T-Rex of Dinosaur Comics realizes that his personal kink involves reversing the arrow of time. And further contemplation just makes things worse.
The construction of jokes involving Boltzmann’s Brains and onanism is a temptation better left resisted.
Below the fold: hott entropy action! Not safe for work, perverts!
Don’t act like you weren’t warned.
I’ll see your unscrambled egg with a pool of non-Newtonian fluid.
It’s a testimony to Sean Carroll’s efforts that I find the movie equally amazing in both directions! 🙂
I for one am looking forward to witnessing what this post is going to do to the poor Google Ads robot.
My favorite pet peeve! Use of the word ‘exponentially’ when you just mean ‘very’!
I’m not sure exponentially is being misused here. If indeed the individual writing the title meant ‘very’ then it’s an annoying misuse. However, I didn’t even consider that it may be meant to mean very. I took it to be a formula for nerdiness to fetish relationships. The unlikeliness of your kink is exponentially related to the quantity and quality of your nerdiness.
Something like this:
(Nerd_Quantity)^(Nerd_Quality) = Unlikeliness factor. 😉
Or it could be that spontaneous decreases in entropy are suppressed by the exponential of the entropy change.
But the important thing is that we all get to share our pet peeves.
My favorite pet peeve! Use of the word ‘exponentially’ when you just mean ‘very’!
That’s funny — my pet peeve is people who think the word ‘exponentially’ is being misused when in fact it’s precisely what’s meant. (Such people are an occasional occupational hazard for computer scientists — and apparently physicists too.)
Here’s something I don’t get about entropy: Why would apparently unrelated physical processes, like optics, conspire to support the second law? For example, you can’t (?) make a lens/mirror/etc system of unlimited low f/ratio, since at a certain point (around f/0.3 I once figured) that would allow a surface image brightness greater than the emitting surface. Then you could set up a source, lens and target in a closed system, and the image region would get and stay warmer than the emitter etc. No, not just “because T2 says so,” I want to understand why something based on molecular collisions gets help from everything else imaginable!
Another issue I thought of: If anything from outside a universe could intervene, then the t-reversed world could perhaps be fiddled with in tell-tale ways. For example, if “a god” with an paraentropic fetish could reach in and snatch away a bullet before it went back into the barrel of a gun (or egg innards before they get back to the shell etc.), then the “past” (to the god, a future!) of that world would be absurd. (If you think it would just be a bullet appearing in mid air and going on, no: the bullet would be snatched away as it approached the smoking barrel and the gases trying to go back in, etc. They’d have an odd time handling the mismatch.) But if the god snatched the bullet away after it was fired in ordinary time progression, it’s just “gone” as we conventionally imagine a disappearance. IOW, intervention from outside causes real problems for the idea of time reversal. It can only be coherent for a self-contained system.
(PS: paradox wrangling is my fetish!)
Bit of clarification: The “god” above could either snatch the bullet etc out of the universe entirely (really weird), or various interferences, including just pushing it aside. The latter would still cause all kinds of trouble as the back-working universe interacted with the new “wrong” inverse trajectory. It is fun to imagine how the inhabitants would experience their absurdly deviant past.
BTW: Simplistically speaking, t-reversal inverts just those quantities with odd power of time in the MLT units composition. So as we’d expect, gravity is still attractive etc. However, there’s an odd problem with the radiative reaction self-force, given (in natural units) as f_rad = 2q(v dot dot)/c^3. Technically the units give force in the same direction, but the c^3 is just a units adjuster with no preferred direction. The v dot dot, what really should count, is actually reversed in TR. If you can imagine roles of emitter and receiver trading places for the self-interaction of a true macroscopic body, maybe no problem. However, the self-force for an (“point”) electron is imagined to be inherent and found through QM, also to prevent runaway solutions. If so, the radiative reaction should be in the opposite direction, making it seems, for a “tip off” to the inhabitants of the reversed world.
(PS: Wave function expansion and collapse obviously go one way. That is an interpretation concept that supposedly does not have observable consequences in TR as long as everything coincidentally happens in a natural-seeming way.)
Neil B.,
It is no surprise at all to me that the laws that govern optics would also conspire to follow the laws of thermodynamics. Remember that the force that governs the laws of thermodynamics as they are usually conceived is the electromagnetic force, after all. If this force causes the laws of thermodynamics to arise out of collections of atoms and molecules, why would it not do the same for optics?
More interesting, I think, is what happens to thermodynamics when we include gravity. When we have systems where gravity is a major factor (e.g. imagine observing the collapse of a star), we find that the laws of thermodynamics, as they are conceived for Earth-bound systems, don’t appear to apply at all. By Earth-bound physics, after all, a cloud of gas is more likely to disperse than to collapse together into a tight ball. Gravity, then, turns the laws of thermodynamics on their collective head.
And yet, it doesn’t appear that the laws of thermodynamics are entirely overturned where gravitationally-bound systems are concerned. The overall principles of entropy always increasing, energy conservation, and the like, appear to be met just fine. It just looks like the definition of entropy must be changed a bit where gravitational systems are concerned. This, to me, makes it seem that the laws of thermodynamics really are fundamental in a very profound way, even if I don’t understand why this is the case.
Jason:
That’s very interesting, about gravity and thermo. I heard of black hole issues with thermo, but not gravity per se. What is the “official position” on that, I can’t find much. Indeed, stuff heats up as it collapses, the work done seems to violate T2 (especially if it is more cleverly arranged than just stuff hanging around.) Then there’s nuclear decay heating up materials, etc. – IMHO, Thermo II is pretty much a highly-caveated rule of thumb only, and requires careful framing to be a true law – is that so?
But just because “electromagnetism” in some sense underlies both molecular collisions and optics, wouldn’t explain the correlation. Remember that statistical mech is independent of the “force mechanism” and just concerns the way particles bounce around, until you have to deal with rotating molecules and such.
BTW, I made a tiny mistake (no impact) in the self-force formula, which should read: f_rad = 2q(v dot dot)/3c^3. That self-force is fun to play with!
Well, the fundamental difference between gravity and the electromagnetic force, where thermodynamics is concerned, is that gravity is always attractive, while the electromagnetic force is both attractive and repulsive. This generates a fundamental difference in the respective systems behave, which, in turn, generates a fundamental difference in how we have to think about the entropy of both systems.
One can begin to understand why thermodynamics appears to be something very fundamental when one studies statistical mechanics. In statistical mechanics, for example, we find that the entropy of a system is twice the natural logarithm of the number of micostates that can replicate the given macrostate. This is, in essence, merely another way of stating that as time moves forward, the random perturbations that knock us all around tend to move everything towards states that are more likely. So, in a way, the laws of thermodynamics aren’t profound at all: they’re just a simple statement in probability.
Oops, minor issue here. I got the proportionality factor wrong in the relationship between entropy and the number of microstates that can replicate a given macrostate. Sorry about that.
For the uniniated, I also figured it might be a good idea to define what is meant by “microstate” and “macrostate”.
A microstate is merely the set of quantum numbers that are required to fully define the state. This includes things like the exact energies, momenta, and spins of the various molecules, atoms, electrons, and other particles that make up the system.
The macrostate is what we can measure of the system. Where classical thermodynamics is concerned, it might be represented as the volume, pressure, and temperature of a volume of air.
I think you can solve Neil’s question about lenses by noting that a lens just magnifies an object, it doesn’t intensify it. The most you can do with a system of lenses is to project an image of the sun from all directions at a point, but that will only make it absorb as much radiation as if it was inside the sun, where it would also “see” the sun from all directions, and we know from thermo that this will make it just as hot as the surroundings. (Making the interior of the device have an index of refraction larger than one will add some complications to this)
Thomas,
That is true in the case of conjunction of eye and optical system: for example an “exit pupil” bigger than our own can’t make an image on our retina more intense than with naked eye. So 20X50 binoculars show dark image at night, 7X50 show full surface brightness since most of us have max. 7mm pupil, but we can’t see super bright images with 2X50 etc. since the extra light is wasted coming out of a 25mm circle at the eyepiece. Same issue basically for simple lens being used to look through.
However, consider just a camera, lens and screen in back. As f/ ratio goes “smaller” (well, the denominator), like f/ 1.4, f/1.0 etc. goes down while keeping diameter the same, the image gets smaller and smaller and the same total amount of light is poured into it. Yes, if we could go down to f/0.1 etc. without losses then the image would actually be brighter than the surface of the object (watts/meter sqd. total emittance from the surfaces compared, not of course than total from the whole object.) Also note it is the surface of the sun etc. in question, that’s all we can “see” from here.
So the question is, why would rules about bending and reflecting light etc. “conspire” to prop up a principle based on particles bouncing off each other? I don’t see why, yet optics says we can’t build such a system that makes a more intense image.
PS – have fun also with my weird thought experiment about intervening in a time-reversed world,
Best,
I get that you want to use Ad Sense to pay the bills, but this is a blog of respectable scientists and some of the Ad Sense advertisements that are popping up should not be associated with this site. I don’t think Cosmic Variance and the physics that is represented here should be used to sell the likes of Quantum Books to learn the secrets of happiness, etc. that have been appearing in your advertisements. I understand that you must pay a hefty price for the bandwidth you get, but I don’t believe that should be payed for by slapping a Pepsi (if only it were pepsi) sticker on the side of science.
It’s all in the wrist, right?
Now I really must settle down and write that post I’m been planning on how to make a nice omelette.
That is the worst job of making (or unmaking) a scrambled egg I have ever seen in my life.
While we wait for Sean’s brutal crackdown on off-topic comments, let me note this new preprint by P. C. W. Davies:
We all know that SC has his own ideas about why eggs scramble but [almost] never unscramble. Question: what is the general feeling in the cosmology community about this? Do most people just hope that a solution will come along when we understand quantum cosmology, or do they really think that there is no problem here? Another way of asking this question: why isn’t there an absolutely gigantic literature on this problem? I have this uneasy feeling that if we don’t understand something so basic, there may be a lot of other, less obvious things that we misunderstand….
Neil,
I don’t think optics is “conspiring” to support the second law, any more than mechanics conspires to support the second law because perpetual motion machines all have flaws. There is a theoretical minimum f-number for lenses in part because a fast lens has to be highly curved, and you can’t make a curved lens surface with an arbitrarily large aperture; it can’t be any bigger than a hemisphere. I’ve read a claim that the theoretical fastest lens would be f/0.5, but don’t know the derivation.
That is not why you can’t use an optical system as a one-way heat conduit. In fact, I could make a big but not terribly fast lens and use it to concentrate light on a small image, like burning paper with a magnifying glass. However, if I succeeded in making the image hotter than the original light source, the image would simply reradiate back through the magnifying glass onto the source.
Ben, you may be right, but I don’t think so, for the following reasons (which I have breezed through in haste and may well have slipped up as often happens thereby):
First, you didn’t take index of refraction (and further subtleties like coatings, variable index, and even the latest “inverted” materials”) into account. That still doesn’t say why the principles would conspire, and remember that if “energy” is like a stuff, then it just can’t be concentrated more than there was. OTOH, having more heat in one spot doesn’t make more of something there can’t be more of (as opposed to mathematical concepts like entropy, but I know the distinction is blurry.) As for the re-radiation from the surface: That isn’t really the point, it’s the energy density. The same energy is being put into various size spots, as we fiddle with focal length and thus f/ratio. Imagine that we have a black body surface. Then, the total power re-radiated will soon be equal to the input. A tiny image spot will emit the same energy as a larger one, to send back onto the source. But it will be hotter because its energy is concentrated into such a small area.
Anyway, that’s my quick take, but if anyone knows better let me know. I do remember, in articles about concentration of sunlight in solar ovens (one I recall in Sci Am.), they have said: the image intensity can’t be made more than the emitting surface or it would violate Thermo 2, not that success in doing so wouldn’t matter anyway.
Dr Who, everyone is certainly aware of the problem, but it’s not something many people work on. Partly it’s from a vague (and untrue) feeling that inflation solves the problem; partly it’s because it’s hard to envision theoretical answers that could be experimentally tested; and partly because most cosmology problems can be considered independently of this one. It’s a similar situation to that of the measurement problem in quantum mechanics, or quantum gravity before the advent of string theory.
“Partly it’s from a vague (and untrue) feeling that inflation solves the problem”
Albrecht says that inflation is *part* of the solution, though as he says it really only passes the buck back to even earlier times! By the way, I found your “battleship” argument very clear indeed, thanks!!
I want to ask physics questions. Mostly about light.
Where to go?
Whom to ask?
Tom