Exploring Mass: Unveiling the Mystery

[dce]

I've been confused on why mass is such an essential component to understanding the physical relationships that we experience. From my limited understanding I want to believe that I can recognize the significance of general relativity, special, the various quantum functions, among recent advancements. I've heard the standard model called a mathematical mess but I don't quite get why. The complexity of the formula itself makes sense to me with there being such a diverse number of forces to account for. With the infinities present in the standard model yielding a possibility of infinite gravitational forces, it seems to me like it would be a statistical anomale. The problem with mass also makes sense to me; because it's possible to envision, from my understanding of the relationship between matter and energy, that mass could be a perceived effect.

I fully expect that my thoughts are flawed most likely from just plainly misunderstanding key concepts, so I would appreciate some feedback on where the flawed logic is.

 

[marcus]

We don't know what mass is.

Do you know what inertia is? It can be measured---you can measure a thing's reluctance to speed up or slow down or change direction. You can measure the force required to produce a certain amount of acceleration.

We can measure inertia---it is defined by how we measure it---that is a pragmatic operational way of defining it. But we don't know what gives things their inertia.

Do you know what gravitational attractiveness is? I suppose for sure you do! That is another thing we can measure---the acceleration of a test particle released at a certain distance.
Inertia is sometimes called "inertial mass" and that kind of attractiveness is called "gravitational mass".

Just as we don't know what gives things their inertia, we also don't know why things have gravitational attractiveness. We don't know why concentrations of matter bend space.

It has to do with the interaction of geometry with matter. Why does matter bend geometry, and why goes geometry guide the motion of matter?

 

[dce]

Alright, it seems clear now that I don't know anything after looking through some of these threads but I appreciate the insight and hopefully i'll be able to contribute to some of these conversations in the future, once I can wrap my head around the actual math involved. Thanks again.

 

[marcus]

Alright, it seems clear now that I don't know anything after looking through some of these threads ...

You may have misunderstood my intent. I didn't mean it as any kind of put down, or as suggesting that it was a dumb question.

It is a very good question. The best kind. What is mass?--it's a question that is going to be hot and spark a lot of thinking and experimenting over the next ten years.

The Higgs business is about what gives things their inertia.

A nobel laureate named Frank Wilczek has written a popular book called "The lightness of being" about this very question.
A gimmicky title---he uses "lightness" to mean "mass" in a kind of reversal.
Measuring lightness of something is the same as measuring its heaviness or its inertia. they are just two ends of the same scale.

Wilczek has some interesting video lectures about the ORIGIN OF MASS the links are at his MIT faculty website. Google. You will enjoy. They are wide-audience lectures about what we know so far about where mass comes from.

You should not back out. You should keep asking.

By my answer I only meant to respond to your question in a truthful straightforward way, as far as I can see we do not yet know what mass is. Our understanding of it is very limited. that is what makes it such an interesting stimulating scientific question.

BTW We don't know why inertial mass and gravitational mass are proportional. Measurements seem to indicate that they are exactly proportional, always. That is, they seem to be the same thing.

 

[humanino]

The Higgs business is about what gives things their inertia.

Quite frankly, I think this overrepeated statement is a conscious fraud. The Higgs (if it exists) gives less than 5% of the mass we know about, the ordinary mass around us, our inertial and gravitational masses. More than 95% comes directly from glue. This is clearly stated in Wilczek's lightness of being.

A gimmicky title---he uses "lightness" to mean "mass" in a kind of reversal.

I think Wilczek was also quite explicit, that he wants to reverse the question "why is gravity feeble ?" into "why is the proton so light ?"

Measurements seem to indicate that they are exactly proportional, always. That is, they seem to be the same thing.

I do not understand why this is not "just" equivalence principle ? I mean, not to state as a "principle" the above equivalence, but the principle that any gravitational field can be locally washed away by going to the referential of an observer in free fall.

 

[marcus]

More than 95% comes directly from glue. This is clearly stated in Wilczek's lightness of being.
...

Sure. But it is still a very interesting 5%.
I want to communicate to a first-time questioner that the origins of mass are a current focus of research. And not say so much that it scares them away.

I have Wilczek's book and like it. I know his message about reformulating the question in terms of lightness "why is the proton so light". For me it goes back to three Scaling Mount Planck essays he had in Physics Today---quite a few years back now!

You have very good additional points to raise, Humanino! Let's see if the first-timer comes back and wants to ask some more, and if so, bring all these things up.

 

[JK423]

I watched Wilczek's lecture that you proposed and it was really great...
Great way to spend an hour. Teaches you a lot!

 

[TFT]

In QFT, mass is just a coupling constant.

 

[Bob S]

I've been confused on why mass is such an essential component to understanding the physical relationships that we experience. From my limited understanding I want to believe that I can recognize the significance of general relativity, special, the various quantum functions, among recent advancements. I've heard the standard model called a mathematical mess but I don't quite get why. The complexity of the formula itself makes sense to me with there being such a diverse number of forces to account for. With the infinities present in the standard model yielding a possibility of infinite gravitational forces, it seems to me like it would be a statistical anomale. .

Gravity is not required to understand the presence of mass. All e/m measurements on charged particles in magnetic fields are a balance of the inertia of charged particle "mass" and Lorentz (Coulomb) v x B forces, giving rise to well understood curved trajectories of relativistic (and non relativistic) charged particles in cyclotrons, synchrotrons, magnetic beamlines, and even electrostatic deflectors.

Bob s

 

[Naty1]

I've been confused on why mass is such an essential component to understanding the physical relationships that we experience.

so are we...
the basic physical relationships revolve around mass,space,time,energy, and the four fundamental forces...but how they are intrinsically related to one another, how they all originated, whether they have a single "unified" origin is unknown.

I've heard the standard model called a mathematical mess but I don't quite get why.

Yes, to the extent it is a hodgepodge of different theories, artifically stuck together, like those of the three forces plus relativity plus quantum mechanics; on the other hand we can explain a lot of the particles and their interactions around us...so we have made great progress such as in combining the strong,weak and electromagnetic forces...but it sucks because nobody knows exactly how gravity fits...Lee Smolin's THE TROUBLE WITH PHYSICS is an inexpensive current book on many of the current issues in physics, without a lot of mathematical sophistication...but with the conceptual issues faced...

 

[bapowell]

In QFT, mass is just a coupling constant.

Right. A coupling constant that requires the relatively complex machinery of spontaneous symmetry breaking to understand consistently. I think the questioner desires a deeper understanding than this

 

[cmc]

Most of the mass of nucleons (by far) is in the binding energy between the quarks. how does the standard model state how to find this bindng energy (fundamentally, not by subtracting the total from the constituents)?

 

[ansgar]

Most of the mass of nucleons (by far) is in the binding energy between the quarks. how does the standard model state how to find this bindng energy (fundamentally, not by subtracting the total from the constituents)?

from QCD... the masses of hadrons can and have been calcluated using something called Lattice QCD... the results are in delicate agreement with data

 

[ansgar]

In QFT, mass is just a coupling constant.

no one does not call the mass a coupling constant, one calls it "mass parameter" since it sits in front of the mass term

 

[ansgar]

Right. A coupling constant that requires the relatively complex machinery of spontaneous symmetry breaking to understand consistently. I think the questioner desires a deeper understanding than this

not in general.. only if you consider gauge theories and chiral theories

 

[cmc]

from QCD... the masses of hadrons can and have been calcluated using something called Lattice QCD... the results are in delicate agreement with data

Anyone have citations to examples of the calculations?

 

[ansgar]

Anyone have citations to examples of the calculations?

http://www.sciencemag.org/cgi/content/short/322/5905/1224PGD ( http://pdg.lbl.gov/2009/download/rpp-2008-plB667.pdf 40MB!) chapter 14.6

http://en.wikipedia.org/wiki/Lattice_QCD

or just google for yourself...

 

[cmc]

http://www.sciencemag.org/cgi/content/short/322/5905/1224


PGD ( http://pdg.lbl.gov/2009/download/rpp-2008-plB667.pdf 40MB!) chapter 14.6

http://en.wikipedia.org/wiki/Lattice_QCD

or just google for yourself...

Newtonian theory gives us calculation accuracy to send satellites to Saturn - millions of miles away. QED gives calculation accuracy for atomic spectra for thouands of atomic electron energy levels. And anyone can calculate them for themselves to verify claims. Physics textbooks is where the meat is found. The internet only touches on subjects. I have many physics QCD textbooks, but none with binding energy calculations. The websites cited don't have calculations. Anyone else have any text citations for me?

 

[ansgar]

Newtonian theory gives us calculation accuracy to send satellites to Saturn - millions of miles away. QED gives calculation accuracy for atomic spectra for thouands of atomic electron energy levels. And anyone can calculate them for themselves to verify claims. Physics textbooks is where the meat is found. The internet only touches on subjects. I have many physics QCD textbooks, but none with binding energy calculations. The websites cited don't have calculations. Anyone else have any text citations for me?

The calculations are of course very complicated and has to be performed on large computers, I suggest you get a couple of books and lecture notes on Lattice QCD.

In principle everybody can calculate masses of hadrons too, there are no secrets in science (or what are you suggesting?), but this calculation is 1000 times more involved than QED calculations

also PDG is not "just something you find on the internet" it IS the particle physics "bible". And the article I gave you is contemporary research, just as QED was in the 1950's

 

[tom.stoer]

There are good papers in arxiv; have a look at Ab-initio Determination of Light Hadron Masses

 

[ansgar]

Also I would say that it is on the internet one can found the real stuff, long calculations etc, textbooks just sketch.

 

[cmc]

The PDG pdf file won't load on my computer.
And i am suggesting that the SU(3)xSU2)xU(1) group structure and weinberg-salam lagrangian get more credit than they deserve. The fundamentals must be simple. Complexity comes from the intricacies of manifestation of instantiation.
Newton's laws are simple. Hamiltonian dynamics of systems is complex (yet based on Newton's).
QED, based on the "relatively simple" Dirac equation & Schroedinger equation.
Complexity comes from the tasks of calculating cross sections and dealing with the integrals of the Hilbert spaces involved in the solution spaces of the equations - for things like annhilation operators, and relating them to Feynman diagrams, etc.
For example, quarks have 3 colors. It doesn't take an SU(2) to make a model with 3 elements.
I think more money should be being spent developing mathematical foundations (besides string theory, supersymmetry and the GUTs that have already monopolized the funding without success after 20+ years), than building bigger accelerators.
For example, the Dirac equation is not the only set of linear differential equations consistent with the Klein-Gordon equation. Another may be found at:
http://www.mathematicalphysicsinstitute.org/documents/aFreshRelativisticWaveEquation3.pdf .

 

[ansgar]

The PDG pdf file won't load on my computer.
And i am suggesting that the SU(3)xSU2)xU(1) group structure and weinberg-salam lagrangian get more credit than they deserve. The fundamentals must be simple. Complexity comes from the intricacies of manifestation of instantiation.
Newton's laws are simple. Hamiltonian dynamics of systems is complex (yet based on Newton's).
QED, based on the "relatively simple" Dirac equation & Schroedinger equation.
Complexity comes from the tasks of calculating cross sections and dealing with the integrals of the Hilbert spaces involved in the solution spaces of the equations - for things like annhilation operators, and relating them to Feynman diagrams, etc.
For example, quarks have 3 colors. It doesn't take an SU(2) to make a model with 3 elements.
I think more money should be being spent developing mathematical foundations (besides string theory, supersymmetry and the GUTs that have already monopolized the funding without success after 20+ years), than building bigger accelerators.
For example, the Dirac equation is not the only set of linear differential equations consistent with the Klein-Gordon equation. Another may be found at:
http://www.mathematicalphysicsinstitute.org/documents/aFreshRelativisticWaveEquation3.pdf .

1) QCD IS simple from a symmetry perspective, it is just the 3 dimensional (in field space) analogy to QED, the equations maybe quite complicated, but the REAL physics - the symmetry is simple.

2) QCD makes perfect match with experiemts

Your concern is that "theory is too difficult", but that is subjective, for me QCD is as simple as Newtonian gravity.

QCD is SU(3) not SU(2)... you want to have your theory local in space-times to preserve causality, then you postulate the existence of 3 quantum numbers called "colour" and derive the properties of such quantum field theory just as you do for QED (where you only have one number - the electric charge, i.e a local U(1)) and compare with experiment

I think more money should be spend on getting people - like you - to understand theory...

 

[cmc]

There are good papers in arxiv; have a look at Ab-initio Determination of Light Hadron Masses

nice article, but wher's the mathematics?

 

[cmc]

Also I would say that it is on the internet one can found the real stuff, long calculations etc, textbooks just sketch.

That's not my experience.

 

[ansgar]

nice article, but wher's the mathematics?

why not try to derive it four yourself or mail the authors?

One could not find the calcluations for QED processes in the 40-50's in ordinary textbooks.. that was too complicated to be publised.

The calculations in lattice qcd takes place on huge computers which have to be running for a loooong time, the lattice qcd is basically just to discretize space time and solve the QCD equations, so each iteration is "simple" but the total calculation is very intricated. From your precious pdf:

"And, why is the wave function for the Dirac equation expressed in iso-spin space, rather than real
space, like Maxwell's equations are?"

is wrong, dirac equation is in space-time, the spin 1/2 arises naturally since the Lorentz Group is isomorpic to SU(2)xSU(2)...

To me, it just seems that you are not willing to study and find things on your own, even though I showed you a code for calculating the mass of the proton, you would not understand it if you didn't know about Lattice QCD, so why beeing a troublemaker?Also you are confused on "mathematics" and "calculations"...

 

[ansgar]

That's not my experience.

Look for instance in sheres intro do ChPT lecture notes, there are much longer derivations there then you will find in any book on ChPT on the market.

 

[tom.stoer]

nice article, but wher's the mathematics?

http://arxiv.org/abs/hep-lat/9807028" - or try the search function with introduction, review etc. in arxiv / hep-lat

 

[humanino]

I think more money should be spend on getting people - like you - to understand theory...

+1

cmc : naive criticism without concrete proposal deserves a more humble tone. It is clear that you have a very limited understanding of professional activity in this business. It is unclear whether the link you posted claims anything new. There is nothing new in there. It's not even published, it's not even correct, it was created with uselessly expensive software, and it does not deserve a second of attention from a professional.

If you want references, please request for them politely.

 

[humanino]

I have many physics QCD textbooks, but none with binding energy calculations.

Please provide a list of the QCD textbooks you have read.

 

[cmc]

Look for instance in sheres intro do ChPT lecture notes, there are much longer derivations there then you will find in any book on ChPT on the market.

Take alook at ay book ny Walter Grenier and you'll see good math in a physics book.
In hig schol and college, math and physics texts have good derivations of subject matter. Articles are more word than derivation - probably because journalists and CEOs are running them.

 

[cmc]

why not try to derive it four yourself or mail the authors?

One could not find the calcluations for QED processes in the 40-50's in ordinary textbooks.. that was too complicated to be publised.

The calculations in lattice qcd takes place on huge computers which have to be running for a loooong time, the lattice qcd is basically just to discretize space time and solve the QCD equations, so each iteration is "simple" but the total calculation is very intricated.


From your precious pdf:

"And, why is the wave function for the Dirac equation expressed in iso-spin space, rather than real
space, like Maxwell's equations are?"

is wrong, dirac equation is in space-time, the spin 1/2 arises naturally since the Lorentz Group is isomorpic to SU(2)xSU(2)...

To me, it just seems that you are not willing to study and find things on your own, even though I showed you a code for calculating the mass of the proton, you would not understand it if you didn't know about Lattice QCD, so why beeing a troublemaker?


Also you are confused on "mathematics" and "calculations"...

The wavefunction is in isospin space.

 

[cmc]

The wavefunction is in isospin space.

Didn't I start out with request for citations of calculations examples so I could calculate some others for myself?

 

[cmc]

1) QCD IS simple from a symmetry perspective, it is just the 3 dimensional (in field space) analogy to QED, the equations maybe quite complicated, but the REAL physics - the symmetry is simple.

2) QCD makes perfect match with experiemts

Your concern is that "theory is too difficult", but that is subjective, for me QCD is as simple as Newtonian gravity.

QCD is SU(3) not SU(2)... you want to have your theory local in space-times to preserve causality, then you postulate the existence of 3 quantum numbers called "colour" and derive the properties of such quantum field theory just as you do for QED (where you only have one number - the electric charge, i.e a local U(1)) and compare with experiment

I think more money should be spend on getting people - like you - to understand theory...

I thought it was against the rules to attack or insult other posters.
Anyway. To the casual observer the qcd lagrangian is not simple compare to classical gravity or electromagnetism - taught in hig hool and te ist years of colege - not subjective. Even the wave equations of general relativity are elementary compared to the qcd lagrangian.
And look publication up in any legal dictionary.

 

[cmc]

http://arxiv.org/abs/hep-lat/9807028" - or try the search function with introduction, review etc. in arxiv / hep-lat

Thanks. This looks useful.