How fundamental are fundamental constants?about a topic I consider elementary and I understood it when I was a high school student. The realization is that the numerical values of dimensionful (having units) universal constants of Nature depend on arbitrary and physically unimportant human decisions and don't really affect the character of the physical laws.

By a more economic parameterization of the physical observables, e.g. the choice of \(1=c=\hbar=\epsilon_0=k=G=\dots \) units, one may completely eliminate the symbols of these constants from the equations describing the laws of Nature. This choice can be made even in situations when some people say that the "constants are evolving in time". To summarize, the number of physical fundamental dimensionful constants that would affect the laws of physics is always zero.

You may compare Duff's paper with some texts of mine such as

Dimensionless Constants in Physics (Physics Stack Exchange, answer, 2011)and elsewhere. I am sure that he would agree that we fully agree. More precisely, Duff would say (2011):

Changes of dimensionful quantities are unphysical (TRF 2009)

Let's fix the value of Planck's constant (TRF 2012)

Parameters of Nature (TRF 2004)

As a fresh member of the Royal Society, I am grateful to my overlords and I am ready to trample on politically incorrect babies in order to be admitted to as many similar societies as possible. So I will happily start by saying that I do not share Lubos Motl’s extreme views on politics, global warming, and sometimes not even string theory. However, he occasionally has some good physics summaries, including a recent one giving a nice history of the triumphs of uniﬁcation [26]Yes, Mike, this introduction of yours was despicable, utterly unethical, and you will be grilled in Hell throughout the infinite asymptotic future. But yes, we agree on the units.

It's remarkable how many authors and papers saying completely stupid things about the dimensionful constants Duff has been able to find.

For example,

**John Moffat**argues that if the dimensionful constants are "evolving", physics is very different, and it would be totally incomprehensible if you tried to switch from some units to others, and so on. Duff correctly replies that switching from one set of units to others is a trivial operation that doesn't affect the form of the fundamental equations at all.

The statement that "these dimensionful constants are varying" isn't a statement about Nature only. It is a statement about the union "Nature plus our conventions". So this statement isn't pure physics. And even if it happens to be true with your choice of conventions, nothing stops you from setting \(1=c=\hbar=\dots\) at each moment of time and at every point of space! It is a very natural choice of units which is why mature conventions

*always*allow us to say that \(c,\hbar\), and others are independent of time, true constants (just like the number one). This statement doesn't restrict the form of the laws of Nature at all; it is not making any assumptions about Nature that could fail. It is always possible to adjust the conventions so that the statement holds.

**Paul Davies**indefensibly disagrees with Duff's claim that theories with varying dimensionful constants are operationally meaningless and claims that such theories exist and specific experimental tests to confirm that they are true are known, too. Duff disagrees and corrects Davies' claim that Dirac was on Davies' side in his misunderstanding of the role of units.

Duff says many correct things – mostly reiterating the insights that were already mentioned above. But the key always is that Davies and others misunderstand that whatever mechanisms exist that make "something" time-dependent, one may always choose units that eliminate all the numerical values of (a correctly large set of) dimensionful universal constants. With this choice, the "time evolution" of "anything" is inevitably translated into the evolution of some dimensionless parameters. And if the laws of physics are complete, they must of course describe the rules that dictate the evolution of these dimensionless constants. They are evolving dynamical parameters just like any others (e.g. the speed of Venus) which means that their changing values aren't "universal" and shouldn't be called "fundamental", either.

Not too surprisingly,

**João Magueijo**is deluded about all these issues, too. This crank has actually made a living out of spreading these totally self-evidently wrong assertions about the variable speed of light theories and he is currently a colleague of Duff's at the Imperial College in London. Holy crap. Magueijo would scream things like "it must be impossible to allow the choice of \(c=1\) units". He just completely misunderstands that certain values depend on human conventions.

The list of people who are completely confused includes

**John Barrow**, a guy who likes to write superficial books stupidly combining physics and God, and, more disappointingly,

**Gary Gibbons**who is otherwise a deep physicist. It probably doesn't make sense to discuss the quotes separately because all the wrong people are reiterating the same delusion in different words. But those people include

**R.D. Reasenberg**;

**J.-P. Uzan**;

**C.J. Copi, A.N. Davis, and Lawrence Krauss**(who ignore the unit dependence of \(\dot G / G\) in a discussion of the Big Bang Nucleosynthesis); and

**Terry Quinn**(who was, ironically enough, a director of the International Bureau of Weights and Measures but who insanely believes that a theory will once calculate the numerical value of \(G\) in SI units).

I find it remarkable that so many people who have become physics professionals are incapable of understanding and agreeing with these very simple things. Many of those are chronic writers of popular books (e.g. Barrow, Krauss, and others) and I used to assume that what they were writing were just silly simplifications to make their books more understandable to the lay audiences (who don't really understand the difference between dimensionful and dimensionless constants or variables and similar nuances). But they seem to be damn serious.

As the mass of the international prototype kilogram changes and still by definition is equal to 1 kg the dimensionful constants are changing all the time without any significant implications for the fundamental physics

ReplyDeleteSome physics professors might only be persons who are exceptionally receptive to pedagogical programming with mathematical physics!? ;-)

ReplyDeleteAm sure we all know that what is broadly referred to as "intelligence" is a diverse and complex conglomerate of capacities (and lackings or shortages) thereof. ;-)

If my knowledge of Germany were like yours, I would have surely written Ravensbrück! But then many other readers wouldn't understand too well...

ReplyDeleteA national laser sounds terrifying but it's behind some virtues of Germans, too, isn't it? ;-)

ReplyDeleteway to dehumanize a bunch of people working to earn a living.

ReplyDeleteNo problem, Kashyap, I hope Sage is right and dropping associativity isn’t that constraining so that surprising results do lie in that direction - that would be very cool.

ReplyDeletesee the most advanced medical team, They don't know how to take a pulse, and when somebody can't feel a pulse. See the mind boggling conclusion.

ReplyDeletehttp://www.youtube.com/watch?v=vT66U_Ftdng

"

ReplyDeleteI do not share Lubos Motl’s extreme views on politics, global warming, and sometimes not even string theory."

Russian Ambassador DeSadeski, "The fool...the mad fool."

String theory is math not physics. Other than that, Luboš has them all pinned. Empirical reality is not decided by peer votes, even if it sums to -1/12 (no units). Nature does not care; we do.

The Right Wing creates empires, the Left Wing consumes them.

My favorite subject, here is the original paper

ReplyDeletehttp://arxiv.org/pdf/physics/0110060v3.pdf

Finally, I really do get it! Thanks, Lubos, for a beautiful explanation. Now I can write Maxwell’s equations on half of a postage stamp rather than using the whole thing. How elegant!

ReplyDeleteAs the string theory landscape is narrowing, is not string theory becoming physics? It certainly is only a subset of mathematics.

ReplyDeleteIf a unique compactification is never found, we will, to some degree, have to accept the anthropic principle. That is a truly disturbing thought but I would not tell God what to do.

I think Lubos understands the nature of string theory very, very well.

The fact that measurements are becoming more precise surely does not mean that the thing being measured is changing. You seem to be confused.

ReplyDeleteLike you, Lubos, I thought (maybe first year U) that dimensionful constants were a convenient fiction that could be parametrized...(sort of like the false singularity at the event horizon in the Schwarzchild metric).

ReplyDeleteIt is kind of amazing that professionals disagree, but looking at the names, I am not overly surprised.

In Mike's insulting, but I am sure tongue-in-cheek comments, he could have removed the "some" from "some good physics summaries" and upgraded "good" to "superb" :)

Thanks for that link.

ReplyDeleteString theory is both,not that I know much. I would write it

ReplyDeletemath/physics.

The weak anthropic principle is so obvious it need not exist. The strong anthropic principle just seems silly.

ReplyDeleteDear Gene, I think that OON just meant that we are still using a very lousy definition of a kilogram, the international prototype.

ReplyDeletehttp://motls.blogspot.com/2012/04/lets-fix-value-of-plancks-constant.html?m=1

It's made of 90% platinum, 10% iridium, and located somewhere in France, with many countries' having their copies.

However, the metal isn't 100% stable and it's absorbing things and evaporating molecules from the surface. It means that the ratio of the weights of different copies of the prototype actually isn't constant (one). It's changing:

http://upload.wikimedia.org/wikipedia/commons/thumb/c/c9/Prototype_mass_drifts.jpg/399px-Prototype_mass_drifts.jpg

Over the century, the mass of a prototype changed by about 50 micrograms (50 parts per billion) according to the gram defined as 1/1,000 of another prototype. These changes can be measured today.

Because the numerical value of the mass is the ratio of the mass of an object and the mass of the international prototype of 1 kilogram, this ratio is clearly changing even if the measured object is much more stable than the prototype - the ratio is changing because molecules are being added or evaporated from the prototype.

So the masses of everything expressed in kilograms - using the current SI definition - are changing because of the molecules on the surface of the prototype. But this has no implications on fundamental physics, OON wrote. This change doesn't mean an ongoing change of all objects in the world - it's just a change of some stupid real-world object in France, the prototype. The changing values reflect the changing conventions rather than the changing nature of everything else in the Universe.

I think that you are really saying the same thing as OON.

non-associativity is a fact of life; when Cauchy presented his first paper on group theory, it was not accepted because the multiplication was not commutative.

ReplyDeleteWhen non-associativity is too jarring, we say that when a Lie algebra is represented with a matrix algebra, that matrix algebra is associative. We then build an associative "universal enveloping algebra" for our Lie algebra, which has the property that any associative algebra representation of our Lie algebra is a representation of the universal enveloping algebra.

But really, Lie algebras have, instead of associativity, a property sometimes referred to as "Jacobi-associativity": [X,[Y Z]] = [[X,Y],Z] + [Y,[X,Z]] (this should resemble the product rule. But it's usually called the Jacobi identity and written [X,[Y,Z]] + [Y,[Z,X]] + [Z,[X,Y]] = 0). The reason for this must be sought in the nature of the Lie algebra as the tangent space to the Lie group. The Lie bracket is then seen as coming from the covariant derivative.

By setting a sufficient number of dimensionful constants to 1, could we get a new value for a fine structure constant?

ReplyDeleteNo

ReplyDeletehttp://en.wikipedia.org/wiki/Natural_units

String theory has no empirical validation, It is strictly mathematics, as was the Fifth Force. Microeconomics real world works. What in macroeconomics accurately predicts Scientific Socialism's astounding failures, or tomorrow's stock market?

ReplyDeleteA quote from your reference: "the fine-structure constant, α ≈ 1/137, cannot be set to 1, because it is a dimensionless number. The fine-structure constant is related to other fundamental constants,

ReplyDeleteα = (ke*e*e)/(ℏ*c)

where ke is the Coulomb constant, e is the elementary charge, ℏ is the reduced Planck constant, and c is the speed of light. Therefore it is not possible to simultaneously normalize all four of the constants c, ℏ, e, and ke."

I agree with you - and with the quote. My point is that we are not allowed just to set an arbitrary number of dimensionful natural constants to 1.So we will always be left with some dimensionful constants.

Well, setting everything else to 1 there, the fine structure constant is equal to the Coulomb constant. Essentially, you can get rid of ke.

ReplyDeleteThe point is that we can set arbitrary values for different "unit systems" that does not affect the physics as shown in the reference.

ReplyDeleteDear Lubos,

ReplyDeleteYou are of course right, but there is still some non-trivial information in the statement that it makes sense to choose units such that these constants are equal to unity -- For instance, we put c=1 because of a symmetry that relates time and space, and we put \hbar = 1 because Schrodinger relates time and energy, k_B = 0 because energy is the same as temperature, etc.. All these "constants" are really parameters that deform one theory into the other, and we put them equal to 1 once we are confident that the theory is correct. A corollary is that the frequency with which \alpha' occurs in the literature is inversely proportional to the confidence in string theory :)

Nice writing, Sage, the Jacobi identity occurred to me since I posted this morning and I guessed that is where you were coming from. General algebras are usually defined as a vector space, or module, that has an additional product making it a ring, so associativity is usually part of the definition. I’m guessing that for physicists interested in Lie algebras the Jacobi identity is probably a lot more important than the associativity of the product - especially because they won’t be using the product a great many times, sort of like with vector cross product computations.

ReplyDeleteDid you ever seriously consider to go away and to stop posting your nonsensical repetitive gibberish, which is still comprehensible enough that one can see at a glance that it is insulting to and trolling about theoretical physics, somewhere else instead of below every TRF physics article..?!

ReplyDeleteNot sure, if Lumo just keeps these nonsensical babblings to remind us about how the default comment sections below not properly moderated physics articles on other places of the world wild web look like, LOL ... :-D

Yes, police should shoot to disable rather than to kill, unfortunately there is nobody can shoot that well.

ReplyDeleteThis is something that you might see on TV or in old movies, in real life anyone who tries it will miss, and may be killed as a result

Anna, your idea is good.

ReplyDeleteThe *real* question is; what laws are important? What laws are so important that those suspected of the violation of such laws need to be subjected to potentially lethal force, in the investigation of suspected violators and in the apprehension of suspected violators?

Selling 'loose' cigarettes, contrary to tobacco tax laws, does not warrant lethal force.

(Selling tobacco, larger-than-liter sugar drinks, trans-fats, and salt to put on your food, are regulated very strictly by current New York City laws.)

(Progressive politics has an ideal of "broken window" policing. Crack down on the small crimes and the bigger crimes can't happen.)

(New York progressives also think that you can not regulate your own consumption of tobacco, sugar, fat, and salt.)

Like Bell's conjecture, the train wreck happens when authority interdicts facts.

Like Bell's conjecture, the train wreck occurs when "what-ought-to-be" intersects reality.

ReplyDeleteThe cause of very much of the unnecessary and adverse interaction between the public and the law enforcement is the many unnecessary laws.

ReplyDeleteThose who desire a conforming society (all members conforming to their ideal social behavior) never allow for the authoritarian governance that is needed to make the populus comply. The people who would never allow a cigarette to be sold without tax are (surprise!!!) outraged when the idiot thugs enforcing the law kill one of the violators of the law by the idiot heavy hands of the enforcers of the law... light hands of application the idiots are not allowed to have, by the idealism of the law makers...

the Jacobi identity is important because a Lie algebra can synthetically be defined as a vector space with an anticommutative product satisfyig the Jacobi identity.

ReplyDeleteSuch a synthetic point of view is mostly useful for telling children lists of facts and then grading them on how diligently they can recite them. To truly appreciate things, one must appreciate them on their own terms. What a Lie algebra really is the tangent space to a Lie group with a product that is the derivative of the group product.

Simply put, the more compulsive and authoritarian that the US of A government is going to be, the more innocent people are going to be killed.

ReplyDelete26 children, and some adults, were killed in a Dept. of Alcohol Tobacco and Firearms raid, in the USA, a few years ago. Don't remember what the original "cause" of the enforcement action was... it must have been very, very, important... weapons of mass destruction, illegal firearm, parking ticket, something like that...

Dear Tom, if you only have a Lie algebra, it generally has no (associative) product! Lie algebra, by definitions, only allow you to calculate the commutator.

ReplyDeleteIf you have a particular representation of a Lie algebra - via operators on a space - then you may compose the operators, and you have the (associative) product. The commutator may then be defined as

[A,B] = AB - BA

But the converse isn't true. If a structure - the Lie algebra in its general form, without a specified representation - allows you (and it does allow you) to calculate [A,B], it doesn't mean that you can calculate any AB! The AB isn't an element of the Lie algebra, after all. It's just some other operators on the representation.

If the product AB on a representation is associative, then the commutators [A,B] defined as AB-BA will obey the Jacobi identity. So it's really the same condition if both structures exist. But they don't *always* exist. In some cases (if we talk about the general Lie algebra only), only the commutator is well-defined.

Sage, your last sentence is a really nicely succinct summary. Spent a couple hours reading some references last night and realized how far off I was when first responding to Kashyap, I was thinking about general algebras and didn’t have in mind how distinct Lie algebras are. Thanks for your comments, you clearly are way up on this stuff.

ReplyDeleteThanks, Lubos, after last night’s reading this make good sense. I gather from my math books that this subject comes up for physicists when they work with Lie groups, where the Lie bracket on invariant vector fields (on group’s underlying manifold) is itself an invariant vector field and so defines the additional product and, hence, the Lie algebra. So, a question. Does this Lie algebra and representation stuff figure in a big way in string theory? I.e., does compactification begin with a differential manifold with a continuous group action - a Lie group - and then one studies how good the choice was by looking at the associated Lie algebra, I suppose by how well the various fields on the tangent planes approximate the physics?

ReplyDeleteDear Tom, Lie algebras and their representations and all the related maths appear everywhere in theoretical physics - including (and perhaps especially) in string theory. No doubts about that.

ReplyDeleteBut to present all the ways how they appear means to teach you *all* of string theory. There is no way to quickly learn string theory just from the aspect of "how Lie algebras appear in it". They appear on every other page of a textbook of string theory. Say it's all the even-numbered pages. But you don't learn the odd-numberred pages as well, you won't really get the points, anyway. So I think that what you have really asked me is to explain all of string theory.

Just to be sure, if you don't know anything about string theory, it's virtually 100% guaranteed that your fantasies what roles Lie algebras should play in it will be wrong.

Right, it would be very silly to ask you to boil strings down to a paragraph. I’m just hoping to get a clue as to where those differentiable manifolds that represent the extra dimensions in string theory come from. I studied manifolds from the math side way back in my graduate days, so I have a slight grip on the terminology and definitions. Since stumbling onto your blog I actually have been trying to gain some understanding of string theory, and I am now at the point of trying to penetrate QFTs. But, sadly, I can report that graduate texts in advanced subjects new to you (like, in particular, Peskin and Schroeder) are a whole lot harder when you add three or four decades onto your prime.

ReplyDeleteTom, I don't think you can learn anything substantial in this way. The whole way how you think about these matters is completely irrational.

ReplyDeleteIn the previous comments, you pretended that your interest was focusing on Lie algebras and reps. Now you have totally switched to differentiable manifolds. These are very different things, do you understand it?

In many contexts or derivations in string theory, one deals both with manifolds and with Lie algebras but they're not synonyms and none of their relationships is canonically more important than other relationships - other contexts where both concepts appear.

I am actually not sure whether you understand what the concept of the manifold means. Your questions just look too confused for it.

String theory is a physical theory. It describes the world - the real world - using some laws of physics, equations that resemble field equations at long distances. It includes gravity so Einstein's equations coupled to matter are approximations of some laws that may be derived from string theory. In the vacuum, they demand that the Ricci tensor is zero.

Because superstring theory needs 10 spacetime dimensions for consistency, the remaining 6 dimensions have to be compactified on a Ricci-flat manifold, to satisfy the Einstein's equations of motion. If expressed mathematically, lots of objects will require Lie algebras and reps to be properly understood. But if I were elaborating upon these things, I would have to be writing my own textbook of string theory, and I would probably have to make it more detailed than those usual 1000 pages of textbooks because your questions suggest that you would need a slower presentation than what is usual. Sorry, I don't want to do that. Can we please stop with these totally ill-defined and totally confused questions?

LM

Sorry to have wasted your time. TWL

ReplyDeleteDear Tom, not a problem but I won't apologize for this dramatic cutoff of this conversation because it's boiled down to my extensive experience with exchanges that started in a very similar way.

ReplyDeleteYes, with the hindsight, I have wasted thousands of hours of my life and maybe I am slowly starting to learn some lessons. ;-)

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