# A Minute of Time

By Sean Carroll | November 14, 2011 7:54 am

For you arrow-of-time freaks who have been looking for a quick and engaging intro to the issues (maybe to show your friends to get them to appreciate your obsession), here’s a guest spot I did for the terrific Minute Physics series illustrated by Henry Reich. If you’re not already familiar with them, check out the entire series.

Previously I did one on dark energy. It came out right after the Nobel Prize announcement, but don’t let that trick you into thinking I won the Prize myself. (Some people were tricked.)

Meanwhile, in a parallel universe, instead of writing Spacetime and Geometry, I wrote a massive tome on Cosmology. This parallel universe was featured on this week’s episode of Fringe. Here’s Walter Bishop retrieving his copy from Peter.

I helped with some of the equations on the episode. Thanks to Glen Whitman and Rob Chiappetta for the shout-out.

CATEGORIZED UNDER: Science, Time, Top Posts
• duhoc

I enjoyed the guitar. I just wanted to reiterate the idea which I have proposed to you before regarding the expansion of the universe. Let us say that we measure a line with a ruler or multiple rulers. Rulers have margins of error but by using multiple rulers we can determine the magnitude of the line to a certain degree of tolerance to which certain rulers would not be appropriate. In fact, by virtue of translational symmetry we could say that the ruler and the line are symmetrical to a certain magnitude defined by its limit of tolerance. We can also apply this idea to space. Let us say we consider a curved surface, or a curved surface in motion which repeats that motion. Could a three dimensional grid which had the ability to telescope to different orders of magnitude and do so in a specific sequence for a specific time resolve this curvature to a certain degree of error. If it could we could say that the spacial system was symmetrical to the four dimensional system i.e. the three dimensional system that repeats its motion. So, if you were of the belief that the universe originated from a hyperstate of curvature which in fact was dynamic, then the four dimensional spatial universe in which we live could be resolving this high dimensional curvature in four dimensional approximations. That would account for the expansion of space that you describe and its adherence to physical laws because it must conform in terms of orders of magnitude to the master grid.

• http://thefloatinglantern.wordpress.com Tim Martin

I will once again pose the question: What does order have to do with the number of accessible energetic microstates in a system? My room has no more entropy when it’s clean than when it’s messy. A glass of water with a cracked ice cube in it will be more orderly once the ice cube has melted, and have more entropy.

• Stephen Crowley

Watching Fringe is a complete waste of “time” and I have a notion its just a front for techno-utopian hooliganism and biased presentation of what really goes on inside security services… people would be better served spending their time reading and seeking enlightenment and developing ideas about compassion and doing their own research….

• James

@2:
If “messy” were the macrostate of your room, it would indeed have more entropy than a tidy room, since a generically “messy” room could have a large number of specific configurations that would all look messy (at least, more configurations than would look tidy).

Essentially, it’s a case of understanding what “order” means in physics sense. The ice cube case, the system is considered to be ordered by virtue of confining some of the H2O molecules to a rigid subspace of the whole glass.
I think many physicists would say this is a bad use of the “order”, though it continues to be taught.

• Charlie

Here’s a question about the expansion of the universe for anyone who wants to answer. I’ve heard some say that this has no effect at “small” scales, small meaning smaller than a galaxy. I’ve also heard that the effect is there but it is too tiny to to matter. These are actually two different answers. Which one is correct?

• http://thefloatinglantern.wordpress.com Tim Martin

@James #4: All of these misunderstandings have been addressed before. I’m just going to quote this 1999 paper from the Journal of Chemical Education in response to your points.

James said: If “messy” were the macrostate of your room…

Entropy does not apply. From the article:

…a collection of ordinary macro things does not constitute a thermodynamic system as does a group of microparticles. The crucial difference is that such things are not ceaselessly colliding and exchanging energy under the thermal dominance of their environment as are microparticles.

James said: I think many physicists would say this is a bad use of the “order”, though it continues to be taught.

I’m not sure how many physicists would say this – many of them seem to be quite happy to explain entropy in this way – but it is indeed a bad use of “order,” or a bad explanation of entropy, because it’s false. Or maybe I’m wrong, but this explanation makes a lot more sense than any I’ve heard saying that order and entropy are the same thing.

There is no more widespread error in chemistry and physics texts than the identification of a thermodynamic entropy increase with a change in the pattern of a group of macro objects. The classic example is that of playing cards. Shuffling a new deck is widely said to result in an increase in entropy in the cards.

This erroneous impression is often extended to all kinds of things when they are changed from humanly designated order to what is commonly considered disorder: a group of marbles to scattered marbles, racked billiard balls to a broken rack, neat groups of papers on a desk to the more usual disarray. In fact, there is no thermodynamic entropy change in the objects in the “after” state compared to the “before”. Further, such alterations in arrangement have been used in at least one text to support a “law” that is stated, “things move spontaneously in the direction of maximum chaos or disorder”.

The foregoing examples and “law” seriously mislead the student by focusing on macro objects that are only a passive part of a system. They are deceptive in omitting the agent that actually is changed in entropy as it follows the second law — that is, whatever energy source is involved in the process of moving the static macro objects to more probable random locations. Entropy is increased in the shuffler’s and in the billiard cue holder’s muscles, in the tornado’s wind and the earthquake’s stress — not in the objects shifted. Chemically unchanged macro things do not spontaneously, by some innate tendency, leap or even slowly lurch toward visible disorder. Energy concentrated in the ATP of a person’s muscles or in wind or in earth-stress is ultimately responsible for moving objects and is partly degraded to diffuse thermal energy as a result.

I recommend just reading the whole paper. It’s short.

• David Galiel

Layperson’s question:

If expansion does not apply to bound systems, and
if large systems like galaxies are bound by gravity, and,
if gravity has no boundary, but weakens rapidly with distance, then

where is the boundary of a bound system like a galaxy or galaxy cluster? I know that it used to be set rather arbitrarily at the Holmberg radius, but we’ve known for decades that bound matter extends far beyond the visible mass of the galaxy.

IOW, how does space “know” precisely at which distance from a galaxy or galaxy cluster dark energy “should” appears, and where it “should” not? Also, does dark matter come into play in calculating the bound boundary?

• David Galiel

Edited above

• Sili

Ooops. Wrong post.

• Rahul Chaturvedi

All the discussion about the expanding universe had the engineer in me thinking. The basics, as I understand them, are that the universe is finite and expanding at an accelerating pace. Finite means there is observable matter at the farthest reaches of the universe beyond which there is no other observable matter. Expanding means all bodies are growing farther apart and accelerating means increasingly faster pace.

The reason for these definitions is my conjecture that there is no dark energy and that the universe is infinite even though there is a finite distance between farthest existing matter. In my simple mind I visualize the universe to be a very large ball of transparent material. Somehow on top of this ball a rather large blob of something like mercury got dropped. This blob broke into many tiny drops that started rolling away from each other and accelerated as they went farther and farther away simply due to the curvature. Some drops collided to form bigger drops.

If we were on one of these drops, at the early stage, we would see a finite but expanding universe where the farthest blob was accelerating the fastest. We would not see the curvature since the very large ball is transparent. We would not even know that the very large ball exists. However, with the passage of time, as the drops roll over the surface of the ball, they would appear to be coming closer. This would be so because we would not be measuring along the surface. Instead, we would be looking along the chord. Of course, for my conjecture to be valid we are not there yet.

Also, with time, all drops would travel to the the other side of the ball and combine back into one large blob.

• Kevin

I was wondering if “Carroll’s Cosmology” was a reference to you! That’s awesome.

• Rahul Chaturvedi

Thanks. Just applying Occam’s razor.

• http://www.astro.multivax.de:8000/helbig/helbig.html Phillip Helbig

“Here’s a question about the expansion of the universe for anyone who wants to answer. I’ve heard some say that this has no effect at “small” scales, small meaning smaller than a galaxy. I’ve also heard that the effect is there but it is too tiny to to matter. These are actually two different answers. Which one is correct?”

Look for papers by Tamara Davis and Charley Lineweaver. This question (which, as you note, is often not answered properly) is specifically addressed in one of them. I don’t want to track down the exact reference since all their joint papers are worth reading. Check them out.

• http://akbmurugan.com/ akbmurugan

I give my conjecture. Let us consider conservation (of matter & energy). What was the amount of matter and energy before big bang? Was it the same as it is now? If we assume that it was the same, it leads to the idea that the universe was an extremely hot and dense point at or before big bang. Instead, I conjecture that the universe was brought to this physical existence from a subtle form during big bang. This means that the universe existed even before big bang, but in a subtle form. We have to agree that the potential of the subtle source is apparently infinite.

This implies that the physical matter and energy (and space also) in the universe are not conserved since any more amount can be created from the subtle source. Apart from the gross creation during the big bang, the space is continued to be created even now, at this observed accelerated rate. This is what we call as dark energy.

As our physical sciences know little about the creation during big bang, do they know little about this current accelerated rate of creation of space.

• James

@6 Tim:

Of course my room isn’t a proper thermodynamic system, but it’s essentially a microscopic system scaled up to a macroscopic size. If I bounce about the room, scattering objects about in a random way (as I do), I’m performing the same job as an energetic particle being sent into a small collection of gas particles. It’s not a perfect analogy for obvious reasons, but I think it’s a perfectly acceptable pedagogical aid – I don’t think there’s anything particularly profound to be found in taking certain analogies too seriously.

• Chris

Oh, I was looking for that. So somehow Peter not being around caused you to write that book. Must be those pesky Observers interfering in this reality.

• http://thefloatinglantern.wordpress.com Tim Martin

#15 James said: It’s not a perfect analogy for obvious reasons, but I think it’s a perfectly acceptable pedagogical aid…

Have you tried to teach physics using this analogy? Because people who have have written papers and given presentations on how it engenders misunderstanding. The paper I cited above is one example, and I’ll cite another below.

Speaking of which, and I mean no offense, you seem to be under such a misapprehension yourself. What does the example of the messy room teach us about energy dispersal? You do not share your energy with the objects in the room. The objects in the room are not constantly colliding and sharing their energies with each other. Nothing about this scenario is similar to a system of microparticles. It’s not just an imperfect analogy; it’s no analogy.

Furthermore, low entropy systems aren’t even orderly to begin with! A 2008 presentation (PDF) from the American Institute of Physics conference explains this well:

The most basic example of the second law is neither difficult nor complex. Place a slightly warmer piece of iron on another piece of iron: the “heat energy” flows to the cooler iron until the two become exactly the same temperature. Technically, the “heat energy that flows” is actually the vibrational energy of atoms dancing in place in the metal that, on average, are moving faster in the warmer iron bar than in the cooler. At the surfaces of contact, the vibrations of the warmer bar interact with slightly slower vibrations in the cooler bar, whereupon over time the surplus energy of the warmer bar disperses. It spreads out so the vibrations of atoms held in place are at the same energy levels in both bars.

Quite clearly, no “disorder” or “order” is involved here! The atoms and molecules of all substances above absolute zero temperature are incomprehensibly disorderly, capable of being in any one of a truly gigantic number of different arrangements of their energy. The crucial point is that energy dispersal or spreading out is at the heart of any process involving thermodynamic entropy change-whether in iron bars or complex chemical reactions.

So it’s not even true that things tend to become less ordered as a result of entropy increase. Order, as pertains to this analogy, is a subjective aesthetic judgement. It doesn’t reliably tell us anything about energy dispersal. You see what a bad analogy this is?

• James

The “order” is the concentration of energy in just one bar. I don’t really see how this is a difficult concept. It’s bordering on semantics.

• Spaceman Spiff

I think Tim is making a valid point…

S = k*ln(W). Where is the disorder in entropy S? Increasing entropy is to increase the number of accessible microstates (~ the distribution of particles in 6-D phase space).

• http://sidudoexisto.blogspot.com Jorge Laris

I now that this argument is wrong, but I want to know how to answer to it:

“Evolution can’t be because of entropy.”

I used to say that entropy only works in close systems, and that living things and earth aren’t close systems, but now i’m confused. If one becomes older because of entropy, then How could we evolve?

• Anchor

“Meanwhile, in a parallel universe, instead of writing Spacetime and Geometry, I wrote a massive tome on Cosmology.”

I know the term in this context has an entirely semantic origin, but actually those alternate universes are anything BUT “parallel” to ‘ours’, or we’d see them. The arrows of all of those others must all be perpendicular to ‘ours’ or we’d be encountering slightly different versions of ourselves over and over…

Oh, wait…

– riddle of the day 8)

• ?

I heard “Carroll’s Cosmology” on the show, and I was curious if it was referring to you! It was a nice shout out.

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