# Inertial frames and Parity symmetry

Do you think you could give me some helpful insight to a follow up question from the discussion of defining inertial frames:

I'm still having trouble figuring out a good way of incorporating parity violation into my intuition. If it wasn't for experiment showing otherwise, I probably would have lumped this symmetry in as a requirement from relativity. Throwing away a whole subclass of frames (right vs left handed coordinate systems) that could equally have been chosen as "inertial frames" is bothering me. We're forced to throw out one or the other, but the fact that we could choose, and even choose arbitrarily, whether we keep right or left handed coordinate systems bothers me.

Is there some way of looking at this that would be more insightful and not seem so adhoc?
I'm clearly still missing something, for this seems to destroy part of the beauty of SR.

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DrGreg
Gold Member
(I drafted the text below to appear in https://www.physicsforums.com/showthread.php?t=227627", but I think it still makes sense in this new thread.)

I know very little about the parity issue, but I guess you're just expecting a bit too much out of SR. To say all the laws of physics are the same for all inertial observers is just a little too sweeping. We already know that SR is only an approximation for GR (so it's not 100.000% true) and we also know GR is not 100% compatible with quantum theory either. (So probably neither are 100.000% true.)

If I understand you correctly, you would like a definition of "inertial frame" that includes all the inertial frames in our own universe, but excludes all the corresponding frames in a mirror-image parity-reversed universe (in which the left-handed helixes in our universe became right-handed in the other). Well, I suppose you could say there's an implicit understanding that we are talking about our universe only and not all possible universes!

By the way, are you aware of CPT-symmetry? I know no more than the article states, but I understand that a mirror-image parity-reversed universe with the direction of time reversed and full of anti-matter instead of matter (e.g. atoms with negatively charged nuclei surrounded by a cloud of positrons) would have exactly the same laws of physics as our own.

https://www.physicsforums.com/showthread.php?t=227627" you talked about the interpretation in terms of symmetry. There are actually some implicit postulates in relativity that aren't explicitly mentioned, such as time-translation symmetry, space-translation symmetry (homogeneity) and space-rotation symmetry (isotropy), although you might perhaps argue they are included within the first postulate. The effect of special relativity is to add Lorentz symmetry (and remove Galilean symmetry) from the list of symmetries in physics. I tentatively suggest that maybe some of the other symmetries (that I haven't mentioned in this paragraph) are "independent" of relativity, in the sense that relativity is just one ingredient in our recipe for the universe and we can add other ingredients as we wish so long as all the ingredients are mutually compatible. (So you can't add a Lorentz-violating ingredient.)

Or to get back to the postulates, the first postulate says all the laws of physics are the same for all inertial observers but doesn't specify what those laws are. So, as we try to construct a model of the universe, we can try lots of different potential laws of physics, but each law must be compatible with the relativity postulates. Whether the laws you choose are parity-symmetric or not isn't relevant to relativity per se, but it is relevant to modelling the real universe.

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I have been mulling this over for a bit, and one of your responses inspired a bit of insight for me (which I wrote at the end of this thread). Hopefully my new "insight" is correct, for I am trying to use it to help me fix my intuition on these matters.

If I understand you correctly, you would like a definition of "inertial frame" that includes all the inertial frames in our own universe, but excludes all the corresponding frames in a mirror-image parity-reversed universe (in which the left-handed helixes in our universe became right-handed in the other). Well, I suppose you could say there's an implicit understanding that we are talking about our universe only and not all possible universes!
There is no need for a different universe. It is not an issue of a parity-reverse universe, it is an issue of parity-reverse coordinate systems. We can choose either right handed or left handed coordinate systems to describe our universe. It is an arbitrary choice. But doing the transformation between these frames and we see that the physics isn't invarient to that transformation. So we have two viable choices, but not equivalent choices. The fact that the universe "cares" / distinguishes between these choices seems a bit odd to me, and thus makes our choice in order to distinguish them adhoc.

I know very little about the parity issue, but I guess you're just expecting a bit too much out of SR. To say all the laws of physics are the same for all inertial observers is just a little too sweeping. We already know that SR is only an approximation for GR (so it's not 100.000% true) and we also know GR is not 100% compatible with quantum theory either. (So probably neither are 100.000% true.)
I think that is somewhat of a cop-out answer since this problem arises even in flat spacetime.

But it did get me thinking... in GR, the lorentz symmetry of SR survives as a local symmetry. This shows how distinct parity transformations are... it's not possible to make that into a local symmetry! (that I can see anyway) Similarly with time reversal.

Now I don't feel so weird saying, as the theorist explained, that SR requires proper ortho-chronous lorentz symmetry. Previously, adding "proper" and "ortho" on the front seemed a bit adhoc to match experiment. Now I can actually see intuitively why extra transformations, which would be included if those words were removed, are distinct and shouldn't be lumped in there.

Does this make sense to anyone else? Or am I misunderstanding something, and deluding myself?

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JesseM