Model Building and Naturalness

By Mark Trodden | February 20, 2006 9:36 pm

Over the last few months (and this will certainly continue over the next few years) I have been spending some time boning up on particle physics phenomenology and the associated model-building issues. Part of my research involves investigating the cosmological implications of such models, while at other times I am interested in how certain outstanding cosmological questions might be addressed by new particle physics beyond the standard model. These, plus the upcoming turn-on of the Large Hadron Collider (LHC), are some of the reasons that I have been spending time on phenomenology.

I’ve been thinking about this particularly today after a nice seminar by Ian Low from the Institute for Advanced Study (IAS) in Princeton. The content of Ian’s seminar isn’t really what I want to discuss here, but part of what he spoke about got me thinking about a question I’ve wanted to get into for a while.

Most models of physics Beyond the Standard Model (BSM) are motivated by one of the outstanding problems of particle physics – the hierarchy problem. This is the problem of reconciling two wildly disparate mass scales; the weak scale (102 GeV) and the Planck scale (1019 GeV). This hierarchy is technically unnatural in particle physics, since, in general, the effect of quantum mechanics (here known as renormalization) is to make the observable values of such scales much closer in size.

For example, one approach is to introduce a mechanism that cancels many of the quantum corrections, allowing the scales to remain widely separated even after quantum mechanics is taken into account. An example of such a mechanism (and the most popular one, for sure) is supersymmetry (SUSY) with TeV-scale SUSY breaking.

Another perspective is to view the hierarchy problem no longer as a disparity between mass scales, but rather as an issue of length scales, or volumes. The general hypothesis is that the universe as a whole is 3+1+d dimensional (so that there are d extra, spatial dimensions), with gravity propagating in all dimensions, but the standard model fields confined to a 3+1 dimensional submanifold that comprises our observable universe. This submanifold is called the brane (as in membrane). The volume of the extra dimensions can be large, and the spreading of gravitational flux into this volume allows gravity measured on our brane to be so weak, parameterized by the Planck mass, while the fundamental scale of physics is parameterized by the weak scale.

Beyond the Standard Model ideas such as these have the added bonus of a natural connection with dark matter, since the new particles and symmetries that are introduced at the TeV scale typically yield a natural Weakly Interacting Massive Particle (WIMP) candidate.

In the last couple of years, a number of authors have begun exploring models of BSM physics that are unconstrained by addressing naturalness issues, and instead are guided only by requiring gauge unification and a dark matter candidate. The motivation for such models arises from considerations of the string landscape, but I categorically do not want to get into that in this post, or in the comments thread, since it has been discussed to death in many, many other threads. Another motivation that is often mentioned is that current collider constraints are pushing even low-scale SUSY models to need some fine-tuning when addressing the hierarchy problem.

An example of this kind of model is given by Split Supersymmetry (see here and here). In these models, since naturalness is abandoned, SUSY is broken at a high scale and the scalar superparticles (and the Higgs) become extremely heavy. It is arranged, however, for the fermions to remain light, so that they help with unification and one of them can serve as a dark matter candidate.

There exists a considerable literature on the collider signatures of this model and a great deal of follow-up work exploring other consequences. Unfortunately I cannot pretend to have read more than a small fraction of these papers and so certainly can’t comment on them.

As part of my continuing phenomenology education, I thought it might be interesting to have a discussion on the various pros and cons of the two broad approaches to BSM model building. I must confess up front that, so far, I haven’t found the newer approach particularly compelling. Beyond the obvious issue of abandoning naturalness, I think I prefer to have dark matter emerge as an output of the particle physics model, rather than an input. Nevertheless, while I am obviously very close to a lot of this material, I am not one of the experts on these models, and I am sincere when I say that I would be interested in a constructive pedagogical discussion of the pros and cons of the approaches. I guarantee that there are subtleties (and perhaps big glaring issues) that I am missing.

I realize I can’t enforce this, but, as mentioned above, I’d like to suggest a ground rule for the discussion. I don’t think there is anything to gain by rehashing the string landscape issues here. It is not what I intend, and we really have gone over it again and again before.

So, with this one caveat, please have at it. What are the pros and cons of BSM models constructed with naturalness in mind and those constructed ignoring naturalness considerations?

  • anon

    One obvious point to make is that almost every natural model is horribly contrived. There’s the MSSM, which is already almost pushed into unnatural corners of its parameter space, and then there’s everything else. Model-builders have come up with clever things, but while they might appear to rescue naturalness they usually involve lots of 10%-ish fine tunings in several other places, so it’s not so clear they’re really an improvement. After staring at such monstrosities for a while, the idea of split SUSY or of just the SM with a Higgs starts to be kind of compelling, even if simultaneously depressing.

  • Aaron Bergman

    It seems to me that the most successful model we currently have is not natural. Naturalness is cool and all that, but getting the experiments right is more important. In other words, I’m all for looking at everything out there in the hope that we might get it right.

  • Mark

    I agree with that Aaron, but until the recent papers of the last couple of years, people basically agreed that this lack of naturalness was a problem. You’re right; if people come up with clever models that can be tested – we should test them.

    What I’m really interested in though, is getting a feeling for the issues in comparing the two approaches. What are the genuine inputs and outputs? Are there advantages/disadvantages of the various models that are not well captured by the simple naturalness/no naturalness division?

  • Sean

    I agree with anon above. Although I love SUSY, it does seem quite surprising that we haven’t discovered it yet, if it’s relevant to the electroweak scale. The models look really finely-tuned, which is a bad quality to have if the point of your existence is to ameliorate some other fine tuning.

    I’m all for investigating split SUSY and whatnot, although I think the motivations from naturalness considerations are very weak. I’m betting that we discover stuff at the LHC and elsewhere that isn’t what anyone has quite thought of yet. In the meantime, naturalness is a useful guide but certainly not a law of nature (as it were). We could easily discover something that seemed unnatural (like, you know, the Higgs sector of the minimal Standard Model) and then only later realize that there was some pretty mechanism that explained it all.

  • Mark

    Indeed; anon’s point is what I meant by “Another motivation that is often mentioned is that current collider constraints are pushing even low-scale SUSY models to need some fine-tuning when addressing the hierarchy problem.”

  • Plato

    From a layman point of view, I wonder too.

    It is interesting that you would be talking about Jo Anne’s forte? You rounded off the group quite nicely I thought. :)

    What tell tale signatures reveal themselves as indications of new physics? How do they become so?

    None of it makes sense until you can see it working it’s way through models of expression. This, provided a new framework with which to see? Develope new experimental models, to test the theory?

    I see how close you and Sean are to the cosmological information, and dark matter, how so? Is there not some dual nature of blackhole that had not been interpreted, to help us see into what the strangelets were?

    So a comparison between D brane thinking and viscosity bound? Clifford’s forte? And the “abstract thinking,” so foreign.

    Some would make light of it.

  • JoAnne

    My favorite example of coincidental fine-tuning in nature can be found here.

  • Ben L

    I agree that many models seem quite contrived. However, it’s also worth pointing out that some of these problems can be removed by simple modifications to the model. For example, adding a single singlet field to the MSSM (i.e. going to the NMSSM) can remove the fine tuning problem. So, while it’s very much worth thinking about models that arise when one gives up on fine-tuning, it’s also very far from impossible that physics at the Electroweak scale *is* natural.

    To make a minor stab at Mark’s question: one feature of the “unnatural” models that has been noticed is that the Dark Matter candidate tends to be heavier than in the MSSM. In Split SUSY, I believe it’s from many hundreds of GeV to several TeV.

  • anon

    So adding an extra field is that much more palatable than a 10% fine-tuning? De gustibus, I suppose….

  • ann nelson

    This is the Big Question we hope the LHC will answer. If the standard model parameters are something we should be able to calcualate in principle from an underlying theory, then if the underlying theory obeys the usual rules and expectations (e.g. locality) we expect the TeV scale effective theory not to look too finely tuned. If we do see susy or other manifestations of naturalness then deciphering the signals will be a lot of fun, but not mind blowing. If we dont see susy/little higgs/extra dimensions/technicolor the implications are even more surprising and radical. Absence of naturalness is not necessarily evidence for a “landscape” or environmental selection, but is evidence for something conceptually at least as challenging.

    I suppose it is time now for theorists ought to make fools of themselves and bet. I’ll bet against the “natural” approach, even though I mostly try to avoid too much fine-tuning in my own models.
    It does make me suspicious of naturalness that avoiding finetuning usually makes models more complex.

    Why build models we dont necessarily believe? Because we dont have complelling arguments either way and will have to let experiment arbitrate.
    Then in order to understand what natural models might look like at a collider, we need to have diverse examples to play with.

  • Paul Valletta

    Is it Natural that when two particles have a certain distance between them, they are classified as “separate/separated” ?

    At what scale does decomposition yeild separation?

  • Stan Seibert

    One thing I haven’t yet understood about the 3+1+d model is how you have gravity propagate in the bulk, but still get a r^-2 power law here on the brane. Shouldn’t gravity go like r^-(2+d) in such a theory?

  • Count Iblis


    It can be explained by applying anthropic reasoning to scientists :)

    Had the moon been larger or closer to the earth then the eclipses would have been easier to predict by ancient people. So, this situation has led to the development of much more mathematics than is strictly necessary to survive.

  • Peter Woit


    The arguments for “naturalness” were always less compelling than often advertised. In particular, the MSSM creates more problems than it solves. But doing away with it just means that pretty much anything goes, since coupling constant unification and a WIMP are also not obviously necessary ingredients of BSM physics.

    I’d be curious to hear what you think of the problem from a different angle: what aspects of BSM physics can one conceivably hope to get information about from cosmology/astrophysics? Dark matter seems to be the most likely candidate for this, but what exactly can we hope dark matter observations will tell us? What about possible future CMB observations (by the way, what’s going on with the WMAP year 2+ data)? What hints about BSM physics can one ever hope to extract from the CMB?

  • ann nelson

    Stan–you would be correct. A length scale has to be introduced, either a curvature of the new dimensions or a campactification scale, so that all physics including gravitational looks 4D at sufficiently long distances. The innovation of the “large” extra dimensions proposal is that this scale is allowed experimentally to be as large as 100 microns.

  • Plato

    Maybe it just had to be looked at in a different way? Of course once you proceed in this direction you are on a slippery slope towards…(?) and alignment with (?), and this brings out the negative journalist, not necessarily the right one? :)

    Speculate sure, but the varying time signatures, “might have been” indicative.

    Another laser beam is used to make the atoms fluoresce, and the amount of fluorescence is measured as a function of the microwave frequency to plot a “resonance curve“. An ultra-precise measurement of time can be made by measuring the frequency of the peak in this resonance curve (see “Atomic clocks” by Pierre Lemonde in Physics World January 2001 pp39-44).

    An oscillatory view?

    The theory has been revived in brane cosmology as the cyclic model, which evades most of arguments levelled against the oscillatory universe in the sixties. Despite some success, the theory is still controversial, largely because there is no satisfactory string theoretic description of the bounce in this model.

    I mean I have to work with what’s avaliable. Are there questions and probems with the way in which oscillatory has been revived?

  • Alejandro Rivero

    If we want to get some insight on mass, naturalness is still a guide, get something zero and break it to just near zero.

  • marco cirelli

    On the issue of Dark Matter and Naturalness in model building, I think one point worth stressing is that it is not totally true that good DM candidates easily “emerge as an output of the particle physics model”: one needs also to impose some ad hoc symmetry that prevents the decay of DM to Standard Model particles. In the MSSM: R-parity; in Extra-Dimensional models: the so called KK-parity; in Little Higgs models: the so called T-parity, and so on. In other (less technical) words: if not for one of these ad hoc symmetry mechanisms, we would have run out of DM in the Universe since a long time, in these frameworks.

    This adds a con, I think, to the BSM models constructed with naturalness in mind. They have very ambitious goals (like solving the hierarchy problem, or unification) that I deeply admire but I feel they fall short on this point for DM.

    So now the naive question is: forgetting the hierarchy problem for now and focussing on the DM problem, is it possible to construct a BSM model where the DM has all the good qualities, including stability, in an “automatic” way?

    The answer is yes. You simply add a single new field to the good ol’ SM, and you find that for some proper assignments of the quantum numbers there is a perfectly good Dark Matter candidate: electrically neutral, with the right abundance in the Universe and, above all, stable without extra mechanisms. The point is simply that there is no allowed decay mode.

    After all, the proton is (luckily) stable on the Standard Model for similar reasons, not because we have to impose an ad hoc symmetry to keep it from decay! So why not investigating this possibility for the only other surely stable massive particle in the Universe?
    (This is something recently published. I don’t want to write an ad for my own work more than I already did so I’ll stop here, but I felt it fits in Mark’s question about pros and cons of model building and DM.)

  • Alejandro Rivero

    As for coincidental fine tuning, I know of one that if if it were coincidental should beat #7, at least as an example for the HEP community: Gamma over m^3, evaluated for pi0 and for Z0

  • Jake Mannix

    What, are no other physicists going to bet here besides Ann?

    I’ll put in my graduate student’s bet: I think we’ll see a bunch of new physics at about the TeV scale which seems to have nothing to do with the standard model – a new gauge group that’s very weakly coupled to us (something like an SU(2)_R that’s broken at 10 TeV or so), and then there’s a natural (at least to the 10% level) and technically natural extension of this extended Standard Model which solves the hierarchy problem, and the only reason we haven’t seen that there’s a relatively easy natural solution in the past is that we’re missing a whole big chunk of the low energy effective theory.

  • Mark

    marco cirelli: I’d have put it differently. The extra discrete symmetry is usually required for particle physics reasons (to avoid problems with precision electroweak tests and proton decay). The stability of the DM candidate is then there for free.

  • A

    Suppose LHC discovers supersymmetry at 1 TeV with a fine-tuning = 666. Is it natural or unnatural?

  • Alejandro Rivero

    Well, as we are addressing the hierarchy problem, my own current bet should be to cancel the fermion loops with diquark loops. If we need some extra force, technicolor or some clever trick I can not tell (but I would join #20 in asking for some techically natural extension of SM), but at least with 3 generations and no “toponium ” mesons we have cherge-by-charge the same degrees of freedom for spin 1/2 fermions than for spin 0 diquarks, so it could be the trick that the elders in the seventies were unable to know.

    In this argument it is implicit that the hierarchy problem is not about the Planck scale, but about controlling the divergences when going up to any scale, particularly the Planck’s one.

  • marco cirelli

    Mark: thanks for your remark. You’re right, I know that the extra symmetries are there for other reasons (and indeed I was careful not to say that DM is the reason why one introduces them), but I feel they are a weak point in the (wonderful) model building. I guess a better way to re-put this is: “the stability of the DM candidates is the result of extra features introduced by hand; it would be nice to look for some solution of the DM problem where these are not necessary”.

    Don’t get me wrong: I’m not discarding decades of neutralino DM investigations (I would be crazy and incredibly arrogant). I’m only saying “it would be nice”. Turns out there is a simple way to achieve this, adding one field with proper quantum number assignments.

    Also, pursuing this way we get precise predictivity on the properties of the DM candidate, essentially because we don’t have a theory as rich and complicated as the MSSM or the KK models or the LH behind. We can compute the DM mass and cross section with nuclei with very good precision, not just select a large region in a parameter space. I think this is also nice.

    But, again, my only point is that I aim to an alternative and admittedly more minimal approach to DM than the well-known BSM ones, now that colliders are telling us that maybe our BSM models are already too fine-tuned to solve the fine-tuning they were invented for, as you were mentioning in your post.

  • JoAnne

    My bet: The LHC will see a whole boatload of new physics at the TeV scale. Some of it will be mis-calculated background, some detector effects, and some real, honest-to-goodness new physics. It will be something that we have yet to imagine and will take us years to figure out what is actually going on. Some people will falsely claim that it is supersymmetry.

    Stan, just to add to Ann’s reply – yes you are correct. An object which can exist in the extra dimensions would feel a gravitational force of r^-(2+d). Because we exist in spatial dimensions larger than the extra dimensions, we feel the 4-dimensional gravitational force law of r^-2.

  • Elliot

    If I’m getting way off track, one of you knowledgeable types just tell me to be quiet but I am wondering if there is some connection between the heirarchy problem and the holographic principle in a way similar to Stan’s query.

    Let me see if I can articulate what I am asking clearly.
    If you assume that in some way gravity (gravitons), or any force carrying particle contains information, and the maximum amount of information in a volume V(d) where d is the total number of dimesions (10, 11 whatever) is limited to the number of planck areas on the surface of that volume A = some factor of V(d-1), that this would provide some form of limitation on how these particles operate in the normal 3+1 set of large dimensions and time we experience.

    Again if I am way off track here. Just say so. I won’t be offended.

  • Jim Graber

    Now that this thread has about died, I’ll put my$.02 in. I would like to focus on another case of unnatural fine tuning, i.e. cold dark matter(CDM). Despite its unquestionable successes in correctly predicting large-scale structure formation, CDM is in trouble, IMO. The fact that the MOND phenomenology works so well forces CDM into a very unnatural fine tuning, which becomes essentially untenable if MOND works for globular clusters as well as early results indicate.* This is particularly true for close-in globular clusters which show evidence of tidal stripping. The recent not yet fully published results** on milky way dwarf satellite galaxies seem to be another fine-tuning strait jacket for CDM.

    The massless neutrino was a walking zombie for almost thirty years before it fell over, how long will CDM last before it, too, falls?

    (I just looked at the program for the APS April meeting. CDM is live and well at APS with plans for several multimillion $ detectors aimed at discovering CDM; and many theory talks. ) (I see by the author list Sean will be there.)

    I once invented a CDM theory myself. It was at a banquet after one of those times Michael Turner presented his famous “moose diagram” of CDM candidates.*** I told him that the CDM was one third axions, one third neutralinos, and one third MOND. He replied “The universe may be preposterous, but it’s not ridiculous.” (I think that conference was the first time I heard the phrase “preposterous universe,” I only came across Sean’s book later.) Anyhow, I think I must now modify my ridiculous universe moose diagram to MOND 90% or more, wimps and CDM of all sorts, 10% or less.

    Unfortunately, CDM is just one more of those beautiful theories killed by ugly facts.

    So I guess I will predict or “bet” that if LHC discovers the Neutralino, or whatever other LSSP, it will prove to have a lifetime or mass unsuitable to be the CDM. Perhaps it will be highly unstable.

    Mark, maybe you should start thinking about MOND-like cosmological models





  • Count Iblis

    Jim, CDM has already been found, see here.

  • Mark

    Jim. MOND disagrees with some galaxy rotation curves. Also, MOND on its own, as a modification of Newtonian gravity, doesn’t agree with gravitational lensing from clusters. THere has been an attempt to write down a relativistic version of MOND, by Bekenstein. It remains to be seen if this makes sense when its effects on the CMB, structure formation etc. are worked out.

    Thanks for the suggestion of what direction to take my research in – I’ll throw it in the mix.

  • James Graber

    My understanding is that the MOND prblems, such as they are, are primarily with galaxy clusters. I agree that TeVeS etc. still have a long way to go. My primary point is that CDM is in trouble precisely because of the fine tuning required in the amount and location of dark matter. I was a fan of dark matter for many years, and I would still like to see strong or weak gravitational lensing evidence for a totally dark matter object, but after hoping for a long time, I no longer expect to see this.* I would love to be proven wrong. Similarly, I hope we see the neutralino, at LHC or elsewhere, and also the axion, but I now expect that the search will be much harder. This is bad news for both LHC and the big underground particle dark matter detectors, but I think the evidence is strong.

    *Or equally, a MOND scale object with little or no dark matter. I thought globular clusters were the sure winner. The contradictory evidence is what has caused me to change my mind.

    My secondary point is to compare CDM to the massless neutrino, and the local gamma ray burst hypothesis, both of which retained their favored positions among the relevant communities long after it was obvious that the neutrino had mass and that the GRBs were at cosmological distances. I expect something similar will happen with CDM both because the community has so much invested in this hypothesis, and because of the structure formation successes, which are hard to duplicate. Just as CDM must reproduce the successes of the MOND phenomenology, TeVeS or whatever must reproduce the impressive successes of CDM, while avoiding its fine tunings, if not outright failures. Otherwise, someone must come up with a convincing explanation for the very fine tuned distribution of the CDM. Now there’s a career enhancing move for a young astrophysics PhD! The career advice was primarily humor, but if I were working on something dependent on CDM, I would be worried.


  • Shantanu

    James, Mark and others, do you have any comments on the pov advocated by
    Mannheim about the dark matter/dark energy problem which is
    different from MOND/TeVes
    See for the abstract of his talk
    at PI.
    (The video of his talk is archived at Perimeter institute website
    but right now that link is down , so I can’t point to the exact url of the talk).
    However I hardly see this model discussed even in papers on alternatives to
    dark matter. But maybe this theory has some problem, which I may be missing. But to me it looks more elegant and less complicated than
    TeVES. Of course that doesn’t mean it is right.

  • Alejandro Rivero

    How is that every discussion on elementary particles evolves into cosmology? Hmm actually even the physicists themselves happen to evolve toward cosmology.

  • Mark

    Shantenu, I think this idea runs into serious problems with primordial nucleosynthesis, if we’re talking about the same idea.

  • Elliot


    Famous quote from David Schramm

    “The universe is the poor man’s particle accelerator”

    quoted on other threads here but the idea is that the only way to probe higher energy scales is by looking back towards the big bang since we cannot “build” terrestrial accelerators powerful enough to reach those scales.

    The second reason is that to unify gravity with the other forces (exhibited by elementary particles) pushes the physics towards cosmological evidence due to the inherent weakness of gravity.

  • Plato

    amen Elliot,

    ….and why high energy particle collisions are very interesting from cosmological events(GRBs?).

    That by changing perspective a bit, it still deals with reductionistic scenarios, but from a “natural” higher energy consideration. An enlightenment of sorts?


    This plate image is a powerful one for me becuase it represents something Greene understood well. His link on the right hand side of this blog is the admission of “cosmological and quantum mechanical readiness,” to tackle the cosmological frontier.

    I think Alejandro understands this well already though.

  • Alejandro Rivero

    I agree with Schramm but only in the sense that a bit of film tape makes a good fly-catcher for muons pions and whoknowsons.

    On the other hand, I have the conjecture that a lot of people starts physics (as opossed, as instance, to engineering or to mathematics) because they love astronomy, and then cosmology is an opportunity to meet this first lover.

    Plato, it could be useful to find some of the early drawings of Alvaro de Rujula when the hunt of the fundamental string did start, in the eighties. I remember a representation/caricature of some physics working “on the ground” and some others “on the sky”, kind of trying a bridge or a tunnel across the clouds. Still, someone should tell the ones in the sky the direction they should to drill towards: down.

  • Plato


    I’ll look, but I have to ask you,”Are you a Platonian, or a Aristolean?

    This should answer your question about the “philosophical adventure” in science. Some of us are really quite imaginative, aren’t we?:)After all it was Plato who gave us the Platonic forms wasn’t it? We can’t all be a Feynman.

  • Jim Graber

    Re Mannheim’s theory: Here is a link to the original 1998 McGaugh-deBlok paper where they found that MOND fit the rotation curves well, and other theories including CDM and Mannheim-Kazanas(M-K) did not.
    (I love their ArXiv comment, “This result surprised the bejeepers out of us, too.” )

    A link to a paper which criticizes MOND, (but not M-K as far as I can tell) on Nucleosynthesis grounds is

    I don’t know if Phil Mannheim has significantly changed his theory since 1998, but I think not.


    Jim Graber

  • Shantanu

    Thanks Mark, Yes I was referring to
    Thanks to you and James for the comments.
    Elliot, I think but not 100 % sure that the quote about
    “universe being is the poor man’s particle accelerator” was I think first made by Zeldovich.

  • Alejandro Rivero

    #37 AFAIK, while Theaetetus rigorised the building of the Platonic solids, it was Euclid who gave us them, in the sense he shows the proof on uniqueness. I can not imagine Plato working out the whole proof (ah, I remember to play with the proof, other student and myself, at the last row during a lecture in a winter course at Karpatz, in Silesia / Poland). Neither Plato nor Aristotle gave any of value to science, except the preservation of some concepts in the same way that inquisitors attacking heresy preserved the information about heresies themselves.

    Form my friends philosphers I have heard that the dichotomy “are you a Plato or an Aristotle?” is very common, and yep perhaps the trap is mounted in some way that it always drive you up to the sky of cosmology. So let me cry “Tertium Datur!”.

  • Plato

    all these particles may be part of the some alternate form of the same thing

    That was in 1950 and in concert with Gellman’s thinking? This statement above, was the third choice.

    As to Plato and Aristotle, we would like to think them dead, but they are “resurrected” time and time again. Whether by Hooft, or Heisenberg or maybe even Krauss, they began and then ended with…now?

    Working Euclid’s postulates and coming to the fifth, Giralamo Sachheri help to expand our thinking some. So did Grossman, in helping Einstein’s writer/mathematical block. :)

    Could we have disassociated our parents from within?

    While you may not known the exact time, you will have voiced their very words.

    Harmony within the two halves of the brain make for some interesting possibilites. While we could have said maybe that we are distinctive of one or the other together the possibilites are endless? :)

    I would have thought, tertium non datur adding the cosmological bend?

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About Mark Trodden

Mark Trodden holds the Fay R. and Eugene L. Langberg Endowed Chair in Physics and is co-director of the Center for Particle Cosmology at the University of Pennsylvania. He is a theoretical physicist working on particle physics and gravity— in particular on the roles they play in the evolution and structure of the universe. When asked for a short phrase to describe his research area, he says he is a particle cosmologist.


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