4 ms·

I believe it is possible that our universe is not orientable, and so there may exist closed paths which, if followed, reverse orientation upon returning to the

I believe it is possible that our universe is not orientable, and so there may exist closed paths which, if followed, reverse orientation upon returning to the starting point. If you were right-handed and traversed such a loop, you would now be left-handed relative to everyone else, everyone would agree your heart was on the "right" side of your body etc. In fact even Atiyah touches on this idea (though without speculating that it might be a property of our universe). In Mind, Matter and Mathematics, he says: "When I was a student in Cambridge our mathematical society invited a distinguished professor of philosophy, C.D. Broad, to give us an evening lecture. He chose to talk on a problem which had much exercised Kant, the difference between right-handed gloves and left-handed gloves. After the lecture, over dinner, I diffidently suggested to Broad that, since Kant’s time, we mathematicians had a much better understanding of “handedness”, or chirality as scientists call it. We could even envisage a universe in which a left-handed glove could wander around to distant regions and return to fit your right-hand. "

amelius 8y ago
But wouldn't that mean that the universe has an edge, like a Mobius strip has an edge?
- ocfnash 8y ago
  Good question, but no. For example the Klein bottle or real projective plane are closed surfaces containing no boundary. Incidentally the Mobius strip need not have a edge; you can leave out the boundary circle at the cost of having a non-compact space. This is exactly analogous to the difference between the closed and open intervals: [0, 1] vs (0, 1). In fact the projective plane can be obtained by taking a disc and glueing its boundary to that of the Mobius strip, which makes the two boundaries "cancel".
paulrouget 8y ago
I think left and right could not just be swapped seamlessly. Radioactive decay (beta) would behave differently. See Wu's experiment and parity violation.
- ramshorns 8y ago
  Meanwhile, a mirror organism, made of antimatter, who travels back in time like Benjamin Button, would be exactly the same as a regular organism. At least I think that's how CPT-symmetry works.
- ocfnash 8y ago
  Great point, I agree! It seems to me that the statement that Wu's experiment holds globally is equivalent to the statement that the universe has an orientation so I now tend to think the universe does not admit one of these orientation-reversing loops. At first I was surprised that we could apparently draw a global conclusion based on local observations but I've mostly convinced myself now based on the following analogy (which I hope is not misleading). Imagine we live in a two-dimensional universe and we want to know whether or not it is orientable. E.g., do we live on the surface of a torus or on the surface of a Klein bottle? We have defined a local orientation in the topologically-trivial patch where we live and so are used to speaking of "left-handed" and "right-handed" gloves. The question of whether these words are globally meaningful is exactly the question of whether our universe is orientable. One day we learn about "colour" and are stunned to discover that all left-handed gloves are red and all right-handed gloves are blue. It seems very unlikely to us that red somehow transitions into blue as we traverse a loop and so we conclude we must live in an orientable universe.
  - skinner_ 8y ago
    > It seems to me that the statement that Wu's experiment holds globally is equivalent to the statement that the universe has an orientation so I now tend to think the universe does not admit one of these orientation-reversing loops. Nice! I tried to play around with this. There's the https://en.wikipedia.org/wiki/Gold_universe https://en.wikipedia.org/wiki/Gold_universe where two inhabitants can honestly disagree about the direction of time. (And the interactions between the two are hilarious.) Can we have a version where one can go far away and come back time-reversed? Or is that excluded by CT=P symmetry breaking? It sounds like it, but it's confusing.
    - 8y ago
IIAOPSW 8y ago
Experimentally such a topology for the universe has already been ruled out below some insanely large scale. Otherwise when we look at the stars we would see repeating patterns.
antidesitter 8y ago
Yup. See the concept of a non-orientable wormhole and Alice universe: https://en.wikipedia.org/wiki/Non-orientable_wormhole#Alice_universe https://en.wikipedia.org/wiki/Non-orientable_wormhole#Alice_... An interesting consequence is that two particles may attract if brought together along one route, and repel if brought together along another.
type0 8y ago
> everyone would agree your heart was on the "right" side of your body etc. Heart on the right side is called Dextrocardia in this universe, so I guess it would be called "Levocardia" in the chiral universe.

amelius 8y ago

But wouldn't that mean that the universe has an edge, like a Mobius strip has an edge?

ocfnash 8y ago
Good question, but no. For example the Klein bottle or real projective plane are closed surfaces containing no boundary. Incidentally the Mobius strip need not have a edge; you can leave out the boundary circle at the cost of having a non-compact space. This is exactly analogous to the difference between the closed and open intervals: [0, 1] vs (0, 1). In fact the projective plane can be obtained by taking a disc and glueing its boundary to that of the Mobius strip, which makes the two boundaries "cancel".

paulrouget 8y ago

I think left and right could not just be swapped seamlessly. Radioactive decay (beta) would behave differently. See Wu's experiment and parity violation.

ramshorns 8y ago
Meanwhile, a mirror organism, made of antimatter, who travels back in time like Benjamin Button, would be exactly the same as a regular organism. At least I think that's how CPT-symmetry works.
ocfnash 8y ago
Great point, I agree! It seems to me that the statement that Wu's experiment holds globally is equivalent to the statement that the universe has an orientation so I now tend to think the universe does not admit one of these orientation-reversing loops. At first I was surprised that we could apparently draw a global conclusion based on local observations but I've mostly convinced myself now based on the following analogy (which I hope is not misleading). Imagine we live in a two-dimensional universe and we want to know whether or not it is orientable. E.g., do we live on the surface of a torus or on the surface of a Klein bottle? We have defined a local orientation in the topologically-trivial patch where we live and so are used to speaking of "left-handed" and "right-handed" gloves. The question of whether these words are globally meaningful is exactly the question of whether our universe is orientable. One day we learn about "colour" and are stunned to discover that all left-handed gloves are red and all right-handed gloves are blue. It seems very unlikely to us that red somehow transitions into blue as we traverse a loop and so we conclude we must live in an orientable universe.
- skinner_ 8y ago
  > It seems to me that the statement that Wu's experiment holds globally is equivalent to the statement that the universe has an orientation so I now tend to think the universe does not admit one of these orientation-reversing loops. Nice! I tried to play around with this. There's the https://en.wikipedia.org/wiki/Gold_universe https://en.wikipedia.org/wiki/Gold_universe where two inhabitants can honestly disagree about the direction of time. (And the interactions between the two are hilarious.) Can we have a version where one can go far away and come back time-reversed? Or is that excluded by CT=P symmetry breaking? It sounds like it, but it's confusing.
  - 8y ago

IIAOPSW 8y ago

Experimentally such a topology for the universe has already been ruled out below some insanely large scale. Otherwise when we look at the stars we would see repeating patterns.

antidesitter 8y ago

Yup. See the concept of a non-orientable wormhole and Alice universe: https://en.wikipedia.org/wiki/Non-orientable_wormhole#Alice_universe https://en.wikipedia.org/wiki/Non-orientable_wormhole#Alice_... An interesting consequence is that two particles may attract if brought together along one route, and repel if brought together along another.

type0 8y ago

> everyone would agree your heart was on the "right" side of your body etc. Heart on the right side is called Dextrocardia in this universe, so I guess it would be called "Levocardia" in the chiral universe.