms down to an extremely cold temperature and trap them in a magnetic and electric field to stop them vibrating all over the place and colliding with each other and therefore emitting a whole bunch of different frequencies in the process. Cooled and trapped, the atoms are mostly still emitting a single measurable frequency. The researchers then measure the frequency of the atom after it absorbed a photon then again once that photon was emitted. The atom’s frequency is lower when it absorbs the photon and increases when it is emitted. The increased weight of the atom causes its frequency to become lower and this is what the Max Planck researchers measured. Shachar Boublil and David Blair (2023) give a great description of the method the researchers used by the Max Planck researchers to demonstrate this phenomenon.
What does it all mean? Or, so what!
Apart from being the first researchers to successfully measure the miniscule change in the mass of an atom when it absorbs a photon (as predicted by Einstein, but never demonstrated until now), this research has also opened the door to new ways to increase the accuracy of atomic clocks. Why do we need to do this? Because greater accuracy in how we measure time will enable us to measure with greater precision what happens when energy effects a change in a system. Building the most precise timekeepers ever imagined can help unravel big mysteries of our universe such as detecting dark matter and the key to build the next generation of quantum technologies.
Cool fact: the latest atomic clocks are so precise that they are (allegedly) out by just a second every 15 billion years. Read a bit more about NASA’s spin-off tech from better atomic clocks.
The Einstein-First Project is a program run by researchers from the University of Western Australia who work with the Gravity Discovery Centre, Ozgrav and the LIGO Scientific Collaboration. This project is a part of the Einsteinian Physics Education Research (EPER) team that involves researchers from Norway, China, South Korea, Italy, Germany, Britain and the United States. The Project teaches the fundamental concepts of modern physics to school students and works to improve STEM involvement in the classroom. They have some really cool resources for teachers and students and I encourage you to check them out.
References
Shachar Boublil and David Blair (2022) Model experiments and analogies for teaching Einsteinian energy, Physics Education, 58 (1) DOI 10.1088/1361-6552/ac96c0
Schüssler R X et al 2020 Detection of metastable electronic states by Penning trap mass spectrometry Nature 581 42–46