But, suppose that the conservation laws of linear and angular momentum were not true laws -- just approximations . . . -- Robert L. Forward
In this section of his essay, Forward suggests an analogy: just as the laws of conservation of mass and conservation of energy were shown to be aspects of a single law (conservation of mass-energy or conservation of energy) so too it seemed possible to him that the laws of linear and angular momentum might be shown to be aspects of a single law, the conservation of momentum. It would therefore follow that as mass can be converted to energy and energy to mass -- happens all the time in the quantum realm -- so too linear and angular momentum will be shown to be converted from one to the other in the quantum realm. The problem with this analogy is that the "law of the conservation of mass" was a misunderstanding brought about because the physicists and chemists of the day (19th century) did not have the measurements or theory to show there was only one law: the conservation of energy. Recall that everything is based on symmetry. Symmetries are how we "see" into the quantum realm. The symmetry associated with conservation of energy is time translation symmetry. It "refers to moving the point in time you define as the origin of your time axis, t = 0, from one moment to another." [QG] This rather unassuming symmetry implies conservation of energy as soon as you apply Noether's theorem. There is no corresponding symmetry for mass.
Now two strong caveats have to be mentioned here. First, outside of the limits of the Heisenberg Uncertainty Relationship (delta E X delta T > h-bar), it is possible to briefly borrow amounts in excess of what the law of conservation of energy would permit. In the quantum world, this sort of thing happens all the time. So in a sense brief (very brief) violations of the time translation symmetry are permitted. Second, mass can result from spontaneous symmetry breaking, such as what happens in the theory of "unified" electro-weak interactions. Because the electro-weak force is extremely short range, the carrier particles must have significant mass. The breaking of complex gauge transformation symmetries permits this to happen. Needless to say this is all very complicated and we won't be getting into it in any depth at all. The point of all of this is that there are symmetries beyond the ones that formed the basis of Noether's original work and that symmetry breaking is a crucial aspect to understanding contemporary physics. Thus while Forward's original analogy is flawed, it is by no means hopeless. We just have to tread carefully.
One of the things I like about Forward is that treading carefully was never his style.
So where are we? Are we any closer to our goal to showing that this conversion of angular to linear moment (or the reverse) is possible on the quantum scale? Or, is there any astronomical observations that would do the same? Recall, that the simple fact that the sun was giving out as much energy as it does for as long as it has been doing it was a solid clue that new forces and processes were taking place that were unknown to the 19th century scientists of earth.
Now in terms of astronomical observations, there are high-velocity neutron stars (i.e. moving in excess of 800 km/sec) relative to their lower velocity cousins (moving in the range of 100 to 200 km/sec).* What we would like to observe is if these high-velocity neutron stars (which make up about 50% of such stars) have anomolously lower angular momentum. If such a correlation could be observed, that would provide evidence for, that under extreme circumstances and a supernova explosion unifying General relativity and Quantum Mechanics in a particularly appalling fasion is about as extreme as you can get, the conversion of angular to linear momentum does take place.
The standard explanation for the observed high space velocities of pulsar is, "this is thought to be due to asymmetric SuperNova II explosions." Just how asymmetric? And why the discrepancy in the velocities? I am simply suggesting that the matter as far as I can see is probably covered by the standard theories and explanations but not yet completely. I highly doubt that any astronomer-physicist is looking for exceptions to the laws of conservation of angular and linear momentum. But now that the modeling of supernova explosions is starting to get much better, perhaps they should.
As for the breakdown of the conservation laws on the quantum scale, that is a good deal more dicier and I will turn to that in the next part.
[to be continued]
*This is the reference: http://antwrp.gsfc.nasa.gov/diamond_jubilee/papers/lamb/node3.html
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