I may be misunderstanding the nuance of this point: “You can’t recast electromagnetism as geometry because you would need a different geometry depending on the charge of the test particle. Sources alone could not determine the geometry.” But didn’t Kaluza and Klein show that electromagnetism can be recast as geometry, albeit requiring a higher dimension?
Very interesting and challenging post. When I read this I get a bit stuck with the concept of mass. Traditionally we tie gravity with mass. Then as you bring up electromagnetism I tend to make an analogy beween charge and mass. In essence we have the same equation for ”force” between two masses and between two charges. Then if you have two massless charges (suposedly diferent sign for simplicity) at a distance what path would the charges then travel? Is there a force acting between the charges? To me this turns very fundamental What is mass? What is charge? In our traditional theories a charge is more complex than mass. Charges have several interactions possible than masses. As we get deeper into what is mass in curved spacetime shall we then expect new interactions between masses?
"Imagination is more important than knowledge" by Albert Einstein, "The important thing is to never stop questioning" by Albert Einstein, and "Science is a way of thinking much more than it is a body of knowledge" by Carl Sagan. These two famous quotes tell you all you need to know. Physicists are very confused and no longer engaged in advancing our knowledge based on theory that fits with empirical findings. I would argue knowledge is at least equal and may be more important than imagination. You may be interested to read that the so called, Universal Law of Gravity, has been falsified. Nature is far more interesting when theories that don't fit observations are discarded and science is used with integrity.
It should be pointed out that you are talking about a local statement? At a point, particles of different properties follow the same geodesic. But in a global spacetime structure, different initial positions lead to different geodesics — and their separation evolves according to curvature. So different regimes: local, equivalence principle, nonlocal, geodesic deviation
You could make the analogy to electric forces, as was done with early atomic models. However, accelerating charges emit EM radiation at a far greater rate than accelerating masses emit gravitational waves.
Therefore, purely classical electric force orbits will quickly destabilize. Objects governed by significant electromagnetic forces can't be in freefall and therefore can't experience weightlessness.
It is worth remembering that all charged fundamental particles are massive, but some massive particles are uncharged. Therefore, gravity acts in the complete absence of EM forces, but EM forces are always accompanied by gravity.
This can't be true, as we can experimentally see clumps of dark matter. For dark matter to be the universe itself then that would mean that there's more "universe" in some parts of the universe than others. This is a reply to @mpc755
Great post! I have read many Substacks, but this is the first that has impressed me enough to subscribe to. Keep it up!
Hard to believe this is still controversial a century after Einstein theory of general relativity and given how many times he was proven right.
I may be misunderstanding the nuance of this point: “You can’t recast electromagnetism as geometry because you would need a different geometry depending on the charge of the test particle. Sources alone could not determine the geometry.” But didn’t Kaluza and Klein show that electromagnetism can be recast as geometry, albeit requiring a higher dimension?
Very interesting and challenging post. When I read this I get a bit stuck with the concept of mass. Traditionally we tie gravity with mass. Then as you bring up electromagnetism I tend to make an analogy beween charge and mass. In essence we have the same equation for ”force” between two masses and between two charges. Then if you have two massless charges (suposedly diferent sign for simplicity) at a distance what path would the charges then travel? Is there a force acting between the charges? To me this turns very fundamental What is mass? What is charge? In our traditional theories a charge is more complex than mass. Charges have several interactions possible than masses. As we get deeper into what is mass in curved spacetime shall we then expect new interactions between masses?
"Imagination is more important than knowledge" by Albert Einstein, "The important thing is to never stop questioning" by Albert Einstein, and "Science is a way of thinking much more than it is a body of knowledge" by Carl Sagan. These two famous quotes tell you all you need to know. Physicists are very confused and no longer engaged in advancing our knowledge based on theory that fits with empirical findings. I would argue knowledge is at least equal and may be more important than imagination. You may be interested to read that the so called, Universal Law of Gravity, has been falsified. Nature is far more interesting when theories that don't fit observations are discarded and science is used with integrity.
It should be pointed out that you are talking about a local statement? At a point, particles of different properties follow the same geodesic. But in a global spacetime structure, different initial positions lead to different geodesics — and their separation evolves according to curvature. So different regimes: local, equivalence principle, nonlocal, geodesic deviation
What if all my cells were magnetic and I orbit a huge iron mass in flat space. Do I feel a force keeping me in orbit? Am I in free fall, weightless?
Magnetic forces cannot cause stable orbits. See Bertrand's theorem. https://en.m.wikipedia.org/wiki/Bertrand's_theorem
You could make the analogy to electric forces, as was done with early atomic models. However, accelerating charges emit EM radiation at a far greater rate than accelerating masses emit gravitational waves.
Therefore, purely classical electric force orbits will quickly destabilize. Objects governed by significant electromagnetic forces can't be in freefall and therefore can't experience weightlessness.
It is worth remembering that all charged fundamental particles are massive, but some massive particles are uncharged. Therefore, gravity acts in the complete absence of EM forces, but EM forces are always accompanied by gravity.
This can't be true, as we can experimentally see clumps of dark matter. For dark matter to be the universe itself then that would mean that there's more "universe" in some parts of the universe than others. This is a reply to @mpc755