Ok, folks: yesterday’s first installment of my mass and energy article, discussing energy and momentum, has been extended with a second installment. Mass has made its appearance now, along with Einstein’s famous relations between energy, momentum, mass and speed, which are described and analyzed using… triangles. Yes, if you can remember what Pythagoras had to say about triangles, you can understand quite a lot about what Einstein was saying about relativity when he proposed his striking revision of Newtonian thinking. And I also address some obvious puzzles that bother everyone the first time they hear about this stuff…
The new material from today starts with the section marked “Mass … “.
5 thoughts on “Relativity for the Energetic Masses”
Matt, your ability of making such an abstract concept (such as mass and energy) an easy read is truly amazing. Thanks.
I do have a great sympathy for “aa. sh.” as he is obviously not a physicist. Of course, the conscious and the spiritual worlds are realities, and I do know (way beyond believe) that both of them are “sub-universes” of the physical one. That is, the physics laws must be the governing laws for those sub-universes. As the current physics laws are unable to describe those subworlds, it simply means that the current physics is still far from to be the final physics.
I also have a great sympathy for Brian Powell and for his view, “…but I can’t test them and so I can’t know them.” If the knowledge of human physics on the Nature physics is less than 80%, then Mr. Powell must be right, and we cannot gain any new knowledge of Nature physics without the verification by test after tests. However, if we already know more than 80% about the Nature physics, we should be able to organize it into an axiom system which has an internal “knowledge” checking mechanism, and the verification “testing” for an axiomatic sentence is no longer a must but is still nice to have as a “side”-evidence. Of course, this is hinged on how much we know about the Nature physics. And, this topic of “mass” can be an indicator for how much we know about the Nature physics. Thus, I would like to discuss about “mass” in terms of the pathways of knowing it in addition to Matt’s great post which is about what we already know about it.
1. In physics, mass was “first” defined only with an operational definition, that is, with measurement, either for accelerating mass or gravitational mass. The epistemology for this is the “interplay of theory and test”, and it can be called as T-physics.
2. After we learned enough from the T-physics, we can organize that knowledge as an axiomatic system, the knowledge physics (K-physics in short). Of course, the epistemology here can be different, by using the rules of axiom system. Thus, the mass or energy can be defined with some axiomatic sentences (or equations). Among the fundamental parameters (time, space, mass, energy, electric charge, etc.) of this K-physics, the electric charge is obviously a derived parameter as it can be written as a function of h-bar and c (light speed). There are also two axiomatic sentences for energy.
a. Einstein, E = mc^2
b. Planck, E = h-bar v(frequency)
If we combine the two axiomatic sentences above, the mass can also be expressed as a function of h-bar and c. That is, the mass and the electric charge differ only in degree, not in kind. Thus, if we can truly understand the definition of mass in this way, it might lead us to a true Super Unification.
Matt has mentioned three different types of energy, the motion energy (in terms of momentum), the rest energy (mass) and the relational energy. If (a big if) there is a Super Unification in the Nature physics, those three types of energy must be unified first. Thus, in addition to Einstein’s E = mc^2 which transforms “mass” into energy, the energy (a massless particle) must be able to become (acquire) “massive”. That is, there must be a mass-rising mechanism.
3. In the marco-world, the mass is simply the aggregate of a pile of elementary particles. Thus, by understanding the mass-rising mechanism for elementary particles, we will know exactly what the “mass” is. There are, at least, two mass-rising mechanisms in discussion, the Higgs-mechanism and the See-Saw mechanism. Basically, if the associated symmetry for a particle is not broken, that particle is massless (no rest mass). Thus, those mechanisms are symmetry breaking procedures. And, the Higgs boson supposes to be the actor in the Higgs-mechanism. Is there a Standard Model Higgs in the Nature physics? This question could be answered in just a few more months with LHC’s upcoming “test” data.
However, with the K-physics (the axiom system of human physics), it can be easily deduced that if (again, a big if) there is Super Unification in the Nature physics, there should be one and only one mass-rising mechanism, not two or many. Thus, both Higgs-mechanism and the See-Saw mechanism are at best the shadows of the real one.
4. While those two mass-rising mechanisms are still under testing, there are some concrete parameters which did give the precise calculation for the mass of weak bosons, the Cabibbo angle (θc about 13 degrees) and the Weinberg angle (θW from 28 to 30 degrees) . The values of these two angles are free parameters in the Standard Model, that is, they were forced into the model with the demand of fitting the data and had no theoretical base for them. Thus, if these two angles can be calculated theoretically, then the “physics” which provides those calculations should be able to give “mass” a theoretical definition.
In my view, as soon as we can give “mass” a theoretical and axiomatic definition, we will know the mass-rising mechanism in detail and can construct a final gravity theory easily. Then, the questions of “dark matter” and of “why is the universe accelerating during its expansion?” will be answered.
TZG: I am sorry, but could I ask you, please, to try to keep your comments shorter and more focused? Today’s article is aimed at laypeople who have not learned particle physics already and are not in a position to understand (and potentially disagree with) your more speculative points. I would especially ask you to make clearer in future that K-physics (along with some of the other ideas in your past comments) is your own personal speculative idea, not something shared with a large physics community. Please keep in mind that this site is aimed not at spreading speculations (which is why there isn’t lots of discussion of all the wacky ideas physicists kick around over beer, and almost nothing about my own wacky ideas) but rather at explaining core established ideas and research directions to a wide audience.
Matt: truly sorry. Thanks for your great blog which does good job for explaining the core established ideas of physics, and I do enjoy it.
I can’t seem to access your new article on mass. Is it still unfinished?
Just wondering, Can’t wait! 😀
Hmm — what is going wrong when you try to access it?
It’s the second half of
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