Albrow2 loopu cartoon intro
What do I mean by a universe with “Closed Loop Time”? Mike Albrow, Fermilab Philosophers Dec 11th 2014 Start with just one space dimension z and one Kme dimension t Finite and bounded. Time has a beginning and an end; a point-‐like parKcle moves about on a line (speed always < c)
z’
Path (world-‐line) of a parKcle
z t’ t Special relaKvity (don’t mess with that!) says that z and t get mixed up when moKons are taken into account: t’ = γ(t – vx/c2) and x’ = γ(x-‐vt) Edges of space and end-‐points of Kme have serious conceptual problems. We can eliminate them:
Consequences or PredicKons
Based on hypotheses: No boundaries to spaceKme and no physical infiniKes: 1) The apparent accelerated expansion of the Universe (if true) must be temporary. There is no “for ever” by hypothesis. Might it also be “local” in space? 2) The Universe is closed, but perhaps “only just”, and Ω = 1 -‐ ε Presumably ε is just such as to allow a mulK-‐billion-‐year-‐old universe (anthropic). 3) The total energy of the Universe is ZERO. (No lines of gravitaKonal force go out) For the same reason the total charge ΣQ = 0 [N(p) = N(e)]. 4) Baryogenesis (U is all maler) could be essenKally “CPT” at the BCBB (~ pair creaKon) The γ/baryon raKo should be explainable without a “great annihilaKon” event. 5) The old quesKons “What happened before the Big Bang?” “Did Kme have a beginning, and will it have an end?” are moot (and you cannot fall off the edge of the Earth!) 6) The Big Crunch Big Bang (BCBB) is not a singularity (no infinitesimals!), can be very small. 7) There cannot be a singularity at the center of black holes either (same reason). Collapse stops at or above Planck scale.
1) Wrap space (z) into a cylinder by idenKfying opposite boundaries thus eliminaKng them. Space is sKll one-‐dimensional but is a ring. Space is finite with no boundaries
z z tA
t
tB
2) Wrap Kme into a torus thus idenKfying tA and tB thus eliminaKng beginnings and ends of Kme. Time is sKll one-‐dimensional but is a ring. Finite with no boundaries to space OR Kme. The whole physical universe (sKll one space dimension) is on the surface of this torus. Space and Kme are in this representaKon orthogonal, But in SR the t and x axes can be rotated by a boost.
Now graduate from one space dimension to two (x,z)
S2
Forget the lines, just showing a coordinate system, All points on the 2D surface are equivalent. To show Kme:
x
S2T
y
t Make Kme a closed loop as before. All of spaceKme is x,y,t (surface, not interior: Interior has a forbidden boundary !)
SKll only two space dimensions (and they can mix with Kme by boosts!)
Constrict area at one point to be very small: BCBB = Big Crunch Big Bang
Now graduate from two space dimensions to three (x,y,z) A simple way to see the 2-‐surface is finite but unbounded: Start anywhere (e.g. at a “pole”) and with a large supply of paint. Start painKng the surface in an increasing spiral palern. The convex outer edge becomes straight and then concave arer painKng half the surface. The concave radius decreases unKl the whole surface Is covered (apart from your feet!) Now we live in 3 space dimensions, start with a ball and cover it with a large (!) supply of tape. If the universe is finite but unbounded: Eventually the ball is so big the surface looks flat. Keep going! It will become concave and eventually you find yourself in a small cavity, having filled to universe with tape! No inside, no outside, no boundary, but a finite volume. S3 Einstein suggested that Now add a closed loop of Kme to this picture: S3T1 This is the whole of spaceKme! Finally Constrict S3 to be very small (not infinitesimal or a singularity, could be < 1 fm) at one (could be > 1 but no need) point on the Kme line. That is my proposed “topology of totality” (may be more dimensions on a Kny scale). Nothing happens “over and over again”. Events only occur once at (x,y,z,t)(‘) Albert: ApplicaKon of “Periodic Boundary CondiKons” at BCBB can constrain the cosmology
z’
Path (world-‐line) of a parKcle
z t’ t Special relaKvity (don’t mess with that!) says that z and t get mixed up when moKons are taken into account: t’ = γ(t – vx/c2) and x’ = γ(x-‐vt) Edges of space and end-‐points of Kme have serious conceptual problems. We can eliminate them:
Consequences or PredicKons
Based on hypotheses: No boundaries to spaceKme and no physical infiniKes: 1) The apparent accelerated expansion of the Universe (if true) must be temporary. There is no “for ever” by hypothesis. Might it also be “local” in space? 2) The Universe is closed, but perhaps “only just”, and Ω = 1 -‐ ε Presumably ε is just such as to allow a mulK-‐billion-‐year-‐old universe (anthropic). 3) The total energy of the Universe is ZERO. (No lines of gravitaKonal force go out) For the same reason the total charge ΣQ = 0 [N(p) = N(e)]. 4) Baryogenesis (U is all maler) could be essenKally “CPT” at the BCBB (~ pair creaKon) The γ/baryon raKo should be explainable without a “great annihilaKon” event. 5) The old quesKons “What happened before the Big Bang?” “Did Kme have a beginning, and will it have an end?” are moot (and you cannot fall off the edge of the Earth!) 6) The Big Crunch Big Bang (BCBB) is not a singularity (no infinitesimals!), can be very small. 7) There cannot be a singularity at the center of black holes either (same reason). Collapse stops at or above Planck scale.
1) Wrap space (z) into a cylinder by idenKfying opposite boundaries thus eliminaKng them. Space is sKll one-‐dimensional but is a ring. Space is finite with no boundaries
z z tA
t
tB
2) Wrap Kme into a torus thus idenKfying tA and tB thus eliminaKng beginnings and ends of Kme. Time is sKll one-‐dimensional but is a ring. Finite with no boundaries to space OR Kme. The whole physical universe (sKll one space dimension) is on the surface of this torus. Space and Kme are in this representaKon orthogonal, But in SR the t and x axes can be rotated by a boost.
Now graduate from one space dimension to two (x,z)
S2
Forget the lines, just showing a coordinate system, All points on the 2D surface are equivalent. To show Kme:
x
S2T
y
t Make Kme a closed loop as before. All of spaceKme is x,y,t (surface, not interior: Interior has a forbidden boundary !)
SKll only two space dimensions (and they can mix with Kme by boosts!)
Constrict area at one point to be very small: BCBB = Big Crunch Big Bang
Now graduate from two space dimensions to three (x,y,z) A simple way to see the 2-‐surface is finite but unbounded: Start anywhere (e.g. at a “pole”) and with a large supply of paint. Start painKng the surface in an increasing spiral palern. The convex outer edge becomes straight and then concave arer painKng half the surface. The concave radius decreases unKl the whole surface Is covered (apart from your feet!) Now we live in 3 space dimensions, start with a ball and cover it with a large (!) supply of tape. If the universe is finite but unbounded: Eventually the ball is so big the surface looks flat. Keep going! It will become concave and eventually you find yourself in a small cavity, having filled to universe with tape! No inside, no outside, no boundary, but a finite volume. S3 Einstein suggested that Now add a closed loop of Kme to this picture: S3T1 This is the whole of spaceKme! Finally Constrict S3 to be very small (not infinitesimal or a singularity, could be < 1 fm) at one (could be > 1 but no need) point on the Kme line. That is my proposed “topology of totality” (may be more dimensions on a Kny scale). Nothing happens “over and over again”. Events only occur once at (x,y,z,t)(‘) Albert: ApplicaKon of “Periodic Boundary CondiKons” at BCBB can constrain the cosmology
