Dear Kashyap,
Feynman was a great teacher of the masses. However, part of the reason he was great was that he had a knack for making use of naive realism just enough to give people a hint of what was being proposed but not so much as to get in the way of the theory (hopefully). He makes it clear in that well known chapter at the beginning that the metaphorical ‘curvature’ applies to spacetime considered as a single metric. He then builds up a story about curved space pretending that we can leave time out, in order to get the concept across.
I agree that it seems that at one point he is telling us that space itself actually y is curved, and I will come back to his metaphysical position, but note that the formula for radius excess he gives is proportional to the mass divided by the square of the velocity of light. I am fairly sure that what this means is that this apparent ‘radius excess’ is what pertains to dynamic relations with the velocity of light - such as light based observations. If we take time out of the analysis and, using a ‘God’s eye view’, ask what curve the space has with no time elapse, or in other words in terms of relations with infinite velocity, then the GM/v(∞) squared term is zero.
So space itself has no curvature.
And I think that has to be so because it would have to be curved in comparison to some other spatial metric and there isn’t one. The story about ants walking on a sphere works because there is a further dimension that shows that someone working with Pythagorus on paper cannot then assume his rules will apply to oceanic navigation. The comparison fails. It is meaningless to say space is curved unless we have a new comparison that fails. The new comparison, as I understand it, is that whenever you try to assume that Euclid applies to space across time you will find the same sort of discrepancy the navigator finds. Since the velocity of light in a vacuum is the maximum possible it seems reasonable to assume that light is ‘God’s yardstick’ and proclaim space to be curved to the extent it seems to be for light ‘paths’. There does seem to be something intrinsically suited to measuring in the velocity of light but I do not think it can be legitimate to go on to say ‘space really is curved this much’ precisely for the reason that Special Relativity had already shown that space and time as separate metrics are no longer viable aspects of physics.
I have become interested in the degree to which modern physicists fail to understand the basic imperatives of dynamic theories that the masters of the seventeenth century told us about. If Feynman had truly understood physics he would have prefaced his lectures by saying that all students should first read Descartes’s Meditations in First Philosophy of 1641 in order to understand that all we are entitled to believe about the outside world is that it shows mathematical regularity of its tendency to give us sensations. They should then read the First Scholium on Space and Time of the Principle Mathematica to understand that ‘time’ and ‘space’ as used in physics are not the time and space of ordinary discourse but mathematical tools that can be used to predict our spatial and temporal sensations. And, most importantly, they should read together Leibniz’s Reflections on true Metaphysics, Specimen Dynamicum and New System from the 1690s in order to understand that there are no objects in the world, only actions or dynamic connections - dynamic units that can be called some name meaning ‘unit’ - monad or quantum.
Einstein is of course often considered the worst naive realist of recent times, with his inability to accept quantum theory. On the other hand Feynman seems to suffer some of the same problem. The difference is that whereas Einstein allowed his naive metaphysics to stop him accepting a theory Feynman accepted the theory and said one should not go in to the ‘filawsify’. But if Feynman had understood Leibniz he would have seen that there is nothing difficult to understand about quantum theory at a metaphysical level because it fits precisely what Leibniz showed the fundamental metaphysical level ought to be like.
There seem to be two major lessons Leibniz gives us. One is that there are no things, just dynamic units or ‘events’ or ‘actions’ or perhaps ‘connections’. That immediately makes a concept of space divorced from time absurd. What is confusing is that alongside probing this fundamental level Leibniz spends a lot of time working out the rules of a mechanical (classical) sort of description, in which he does separate space (ordering of coexistents) and time (ordering of sequentials). Although he saw both space and time as relative (contra Newton) he believed in simultaneity at least as a valid abstraction. That might seem at odds with his fundamental dynamic account but he makes it clear that the two sorts of account are incommensurable (but always corresponding as in the modern principle). Einstein seems to have got the dynamic idea right, even if maybe reluctantly. Feynman may not have been quite so good at it, as indicated by the chapter you quote. If he pointed out that none of it means anything except in a dynamic context the sort of confusion people run into would perhaps have been avoided.
Feynman accepts quantum theory more than Einstein but reluctantly too, and with the complaint that nobody can understand it. He uses notional ‘paths' to ‘sum over’ in a way very reminiscent of Leibniz and he admits that these are just tools, but if he had fully understood what Leibniz said about dynamic indivisibles he would have found his own theory perfectly easy to understand. Leibniz points out that individual dynamic units have to have a counterintuitive ‘telic’ description, a priori, which takes us far away from anything like particles or waves and closer to a knight’s move in chess.
The practical relevance, it seems to me, is that saying space is curved confuses everyone. There are no rails laid down by the sun. There is just a non-Euclidean relation between the four dimensions that depends on mass. A curved spacetime built on a naive realist view of ‘how the world seems to light’ may be a good mathematical prop but for things moving much slower like cannon balls, the ‘distortion' of trajectory is quite different. So we end up with questions about curved space in centrifuges.
My guess is that there is a third message for us from Leibniz: that every dynamic relation is always an asymmetric relation of monad to universe and that we should not think that monad and universe should be considered of the same notice category.IN a sense one is quantum and one is classical, so all relations involve both sorts of incommensurable descriptor. Maybe that is why QM and GR seem incommensurable - they are supposed to be?
Best wishes
Jo
May 30, 2017
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Priyedarshi,
Whatever happened but in most people’s mind Feynman had the highest intuitive physical Ideas ever seen in a physicist. Not even Einstein!! He is recognized even for his idea on quantum computers. While we are talking about intellectual honesty, S.N. Bose’s case is very interesting for Indians. He tried to publish his paper on photon statistics in German journals. But being from India he was not getting anywhere. So he sent a copy of his paper to Einstein. Einstein recognized importance of Bose’s work, translated into German and got it published. Later Einstein made some additions to it and it became Bose- Einstein statistics. If Einstein did not get Bose’s paper published under Bose’s name we would have either Einstein statistics or at best Einstein- Bose statistics instead of Bose-Einstein statistics! Well! Scientists are human beings and they like fame and fortune like everybody else. Occasionally some of them are real honest, not all!! All of us in this publishing business find out about it!!
Kashyap
May 31, 2017
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Dear All,
There is an intense debate on validity of Bohm’s theory/hypothesis/interpretation is going on this blog!! Admittedly, I have not read Bohm’s or Sutherland’s papers. But these days there are so many papers published that no one can read all of them. Now, number of physicists on this blog is a tiny, tiny, tiny fraction of total number of physicists. I read many physics blogs also. So far none of the top level physicists has come out in favor of Bohm/Sutherland’s theory. If you say it is a matter of time and my attitude is unscientific. Science should not be a popularity contest! Ok! It is possible that 1000 persons may be wrong and one person may be right. But I think, Bohm/Sutherland’s theories have still terrible problems.
Quantum mechanics works beautifully in the present linear form and it agrees with experiment to better than 1 part in a billion or more. If Bohm/Sutherland have to make it highly non-linear to make it compatible with experiments, nobody is going to buy it, not even on Einstein’s authority! By the way, Einstein was probably the greatest scientist ever born , but he was wrong in connection with quantum mechanics (God does not play dice and EPR reality issue). So, although I have an open mind, in my heart, I seriously doubt if these efforts to make QM realist will succeed. Personally I like non-realistic interpretation of QM in agreement with Advaita (Maya) philosophy. Again, since there is no consensus about interpretation of quantum mechanics after 90 years of debate, may be something very subtle could be going on!
Best Regards
Kashyap
May 31, 2017
...
Princeton Bhakti Vedanta Institute: http://bviscs.org
Sri Chaitanya Saraswat Institute: http://scsiscs.org
Sadhu-Sanga Blog: http://mahaprabhu.net/satsanga
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