You can be damn sure Uber has a record of every Uber ride ever taken. Even if Uber had incorrect records in their database about which car picked up the rider, because the driver had e.g. failed to update Uber with their current car and plates, there is no plausible reason why Uber would believe that the ride itself had never occurred, because they have the rider's account information. They could have produced "rider account X requested a trip in Boston on such-and-such date, we matched that person with driver account Y, and driver account Y was registered in 20xx to Vernon Dudley, 4 Privet Drive, ...". But they deliberately didn't provide that information.
"this article is muddled and confusing"
Reality is muddled and confusing. Real life never has the clarity of an omniscient third-person narrator telling the reader the actual facts of the matter.
Your analogy is incredibly bad. Imagine if GrubHub itself provided the menu and contracted out to semi-anonymous restaurants to cook the food; then imagine that it wasn't salmonella or the like, but rather that the cook had pissed in the food; and THEN imagine that GrubHub refused to tell the police which restaurant cooked the meal and then blatantly lied to the cops that no food from that (still unnamed) restaurant had been on GrubHub's menu for two years anyway.
In that scenario, you're damn right you could sue GrubHub; they'd be complicit in the coverup of a crime.
If Subway tells the cops "I won't say who it was", and they say "he hasn't worked at Subway for two years anyway" (this being a bald-faced lie), AND the medical bills from the stabbing set you back millions of dollars... damn right, Subway owes you millions. They're making themselves complicit in the crime by obstructing justice, and making it clear that Subway was OK with the stabbing.
Oh I agree completely, but you're adding to what I said. There are many here saying Subway is at fault no matter what.
Eg, if they didn't do anything wrong, the person just randomly stabbed me, many here think Subway owes me millions. What do you think?
I disagree, it seems bizarre to me because Subway can't possible know what crimes all employees might commit and somehow fight to prevent that. Right?
.. actually let me ask you this:
In what scenario should Subway not be held liable? So many here blame Subway in my scenario, when they were not even involved.. so what does a company have to do to prevent being sued by employees random, un-predictable actions?
As I understand it (not being a physicist): the graviton, if it exists at all, would have to be a massless chargeless spin-2 boson for it to fit our understanding of what particles are. But the graviton has never been observed, nor has any quantized behavior of gravity or its General Relativistic effects, so it doesn't count as an observation by String Theory; there are other models that also give rise to gravity-as-we've-observed-it, up to and including just gluing the Standard Model to General Relativity and calling it a day.
While it's true that the graviton has never been observed, the point is that string theory was not, originally, a "theory of everything" candidate! It was originally a way of trying to understand QCD and strong dynamics. In 1974 people discovered that the massless chargeless spin-2 boson "popped out" of the theory accidentally! Since people knew that such a particle behaves like a graviton, and is manifestly quantum-mechanical, suddenly it occurred to them that string theory might be a theory of quantum gravity. In fact, General Relativity can be viewed simply as the low-energy effective theory of massless chargeless spin-2 bosons, as emphasized in Feynman's Lectures of Gravitation, where he derives GR from a particle-physicist point of view, rather than a differential-geometry point of view.
This led to the tongue-in-cheek saying that string theory post-dicted the existence of gravity at all---since it isn't built into the foundational assumptions of the theory at all (which is more than a lot of the other models, such as the "gluing" you propose, can say). And since string theory is guaranteed to be quantum-mechanical, a lot of interest developed towards understanding it as a theory of quantum gravity (most other models fail to account for how GR can be made compatible with quantization and how the renormalization works sensibly).
The Higgs explains why fundamental particles have mass in the "F=ma" Newton's-Laws-Of-Motion sense. But you can formulate classical mechanics without gravity at all. The m in this equation is sometimes referred to as the inertial mass.
F_gravity = G M m / r^2 on its face looks like it is talking about the same inertial mass (or, by adjusting G, something proportional to the inertial mass). But, this is an assumption---a body could equally well have a gravitational mass independent of its inertial mass.
If inertial and gravitational masses are proportional to one another then when you calculate the acceleration due to gravity you can cancel the m from both sides, and you find that all bodies fall the same way (even light, which has m=0 and might cause concern that the cancellation isn't valid). This is a repercussion of inertial = gravitational mass. Einstein promoted this observation to the Equivalence Principle (and people do experimental searches for violations of this assumption).
The Higgs gives particles inertial mass. But the Higgs doesn't cause things to fall "down" (assuming you can define "down" without a gravitational field). You need the gravitons to communicate the gravitational attraction, which is independent of the existence of mass.
Oh, duh, because while "physics" (general relativity) shows that mass is gravity, the whole point of this exploration is see if we can derive that equivalence (or something extremely close to it) from core QM principles rather than assuming it a-priori. Because the a-priori assumption (general relativity) contradicts QM. So some deeper principle needs to unfold to present both Higgs bosons (inertial mass) and gravitons (gravitational mass) and their relationship, from which something very very very close to general relativity can be derived. Is that right?
If so, has any actual string-theoretical mathematical relationship between gravitons and Higgs bosons been developed that would explain general relativity? Or is it stuck at "in string theory, something like 'gravitons' could exist"?
the "problem" here is that the graviton "has to" exist. why?
Forces have to be conveyed by something. If you want to push someone, you have to physically touch them. you have to REACH them. you cant just push the air, across the room, and expect them to feel the push.
this is true on the microscopic level as well. when particles exert gravity on each other, they do so at a distance. but something has to cross this distance. it is not ordinarily obvious how the sun traps our planet in its gravitational field - at a distance. there has to be something that exchanges the gravitational force between sun and earth. we call this thing the graviton. it is important to notice that something that does the "job" of the graviton HAS TO exist. maybe its not a particle. but something causes the exchange of gravitation and thats what we're looking for.
you know that "in space, no one can hear you scream". thats because there is no air that could make the sound waves travel.
in a similar way, without the graviton, there would be no "medium" that conveys the gravitational force.
the problem with detecting the graviton is that it is very weak. we would have to build really expensive machines to "observe" it.
explaining this theoretically is not difficult. we have plenty of "theories". the problem is confirming them with experiments.
I'm not an expert, but I simply don't understand your reasoning here.
For example, lets suppose some mass is moving at a constant inertial velocity through empty space. To me it seems that your reasoning would require gravitons to communicate to the mass that there are not other masses nearby and so to 'tell it' that 'straight line' for it means to go in a euclidian straight line. Otherwise, how does it know?
I think baked into your logic is that there is something special about geodesics in the presence of masses and so you need to tell the moving mass to 'curve', but to the mass it is just going straight, even if to an external observer it appears that it is curving or even orbiting.
- its not my reasoning, i'm just trying to explain quantum field theory.
- whether you call it "gravitational force" or "curvature of spacetime along whose geodesics massive objects slide" - the effect has to be mediated by a "particle". for popular media, "particle" is too big a word, because people tend to think of protons or atoms. subatomic particles are just excitations of quantum fields. little blips of localized energy, of which we are only able to see the top layer.
^ this has nothing to do with general relativity. general relativity describes the macroscopic world pretty well. it generally breaks down on very small scales.
how planets move is described very well by general relativity. how they mediate the involved forces is not described at all.
edit: i just thought about that straight line statement. there seems to be a misconception that a geodesic is a "generalized straight line". That is not remotely true. Geodesics, in mathematics, are "shortest paths". While that happens to coincide with what a straight line does in a plane, generalizing that meaning in the other direction doesn't work.
In general relativity, we talk about geodesics when we mean "out of all the possible paths we can take, we are choosing the one that minimizes energy loss". That is, then, a geodesic. But a geodesic is far from a straight line in terms of movement. Its the path of least resistance in the energy picture.
If you ask "whats the difference?" - the difference is that a straight line in energy space is not a straight line in regular space. Earth, for example, is travelling along a geodesic. But it is clearly accelerated towards the sun. There is nothing "straight line" about it.
When you fall into a black hole, you travel along a geodesic. But it wont feel like a straight line to you at all.
That you happen to be travelling along a straight line in the absence of forces is just a tautological truth. Applying differential geometry to that statement just makes it way more complicated to state the obvious.
there seems to be a misconception that a geodesic is a "generalized straight line". That is not remotely true. Geodesics, in mathematics, are "shortest paths".
Geodesics being generalized straight lines is exactly true. Also note that they are not necessarily shortest paths: In the framework of affine connections, they are defined as autoparallels.
Earth, for example, is travelling along a geodesic. But it is clearly accelerated towards the sun.
Earth is in free fall around the sun, so accelerometers will read 0. That's the whole point of General Relativity: Geodesic motion is not a consequence of Newton's second law, but the first one.
> whether you call it "gravitational force" or "curvature of spacetime along whose geodesics massive objects slide" - the effect has to be mediated by a "particle"
Why are you so convinced that curved spacetime is only an appearance and that there has to be particles behind it that create the appearance? Why cannot curved spacetime be the fundamental explanation itself?
The equation that defines curvature in GR depends on the stress-energy tensor which describes the distribution of matter/energy in spacetime. This depends exactly on position and momentum of the matter involved, which is in direct contradiction with the quantum mechanical nature of the stuff.
Normally this doesn't matter because gravity is so weak compared to the scale where QM effects dominate but it is a mathematical inconsistency that becomes very relevant towards the extremes of both theories, in particular: the very early universe just after the big bang and the dynamics near black holes.
> to the mass it is just going straight, even if to an external observer it appears that it is curving or even orbiting.
You're hiding a lot of assumptions in this idea. That model of curved geodesics sounds sensible in isolation, but it's completely contrary to how all other known forces work and seems incompatible with quantization (which is again how all other known physics works). I mean sure the universe conceivably could have three fundamental forces that work via particle exchange and one that works by curved spacetime, or magic, or the hand of god. But that doesn't seem very likely, and that kind of inconsistently would go against the history of physics up to this point.
But we know gravity is by far the weakest force, 10^-36 that of electromagnetism compared to 10^-7 of the next weakest force. It's so out of scale with the other four fundamental forces, maybe it is fundamentally different.
My description is, from my limited understanding, just describing General Relativity, which is a totally accepted and highly verified by observation and experiment.
Where you say it is incompatible with quantization, you are assuming that gravity has any quantization to begin with, which has never been observed. You are literally 'begging the question' here, assuming that gravity quantization needs to be explained by gravitons, when neither quantization of gravity nor gravitons have ever been observed.
> My description is, from my limited understanding, just describing General Relativity, which is a totally accepted and highly verified by observation and experiment.
Grandparent is indeed describing GR. I wanted to try to give a more outside perspective; I think we forget just how weird GR is just because we're used to it. I wonder how we'd be thinking about quantum gravity if we'd discovered QM (which has been verified far more rigorously than GR) first.
> Where you say it is incompatible with quantization, you are assuming that gravity has any quantization to begin with, which has never been observed.
Sure, but as I said quantization is how all other known physics works. While indeed we haven't observed quantization of gravity, fundamentally gravity happens in the same universe as the rest of physics, so something has to give. (And continuous approximations to quantized reality are again exactly how the rest of physics works, whereas I struggle to even imagine how you could recover quantum behaviour from a continuous underlying theory - though I'd be fascinated to hear about any such efforts).
So what about my initial point? How does a mass moving in the absence of other masses know that a geodesic for it is a euclidian straight path?
I would say that it doesn't, and that inertial motion in the absence of other masses is meaningless, and I think this is a key insight that allowed the development of GR in the first place (since any attempt to introduce absolute coordinate systems breaks causality because you can have multiple outcomes from the same boundary conditions, at least in the Hole Paradox).
I would say in addition that every other part of physics that I am aware of can be described locally, for example you can detect if you are in an magnetic field (at least in theory) even at the level of a single proton (since it has a magnetic moment). There is NO test you can do locally to detect that you moving inertially in the presence of a gravitational field. If you can't detect it locally, either there is a huge coincidence (in this case the coincidence is that inertial mass and gravitational mass are identical) or you can't expect to find any messenger particles, since why would you need to 'tell' a mass that it is in a gravitational field when it can't even detect it to begin with.
Sorry for interrupting your discussion with maybe dumb question, but isn't gravitation defined by spacetime geometry rather than some sort of particle exchange? Do not particles always fly forward, with forward changing its meaning with time?
"spacetime geometry" is a mathematical formulation of the physics that happens to correctly describe WHAT is happening.
it makes no prediction at all about WHY its happening. einsteins theory does not explain, and does not try to explain, why the gravitational field exists. it just tells us the effects of the gravitational field being around.
That's "why" thing is new to me. I read before that there is no why, only how. "Why do particles exist? Why is something fundamental like it is?" Are these questions to be answered in ST framework?
Not a physicist, but questions of "how" and "why" are complicated by their ambiguity in English.
In common English, "how" means the mechanics of a system, and "why" generally means for what purpose someone has undertaken an action. Think of "Why did you build a garage?" (for what purpose or to what end?) vs. "How did you build a garage?" (what exact method did you use).
To complicate things, for action by non-agents, "why" can also mean "how". Children might ask "Why is the sky blue?" but what they mean (or the answer they get) is "How is the sky blue".
So when it comes to physics, we generally say there is no "why" (teleology, or mental purpose of an agent), only "how" (observable physical mechanisms). As far as physics is concerned, there is no God who set up the universe in a particular way, because he liked things a certain way, or he wanted a certain outcome.
However, the ambiguity of "why" can still be re-purposed, if you will, in physics. It's not referring to the will of an agency, but instead to lower-order phenomena that give rise to higher-order phenomenal. Why does the Earth sky have to be blue instead of, say, red? We're asking about why the mechanics of Releigh scattering play out one way verses another.
The whole point of general relativity is that there doesn't need to be a particle that does something, but that gravity is just an emergent property of space. So no, we don't know that a gravity particle has to exist.
The problem is that we have two formulations of physics. Basically, gravity and everything else. Theories such as QCD, QED, etc give rise to quantum mechanics, electricity and magnetism, etc. In these theories + and - charges for example feel an attraction to each other due to an exchange of "virtual" particles. General relativity is based on geometry as you say. Physicist would like to have one framework to describe everything--that's why it would be nice to find a graviton.
So are gravitons related to higgs bosons in the same way? Or are gravitons, assuming higgs boson === inertial mass, more like the difference between (higgs bosons aka inertial mass) and gravitational mass (thus unrelated to / independent of higgs bosons)?
We've only measured gravitational waves directly last year. The theoretical graviton is still ways off - the energies required are incomprehensible to mere mortals.
the graviton is too small to be observed directly by our machinery.
if you can provide a detector the size of the solar system, proving/disproving its existence will be simple.
we could derive anything from first principles if we knew them. theres nothing probable about that. thats the whole point of first principles. do you want me to call you captain obvious?
Mass is essentially rest energy by another name. The presence of a non-zero Higgs field gives certain elementary particles that would otherwise be massless such a non-zero rest energy.
In contrast, compound 'particles' (hadrons, atoms, chairs and tables, ...) only gain a miniscule amount of mass from the Higgs mechanism: They are bound states of interacting constituents that are whizzing around, generating ripples in various quantum fields (sometimes described as clouds of virtual particles), with the biggest contribution by ripples in the field of the strong nuclear force.
Now, in quantum theory, any field comes with associated particles, and for the Higgs field these are the Higgs bosons, and for the gravitational field these are the (conjectured) gravitons.
While gravitons would be intimately related to how gravity works at the quantum level, the relation of Higgs bosons to inertia is rather incidental.
As far as I know, string theory is the only complete theory that incorporates these two observations:
1. Nature includes the force of gravity, described at low energies by Einstein's theory with a gravitational field.
2. Matter in Nature is quantum mechanical.
We believe that spin 2 particles will exist in any such theory (as they do in string theory), but even without this assumption it is still difficult to come up with such a theory.
The example you give of gluing the Standard Model to General Relativity does not achieve this goal and does not correctly describe nature. This is because the quantum matter of the Standard Model does not correctly back-react on the classical gravitational field.
When we couple the classical theory of General Relativity to classical matter, the gravitational field pushes matter around, and the matter in turn back-reacts on the gravitational field and changes it. When coupling quantum matter to classical General Relativity, the classical gravitational field can act on matter just fine, but it does not work in the other direction. The problem is that when matter is in a quantum superposition, it is not clear how to update the classical gravitational field (which cannot itself be in superposition). This missing part of the interaction means that SM+GR is not a complete theory.
I'm not an expert, but from what I understand GR and standard model don't exactly contradict each other, they are both considered "valid" and self-consistent on their own as they merely describe different processes on different scales?
On their own, they work just fine but if we try to stick the two of them together, to get a "unifying theory", we get different outcomes than we expected, that's why we are now trying to find the "glue" that fits the two of them together while still making sense in the end.
At least that's my layman's take on this whole situation.
I also don't know much about this. But I don't think there's anything serious yet that glues them together.
Years ago someone on slashdot made an attempt. It's silly humor.
Your moma so fat even if I'd entangle
with her no information would be able
to leave her event horizon.
Nobody has managed to put gravitation
and QM together yet, and you want to
do it in a your-momma-so-fat-joke? Wow.
It's squared because energy is work, work is force times displacement (distance), force is mass times acceleration, acceleration is velocity per time, and velocity is vector distance per time. So you get:
> The claim is that you can not adequately model the Human mind with a Turing machine. Pointing out that Human's are not logical only strengthens this claim and does not refute it.
False. "2+2=5" is not a true statement, but I can construct a computer program that purports to compute the sum of 2 and 2 yet produces 5 as an answer. You can object "you got the addition wrong!" but that's irrelevant. If there is a person who believes (falsely) that 2 plus 2 equals 5, then the computer program could be an accurate model of their thought processes. There's nothing about "computers consistently produce the same answer" that implies "computers always produce the correct answer". "Computers always produce the correct answer" is a much more powerful claim, so the onus is on those who make the claim to prove it.
Yes, you can make a computer spit out nonsense, but this is a far cry from the computer actually behaving in an illogical way. A Turing machine's entire operation is logical. It is built with logic. It is a logical machine.
Penrose claims the human mind is not a Turing machine. That it is not logical. That it is not built with logic. That it is not a logical machine.
Pointing out that the human mind is not logical is thus restating Penrose' point and not refuting it.
It's easy to write a computer program that outputs every statement provable from the Peano axioms: start with the most primitive possible statements, then progressively output more complex ones. This is because the Peano axiom system is "recursively enumerable", to use Computer Science terminology. The program never terminates, but any provable statement you name will be output at some finite time.
Additionally, it's easy to write a computer program that outputs every possible combination of symbols. Most of the combinations aren't statements at all. Of the ones that are statements, most of them are not consistent with the Peano axioms. Of the ones that are consistent with the Peano axioms, most of them are unprovable. But if the set of truths is countable, this scheme guarantees that the program will output every true statement that exists.
It is possible to write a computer program that checks if a statement is provable from the Peano axioms. The naïve way is to run the program that outputs every statement as a subroutine, then halt if the subroutine prints out the statement which we wish to verify. This program will halt iff the statement is provable.
It is NOT possible to write a computer program that checks if a statement is unprovable from the Peano axioms. Such a program may be able to detect a subset of unprovable statements. The subset it can detect may even be countably infinite. But there are some statements which will cause the program to run forever.
Let statement X represent a formulation of "the Goldbach conjecture is true" written in the language of Peano arithmetic. Does the program run forever if asked whether X is provable? If you are a non-Gödelian being, you will be able to answer that question with no error, because Gödel's Incompleteness Theorem only applies to formal systems which can prove all true statements.
Penrose is not arguing that the human mind is illogical. He is arguing that it is uncomputable, which is a big difference.
In particular, he's saying that the human mind is capable of outputting true statements that cannot be proven to be true via any bounded number of proof steps. I don't disagree with that.
However, given that the human mind is capable of outputting false statements -- witness this conversation, wherein at least one of us is outputting false statements -- Penrose has failed to prove that the human mind is non-Gödelian, i.e. can output all the true statements that exist, while outputting no false ones.
