The Computational Universe: Debunking the Myth or Proving the Possibility?

[sirchasm]

There's a handful of cosmologists and QM types who claim "the universe computes".
There's another crowd who insist this is rubbish - the universe isn't a computer.

However, it certainly appears to be 'computational'; this is demonstrable: if we can write a program that simulates a real physical process (the gas laws, say), and do this for all of the processes we know about (so all the simulations then prove that we do know, if they exactly reproduce these processes in "computer-space", i.e. virtually), then a simulation of the known universe exists.

If there is no actual physical computation (the universe we simulate is only our imaginary version of whatever it really is) then we should be able to write a program that demonstrates 'no physical computation exists', using a real physical computer, since the computer (we use to write the simulation) really isn't physical...

See where this is going?

Alternately, we should be able to write a program (on a real/imaginary computer) that proves "no computation occurs, the universe does not compute, it isn't computational". So why haven't we?

 

[marcus]

There's another crowd who insist this is rubbish - the universe isn't a computer.

Name a few scientists in that crowd, please.

I'd be interested in seeing links to actual articles by these people insisting that the universe is not a computer.

 

[sirchasm]

Hmm. Well, I can't say I have found any that specifically deny it, or even argue why it isn't.

I keep running into "crusty&old" types on forums who claim it's wrong, anytime I bring up the subject. I would guess they are only pseudo-cosmologists.

Me, I'm a cosmologist who hasn't done any "real" study other than on my own.

 

[Vanadium 50]

Me, I'm a cosmologist who hasn't done any "real" study other than on my own.

That's an interesting description. How does that differ from someone who is "interested in cosmology"?

 

[marcus]

If I remember correctly there was a brief time like 2003-2005 when some in the professional research community tried thinking of the universe as a network of finite-state automata.
Space was a network of cells, each cell was a computer of some simple sort.

Then it seems like everybody lost interest. They found out some stuff. Proved some theorems. And moved on.

Currently there seem to be other concepts getting more attention---other ways of imagining the most fundamental building blocks of reality and how they interact.

That's just my impression. I could be wrong.

As I recall the brightest most excited person in that bunch was
Seth Lloyd. He's at MIT. You could look up his papers. I think they would be mostly 2004 and 2005. I think he has moved on to other stuff since then.
Here's a sample 2005 paper of Lloyd's
http://arxiv.org/pdf/quant-ph/0501135v8
I never heard of anyone in the professional research community attacking the idea.
It is, for a lot of people, just not the most interesting way to approach the fundamental nature of space, time, and matter.

If something is not too interesting and just produces a few results, then people don't attack they just pay less attention.

There is a new book coming out next month called Approaches to Quantum Gravity,
Towards a New Understanding of Space, Time, and Matter. It will give a semi-up-to-date picture of the different research areas and which ideas are getting the attention now.
You might check out the table of contents. It could even be that Seth or one of the other who pursued that idea has been included. The book is broadly inclusive of all the current approaches.
http://www.cambridge.org/uk/catalogue/catalogue.asp?isbn=9780521860451

 

[sirchasm]

Seth Lloyd. He's at MIT. You could look up his papers.

Bingo - I "took on" his online course on QIS (I have a 1/2 postgrad in IS) and have only really started to think about the informational angle - which is kind of obvious if you've done any Optics lately, or EE (which I have), so uh huh, etc.

Dr Lloyd led to various other online lecture notes, encoding anyon states and the Hall effect-AB link (if that's what it is) superconduction, trapped ion research.

Eventually, if you've done any (real) IS, you have to ask yourself, "which part is the signal" when you look at QM.

 

[sirchasm]

How does that differ from someone who is "interested in cosmology"?

Well, there's forum stuff, like this, there's online lecture notes, then there's actual lectures, I suppose.

 

[sirchasm]

I have this 'kind-of' model of spin as a 'smallest' potential that generates virtual particles; because spin is binary (and has a dual space in the EM field) we get a smallest process - which is a spin-flip.

Because you have to have minimum 1 d.o.f. to flip something, the dual space has to occupy two others. The signal here is photon momentum or p, and a single flip in arbitrary t and s is a virtual photon, in spacetime. There's a Planck 'process' driving a background 'noise' that is a medium for transmission. the dual space has a dual transmission limit, overall transmission limit is then the interactions between background noise and the signal, or p.

 

[zankaon]

Nature as a computer?

Nature can not be calculating orbits. If it did, then there would have to be rounding off at certain significant number of digits; hence accumulated error and instability. Alternatively, if the calculation continued to any degree of accuracy, then the Turing tape (i.e. universal computing machine) would never end. http://en.wikipedia.org/wiki/Turing_machine" So it would seem that nature has a geometric description for orbits; hence not a computer analogy.

 

[Chronos]

The computational model is attractive. The universe does appear to be mathematically consistent.

 

[sirchasm]

... it would seem that nature has a geometric description for orbits; hence not a computer analogy.

A TM can't enumerate irrational numbers, but e.g. pi can be encoded - any exact geometrical number can be. But any TM, even a UTM, can only enumerate rationals. We can only rationalise the universe with TMs, but we can rationalise the TMs are complete.

 

[Chalnoth]

Well, there is a fundamental difference between the basic building blocks of the universe acting as computers, and the universe as a whole acting as one. There is no question, really, that the universe as a whole does not act like a computer. There is also no question that at least certain parts of the universe do (i.e. computers).

But do the fundamental building blocks act like very simple, interacting computers acting out a simple program? I would tend to suspect that any method of interaction between fundamental particles could be described in this way, so it sounds more like a potentially useful tool for understanding or calculating these interactions than a deep statement about the nature of reality.

 

[sirchasm]

There is no question, really, that the universe as a whole does not act like a computer. There is also no question that at least certain parts of the universe do (i.e. computers).

But there is so a question, that the universe is not a computer. When you say computers (the one you use to post in threads, e.g.), are you excluding things like chemistry, spectroscopy, instrumentation - oscilloscopes, counter-timers, voltmeters etc?

The universal question is: Is the universe made of computers, and if so, is the universe also a computer?

(translation: is the universe made of processes, and is the universe a process?)

Alternately, can you write a program that gives a result = "the universe is not a computer?" (see OP)

 

[Chalnoth]

But there is so a question, that the universe is not a computer. When you say computers (the one you use to post in threads, e.g.), are you excluding things like chemistry, spectroscopy, instrumentation - oscilloscopes, counter-timers, voltmeters etc?

The universal question is: Is the universe made of computers, and if so, is the universe also a computer?

(translation: is the universe made of processes, and is the universe a process?)

Alternately, can you write a program that gives a result = "the universe is not a computer?" (see OP)

There are a multitude of reasons why the universe as a whole does not act like a computer.

One simple reason is that it is impossible for regions of the universe far enough away from one another to communicate.

 

[sirchasm]

So these parts that can't communicate as far as we can define regions, imply that much of the universe isn't 'in' communication?

But since it's expanding, the parts that are now "informationally separated", are the result of expansion = a process.
Therefore, the result of this process = informationally separated parts of the universe, including all the parts that have expanded beyond an informational horizon at infinity"

What you mean is, when you include real noise, communication is attenuated for a signal p.
Attenuation is infinite for an infinite real noise = mass. Mass separated by a distance greater than the universal signal limit cannot communicate.

 

[dilletante]

One simple reason is that it is impossible for regions of the universe far enough away from one another to communicate.

It is impossible for people to communicate, but does that mean it is impossible for the universe to communicate? We cannot use entanglement for example to exchange information but maybe the universe can?

 

[Chalnoth]

It is impossible for people to communicate, but does that mean it is impossible for the universe to communicate? We cannot use entanglement for example to exchange information but maybe the universe can?

Entanglement doesn't exchange information.

 

[TalonD]

It is impossible for people to communicate, but does that mean it is impossible for the universe to communicate? We cannot use entanglement for example to exchange information but maybe the universe can?

how do particles become entangled? Is it merely proximity? so since the universe was in the beginning a singularity does that mean all particles are quantum entangled? Doesn't seem to be so.

Also...
how are we defining what a computer is?

 

[sirchasm]

We might consider entanglement as a kind of superposition; connections between mass (with intrinsic spin) that are 'distance-free', or fixed in time.
Measurement appears here as an operator that fixes one end of a connection to a local frame; distance is then an operator that measures entanglement.

Entanglement entropy is the weight of the connection(s) over a time interval of distances. Or the entropy is a distance measure which is time-independent.

Although it can't exchange information, it is an exchange; in what degree of freedom though?

 

[Chalnoth]

how do particles become entangled? Is it merely proximity?

They undergo some interaction which forces them into a superposition of states where neither particle is in a definite state, but with a definite correlation.

For example, if we examine the two electrons in the ground state of the helium atom, they are entangled: Both of the electrons are in a superposition of spin up and spin down, but the physics of being in the ground state necessitates that their spins be opposite. Therefore if we measure one to be spin up, a measurement of the other will necessarily generate spin down.

so since the universe was in the beginning a singularity does that mean all particles are quantum entangled? Doesn't seem to be so.

The universe wasn't a singularity, though everything we observe today was once very close together. Either way, though, this doesn't mean that stuff far away is entangled, as entanglement is lost through interaction with the environment. In the above example with the helium atom in the ground state, for instance, once I've measured the spins of the two particles, they are no longer entangled, as the way in which I disturbed the electrons in order to obtain their spins messed that up.

Also...
how are we defining what a computer is?

Well, in the most general sense, a computer is a device which takes some sort of input and produces an output. This is one reason why it's difficult to consider the universe as a whole as a computer: different regions become causally disconnected from one another, meaning that it's impossible to determine this "output".

 

[sirchasm]

Well, in the most general sense, a computer is a device which takes some sort of input and produces an output.

And specifically. we can't build a computer out of "nothing"; a computer has to have a logic - a logic has a representation. A representation is also a computer, or the result of a computation.

This is one reason why it's difficult to consider the universe as a whole as a computer: different regions become causally disconnected from one another, meaning that it's impossible to determine this "output".

The above is why it's easy to consider the universe as a computer. The apparently disconnected regions (differentially limited) are an output.
This has been covered already:: "Mass separated by a distance greater than the universal signal limit cannot communicate."
This means that the incommunicado mass has a cause. It is causally connected after all.

 

[Chalnoth]

And specifically. we can't build a computer out of "nothing"; a computer has to have a logic - a logic has a representation. A representation is also a computer, or the result of a computation.

Not quite sure what you're getting at here.

The above is why it's easy to consider the universe as a computer. The apparently disconnected regions (differentially limited) are an output.
This has been covered already:: "Mass separated by a distance greater than the universal signal limit cannot communicate."
This means that the incommunicado mass has a cause. It is causally connected after all.

This wouldn't be the universe as a whole as a computer, though. This would be local interacting components as computers. And that's a fairly reasonable proposition, particularly as we have, you know, computers. The whole universe as a computer is not.

 

[sirchasm]

Why not? Why isn't "(the separated regions)" an output = a result?

Even though it means each region specifically has a static information entropy in terms of any other separated region? Which is zero for all future values of t globally and locally?

If there is no "cosmic computer", what is expansion?
Local manifolds are submanifolds, with disconnected t values over the global M.
Is M still connected globally? in what sense is or isn't it?

 

[Coin]

However, it certainly appears to be 'computational'; this is demonstrable: if we can write a program that simulates a real physical process (the gas laws, say), and do this for all of the processes we know about (so all the simulations then prove that we do know, if they exactly reproduce these processes in "computer-space", i.e. virtually), then a simulation of the known universe exists.

So there are several problems with this line of thinking.

First off: We don't know what the laws of the universe are. We therefore cannot say whether the laws of the universe are computable or not. You do specify "known" physical processes. I don't think "known" processes are very interesting for this purpose. For example, imagine you came up with a really ingenious proof that gas dynamics are computable. But it might be that gas dynamics are just a computable process that exists inside of a non-computable universe; similar to how (as Chalnoth points out) a computer is a computable mechanism, but this doesn't tell us the universe it exists inside is computable.

Second off: Even some of the physical processes which are "known" defy accurate calculation given the mathematics we have available to us right now February 2009. For example, quantum physics is part of "known" physics, and relativistic gravity is part of "known" physics. But no one knows how to construct a calculation where the two interact, and there will be nobel prizes handed out on the day someone demonstrates a workable way of doing so. So it is going to be very difficult to make any meaningful statements about the behavior of a hypothetical program which simulates even these known parts of physics.

Finally, consider your suggestion that we write a program that simulates "a" physical process, and use the failure or success of such an attempt to judge whether the universe is computable, and consider that your recommended target is the gas laws. But, there are people who write simulations of the gas laws already! They call it climate modeling. To put things a bit vaguely, what I would point out is that these people don't simulate the gas laws exactly. Simulating the gas laws exactly is not something that is even talked about. What is talked about is simulating the gas laws over some period of time within some bounded error, such that the bounded error gets worse and worse the longer the computation runs.

Looking at this from the perspective of a CS person rather than a cosmologist, there really seems to be only one possible answer: Maybe the laws of the universe are computable, and maybe they're not, it depends on what those laws are. There are different possible completions of our physical laws which are computable, aren't computable, or which are computable by different models of computation (TM, probabilistic TM, hypercomputer). But we don't know which completion of our physical laws is the correct one.

Certainly if we limit ourselves to the more naive systems of physical laws, say Newtonian physics, this makes computability seem impossible. The point zankaon raises can't just be brushed off: The immediate, "known" physical laws concern things which are smooth, which appear to incorporate real numbers. These things just aren't suitable for computation (under any nonexotic model of "computation"). You can only approximate, and the error in your approximation will compound on itself with time until it is completely out of control. Now, you seem to be suggesting that by eschewing all rounding and assuming all physical quantities to be limited to some computable subset of the reals (surely not the rational numbers-- the algebraic numbers maybe), something like these people seem to be trying to do, you could create a simulation which may be computationally impractical but which can in principle precisely simulate some physical law or other. Um, maybe? I don't know. I would not discount such a possibility out of hand, but I DEFINITELY wouldn't make a statement like "it's possible" either without seeing some very specific discussion of models and proofs. If you want the universe to be computable, what you really want to hope for is that the smoothness is only apparent, that all the seemingly-uncomputable "known" physical laws are emergent from large-scale interactions of some simpler, discrete structure. There are some theories of quantum gravity that seem to me to hint such a thing could be true. But maybe those theories of quantum gravity are not the right ones.

 

[sirchasm]

We ...cannot say whether the laws of the universe are computable or not.
...it might be that gas dynamics are just a computable process that exists inside of a non-computable universe; similar to how (as Chalnoth points out) a computer is a computable mechanism, but this doesn't tell us the universe it exists inside is computable.

It might be that we can simulate the gas laws (which appear to be consistent with real physical gases); can we simulate a non-computable gas?

A computer computes: this doesn't tell us that the universe it exists inside of is computable, but we can't build a computer that can tell us it isn't.

 

[sirchasm]

some of the physical processes which are "known" defy accurate calculation given the mathematics we have available to us right now February 2009.

Nonetheless, these processes are physical; they compute what they want to regardless.

For example, quantum physics is part of "known" physics, and relativistic gravity is part of "known" physics. But no one knows how to construct a calculation where the two interact, and there will be nobel prizes handed out on the day someone demonstrates a workable way of doing so.

If there are 10 or 11 dimensions in the universal machine, certainly that is a lot of possible ways to move around in a physical way.

Again, they move physically just how they ought to, according to physically real processes.

So it is going to be very difficult to make any meaningful statements about the behavior of a hypothetical program which simulates even these known parts of physics.

But it might get easier if we don't assume constantly that we can never make any meaningful statements, or ask any precise questions.

 

[sirchasm]

Mods: I'm going to explore this regardless of any warning lights you want to switch on.
I'm going to think about whatever I choose to (if that's ok with you). I might even post some of it... If buttons get pressed, well I've done that before so I'm big and old enough to handle a lack of intersection.

can we simulate a machine that has no physical existence?

"Simulate" means: can we write a program that is equal to a machine of some kind, that does work, but doesn't use anything physical?

Well, no we have to use something, even the theories we know about are something.
Theories are also a kind of machine. Generally an enumerable theory has a Von Neumann or Turing equivalent. Both models are abstract logical machines, but require physicality - if we want to actually enumerate a quantity. Otherwise these machines are potential or possible machines, but with a known logic. Empty machines, that we connect to a construction in the real world.

If we can, can we ask it to simulate a known physical process?

Is there any resource in the universe we can exploit, that is, or appears to be 'unphysical'? That isn't connected to mass or energy? Entanglement has entropy - what does this mean?

 

[Chalnoth]

Why not? Why isn't "(the separated regions)" an output = a result?

It's not a result, though. It's many separated results due to local interactions that can have no input from causally-disconnected regions.

Even though it means each region specifically has a static information entropy in terms of any other separated region? Which is zero for all future values of t globally and locally?

What do you mean by this? And there is stuff out there that has never been in causal contact with our region and likely never will be.

If there is no "cosmic computer", what is expansion?

Uh, how can expansion be considered anything remotely like computation?

Local manifolds are submanifolds, with disconnected t values over the global M.
Is M still connected globally? in what sense is or isn't it?

It may be simply connected geometrically, but regions of the manifold cannot communicate and thus act independently.

 

[Coin]

It might be that we can simulate the gas laws (which appear to be consistent with real physical gases); can we simulate a non-computable gas?

I'm not sure what you're asking here? The way I'd normally use those words, I'd say that by definition we cannot simulate something which is non-computable; if we can simulate it, then it is by definition computable. Right? Maybe you should clarify what you mean by "compute" or "computable". I mean:

some of the physical processes which are "known" defy accurate calculation given the mathematics we have available to us right now February 2009.

Nonetheless, these processes are physical; they compute what they want to regardless.

When we talk about something being "computable", what we usually mean is that it can be simulated by a deterministic turing machine. Given the subject matter at hand, it might be reasonable to adopt in this particular discussion a more general definition of "computable", like "it can be simulated within some mathematically definable model of computation" or "it can be simulated by some physically realizable model of computation". But you need to pick a specific definition of "compute" and stick to it.

If you're interested in the idea of just saying, never mind digital computers and traditional turing machines exactly, let's just say that if a physical process produces some result, then we define that as a computation-- then you might be interested in this paper by Lee Smolin. The paper discusses the idea of defining sort of universality classes of dynamical theories, such that you can "simulate" the behavior of one theory using structures within the other by carefully setting up initial conditions. Probably none of these theories can be simulated by a UTM, but they can simulate each other.

 

[Chalnoth]

I'm not sure what you're asking here? The way I'd normally use those words, I'd say that by definition we cannot simulate something which is non-computable; if we can simulate it, then it is by definition computable. Right? Maybe you should clarify what you mean by "compute" or "computable".

Well, I think by computable here it means that you'd have to simulate it perfectly. I think sirchasm's objection was that this isn't ever done in reality.

But naturally it could be estimated by taking a hypothetical Turing machine and let it run to infinity: an incomputable system won't even finish as t->infinity, while a computable system will. So PI, for instance, is an incomputable quantity because there is no last digit. I think this is what you meant?

 

[Coin]

Well, I think by computable here it means that you'd have to simulate it perfectly. I think sirchasm's objection was that this isn't ever done in reality.

But naturally it could be estimated by taking a hypothetical Turing machine and let it run to infinity: an incomputable system won't even finish as t->infinity, while a computable system will. So PI, for instance, is an incomputable quantity because there is no last digit. I think this is what you meant?

Um, you may or may not have some names flipped here?

Anyway, I could buy the notion of an algorithm which "simulates" a dynamical system by producing successively better approximate simulations of the system as it runs forever. And this would be consistent with the notion of "computable" as in "computable number", I.E., a computable number is one (like PI) that a TM can produce in the limit as its runtime goes to infinity.

I'm not sure though whether or not this notion of "computing" is totally consistent with sirchasm's original question, which had something to do with whether the universe "is a computer"...

 

[sirchasm]

It's not a result, though. It's many separated results due to local interactions that can have no input from causally-disconnected regions.

The observable fact that regions of the current universe are disconnected informationally isn't an outcome for a single expanding universe, you mean?

how can expansion be considered anything remotely like computation?

Well, we would need to build a logical machine that can prove: "expansion is not computable, therefore cannot be a computation", I guess.

 

[sirchasm]

Although entanglement with entropy looks like at most a connection. a distance operator that looks fixed; it does encode something, which is a direction or an angle in 'entanglement space'. The dimension of the connection is 1, but the signal is "there is a connection", this signal has a different limit (it must have, since it's FTL, effectively). The distance operator also encodes a rotational symmetry or SU(2). ??

The "yes, there is a connection' signal is probabilistic, we can set this to 1 locally, but between two 'near' states.
Extending this to 'distant' states is a bit of a problem (nyar ...nyar)

 

[sirchasm]

Well we've thrashed the idea of building a machine and physicality; done the entanglement thing; and still here.

So can we build a 'circuit' with entanglement? Sure, we already do.
Can we measure distant entanglement? we have to prepare something - we have to make a local pair of massive (or momental) quanta 'coherent' -i.e. aligned in the independent-of-distance entangled space.

But there is the polarization in the CMB; if we can build a device = a circuit, that measures this, we have a 'fix' on the content of an entropy-space.

If we consider the angle that entanglement encodes as a polarizable potential, then we need a machine that can 'expand' and 'deform' it - by re-polarizing it.

 

[Chalnoth]

Well, entanglement is just about maintaining particles in a quantum superposition of states. This is important for quantum computers because any time you collapse a superposition, you lose information about the other components of the superposition.

It isn't about information transfer between separate parts of the quantum computer (you can't do that with entanglement). It's about preventing information loss due to interactions.

 

[sirchasm]

See how I'm using "potential" abstractly, it's just "something we might use" in this context.
Polarization of EM fields and radiation (from small to large wavelengths = distance operators on momentum), are connected to entanglement, since we can entangle photons.

There's a 'tanglement' potential which we entangle = connect; this is the machine needed. Entangled photons, then have a distance operator which acts in a 'moment-free' space, as a photon's distance acts in a 'mass-free' one. Down-converting is an operator that rotates a potential in photons (in their momentum) so it's now at right angles to itself as 2 photons, 1 e-bit. This implies a photon is entangled 'with' itself; a photon implies a rotational group on U(1) called SU(2), because mass-charge is scalar for all d.o.f. in wherever e-space is (obviously it's a subspace of momentum-space).

We can derive entangled states from momentum (of mass charge spin) as exchanges along mass-spin and charge-spin directions (pair-production and Hawking-Bekenstein radiation, q-bits or 'qubits'); spin-spin directions (Stern-Gerlach, neutron interferometry, QH-effect, AB effect, q-bits); but not mass-charge, because [h, \hbar]\; has to encode entanglement; mass-charge terms are scalar in e-space.

QIS calls an entangled quantum 'direction' an e-bit, which interacts with q-bit representations (atoms, electrons, photons); we haven't managed to encode e-bits in terms of quasiparticles yet. Or have we?

 

[Chalnoth]

See how I'm using "potential" abstractly, it's just "something we might use" in this context.
Polarization of EM fields and radiation (from small to large wavelengths = distance operators on momentum), are connected to entanglement, since we can entangle photons.

There's a 'tanglement' potential which we entangle = connect; this is the machine needed. Entangled photons, then have a distance operator which acts in a 'moment-free' space, as a photon's distance acts in a 'mass-free' one. Down-converting is an operator that rotates a potential in photons (in their momentum) so it's now at right angles to itself as 2 photons, 1 e-bit. This implies a photon is entangled 'with' itself; a photon implies a rotational group on U(1) called SU(2), because mass-charge is scalar for all d.o.f. in wherever e-space is (obviously it's a subspace of momentum-space).

We can derive entangled states from momentum (of mass charge spin) as exchanges along mass-spin and charge-spin directions (pair-production and Hawking-Bekenstein radiation, q-bits or 'qubits'); spin-spin directions (Stern-Gerlach, neutron interferometry, QH-effect, AB effect, q-bits); but not mass-charge, because [h, \hbar]\; has to encode entanglement; mass-charge terms are scalar in e-space.

QIS calls an entangled quantum 'direction' an e-bit, which interacts with q-bit representations (atoms, electrons, photons); we haven't managed to encode e-bits in terms of quasiparticles yet. Or have we?

Honestly, I can't tell whether you're just writing gibberish or you merely haven't explained yourself properly.

 

[sirchasm]

Well, you see, I'm 'talking' in code.
What would you describe the potential in EM radiation as? The gauge of QFT?
Can you describe the connection or disconnection between nonlocality, superposition and measurement?

 

[Chalnoth]

Well, you see, I'm 'talking' in code.

Uh-huh.

What would you describe the potential in EM radiation as?

The potential is a function which, when differentiated, gives the value of the EM field.

The gauge of QFT?

A gauge transformation is a way in which a function in the theory can be varied without changing the physical effects of the theory. For example, since the physical stuff in EM is the field, and since the derivative of the potential is the field, you can add to the potential any function that has a derivative of zero. Different choices of the function added to the potential are different choices in gauge.

The way the word gauge is used throughout QFT, as well as gravity, is essentially the same as this. In General Relativity, for instance, a coordinate transformation is also a gauge transformation: whether you look at a system with one set of coordinates or another, the physics is still the same. So a change in coordinates doesn't change the physics, and is sometimes called a gauge transformation.

In QFT, the gauge is very important when, for example, you do a path integral. With a path integral, you're integrating over different paths. But some of those paths are going to be related to one another by a gauge transformation: they're actually the same path. So you have to take the gauge invariance of the theory into account when performing certain calculations if you want to be sure to not double-count things.

Can you describe the connection or disconnection between nonlocality, superposition and measurement?

There is no non-locality in quantum physics, as quantum physics is a fully local theory.

 

[sirchasm]

There is no non-locality in quantum physics, as quantum physics is a fully local theory.

Do you have references to articles that confirm the non-nonlocality of quantum transportation of states? Or that confirms Bell's experiments are entirely local, or the results of any quantum experiment that can determine the local states of double-slit experiments, at all times?

The latest is: QM is a nonlocal theory of quantum states; nonlocal because time and space are in an independent frame - our frame.

A gauge transformation ...

What does a gauge transformation transform? I asked what the gauge is, not what transforming a gauge is. The photon is the gauge of the EM field; what is "the photon"?

So, what is THE connection between superposition, nonlocality and measurement? Three things, one connection? Or isn't there one?

 

[Chalnoth]

Do you have references to articles that confirm the non-nonlocality of quantum transportation of states? Or that confirms Bell's experiments are entirely local, or the results of any quantum experiment that can determine the local states of double-slit experiments, at all times?

Meh, I don't see why I should. Intrinsic non-locality is patently absurd. But regardless, this is off-topic for the thread and for the forum.

What does a gauge transformation transform? I asked what the gauge is, not what transforming a gauge is.

A gauge is a type of transformation.

The photon is the gauge of the EM field; what is "the photon"?

Hardly. When talking about a "gauge boson", the word "gauge" is an adjective to describe the boson. It is not a noun. The reason it is used is because the interactions between gauge bosons and matter can be derived just by stating that they each transform under the right sort of gauge symmetry.

 

[sirchasm]

Intrinsic non-locality is patently absurd

Then, it shouldn't be difficult to explain why locality is patently non-absurd?

Quantum electrodynamics is an abelian gauge theory with the symmetry group U(1) and one gauge field, the electromagnetic field, with the photon being the gauge boson.

Why doesn't this say "the photon being the boson gauged by the field, it's a gauged boson"?

You mean the photon is a gauge of the field = it's a transformation of the e and u in the field?

 

[Chalnoth]

Then, it shouldn't be difficult to explain why locality is patently non-absurd?

Because locality doesn't involve faster-than-light transmission of information. Which entanglement in QM doesn't do, by the way.

Why doesn't this say "the photon being the boson gauged by the field, it's a gauged boson"?

Why would it?

You mean the photon is a gauge of the field = it's a transformation of the e and u in the field?

No. The photon is a quantum of the field. "Gauge of the field" doesn't make any sense.

 

[sirchasm]

locality doesn't involve faster-than-light transmission of information.

(and, this is why locality isn't absurd?

A gauge is a type of transformation. ... The photon is a quantum of the field. "Gauge of the field" doesn't make any sense.

But a photon is "the gauge of the EM field". How many published articles would you estimate I can locate that say exactly those 6 words? Are these papers nonsensical??
You say: it's a transformation, which implies it's 'gauged', not 'a gauge'...

Nonlocality in quantum mechanics

[edit] Einstein, Podolsky and Rosen

Main article: EPR Paradox

In 1935, Einstein, Podolsky and Rosen published a thought experiment [2] with which they hoped to expose the inadequacies of the Copenhagen interpretation of quantum mechanics in relation to the lack of determinism at the microscopic scale that it described.
In particular, they hoped to demonstrate that the probabilistic nature of the results of measurements on particles could be described through the means of some ‘hidden’ variables that predetermine the result of a measurement, but to which an observer does not have access.

In physical terms, this experiment can be represented as a spin-zero particle decaying into two spin-half particles such that there is no interaction between the two particles after decay. Since spin is a conserved quantity, measurements of spin on the two particles must anti-correlate. The quantum state of the two particles prior to measurement can be written as[3]

\left|\psi_{AB}\right\rangle=\frac{1}{\sqrt{2}} \bigg(\left|\uparrow\right\rangle_A \left|\downarrow\right\rangle_B + \left|\downarrow\right\rangle_A \left|\uparrow\right\rangle_B \bigg)

Here, subscripts A and B distinguish the two particles, though it is more convenient and usual to refer to these particles as being in the possession of two experimentalists called Alice and Bob.

This state allows us to predict the probability of a particular result. Alice, for example, will measure her particle to be spin-up in an average of fifty percent of measurements. However, when Alice measures her particle it causes the state to collapse so that if Alice measures spin-up, Bob must measure spin-down and vice versa. Hence, either party is capable of setting the spin of the other’s particle instantaneously. Such behaviour is non-local because the measurement of one particle is able to influence the physical state of another independently of the distance between them, so that no information could travel between them.

Einstein, Podolsky and Rosen saw this as evidence of a causal effect propagating at superluminal speeds, which is in violation of the laws of special relativity[2]. They further pointed out that such an unwanted result could be avoided by admitting the presence of hidden variables that determine the results of measurements for each of the entangled particles, which would restore locality to physics.)

BUT (that's a big but), there are no 'hidden variables'; this is nonsensical...

 

[Chalnoth]

(and, this is why locality isn't absurd?

Basically, yes. Non-locality, in essence, requires magic.

But a photon is "the gauge of the EM field". How many published articles would you estimate I can locate that say exactly those 6 words? Are these papers nonsensical??

Quite a few. But find me one that says it's a photon.

You say: it's a transformation, which implies it's 'gauged', not 'a gauge'...

A gauge transformation is a type of transformation. A gauge field is a field which is invariant under this sort of transformation. A gauge boson is a quantum of a field that is invariant under this sort of transformation. In all situations, the word 'gauge' is an adjective.

BUT (that's a big but), there are no 'hidden variables'; this is nonsensical...

Locality is restored if you just drop the postulate of wavefunction collapse from quantum mechanics. It's not needed.

 

[sirchasm]

Non-locality, in essence, requires magic.

Then EPR, Stern-Gerlach, double-slit and any experiments with nonlocal effects demonstrate magic.

When you say "locality is restored", do you mean you know where each electron is that passes through a double-slit, or any interferometer?

And if a photon is a gauge transformation, is it scalar? The gauge is a scalar quantity?
I don't see how I can transform an adjective into anything except another adjective, unless "transformation" of the adjective makes it something else.

"Hot" is an adjective = a gauge ; I can do a "hot" transformation, into something else? What else, it doesn't even make sense??

 

[sirchasm]

If I use "hot", I can differentiate objects - the transformation - into more and less "hot". It's a gauge that can make sense.
If I want to transform an area into a known quantity, I might measure or calculate it with angles and distances.

The gauge I might use could be sticks stuck in the ground, or say rocks. I could use both, the gauge is invariant because it "transforms" the area into a bounded one, whether I use sticks or rocks or something else as a marker (of position).

 

[Chalnoth]

This is too far off topic for me. I'm done.

 

[sirchasm]

Well, that could mean I've either presented an argument you can't answer; or it could mean I am 'off-topic'.

If the latter, my pick is I've got to here, because you asked me to, in order to argue your position.
So if you withdraw your argument (after posting it), I'll get back to the topic (I'll have another look at the OP, and see if I can remember why I posted it)

 

[sirchasm]

Note: gauge theories treat fundamental objects, like the photon. There are gauges for all kinds of things - after all it's just a way to measure something.

However the theories use gauges that represent fundamental physical measurements - which are invariant for some aspect of the space which is gauged. The photon is an invariant gauge for EM theory in a quantum basis (since it's a quantized one).