6 ms·

The symmetry and simplicity of the laws of physics and the Higgs boson (2015)

128 points by nocoder 8y ago

natch 8y ago
Delightful presentation. I love how they used approachable analogies with things like currency exchange, and pushed the math off to an appendix.
semi-extrinsic 8y ago
Since his name is not as widely known outside the physics community, I'll just point out that Juan Maldacena (the author of this) is the guy who discovered the gauge/gravity duality (aka AdS/CFT correspondence), which is what people are on about when you hear the phrase "holographic universe". His original 1997 paper on it has been cited 17,000+ times, more than any other paper in the history of high energy physics.
- mlevental 8y ago
  sorry isn't the holographic principle related to Hawkins thing about information content in a black hole being proportional to the surface area of the event horizon (or something like that)
  - improv32 8y ago
    (Just a layman, but here's my understanding) 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_paradox 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
    - mlevental 8y ago
      > 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. this was useful. thanks.
Avshalom 8y ago
"Symmetry" is reflective not rotational. Currency exchange is a map not a graph. "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 ONE?!
- tbabb 8y ago
  Why do you object to rotational symmetry?
  - _Microft 8y ago
    Maybe the commenter is unfamiliar with what constitutes a symmetry in physics. 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) https://en.wikipedia.org/wiki/Symmetry_(physics)
    - raverbashing 8y ago
      There's even a specific page for rotational symmetry https://en.wikipedia.org/wiki/Rotational_symmetry https://en.wikipedia.org/wiki/Rotational_symmetry
- raverbashing 8y ago
  > "Symmetry" is reflective not rotational. Currency exchange is a map not a graph. "we" is "i". 3 out of the first 3 wrong, I'm curious why is this being objected so much, maybe people are annoyed about Thanksgiving.
dschuetz 8y ago
"The Beauty and The Beast" Seriously? Also, they initially make the bold statement that all four fundamental forces follow the gauge symmetry only to say later that it's just another way to look at electromagnetism, through the lens of Gauge Theory. What is it then? Why not just say that the forces follow an underlying symmetry which is described best by the Gauge Theory? Then I have to read several pages of analogy without any explanation and correspondence to the real thing. No, sorry, didn't help. Next, please!
bfirsh 8y ago
If you're on a phone, here's an HTML version: https://www.arxiv-vanity.com/papers/1410.6753/ https://www.arxiv-vanity.com/papers/1410.6753/
dschuetz 8y ago
If the number of citations is a measurement for achievement then perhaps we should put more value to the Like buttons we so frequently use. But, I'm sure he's good in what he does since so many people agree on his thoughts.
- annadane 8y ago
  ...stupid.
- diegoperini 8y ago
  I understand the criticism but do you really think a like is the same thing as a citation? A like requires a single mouse click. A citation requires a published article.
  - dschuetz 8y ago
    No, of course those are completely different things. The number still doesn't say whether his work is right or wrong. You can cite the Bible up and down and it still doesn't make it anywhere near plausible. As far as I know, Juan Maldacena is a supporter of String Theory, and despite of his minor achievements in science might being correct in context of his field, 17.000+ citations doesn't say anything about the quality of his original work on String Theory. So why even mention it? Just so to say that he's an authority in particle physics? If I had the same scientific authority as he does for a completely bonkers theory, I'd instantly say that the guy is nuts.
    - sgt101 8y ago
      I disagree - citations count is not a linear measure of quality of work, or importance, and there are significant anomalies and unfairness's in the way things get cited. For example, write an early text book and you may get a tranche of citations without doing a significant amount of important original research. Grad students who co-author with famous authors also get a significant boost due to the reputation and connectivity of their mentor. 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.
mickrussom 8y ago
higgs landed almost exactly in the middle of the range between supersymmetry and multiverse - first, the higgs is in the metastable range - a middling result. second - Higgs above the max of 115 GEV needed for supersymmetry to work and less than the 140-145 that make the multiverse theories work out. Its exactly where none of the theoretical physicists wanted it to be. back to the drawing board.
nyc111 8y ago
Since he described symmetry in terms of rotations, I would expect that the object labeled (g) in the first figure would be symmetric under 360 degrees rotation. He says it's not symmetric.
- alanbernstein 8y ago
  I suppose it's a shorthand for "no symmetries other than the trivial identity symmetry"?
  - IngoBlechschmid 8y ago
    Yes, that's indeed the case. 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.
nyc111 8y ago
> Beauty represents the forces of nature: electromagnetism, the weak force, the strong force and gravity. 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.
- frutiger 8y ago
  There are possibly two misconceptions here. 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?
  - nyrikki 8y ago
    I would clarify on this. 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.

128 points by nocoder 8y ago

Delightful presentation. I love how they used approachable analogies with things like currency exchange, and pushed the math off to an appendix.

semi-extrinsic 8y ago

Since his name is not as widely known outside the physics community, I'll just point out that Juan Maldacena (the author of this) is the guy who discovered the gauge/gravity duality (aka AdS/CFT correspondence), which is what people are on about when you hear the phrase "holographic universe". His original 1997 paper on it has been cited 17,000+ times, more than any other paper in the history of high energy physics.

mlevental 8y ago
sorry isn't the holographic principle related to Hawkins thing about information content in a black hole being proportional to the surface area of the event horizon (or something like that)
- improv32 8y ago
  (Just a layman, but here's my understanding) 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_paradox 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
  - mlevental 8y ago
    > 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. this was useful. thanks.

Avshalom 8y ago

"Symmetry" is reflective not rotational. Currency exchange is a map not a graph. "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 ONE?!

tbabb 8y ago
Why do you object to rotational symmetry?
- _Microft 8y ago
  Maybe the commenter is unfamiliar with what constitutes a symmetry in physics. 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) https://en.wikipedia.org/wiki/Symmetry_(physics)
  - raverbashing 8y ago
    There's even a specific page for rotational symmetry https://en.wikipedia.org/wiki/Rotational_symmetry https://en.wikipedia.org/wiki/Rotational_symmetry
raverbashing 8y ago
> "Symmetry" is reflective not rotational. Currency exchange is a map not a graph. "we" is "i". 3 out of the first 3 wrong, I'm curious why is this being objected so much, maybe people are annoyed about Thanksgiving.

dschuetz 8y ago

"The Beauty and The Beast" Seriously? Also, they initially make the bold statement that all four fundamental forces follow the gauge symmetry only to say later that it's just another way to look at electromagnetism, through the lens of Gauge Theory. What is it then? Why not just say that the forces follow an underlying symmetry which is described best by the Gauge Theory? Then I have to read several pages of analogy without any explanation and correspondence to the real thing. No, sorry, didn't help. Next, please!

bfirsh 8y ago

If you're on a phone, here's an HTML version: https://www.arxiv-vanity.com/papers/1410.6753/ https://www.arxiv-vanity.com/papers/1410.6753/

dschuetz 8y ago

If the number of citations is a measurement for achievement then perhaps we should put more value to the Like buttons we so frequently use. But, I'm sure he's good in what he does since so many people agree on his thoughts.

annadane 8y ago
...stupid.
diegoperini 8y ago
I understand the criticism but do you really think a like is the same thing as a citation? A like requires a single mouse click. A citation requires a published article.
- dschuetz 8y ago
  No, of course those are completely different things. The number still doesn't say whether his work is right or wrong. You can cite the Bible up and down and it still doesn't make it anywhere near plausible. As far as I know, Juan Maldacena is a supporter of String Theory, and despite of his minor achievements in science might being correct in context of his field, 17.000+ citations doesn't say anything about the quality of his original work on String Theory. So why even mention it? Just so to say that he's an authority in particle physics? If I had the same scientific authority as he does for a completely bonkers theory, I'd instantly say that the guy is nuts.
  - sgt101 8y ago
    I disagree - citations count is not a linear measure of quality of work, or importance, and there are significant anomalies and unfairness's in the way things get cited. For example, write an early text book and you may get a tranche of citations without doing a significant amount of important original research. Grad students who co-author with famous authors also get a significant boost due to the reputation and connectivity of their mentor. 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.

mickrussom 8y ago

higgs landed almost exactly in the middle of the range between supersymmetry and multiverse - first, the higgs is in the metastable range - a middling result. second - Higgs above the max of 115 GEV needed for supersymmetry to work and less than the 140-145 that make the multiverse theories work out. Its exactly where none of the theoretical physicists wanted it to be. back to the drawing board.

nyc111 8y ago

Since he described symmetry in terms of rotations, I would expect that the object labeled (g) in the first figure would be symmetric under 360 degrees rotation. He says it's not symmetric.

alanbernstein 8y ago
I suppose it's a shorthand for "no symmetries other than the trivial identity symmetry"?
- IngoBlechschmid 8y ago
  Yes, that's indeed the case. 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.

nyc111 8y ago

> Beauty represents the forces of nature: electromagnetism, the weak force, the strong force and gravity. 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.

frutiger 8y ago
There are possibly two misconceptions here. 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?
- nyrikki 8y ago
  I would clarify on this. 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.