If you are aware of an interesting new academic paper (that has been published in a peer-reviewed journal or has appeared on the arXiv), a conference talk (at an official professional scientific meeting), an external blog post (by a professional scientist) or a news item (in the mainstream news media), which you think might make an interesting topic for an FQXi blog post, then please contact us at forums@fqxi.org with a link to the original source and a sentence about why you think that the work is worthy of discussion. Please note that we receive many such suggestions and while we endeavour to respond to them, we may not be able to reply to all suggestions.

Please also note that we do not accept unsolicited posts and we cannot review, or open new threads for, unsolicited articles or papers. Requests to review or post such materials will not be answered. If you have your own novel physics theory or model, which you would like to post for further discussion among then FQXi community, then please add them directly to the "Alternative Models of Reality" thread, or to the "Alternative Models of Cosmology" thread. Thank you.

Please also note that we do not accept unsolicited posts and we cannot review, or open new threads for, unsolicited articles or papers. Requests to review or post such materials will not be answered. If you have your own novel physics theory or model, which you would like to post for further discussion among then FQXi community, then please add them directly to the "Alternative Models of Reality" thread, or to the "Alternative Models of Cosmology" thread. Thank you.

Contests Home

Current Essay Contest

Previous Contests

**Undecidability, Uncomputability, and Unpredictability Essay Contest**

*December 24, 2019 - April 24, 2020*

Contest Partners: Fetzer Franklin Fund, and The Peter and Patricia Gruber Foundation

read/discuss • winners

**What Is “Fundamental”**

*October 28, 2017 to January 22, 2018*

*Sponsored by the Fetzer Franklin Fund and The Peter & Patricia Gruber Foundation*

read/discuss • winners

**Wandering Towards a Goal**

How can mindless mathematical laws give rise to aims and intention?

*December 2, 2016 to March 3, 2017*

Contest Partner: The Peter and Patricia Gruber Fund.

read/discuss • winners

**Trick or Truth: The Mysterious Connection Between Physics and Mathematics**

*Contest Partners: Nanotronics Imaging, The Peter and Patricia Gruber Foundation, and The John Templeton Foundation*

Media Partner: Scientific American

read/discuss • winners

**How Should Humanity Steer the Future?**

*January 9, 2014 - August 31, 2014*

*Contest Partners: Jaan Tallinn, The Peter and Patricia Gruber Foundation, The John Templeton Foundation, and Scientific American*

read/discuss • winners

**It From Bit or Bit From It**

*March 25 - June 28, 2013*

*Contest Partners: The Gruber Foundation, J. Templeton Foundation, and Scientific American*

read/discuss • winners

**Questioning the Foundations**

Which of Our Basic Physical Assumptions Are Wrong?

*May 24 - August 31, 2012*

*Contest Partners: The Peter and Patricia Gruber Foundation, SubMeta, and Scientific American*

read/discuss • winners

**Is Reality Digital or Analog?**

*November 2010 - February 2011*

*Contest Partners: The Peter and Patricia Gruber Foundation and Scientific American*

read/discuss • winners

**What's Ultimately Possible in Physics?**

*May - October 2009*

*Contest Partners: Astrid and Bruce McWilliams*

read/discuss • winners

**The Nature of Time**

*August - December 2008*

read/discuss • winners

Current Essay Contest

Previous Contests

Contest Partners: Fetzer Franklin Fund, and The Peter and Patricia Gruber Foundation

read/discuss • winners

read/discuss • winners

How can mindless mathematical laws give rise to aims and intention?

Contest Partner: The Peter and Patricia Gruber Fund.

read/discuss • winners

Media Partner: Scientific American

read/discuss • winners

read/discuss • winners

read/discuss • winners

Which of Our Basic Physical Assumptions Are Wrong?

read/discuss • winners

read/discuss • winners

read/discuss • winners

read/discuss • winners

Forum Home

Introduction

Terms of Use

RSS feed | RSS help

Introduction

Terms of Use

*Posts by the author are highlighted in orange; posts by FQXi Members are highlighted in blue.*

RSS feed | RSS help

RECENT POSTS IN THIS TOPIC

**Brian Beverly**: *on* 1/18/09 at 3:47am UTC, wrote Dear Cha-Hsiung Tze, You are absolutely right there is not typo my...

**Chia-Hsiung Tze**: *on* 12/9/08 at 6:23am UTC, wrote Dear Brian Beverly, Glad that you like where our essay is going....You are...

**Cristi Stoica**: *on* 12/8/08 at 8:55am UTC, wrote Dear Drs. Jejjala, Kavic, Minic and Tze, I was impressed by the...

**Tevian Dray**: *on* 12/7/08 at 19:25pm UTC, wrote A very clear discussion of the fundamental differences between time in...

**Djordje Minic**: *on* 12/7/08 at 2:52am UTC, wrote I agree with you as long as we do not talk about quantum theory of gravity....

**Rahul Kulkarni**: *on* 12/7/08 at 2:32am UTC, wrote Your essay made for very interesting reading, although most of it was...

**Brian Beverly**: *on* 11/25/08 at 20:18pm UTC, wrote I have read your paper a few times and I think I like where it is going,...

**Hsiung Chia Tze**: *on* 11/24/08 at 9:32am UTC, wrote **Essay Abstract** We present a novel perspective on the problem of...

RECENT FORUM POSTS

**Steve Dufourny**: "ps the clifford algebras also are important in my theory, the aim being to..."
*in* Is Causality Fundamental?

**Steve Dufourny**: "what I find relevant is that he try to unify the electromagnetism and this..."
*in* Is Causality Fundamental?

**Steve Dufourny**: "Hi Mr Snowdon, I beleive indeed that there is a link with the rotations of..."
*in* The Nature of Time

**Jim Snowdon**: "Hi Steve, We are inclined to assume that time exists, as the..."
*in* The Nature of Time

**Steve Dufourny**: "I repeat this simple general intuitive idea, what are your thoughts? .... ..."
*in* Undecidability,...

**Steve Dufourny**: "You know Tejinder, I don t want to destroy the works of strings theorists,..."
*in* Undecidability,...

RECENT ARTICLES

*click titles to read articles*

**Lockdown Lab Life**

Grounded physicists are exploring the use of online and virtual-reality conferencing, and AI-controlled experiments, to maintain social distancing. Post-pandemic, these positive innovations could make science more accessible and environmentally-friendly.

**Is Causality Fundamental?**

Untangling how the human perception of cause-and-effect might arise from quantum physics, may help us understand the limits and the potential of AI.

**Building Agency in the Biology Lab**

Physicists are using optogenetics techniques to make a rudimentary agent, from cellular components, which can convert measurements into actions using light.

**Think Quantum to Build Better AI**

Investigating how quantum memory storage could aid machine learning and how quantum interactions with the environment may have played a role in evolution.

**Outside the Box**

A proposed quantum set-up that could predict your game-playing strategy resurrects Newcomb’s classic quiz show paradox.

RECENT FORUM POSTS

RECENT ARTICLES

Grounded physicists are exploring the use of online and virtual-reality conferencing, and AI-controlled experiments, to maintain social distancing. Post-pandemic, these positive innovations could make science more accessible and environmentally-friendly.

Untangling how the human perception of cause-and-effect might arise from quantum physics, may help us understand the limits and the potential of AI.

Physicists are using optogenetics techniques to make a rudimentary agent, from cellular components, which can convert measurements into actions using light.

Investigating how quantum memory storage could aid machine learning and how quantum interactions with the environment may have played a role in evolution.

A proposed quantum set-up that could predict your game-playing strategy resurrects Newcomb’s classic quiz show paradox.

FQXi FORUM

August 4, 2020

CATEGORY:
The Nature of Time Essay Contest (2008)
[back]

TOPIC: About Time by Hsiung Chia Tze [refresh]

TOPIC: About Time by Hsiung Chia Tze [refresh]

We present a novel perspective on the problem of time in quantum gravity. Inspired by Einstein's analysis of the concept of time and the equivalence principle and guided by the geometric structure of quantum theory, we offer new insights into the nature and the origin of time.

V. Jejjala: Ph.D. University of Illinois, Urbana-Champaign. Postdoctoral research associate, Institut des Hautes Etudes Scientifiques. Fields of interest: quantum field theory, string theory, quantum gravity, mathematical physics. M. Kavic: Ph.D candidate in physics, Virginia Tech. M.S. UNC-Chapel Hill. B.S. University of Minnesota, Fields of interest: quantum gravity, and astrophysics. D. Minic: Ph.D. University of Texas at Austin. Associate professor of physics, Virginia Tech. Fields of interest: quantum field theory, string theory, quantum gravity, mathematical physics and foundations of physics. C. H. Tze: Ph.D. University of Chicago. Emeritus professor of physics, Virginia Tech. Fields of interest: quantum field theory, mathematical physics and foundations issues in quantum theory.

I have read your paper a few times and I think I like where it is going, however, I find some of it is ambiguous. Would you mind clarifying some points?

I noticed you used the Schrodinger equation for a relativistic theory. The Dirac equation is typically the beginnings of relativistic quantum mechanics. When Maxwell's equations are applied to it we get into field theory. But your reason for not using field theory is microcausality and that local instead of global wavefunctions explains the big bang...? I had a little trouble following the argument to not use field theory.

I can't help but notice with the Schrodinger equation that global phase factors leave the physical predictions of wavefunctions unchanged. A local phase factor signifcantly changes the physical predictions of quantum mechanics.

I don't know if you inferred that the position-momentum uncertainty implied the time-energy uncertainty principle.

I know this is an essay contest so I hate asking for more derivations but I think a PDF post in the comments section would help me significantly.

The only mistake I noticed, more of a typo really, is that i is written as the square root of -1 instead of i "times" i = -1. The reason that is a "typo" is why I hate complex analysis in physics.

I noticed you used the Schrodinger equation for a relativistic theory. The Dirac equation is typically the beginnings of relativistic quantum mechanics. When Maxwell's equations are applied to it we get into field theory. But your reason for not using field theory is microcausality and that local instead of global wavefunctions explains the big bang...? I had a little trouble following the argument to not use field theory.

I can't help but notice with the Schrodinger equation that global phase factors leave the physical predictions of wavefunctions unchanged. A local phase factor signifcantly changes the physical predictions of quantum mechanics.

I don't know if you inferred that the position-momentum uncertainty implied the time-energy uncertainty principle.

I know this is an essay contest so I hate asking for more derivations but I think a PDF post in the comments section would help me significantly.

The only mistake I noticed, more of a typo really, is that i is written as the square root of -1 instead of i "times" i = -1. The reason that is a "typo" is why I hate complex analysis in physics.

Your essay made for very interesting reading, although most of it was beyond my ken :-) . I was intrigued by your take on the cosmological arrow of time. As it is usually stated, the puzzle lies in understanding why the Universe started in a *very* special part of phase space with extremely low entropy. However given that you accept that it started there, the arrow of time follows naturally and does not require modifying any basic laws of physics.

For simplicity, consider a classical universe. Then, the Gibbs entropy is a constant of motion and does not change (the quantum analog would be conservation of von Neumann entropy for a closed isolated system). The constancy of the (fine-grained) Gibbs entropy is nevertheless consistent with the arrow of time because the entropy that increases refers to a coarse-grained entropy (a la Boltzmann).

In your formalism, however, it seems as if even at the most fundamental(or fine-grained) level, entropy is not constant but increases. Is that correct? Also what is the explanation for the special starting point (a metric with vanishing distance between phase space points) in your theory i.e. as we go back in time why do we zero in on this special metric as opposed to any of the non-zero distance metrics? That, i.e. the initial condition, is the key to the cosmological arrow of time.

For simplicity, consider a classical universe. Then, the Gibbs entropy is a constant of motion and does not change (the quantum analog would be conservation of von Neumann entropy for a closed isolated system). The constancy of the (fine-grained) Gibbs entropy is nevertheless consistent with the arrow of time because the entropy that increases refers to a coarse-grained entropy (a la Boltzmann).

In your formalism, however, it seems as if even at the most fundamental(or fine-grained) level, entropy is not constant but increases. Is that correct? Also what is the explanation for the special starting point (a metric with vanishing distance between phase space points) in your theory i.e. as we go back in time why do we zero in on this special metric as opposed to any of the non-zero distance metrics? That, i.e. the initial condition, is the key to the cosmological arrow of time.

I agree with you as long as we do not talk about quantum theory of gravity. But when we do talk about quantum theory of gravity there is a clear tension between the way time features in the canonical quantum theory and the way time features in a theory in which apparently there is no time i.e. classical general theory of relativity. Similarly, I agree with what you say in every situation in...

view entire post

view entire post

A very clear discussion of the fundamental differences between time in relativity and in quantum mechanics. And a wonderful argument in favor of the geometric formulation of quantum theory. Geometry rules! The extension of phase space to Grassmanian is a profound and intriguing idea -- if perhaps a bit sophisticated for this audience.

Dear Drs. Jejjala, Kavic, Minic and Tze,

I was impressed by the well-documented and highly objective presentation of the difficulties encountered by the attempts of unifying the General Relativity (and cosmology) with the Quantum Theory. I particularly liked the geometric view on Quantum Mechanics you presented, your adjustment involving the non-linear Grassmannian, and the consequences you derive on the cosmologic and thermodynamic time arrows.

Best regards,

Cristi Stoica

“Flowing with a Frozen River”,

http://fqxi.org/community/forum/topic/322

I was impressed by the well-documented and highly objective presentation of the difficulties encountered by the attempts of unifying the General Relativity (and cosmology) with the Quantum Theory. I particularly liked the geometric view on Quantum Mechanics you presented, your adjustment involving the non-linear Grassmannian, and the consequences you derive on the cosmologic and thermodynamic time arrows.

Best regards,

Cristi Stoica

“Flowing with a Frozen River”,

http://fqxi.org/community/forum/topic/322

Dear Brian Beverly,

Glad that you like where our essay is going....You are right : this forum is not the appropriate place for derivations and long, technical explanations etc. For the latter I point you to the key papers given in the references section of our essay. My answers to your three questions are therefore very brief. I shall take them up in succession:

1. In the essay, the Schrodinger equation is over the complex projective phase space of pure quantum states and NOT , as we usually do, over spacetime. Time is primary in our scheme, in the cosmo0logical scheme of things it “predates” space which will be emergent as is envisioned in M-Theory. This means that Lorentz invariance is emergent ( e.g, relativistic wave field equations such as Dirac’s, Yang-Mills gauge fields etc. will be effective) and so is general coordinate invariance i.e spacetime emergent ( e.g. the spacetime metric , Einstein equations)

2. Relative phases are of course important as they account for quantum interference phenomena and they are fully accounted for in the geometric formulation of quantum mechanics.

3. There is no mistake and typo when it comes to i which, being the unit imaginary, is defined as the root of -1. Time is inherently bound to the complex structure of quantum mechanics. For someone who has meditated long on time, you may indeed have much to gain in revisiting, in casting a less hostile second look on complex analysis and complex differential geometry.

Glad that you like where our essay is going....You are right : this forum is not the appropriate place for derivations and long, technical explanations etc. For the latter I point you to the key papers given in the references section of our essay. My answers to your three questions are therefore very brief. I shall take them up in succession:

1. In the essay, the Schrodinger equation is over the complex projective phase space of pure quantum states and NOT , as we usually do, over spacetime. Time is primary in our scheme, in the cosmo0logical scheme of things it “predates” space which will be emergent as is envisioned in M-Theory. This means that Lorentz invariance is emergent ( e.g, relativistic wave field equations such as Dirac’s, Yang-Mills gauge fields etc. will be effective) and so is general coordinate invariance i.e spacetime emergent ( e.g. the spacetime metric , Einstein equations)

2. Relative phases are of course important as they account for quantum interference phenomena and they are fully accounted for in the geometric formulation of quantum mechanics.

3. There is no mistake and typo when it comes to i which, being the unit imaginary, is defined as the root of -1. Time is inherently bound to the complex structure of quantum mechanics. For someone who has meditated long on time, you may indeed have much to gain in revisiting, in casting a less hostile second look on complex analysis and complex differential geometry.

Dear Cha-Hsiung Tze,

You are absolutely right there is not typo my sincerest apology! I love where your essay is going! However, I disagree about time being related to the complex space. I took your advice and studied complex analysis again (my last course was 3 years ago) since you only responded to me I would hate to let that dialog die here is my "latest" argument:

The measurement problem in physics is where it is implied that imaginary time is ordered:

(...[-itn,...,-it2,-it1,0,it1,it2,...,itn]...)

The mathematical axioms tell us that complex numbers can not be ordered.

Order Axioms:

1) A number can not be less than itself

2) x > y, x < y, or x = y

3) if x > 0 and y > 0, then xy > 0

4) if x < y, then for all z, x + z < z + y

5) if x < y, then for all z, xz < yz

set x = i and y = 2i and z= 2 + i

1) makes sense

2) i < 2i makes sense

3) a bit tricky:

0 = 0 + 0i and i = 0 +1i therefore i>0 and 2i>0

(i)(2i) > 0 ---> -2 > 0 FALSE!

4) 2 + 2i < 2 + 3i (complex # is of the form a + bi)

5) This is the key axiom!

xz = what exactly? xz or x*z (* is complex conjugate i*=-i)

If we distribute xz as we do for real numbers then axiom 5 is false. If we take the complex conjugate x*z then axiom 5 is true.

Quantum mechanics relies on C* algebra which is ordered. What is the big idea of C* algebra? C*C, multiply a complex number by a complex conjugate and you end up with a real order/countable number.

By the axioms of math the measurement problem does not exist in physics.

From Wolfram's mathworld:

http://mathworld.wolfram.com/ComplexNumber.html

"Hi

storically, the geometric representation of a complex number as simply a point in the plane was important because it made the whole idea of a complex numbers more acceptable. In particular, "imaginary" numbers became accepted partly through their visualization. Unlike real numbers, complex numbers do not have a natural ordering, so there is no analog of complex-valued inequalities. This property is not so surprising however when they are viewed as being elements in the complex plane, since points in a plane also lack a natural ordering."

You are absolutely right there is not typo my sincerest apology! I love where your essay is going! However, I disagree about time being related to the complex space. I took your advice and studied complex analysis again (my last course was 3 years ago) since you only responded to me I would hate to let that dialog die here is my "latest" argument:

The measurement problem in physics is where it is implied that imaginary time is ordered:

(...[-itn,...,-it2,-it1,0,it1,it2,...,itn]...)

The mathematical axioms tell us that complex numbers can not be ordered.

Order Axioms:

1) A number can not be less than itself

2) x > y, x < y, or x = y

3) if x > 0 and y > 0, then xy > 0

4) if x < y, then for all z, x + z < z + y

5) if x < y, then for all z, xz < yz

set x = i and y = 2i and z= 2 + i

1) makes sense

2) i < 2i makes sense

3) a bit tricky:

0 = 0 + 0i and i = 0 +1i therefore i>0 and 2i>0

(i)(2i) > 0 ---> -2 > 0 FALSE!

4) 2 + 2i < 2 + 3i (complex # is of the form a + bi)

5) This is the key axiom!

xz = what exactly? xz or x*z (* is complex conjugate i*=-i)

If we distribute xz as we do for real numbers then axiom 5 is false. If we take the complex conjugate x*z then axiom 5 is true.

Quantum mechanics relies on C* algebra which is ordered. What is the big idea of C* algebra? C*C, multiply a complex number by a complex conjugate and you end up with a real order/countable number.

By the axioms of math the measurement problem does not exist in physics.

From Wolfram's mathworld:

http://mathworld.wolfram.com/ComplexNumber.html

"Hi

storically, the geometric representation of a complex number as simply a point in the plane was important because it made the whole idea of a complex numbers more acceptable. In particular, "imaginary" numbers became accepted partly through their visualization. Unlike real numbers, complex numbers do not have a natural ordering, so there is no analog of complex-valued inequalities. This property is not so surprising however when they are viewed as being elements in the complex plane, since points in a plane also lack a natural ordering."

Login or create account to post reply or comment.