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?
> 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.
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?
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.
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.