I'm enjoying Rob's analysis which I think is very helpful.
Based on his comments it occurred to me that it might be useful to recall that Aristotle talked about four kinds of explanatory causes for any phenomenon: material, efficient, formal, and final. In these terms Jack is content with a formal cause (the symmetries) as an explanation,
while Jim and Paul regard that as inadequate. Instead they seem to be looking for a material and/or efficient cause.
Are they? Let's review.
Four Causes refers to an influential principle in Aristotelian thought whereby causes of change or movement are categorized into four fundamental types of answer to the question "why?". Aristotle wrote that "we do not have knowledge of a thing until we have grasped its why, that is to say, its cause." While there are cases where identifying a cause is difficult, or in which causes might merge, Aristotle was convinced that his four causes provided an analytical scheme of general applicability.
- A change or movement's material cause is the aspect of the change or movement which is determined by the material which the moving or changing things are made of. For a table, that might be wood; for a statue, that might be bronze or marble.
I say the material cause is the "marble" of Einstein's geometrodynamical field molded by the "wood" of the stress-energy current densities of all the non-gravity fields.
Therefore, I invoke a material cause as well as symmetries.
- A change or movement's formal cause is a change or movement caused by the arrangement, shape or appearance of the thing changing or moving. Aristotle says for example that the ratio 2:1, and number in general, is the cause of the octave.
- A change or movement's efficient or moving cause refers to things apart from the thing being changed or moved, which interact so as to be an agency of the change or movement. For example, the efficient cause of a table is a carpenter, or a person working as one, and according to Aristotle the efficient cause of a boy is a father.
- An event's final cause is the aim or purpose being served by it. That for the sake of which a thing is what it is. For a seed, it might be an adult plant. For a sailboat, it might be sailing. For a ball at the top of a ramp, it might be coming to rest at the bottom.
I am definitely into teleological final cause - Destiny in a Block HOLOGRAM Universe.
the future and past cosmological horizons encode the interior bulk
the horizons are the hologram plates (computers)
the interior bulk are the hologram images
I think this points up how important it is to be aware there is a meta-question involved here concerning what constitutes an adequate explanation and that this is probably what most of the disagreement is really about. Is there a 'right answer' to this? I doubt it, but it's probably good to have as many of the 'causes' addressed as possible (except perhaps for 'final cause' which invokes notions of design and takes us farther away from modern science as usually understood).
Jim,I anticipated that part of your criticism might be that Jack is accepting things as primitives that aren't - that circles around the sun are nice and symmetrical but that circles being an observed fact doesn't explain why they are there. Sounds like you intend to do a detailed note or two here - so thanks, this should be more interesting than rehashing the fictitious forces argument as it stood (although I realize that this discussion will likely at some point lead right back into it).One thing I'm curious about is where does the inertial reaction force fit into, align with or contradict Jack's gauge invariance math? I can make a verbal argument of sorts about how such a force would relate to the conservation law (along the lines that it is what causes an opposite and equal reaction), but I don't know where to try to plug it into the sort of detailed discussion going on here.Also, I'd like to add Happy New Year to everyone here who uses the standard western calender!Sent from my BlackBerry 10 smartphone on the Rogers network.
Paul will tell you, I expect, that Jack's "explanations" in terms of transformation invariance and Noether's theorem and the like aren't really explanations at all. And I agree. Saying that a conservation law is the physical cause of mass and inertia is really just silly. It's like saying that the Sun and Moon are circular because circles have the most perfect symmetry. Sounds profound. And says nothing about the physics of gravitational accretion and energy minimization.
To characterize my position as in some sense a theory that is independent of general relativity and so dismissable without doing violence to general relativity is also wrong. I assert that general relativity and the standard procedures of field theory, with the WMAP results, accounts for inertia and inertial forces without ANY further theoretical assumptions. Those determined to believe that the quantum vacuum has something to do with inertia are, understandably, not please with this as it renders their speculations irrelevant. But physics is about what's right, not what makes us feel warm and fuzzy.
I had planned on addressing this tonight. But it is late; and I have an early trip into LA in the morning. And I want those who are not professional physicists on the list to be able to follow the main points of the argument. That means providing some historical context, for this stuff is hard enough to follow when you know the context. Without the context, it's all a bunch of symbol salad for most. So I'll tackle this maybe tomorrow. And do it in as many digestible pieces as seems warranted. Jack can then tell everyone it's a bunch of word salad. And Paul can correct my errors. :-)
One point I should add: when I talk about the causally connected universe from the point of view of Jim's phi=c^2 gravity, I talk about the future cosmological horizon (where the event horizon and hubble sphere coincide) because we've been assuming that Wheeler-Feynman advanced radiation-reaction is the mechanism for some of this stuff. Basically an effect propagates (ie. radiates) through spacetime in the "forward" time direction and interacts with other matter in our future, which then sends a reaction wave back through spacetime in the "backwards" direction.There would be a different (more complete) definition if you were talking about the causally connected universe extending into our past.However, I didn't get into such details (which have been argued over before) because I wanted to stay with relatively simple analogies that I wouldn't get terribly wrong ;)Rob
There is actually potentially a really interesting discussion here. We have Jack’s theory that particles with mass exhibit inertial resistance to being pushed off geodesic because action-reaction arises purely locally based on gauge invariance and gauge transformation – a local theory. And, we have the opposite, a distance approach – Jim’s argument that the origin of inertia is to be found in the gravitational interaction of all matter in the causally connected universe. Both claim to be consistent with GR, but are at opposite ends of a spectrum.If we agree that spacetime curvature around sources and off-geodesic acceleration are frame invariant objective realities, then we all agree that objects in free fall will “fall” towards the COM of the Earth and that objects “hovering” in the Earth’s gravity field on the surface of the Earth due to electrical contact forces always weigh the same on a scale. So, then the question of whether there is a real Newtonian gravity force comes down to whether a force is needed to explain why objects remain on inertial trajectories until pushed off them by electrical contact forces (ie. an “origin of inertia”) or whether the gauge invariance idea is sufficient.So in terms of Jack’s gauge invariance discussion – is it wrong? If so, why? Is it not wrong but incomplete? If so, why? Then we can compare its strengths and weaknesses to the strengths and weaknesses of Jim’s argument.Again, Jack’s argument (highlighted in red):I actually have not seen it in any textbooks, which treat the gauge transformations purely as formal manipulations with no direct physical meaningAgain because the basic idea is so simple and beautiful that it's amazing that not even Feynman noticed itIn the case of Maxwell's electromagnetic field the argument goes like thisThe Canonical momentum of a test charge isP = mv + eAP is gauge invariant under U1 internal symmetry gauge transformationsmv -> mv + hgradSeA-> eA - hgradSS = quantum phase of test particle of inertia m and electric charge emv is charge's kinetic momentumeA is the electromagnetic field momentum sitting smack on the center of mass of the chargeThis is as local a contact force as one can imaginehgradS is the momentum exchange of a virtual longitudinal near Field photonTherefore newton's third law of action with equal and opposite reaction is trivially automatically obeyed locally between field and charged particledP/dt = 0Canonical momentum is conserved in time when there were only virtual photon exchanges between particle and field forming a closed systemOf course A depends on faraway sources via the greens function propagator integrals with the source distributionsImpliesmdv/dt = - edA/dt = eEE = electric real force fieldWhen we do this in special relativity we get more termsI know how to extend the same kind of argument to the gravity field