# Thermal time hypothesis vs. cosmological time

How can Rovelli's thermal time hypothesis be consistent with the apparent existence of a privileged time in the sense of cosmology?

• What do you mean, "privileged time in the sense of cosmology?" – N. Steinle Aug 25 '18 at 20:39
• Cosmological time, the one given by the cosmological arrow of time, seems to be a distinctive and privileged reference time. – riemannium Aug 25 '18 at 20:44
• The thermal hypothesis of time was discovered by Rovelli precisely to try to explain the arrow of time – N. Steinle Aug 25 '18 at 20:48
• Here's an old but classic paper on the subject < alainconnes.org/docs/carlotime.pdf > – N. Steinle Aug 25 '18 at 20:56
• from the abstract, " based on the hypothesis that in a generally covariant quantum theory the physical time-flow is not a universal property of the mechanical theory, but rather it is determined by the thermodynamical state of the system" – N. Steinle Aug 25 '18 at 21:19

As you know, within the thermal time approach you start from a probability distribution function (or density matrix in the quantum setting) $\rho$, you derive an Hamiltonian (or Hamiltonian operator) $H=-T\,\ln\rho$ and define the time $t$ as the variable with respect to which the system evolves given the Hamiltonian $H$.

Now, $\rho$ can be really any physically meaningful distribution density, and different $\rho$'s will give rise to different thermal times. In other words, $t$ is defined with respect to the observer that measures the distribution $\rho$. If as your $\rho$ you choose the distribution which describes a cosmological fluid in the cosmological frame of reference, then you should obtain as your thermal time the "unique" cosmological time referred to in your question. In Rovelli's book "Quantum Gravity" (sec. 3.4) it is stated that

The thermal time hypothesis works surprisingly well in a number of cases. For example, if we start from a radiation-filled [...] cosmological model [...] and write a statistical state representing the cosmological background radiation, then the thermal time of this state turns out to be precisely the Friedmann time.

This "Friedmann" or "cosmological" time is privileged in the following sense: it is just the appropriate time variable to use when describing the evolution of the cosmological fluid. In other words, again, you are starting from a (matter/radiation/etc.) distribution to find the appropriate time variable, which is exactly what you do (albeit following a very, very different path) in the thermal time approach. Therefore the thermal time hypothesis is completely consistent with the existence of a (not so) privileged cosmological time.

I cannot disagree about my need to make the distinction you noted above, but that is not inappropriate on my part, as you so claim, due to this in Wikipedia:

"Hypothesis

Even though the words 'hypothesis' and 'theory' are often used synonymously, a scientific hypothesis is not the same as a scientific theory...." 4Sept2018.

The so-called "arrow of time" has always pointed toward the future, yet the future does not exist, but even if it did, it is absurd to say time flows toward the future. How could anyone make such a silly claim? Time passes, alright, but only in the present-time because the past does exist in our physical reality either. Plus, time is a property only of discrete matter, like gravity is a property of all masses. Like gravity, time is a fundamental force, too. It has the power to age all discrete matter inversely proportional to its speed, which explains the time dilation phenomenon. Fundamental forces do not interact with each other, per se, yet gravity can indirectly affect time rates due to the gravity potential increasing the speeds of matter in free fall, which acts to decrease their time rates.

The thermal time hypothesis is not yet a theory since it makes no predictions nor does it present any falsifiable premises. Thus, I believe there is only cosmological time - if we prefer to call it that.

• You didn't answer the question at all. It's already called "hypothesis" so why do you feel the need to say it's not a theory (that's obvious). The OP asked how the hypothesis is consistent with the arrow of time. Not about whether or not you philosophically agree with the assumptions of the hypothesis – N. Steinle Aug 27 '18 at 14:29
• And what in the world do you mean, "time is a fundamental force" ???? – N. Steinle Aug 27 '18 at 14:29
• Wikipedia: hypothesis vs. theory: "Even though hypothesis and theory are often used synonymously, a scientific hypothesis is not the same as a scientific theory'" In my model of the universe, time is a fundamental force similar to gravity. – Tomas Garcia Aug 28 '18 at 20:03
• I'm not disputing the theoretical status of the thermal time hypothesis - I was saying that it's pointless to say it's not a theory, as you do. Of course it is not! The word hypothesis is in its name! Everybody and their uncle has a theory of gravity these days. What makes yours so special? And why is it relevant for this question? – N. Steinle Aug 28 '18 at 22:33