Posted on 12/06/2001 4:46:03 AM PST by Darth Reagan
Forgive a humble engineer for interrupting when physicists are speaking about the secrets of the universe, but something about your statement struck me as strange.
I am used to thinking about mass (gravitational or inertial) as being a fundamental property of things, not to be explained so much as described or measured. The concept of mass would seem to be more basic than the Higgs mechanism; how, then, can the Higgs mechanism explain why things have mass?
Would you agree that degrees of freedom are more fundamental than properties? The Higgs mechanism works on a mathematical level by making an extra degree of freedom available to the elementary particles, and this degree of freedom manifests itself as mass. (There are also extra degrees of freedom left over known as Goldstone bosons; the Higgs particle itself is an example of a Goldstone boson.)
The physical interpretation of that math would go like this: the "massless" elementary particles are coupled to the Higgs field, which "dresses" the particles in a cloak of virtual Higgs particles, and it is this cloak that plays the role of mass. The stronger the coupling, the heavier the cloak.
You might want to look at the site, Higgs Revealed. It has several accounts written in response to a challenge to explain the Higgs boson on 1 page.
Accelerators hurl particles at nearly the speed of light on a collision course to break them up so scientists can study the nature of matter.
I can see it now, some poor SOB out there in a parallel universe is home watchin the evening news. Then....WHAM! We vaporize his Volkswagen.
Just Kidding :-)
I might agree if I knew what you meant.
The physical interpretation of that math would go like this: the "massless" elementary particles are coupled to the Higgs field, which "dresses" the particles in a cloak of virtual Higgs particles, and it is this cloak that plays the role of mass. The stronger the coupling, the heavier the cloak.
Hmm... I think I see what you are getting at. The Higgs mechanism is a mathematical concept that may be interpreted physically. Degrees of freedom would also be a mathematical concept.
Allow me to try to explain the difficulty I had with your original statement. It is not that I think it was incorrect; but rather, it reflects a way of looking at the world that is different from the way that I, as an engineer, view it.
Consider gravitational mass. Everyone has an idea, acquired by direct experience, that massive objects are attracted to the earth. Since Newton's time, we have written F = mg. But does this equation "explain" or "account for" gravitational mass? My contention is no: F = mg is a convenient mathematical description of what we observe to happen (at least in most everyday applications).
Put it another way, does nature obey our mathematics? Or do we hope our mathematics describes nature? My impression is the mathematician or mathematically inclined physicist considers the equations more real than nature. Thus, Goldstone bosons are not objects but degrees of freedom.
Well, you asked me a question about how the model behaves, and so my answer was of course written in the context of the model being correct, which it may not in fact be. As for my original statement, "the Higgs mechanism may explain why quarks and leptons have mass," what it means is that--take a flyer for a moment--assuming that SU(2) X U(1) is the correct symmetry to describe a unified electroweak force and assuming that it is spontaneously broken by the Higgs mechanism, lepton and quark masses follow as an unavoidable corollary. (Yeah, I know that didn't make sense to you on its surface, but pretend it's an opera: ignore the Italian and groove to the music.)
But you are asking a deeper question, now. The way I look at it is that nature is, at its core, consistent with mathematical truth. When you talk about "our mathematics", you mean, "our mathematical formalism", that is, our choice of symbols and our methods for manipulating them. Using "our mathematics", however, we do uncover real mathematical truths. These truths are universal, and they do constrain the possible behavior of reality.
Mathematical truth is more fundamental than reality; mathematical formalism is not. We attempt to use our mathematical formalism in such a way as to uncover those truths that are relevant to the description of reality. When we have a description of reality (say, a description of how particles acquire mass) then we can make ironclad predictions about how nature would behave in such a universe, and test to see whether our universe does, in fact, match those predictions. The Higgs boson is one such prediction.
Is mathematical truth discovered, or is it constructed?
Apparently, you would agree with those who say that mathematics exists to be discovered: in fact, mathematical truth is more fundamental than reality!
If pressed, I would probably say that physical reality is more fundamental, and that mathematics is something that we humans construct. Sometimes, if we are careful, our math adequately approximates reality.
Actually, I think its running on an old VIC-20, with external cassette tape drive backup.
Apparently, you would agree with those who say that mathematics exists to be discovered: in fact, mathematical truth is more fundamental than reality!
Look carefully at your language and mine: you are using "mathematics" to mean two separate things. I say mathematical truth is discovered, and mathematical formalism is constructed.
Mathematical truth is more fundamental, because our reality is only one of an infinite number of potential realities, but there is only one set of mathematical truth, and it is common to them all.
If mass were basic, then would it be convertible into something else, such as energy? What they do is rotate their dimensional unit matrices until they become relatively simple; then one of the dimension units becomes mass. But there are other possibilities.
Could that be used as 'reasonable doubt' in court to the possesion of any banned or regulated object or substance?;-)
Sure, but the world didn't resemble our present world until later. Stars and planets, heavenly bodies were created later. Why did they tell us that if not to make us use our ability to reason to figure out the universe? Such as to figure out what the firmament is. What is the firmament? How thick is it? How many other earths were created? Aren't we supposed to use our talents, or was that a NT kind of thing?
I agree with the first part of what you say, but that mathematical truth would be common to ALL potential realities made me pause. Why should that be? There can of course be different algebras and different geometries. Or by mathematical truth do you mean some sort of meta-truth of which the truths of particular universes would be subsets?
I was not aware of using mathematics that way. Indeed, I am not sure what you mean. Can you give a (simple) example of the difference between mathematical truth and mathematical formalism?
Mathematical truth is more fundamental, because our reality is only one of an infinite number of potential realities, but there is only one set of mathematical truth, and it is common to them all.
That is quite a leap of faith, isn't it? Not that I have anything against faith, you understand. But how can we know that there are infinitely many potential realities but only one mathematical truth? (We seem to have wandered into the thickets of metaphysics, an adventure I am not prepared to undertake.)
In the beginning was the word, and God laughed. 15 billion years and still laughing. Then God created Man in his image, so why isn't Man laughing? Well, some do.
Disclaimer: Opinions posted on Free Republic are those of the individual posters and do not necessarily represent the opinion of Free Republic or its management. All materials posted herein are protected by copyright law and the exemption for fair use of copyrighted works.