
The symmetry and simplicity of the laws of physics and the Higgs boson (2015) - nocoder
https://arxiv.org/abs/1410.6753
======
semi-extrinsic
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
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
(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_parad...](https://en.m.wikipedia.org/wiki/Black_hole_information_paradox)

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
> 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.

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bfirsh
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/)

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

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mickrussom
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.

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nyc111
> 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
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
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.

~~~
nyc111
> It is a force observed which is an artifact of your reference frame.

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.

~~~
nyrikki
Correct, in GR gravity is not a force between masses but an effect of the
warping of space and time in the presence of mass. That said, Using the
concept of "Gravity" as a "force" is very useful in the special or limited
cases. In fact it may be the only way to model some problems where one can't
find an exact solution to the EFEs. The concept is invaluable as a tool for
visualization. Most of us cannot visualize the non-euclidean impacts of the
Ricci tensor or the Weyl terms.

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.

------
nyc111
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
I suppose it's a shorthand for "no symmetries other than the trivial identity
symmetry"?

~~~
IngoBlechschmid
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.

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dschuetz
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.

~~~
throwawaymath
Just to be clear here, you're drawing a comparison between citations in peer
reviewed papers - written and refereed by experts in a field - and Like
buttons clicked by non-experts on social media? I feel compelled to ask if
you're arguing in good faith, because if you have a valid point I can't
immediately think of a worse comparison to use.

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.

~~~
wallace_f
I wonder if there is a good way to study biases in academia, which is maybe
what the poster was getting at? Feynman criticized aspects of academia as
being "rotten" for the record...

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dschuetz
"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!

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Avshalom
"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
Why do you object to rotational symmetry?

~~~
_Microft
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
There's even a specific page for rotational symmetry
[https://en.wikipedia.org/wiki/Rotational_symmetry](https://en.wikipedia.org/wiki/Rotational_symmetry)

