Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

A Is spacetime orientation a convention?

  1. Apr 25, 2017 #1
    I thought this was an easy enough question but then I managed to obtain arguments both for and agaisnt it and confused myself. Is there a clear demonstrable answer to this question in relativistic field theory? Is spatial and temporal orientation a convention?
     
  2. jcsd
  3. Apr 25, 2017 #2

    Nugatory

    User Avatar

    Staff: Mentor

    What do you mean by "orientation"?
     
  4. Apr 25, 2017 #3

    martinbn

    User Avatar
    Science Advisor

    What do you mean by a convention?
     
  5. Apr 25, 2017 #4
    By orientation I refer to the usual right and left handed(or rght-chiral and left-chiral options for the space part and future versus past direction for the temporal part.

    The usual meaning in physics, the arbitrary(not dictated by nature or the physics) and chosen out of convenience agreed or convened picking of one of the possible orientations I refer to above.

    By spacetime(just in case) I mean an orientable lorentzian manifold.
     
  6. Apr 25, 2017 #5

    PeterDonis

    User Avatar
    2016 Award

    Staff: Mentor

    The spatial handedness and temporal orientation (which half of the light cones we call the "future" half) of a coordinate chart is a convention. But the spatial handedness of an actual, physical measuring device (such as a set of three mutually perpendicular rulers labeled "x", "y", and "z") and the temporal orientation of an actual clock (which direction along its worldline corresponds to its reading increasing) are not.
     
  7. Apr 25, 2017 #6
    Sure but my question was referring to coordinate independent relativistic theories in Minkowski spacetime (to be more specific). I guess by your remark about measuring devices that your answer is that orientation is not a convention in them.
     
  8. Apr 25, 2017 #7

    PeterDonis

    User Avatar
    2016 Award

    Staff: Mentor

    Which, I'm guessing, means you think the answer about coordinate charts is irrelevant, since we can always express such theories without choosing a coordinate chart.

    That is my answer, yes.
     
  9. Apr 25, 2017 #8

    pervect

    User Avatar
    Staff Emeritus
    Science Advisor

    By space-time orientation, do you mean that the space-time manifold is time orientable?

    I'm not sure I know the answer if that is the question. But it's not quite clear what the question is.
     
  10. Apr 25, 2017 #9

    PeterDonis

    User Avatar
    2016 Award

    Staff: Mentor

    There are manifolds that are not time orientable (I believe the Godel universe is one), but AFAIK none of them are considered physically reasonable.
     
  11. Apr 26, 2017 #10
    I reasoned along these lines, however mathematically Minkowski space is orientable(see below) and all tensorial fields on it respect this orientability by virtue of their tensorial transformation properties, while pseudotensors do preserve a preferred orientation but then these are not coordinate-independent.

    Both space and time orientable, and this orientability of Minkowski spacetime implies that any of the possible specific spacetime orientations of the spacetime and objects on it are ultimately conventional.
     
  12. Apr 26, 2017 #11

    PeterDonis

    User Avatar
    2016 Award

    Staff: Mentor

    Yes, but "orientable" is not the same as "having a preferred orientation". Orientable just means that one can make a continuous choice of time and space orientation--which half of the light cone is the future half, and which handedness the spatial axes have--throughout the spacetime. But either choice (for both time and space) will work in Minkowski spacetime; there is no specific choice "built into" it. So even though Minkowski spacetime is orientable, meaning you can choose an orientation, whatever orientation you actually choose is a convention.
     
  13. Apr 26, 2017 #12

    Paul Colby

    User Avatar
    Gold Member

    What about parity non-conservation in weak interactions? Your choice for the handedness of your coordinates may well be ones personal business, but the underlying physics does care.
     
  14. Apr 27, 2017 #13
    Yes
    Why do you say "but" ?, this is what I explained in #10. However in #7 your answer was that the orientation was NOT a convention.
     
  15. Apr 27, 2017 #14

    PeterDonis

    User Avatar
    2016 Award

    Staff: Mentor

    Is it? In #10 you said:

    If you had left out "and the objects on it", this would be the same thing as I said. But you put that extra phrase in, which makes a big difference.

    In #7 my answer was that the orientation of particular objects (measuring devices, but the same would apply to other objects) was not a convention. I did not say that assigning an "orientation" to spacetime itself (via a choice of coordinate chart) was not a convention.
     
  16. Apr 27, 2017 #15
    Ok, thanks for clarifying. You probably understood "in them" in #6 to be referring to the measuring devices while I meant the relativistic theories of the previous sentence. Typical forum communication hazards.

    So let me try and be more specific, by "the objects on it" I meant tensorial(such as scalar,vector and spinor fields) objects on Minkowski spacetime, are these fields's spacetime orientation in relativistic field theories conventional like the spacetime itself or not conventional like the "measuring devices" you mentioned. By the way, Paul Colby gave an example of a specific vector field witn non-conventional orientation. So one possible answer could be the option that objects with conventional and non-conventional orientation might coexist.
     
  17. Apr 27, 2017 #16

    PeterDonis

    User Avatar
    2016 Award

    Staff: Mentor

    Physical objects (and processes, see below) have a spacetime orientation that is not a convention. But you can choose to represent the same physical process in different ways mathematically. So I'm not sure how to answer the question of whether the orientation of the mathematical objects is a convention; it partly is (because of the freedom of choice in representation) and partly isn't (because the underlying physics being represented doesn't change).

    No, he gave an example of a specific physical process (weak interactions) in which the observed properties of the process (scattering cross sections, for example) depend on the orientation (parity) of the particles involved. But you can choose to represent this process in coordinates with either handedness, as he said.
     
  18. Apr 27, 2017 #17
    Right, this was the confused starting point I referred to in the OP. But to me this "partly is and partly isn't" answer is not quite satisfying because it seems a bit like having objects transforming partly like they should and partly like they shouldn't at the same time, it doesn't seem a consistent way to model the underlying physics.
    Does someone have a clue on how to address this in a more consistent manner?
     
  19. Apr 27, 2017 #18

    PeterDonis

    User Avatar
    2016 Award

    Staff: Mentor

    I wasn't talking about transformation properties, I was talking about a coordinate choice. You can have objects with scalar, vector, tensor, spinor, etc. transformation properties in a right-handed coordinate system or a left-handed coordinate system (and similarly for your choice of future/past light cones in the timelike case). Changing the orientation of the coordinates doesn't affect the transformation properties of any objects.

    If you are asking whether the transformation properties of a particular kind of object (scalar, vector, tensor, spinor, etc.) are a matter of convention, the answer is no. The transformation properties are what define each type of object. The only convention involved is your choice of what kinds of objects to use to represent a particular physical process; usually that depends on which aspects of the process you want to model and which ones you are willing to leave out.
     
  20. Apr 27, 2017 #19

    PeterDonis

    User Avatar
    2016 Award

    Staff: Mentor

    To illustrate this, we can look at the example of weak interactions. In the Standard Model, in order to capture the non-conservation of parity in weak interactions, left-handed and right-handed spinor fields (leptons and quarks) are treated differently: the left-handed fields are SU(2) doublets, while the right-handed fields are SU(2) singlets. However, for some purposes (cases in which parity non-conservation is not significant in whatever experiment you are modeling) the old Fermi model of weak interactions, which just had a four-fermion vertex with no intermediate gauge boson, might still be serviceable. In this model there is no difference between left-handed and right-handed spinor fields.
     
  21. Apr 27, 2017 #20
    I know, but just as long as you are consistent with the choice or the absence of choice for the objects on your theory, no? Or you mean that you can have objects modelling fixed handedness together with objects in wich the handedness is just dependent on the coordinate choice?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Is spacetime orientation a convention?
  1. Spacetime/Proper Length (Replies: 14)

  2. Spacetime and Gravity? (Replies: 13)

Loading...