What makes the right hand rule not the left hand rule?

[hamster_nz]

So I know about Right-Hand Rule, and the general principle that a charge moving though a magnetic field has a force exerted on it, and the force is at right angles to the field and velocity. I also know about cross products of vectors, gives you a vector that is perpendicular to both.

However for any situation there are always two vectors that are perpendicular to both, a bit like how there are two answers for sqrt(2)).

What apart from mathematical conventions decides which of these two is the answer? Is there a fundamental "handedness" to the universe? If so, what is this property called?

[jogri]

That "handedness" is called chirality, it basically means that you can't transform item A into item B (for example: left hand rule into right hand rule) by rotation and translation alone, you have to mirror it (by changing the sign of one vector: let's say 0|0|1 is your perpendicular vector AxB, 0|0|-1 would be its mirror image).

One example of chirality in nature would be enantiomers in chemistry, the interaction of a lot of chiral molecules with your body depends on their handedness (an infamous example would be Thalidomid, one enantiomer was perfectly save while the other had devastating effects).

[edy]

Interestingly with biological molecules, would it be feasible to have a completely "mirrored" version of life on another planet where all molecules were reversed, and everything still work? Or perhaps some more fundamental issue allows only one type of "handedness" to work?

The good news is that if such an alien world existed we would probably not make good food to them, and vice versa, assuming the same molecular systems. Granted, our biological enzymes would probably not be able to handle things if there were even some minor differences in the life chemistry.

The question still remains, is there a fundamental BIAS towards one chirality versus another in life chemistry at the outset of life forming or was it just a fluke and then everything following it obviously evolved by necessity to the same chirality? The other question is if both chiralities could exist on the same planet, would independent life systems coexist yet be unable to eat each other? Which brings me to seashells and whether there is one direction the spiral always goes or if variety exists in their shells?!?

[coppice]

The question still remains, is there a fundamental BIAS towards one chirality versus another in life chemistry at the outset of life forming or was it just a fluke and then everything following it obviously evolved by necessity to the same chirality? The other question is if both chiralities could exist on the same planet, would independent life systems coexist yet be unable to eat each other? Which brings me to seashells and whether there is one direction the spiral always goes or if variety exists in their shells?!?

I've read in biology texts that things just happen to be this way around. However, it wouldn't surprise me to find that something like the motor/generator rule affects things at some deep level in the molecular scale machines, like proton pumps, that drive living processes.

[jogri]

The other question is if both chiralities could exist on the same planet, would independent life systems coexist yet be unable to eat each other? Which brings me to seashells and whether there is one direction the spiral always goes or if variety exists in their shells?!?

Probably not that likely as this system would be extremely unstable: You have to maintain a perfect balance between four different species (plants & animals w R chirality and the same for the S type). How do those animals know which plants to eat? They all look the same, yet only half of them are edible. Same goes for the animals. At some point one of those four groups is going to increase/decrease enough to collapse this system.

[T3sl4co1l]

Blame Franklin -- https://xkcd.com/567/

The question then would be, why are poselectrons left-handed and not right?

You're welcome.

The reason there's any handedness, is simply the order we assign to the vectors, and the commutativity of the cross product between them.  Namely, A x B = -B x A.

As it happens, it's a sign change, but it's worth emphasizing that vectors and matrices (in general, linear algebra; and for fields, its extension, vector calculus) need not have the commutative multiplication we take for granted with scalars.

Which, may seem trivial in grade school or high school algebra classes -- of course numbers are commutative, we've been doing it that way our entire lives, and of course there's no way that 6 x 9 != 9 x 6 = 54.  Well, they never get around to providing examples to the contrary, but it turns out there was a reason after all that they made note of these things, because some number systems -- algebras, rather -- indeed do not exhibit commutativity, associativity and such.

But anyway, I don't think the present example is chirality as such, so much as that's the convention, and that we must have some consistent convention to do work in this space.  But on that note. . .

That "handedness" is called chirality, it basically means that you can't transform item A into item B (for example: left hand rule into right hand rule) by rotation and translation alone, you have to mirror it (by changing the sign of one vector: let's say 0|0|1 is your perpendicular vector AxB, 0|0|-1 would be its mirror image).

One example of chirality in nature would be enantiomers in chemistry, the interaction of a lot of chiral molecules with your body depends on their handedness (an infamous example would be Thalidomid, one enantiomer was perfectly save while the other had devastating effects).

Indeed, chemistry, and on even smaller scales, quantum mechanics itself, exhibits chirality, in a very fundamental way.  In QM, the same vector equations, and linear algebra, that gives us questions like this, also yields a fundamental degree of freedom (spin), and deeper still (QED, Standard Model, etc.), chirality and handedness of fundamental particles.  Or going back to EM, there's circular polarization of waves, for instance.

At its most basic, this simply arises because there are certain ways to move through 3-dimensional space (and 4D spacetime when applicable), and every kind of motion, every symmetry, begets a conservation law in our system of equations.

Tim

[coppice]

At its most basic, this simply arises because there are certain ways to move through 3-dimensional space (and 4D spacetime when applicable), and every kind of motion, every symmetry, begets a conservation law in our system of equations.

Quite a Noether-ble point.

[basinstreetdesign]

This is an excellent question.  And it seems that at least 9 out of 10 people, supposedly learned, will answer with lengthy answers to the effect of "it is what it is because it is what it is".  I get tired of reading these.  So after some googling I find at:

https://physics.stackexchange.com/questions/433280/in-electromagnetism-why-does-nature-prefer-the-right-hand-rule-over-the-left-ha

what may be the most cogent answer which gets closest to the heart of the matter.  It is:


    [Q:]"My question is, why this direction and not the opposite? Nature tends to be symmetric and not have apparent preferences for two equal options, so in a so why is one direction preferred over the other one? Why doesn't a "left hand" rule apply?"

[A:] "The direction on which a subatomic particle gets deflected under the influence of an external magnetic field has to do with the magnetic dipole moment of these particles. Every of the described above particles [electrons, positrons, protons] has the intrinsic property of magnetic dipole moment and this moment is described as parallel or antiparallel to its spin.

So nature is not symmetric in all cases and if the electron would have the tendency to be deflected in both direction perpendicular to both the external magnetic field and the trajectory of its movement we would not be able to drive electric devices nor get an electric current from generators.

The mechanisms behind the deflection has to do with the emission of electromagnetic radiation during the deflection. You has to remember that the external magnetic field does not weaken during electron passage (any permanent magnet would work for years without loosing its strength). Imagine a bar magnet, moving into a magnetic field. The bar magnet gets aligned with this external field and so does an electron. But the electron during this alignment emits photons, all of them in the same direction and the moment of this radiation makes the electron slower and deflects it from the previous trajectory. The electron moves not in a circle, it moves in a spiral path and more than this, this path is made of tangerine slices. [??] A positron will do the same but in the opposite direction."

Unfortunately the author of this answer is identified only as "HolgerFiedler" but I don't know if that is a person or an organization.

But to say that these rules are the result of arbitrary convention one way or another is complete balderdash.

But it still begs the question of why are the magnetic dipole moments of these particles arranged like that?