Pretty nice. Although admittedly I still have never understood how three very light quarks can make a neutron/proton with all mass. Where does the energy come from?

And, if there is a transformation of electro-nuclear energy into gravity (which seems the simplest explanation), then why physicists haven't been able to explore it in order to unify both forces?

Almost all of the mass-energy (90%+) is in the gluons, that gluons have mass when they are in motion even though they don't have "rest mass", and that a majority of that mass-energy of a proton or neutron is concentrated in the middle 1/3rd of the radius of the atom.

A subtle point that doesn't get made as clearly as it should be is that gravity acts on both mass and energy. For example, when matter and antimatter collide creating pure energy in the form of photons, a very dramatic reaction that destroys lots of matter, the gravitational pull exerted by those particles immediately before they collide and immediately afterwards is identical. The conversion of matter into energy doesn't change the gravitational pull of the system.

One of the biggest problems with unification is that electro-magnetism, the weak nuclear force and the strong nuclear force are all expressed in the form of equations that are only valid in a single perferred frame of reference (called Minkowski space), which is fundamentally incompatible with the equations of general relativity (which is "background independent"). Trying to combine them is a bit like trying to add a quantity expressed in meters and a quantity expressed in kilograms to each other.

Also, the kinds of schemes you would imagine that would naively "glue together" general relativity and the Standard Model generically face the problem that they don't truly "unify" gravity and the other forces (in the sense of all four forces being manifestation of the same underlying force that are only distinguishable at low energy levels due to "symmetry breaking") because gravity isn't nearly as strong as you would expect it to be in any unification theory without lots of extra dimensions with nothing but gravitons in them.

Thanks a lot for the explanation, Andrew. Naturally I still have even more doubts but I'll try to be concise:

Per Wikipedia the Minlowski space is "the mathematical setting in which Einstein's theory of special relativity is most conveniently formulated". No mention of electronuclear quantum stuff. Also for all I've read, including Einstein's own work (took me a while, specially because nobody with math training in my environment knew anything about tensors - but I read it), it'd appear to me that the Minkowski space is precisely what General Relativity is about, including the expresion of time in i units.

Although admittedly I never got clear if Einstein's time is a fourth dimension measured in i units or rather, my actual impression, the i aspect of space (i.e. a tridimensional "imaginary" aspect of space itself) - or maybe both. Do you mean this last when you say that Einstein's model is "background independent"? That he does not make a clear judgment about the nature of time but leaves it as something ambiguous?

Also it'd appear to me that most attempts to unify have tried to push Relativity into the materialist corset of quantum physics, wouldn't be interesting to attempt to do exactly the opposite: fitting (expanding, liberating) quantum physics into the frame of Relativity? Has anybody tried that?

Einstein's General Relativity is four dimensional, but in a 3+1 dimensional way. Time units and space units can be converted to each other via the speed of light constant, but they aren't identical.

Probably the best way to understand approximately what is meant by Minkowski space is as a Cartesian four dimensional world in which objects moving at close to the speed of light experience time dialation, length contraction and require disproportionately high momentums to reach higher speeds. You might think of it as Cartesian space with an aether in it that pushes back especially hard against very fast moving objects. But, a single four element location can precisely and exactly define a particular point in time and space which is always at the precisely identical distance in time and space from any other particular point in time and space. Quantum mechanics and special relativity (without general relativity) both "live" in Minkoski space.

In the space-time of general relativity, whose name escapes me at the moment, doesn't share this property. For example, the distance between Point A and Point B change change in general relativity, but not in special relativity. What is in a space changed the space itself in general relativity, whie it doesn't in Minkowski space, and general relativity doesn't allow you to assume that the universe is deep down identical for every observer in every reference frame even though each reference frame can be translated into any other reference frame.

## 5 comments:

Pretty nice. Although admittedly I still have never understood how three very light quarks can make a neutron/proton with all mass. Where does the energy come from?

And, if there is a transformation of electro-nuclear energy into gravity (which seems the simplest explanation), then why physicists haven't been able to explore it in order to unify both forces?

Almost all of the mass-energy (90%+) is in the gluons, that gluons have mass when they are in motion even though they don't have "rest mass", and that a majority of that mass-energy of a proton or neutron is concentrated in the middle 1/3rd of the radius of the atom.

A subtle point that doesn't get made as clearly as it should be is that gravity acts on both mass and energy. For example, when matter and antimatter collide creating pure energy in the form of photons, a very dramatic reaction that destroys lots of matter, the gravitational pull exerted by those particles immediately before they collide and immediately afterwards is identical. The conversion of matter into energy doesn't change the gravitational pull of the system.

One of the biggest problems with unification is that electro-magnetism, the weak nuclear force and the strong nuclear force are all expressed in the form of equations that are only valid in a single perferred frame of reference (called Minkowski space), which is fundamentally incompatible with the equations of general relativity (which is "background independent"). Trying to combine them is a bit like trying to add a quantity expressed in meters and a quantity expressed in kilograms to each other.

Also, the kinds of schemes you would imagine that would naively "glue together" general relativity and the Standard Model generically face the problem that they don't truly "unify" gravity and the other forces (in the sense of all four forces being manifestation of the same underlying force that are only distinguishable at low energy levels due to "symmetry breaking") because gravity isn't nearly as strong as you would expect it to be in any unification theory without lots of extra dimensions with nothing but gravitons in them.

Thanks a lot for the explanation, Andrew. Naturally I still have even more doubts but I'll try to be concise:

Per Wikipedia the Minlowski space is "the mathematical setting in which Einstein's theory of special relativity is most conveniently formulated". No mention of electronuclear quantum stuff. Also for all I've read, including Einstein's own work (took me a while, specially because nobody with math training in my environment knew anything about tensors - but I read it), it'd appear to me that the Minkowski space is precisely what General Relativity is about, including the expresion of time in

iunits.Although admittedly I never got clear if Einstein's time is a fourth dimension measured in

iunits or rather, my actual impression, theiaspect of space (i.e. a tridimensional "imaginary" aspect of space itself) - or maybe both. Do you mean this last when you say that Einstein's model is "background independent"? That he does not make a clear judgment about the nature of time but leaves it as something ambiguous?Also it'd appear to me that most attempts to unify have tried to push Relativity into the materialist corset of quantum physics, wouldn't be interesting to attempt to do exactly the opposite: fitting (expanding, liberating) quantum physics into the frame of Relativity? Has anybody tried that?

Thanks in advance.

Einstein's General Relativity is four dimensional, but in a 3+1 dimensional way. Time units and space units can be converted to each other via the speed of light constant, but they aren't identical.

Probably the best way to understand approximately what is meant by Minkowski space is as a Cartesian four dimensional world in which objects moving at close to the speed of light experience time dialation, length contraction and require disproportionately high momentums to reach higher speeds. You might think of it as Cartesian space with an aether in it that pushes back especially hard against very fast moving objects. But, a single four element location can precisely and exactly define a particular point in time and space which is always at the precisely identical distance in time and space from any other particular point in time and space. Quantum mechanics and special relativity (without general relativity) both "live" in Minkoski space.

In the space-time of general relativity, whose name escapes me at the moment, doesn't share this property. For example, the distance between Point A and Point B change change in general relativity, but not in special relativity. What is in a space changed the space itself in general relativity, whie it doesn't in Minkowski space, and general relativity doesn't allow you to assume that the universe is deep down identical for every observer in every reference frame even though each reference frame can be translated into any other reference frame.

Yes, the math is nuts.

"the radius of the atom."

Correction. I meant to say "the radius of the baryon."

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