In the arguments between Bohr and Einstein I think it is clear that Bohr got the upper hand. Einstein was frankly wrong about all his concerns over quantum mechanics. He insisted there must be some noncontextual reality, but from Bohr, to Bell and then to Kochen-Specker it is clear that to impose such leads to logical contradictions.
Quantum mechanics is just plain weird.
Cheers LC
He lost the argument with Bohr, but he won the argument for mathematical completeness, or there would be no more theorists today.
Tom
Tom,
The reason for me to question some fundamentals of set theory were obviously and admittedly not satisfactory resolved problems concerning zero and infinity.
I came to the result that mathematics lost to some extent its anchoring in realism. We may safely benefit from idealizations as long as we are aware in what they are different from reality.
What about completeness and compactness, e.g. the expansion of an impulse into a converging series is a good example while the usual interpretation of delta(0) reveals to me the mentioned imperfections of current arbitrariness. Did you deal with the appendices of my essay?
Eckard
LC,
The petition was mainly signed by those who did not swallow SR. There are, however, also proponents of SR who signed because are desperately seeking for answers. NPA is serious.
What about the factor two, I picked up this strange peculiarity almost 50 years ago in Dresden when Prof. Mierdel told it in his lecture on electro-physics. Look at the appendices of my essay for examples. I already mentioned Schroedinger's non-relativistic result. Mybe, I found it in his original papers, maybe in "Schroedinger - Life and Thought".
I also recall Hendrik van Hees putting a request in sci.physics.research because a result of his calculation was at odds with literature again by a factor two.
As a schoolboy I simply wondered why E=mc^2 is just twice as large as the kinetic energy integral mvdv.
In general it might be a moot point where to start the integration. While an integral over delta (x) dx from minus infty to plus infty = 1 is used for normalization, retardation of potential starts at r=0 and t=0.
As I already tried to explain elsewhere, I do not question the limitation to the velocity of propagation of action. SR might instead be unrealistic because Galilei's principle of relativity is restricted to closed system while electromagnetism is definitely "contextual" in the sense electric and magnetic fields do not have any spatial restriction except for their restriction to a past cause.
Eckard
"We may safely benefit from idealizations as long as we are aware in what they are different from reality."
We here this same objection over and over in this forum.
It is based on a false premise, however, and is therefore invalid. Science discovers reality; science does not presume reality.
Tom
Hear, not here.
The E = mc^2 result is not hard to see. We start with the elementary work-energy theorem
E = ∫F*dx
Where the * means a dot product. The force is by Newton's second law F = d(mv)/dt. We express everything according to velocity and so dx = vdt. This means the energy is
E = ∫dtv*d(mv)/dt = ∫v*d(mv).
The endpoints are 0 to mv and in what follows limits are assumed. In a nonrelativistic setting the mass is constant and E = m∫v*dv = (1/2)mv^2. In a relativistic setting we have that the mass is m = m_0/sqrt{1 - (v/c)^2}. Now put that into the work-energy formula
E = m_0∫v*d(v/sqrt{1 - (v/c)^2})
= m_0∫v*(v/sqrt(1 - (v/c)^2} - (v^3/c^2){1 - (v/c)^2} ^{-3/2})
= m_0∫v*dv{1 - (v/c)^2}^{-3/2}
and the integration gives
E = m_0c^2(1/sqrt{1 - (v/c)^2} - 1) = E' - m_0c^2
So the final result is a total energy with a rest mass energy m_0c^2 subtracted out. The kinetic energy term E' = E m_0c^2. Now for low velocities the total energy is
E' =~ m_0c^2[1 v^2/2c^2} = m_0c^2 (1/2)mv^2.
LC
Tom,
"We may safely benefit from idealizations as long as we are aware in what they are different from reality."
Example: A railroad is something real. It is idealized as a one-dimensional line by neglect of two less important dimensions.
You did disagree:
"We hear this same objection over and over in this forum. It is based on a false premise, however, and is therefore invalid. Science discovers reality; science does not presume reality."
What false premise do you refer to?
A line is not something real that can be discovered. I cannot measure future data, I cannot predict the future from the laws of nature alone. I got increasingly aware that just the laws of nature are independent from frame of reference. Reality depends on influences from the past unless one takes the (criticized by Popper) point of view of reality as a closed system.
Eckard
LC,
In reality, past and future are different because reality is not a closed system. So far, physics ignores this and postulates time a priori extending from minus infinity to plus infinity. From this point of view, SR would be understandable. However, apparent discrepancies, sometimes by a factor two, arise when this somewhat bizarre "relativistic" theory is confronted with the realism of the non-relativistic view.
I reiterate: Galilei's principle of relativity is restricted to closed systems.
A harmonic oscillator would likewise oscillate forever.
However, electromagnetism is definitely "contextual" in the sense electric and magnetic fields do not have any spatial restriction except for their restriction to a past cause.
Doesn't this preclude the equivalence of all imaginable frames of reference?
Mustn't a realistic shift of the origin of elapsed time be restricted to the past? The situation is similar with sound pressure in acoustics. While it is reasonable to choose the atmospheric pressure as frame of reference and consider usually just the AC component, the absolute pressure cannot get negative.
Eckard
"What false premise do you refer to?"
That science presumes any particular form of reality.
"Reality depends on influences from the past unless one takes the (criticized by Popper) point of view of reality as a closed system."
Same false premise. Physical science assumes only that reality is objective, i.e., independent of the observer. Objective reality is determined solely by correspondence of theory to measured result. Causality is not necessarily time dependent -- in a positive feedback loop, cause and effect are not distinguishable.
Tom
I have to confess I don't quite understand what you are writing about here. I am not sure what is meant by "electric and magnetic fields do not have any spatial restriction except for their restriction to a past cause."
Cheers LC
LC,
Stationary electric monopoles and magnetic vortexes in empty space are thought to do not have any spatial restriction but extend from r=0 to infinity. Transversal electromagnetic dipole fields propagate in it from a cause at r=0 to r=ct where t is a measure of past (elapsed) time. This restriction to reality is their spatial restriction. So called future Minkowski cone is merely a theoretical limit to reasonable speculation outside sound physics.
Regards,
Eckard
Tom,
"Physical science assumes only that reality is objective, i.e., independent of the observer."
A god is also objective in the sense of not observable. Sound physics must not be based on something like future that can not be measured in any case. Future is objective but not yet a reality.
"Objective reality is determined solely by correspondence of theory to measured result."
Objective reality as a whole cannot be determined at all. We merely can construct and possibly falsify some models of it. According to Popper, any agreement between theoretically predicted results of a preparation and measured data may just help us to find out theories that are perhaps appropriate.
"Causality is not necessarily time dependent -- in a positive feedback loop, cause and effect are not distinguishable."
The arrow of causality is already to be seen in the word feedback. Chicken_n and its egg that becomes chicken_n+1 are distinguishable.
Eckard
Causality is not necessarily time dependent -- in a positive feedback loop, cause and effect are not distinguishable.
Electric and magnetic fields are spatial quantities. Changes in these field propagate on a light cone. A light cone is the projective space in a Lorentzian flat spacetime. To be honest I have a hard time seeing what you are writing about as something which is of any real concern.
LC
LC,
It is all about misuse of abstraction and questionable anticipation, i.e. the lost link to reality. Karl Popper implicitly declared SR wrong when he declared the world open and he called Einstein Parmenides.
You wrote: "Electric and magnetic fields are spatial quantities. Changes in these field propagate on a light cone. A light cone is the projective space in a Lorentzian flat spacetime."
Wasn't it Minkowski with reference to Einstein who introduced the two quite different cones, the cone of history and the cone of possibility?
Anyway, they used the common abstract notion of time as something a priori given from infinity to infinity, amen. Considering this scale like something one can move within as along a x-scale, they neglected the fact that the future is open. Actually, negative values of elapsed time rather resemble likewise not measurable negative values of spatial distance r.
Their very useful but nonetheless unrealistic view was already anchored in mathematics at least since Descartes introduced Cartesian coordinates. It resembles the likewise superior abstraction of small-signal AC components.
However, many arguments of the opponents of SR are also correct.
When these opponents were looking for a flaw in SR, they typically questioned the limitation of the velocity of light to c, because they readily accepted the seemingly appealing postulate that the laws of physics must be the same in all frames of reference. While this Galilean principle of relativity holds in cases of closed systems, i.e. without action at distance, the forces of electric and magnetic fields are not enclosed in an overlookable part of the infinite space.
In the real world the future is open and the past unchangeable. This does not at all allow the shift along the scale of elapsed time, which can be performed so elegantly by multiplication with exp(iwt) in our models.
Already Bohm admitted and Van Flandern further explained why so many putative experimental confirmations of SR can be interpreted otherwise. The matter is actually somewhat tricky, and there is a lot on the stake for speculative theories that were build on SR.
Any objection?
Regards,
Eckard
To be honest I have a hard time seeing what you are writing about as something which is of any real concern.
The Popper idea of an open world, where I have his book on this and read it many years ago, is concerned more with QM than relativity as I recall. I don't know how to put this, but bluntly there are really no concerns with the physical basis of special relativity. Further, the general relativity is also heavily substantiated as well. There are questions of course with quantum gravity and the foundations/origins of the universe and black hole singularities and the rest. Yet special relativity is less a research issue and more of an application. Every time a person gets a synchrotron radiation treatment to kill tumors and a whole range of other technologies they are getting an application of special relativity. These issues and problems you are raising simply do not exist.
Cheers LC
LC,
Why do you believe that there are applications of SR that may prove it correct?
I am ready to check your claim that synchrotron radiation would not work without SR. I just have at hand some textbooks including "SR applications to particle physics and the classical theory of fields" by Saleem and Rafique and where I did not find something that could refute the arguments e.g. by Von Flandern and Popper.
What about the latter, it might well be that he did not seek a detailed personal confrontation with Einstein after he clearly put him into the drawer of those who anticipate the future by calling him Parmenides. Perhaps he did not feel obliged to draw the due consequences in public. Do you have access to belonging documents?
Regards,
Eckard
Meanwhile I found written by Jeffrey Ketland in a discussion at FOM:
Apparently, Einstein referred to his own world-view as
`Spinozistic' and made repeated references to God ("The Lord is subtle
but not malicious", "God doesn't play dice"). Popper referred to
Einstein's General Theory as `Parmenidean' (and Einstein didn't
object):
See
[12] Popper, Karl 1982: `A Conversation with Parmenides', in The
Open Universe: An Argument for Indeterminism (Hutchinson),
Chapter IV, Section 26.
Eckard
Einstein made reference to his idea of Spinoza's God.
Theories are of course never proven. My point is that special relativity is sufficiently well supported that within the classical domain of applicability. Quantum gravity may be a departure, though it is not likely to recover some Galilean perspective. In fact recent observations of gamma ray bursts and the coincidence of radiation with widely different wavelengths put tight constraints on Lorentzian violations. Special relativity is well enough supported that it is used in some engineering and applications.
Without special relativity Brehmsstralung radiation emitted by a charge in a circular accelerated orbit (eg a cyclotron) would be emitted in a direction normal to the tangent velocity, or along the direction of the centripetal force on the electron. Special relativity transforms this into a beam-like cone that is more tangent to that velocity. This focused relativistic X-ray production is what is used in various applications of synchrotron radiation, from X-ray deposition on solids to medical treatments.
One problem I see is it is clear you will keep shaving the point of argument to ever smaller scales of minutia. This is something which I have seen by those who argue against Darwinian evolution or the problem of climate change by our production of CO_2. There are even some rather intelligent people who argue this way, from Berlinsky who argues against evolution to Motl who has largely transformed himself from physicist to climate change denialist --- based BTW on rather extreme right winged opinions. I happen to think these are intellectual pits which are best avoided. You apparently have joined a sort of anti-relativity movement (intellectual pit), but as I see things this suggests this sort of argument can persist indefinitely, largely because theories are never proven, they are only supported by data.
Cheers LC
LC,
Perhaps it doesn't matter much that I am unable to get access to the link you provided. I do anyway not expect being in position to judge the particular case. Likewise I feel not competent to contribute to the issue of global warming and Darwinism. I agree with you: In these questions there is little room for doubt.
Please do not consider me a denialist. I simply did not yet find convincing counterarguments against my reasoning: In reality the past cannot be changed while the future depends. Physics does not really deal with the original and complete reality but always with models that are abstracted from it. This worried even the late Einstein. For a while I was hoping that Galilean Electrodynamics could overcome some obviously not yet resolved inconsistencies of modern physics. Meanwhile, I found out that the Galilean relativity might not apply to fields with unbounded extension. Moreover, Poincaré synchronization is not convincing to me. I argue that past and future must not be mingled.
Usually, I dislike both extremes: those who speak of an Einstein hoax and those like you and Tom who more or less blindly admire Him. I trust in what already David Bohm admitted and Van Flandern further specified: One cannot easily decide whether putative evidence actually confirms the claims. Maybe, Lorentz arrived at a useful formalism, maybe the approach was nonetheless wrong, maybe just some implications for theory require reconsideration. I need some time for more homework. Thank you for your effort.
Regards,
Eckard
