Revisiting "Spin Drive to the Stars" -- Part IV

After I completely my previous post, I realized there were some points that needed expansion and clarification. One of the analogies that Forward used was in reference to the first nuclear reactor at the University of Chicago (1941) -- under the football stadium to be precise. The idea being that just as this device showed that the conservation laws of matter and energy were one in the same, i.e. by transforming an isotope of uranium into energy, (a notion that has already been shown to have problems since there is no such law as the conservation of mass), so too Forward imagined it might be possible in the future to create a "momentum reactor" that allows the transformation of angular momentum to linear momentum. In fact, long before (1.7 billion years before for those who are curious) Fermi assembled the first "atomic pile," there had already been natural nuclear reactors in Oklo, Africa. The particular geological conditions at the site (there was plenty of water for example and that was crucial for slowing down the neutrons so the reaction could occur) allowed the uranium isotopes to interact in a true nuclear reaction. Even plutonium was generated at the site -- showing that nuclear reactors and plutonium despite what you may have heard are as natural as kittens and sunlight.

Now these natural reactors were discovered in 1972, but they might have been found decades earlier providing a remarkable proof of concept for a man-made reactor.

Historically, there have been other examples of natural nuclear reactors, e.g. the nearest star, our sun. In the late 19th century, it was realized that the sun and the earth were far older than had been realized, which raised all manner of difficult questions. The known energy reactions at the time would have left the sun a dead cinder after a few thousand years. Since the sun was a good million times older than that, obviously something radically different in the way of energy production/processes was going on, long before fusion reactions in the stars were understood. Once they were understood, of course, even more spectacular sources of stellar energy (e.g. supernovas) began to be understood as well.

The point of all this is that if the conversion of angular momentum <--> linear momentum does take place, it has to do so at the quantum level. Then, if this hypothetical conversion is to have any observable consequences, the stars are the place to look for it, the stars undergoing extreme changes of state shall we say. So far there are no observed exceptions to the conservation of energy with any of the extreme stellar events that have been observed. Despite the fact that short term, out of sight, violations of conservation of energy are permitted and do happen at the quantum level, they are not carried forward into the universe we are familiar with. Which is unfortunate, because as Anastopoulus [PoW, pg. 145] writes: "General Relativity is not characterized by the symmetry of time translation because the notion of time depends on the geometry, and the geometry changes dynamically. For this reason, the concept of energy is not defined in General Relativity." But for all known observations it might as well be.

The same follows for the concept of momentum (angular and linear).

So time translation symmetry holds as far as we can see even given the General Theory of Relativity, which as noted is not a friendly domain for the Poincare space-time symmetries we are familiar with. The geometry of space-time is "not predetermined and absolute like in Special Relativity."

But, and this cannot be emphasized enough, so far no observed deviations from the fundamental conservation laws have been found.

So what is a physicist to do? One approach to seeing if this conversion of angular to linear momentum takes place is to maintain and expand the neutron star research program to get to the bottom of the anomalous neutron star velocities. This is priority number one. A real physicist would say that because a supernova explosion in its early stages results in a number of asymmetrical jets, known physics can count for all unusual observations to date. Maybe so, but the evidence is insufficiently conclusive to me and on that basis I would like the observations and modeling to continue as far as possible for as long as possible. Theory both at the quantum and GR level says the conversion of angular <--> linear momentum, the breaking of the Poincare symmetries, cannot be ruled out. But if the symmetry breaking isn't observed at the most extreme conditions taking place in the universe, i.e. the core of a star going supernova, that would put some serious constraints on the theory of Quantum Gravity. The implications to science are too crucial to do anything less than carry forward on this program.

Revisiting "Spin Drive to the Stars" -- Part III

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

Revisiting "Spin Drive to the Stars" -- Part II

" . . . there is another conservation law standing in the way of progress -- the law of conservation of angular momentum -- spin. "

-- Robert L. Forward

So what is spin, i.e. angular momentum in the quantum realm, as exhibited for example by an electron or proton? Well, the first image that comes to mind, as it did to the physicists investigating the phenomenon in the 1920's is that of a rapidly rotating electron or proton (the only particles known at the time.) This picture at least provides a simple mental image for those still nostalgic for the old Bohr solar-system model of the atom. There is this electron "planet" orbiting a "proton" sun (let's stick with the hydrogen atom, please) and both are "rotating" about their mutual axis just like the planet earth and the sun spin about theirs. It is a pleasing picture, cute in a way, but it is wrong. Worse, it is unhelpful. The fact that it is so wrong brings us to one of the immediate problems in thinking about the quantum world, the world of "micro-physics," and we might as well get it out of the way. As the great physicist Pauli noticed almost at once, if you calculate the "rotation" velocity of an electron, assuming it is behavior like a rotating planet, it turns out to be faster-than-light. This is presuming the electron is an extended body of some sort, not a point particle, which is in fact how most physicists think about it. Faster-than-light is a big no-no and as every physicist will tell you a calculation that yields such is giving a strong indication that the initial picture is wildly in error. No way to get around it. Moreover, if we think of an electron as a spinning ball, how the heck does it hold together given the enormous electrodynamic forces that must be coursing through it?

There are some things, given the current state of our knowledge, it is best not to go there -- at least so current wisdom tells us. Though some activity is taking place that can be measured in quantum terms that resembles what in the macro-world we would call "angular momentum" (it is a conserved something after all), try as best as you can to put the rotating mini-planet image out of your mind -- forever.

Now, I don't mean to suggest that pictures as such are a bad thing. That is the way we learn to interact with our environment and it is far from clear to me that a blind physicist or mathematician would be an any advantage in thinking about the quantum world as compared to his sighted compatriot. Moreover, using mental pictures to guide experiments, thought or otherwise, has been a key skill for physicists, e.g. Einstein, and you can't go wrong as a physicist when following Einstein. But the fact of the matter is that the quantum realm is best understood in terms of abstractions, symmetries in particular which have been all the rage since Noether's pioneering work. So if we think of "spin" in terms of a symmetry what do we learn?

". . . while spinning is mathematically similar to rotation, it is unlike any rotation that we can ever perceive with our senses." -- Charis Anastopoulos [PoW]

"Even if the symmetries of a physical system are the only thing we know about it, we can still understand many aspects of its structure." [PoW]. And that is the key to grasping the quantum world. The rotations and translations of [Minkowsky flat] spacetime together form what is called the Poincare symmetry. What this means is that once we have confirmed the presence of this symmetry, "we can decompose any system with a given symmetry into smaller systems that still possess the symmetry. We then decompose these smaller systems into yet smaller ones possessing the symmetry." [PoW, page 139.] And so on, until we arrive at the fundamental or irreducible systems. These components describe the motion of free (i.e. no external forces) particles.

In the end, the analysis reveals two numbers which describe these free particles. The first number describes the particles rest mass. The second describes something that resembles "intrinsic spinning. It is therefore called spin." [PoW, page 140].

This is a marvelous result and is as solid as you can get in the quantum realm. But unfortunately, and this point cannot be emphasized enough, it falls apart in General Relativity. As the great physicist John Wheeler (1911 -- 2008) was to discover, there is no way to incorporate "spin" into General Relativity except in very special circumstance. This was a big disappointment to him because he was hoping to develop a kind of ("already", as he referred to it) unified field theory just using topology in GR. but because the flat Minkowsky spacetime completely breaks down in GR (recall the "fields upon fields" description means good-bye to the spacetime backdrop), so does the beautiful Poincare symmetry. And that means notions of conservation of mass and angular momentum become much more dicey and difficult to deal with.

I'm not sure what Emmy Noether would have made of this but I suspect she would not have been altogether happy with this development. Nor would a classical physicist. But for those of us seeking the spin drive to the stars, this "unfortunate" development, offers hope towards that end.

[to be continued].