Let's fix the value of Planck's constant.The SI system of units is based on 1 meter, 1 second, 1 kilogram, 1 kelvin, 1 ampere, 1 candela, and 1 mole. They have some definitions that are not really optimal yet.

I claim that a theoretical physicist prefers units in which a maximum possible subset of the universal fundamental constants of Nature such as \(\hbar,c,\epsilon_0,e,k_B,N_A\) and perhaps even \(G\) have well-known values. In theory papers, we really want to put them equal to one but that requires one to use natural (e.g. Planck) units that are numerically different from what the people are used to.

If these constants are set equal to a precisely specified numerical value, it's equally good – up to some simple multiplication. For example, the speed of light \(c\) was set to a fixed constant, \(299,792,458\,{\rm m/s}\), in the early 1980s when the relative error in the measurement of \(c\) using the older definition improved to one part per billion, \(10^{-9}\), or so. Since that time, the accuracy with which times and distances are being measured has increased and due to the fixed value of \(c\), this progress is automatically reflected in the accuracy of times and distances, too.

In 2012, I proposed to do the same thing for \(\hbar\) and redefine one kilogram.

A theorist focusing on gravity (or quantum gravity) would ideally want to fix the value of Newton's constant \(G\), too. However, this would be bad for another, experimental reason. In the current SI units, \(G\) is only measured with the relative uncertainty \(1.2\times 10^{-4}\) which is a huge error. You surely don't want all masses that people talk about carry this error of 0.01% caused by our inability to accurately measure the strength of gravity.

So it's not time to set \(G\) to a well-defined constant (in the real world; in theory papers, we're doing it all the time). By the way, if you primarily care about the real-world accuracy – about the need to avoid spurious extra unnecessary uncertainties introduced by impractical definitions of units – you should be interested in products of powers of the fundamental constants that are known more accurately (when it comes to the relative error) than the constants themselves.

On the other hand, some other constants have been measured much more accurately so there's no reason not to fix the appropriate constants equal to fixed numerical values.

Nature just published an article about some plans (that may be realized in 2018 so they are not imminent) to redefine one ampere:

Ampere to get rational redefinitionIt's mostly based on the December 2013 preprint

A self-referenced single-electron quantized-current sourcewhich, if I understand it well, effectively wants to set \(e\), the elementary positive electric charge, equal to a fixed value in such a way that each lab could be equipped with a canonical gadget that measures the charge and other electric quantities accurately in the globally agreed units. The gadget is based on a single-electron pump.

There's nothing really wrong about setting \(e\) to a well-known value which is currently \(4\pi\times 10^{-7} \,{\rm (V\cdot s) / (A\cdot m)}\) which was chosen to agree with some 19th century semi-natural CGS (Gauss') units. After all, theory papers like to set \(e=1\) or something like that – which is not incompatible with setting \(\epsilon_0=\hbar=c=1\) as long as we insert the fine-structure constant to the appropriate formulae and laws of physics. It's not bad to fix \(e\) because its value is known with the standard uncertainty \(2\times 10^{-9}\) or so which is pretty accurate.

But I don't have anything against setting \(\mu_0=1/\epsilon_0 c^2\) to a fixed value, either. That's what the SI system is doing these days. So I don't really see any progress here. The fine-structure will have some uncertainty, anyway – currently it is about \(3\times 10^{-11}\) which means that it is known really accurately but it will never be known absolutely accurately (unless we derive its value from the right string vacuum).

As you can see, I am not too enthusiastic about switching from setting the vacuum permeability \(\mu_0\) to a well-defined value (the vacuum permittivity \(\epsilon_0\) is also fixed because \(c\) is fixed today). It seems much more important to me to get rid of the silly "international prototype kilogram", probably by fixing the value of \(\hbar\). The prepared reform of the definitions of the units is expected to redefine four units at the same moment – kilogram, mole, ampere, and kelvin. The apparent high influence of the experimental December 2013 papers suggests that good theorists aren't really well-represented in the metrological institutions.

To summarize my viewpoint, I would define the units so that \(c,\hbar,k_B,N_A,\mu_0\) are set to fixed numerical values and one second is linked to the atomic clocks (the currently used cesium is good enough). I am convinced that gadgets measuring and therefore "operationally defining" the quantities with the accuracy that wouldn't be worse than the current one could be designed and described as well. I feel that the fundamental units shouldn't be linked to some arbitrary systems used in measuring apparatuses unless it is really a superior choice – which is the case of the measurements of time via atomic clocks (and distances as well, thanks to the fixed value of \(c\)).

Isn't it better to instead make the electric charge of a down quark a fundamental unit in place of the magnetic constant? This will remove the messy problem of fractional charges. Also using the magnetic constant just doesn't 'feel' right.

ReplyDeleteDear TheDoc,

ReplyDeleteelectric and magnetic fields - and quantities - are exactly equally fundamental. I understand that you may imagine that the electric charges are more fundamental because the magnetic fields are created by the electric charges' motion. But the same holds in the other way around - electric fields are produced by moving magnets, too. There is a duality here, implying democracy between both concepts.

Whether e or e/3 is really more fundamental is a subtle question. Quarks are confined. e is the minimum positive charge of an object that may exist in isolation. And by the way, it's not guaranteed that fractional charges not being multiples of e/3 don't exist. String theory vacua may imply the existence of fractional charges like e/5 etc. carried by some very heavy and rare particle species. These models may be compatible with everything we know. So it's risky to exaggerate the lessons learned from quarks' having e/3 charges because this fact doesn't have to be the last fact of a similar kind.

Best wishes

LM

Very interesting... I had no idea that other fractional charges could exist. I agree with all your other points. But I remain skeptical. One question will pretty much settle the issue: As a high-energy physicist, what do you use more: the magnetic constant or combinations of the fine-structure constant and the electric charge?

ReplyDeleteAs a high-energy physicist, I use units with c=epsilon0=mu0=1, both electric and magnetic constants are set to one so I don't have to use any of the dimensionful constants.

ReplyDeleteOnly the dimensionless constants similar to the fine-structure constant included the usual one enter sensible physics calculations.

When comparing to experiments and experimenters who use down-to-earth units, one needs *all* the constants.

Oh noes! Not again! When I was an undergraduate engineering student we were taught several systems of units and were expected to convert between them. This was for historical reasons as many existing structures and machines were designed on these older systems of units. Some of them were gravitational (F=ma/gc) and some dynamic (F=ma). Then someone insisted on SI, which has never become established in the US other than for the military. And even there, we rate jet engines in lbf of thrust, not newtons, which the NASA idiots some much trouble in Mars probes years ago.

ReplyDeleteMost American engineers use a mixture of SI and the traditional lbm/lbf/ft/sec/F/Btu/... Most medical people are still in the cps era. In Europe, many engineers use a gravitional version of the mks system: kgm/kgf/m/s ...

Very interesting comment Lubos."String theory vacua may imply the existence of fractional charges like

ReplyDeletee/5 etc. carried by some very heavy and rare particle species.Can you say something more about e/5 charges? If some particles whose charges can be understood by multiples of e/5 only, that would be a great triumph for ST.

Dear Kashyap, if you have read e.g. The Elegant Universe by Brian Greene, fractional charges are discussed in the Smoking Gun Chapter 9.

ReplyDeleteThey appear if the Calabi-Yau has a 1-cycle that is noncontractible but 5 times the cycle is contractible, i.e. the holonomy or homotopy includes a Z5 cyclic group, and so on.

You may try to search for some papers

http://scholar.google.com/scholar?q=fractional+electric+charges+string-theory&hl=en&lr=&btnG=Search

Yes, it would be cool. It's a very long shot, too.

In vacuum, electric and magnetic fields are equally fundamental. But if one looks at matter, then one recognizes that it is the ELECTRIC current that is the source of Maxwell's inhomogeneous equation. This electric current is conserved and leads to the conserved electric charge. In this sense, the ELECTRIC CHARGE is the decisive quantity and I tend to think that this is the quantity that should be used as the basic unit in electrodynamics.

ReplyDeleteDear Fred,

ReplyDeletethe only reason why one set of Maxwell's equations is homogeneous is that we haven't observed magnetic monopoles yet. That's also why we think we may always define the electromagnetic 4-potential A_mu globally.

In reality, the magnetic monopoles probably exist - they are heavy elementary particles - and both sets of Maxwell's equations have a right-hand side.

Cheers, LM

Dear Lubos, "In reality, the magnetic monopoles probably exist--they are heavy elementary particles--and both sets of Maxwell's equations have a right hand side" How are you so sure about reality, when all high energy experiments run so far find no eveidence whatsoever for a U(1) magnetic monopole? See Milton, Rep.Progr.Phys. 2006, and also P.C.W.Davis, Int. J. Th. Phys. 2008. The induction law is, in fact, a conservation law for magnetic flux. The latter quantity is basic for magnetic properties, the magnetic charge is just a far-fetched assumption without experimental basis.

ReplyDeleteBest, Fred

o

Dear Fred,

ReplyDeletea reason for my certainty is that consistent motivated models of high-energy physics (especially GUT theories) imply the existence of magnetic monopoles.

But the real reason why I feel so sure that it's not just a property of some (grand unified etc.) models is quantum gravity. Black holes may be pair-created and this process must have a nonzero probability even if the magnetic flux is asymmetrically divided in between the regions of the two future black holes. Consequently, it must be legal for a nonzero magnetic flux to exist around each of the two black holes, and such a black hole microstate is therefore a magnetic monopole.

We actually seem to know much more than the pure existence. The lightest objects with a relevant charge must be lighter than a certain threshold, see e.g. our paper

http://arxiv.org/abs/hep-th/0601001

Cheers

Lubos

Dear Lubos, at least in Einstein-Maxwell theory, the Kerr-Newman black hole can consistently exist without magnetic charge. Also the black hole uniqueness theorems work very well without magnetic charge. Thus, we have Maxwell's theory coupled to GR and we don't need a magnetic charge for that combined theory to work. At least in this context, I cannot see a need to speculate about magnetic charges.

ReplyDeleteBest wishes,

Fred

Dear Fred, the problem isn't that some special black holes exist. The problem is that you want to ban most of the black holes - those with the magnetic charge.

ReplyDeleteThey're effectively the same holes as Kerr-Newman with a different interpretation of the electric field but you can't prevent these objects from pair creation.

Magnetic charges of general black holes aren't speculations, they're facts.