Standing Still
After a few pleasant days in Wanaka I found myself in Christchurch once again, so I went to see the movie The day the Earth stood still. I especially enjoyed the bit where the alien crosses out the Dark Force term in the equations of relativity.
posted by Kea | 1:01 PM
5 Comments:
Yup, USA today had an article about this, where they interview Sean Carroll about Professor Barnhardt's chalked up equations:
"The equations were right," Carroll says. "Unfortunately the chalkboard is turned at an angle in the film where they solve everything. I craned my neck to see but couldn't make it out. I could have gotten some real answers there," he jokes. (NASA has announced it will release some Dark Energy news this Tuesday, by the way.)
The alien (Reeves) really did cross out the Lambda term. I saw it, clear as can be.
Hee hee, Klaatu is far smarter than Earth physicists. I appreciate his concern for the damage humans do to the planet. If an Earth student today crossed out "lambda" she would get into trouble with her professors.
In the original 1951 film Klaatu remarks about his equation, "It got me here." If physicists would stop blaming everything on "dark energy" maybe we would have flying saucers too.
If I can be a bit unpopular, there is a reality to "dark energy". The error is in the original fitting of general relativity to Hubble's recession law. There are two times, time since the big bang t and time past T, which are related to one another by the formula t + T = 1/H (for proof of this relationship, simply see Fig. 1 here) in a flat spacetime cosmology (H being Hubble's parameter). Hubble's empirical law v = HR can - if Minkowski's concept of spacetime R = ct is true - then be written as v = HR = H(ct) = Hc[(1/H) - T] = c(1 - HT). If we differentiate the expansion rate v as a function of time since the big bang T, we get acceleration, a = dv/dt = d[c(1 - HT)]/dT = -Hc = 6*10^(-10) ms^(-2), which is the observed tiny acceleration of the universe (so small that it is only detectable over immense amounts of spacetime, hence the reason why it was only discovered in 1997 by Perlmutter et al., for extremely redshifted supernovae at half the age of the universe). This was predicted and published well before Perlmutter, but that isn't the point. The main point is that it is still ignored.
"Dark energy" isn't so wrong, as the use of spacetime in general relativity as applied to cosmology. By choosing to interpret the Hubble recession as v = HR instead of (Minkowski's equivalent of) v = Hct, the effective variation of velocity as a function of time (acceleration = dv/dt) is obscured from sight, and valuable physical insight is lost from mainstream cosmology. When the facts are pointed out, instead of cosmologists grasping the significance of this, they try to ignore it.
The significance is that the acceleration of the flat universe is inherent in the way the universe is expanding according to Hubble's 1929 discovery. In other words, the expansion and the acceleration are not two separate things, but different aspects of the same thing: the dark energy isn't just causing the acceleration of the universe, it's causing the very expansion of the universe, too. So now there is general repulsive force, powered by dark energy, causing the expansion of the universe.
Now we have to introduce gravitons. Fietz and Pauli in the 1930s originally ignored all the mass-energy in the universe except for two small test particles when analyzing quantum gravity. If a quantum exchange between two masses (similar gravitational charges) results in attraction and there is no other process going on, then the graviton would have to have spin-2.
However, clearly there is a lot more going on, because there is no mechanism to stop gravitons being exchange not merely between two test masses, but between each of those masses and all the other masses in the universe.
Normally we can ignore the other masses in the universe when thinking of gravity, but not with graviton exchange. The problem with ignoring the rest of the mass of the universe is that it is nearly 100% of the total mass partaking in the interaction between your test masses, so yo would be ignoring nearly all of mass involved. Although classically you can often ignore the rest of the distant mass of the universe because it is quite uniformly distributed across the sky, this doesn't cancel out when you are considering quantum graviton exchanges. In any case, gravitons will be converging as they travel from the distant masses in the universe to any particular small test mass. This convergence of gravitons has geometric effects. The short story is that Pauli and Fietz's approximation of ignoring 99.9999...% of the mass in the universe when "proving" that gravitons must be spin-2, is plain wrong. Once you involve the entire mass of the universe - because there is no mechanism known which can stop such graviton exchanges becoming involved in every single quantum gravitational interaction between a few small masses - you find that gravitons must have spin-1 and must produce observed gravitation by pushing masses together over distances up to something like the average supercluster separation distance.
Beyond that distance, the exchange causes the net repulsion that is responsible for the expansion and also the acceleration of the universe.
That "attraction" and repulsion can both be caused by the same spin-1 gravitons (which are dark energy) can be understood by a semi-valid analogy, the baking cake. As the cake expands, the particles in it recede as if there is a repulsion between them. But if there are some nearby raisins in the cake, they will be pressed even closer together by the this pressure, because they are more strongly bound against expansion than the dough, and because they are being pressed on all sides apart from the sides facing adjacent raisins. So because there is no significant amount of expanding dough between them, they shield one another and get pressed closer together by the expansion of the surrounding dough.
In quantum gravity, one simple way to analyze this mathematically is by the empirical laws of mechanics. The acceleration of the universe means that distant receding masses have an acceleration outward from the observer. If the mass of a particular receding object is m and its acceleration a, for non-relativistic recession velocities this mass possesses an effective outward force given by Newton's 2nd law, F = ma. So a 1 kg mass receding at 6*10^(-10) ms^(-2) will have an outward force of 6*10^(-10) Newtons. This sounds trivial, but actually the mass of the receding universe is very large, so the total outward force is very large indeed. Newton's 3rd law then tells you of an equal and opposite reaction force. This is the inward-directed graviton-mediated exchange force. So you can make quantitative predictions immediately.
The clever thing is that for two nearby masses which are not significantly receding from one another (say apple and Earth), this mechanics tells you immediately that there is no significant reaction force of gravitons from apple to Earth or vice-versa.
So by this effect there is a "shadowing" of gravitational charges by each other (because gravitons interact with gravitational charges in order to mediate the force of gravity, and don't go straight through unaffected), providing that they are nearby enough that they are not receding significantly. Thus, the gravitons exchanged between the apple and the receding masses in the universe above it cause most of the observed gravitational effect: the apple is pushed downwards towards the earth by spin-1 gravitons.
So the mainstream QFT gets off beam by focussing on (1) spin-2 graviton errors without correcting them, (2) Hubble v = HR obfuscation in place of the more physically helpful spacetime equivalent of v = Hct, and (3) high energy quantum graviton interactions such as Planck scale unification, instead of focussing on building a empirically-defensible, checkable, testable, falsifiable model of quantum gravity which is successful at the low-energy scale and which resolves problems in general relativity by predicting things such as
(1) G,
(2) the amount of dark energy/cosmological acceleration, and
(3) the flatness of the universe without the speculative inflation hypothesis.
I.e., it's a non-speculative theory, a fact-based theory which at each step is defensible, and which produces predictions that can be checked.
The reason for the ignorance of the simplicity of QFT at low energy is due to the fact that mainstream QFT is contradictory in:
(1) accepting Schwinger's renormalization work, in which the vacuum is only chaotic (with spacetime loops of pair-production virtual fermions continually annihilating into virtual bosons, and back again) in electric fields above ~10^18 volts/metre, which occurs only out to a short distance (a matter of femtometres) from fundamental particles like quarks and electrons. These virtual spacetime creation-annihilation "loops" therefore don't fill the entirity of spacetime, just a small volume around particles of real matter. Hence, the vacuum as a whole isn't filled with chaotic annihilation-creation loops. If it was, the IR cutoff energy for the QED running coupling would be zero, which it isn't. There has to be a limiting range to distance out to which there is any virtual pair production in the vacuum around a real fermion, otherwise the virtual fermions would be able to polarize sufficiently to totally cancel out the electric charge of real fermions. Penrose makes this clear with a diagram in "Road to Reality". The virtual fermions polarize radially around a real fermion core, cancelling out much of the field and explaining why the "bare core" charge of a real fermion is higher in QFT than the observed charge of a fermion as observed in low energy physics. If there was no limit on this range of vacuum polarization due to pair production, you would end up with the electron having an electric charge of zero at low energy. This isn't true, so as Schwinger argued, the vacuum is only polarized in strong electric fields (ref.: eq. 359 of http://arxiv.org/abs/quant-ph/0608140 or see eq. 8.20 of http://arxiv.org/abs/hep-th/0510040 - this is all entirely mainstream stuff, and is very well tested in QED calculations, and is not speculative guesswork).
(2) claiming that the entire vacuum is filled with chaotic creation-annihilation loops. This claim is made in most popular books by Hawking and many others. They don't grasp that if the vacuum were filled with virtual fermions in such loops, you'd get not just geometric (inverse-square law) divergence of electric field lines from charges, but also a massive exponential attenuation factor which would cancel out those radial electric field lines within a tiny distance. Even if we take Penrose's guess that the core electric charge of the electron is 11.7 times the value observed at low energy, then the polarized vacuum reduces the electric charge by this factor over a distance of merely femtometres. Hence, without the Schwinger cutoff on pair-production below ~10^18 v/m, you would get zero observable electric charge at distances beyond a nanometre from an electron. Clearly, therefore, the vacuum is not filled with polarizable virtual fermions, and isn't therefore filled with annihilation-creation loops of virtual particles.
This argument is experimentally defensible, and so is extremely strong. The vacuum effects which cause chaos are limited to strong fields, very close to fermions. Beyond a matter of mere femtometres, the vacuum isn't chaotic and is far simpler, with merely virtual (gauge) bosons which can't undergo pair production until they enter the strong field near a fermion.
It's simple to understand all this if you know about radiation. Lead, and other high atomic number elements, attenuates real gamma rays of high energy primarily by pair production. The gamma ray passes into the strong field near the nucleus, and is transformed into an electron and positron pair. This pair can then be polarized by an external electric field, attenuating or shielding that external electric field, before the pair annihilate back into a fresh gamma ray. The field shielding process with virtual photons and virtual fermions is similar in principle to that observed with real radiation and with the real dielectrics you put inside capacitors between the plates, so the dielectrics polarize to store large amounts of energy. (There is nothing mysterious or speculative in this basic physics.)
Away from the strong fields that exist very close to real fermions, the vacuum is very simple and just contains virtual bosons flying around. Because they don't (unlike fermions) behave the exclusion principle, they don't behave like a compressed gas. They mediate fundamental forces by being exchanged between fermions, simply, without loopy chaos.
For this reason, the complexity normally present in a QFT path integral - due to an infinite number of terms that correct for vacuum loops - not simply present in the real vacuum dynamics that model low energy QED and quantum gravity phenomenon. The path integral reduces to a simple geometric summation of straight lines where there are no loops (i.e. at low energy), as shown by Feynman for the case of light diffraction by glass in his book QED.
Quantum gravity can be done the same way at low energy! It's a simple geometric situation. Loops are important only at high energy where they occur due to pair-production as already proved, so it's amazing how much ignorance, apathy and sheer insulting dumbness there is amongst some QFT theorists, obsessed with unobservable Planck scale phenomena and uncheckable imaginary spin-2 gravitons.
"Dark energy" is badly understood by the mainstream, and having a Lambda term in the field equation of GR is not sufficient physics. It's ad hoc juggling. I just think that for the record, there is evidence that "dark energy" is real, it's spin-1 gravitons and low energy quantum field theory physics is nothing like the unphysical mathematical obfuscation currently being masqueraded as QFT. Fields are due to physical phenomena, not equations that are approximate models. To understand QFT, what is needed is not just a Lie algebra textbook but understanding of physical processes like pair production (which is real and occurs when high energy gamma rays enter strong fields), polarization of such charges (again a physical fact, well known in electronics since it's used in electrolytic capacitors), and spacetime.
The right way to deny all progress in the world is to be reasonable and quiet to fit in with status quo, in an attempt to win or keep friends. As Shaw wrote in 1903:
"The reasonable man adapts himself to the world; the unreasonable one persists in trying to adapt the world to himself. Therefore all progress depends on the unreasonable man."
I think Louise is right in her basic equation, and also in dismissing the terrible ad hoc mainstream approach to "dark energy", but that doesn't mean that fundamentally there is dark energy in the form of gravitons flying around, allowing predictions to be checked.
Please delete if this comment is unhelpful to the status quo here. (I'll copy it to my blog as proof of my unreasonableness. Maybe it's just too long, but it does take space to explain anything in sufficient detail to get the main points across.)
I've solved the dark energy problem and will eventually blog it. Basically, it comes about as a consequence of the same thing that differentiates Newtonian 1/r^2 gravity from Einstein's gravity, a graviton-graviton interaction that creates more gravitons.
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