The radical conclusion that Cold- or Warm-Darm-Matter cosmology ought to be discarded as a viable description of physical reality would imply, as a strict logical process, that this physical reality must be non-Newtonian in a certain physical regime which is found on galactic scales and beyond. This goes hand-in-hand with discarding Newtonian dynamics in these regimes.
Indeed, changing dynamics away from Newtonian dynamics is actually already a very well established tradition in physics and results from the desire to understand how objects with “mass” move about and influence each other in our four-dimensional “space-time” world.
Before proceeding, the distinction between mechanics and dynamics in physics ought to be clarified: Mechanics is the science “concerned with the set of physical laws governing and mathematically describing the motions of bodies and aggregates of bodies geometrically distributed within a certain boundary under the action of a system of forces.” Dynamics, on the other hand, is the study of the “causes of motion and changes in motion”. In what follows we do not distinguish these two, but interchangeably refer to Newtonian dynamics and Newtonian mechanics (or in short just Newton) as meaning the classical mathematical description of the motions and changes of motions. These are Newton’s three laws and his 1/r^2 law of gravitation.
Now, lets take a time machine and go back about 120 years. On arrival we find that after centuries of applying pure Newtonian mechanics to describing natural phenomena highly successfully indeed and after a brilliant history of applying this theoretical knowledge to practical utilisation (industrial revolution, planetary motions, long-range travel with trains pulled by steam engines, building ever bigger and more powerfull machines), problems had begun to emerge:
The first failure of Newton (on small spatial scales)
The first famous example was the break down of Newtonian mechanics on small scales.
The historical events leading to the full-fledged theory of (non-Newtonian) Quantum Mechanics we know today appear to share some parallels with our problem at hand (speculative dark matter versus non-Newtonian gravitational dynamics):
As noted here:
“In 1802, William Wollaston in England had discovered that in fact the solar spectrum itself had tiny gaps – there were many thin dark lines in the rainbow of colors. These were investigated much more systematically by Joseph von Fraunhofer, beginning in 1814. He increased the dispersion by using more than one prism. He found an “almost countless number” of lines.”
“Johann Balmer, a math and Latin teacher at a girls’ school in Basel, Switzerland, had done no physics before, and made his great discovery (in about 1885) when he was almost sixty. He decided that the most likely atom to show simple spectral patterns was the lightest atom, hydrogen. Angstrom had measured the four visible spectral lines to have wavelengths 6562.10, 4860.74, 4340.1 and 4101.2 in Angstrom units (10-10 meters). Balmer derived the empirical formula to describe the wavelength of spectral lines in the Hydrogen atom.”
These were thus the first empirical hints for quantisation of energy.
In 1901 Max Planck solved the long standing unsolved problem of how the shape of the black body energy spectrum comes to be.
“At first Planck considered that quantisation was only ‘a purely formal assumption … actually I did not think much about it…’; nowadays this assumption, incompatible with classical physics, is regarded as the birth of quantum physics and the greatest intellectual accomplishment of Planck’s career.”
Balmer’s empirically derived formula (with a constant that had no explanation at that time) was later explained by the Nils Bohr model of the hydrogen atom of 1913 which showed that electrons were arranged in discrete shells about the nucleus.
Albert Einstein’s explanation of the photoelectic effect in 1905 further gave strong evidence for the quantum nature of matter and energy.
These discoveries show how the long-cherished concept of a Newtonian world broke down fundamentally on small scales. The (nowadays famous) scientists of the day had bits and pieces of partially computable theoretical understanding (e.g. Planck’s spectral energy distribution, Bohr’s atomic model, Balmer’s spectral line rules). But the Theory of Quantum Mechanics we know today did not exist yet. This theory was developed largely in the late 1920s by Werner Heisenberg and Erwin Schroedinger.
Note that this failure of Newton implies that particles can “magically” appear at a place where Newton would not have allowed them to. A physicist stating this may be referred to as being nuts, but tunneling is in fact an established physical process of quantum mechanics which also happens to be quite fundamental to important technologies we are using without even being aware of it.
Thus we had the following historical development away from Newtonian mechanics to Quantum Mechanics:
- 1802 – spectral lines exist – William Wollaston.
- 1885 – Balmer lines – Johann Balmer.
- 1901 – Black body spectrum explained by quantisation of energy – Max Planck.
- 1905 – Photoelectric effect as a quantum effect – Albert Einstein.
- 1913 – mathematical model of Hydrogen atom based on quantised states – Nils Bohr.
- late 1920s – development of the mathematical theory of quantum mechanics – Erwin Schroedinger and Werner Heisenberg.
The second failure of Newton (at large velocities)
A famous case of the break down of Newtonian mechanics occured at large velocities. This was first hinted at by the inexplicable discovery that the speed of light is constant independent of the velocity of the light source (the Michelson-Morley experiment). And directly related to this, after a major research effort to constrain its properties, the Ether had to be abolished as a physical reality. The outcome, in 1905, was the Non-Newtonian Theory of Special Relativity by Albert Einstein. As we all know, this theory was not the final word in physics.
The third failure of Newton (at large gravitational accelerations)
The precession of Mercury’s perihelion is a famous example of the break-down of Newtonian dynamics within the SolarSystem. We read:
“Einstein showed that general relativity agrees closely with the observed amount of perihelion shift. This was a powerful factor motivating the adoption of general relativity.”
In strong space-time curvature, space and time are distorted such that locally clocks go faster and lengths are contracted. This leads to objects moving on different trajectories than an observer interpreting the world through Newtonian eyes would expect. The Theory of General Relativity was able to precisely account for Mercury’s perihelion shift, and also correctly predicted the deflection of light by the Sun.
The fourth failure of Newton (at small accelerations)
Today we have a similar situation as in the first case above, but now in the realm of very small accelerations (i.e. vanishing space-time curvature), but the job of finding the underlying mathematical theory is not yet done:
- 1933 Fritz Zwicky demonstrates that galaxies must be about 500 times heavier in the Coma galaxy cluster than judged from their light emission (e.g. Zwicky 1937).
- 1956 Fritz Zwicky demonstrates that new dwarf galaxies are born when larger galaxies interact (Zwicky 1956, p.369, point 4). Today these are called Tidal Dwarf Galaxies.
- 1970 – discovery of the super-Keplerian rotation curve of the Andromeda galaxy – Rubin and Ford .
- 1981 – all observed disk galaxies have super-Keplerian curves – Bosma.
- 1983 – Modified Newtonian Dynamics with new constant a_0 – Mordehai Milgrom.
- 2004 – Relativistic theory of MOND – Jacob Bekenstein.
- 2005 – Modified Gravity – John Moffat.
- ?when? – development of the mathematical theory of space-time and gravitating and inertial mass – ?by whom?.
The Fritz Zwicky Paradox arises under the hypothesis that (1) Newtonian/Einsteinian dynamics is valid on galaxy-cluster scales (Zwicky 1937) and that (2) tidal dwarf galaxies are formed in galaxy encounters (Zwicky 1956). Both together lead to a logical inconsistency. This Fritz Zwicky Paradox can only be solved by discarding the assumption that Newontian dynamics is valid (Kroupa et al. 2010).
Note that Bekenstein’s TeVeS theory includes Einstein’s Theory of General Relativity, Milgrom’s dynamics and Newtonian dynamics as limiting cases in the relevant physical conditions (e.g. TeVeS gives normal Newtonian dynamics on Earth, but leads to MOND dynamics in the outer regions of galaxies and to General Relativity near black holes).
Today it is known that MOND (Modified Newtonian Dynamics, e.g. Milgrom & Bekenstein 1984) or some other modification of gravity such as MOG (Modified Gravity, Moffat 2006) are the preferred descriptions of galactic dynamics in the weak field limit (small curvature case). Does this mean that gravity per se differs from the Newtonian law (i.e. space-time curvature as resulting from General Relativity), or does it mean that the principle of equivalnce between inertial and gravitating mass is violated in the regime of very small space-time curvature (see Bekenstein & Milgrom 1984)? We do not know.
Thus, in the past it was realised that Newtonian mechanics and dynamics broke down on small spatial scales, at high velocities and at large gravitational accelerations. Today we are learning that it also breaks down when the accelerations are small. Note this progression of the time derivative of physical quantities describing our four-dimensional world (scale=zeroth derivative, velocity=first derivative and acceleration=second derivative). Does this mean something? No idea.
But, it is clear that Newton’s mechanics was found to not work when technological advance, based on Newtonian mechanics, allowed us to probe large velocities and small spatial scales. The new theories allowed us to build better machines (e.g. telecommunication being based on Einstein’s theories and computers and measuring devices being based on quantum mechanical concepts). The theoretical insights into the properties of matter via quantum mechanics and relativity gave us access to an unprecedented control over matter and to unimaginable amounts of energy.
Today we can probe regions of physics where space-time curvature is extremely small finding that, again, Newtonian mechanics fails. This may mean that the Theory of General Relativity needs an extension or that we do not yet understand what “space-time” and “mass” are nor how they are fundamentally related. Perhaps it just boils down to the problem of us not understanding the vacuum.
The four failures of Newtonian dynamics can be rephrased as follows: The real physical world, when interpreted strictly through Newtonian eyes, misbehaves badly on small spatial scales, at high velocities and at large and small accelerations. Clearly, Newtonian mechanics and dynamics are a useful, but limited, mathematical description of the physical world.
Similarly as above we can state that (some) scientists of the day have bits and pieces of partially computable theoretical understanding (e.g. galactic rotation curves, the Bullet Cluster, tidal dwarf galaxies, the Local Group of galaxies, modified dynamics). But a full theory of gravitation and mass is still lacking.
We can thus rest in comfort that in the realm of low accelerations dynamics is MOdified rather than Newtonian and that we live in a world without Cold or Warm Dark Matter. But, the fundamental theory underlying MOND or MOG (the final word in physics explaining space-time and mass) is yet to be discovered. This is a great present-day chance for mathematical physicists to get to play.
Exciting Times – Our Times
The present epoch is an extraordinarily exciting time indeed: How was it to live, as a physicist, during the legendary time of the theoreticians Einstein, Bohr, de Broglie, Planck and Heisenberg and Schroedinger? Well, perhaps much like today which is, perhaps, the time of Milgrom, Bekenstein, Moffat, Blanchet, Zhao, Famaey and others perhaps yet to emerge.
by Anton Ippendorf, Pavel Kroupa and Marcel Pawlowski (01.09.2010, “The Fritz Zwicky Paradox: the fourth failure of Newton (MOND, MOG, etc)” in “The Dark Matter Crisis – the rise and fall of a cosmological hypothesis” on SciLog. See the overview of topics in The Dark Matter Crisis.