The most ruthless Internet forum I know is the Clarinet Bulletin Board, where if anyone ever, ever says that there’s many ways to trim a reed, “but only one of them is right” —

That person is dealt with. You do not want to be fingered by a community that has The Fingering Forum as a side board. And I really feel I have to deal with this egregiously smug article according to Clarinet Board rules. With full force.

Light goes at c, you say. And we use light to measure the dimensions of the Universe — until LIGO came along to change the game, what else could we possibly have used? Our yardstick is the so-called “light year”, which always gives trouble to physics teachers, because kids tend to think it’s a time, not a distance.

Time is defined in terms of vibrations of light: the duration of 9,192,631,770 cycles of a certain emission of caesium is officially defined as “one second”. I listed this as my “favourite scientific fact” on Quora. If you count a caesium atom emitting 9,192,631,770 cycles, then the length of that wave train as it travels through space is exactly what you would call “one light-second”, by definition. You can measure it with a metre stick, Einstein populated the whole of space with metre sticks.

If you use this “light-second” or “light-year” as your unit of length, in measuring astronomical distances, then you are making two astronomical assumptions: (1) You are automatically assuming that light always travels at c; this is an empirical finding, sure, but now you have frozen it into your whole system of measurement. If, in fact, the speed of light changes over time or in certain regions of space, then your metre stick will be “uneven” — but you will have no way to detect this, lacking some absolute cosmic metre stick that can tell if maybe that 9,192,631,770-cycle wave train is a bit shorter in this bit of vacuum rather than that as light travels from a distant star.

(2) You are also assuming that the vibratory rate of caesium stays constant. And if it changes, you have absolutely no way of detecting this, because your very definition of time is based on these cycles; and one would presume that if caesium was “running fast”, other atomic clocks like those based on ytterbium would also “run fast”. So you need to invent a non-atomic clock that can track real-time changes in caesium emissions, if you really want to prove your definition of the second is stable. Any suggestions?

So: you say the speed of light is c. Now, what I say you are doing is using light to measure light; you are using a tape measure to measure itself. You take the distance travelled by light from a star as ct, where t is the time taken for light to reach us from the star. If you use your system to calculate the speed of this light, you can only get one possible answer: it moves at “one light-year per year”, or “one light-second per second”, by definition, not by measurement. Your measurement of time is tautologous with the phenomena it’s measuring; and if you use this circular definition of time to measure distance, then your entire system of measurement is self-referential and redundant.

So much for the obvious part of the “only correct” way to see these things. I wish the above was all my own argument, but I get it mainly from an engineer called Konstantin Meyl, who is extremely entertaining if nothing else. He has been sending kits demonstrating superluminal scalar waves to universities all over the world (he says it’s nonsense that light only travels at c and he can prove it — call him out, get one of his kits.) He maintains that the Big Bang is a Big Bluff.

I just pose one p.s. to the above: what would happen if the Universe was speeding up? If vibrations of caesium were actually getting faster, according, again, to some absolute cosmic clock? What would happen if you looked at light from distant stars, when caesium was younger and was vibrating slower? It would appear lower in frequency, or “red-shifted”. How do we know that the red shift from distant galaxies does not actually represent different physical conditions in earlier times?

Which is where we get, finally, to the really “counterintuitive” idea that the Universe is expanding, and hey wow, that means space itself is expanding. Now, I wrote my first dissertation on general relativity back in 1975, in my second year, with a full interrogation from the famous and/or infamous astronomer David Block, quizzing me, “What does it mean if a black hole has no hair? What does it mean?” So the whole idea of the Big Bang and space expanding from a singularity is not such big news, nor necessarily so counterintuitive, after more than a century of general relativity in general useage.

Here the mysterious “dark energy” appears, that is pushing the Universe apart, so that there are elements that we will never see, at least if the speed of light is always c. Regions in spacetime that are “unknowable” to each other.

What is this mysterious dark energy? I chirped this column once before, saying, it’s associated with negative probabilities in quantum physics. There was a debate on Quora, what is the most difficult concept to understand in physics: I put negative probabilities forward. And I don’t recall anyone saying that it wasn’t difficult enough.

So let me try explain the hardest concept in physics quickly. Probabilities of anything happening in the real, physical world always lie between 0 and 1. Zero is impossible; one is certain. An event with zero probability cannot, will not, certainly should not ever happen, if this probability has accurately been measured. An event with probability one must happen, is inevitable.

In quantum mechanics, you have quantities that are “incommensurable”, you can’t measure them at the same time. You can’t measure the position and the momentum of a particle at the same time. Everyone knows that one. The less intuitive one is the following: You can’t measure the time taken for a “happening” to happen, and the energy that that “happening” contains, at the same “time” (you see how this one is much trickier — but every time they tell you that a virtual particle can “borrow” energy from the Universe to pop out of the vacuum and disappear again, as long as it does it quickly enough, this is the logic they are using.)

Now, the physicist Richard Feynman was the one who picked up on Dirac’s clues and noted something truly anomalous going on with these quantum calculations physicists were doing. These calculations gave phenomenally accurate results; but the bookkeeping behind them was decidedly “counterintuitive”. He found that when you were measuring quantities that did not commute, like position and momentum, shadow states started appearing in your calculations with negative probabilities, and also over-unity probabilities, greater than one.

You can read a great essay Feynman wrote on the subject here, where he says the idea of negative probabilities gave him “cultural shock” when he first encountered it. According to various accounts I’ve seen, he proved not only that you could not get rid of these negative probabilities, but that you could quite consistently formulate the whole of quantum mechanics with negative probabilities as fundamental. He stated that the real difference between classical and quantum physics was precisely this unavoidable appearance of negative probabilities in the latter.

Again: please, remember, there is no question that QM predicts that everything that physically occurs in the Universe must have a probability between 0 and 1. So let me try explain exactly how we infer the existence of these unobservable states of negative and over-unity probability.

Suppose you have two dice, and someone is throwing them together in another room and providing you the results. But all they tell you is the sum thrown with the two dice, you don’t know what the individual scores are. This is like quantum indeterminacy. You get these inextricably combined results, and have to try infer what underlying dynamics are producing this pattern.

You see nothing lower than a “2”, and nothing higher than a “12”. You find over time that these both occur with probability 1/36. You find that “3” occurs 1/18 of the time; and so on. And after a while, you say: this looks exactly like the pattern I would expect, throwing two ordinary dice and adding the numbers together.

Now you do an experiment with quantum dice. Again, you can’t see what the individual dice are showing, just the composite result. You start seeing something that looks like a pattern formed by the sum of two dice. You try to fit the observed pattern with any underlying logic that you can calculate, like you did with the two ordinary dice. And indeed, you work out the probabilities of the underlying phenomena in such a way that you predict exactly the outcome that is observed. You’ve worked out the rules of these quantum dice. The trouble is this. The quantum dice show, for example, that the probability of a “7” works out nicely as the probability of a 1 + 6, or 2 + 5, or 3 + 4, in either order. However, when you add up the probability you got for the 2 + 5, and add it to the probability for 3 +4, you get a number that is greater than 1. The only way you can get physically meaningful calculations — and remember, this is all trying to predict an observed physical pattern in the real world, so the final probabilities must always be between 0 and 1 — is thus that the probability of getting a 1 + 6 is actually somehow negative.This is exactly where quantum physics deviates from the classical picture, in insisting that some of these underlying states have over-unity probabilities — are “more than certain” to occur; while others have negative probabilities, are “less than impossible”.

Now, it should be stressed: while these states are unobservable, they have very real energy. Indeed: if you look at the Sun as a ball of Time, rather than as a ball of burning hydrogen, then its “duration” is incommensurable with its “energy”, these do not commute. This is precisely the situation where you expect states of negative and over-unity probability to come into play,with very real energies and very real consequences in the real physical world.

Astronomers are looking in all directions for the source of “dark energy”, some 75% of all the energy in the Universe, which seems to be driving the expansion of space itself. Something exceeding weird is going on, everywhere; and we cannot see it. It’s not called “dark energy” for nothing.

My suggestion, now speaking as an applied mathematician, not a physics teacher: instead of looking for this dark energy with your telescopes, look for it in your equations. And you can tell me if unobservable states of over-unity and negative probabilities don’t look like good candidates to explain the distinct underlying tensions we detect in the large-scale dynamics of the Universe; gravity pulling in, and “something”pushing out.

For what it’s worth, my interpretation is the same as that of Chairman Sheng-ji Yang of Alpha Centauri:

Einstein would turn over in his grave. Not only does God play dice, the dice are loaded.

Of course God loads the dice, and heavily. You find this over and again in the Bible: that which God decrees, cannot be undone, by any means. And that which God banishes from all existence, stays banished.

There’s another word for “unobservable” — it means precisely the same thing, and it’s used in precisely this sense in mundane astronomy. That word is that word that gets both the physicists and the born-agains alike frothing at the mouth , so there must be something to it. That word is occult. Absolutely without mysticism, absolutely unambiguously, negative probabilities are pointing at occult realities, invisible states of existence that crucially influence the physical world. And when physicists are ready to face the fact that their discipline truly needs a science of the occult, the invisible, the unobservable, the supersensible: they may even turn to a book like Occult Science, by Rudolf Steiner — his completely scientific description of invisible realms and how the visible world is woven from them. It starts quite sensibly, goes completely nuts, and then ends quite sensibly again, with very straightforward and ancient Rosicrucian meditation exercises, to develop the image-making mental facility you need to start perceiving in the invisible.

When you see meditation being taught in a physics class, you’ll know we’re finally getting somewhere in understanding quantum mechanics. I don’t say this lightly, there’s a vast amount of shit talked about mysticism and quantum physics, this is why I stress the scientific investigation of spiritual realities. I am talking about a far, far more rigorous approach than anything exemplified by the above hand-waving argument that presents itself as the “only” correct view of reality.