Does thermal time hypothesis finally resolve Zeno's paradox?

Question

Is Time Just A Trick Of The Mind? (read article)

Carlo Rovelli, one of the founder of Loop Quantum Gravity theory likes to think so. Furthermore wikipedia entry highlights:

This position has lead him to face the following problem: if time is not part of the fundamental theory of the world, then how does time emerge? In 1993, in collaboration with Alain Connes, Rovelli has proposed a solution to this problem called the thermal time hypothesis. According to this hypothesis, time emerges only in a thermodynamic or statistical context. If this is correct, the flow of time is an illusion, one deriving from the incompleteness of knowledge.

Background: Aristotle to Zeno

Aristotle, who pioneered many fields, writing treatises from Sleep to Dream Interpretation, Memory to Breath and of course from Soul to Time, defined Time as:

It is clear, then, that time is ‘number of movement in respect of the before and after’, and is continuous since it is an attribute of what is continuous.

Aristotle conceived time in relation to change or movement (BOOK IV, CH 12):

Not only do we measure the movement by the time, but also the time by the movement, because they define each other. The time marks the movement, since it is its number, and the movement the time.

After Zeno of Elea introduced his four paradoxes, Aristotle tried to dismiss the dichotomy in terms of potential and actual infinities. But to what extent? As Silagadze (2005) rightfully points out:

But all this mathematical developments, although very wonderful, do not answer the main question implicit in Aristotle’s rebuttal of Zeno: how the real motion actually takes place and whether its present day mathematical image still corresponds to reality at the most fundamental level.

Modern science tackles ancient problem

With advent of quantum mechanics, scientists are perhaps on a strong footing to answer the question. Rovelli, along with Connes, constructed a quantum mechanical system without time, perhaps for the first time, refuting Aristotle empirical notion that time and number must be interrelated concept. Formally TTH states:

The thermal time hypothesis. In nature, there is no preferred physical time variable t. There are no equilibrium states (rho sub zero) preferred a priori. Rather, all variables are equivalent; we can find the system in an arbitrary state (rho); if the system is in a state (rho), then a preferred variable is singled out by the state of the system. This variable is what we call time. (Rovelli 2008)

Time, according to Rovelli, is just an illusory concept. In conclusion he writes:

What we call the flow of “time” is the Tomita flow of the statistical state (rho) in which the world happens to be, when described in terms of the macroscopic parameters we have chosen.

Adieu Zeno?

Does Quantum Loop Gravity put a final nail to an age old paradox? If not, what are some major criticisms or flaws in Rovelli's theory?

Answer 1

Rovelli claims that time is an illusion, deriving from the incompleteness of knowledge.

Since that incompleteness of knowledge is a permanent (and necessary) state of affairs, his hypothesis does us no good at all-- we are still firmly stuck inside of time, illusory as it may be, with no hope of escape. And thus, for us trapped within the illusion, Zeno's paradox remains unaffected. The fact that his theory maintains that the difference between the past and the future is illusory doesn't change the fact that we perceive (and cannot help but perceiving) a significant difference between them.

Put another way: Rovelli appears to have proposed an untestable hypothesis which, even if true, would have no bearing on the majority of philosophy as practiced.

A few general rules of thumb: 1) getting your philosophy from a physicist is akin to getting your physics from a philosopher; 2) Forbes magazine is not a good source for physics or philosophy: 3) if it has the word "Quantum" in it, it can usually be safely ignored.

Answer 2

I am a mathematician that found this page by accident, so I can't help you with the Zeno's paradox part (I think that was solved by calculus hundreds of years ago). But I would like to clarify some misconceptions.

• The thermal time hypothesis is not directly related to loop quantum gravity. It is instead a mathematical result from the theory of von Neumann algebras. Without going into their mathematical origin or purpose, von Neumann algebras are one of the primary mathematical ingredients used to construct a version of quantum statistical mechanics and quantum field theory that usually goes by the moniker algebraic quantum field theory. A quantum system's associated von Neumann algebra describes what you can observe about the system - the 'algebra of observables'.
• Algebraic quantum field theory has many problems for physicists - it is too restrictive to describe many physical systems. Personally I am only familiar with how it describes quantum statistical mechanics, but nothing about how it describes quantum field theory in general, so I can't say much about the quantum field theory aspect. But it is completely rigorous, which is its main appeal to mathematicians.
• A completely mathematical result is that von Neumann algebras come 'naturally equipped' with a time evolution. This was an extremely surprising result that first became known during the 60's and 70's.
• What Connes and Rovelli accomplished was to show that this 'natural' time evolution that von Neumann algebras come equipped with can be interpreted as arising from purely quantum statistical mechanical reasons - e.g. equations that govern the thermodynamics of many-body quantum systems.

In summary: the result is not a result about loop quantum gravity (though it may have relevance there - I do not know anything about LQG so I cannot say), but rather a hypothesis that a purely mathematical result from the theory of von Neumann algebras is linked to the thermodynamic notion of time present in a specific mathematical framework of the quantum theory of many-body systems. This hypothesis is on very solid ground mathematically, but it is usually very difficult to tell when mathematical truth corresponds to physical truth.

Answer 3

I think Michael has given a good answer pertaining to the philosophical aspect of the question. I just want to add something about the physics aspect.

Rovelli is peddling a profound misunderstanding of the implications of thermodynamics and statistical mechanics concerning time. They do not at all imply that time is an illusion. Especially the incompleteness of knowledge part is complete bullshit. It's akin to saying that Hiroshima is an illusion due to the fact that we didn't have knowledge of the exact positions of all atoms at the moment of the explosion. Go tell that to the victims.

It's a sad state of affairs to see top physicists peddling such nonsense. I'd greatly recommend reading "Science of Chaos or Chaos in Science" by Jean Bricmont which dispells many of these misconceptions.