In the perhaps not too distant future, every radio telescope on Earth receives the same massive data   dump from what can only be an advanced alien species.

It seems to contain the detailed   instructions for building a faster-than-light  propulsion device, along with a reference manual   containing what amounts to all physics known by the aliens - including the equations of   their laws of physics and a list of all elementary particles and their properties and interactions.

If we can correctly decipher this  stuff, we can build warp-ships   and join the galactic civilization.

Of course  if we get it wrong we might blow up the planet.

How hard can it really be to decode  alien physics and engineering?

It’s gotta map to our own physics - I mean, we live in the same universe after all.

We start by noticing that the alien technology seems to use good ol’ fashioned electronics,   even if it is insanely complex.

We know  this because the particle carried by the   alien circuitry looks like the electron.

We  decide this through a process of elimination.

The aliens describe two sets of spin-1/2  particles, each with 3 generations - these   must be the quarks and the leptons, which  are distinguishable from each other by   their relative masses, color charge, etc.

The  particle running through the alien circuitry   is the lightest lepton and has negative  electric charge.

Obviously the electron.

Actually, no.

Unbeknownst to us, these aliens use positronic circuitry, not electronic.

It’s just   that they define electric charge in the opposite way - electrons positive, positrons negative.

But how could we make such a blunder?

Surely, a quick glance at the alien Maxwell’s equations   which govern the interactions of charged  particles will reveal that they use a flipped   sign convention.

Nope.

It turns out that  not only is th e sign convention arbitrary,   but there’s no way to tell which was  chosen based on the laws of physics alone.

So we build the device with its  incorrect electronic circuitry.

The President exerts some pressure  to switch it on already because   an election is coming up.

But just before  we flip the switch and destroy the planet,   a few cautious scientists take one last look  at the alien documentation.

So what do you think?

Is there anything in the way the aliens wrote down their laws of physics that might reveal our error?

Before we figure that out, let’s recall how we  humans decided on our own electric charge sign   convention.

It was a pretty arbitrary choice  based on a mistake.

Made by this guy, Benjamin   Franklin.

The nature of electricity was just  one among Franklin’s many scientific interests.

By Franklin’s time, we already knew that if  you rub a glass rod with a piece of cloth,   both gain an electric charge.

Franklin was the first to guess   that both rod and cloth gain the same type of charge, just with opposite signs to the charge.

He imagined an electric fluid that flowed  from one to the other, so that in one you   have an excess of fluid and in the other  an absence.

Then the direction of the force   comes from multiplying the signs of the density of this fluid together  - bring together two positive charges or    two negative charges and you get a net positive force - which means a repulsive force by the way.

But   a negative and positive charge brought together leads to a negative force - and that is an attractive force.

The choice of sign convention actually doesn’t matter as long as you stay consistent.

Which   is lucky, because the reasoning  behind Franklin’s choice was wrong.

He noticed that when you rub the glass  rod with a piece of cloth, you can get a   more powerful shock from the rod compared to the cloth.

He imagined the electrical fluid   building up in the rod and flowing into your hand - so he defined the rod's charge as positive.

We now know that it’s the other way  around.

Electrons from the rod are actually   rubbed off onto the cloth, so there’s a  flow of matter in the opposite direction.

You get a stronger shock from the rod because the charge moves around more easily inside the glass.

That means a large charge difference builds  up in the rod near your point of contact,   and that causes electrons to jump  from your hand into the rod.

This was in the early part of the 1700s.

It was a century and a half later before we actually discovered that the electron existed.

That discovery finally allowed us to figure out which way this “fluid” was really flowing.

But by then it was too late; what we now call  the Franklin convention was fully entrenched.

Electrons came to be defined as having  negative charge, and that defined the   relative charge of everything else - including  the positive charge for protons and positrons.

Happily, Benjamin Franklin’s misguided choice doesn’t make any difference to the laws of   electromagnetism - the Maxwell’s equations.

Those equations tell us how particles with    electric charges respond to each other.

They  don’t care what names we give those particles.

Had Franklin defined charge the other way  around, Maxwell’s equations would be unchanged.

But this is bad news for our fictional scenario because we can’t rely on the equations describing   the laws of physics to determine the  alien sign convention for electric charge.

Our problem is compounded by the fact that matter and antimatter seem to be identical except for   having exactly opposite charges.

The universe is mostly symmetric under charge conjugation - switch   all matter with antimatter and vice versa and the universe would keep ticking along almost exactly   the same.

But not quite exactly.

It’s clear that the universe itself knows the difference between   matter and antimatter; after all, it contains  almost exclusively the former.

And that fact   tells us that somewhere buried deep in the laws of physics is a subtle breaking of charge symmetry.

So in order to save the world from poorly assembled alien technology, we need to find a single   manifestation of this symmetry breaking.

The classic example is the decay of the kaon particle,   which we’ve talked about in detail previously.

The long story short is that this unstable   meson decays very differently compared to its antiparticle.

So as long as our compendium   of alien physics describes the interactions  of specific particles, we can distinguish   matter from antimatter in the case of kaons.

That breaks the frustrating symmetry of the   entire alien system of physics, allowing  us to identify its charge sign convention,   distinguish positrons from electrons,  and hopefully not explode the planet.

But maybe we’re not quite there yet.

The Franklin convention for the sign of electrically charged   particles is not the only arbitrary choice we’ve  made in our development of the laws of physics.

What if alien physics made other choices differently?

Let's say that this rather finicky device   also cares about the handedness of the positron.

Weirdly, there are right-handed and left-handed   versions of all particles with quantum spin.

If we build the device with positions that   are spinning the wrong way then, I dunno,  maybe we create a black hole that eats the   planet.

But the definition of handedness  also depends on an arbitrary convention,   just like the sign of electric charge - in this  case, something called the right-hand rule.

Let’s put aside quantum spin for a minute to  define this rule.

Say you have an electron moving   through a magnetic field.

That field is going to apply a force in some direction to that electron.

To find that direction you just point the index finger of your right hand in the direction the   electron is moving and your middle finger in the direction of the magnetic field, then your thumb   will be pointing in the direction of the force.

  Mathematically we calculate the force using  something called the cross product.

Force equals   charge times velocity cross magnetic field.

This is a type of vector multiplication where   the direction of the final vector - in this case  force - can be found using the right hand rule.

Cross products are everywhere in physics, for example in calculating torque, angular momentum,   and through Maxwell’s equations.

The right hand rule is another arbitrary  convention, and its choice also determines how we   define particle handedness or partical chirality.

What if our aliens were predominantly left-handed   or left tentacled or whatever?

They might  define chirality in the opposite way,   with devastating existential  consequences.

Fortunately,   this switch in convention does seem to change the actual equations of the laws of physics.

To make   a LEFT-hand-rule work you need to either flip the order of the two vectors in the cross product,   so field cross velocity instead of the other way around, OR you need to add a minus sign in front   of the equation.

So it sounds like we could figure out which convention the aliens used just by   looking at their Maxwell’s equations.

But actually no - at least not without other information.

To understand why, imagine that all right hands in the universe were transformed into left hands and   vice versa.

In other words, imagine reflecting the whole universe in a mirror.

We call such   a transformation a parity inversion.

Parity is  another fundamental and broken symmetry of nature   like charge, and just as with charge symmetry, parity is related to an arbitrary convention - the right hand rule.

In fact charge and parity are intimately tied.

I just told you that you can undo the effects   of using the left-hand rule by placing a minus sign in front of your magnetic force equation.

Well that minus sign can equally be interpreted as a flip in the sign of the electric charge in that equation.

If you change the convention for parity by using the left-hand-rule AND you change the convention   for charge by flipping its sign then the  differences cancel out and you’re left with the   same laws of physics.

So can we figure out what parity convention our alien benefactors are using?

Well, only if we also know their sign convention.

But if we don’t know that then   there’s no way to tell from the  master equations themselves.

But   just as with charge, if we dig into the  way particles interact we can find a clue.

Parity is the symmetry between left and right handed chirality for particles with quantum spin,   and in our universe P-symmetry is broken in  much more obvious ways than charge symmetry.

That’s because the Weak Force only interacts with left handed particles and right handed   anti-particles, not at all with right-handed particles nor left-handed antiparticles.

If we search the   alien user manual for the part that describes weak force interactions we should be able to figure out   which handed rule the aliens are using.

But again, this depends on our ability to distinguish matter   from anti-matter, so we still need to know which sign convention they use for electric charge.

The combination of charge and parity  transformation - appears to bring our equations   back to where they started.

This is CP symmetry.

A mirror-reflected, antimatter universe has the   same laws of physics as ours.

But actually,  such a universe works differently in very,   very subtle ways.

That universe works just like our universe if you reversed the flow of time.

The final symmetry and the final convention that we need to figure out is how the aliens define   the flow of time.

Do they define the future as an increasing progression of positive times like we do,   and the past as negative?

Or do they do it the other way around?

The laws of physics shouldn’t care   which you choose - so we say those  laws are time reversal symmetric.

But if time reversal is equivalent to  charge-parity inversion, and the latter   is a broken symmetry, then time symmetry  must also be broken.

The grand, unbroken   symmetry - CPT symmetry - is a combination of all three.

The laws of physics and the behavior   of nature is unchanged under simultaneous inversion of charge, parity and time.

And here we might have our  final, insurmountable problem.

What if the aliens use reverse conventions for the sign of electric charge, the handedness of parity,   and the direction of the flow of time?

The change in the time-flow convention along with the changes   in charge and parity would change how they represent their particle interactions in a way that we couldn’t   distinguish.

We might build a time-forward,  right-handed, electronic device instead of   the alien’s intended time-reversed, left-handed, positronic doodad.

And guess what - that should be   totally fine.

The unbroken nature of CPT symmetry means the thing should work just as intended.

Like assembling a bookshelf upside down because you inverted the instruction manual - the thing   still holds books just fine.

It may be  embarrassing when we warp into the galactic   civilization with our spaceship on backwards, but the important thing is we get there.

The takeaways from all of this: 1) check if your alien instruction manual is upside down, and 2)   remember that whenever we measure something, anything, we are making choices.

Those choices   can seem inconsequential, but every seemingly arbitrary choice reveals something powerful.

It points to the existence of an  underlying symmetry of space time.