Relativity in brief... or in detail..

## Why there would be no chemistry without relativity

Any chemist will tell you that with no chemistry, there would be no biology, and without biology there would be no psychology.... It's obvious that physics (especially electricity, mechanics and thermal physics) underlies chemistry. It may not be so obvious that chemistry as a whole is dependent on effects that involve relativity, and that the existence of different chemical elements can only be adequately described in terms of relativity. But to see how, we first need to know a little bit about:

### The uncertainty principle

It took theoreticians quite a while to realise something that experimentalists have always known: you can't measure something exactly. Fourier was the first to admit that you have to compromise: if you want to measure frequency (how frequently something happens, or the number of occurrences per unit time) then you need to measure for a certain interval of time. And the longer you make that interval, the better your measurement. You don't have infinite time (your research grant runs out before then), so you don't measure frequency precisely. If you measure over a time Δt , you end up with an error in frequency that cannot be better than approximately

Δf = 1/2πΔt
Rearranging this gives:
Δf.Δt > ~ 1/2π
where the "~" means that the "approximately" still applies. (For more about Fourier's and Heisenberg's uncertainty principles, see
Introduction to the uncertainty principle.)

Now, in 1905, Einstein was not loafing around. As well as special relativity, he wrote a paper about the photoelectric effect: a key paper in the development of quantum mechanics. Energy transmitted by light of a certain colour is not continuous, but comes in lumps with energy

E = hf
where f is the frequency of the electromagnetic wave, and h is a constant, called Planck's constant, after Max Planck. The 'packets' of light are now called photons.

Werner Heisenberg applied Fourier's result to photons: an error in frequency (Δf) impies an error in energy (ΔE = hΔf). Multiply Fourier's result by h and you get

ΔE.Δt > ~ h/2π.
ie the time it takes you to do your measurement experiment times the minimum error in the energy is always greater than about h/2π.

This constraint is not confined to electromagnetic radiation. Other ways of storing energy involve oscillations too, and this equation is general. Further, it is a statement about waves and oscillations, not (only) about our measurement of them. One poetic way of putting it is that Nature can't measure energy and time better than this either.

So Heisenberg's uncertainty principle has a strong implication for the law of conservation of energy. The variation in total energy with time is not necessarily exactly zero. Rather, the law of conservation of energy may be written that energy is conserved with a precision of ΔE, where

ΔE < ~ h/(2π.Δt) .
I've been asked to explain the reversal of the "<" and ">" signs in the two preceding inequalities. The former puts a lower limit on uncertainty: in any given case, experimental error may yield greater uncertainties than this limit. The lower bound is the theoretical limit. The principle of conservation of energy -- if it truly is a law -- cannot be (observed to be) violated. So in this case the bound given is an upper limit: a greater uncertainty than this in energy conservation would be observable by measurements approaching the Fourier/ Heisenberg limit, and so the principle would be falsified.
So energy can fluctuate, even in a vacuum. However it can only vary by small amounts, unless the variation is for a very short time. Why haven't you noticed? Why didn't this show up in the experiments you might have done in the teaching lab? Well, h is small. In our ordinary units it is 6.63 x 10-34 Js. If you "borrow" a milliJoule of energy (enough energy to pick up your pencil), and you have to give it back within 10-31 Js.

### E = mc2 and virtual particles

When a particle and an antiparticle collide, such as the electrons and positrons do in modern particle accelerators, they annihilate and their proper energy 2mc2 is carried away by electromagnetic radiation (gamma rays, in this case). Reversing this, we could say that, if we had energy 2mc2, where m is the mass of an electron, we could create an electron and positron. And indeed this reaction often occurs in nuclear physics experiments, too.

Hey, but who needs energy? Taking advantage of the limited fluctuations discussed above, let's borrow 2mc2 and give it back in a time t that satisfies

2mc2 < h/2π.Δt .
Conservation of energy does allow this. When particles are created from fluctuations in energy allowed by the uncertainty principle, they are called virtual particles. Their ghostly existence is very important not just to nuclear physics, but for other physics too. The most important role for virtual particles is the transmission of forces: two real particles may interact by exchanging virtual particles. If the particles have no mass, then little energy is required to make them: two photons require only 2hf, which can be very small for low frequency or long wavelength photons. If you don't 'borrow' very much energy to create the virtual particles, they have time to travel a reasonable distance before winking out of existence. So the range of the electromagnetic force can be very large, like that of gravity. But what if there are forces transmitted by virtual particles with non-zero mass?

### The strong force, the Yukawa meson, gluons...

Enjoy this story, because it is the heart of the work that won Japanese physicist Hideki Yukawa the 1949 Nobel prize for physics.

A force with finite range? Doesn't that suggest a force mediated by virtual particles? So, they only travel a few times 10-15 metres which, at the speed of light, takes 10-23 seconds. Substitute that into the equation above and you get a mass of about 10-28 kg. This is much more massive than an electron (a light particle or lepton) and rather less massive than a proton (a massive particle or hadron). Let's call such particles mesons, for medium mass particles.

Medium-mass particles were found and Yukawa received his Nobel prize.

Particle physics has moved on, and virtual particles are now also used to explain the forces within nuclear particles. Protons and neutrons are made of (electrically charged) quarks. The attractive force between quarks is called the colour force and is transmitted by virtual gluons (for a while, particle physicists competed in inventing whimsical names) and, in analogy with quantum electrodynamics for understanding the atom, the new theory is quantum chromodynamics.

But to return to the title: without E = mc2, there would be no virtual particles, so no strong forces, so no attraction to hold nuclei together. The periodic table would have only one entry, chemistry wouldn't exist, animals made of biochemicals wouldn't exist and you wouldn't be here reading obscure footnotes.

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