Physicist and dabbler in writing fantasy/science fiction.
Ben
Karma: 2,392
I find that surprising, given that so much of your writing feels kind of crisp and minimalist. Short punchy sentences. If that is how you think your mind is very unlike mine.
Much as I liked the book I think its not a good recomendation for an 11 year old. There are definitely maths-y 11 year olds who would really enjoy the subject matter once they get into it. (Stuff about formal systems and so on). But if we gave GEB to such an 11 year old I think the dozens of pages at the beginning on the history of music and Bach running around getting donations would repel most of them. (Urgh, mum tricked me into reading about classical music).
I am all for giving young people a challenge, but I think GEB is challenging on too many different fronts all at once. Its loooong. Its written somewhat in academic-ese. And the subject matter is advanced. So any 11 year old who could deal with one of that trinity also has to face the other two.
Yes, you could fix it by making the portal pay for lifting. An alternative fix would be to let gravity go through portals, so the ball feels the Earth’s gravity by the direct route and also through the portal. Which I think makes the column between the two portals zero G, with gravity returning towards normal as you move radially. This solution only deals with the steady-state though, at the moment portals appear or disappear the gravitational potential energy of objects (especially those near the portal) would step abruptly.
Its quite a fun situation to think about.
“If I’m thinking about what someone else might do and feel in situation X by analogy to what I might do and feel in situation X, and then if situation X is unpleasant than that simulation will be unpleasant, and I’ll get a generally unpleasant feeling by doing that.”
I think this is definitely true. Although, sometimes people solve that problem by just not thinking about what the other person is feeling. If the other person has ~no power, so that failing to simulate them carries ~no costs, then this option is ~free.
This kind of thing might form some kind of an explanation for Stockholm Syndrome. If you are kidnapped, and your survival potentially depends on your ability to model your kidnapper’s motivations, and you have nothing else to think about all day, then any overspill from that simulating will be maximised. (Although from the wikipedia article on Stockholm syndrome it looks like it is somewhat mythical https://en.wikipedia.org/wiki/Stockholm_syndrome)
I agree that its super unlikely to make any difference, if the LLM player is consistently building pylons in order to build assimilators that is a weakness at every level of slowdown so has little or no implications for your results.
An interesting project. One small detail that confuses me. In the first log is the entry:
"Action failed: BUILD ASSIMILATOR, Reason: No Pylon available"But, in SC2 you don’t need a pylon to build an assimilator. Perhaps something in the interface with the LLM is confused because most protos buildings do need a pylon and the exception is no accounted for correctly?
I am sure that being cited by wikipeida is very good for giving an article more exposure. There is an “altimetric” thingy on some journals that is used to help funders see what other useful impacts an article had on the world beyond citations from other articles, and it thinks wikipedia mentions are high-value (it also likes things like newspaper coverage).
I suspect that it is not that rare for the authors of a paper to go and put a link in wiki to their own paper. I have certainly seen wiki articles mention something with a cite, which, while true, feels weirdly specific.
Thank you very much, that sounds like a fascinating wider discussion. Personally, I suspect the Abraham-Minkowski question is only unusual in the sense that it is a known unknown. I think the unknown unknowns are probably much larger in scope. Although it is probably quite dependent on where exactly you draw the physics/engineering boundary.
In my post the way I cited Lubos Motl’s comment implicitly rounded it off to “Minkowski is just right” (option [6]), which is indeed his headline and emphasis. But if we are zooming in on him I should admit that his full position is a little more nuanced. My understanding is that he makes 3 points:
(1) - Option [1] is correct. (Abraham gives kinetic momentum, Minkowski the canonical momentum)
(2) - In his opinion the kinetic momentum is pointless and gross, and that true physics only concerns itself with the canonical momentum.
(3) - As a result of the kinetic momentum being worthless its basically correct to say Minkowski was “just right”(option [6]). This means that the paper proposing option [1] was a waste of time (much ado about nothing), because the difference between believing [1] and believing [6] only matters when doing kinetics, which he doesn’t care about. Finally, having decided that Minkowski was correct in the only way that he thinks matters, he goes off into a nasty side-thing about how Abraham was supposedly incompetent.So his actual position is sort of [1] and [6] at the same time (because he considers the difference between them inconsequential, as it only applies to kinetics). If he leans more on the [1] side he can consider 12.72 to be valid. But why would he bother? 12.72 is saying something about kinetics, it might as well be invalid. He doesn’t care either way.
He goes on to explicitly say that he thinks 12.72 is invalid. Although I think his logic on this is flawed. He says the glass block breaks the symmetry, which is true for the photon. However, the composite system (photon + glass block) still has translation and boost symmetry, and it is the uniform motion of the center of mass of the composite system that is at stake.
Yes, you are certainly right it is a quasiparticle. People often use the word polariton to name it (eg https://www.sciencedirect.com/science/article/pii/S2666032620300363#bib1 ).
I think you might have muddled the numbering? It looks like you have written an argument in favor of either [2] or [3] (which both hold that the momentum of the full polariton is larger than the momentum of the photonic part alone—in the cartoon of the original post whether or not the momentum “in the water” is included), then committed to [1] instead at the end. This may be my fault, as the order I numbered the arguments in the summary at the end of the post didn’t match the order they were introduced, and [2] was the first introduced. (In hindsight this was probably a bad way to structure the post, sorry about that!)
″ “passing by atoms and plucking them” is a lie to children ”—I personally dislike this kind of language. There is nothing wrong with having mental images that help you understand what is going on. If/when those images need to be discarded then I don’t think belittling them or the people who use them is helpful. In this case the “plucking” image shows that at any one time some of the excitation is in the material, which is the same thing you conclude.
[In this case I think the image is acceptably rigorous anyway, but lets not litigate that because which mental images are and are not compatible with a quantum process is a never ending rabbit hole.]
Thank you very much for reading and for your thoughts. If I am correct about the numbering muddle it is good to see more fellow [2/3]’ers.
I presented the redshift calculation in terms of a single photon, but actually, the exact same derivation goes through unchanged if you replace every instance of with and with . Where and are the energy of a light pulse before and after it enters the glass. There is no need to specify whether the light pulse is a single photon a big flash of classical light or anything else.
Something linear in the distance travelled would not be a cumulatively increasing red shift, but instead an increasing loss of amplitude (essentially a higher cumulative probability of being absorbed). This is represented using a complex valued refractive index (or dielectric constant) where the real part is how much the wave slows down and the imaginary part is how much it attenuates per distance. There is no reason in principle why the losses cannot be arbitrarily close to zero at the wavelength we are using. (Interestingly, the losses have to be nonzero at some wavelength due to something called the Kramers Kronig relation, but we can assume they are negligible at our wavelength).
I think the point about angular momentum is a very good way of gesturing at how its possibly different. Angular momentum is conserved, but an isolated system can still rotate itself, by spinning up and then stopping a flywheel (moving the “center of rotation”).
Thank for finding that book and screenshot. Equation 12.72 is directly claiming that momentum is proportional to energy flow (and in the same direction). I am very curious how that intersects with claims common in metamaterials (https://journals.aps.org/pra/abstract/10.1103/PhysRevA.75.053810 ) that the two can flow in opposite directions.
“And then conservation of momentum implies uniform motion of the center of mass, right?”—This is the step I am less than 100% on. Certainly it does for a collection of billiard balls. But, as soon as light is included things get less clear to me. It has momentum, but no inertial mass. Plus, as an admittedly weird example, the computer game “portal” has conservation or momentum, but not uniform motion of the centre of mass. Which means at the very least the two can logically decouple.
I consider momentum conservation a “big principle.”, and Newtons 3 laws indeed set out momentum conservation. However, I believe uniform centre of mass motion to be an importantly distinct principle. The drive loop thing would conserve momentum even if it were possible. Indeed momentum conservation is the principle underpinning the assumed reaction forces that make it work in the first place. To take a different example, if you had a pair of portals (like from the game “portal”) on board your spaceship, and ran a train between them, you could drive the train backwards, propelling your ship forwards, and thereby move while conserving total momentum, only to later put the train’s breaks on and stop. I am not asking you to believe in portals, I am just trying to motivate that weird hypotheticals can be cooked up where the principle of momentum conservation decouples from the principle of uniform centre of mass motion. The two are distinct principles.
Abraham supporters do indeed think you can use conservation of momentum to work out which way the glass block moves in that thought experiment, showing that (because the photon momentum goes down) the block must move to the right. Minkowksi supporters also think you can use conservation of momentum to work out how the glass block moves, but because they think the photon momentum goes up the block must move to the left. The thing that is at issue is the question of what expression to use to calculate the momentum, both sides agree that whatever the momentum is it is conserved. As a side point, a photon has nonzero momentum in all reference frames, and that is not an aspect of relativity that is sensibly ignored.
You are actually correct that the photon does have to red-shift very slightly as it enters the glass block. If the glass was initially at rest, then after the photon has entered the photon has either gained or lost momentum (depending on Abraham or Minkowski), in either case imparting the momentum difference onto the glass block. The kinetic energy of the glass block is given by where p is the momentum the block has gained, and m is the block’s mass. The photon’s new frequency is then given by (by conservation of energy) where was its initial frequency. In practice a glass block will have a very gigantic mass compared to , but at least in principle the photon does red shift.
Going into the full gory detail for Abraham.
Abraham:
Photon momentum before entering glass
Photon momentum after entering glass (note, new frequency , not the old one)
Change in photon momentum
The same momentum goes into the glass, soWe can re-arrange to put the c^2 in the denominator next to the mass of the glass block. So that the change in the frequency/energy of the photon is scaled by a term that has something to do with the refractive index, along with how the photon energy compares to the rest mass energy of the glass block (). So, as previously said, this is negligible for a glass block that weighs any reasonable amount.
The Minkowski version is almost the same derivation, except the division by refractive index becomes a multiplication, giving:
Playing with these quadratic equations, to solve for , you find that the Abraham version never breaks. In contrast, if you assume it is possible to have a glass block with a reasonably high refractive index, but arbitrarily small mass, then Minkowski eventually breaks and starts giving an imaginary frequency. This maybe says something vaguely negative about Minkowski, but a block of material with a high refractive index but negligible mass is such an unrealistic setup that I don’t think failing in that case is too embarrassing for the Minkowski equation.
My thoughts on this are not going to be fully coherent, because I am in the process of possibly changing my mind.
I agree that if we take the uniform motion of centre of mass as an absolute principle then the weird light-in-circles machine does not work. However, I had never before encountered this principle, and (to me) it still carries the “I learned about this last week, how much do I trust it?” penalty. But, even accepting it, that doesn’t explain why the machine fails. Does it remain the case that the actual mechanical momentum and energy transport directions are opposite in the right metamaterial (as claimed in, for example: https://journals.aps.org/pra/abstract/10.1103/PhysRevA.75.053810 ), but the machine fails for some other reason (eg. recoils on the interfaces)? Showing the machine to be impossible while leaving this unanswered doesn’t get to the roots of my various related confusions, I still don’t know whether energy flow and momentum can ‘really’ point opposite directions, or whether it’s all just an accounting trick.
The uniform motion of centre of mass implies other things. For example, it means anything like a portal from the game “portal” is impossible as the centre of mass would change discontinuously as something went through the portal. [We can even “re-skin” of the photon loop by instead having a train with portals, so it can keep reusing the same track on our space ship repeatedly].
Numbering the options properly is a good idea, done.
To answer your points:
This is interesting. Symmetry under rotations gives us conservation of angular momentum. Symmetry under translations conservation of linear momentum. You are saying symmetry under boosts gives conservation of centre of mass velocity. Although in “normal” situations (billiard balls colliding) conservation of centre of mass velocity is a special case of as conservation of linear momentum—which I suppose is why I have not heard of it before. I need to look at this more as I find I am still confused. Intuitively I feel like if translation symmetry is doing momentum for us boost symmetry should relate to a quantity with an extra time-derivative in it somewhere.
There is no symmetry under angular boosts, which I imagine is why fly-wheels (or gyroscopes) allow for an “internal reaction drive” for angular velocity.I did not know that the kinetic and canonical momentum had different values in other fields. That makes option (1) more believable.
Yes, the k-vector (wavevector) certainly extends by a factor of . So if you want your definition of “momentum” to be linear in wavevector then you are stuck with Minkowski.
I believe, that at the interface between the water and the air we will have a partial reflection of the light. The reflected component of the light has an evanescent tail associated with it that tunnels into the air gap. If we had more water on the other side of the air gap then the evanescent tail would be converted back into a propagating wave, and the light would not reflect from the first water interface in the first place. As the evanescent tail has a length of the order of a wavelength this means that random gaps between the atoms in water or glass don’t mess with the propagating light wave, as the wavelength is so much longer than those tiny gaps they do not contribute.
Applying this picture to your question, I think we would expect to interpolate smoothly between the two momentum values as the air gap size was changed, with the interpolation function an exponential with decay distance equal to the length of our evanescent wave.
Thanks for reading. Enjoy your option (1)!
Momentum of Light in Glass
This is very interesting, thank you for sharing it.
I find the 5 day limits (without approval) quite insane. Even assuming that means 5 actual days (and not 20% of 5 days = 1 full day). Lets say you have an employee who has now put 5 days into their preferred passion project. You end it. They then put 5 says into their second-favourite passion project. The end result is an annoyed employee who has half-finished a train of side-projects and is still putting 20% of their time to one side from core duties.
My current work (university) is thankfully very flexible, so maybe I am seeing things from the wrong perspective.
I agree with this.
In my very limited experience (which is mostly board games with some social situations thrown in), attempts to obscure publically discernible information to influence other people’s actions are often extremely counter-productive. If you don’t give people the full picture, then the most likely case is not that they discover nothing, but that they discover half the picture. And you don’t know in advance which half. This makes them extremely unpredictable. You want them to pick A in preference to B, but the half-picture they get drives them to pick C which is massively worse for everyone.
In board games I have played, if a slightly prisoner’s dilemma like situation arises, you are much more likely to get stung by someone who has either misunderstood the rules or has misunderstood the equilibrium than someone who knows what is going on. [As a concrete example, in the game Scyth a new player believed that they got mission completion points for each military victory, not just the first one. As they had already scored a victory another played reasoned they wouldn’t make a pointless attack. But they did make the pointless attack. It set them and their target back, giving the two players not involved in that battle a relative advantage.]
“The best swordsman does not fear the second best, he fears the worst since there’s no telling what that idiot is going to do.” [https://freakonomics.com/2011/10/rules-of-the-game/#:~:text=%E2%80%9CThe%20best%20swordsman%20does%20not,can%20beat%20smartness%20and%20foresight%3F]
This best swordsman wants more people to know how to sword fight, not fewer.
This idea (without the name) is very relevant in First Aid training.
For example, if you learn CPR from some organisations they will teach you compressions-only CPR, while others will also teach you to do the breaths. I have heard it claimed by first aid teachers that the reason for this is because doing the best possible CPR requires the breaths, but that someone who learned CPR one afternoon over a year ago and hasn’t practiced since is unlikely to do effective breaths, and that person would be better of keeping to compressions only.
In First Aid books a common attempt to solve this problem is to give sweeping commands at the beginning (often with the word “never” somewhat abused), and then give specific exceptions later. The aim is that if you will remember one thing it will hopefully be the blanket rule, not the specific exception. I think that method probably has something to recommend for it, its hard to imagine how you could remember the exception without remembering the rule it is an exception too.
[For example the Life Support book, tells you ‘never’ to give anyone medicine or drugs, as you are a First Aider, not a Doctor. It also tells you to give aspirin to someone having a heart attack if they have not taken any other drugs. I think it also recommends antihistamines for swelling insect stings.]