Sorry for the short absence. I had guests in town the last few days…
Almost without exception textbooks make the statement that “exchange forces are not really forces, but instead are geometric phenomenon.” And it’s true that you can draw diagrams that show the probability waves of fermions canceling out as they approach each other’s position, and constructively interfering as they get further apart. But this “non-force” stabilizes the mind-boggling, crushing gravity of neutron stars for God’s sake! It’s clear that as fermions are smashed together in stellar objects their frequency must increase and therefore so must their energy. But why, specifically, must this interaction not be considered a force? Is it just that in QM everything is Hamiltonians or Lagrangians?
Can you call the repulsion that prevents two fermions from entering the same state a force? I suppose so, to the extent that its useful. In a spatial scenario – say, where the fermion states differ only in the spatial part of their wavefunctions – you could write down a potential that describes the energy cost of moving one fermion relative to the other, and if you do that, you could take the gradient of that potential and call it a force. But the exclusion principle is more general than that. You could have two identical fermions with identical spatial wavefunctions (perhaps trapped in a potential well), with the only difference in their states being their spin. An attempt to flip one of the spins while keeping the spatial wavefunctions the same will fail. Is this a force? It’s a bit harder to cast it as one. Another: A low-energy electron striking a proton can create a neutron (plus a neutrino). Now assume the target proton is part of a large nucleus. This same low-energy electron may be unable to convert the proton to a neutron since all available neutron states are already taken up by the nucleus’s spectator neutrons. Thus, the interaction cross section goes to zero.
The easiest description of all this is just what it is: states that are not allowed are, well, not allowed. Transitions into those states don’t exist.
One could prevent transitions into disallowed states by invoking forces, and that’s how you would need to do it in a classical picture. But the non-existence of these states (and transitions into them) is a fundamental consequence of relativistic quantum mechanics for particles with half-integer spin. You can’t not have it.
So, on a macroscopic or classical level, the exclusion principle is a force, full stop. On the quantum level, the exclusion principle is just the general statement that not every system state you can write down actually exists.
OK, well then I don’t see why the Higgs boson is such a big deal. While it may help finish off the Standard Model’s suite of force-carrying particles, it’s not gonna change any paradigms and it’s not gonna add weight to the Standard Model.
You’re not too far off here. If all that comes from the LHC is the discovery of a single Higgs with expected decay modes, then certain Standard Model calculations are improved (which helps the search for new physics), but people will still be generally disappointed. If the Higgs is not seen, that is more interesting (as it should be seen by the time the LHC reaches its maximum energy, so if it isn’t, then something else is going on). But, the real prize will be anything not in line with Standard Model predictions, be it something explicit like a candidate supersymmetric particle or something inferred like decay rates that reveals some new underlying physics.
Relatedly…
I find it deeply dissatisfying to think of particles moving through space, and much more satisfying to think of a paradigm where particles are space, moving. Such a model would solve both duality and entanglement much more elegantly (in my ignorant opinion), as well as this little dilemma where stuff just shows up de novo and also disappears. Of course it does if stuff is just another behaviour of space itself.
The questions you outline are the goals of particle physics. The fact that we work with (and study the properties of) particles is just because our hands are tied. Humans can only probe nature with the probes she gives us, and fundamental particles plus their interactions are the best probes we’ve got. Nobody particularly cares if the Higgs mass is 213 GeV or 227 GeV. But, knowing it will help put together the picture of what the hell is going on under the hood. To ask “what is space?” is to ask “what can we learn about ‘what is space?’ via the particles that interact in it?” And if particles and space are not distinct (as your heart desires), our description of them as distinct will eventually break down if we keep pushing on it hard enough. The particular way in which it breaks down will guide the evolution of our description of nature, and if the new-and-improved description ties particles and space together in some way, so be it. If not, so be it.
By what mechanism do virtual particles pop into and out of existence? Do they break the law of conservation of energy?
They do not break conservation of energy because they are not around long enough to break it. More rigorously, the energy of a quantum system (like a pair of virtual particles coming and going again) is only well-defined if the system stays around for long enough. Some semblence of balance is maintained by the fact that the longer the virtual particles exist, the less apparent energy they can have.
How close are we to understanding what gravity, space and time really are?
We will never know what they “really” are. The best we can do is come up with a description that matches all observations. When observations go against our description, we can say for sure that the description is wrong and needs to be fixed or replaced. But when all our observations to-date agree with our description of nature, all we can say is is that, well, they agree.
Any guess as to what dark energy really is?
Not a clue. It appears consistent with a vacuum energy density that remains constant and non-zero in the absence of matter, but (in line with the above paragraph), that doesn’t actually mean it is a vacuum energy density.
Can the energy from gamma rays and other things hitting the upper atmosphere be harvested as an energy source?
A back-of-the-envelope calculation: if you take a 50 m cube of water (that’s 125,000 metric tons of water), it will be absorbing cosmic ray energy at about 0.02 watts. Not terribly useful, unfortunately!
About those ultra-high energy cosmic rays that have been observed: I presume that what was actually observed was a flash of light that was interpreted as a collision of an ultra-high energy particle. Can you explain why the interpretation is held with such confidence, especially when it leads to a such an unlikely conclusion (cosmic rays with absurdly high energies)? How was every other possible source of a flash of light ruled out?
The signal is basically flashes of light, but there is a lot of information in it. (a) The total duration from start-of-signals to end-of-signals is only hundreds of nanoseconds, which ensures that only one event is occurring. (b) The products of a particle collision will travel through the detector materials (typically either the atmosphere or a chunk of continental ice) in correlated ways. That is, the outgoing particles will leave lots of trails of light stemming from a common location (the interaction point) and heading in the same general direction. © The total distance a “daughter” particle travels is governed by how much energy it has. The longer the trail it leaves, the higher its energy had to be. (d) The light produced by particles traversing the detector medium is directly related to the amount of energy they leave behind. By adding up all the light you see, you can determine the total energy deposited by the daughter particles.
So, it’s a combination of appropriate spatial patterns, temporal patterns, and total light production that lead to the inference that a single very-high-energy particle has induced a given set of signals.
I heard monopoles have been discovered experimentally. Any thoughts on this? I understand it’s outside your speciality.
After a short glance at the paper, I’m not sure yet if this is a consequence of the meta-material they are working with (spin glass) or not. They imply that they see evidence of measurable magnetic currents, which is pretty cool, but they are not (I think) claiming the presence of a fundamental magnetic monopole. I might take a look at the paper more closely if I get a chance. Perhaps someone in this thread is already familiar with the research.
