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Physics, Astronomy & Cosmology / Two-Time Physics Questions
« on: 05/02/2021 16:57:40 »
This will be hard but please help me understand this pdf webhome.phy.duke.edu/~muller/Talks/Columbia_100412.pdf by answering these questions. I only need rephrasing of those technical statements in layman's terms.
1. On the 3rd page, what does it mean to implose a simplectic gauge constraints on states in D+2 dimensions? It says it renders time effectively 1-dimensional. How is it? Could 2 time dimensions always be perceived as 1D time?
2. Please explain the implications of spacetime interval on the 4th and 5th pages. How did that math work? Did we always travel in timelike trajectory and met ourselves in the past ready to start that journey? How is the worldline partly space like?
3. On the 10th page, it says motion in second time dimension is assumed to be regular, defined by initial condition, then it says small changes in initial conditions could lead to exponentially growing deviations. What is the meaning of this? How does finding a closed timelike loop become unlikely by this? Is the initial condition talking about the bold assumption that we have to move in both of the 2 dimensions all the time, or we could choose to move in one and not move in another? What is microcanonically ergodic and why should we consider one of the dimensions to be thermalized, what does it mean?
4. On the 11th page, it says energy is a two component vector in 2 timelike dimensions. How is it two component vector and what are its implications? Is it related to 5-velocity and 5-momentum and what are its implications? What are the implications of temperature becoming 2 component vector? How did temperature become 2 component vector? Please explain the whole 11th page about hot and cold time.
5. Please explain the pages from 13 to 22 in simple terms, I am specifically interested in understanding thermal stuff. How is it relating to entropy and thermal equilibrium?
6. Please explain the first two points on 25th page.
7. I can't even understand the questions posed on 29th page. Please rewrite those temperature questions in simple terms.
Please also tell me your insights on two time dimensions, and two time physics by Itzhak Bars and how he avoids stuff like closed time like loops.
1. On the 3rd page, what does it mean to implose a simplectic gauge constraints on states in D+2 dimensions? It says it renders time effectively 1-dimensional. How is it? Could 2 time dimensions always be perceived as 1D time?
2. Please explain the implications of spacetime interval on the 4th and 5th pages. How did that math work? Did we always travel in timelike trajectory and met ourselves in the past ready to start that journey? How is the worldline partly space like?
3. On the 10th page, it says motion in second time dimension is assumed to be regular, defined by initial condition, then it says small changes in initial conditions could lead to exponentially growing deviations. What is the meaning of this? How does finding a closed timelike loop become unlikely by this? Is the initial condition talking about the bold assumption that we have to move in both of the 2 dimensions all the time, or we could choose to move in one and not move in another? What is microcanonically ergodic and why should we consider one of the dimensions to be thermalized, what does it mean?
4. On the 11th page, it says energy is a two component vector in 2 timelike dimensions. How is it two component vector and what are its implications? Is it related to 5-velocity and 5-momentum and what are its implications? What are the implications of temperature becoming 2 component vector? How did temperature become 2 component vector? Please explain the whole 11th page about hot and cold time.
5. Please explain the pages from 13 to 22 in simple terms, I am specifically interested in understanding thermal stuff. How is it relating to entropy and thermal equilibrium?
6. Please explain the first two points on 25th page.
7. I can't even understand the questions posed on 29th page. Please rewrite those temperature questions in simple terms.
Please also tell me your insights on two time dimensions, and two time physics by Itzhak Bars and how he avoids stuff like closed time like loops.