The symmetry and simplicity of the laws of physics and the Higgs boson (2015)
arxiv.org
arxiv.org
That's another instance where the holographic principle applies. To hand-wave, the holographic principle applies to any theory describing a system, where you can make an equivalent description of the system using only information on its boundary. For example, in the black hole case, if you know the state of the system inside the event horizon, every particles' position and momentum in 3D, then you could describe how the state will evolve based on the usual laws of physics.
But by definition, that information is unavailable to an observer outside the event horizon. This presents a thermodynamic conundrum. We take as an axiom that in a closed system, total entropy can never decrease. Think of entropy as the compressibility of information. A string of a thousand 0 bits followed by a thousand 1 bits is highly compressible (low entropy/high order), while a perfectly random sequence of bits cannot be compressed at all (high entropy/low order). Equivalently in the physical world, an egg has somewhat low entropy, yolk encased in egg white encased in shell, a complete description is succinct. But if you scramble the egg, suddenly full knowledge of its state requires lots of information, you have to know the specific positions of every particle of yolk and white to have the whole picture.
We consider this an axiom because we want physical law to obey time-symmetry. In a deterministic universe, you should be able to take a full physical state and "run it in reverse" to get previous states. If you could decrease entropy, go from a globally random state to a globally ordered one, then you would lose information about the starting conditions. Just like matter and energy, information can never be destroyed (we suppose).
Okay so the universe taken as a whole is a closed system, with ever increasing entropy, i.e. over time more bits are required to understand its full state. Now toss your scrambled egg into a black hole. It crosses the event horizon and poof it's gone. Is information lost? Can we, in principle, run the universe in reverse and see an egg come back out? Where did those bits go?
The interesting thing about black holes is that all the information required to understand their behavior right there on the boundary of the event horizon. Specifically, the number of distinct physical states that a black hole can take on is proportional to its surface area, not its volume as you'd expect for an spherical region of ordinary space.
How exactly does that work? At this point my understanding sadly falls off. But I can point to this as a good starting point for the so inclined: https://en.m.wikipedia.org/wiki/Black_hole_information_parad...
The Ads/CFT correspondence is also a bit above my head, but it relates string theory to quantum field theory. It introces the anti-de Sitter space, which is a space in which geometry is non-euclidian, very similar to a hyperbolic space, where the boundaries are like asymptotes, you can get as close as you want but never reach it. The interesting thing is the geometry of that boundary space. For an appropriate Ads, its boundary has the same geometry as our 4D spacetime (it's a Minkowsy space, to be precise). The idea is that low-dimensional string-theory stuff happens in the interior (bulk) of the Ads space, and the boundary is the spacetime we know and love. The correspondence is that a complete theory of the boundary (QFT describing spacetime) can also completely describe the action in the bulk, and vice-versa. The mind bending thing about an Ads is that it's boundary is actually higher dimensional than the space as a whole. Analogous to how in linear algebra, you can project a space into a higher dimensional space without losing information.
Wow didn't mean for that to be so long. If anyone knows better than me and I've made a mistake please do point it out, I'm just a casual observer who loves getting in deep with this stuff.
EDIT: Oops, just now went back read your question and realized you probably knew all of that and I didn't even answer your actual question. Hopefully someone else finds this interesting! Specifically about the surface area thing, when something falls into a black hole from an outside view you never actually see it cross, as gravity increases on the object from your point of view it undergoes time dialation, redshifting the light it emits, and length contraction, flatting it along an axis normal to the black hole's surface. In the limit the object falls slower and slower, getting flatter and flatter, and dimmer and dimmer and ultimately "smeared out" across the surface, Hawking radiation emitted from some kind of virtual particle interaction I don't understand interacts with the object on the boundary, making the information recoverable from those interactions. Or something like that
this was useful. thanks.
Its exactly where none of the theoretical physicists wanted it to be.
back to the drawing board.
The point of General Relativity is that gravity is not a force. I'm familar with standard argument that Newtonian force is a suitable approximation. But he is being careless with a very fundamental concept. Gravity is either a force or it is not. In physics it looks like it is a force when the author needs a force and it is not a force when the author feels like it.
Firstly, there is a possible misconception that gravitational effects can be transformed away under GR, since GR permits non-inertial reference frames as valid frames to view gravitational phenomena. The usual consideration is that a mass in a gravitational field is at rest in a free-falling frame (e.g. a ball in an elevator in free-fall). This is a misconception! For example, two such masses in free-fall around a spherically symmetric field will actually converge as they approach the centre of the field. This aspect of gravity is known as "tidal gravity". And the formulas of GR relate stress-energy with curvature precisely to explain tidal gravity. This aspect of gravity is the real physical aspect; if all gravity could be transformed away, there'd be nothing to say about gravity at all!
Secondly, there is a possible misconception about what a force is. It is not as simple as F = ma (or even F = dp/dt). We say there is a field that influences the motion of objects which couple to the field. For gravitation, there is indeed such a field (the spacetime metric) and it couples to anything that has mass, just as for electromagnetism, there is a field that couples to anything that has electromagnetic charge. Why then, would gravity not be a force?
1) Gauge theory only includes Special Relativity, a quantum theory of gravity is simply an unsolved problem so far.
2) In GR gravity is a 'fictitious force', which would cause less problems if they had use the term 'apparent' or 'inertial' force. It is a force observed which is an artifact of your reference frame.
3) In natural units 1 unit of "time" is a huge dimension compared to the spacial dimensions and the Earth is following the geodesic or the "straightest" path around the sun due to curvature in that dimension.
4) While 'radially inward' does happen with inward falling, that is more of an issue about trying to extend euclidean space past it's useful domain, you are going non-local at that point. That radial inward path convergence is length contraction in the spacial domain, which is smaller than the more observable time effects but it is still an artifact of one's reference frame.
Most proposed quantum theories of gravity view it as a force field that is like the other force fields in QFT. Time will tell if they can accurately create a model that works in a way that can stay in a euclidean space.
Everyone has their favorite. To be honest I like geometry more than algebra so I prefer GR, but really I just someone comes up with a model that works. Noting my bias, I think eventually QM is going to have to give up on the quantum mechanical hope for gravitation and resort to a non-euclidean solution. As I can't imagine 4D I would be happy for someone to prove me wrong.
So it is not a force then! A force is an action at a distance between two masses. This is what I'm trying to say. Maldacena is using the word force in the context of GR but we do not know what he means by that word.
I should warn than in QM the notion of "force" is based on operators and not variables and the stricter Newtonian definition is going to run into problems.
But you did not explain force you just redefined it to suit your argument. In the Newtonian regime force is defined as action at a distance between two masses. Your notion of field does not exist in the Newtonian regime.
Einstein did not believe that action at a distance is possible so he tried to explain gravity without action at a distance, ie, without force.
Gravity cannot be a force and not a force at the same time. It's either a force or not a force.
A bit of background: Every object has a "group of symmetries". The smallest and easiest groups are those groups which contain only a single element, in case of symmetry groups the trivial identity symmetry. All those one-element groups are also referred to as "the trivial group". By abuse of language, we sometimes say that a object has "no" symmetries if it only has the trivial one.
A like requires a single mouse click. A citation requires a published article.
But, I think that most senior academics will have less than 15k citations in total. 17k citations for a single paper is remarkable; it's an indication of work that was important, original and definitive.
I only referee in compsci, but in compsci citing papers that are nothing to do with the work in hand, and citing them to generate authority for your arguments does not wash and leads to rejections. Citations point to the basis of your work; establishing that you are building on firm foundations and differentiating your contribution from previous contributions to enable the reader to learn. Being cited in this way is being a teacher to the community.
"The problem here is that of what is an “interesting region of theory space”. At this point the failures of string theory unification strongly indicate that it’s not such an interesting region. It seems likely that we’d be better off if most theorists focusing on phenomenology of this failed program were to pick something else to work on."
And as far as I could follow his work and attempts to explain symmetry with economics analogies, I think my concerns are valid. https://www.math.columbia.edu/~woit/wordpress/?p=9375
One must also cite a work if one is writing a paper which disagrees with that work's conclusions, criticizes its methods, or points out a fault in its theoretical content. This has a particular benefit for readers.
Woit himself carefully cites works he strongly objects to in his book[1] that shares its name with the blog you linked to.
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[1] Woit P. Not even wrong: The failure of string theory and the search for unity in physical law. Basic Books (AZ); 2006 Sep 4., pp 268-274. (cf. http://www.math.columbia.edu/~woit/NEWerrata.html )
Not in physics. Most physicists cite without reading original sources. This is a real problem. The citations standards in physics is really low. There was a research about this but I cannot find it now. It was about the corruption in the title of one of Einstein's most cited papers. Like generations of photocopying corrupts the original, physicists copied the citation from other citations without bothering to check the original and the title became something else. It was funny.
It would be a nice project to get the ADG of citations with this paper as root and make a graph of it. My guess it that it will be something that looks similar to tree (each paper in a branch would cite a few recent papers in the same branch), but most of the papers in the tree would cite also the root paper too.
Finally, i'm guilty of occasionally looking at some HN user profile and just to see how many upvotes it has. If the user has 15k+, I always go "wooooow" ^^ So yeah.
But then again, as a fellow commenter has already pointed out, a like requires a click and a citation a publication.
(and if that's the case, is there any way to separate the two?)
Yes, obviously citations are a heuristic for achievement and Likes are not. Citations signal that one piece of research has had impact on another. It doesn't immediately declare the research is true and valid, but it does signify the research has held up to the scrutiny of n other researchers who felt it worthwhile enough to include in their own work.
Likes do not involve any of that reputation staking mechanism, nor do they involve experts in a review process that can reject papers by design. It would be incoherent to claim 17,000 upvotes on reddit give a paper anything resembling the weight of 17,000 citations.
"we" is "i".
if physics is simpler than economics than using economics as a metaphor for physics is the exact fucking opposite of useful.
There is no cited proof that "An extra dimension is not a necessary assumption, only the symmetry is."
The Maxwell equations bare no resemblance to exchange rates.
It turns out that the mass of the particle is related to the energy cost to excite a very long wavelength wave. This is related to the famous formula E = mc 2 . Unfortunately I have not found a short way to explain this, so you will have to trust me on this. In our economic analogy we have not talked about energy. Let us simply say that the energy increases as the gain available to speculators increases. This makes intuitive sense, the more the speculators can earn, the harder it is for the banks!
Okay I admit this analogy makes no sense but lets keep going...?
3.1 Apologizing for one oversimplification
In physics, a symmetry of a physical system is a physical or mathematical feature of the system (observed or intrinsic) that is preserved or remains unchanged under some transformation, from https://en.wikipedia.org/wiki/Symmetry_(physics)
3 out of the first 3 wrong, I'm curious why is this being objected so much, maybe people are annoyed about Thanksgiving.