Theoretical physicists commonly say their biggest challenge is to unite general relativity with quantum theory. But at this month’s FQXi conference in Puerto Rico, Carlo Rovelli said they have an even bigger challenge: to unite general relativity with thermodynamics. After all, physicists do have proposed solutions to the first problem, such as string theory and loop quantum gravity, and the rivalry among them is not so bitter that theorists can’t find the humor in it. Physicists routinely and uncontroversially work with an effective theory of gravity which, while not the full story, captures quantum corrections to Einstein’s theory.

But it’s one thing to describe the inner workings of gravity, quite another to understand how gravity behaves in big complicated systems, which are the subject of thermodynamics. “We are totally in the dark about the foundations of statistical thermodynamics and general relativity,” Rovelli told his colleagues at the conference. Gravity inverts our usual intuition about thermodynamic concepts such as entropy: a spread-out gas has a high entropy mechanically, but a low entropy gravitationally. Amadeo Balbi remarked to me, “There is no consensus on how to precisely calculate entropy when gravity is important, except in special cases, such as black holes.” And for black holes, physicists confront the notorious information paradox, whose latest incarnation as the firewall argument sparked a suitably fiery debate at the conference.

Perhaps most dramatically, Rovelli has been arguing for two decades that space and time themselves are not fundamental to nature, but emerge thermodynamically. He made the case in his prize-winning essay in FQXi’s first essay contest, and others have presented similar ideas at past FQXi meetings. To advance this broader program, Rovelli’s talk in Puerto Rico went back to basics. He didn’t concern himself with the much-discussed second law of thermodynamics, nor the third law, nor the first. He focused on the zeroth law. (You’d think that a discipline—statistical mechanics—that prides itself on counting 10²³ molecules at a time would have done a better job of numbering its laws.)

The zeroth law says that a gas or other system that has reached equilibrium has a uniform temperature. This deceptively simple principle underpins the other laws, not least by defining temperature as the collective property that an equilibrium system possesses. Systems that are not in equilibrium do not have well-defined temperatures.

So what’s up with gases in a gravitational field? When they reach equilibrium, they do not have a uniform temperature, but cool off with altitude in a phenomenon known as the Tolman-Ehrenfest effect. As Rovelli and Matteo Smerlak have showed, the effect is basically a consequence of gravitational redshift. Light or anything else that climbs away from Earth’s center loses energy, which is tantamount to cooling off.

In practice, we never see this effect. The air temperature does drop when you climb a mountain or fly a plane, but that’s ultimately because of the disequilibrium between the sun-basked ground and the cold of deep space. Imagine the far future of Earth after the sun goes dark, radioactive ores decay away, and the planet comes into thermal equilibrium with the cosmos. The inhabitants of that sorry world will still feel colder when they climb a mountain. The temperature will fall by one part in 10¹³ at an altitude of 1 kilometer. Not enough to put on mittens, but more than enough to flout the zeroth law.

To restore the primacy of the law, Rovelli sought a generalized version that holds under all conditions. He noted an interesting fact about temperature. Although we typically measure it in units of degrees or kelvins, according to basic physical laws it really has units of inverse seconds—a rate. One way to see this, Rovelli and Hal Haggard argued last year, is Heisenberg’s energy-time uncertainty relation. The time it takes a quantum system to change discernibly is inversely proportional to the spread of its energy, which is proportional to temperature for systems in thermal equilibrium. Thus time is inversely related to temperature, and vice versa. The same goes for classical systems as well.

Specifically, Rovelli argued that temperature is the rate at which systems change their internal state. Air at room temperature, for example, changes state 3 trillion times per second as the molecules feverishly reshuffle themselves. In this spirit, Rovelli proposed defining equilibrium as a condition not of uniform temperature, but of a common rate of changing state. The Tolman-Ehrenfest effect then makes perfect sense. By warping time, gravity mucks with the time standard by which rates are measured. As you climb a mountain, time passes more quickly and rates slow down. The rate at which a gas changes state—and thus its temperature—thus decreases even though the gas molecules are as feverish as ever.

To make the connection to the conference theme, the physics of information, Rovelli suggested thinking of an interaction between two systems in terms of information. Each system gets a glimpse into the internal structure of the other system. If both systems are changing state at the same rate, both gain the same amount of information about each other. And that, Rovelli argued, is what equilibrium really means. The situation is like two poker players reading each other’s expressions. If one poker player is expressionless, while the other is an open book, then the two will be out of equilibrium—which translates, quite tangibly, into a flow of money from the second to the first. But if the two are equally able to read each other, they can play equally well and reach a stalemate.

Rovelli has put so much effort into understanding equilibrium because it is crucial to his program of explaining time as emergent. Traditionally physicists have taken time as a given and expressed all physical change with respect to it. A pendulum swings, a clock ticks, and a heart beats once per second. But Rovelli thinks you could eliminate the little t and express all these changes with respect to one another. A pendulum swings once per clock tick or heart beat, and vice versa.

External time vs. relational time

Time here plays the same role that money does in an economy: it provides a convenient medium of exchange, but has no value on its own. In principle, you could shred all the dollar bills and instead perform a complex series of barter transactions. In his charming little autobiographical book What Is Time? What Is Space?, Rovelli wrote: “Time is an effect of our ignorance of the details of the world. If we had complete knowledge of all the details of the world, we would not have the sensation of the flow of time.”

Quantitatively, Rovelli solves for t by inverting the equation describing equilibrium states. This is subtle: equilibrium states are not changing macroscopically, by definition, so they seem like an odd choice for defining time. Rovelli argues that time evolution is latent in the statistics of equilibrium states, since a system, if displaced from equilibrium, will return to it. The time evolution given by the second law of thermodynamics builds on how equilibrium states are defined. “I think there’s a clear way of getting time out of a timeless theory,” Rovelli told me.

That said, he has yet to show conclusively that time is a collective phenomenon. Yasunori Nomura said he shares Rovelli’s general aim of recovering time from correlations within a system, but questions his focus on equilibrium states. There seems little risk that theorists will reach equilibrium on equilibrium anytime soon.

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"But Rovelli thinks you could eliminate the little t and express all these changes with respect to one another."

All observations and measurements are "with respect to one another". The notion of a "unit" of measurement, such as a "second" or "meter", is nothing more than a shorthand notation for a ratio of measurements. An elapsed time of "10 seconds" simply means that the ratio of the measurement and the arbitrary standard, is equal to 10.

It is arguably more correct to think of Rovelli's concept not as "doing away with non-emergent time", but rather as picking a different standard to use in the ratio.

Rob McEachern

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“Time is an effect of our ignorance of the details of the world. If we had complete knowledge of all the details of the world, we would not have the sensation of the flow of time.”

This is nonsense. What if we were to say; If we have complete knowledge of all molecular motions in a body of water, we wouldn't have the sensation of temperature?

Of course we would. Temperature is the average of all the actions.

If we knew both the position and momentum of all parts of the world, there would still be a rate of change and thus effect of time. We would simply know the average rate and thus a potentially universal rate of change.

A universal time is the collective, composite rate of change. There is no blocktime of all those events. The thermodynamic process is explicitly about that dynamic process and its resulting change. If we knew the entire process, we would still have that sum total effect of time/rate of change, not no time.

The real problem is that the idea of blocktime is incompatible with thermodynamics, since blocktime replaces that dynamic process with a static dimension of all events.

Regards,

John M

The state of equilibrium is one where all effects balance out, so only if all those details were to effectively cancel out, then there would be no change/no rate of change and no time.

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"George Musser:But at this month’s FQXi conference in Puerto Rico, Carlo Rovelli said they have an even bigger challenge: to unite general relativity with thermodynamics."

The Arrow of time concept was held in mind when I read about Alan Guth's ideas here that I did not see included in your write up. I thought it might be significant to what over all was noted from your perspective of that same event.

"An arrow of time—the steady growth of entropy with time—has been generated, without introducing any time-asymmetric assumptions.The Universe Began In A State Of Extraodinarily Low Entropy by Alan Guth"

I would also like to add something for reference.

" The old version of string theory, pre-1995, had these first two features. It includes quantum mechanics and gravity, but the kinds of things we could calculate were pretty limited. All of a sudden in 1995, we learned how to calculate things when the interactions are strong. Suddenly we understood a lot about the theory. And so figuring out how to compute the entropy of black holes became a really obvious challenge. I, for one, felt it was incumbent upon the theory to give us a solution to the problem of computing the entropy, or it wasn't the right theory. Of course we were all gratified that it did."Black Holes and Beyond: Harvard's Andrew Strominger on String Theory I have to apologize as link is now dead. See instead to follow up: The Cosmic Hologram

"Holography encodes the information in a region of space onto a surface one dimension lower. It sees to be the property of gravity, as is shown by the fact that the area of th event horizon measures the number of internal states of a blackhole, holography would be a one-to-one correspondence between states in our four dimensional world and states in higher dimensions. From a positivist viewpoint, one cannot distinguish which description is more fundamental.Pg 198, The Universe in Nutshell, by Stephen Hawking"

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Again and again, that false statement: "Light ... that climbs away from Earth’s center loses energy, which is tantamount to cooling off". On the contrary, this is what Einstein believed: "...we can regard an atom which is emitting spectral lines as a clock, so that the following statement will hold: An atom absorbs or emits light of a frequency which is dependent on the potential of the gravitational field in which it is situated. The frequency of an atom situated on the surface of a heavenly body will be somewhat less (not more) than the frequency of an atom of the same, element which is situated in free space ...". If E =hf is still correct, then we can from the quote say, the energy, E of an atom situated in free space will be somewhat more than the energy of an atom of the same, element which is situated on the surface of a heavenly body. These things have been verified experimentally in Pound and Rebka's experiment and same in the Gravity Probe A. Indeed the Gravity Probe A claims that at 10,000km a clock should run 4.5 parts in 10^-10 faster than one on the Earth. That is frequency, f and therefore energy, E is higher up and lower down.

So why the false statements persist beats me. Does a falsehood repeated severally become a truth? Or is this a genuine mistake?

Akinbo

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" ... the representative molecule has moved towards that average."

Or away from it.

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Akinbo,

"Even someone as anti-Einstein as Pentcho has been unwittingly conscripted into the belief that clocks run slower up the mountain than lower down so now on the same side as those he claims to be against in Einsteiniana"

Too much misstatement. Let me suggest something. We study, carefully, a good relativistic source (without paying attention to other sources) and then restrict the discussion to this source only:

David Morin: "The equivalence principle has a striking consequence concerning the behavior of clocks in a gravitational field. It implies that higher clocks run faster than lower clocks. If you put a watch on top of a tower, and then stand on the ground, you will see the watch on the tower tick faster than an identical watch on your wrist. When you take the watch down and compare it to the one on your wrist, it will show more time elapsed. (...) This GR time-dilation effect was first measured at Harvard by Pound and Rebka in 1960. They sent gamma rays up a 20m tower and measured the redshift (that is, the decrease in frequency) at the top."

Pentcho Valev

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I'm with Carlo when it comes to time being derived from motion. You can hold your hands up with a gap, a space between them. And you can waggle your hands. That's motion. Space and motion are empirical. But there is no time flowing between your hands or anywhere else. Open up a mechanical clock and you don't see time flowing through it like some cosmic egg-timer. You see cogs and things. Moving. Through space.

And George, if you're there, when light climbs away from Earth's center, it doesn't lose any energy. Clocks run slower when they're lower, so the frequency looks higher, that's all. Take that clock to the top of a tower and measure the photon frequency, and you measure it to be slower. But it hasn't changed. You clocks have changed instead. And so have you. It takes work to climb to the top of the tower. You have more mass-energy. So it looks like the photon has less. But it doesn't.

That might sound unfamiliar and even alarming. But imagine you've got a 511keV photon and you direct it into a black hole. The black hole mass increases by 511keV/c². No more. It's the same if you drop an electron into a black hole. Conservation of energy applies. There is no magical mysterious action-at-distance mechanism by which a photon or an electron gains or loses energy on the way down or on the way up. Gravity is not an external force that adds energy to a falling body. There is no force upon that falling body. The principle of equivalence likens the body on the ground to the body accelerating through gravity-free space.

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To me, Rovelli's position that time is just a function of the spread of its energy, which is due to the physical components of a system changing, seems clearly correct. I'm no physicist, but my sense (or possbily lack thereof) would tell me that if there were no physical change at any level in the universe, there would be no time. So, as mentioned, time is just a way of keeping track of the amount things physically change in a system. And, if the components are more resistant to being changed (e.g. have higher mass?), then time would move slower as relativity shows. This also seems to explain the arrow of time. If time is just a measure of physical components changing, then even if they change in reverse direction back to their original state (e.g. a broken coffee cup reforming itself), the arrow of time is still going forward because as the components reverse their direction, change is still happening, and thus time is moving forward. That is, time can't go backwards because you can't take back the fact that components have changed. Even if you try to take it back, that action is itself change and thus time still moves forward.

Also, it seems like that if the universe started with a single existent entity that could replicate itself to create the multiple existent entities we see in our universe now and if these existent entities could change, this would explain the low entropy at the beginning of the universe. The single initial entity would have very low entropy and due to the changes occurring in the replicated entities, entropy would increase.

This is just what it seems like to an amateur thinker/"crackpot". Thanks for listening!

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The only time exists is absolute time or universal time. However there is no clock time unit (including a clock second) that represents the same amount of absolute time in different frames of reference. The observer's clock second represents a specific amount of absolute time. He uses the SR/GR or IRT math to predict the clock time value on a moving clock for an interval of absolute time on his clock.

For example: according to SR one second of proper time on the observer's clock is predicted to have a clock time value of 1/gamma seconds on a moving clock. According to IRT one second on the IRT observer's clock is predicted to have a clock time value of 1/gamma seconds or gamma seconds on a moving clock.

IRT is a new theory of relativity. The math of IRT includes the math of SRT as a subset. Also the math of IRT is valid in all environments. including gravity. A paper on IRT is available in the following link:

http://www.modelmechaniics.org/2011unification.pdf

Ken Seto

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Rovelli's approach is certainly worth an attempt, but I am skeptical about how useful it will be.

In general, temperature is one dimensional and time is one dimensional and since temperature evolves in time, it is perfectly reasonable to back fit time with temperature as well. The real question is whether or not this will be useful. Not only is this approach complex, the action of temperature is now a hodgepodge of quantum action and gravity action and it just seems like it will a much more difficult approach than even the muddle that is space time.

The paper implies that thermodynamics may reveal a hidden connection between gravity and quantum action. It’s possible and worth looking at, but it is much more likely that without a single quantum action from the start, the tensor algebra will be even more onerous that GR. Given the partition functions of statistical mechanics and the fact that the universe has a very large range of temperatures, the back fits to eliminate time look to be really complex.

Temperature is a property of both matter and action. The matter of an object increases if you heat it up and decreases if you cool it down. Action increases and decreases as a temperature gradient increases and decreases as well. Therefore, temperature as time will be convolved with differential changes in both matter and action. That does not sound very pretty.

To further complicate things, an object can have any number of different temperatures for its different ensembles of internal states: kinetic, magnetic, vibrational, rotational, translational, electronic, ion, electron, hole, etc., and that is before we get to nuclear stuff and black holes. These ensembles can be completely separate, partially, or fully connected. So, good luck.

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I would like this discussion turn to other direction:

Symmetry without Time

About the Concept of Symmetry.

It seems to me necessary to throw away the notion "time".... from concept of symmetry and use only notion "space”.

Because the natural symmetry.... only static symmetry without motion.

Motion implies “time”...

Continuous symmetry is tautology.Only discrete symmetry is valid.

“Tautology does not have sense”(Ludwig Witgenstein)

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Georgina

Where there is motion, there is also the speed from 0 to C.

From speed depend deformation, according Relativity.Deformation violates symmetry.

It is paradox...Time should be discarded.

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