Is spacetime orientation a convention?

[RockyMarciano]

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?

 

[Nugatory]

What do you mean by "orientation"?

 

[martinbn]

What do you mean by a convention?

 

[RockyMarciano]

What do you mean by "orientation"?

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.

What do you mean by a convention?

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.

 

[PeterDonis]

Is spatial and temporal orientation a convention?

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.

 

[RockyMarciano]

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.

 

[PeterDonis]

my question was referring to coordinate independent relativistic theories in Minkowski spacetime

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.

I guess by your remark about measuring devices that your answer is that orientation is not a convention in them.

That is my answer, yes.

 

[pervect]

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.

 

[PeterDonis]

I'm not sure I know the answer if that is the question.

There are manifolds that are not time orientable (I believe the Godel universe is one), but AFAIK none of them are considered physically reasonable.

 

[RockyMarciano]

That is my answer, yes.

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.

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

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.

 

[PeterDonis]

Minkowski space is orientable(see below)

Both space and time orientable

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.

 

[Paul Colby]

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.

 

[RockyMarciano]

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.

Yes

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.

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.

 

[PeterDonis]

this is what I explained in #10

Is it? In #10 you said:

this orientability of Minkowski spacetime implies that any of the possible specific spacetime orientations of the spacetime and objects on it are ultimately conventional

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 your answer was that the orientation was NOT a convention

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.

 

[RockyMarciano]

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.

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.

 

[PeterDonis]

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

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).

Paul Colby gave an example of a specific vector field witn non-conventional orientation

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.

 

[RockyMarciano]

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).

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?

 

[PeterDonis]

it seems a bit like having objects transforming partly like they should and partly like they shouldn't at the same time

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.

 

[PeterDonis]

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.

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.

 

[RockyMarciano]

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.

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 which the handedness is just dependent on the coordinate choice?

 

[PeterDonis]

just as long as you are consistent with the choice or the absence of choice for the objects on your theory

I'm not sure what you mean. I was saying that changing your choice of coordinates doesn't change a spinor into a vector, or a left-handed spinor into a right-handed spinor, etc., etc. That's true regardless of what kind of object you choose to use to model a particular physical process.

objects in which the handedness is just dependent on the coordinate choice

AFAIK there are no such objects, except for the coordinates themselves. There are objects that don't have any "handedness" at all, but that doesn't depend on the coordinate choice either.

 

[RockyMarciano]

There are objects that don't have any "handedness" at all, but that doesn't depend on the coordinate choice either.

Right, those, they don't have a preferred handedness, for instance regular polar vectors. I meant mixing this objects with objects like chiral fermions(spinor fields) that do have non-conventional handedness.

 

[PeterDonis]

I meant mixing this objects with objects like chiral fermions(spinor fields) that do have non-conventional handedness.

You can do that, yes (the Standard Model does it).

 

[RockyMarciano]

You can do that, yes (the Standard Model does it).

Ok, I suppose this is an example of what you were saying about my question not having a clear answer because you have objects with orientation partly conventional and partly nonconventional together.
Thanks.

 

[vanhees71]

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).

I'm a bit puzzled by this statement. I understand that spacetime is (in a local sense) "orientable" in time, i.e., it is possible to define a causality structure in the sense that at any point in spacetime you can use a free-falling reference frame, where locally the laws of SRT are valid, and thus you have locally a Minkowski space, and you can define a tetrad, with the time-like basis vector defining the direction of "positive" time pointing to the future of the event (defining a future and past lightcone). The three space-like basis vectors may then define what you call a positive orientation (usually using the right-hand rule to be specific for us human beings, but it's still a definition or convention that you call that positive orientation). After that the orientation of any other three vectors is either positive or negative relative to the so defined positive orientation. The same holds for axial vectors defining rotational directions around a axis (again positive in the sense of a right-hand rule, which however, is convention).

The only way to establish a physically objective orientation of space is provided by the weak interaction, and (with some caveat) you can use neutrinos to define what's left- and right-handed (again by our convention, we call neutrinos in the standard model left-handed and antineutrinos right-handed; that's an objective definition of spatial orientation.

 

[PeterDonis]

"orientable" in time, i.e., it is possible to define a causality structure in the sense that at any point in spacetime you can use a free-falling reference frame, where locally the laws of SRT are valid, and thus you have locally a Minkowski space, and you can define a tetrad, with the time-like basis vector defining the direction of "positive" time pointing to the future of the event (defining a future and past lightcone).

Time orientable means more than that. It means that you can define a tetrad field on the entire spacetime such that the "future" direction defined by the timelike basis vector in each tetrad is continuous from event to event.

 

[vanhees71]

Ok, but isn't that a quite strong assumption? I thought, usually one considers local properties in GR.

I still don't get, what you mean by "Physical objects (and processes, see below) have a spacetime orientation that is not a convention." In which sense do you think a "right hand" is a right hand in a way that's not convention? The only thing I can say is that there's no continuous transformation to map my "right hand" into my "left hand" and vice versa. So the one hand is oriented oppositely to the other. Which one I call left and which one I call right is convention. The only physically objective way that comes to my mind is to use the weak interaction, defining a neutrino as "left handed". It's also a convention in a way, but making the definition objective in the sense that it is unique (as far as the standard model is strictly valid, but let's assume that for a moment) you can everywhere at any time and independently from any given convention determine, whether some chiral object is left or right handed.

 

[PeterDonis]

isn't that a quite strong assumption?

It's stronger than the basic assumption of the spacetime being locally Minkowski (which is what you described), yes. In practice I don't think it's very restrictive, since AFAIK all spacetimes of any physical interest are time orientable in the sense I described.

Which one I call left and which one I call right is convention.

Yes, but the fact that one cannot be continuously transformed into the other is not. So there are two orientations, which we can label however we want, and given any physical object, we can check which orientation it can be continuously transformed into and which one it can't. The result of this check is independent of any coordinate choice or any choice of labeling of orientations; that is the sense in which a physical object has an orientation that is not a convention. (The only complication here is that some objects, for example a perfect sphere, will not have an orientation in this sense.)

 

[martinbn]

It's stronger than the basic assumption of the spacetime being locally Minkowski (which is what you described), yes. In practice I don't think it's very restrictive, since AFAIK all spacetimes of any physical interest are time orientable in the sense I described.

If it is not orientable, a double cover will be, and the double cover is locally the same. I suppose that means that from a physics point of view, time orientability is not restrictive.

 

[RockyMarciano]

If it is not orientable, a double cover will be, and the double cover is locally the same.

I don't understand this sentence. The double cover is locally the same as what?