4

I have just found out that in order to modify mass in his special theory of relativity, Einstein assumed that energy and momentum are always conserved.$^\dagger$ I think surely there are other ways to fit the data. It makes me wonder: is there a fundamental reason for symmetry in nature? and why are there so many symmetries in nature?

Besides, I wonder whether physicists still assume symmetry today in their own cutting-edge research.

$^\dagger$ In the language of analytical mechanics, energy-momentum conservation corresponds to spatial and time translation symmetries. In other words, it doesn't matter when and where you measure the Lagrangian, you get the same result.

innisfree
  • 15,147
Shing
  • 2,774
  • 1
    You could consider adding a term that breaks translational symmetry in the Lagrangian. Then you don't have momentum conservation. However, you should then also consider that the Lagrangian you use in practice is only an effective Lagrangian, it only describes the physics up to certain length scales. To get the effective Lagrangian from a fundamental Lagrangian involves integrating out the degrees of freedom we don't consider in the effective theory. This process is called renormalization. Now, it turns out that symmetry breaking terms typically tend to zero under renormalization. – Count Iblis Aug 06 '15 at 02:08
  • "why Physicists always prefer symmetry, given other possibility"...show me the other possibilities. – ACuriousMind Aug 06 '15 at 11:23
  • "fit-in-data-type possibilities" is trivial. I am not sure if that's what you are asking. if you are interested, you may take a look in history of science, many brave souls have tried but in vain. – Shing Aug 07 '15 at 02:30
  • 2
    one of the non-trivial (but very unlikely) possibility is "all symmetries will break tomorrow." So I want to know whether or not if there is fundamental reason for symmetry. If no, then we will have to get over it - we will have to assume symmetry will not break; if yes then symmetry will not break, as long as the fundamental reasons hold. edged: in h bar, member told me there is no such reason so far. – Shing Aug 07 '15 at 02:51
  • 3
    Personally, I think "why are there so many symmetries in the physical world" is a really interesting question, and a very clear one. It's one of those questions where you think, "huh, I never even thought of asking that before, but I'd really like to know if anyone has attempted to answer it." So I'm voting to reopen. – N. Virgo Aug 07 '15 at 04:13
  • 1
    Symmetries help us get to concise descriptions of the World in many ways, by data compression and also through conservation laws arising through Noether's theorem, as you clearly understand by your last sentence. Unfortunately once most scientists (this one included) get hold of a unifying law whose predictive power arises from symmetries, they tend to be reluctant to question that source of power! And I don't think I ever thought about explicitly about that reluctance till you asked this question, which is both a startling and an excellent one. – Selene Routley Aug 07 '15 at 10:26
  • 2
    Maybe we physicists tend to be of a certain broad mindset that likes symmetry. There's a correlation between a like of symmetry and asperger traits :) Maybe therefore we cluster around symmetry because it is genuinely part of nature but it could be that our personalities lead us to the branch of science that tends to occupy itself with the simplest and most symmetric things in the World this is especially so for mathematical physics. Those whose personality can brook more symmetry breaking perhaps go in for harder, complexer, messier stuff like biology. VERY broad generalizations but .. :) ! – Selene Routley Aug 07 '15 at 10:35
  • The question is unclear because most of these symmetries "aren't in nature", they are in our description of it. E.g. every gauge symmetry may in principle be eliminated by solving the constraints it represents, it's just that that doesn't make the description easier, it makes it harder to work with. Also, it doesn't matter whether we do experiments here or there, or today and tomorrow, so time- and spatial translation invariance arise very naturally. I don't know what it means to ask "why" they are there. Related: This Feynman talk – ACuriousMind Aug 07 '15 at 12:32
  • It is a physics question, although it can be "answered" by philosophy. Asking why symmetry is not asking why nature obey physics law, but asking "what are the causes?" "How is it the way it is instead of the other way around?". Given Dirac once suggests that our universal constant can be possibly change over time, as universe is expanding. that means our laws of physics will change over time, and hence energy is not conserved at a cosmic time scale (a guess so far no positive experimental result). Symmetry is not something always taken for granted. – Shing Aug 10 '15 at 00:25
  • If we can ask why energy is conserved, and that leads us to symmetry, then why we can't ask why there is symmetry? Maybe that will lead us to another great happiness? Do I clarify my question? sorry for your confusion. The only problems with my question as I see is 1.) my lousy English (which is solved) 2.) too board. (but forgive me, I don't even start taking quantum physics course.) – Shing Aug 10 '15 at 00:29

0 Answers0