In December 2009, Sabine Hossenfelder wrote a mostly correct (yes!) paper,
The box-problem in deformed special relativitywhich was good news because after several years of intermittent communication between the two of us about this point, she finally understood that the theories trying to impose nonlinear Lorentz transformation laws for the momentum and energy, and theories trying to half-obey the postulates of special relativity, can't be right.
We're talking about various "doubly special relativity" or "deformed special relativity" theories that have been shown incorrect in many texts on this blog.
For example, in February 2006 and December 2006, I explained why nonlinear transformations needed for the hypothetical nonlinear dispersion relations in the so-called "doubly special relativity" act non-locally on the spacetime: if two events coincide in one inertial frame, they won't coincide in the other reference frame. That's the basic observation behind Hossenfelder's paper.
Other articles, like one from May 2007 or June 2009, discussed the variable speed of light theories. In December 2006, Sabine Hossenfelder wrote an article called "deformed special relativity" where she defended the framework and the upper bound on the density of energy T_{00} in any frame.
Your humble correspondent and one or two anonymous physicists were explaining her why it was incompatible with the tests of the Lorentz symmetry and why only Lorentz-invariant quantities may be constrained by the universal laws of physics: in 2006, we failed. She hysterically denied any counter-proof against DSR, a theory she religiously defended. That was also the case of her December 2006 paper where she argued that DSR can be extended to the position space "in a consistent way".
In February 2006, I also explained why the nonlinearity of the dispersion relations implies nonlocality because the additivity of energy (and momentum) is related to the fact that different regions evolve "independently": the Hamiltonian of the "big system" (which generates the evolution) reduces to the sum of the partial Hamiltonians exactly if the two "subsystems" can exist independently - a weak form of locality.
The "doubly special relativity" and similar theories therefore suffer from various problems - one of them has been referred to as the soccer-ball problem because some theories even predicted that the total energy of a macroscopic object such as a soccer ball can't exceed the Planck energy - which is utterly preposterous because you wouldn't be allowed to kick into the ball.
Happily enough, Sabine Hossenfelder - who would previously write lots of incorrect papers about the observable effects of quantum gravity (which meant various "minimal [coordinate] length scale" and other things that can't occur) - understood these elementary things by the end of 2009 and she could write the paper. None of these pathological phenomena that some people incorrectly associated with "quantum gravity" - even though such violations of relativity have nothing to do with "quantum gravity" (they're pure crackpot speculations about huge modifications of physics that their authors decided to link to "quantum gravity" because the term sounds smart and sexy) - can be observed. The theories that would predict such new effects can be safely ruled out by elementary observations and simple thought experiments.
She correctly explains that the nonlinear relations between the energy and momentum would mean that the notion of "one spacetime event" would become observer-dependent and it would ruin locality. In fact, because we know that such violations of locality don't occur in the existing particle interactions, we can derive an upper bound on the DSR-like deviations from special relativity that are 20+ orders of magnitude stronger than those obtained by Fermi.
This should not be too surprising. Fermi measured the hypothetical delay of high-energy gamma rays directly and it could tell us that it was less than 10^{-1} seconds or so - which translates to the requirement that the coefficients of the hypothetical Lorentz-breaking, energy-dependent, linear terms in the formula for the speed of light are smaller than 100% per Planck energy of the photon. However, we indirectly know that the delay must be smaller than 10^{-23} seconds or so - the minimum observable time scale - because we don't observe the nonlocalities in the particle physics experiments. So the brutal violations of locality, as envisioned by doubly special relativity, are safely ruled out. A simple thought experiment is enough to see it.
Adrian Cho wrote a story for the Science magazine,
Thought experiment torpedoes variable-speed-of-light theorieswhich is kind of fine. And be sure that I don't care much that she hid the source where she learned the ideas because my argument had to be obvious to almost everyone who has some idea about physics. So I don't care about the credit. I think it's more important that some sanity may be returning to those places.
The article also quotes two authors whose DSR theories' failure has been understood even by Sabine Hossenfelder by now, namely Lee Smolin and Giovanni Amelino-Camelia. They hypothesize that Hossenfelder's argument may not apply to their theories if the spacetime is discrete.
Needless to say, it's just a completely illogical and hopeless attempt to spread fog. Hossenfelder's argument, if I may call it in this way, makes no assumptions about the strict continuity of the spacetime at the Planck scale. It only analyzes the actual observable effects that occur at the particle physics scales and their interrelationships with the cosmological distances and the Lorentz transformation.
Because she doesn't assume anything about the continuity at the Planck scale, it's clear that a hypothetical discreteness can't "resuscitate" the dead theories. It's just about pure logic. Hossenfelder's argument looks at a completely different - much longer - time scale than the Planck time. Saying that some details at the Planck time could invalidate her arguments is as preposterous as saying that the existence of multiple Higgs bosons could mean that HIV doesn't cause AIDS.
But this observation about the "non-existence of a loophole" doesn't mean that the discreteness is possible. There are other, related simple arguments showing why the spacetime cannot be discrete in the Amelino-Camelia-Smolin way, either: see e.g. Myths about the minimal length, discrete physics, and other texts. Such a discreteness would bring additional violations of the principles of special relativity so it would surely make these problems worse, not better. And some forms of discreteness are simply incompatible with any form of the equivalence between different inertial frames: but this equivalence is an experimentally confirmed postulate of relativity.
After a couple of naive years when I was uncertain, I learned that Lee Smolin in particular is defending claims that are wrong and he realizes pretty well that they are wrong. But he is defending them anyway, for purely egotistic reasons, because he doesn't want to reveal that his whole career in science was about the production of kilotons of plain garbage.
So the percentage of statements he made that were lies was systematically growing and today, he prefers to lie all the time instead of admitting the obvious things. Nowadays, his scientific integrity is zero. While I don't know Amelino-Camelia well, I guess that he's on the path of doing the very same thing.
Sabine Hossenfelder is unlikely to earn too much professional feedback - because the good physicists have always realized that those DSR-like theories can't work while the bad ones don't want to realize and they will find Hossenfelder's thought experiment inconvenient. So the popular article in Science will actually remain a more reasonable description of the status of DSR than what you will find in the professional DSR literature - an anomalous sorting of qualities that can only happen in disciplines whose experts are no real experts in anything.
The communication between those people must be strange. Do they know which of their colleagues actually realize that this who "research direction" is indefensible? Do those who know why it's worthless stuff pretend that they believe these theories even in front of their closest colleagues? Or does everyone know that it is just a game and the whole community is playing a game? Has Sabine Hossenfelder written the dozens of wrong papers about various "possible" violations of relativity because Lee Smolin pressured her to do so?
There are too many sociological questions I simply can't understand because my viewpoint on the world is simple. The truth, and only the truth, deserves to be defended, and as soon as we learn that something else is the truth, we should change our statements correspondingly, regardless of our personal interests and external pressures.
And that's the memo.
snail feedback (5) :
"... only Lorentz-invariant quantities may be constrained by the universal laws of physics ..." This is the conventional wisdom, but is it 100% correct?
According to Fredkin and Wolfram, quantum field theory and general relativity theory are merely excellent approximations to an information process that proves that nature is finite and digital.
Consider 2 hypotheses:
(1) Einstein's equivalence principle is not 100% correct, because of dark matter (among other reasons).
(2) Corrections to the Bekenstein-Hawking radiation law in the form of paradigm-breaking photons suggest that the multiverse is a Fredkin-Wolfram information process that computes M-theory.
Can you prove that (1) & (2) are wrong?
Dear doggytwit,
yes, one can disprove the idea that the world is fundamentally a discrete "digital" process, and I have done it many times.
Lorentz invariance for all particle species can't emerge from a Lorentz-breaking fundamental theory because that would require fine-tuning for at least 100 parameters of the Standard Model - various speeds of individual particle species and ratios of spatial and temporal coefficients of otherwise similar terms in the effective theory.
Moreover, even if you wanted to accept that a theory can be fine-tuned to look Lorentz-invariant even though it's fundamentally not, just to "hide the decline", you will still run into numerous fundamental and lethal contradictions. It will always be possible, in principle, to design a process that is "macroscopically" Lorentz-violating.
Your two specific "hypotheses" are even more unreasonable than the general statement that the world is discrete.
1) Dark matter, by definition, means a new type of matter that was introduced exactly for the general theory of relativity - and the equivalence principle it's based upon - to continue to be 100% correct. The alternative to dark matter is that you don't need any dark matter but you have to modify the laws of GR - and/or even the equivalence principle - in some way. This is a very negative option because of both theoretical and experimental reasons. Theoretically, the equivalence principle is woven deeply inside GR and it is needed for the removal of unphysical polarizations of gravitons, i.e. removal of negative probability ghosts, and so on. Experimentally, the equivalence principle holds with a huge accuracy - currently better than 1 part in 10^{16}. So the "sacrifice" of the equivalence principle is an extremely serious sacrifice. But to "sacrifice" the equivalence principle for no good reason whatsoever is just silly. One can't "rigorously prove" and reduce to experiments that the equivalence principle holds 100% accurately - because experiments are never 100% accurate, they are never enough for any 100% proof - but one can surely see that it's extremely unlikely for your combination to be an improvement. In proper physics, the dark matter is mostly 1 new kind of a particle, neutralino. Your proposal is on par with saying "2+2 is sometimes 3.998 instead 4", just for fun, let's try it. Well, first of all, it is empirically known to differ from 4 by less than 0.0000000000000001, and second of all, theories where it differs by anything don't work mathematically. They have qualitative problems. To say the least, the speculation of yours contradicts the known physics if taken naturally, and you can fine-tune it in such a way that it becomes indistinguishable from the observed physics - but such an adjusted theory will be completely unjustified by anything, extremely ugly, and for this reason, extremely unlikely.
2) Sorry but this combination of Bekenstein-Hawking entropy, its corrections, multiverse, "paradigm-breaking photons", and M-theory shows that you're on crack. Corrections to the BH entropy are inevitable - and increasingly important (relatively) for small black holes - because there are corresponding corrections to the Einstein-Hilbert action in the effective action for gravity, as derived from string/M-theory. There are no "paradigm-breaking photons", and even if such photons were "paradigm-breaking", they wouldn't play any special role in the physics of black hole. Physics of black holes is about gravity - communicated by gravity - and photons are always just "ordinary, mundane" matter particles - one species among dozens of them.
None of these things about black holes - and even photons - has anything direct to do with the multiverse. But even if there were such a multiverse, M-theory is explicitly not a "Fredkin-Wolfram information process". For example, it's not "quite discrete". All known - and probably all mathematically possible - definitions of string/M-theory vacua have to depend at least on some strictly continuous degrees of freedom. They do. They have to.
So apologies but what you write makes no sense in physics. One can randomly combine catchy words of various types. But physics is not a process of a random combination of meaningless words. Physics is about the search for theories that agree with the observations - as accurately, naturally, predictably, and comprehensively as possible.
Best wishes
LM
Is it just a coincidence that the speed of light is 186,000 miles per second and the wavelength of a 1 Hertz wave is equal to 186,000 miles? I think not.
Dear foggy, if your question is a real one, be sure it's not a coincidence.
A one-hertz vibration means that there is one period per one second. It means that the period of the vibration lasts 1 second.
So if you wait for this 1-second interval, and the vibration creates the electromagnetic waves, the radiation escapes to a certain distance, x=vt. The time t is 1 second, the velocity is 186,000 miles per second, so it escapes 186,000 miles.
Exactly when it does, you start a new wave. So the distance between the two equal positions on the wave will be exactly the wavelength and it's the distance I just calculated, 186,000 miles.
Cheers, LM
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