Did the Early Universe Have Just One Dimension?


From a University of Buffalo press release:

Did the early universe have just one spatial dimension? That’s the mind-boggling concept at the heart of a theory that physicist Dejan Stojkovic from the University at Buffalo and colleagues proposed in 2010. They suggested that the early universe — which exploded from a single point and was very, very small at first — was one-dimensional (like a straight line) before expanding to include two dimensions (like a plane) and then three (like the world in which we live today).

The theory, if valid, would address important problems in particle physics.

Now, in a new paper in Physical Review Letters, Stojkovic and Loyola Marymount University physicist Jonas Mureika describe a test that could prove or disprove the “vanishing dimensions” hypothesis.

Because it takes time for light and other waves to travel to Earth, telescopes peering out into space can, essentially, look back into time as they probe the universe’s outer reaches.

Gravitational waves can’t exist in one- or two-dimensional space. So Stojkovic and Mureika have reasoned that the Laser Interferometer Space Antenna (LISA), a planned international gravitational observatory, should not detect any gravitational waves emanating from the lower-dimensional epochs of the early universe.

Stojkovic, an assistant professor of physics, says the theory of evolving dimensions represents a radical shift from the way we think about the cosmos — about how our universe came to be.

The core idea is that the dimensionality of space depends on the size of the space we’re observing, with smaller spaces associated with fewer dimensions. That means that a fourth dimension will open up — if it hasn’t already — as the universe continues to expand.

The theory also suggests that space has fewer dimensions at very high energies of the kind associated with the early, post-big bang universe.

If Stojkovic and his colleagues are right, they will be helping to address fundamental problems with the standard model of particle physics, including the following:

The incompatibility between quantum mechanics and general relativity. Quantum mechanics and general relativity are mathematical frameworks that describe the physics of the universe. Quantum mechanics is good at describing the universe at very small scales, while relativity is good at describing the universe at large scales. Currently, the two theories are considered incompatible; but if the universe, at its smallest levels, had fewer dimensions, mathematical discrepancies between the two frameworks would disappear.

Physicists have observed that the expansion of the universe is speeding up, and they don’t know why. The addition of new dimensions as the universe grows would explain this acceleration. (Stojkovic says a fourth dimension may have already opened at large, cosmological scales.)

The standard model of particle physics predicts the existence of an as yet undiscovered elementary particle called the Higgs boson. For equations in the standard model to accurately describe the observed physics of the real world, however, researchers must artificially adjust the mass of the Higgs boson for interactions between particles that take place at high energies. If space has fewer dimensions at high energies, the need for this kind of “tuning” disappears.

“What we’re proposing here is a shift in paradigm,” Stojkovic said. “Physicists have struggled with the same problems for 10, 20, 30 years, and straight-forward extensions of the existing ideas are unlikely to solve them.”

“We have to take into account the possibility that something is systematically wrong with our ideas,” he continued. “We need something radical and new, and this is something radical and new.”

Because the planned deployment of LISA is still years away, it may be a long time before Stojkovic and his colleagues are able to test their ideas this way.

However, some experimental evidence already points to the possible existence of lower-dimensional space.

Specifically, scientists have observed that the main energy flux of cosmic ray particles with energies exceeding 1 teraelectron volt — the kind of high energy associated with the very early universe — are aligned along a two-dimensional plane.

If high energies do correspond with lower-dimensional space, as the “vanishing dimensions” theory proposes, researchers working with the Large Hadron Collider particle accelerator in Europe should see planar scattering at such energies.

Stojkovic says the observation of such events would be “a very exciting, independent test of our proposed ideas.”

Sources: EurekAlert, Physical Review Letters.

28 Replies to “Did the Early Universe Have Just One Dimension?”

  1. A very interesting concept.

    Who say 3 spatial and 1 temporal dimensions is how we started or how we will end, more dimensions for the people 🙂

    but well if you follow string theory there is like 11-26 dimensions and i have no idea what they all do but the 4 dimensions i am aware off i love.

    very mind boggling to comprehend but fairly logical in a way.

  2. There is a fifth dimension, beyond that which is known to man. It is a dimension as vast as space and as timeless as infinity. It is the middle ground between light and shadow, between science and superstition, and it lies between the pit of man’s fears and the summit of his knowledge. This is the dimension of imagination. It is an area which we call The Twilight Zone.

  3. Another ridiculous idea, I think a lot of the time Physicists just need something to do/think about in order to justify grants etc. This will undoubtably come to nothing.

    He talks about the need to stop extensions upon extensions of ideas and this is exactly what this nonsense is.

    1. @lazyfruit

      So… if what you say is correct than what basic idea or principle is this an extension to an extension of –anyway? Additive extensions aside, is what this article tells you; what you are saying? In other words are you reading the same article as we are, cause it seems like you might be thinking of something other than what is written here. Maybe you are conflating this article with your own views, those views which cause you to capitalize Physicists, for example. If this is not a conflation and you estimation of it “…. undoubtably [sic] come to nothing.” may undoubtedly be mistaken for an incorrect viewpoint.

      As to the need to justify the granting of time and money to an idea, do you think we should just give anyone who asks for funding what they ask for with no strings, no qualitative inquire to lock down what they plan to do with it, much less what they expect to discover. I hope you do not mean that, because I see a short future for that account.

      Now, on the other hand…

      How many of the basic concepts have been discovered as a result of the granting of funds throughout the ages vs someone piddling with what they already have to hand.

      How many of the greatest discoveries can lay claim to “…was found with a government grant” [substitution of your favorite for the term government is allowed]. How many are able to say, “I found this here idea while I was in the factory and I can’t wait to take it home to the lab funded by the rich guys.”

      Most discoveries have this 10% in common — “gee, that’s odd.” Taking it the further step is the other percentage of science, the 90%, perspiration. You want they should pay for that themselves?

      You work with what you have is what this article said, and sometimes you need to think outside the box it adds. There is nothing ridiculous about that in my view.

      These suggestions are made toward a better understanding of our beginnings, our origins, and they speak to a future which contains greater depth and vaster scope than any we may currently obtain.

      “It is not what you think,” says the wizard of OZ, “it is how well you think with what you have that makes you greater than you were.”

      Mike C

      1. 10’ll get you 100, all they read was the headline and formed their entire hypothesis based on that. (as they sounded as though they are someone that neither likes nor understands science in general, I doubt they even WANTED to know what the idea was about, let alone would be able to understand [or even want to] what is being described)

  4. What is a ‘dimension’ here? Not that they need to be plausible, but…

    Isn’t it a way too premature to give a deliberately false impression about the status of this idea? It is very much not like they have formulated a testable hypothesis, let alone formulated any internally consistent theory with sound mathematical structure?

    Have these ‘dimensions’ something to do with ‘degrees of freedom’, in a way how the concept is being used in statistical analysis? Meaning that underlying ‘idea'(?) might not be ‘physical’ at all? Of course, it is impossible to tell what they are really after based on press releases alone, but is there any additional info what could be said about the idea using layman terms?

    Or has this something to do with ‘available paths’ in a ‘much idealized’ physical system?

    1. I agree with your assessment here, Viljuri, we need more to chew on before we spit the fat into the fire, therein a light blossoms from our efforts.

      It might be the latter idea you toss out there, it might be ‘degrees of freedom’ or even something enticingly ‘new’.

      Mike C

    2. The article states that they DID form a testable hypothesis and are waiting for LISA to launch in order to test it, no?

  5. You are correct on there being no gravity waves in dimensions 3 = 2 + 1 spacetime or less. Gravity waves are Weyl curvatures without direct sources, and the Weyl curvature is zero in dimensions less than 4. I review some things which suggest that the degrees of freedom for quantum gravity are one dimensional. This seems to be a growing realization on a number of fronts.

    Jacob Bekenstein and Avraham May demonstrated how black holes are one dimensional channels of quantum information back in 2001. Ashoke Sen demonstrated something similar to this. An anti-de Sitter (AdS) spacetime of dimension n is equivalent to a conformal field theory of dimension n-1. The isometries of the AdS spacetime are equivalent to the conformal symmetries of a conformal field theory (CFT) on the boundary. The near horizon condition for a black hole in an AdS spacetime is AdS_2xS^{n-2}, where S^{n-2} is a sphere or dimension n – 2. The AdS_2 is a hyperbolic spacetime with a structure similar to the Escher prints of tessellated disks called circle limits. The boundary of this spacetime is CFT_1, in one dimension, where the isometries of this space are the group of conformal quantum mechanics. The group is the set of diffeomorphisms of the circle (which bounds the AdS_2 disk) and this defines the set of bosonic string states. The AdS_2 is then equivalent to a circle group on CFT_1 ~ S^1xS^0 (where this is a generalization of CFT_n ~ S^1xR^{n-1}) and the S^0 defines two points. These two points turn out to be dual states for the Hartle-Hawking vacuum (HHV). The HHV comes from their seminal paper in 1984 on the wave function of the universe.

    The next interesting direction is that Borsten, Duff, Marrani, and Rubens published a paper which illustrates a mathematical correspondence between entanglements in 3 and 4 qubit quantum systems with BPS and extremal black holes respectively. To illustrate this it requires one work in the STU system with radial symmetry. In that case all the Killing isometries of the theory are timelike, and they are defined in one dimension of a moduli space. I have submitted for review a paper which connects this with the AdS theory above with AdS_2 ~ CFT_1, and a coset structure on the AdS constructs the counting of possible microstates on a black hole event horizon. This is a physical partition function, but it is equivalent to a partition function of the integers. This has been one of those unsolved problems in mathematics, which Brunier, Folsom, Kent, and Ono proved in January. This is the mathematics for counting up quantum states on a black hole, or equivalently on the boundary of an AdS spacetime. I have been working up a variant of the proof by Brunier, Folsom, Kent, and Ono, but where the partition function is derived by compactification condition with respect to the correspondence between multi-partite entanglements BPS/extremal black holes.

    Lots of stuff has been going on in just the last 3 months — it is amazing! So what does all of this mean? There is a lot of mathematics here, and it might connect up with the results written up here. The foundations of the universe are a one dimensional space, where the diffeomorphisms of that circle constructs an infinite algebra used in string theory. So these states can have gravitons, but they define the vacuum state for gravitons. All of this physical content in one dimension sits in a space of 27 dimension, which is reduced to 26 by a constraint. This 26 dimensional space is the bosonic string space, and it decomposes into 10+16 dimension for 10 spacetime dimensions and SO(32) theory. The SO(32) comes from the fact one can decompose 26 dimensions in a dual fashion. So in this “void” there is a 1-dim space for the HHV with two physical vacuum states, and where the off shell condition on the vacuum is within the other 25 dimensions.

    The paper by Mureika and Stojkovic appears to work with the idea this state of affairs exists at the TeV range of energy. To be honest I doubt spacetime reduces its dimension in quite that manner. It might be there is the start of a renormalization group of a running parameter which adjusts gravity into such a behavior as energy is scaled upwards in a conformal system above 1TeV. The theory here by Mureika and Stojkovic assumes some sort of entropy at a transition temperature T_* that is commoving with the de Sitter spacetime expansion. It is interest for me to ponder how this might connect up with the CFT_1 vacuum space and the HHV.


    1. @LC

      Chiming in here since you brought up Escher Circle Limits:

      I loved the paper by Melissa Potter and Jason M. Ribando in 2003/4. So much history and so much practicably demonstration within that paper. Of course it is not the math part they dwell upon but the physical construction of these non-Euclidean figures of Escher, this is almost as fascinating as a snake and bird dance.

      Isometries, Tessellations and Escher, Oh My! found at

      Mike C

      1. Hyperbolic tessellations are examples of a modular group, or a discrete subset of a group with modular structure. Modular forms play an absolutely key role in what I am working on. These tessellations are discrete modular forms, and in general for these there exists four number a, b, c, d such that for any x in one of the tessellation cells it is mapped to x’ in another cell by

        x’ = (ax + b)/(cx + d).

        In the case that a = d = 0 this is a form of the S-duality in string theory.

        Here is the interesting puzzle. The hyperbolic disk is tessellated by arcs that are the geodesic (extremal paths) of a “particle.” Now in the Lorentzian case this disk is a spacetime, and the angular direction is a “time.” Particles flow from the boundary and back to the boundary. This space has negative Gaussian curvature, which means the particle flies away from the boundary at maximal speed (speed of light) and ultimately returns there with zero velocity. The boundary is sort of the inverse of a black hole horizon, where if you watched a clock closer to the boundary it would speed up until it registers near infinite time near the boundary. The boundary is a sort of “repeller.” It is for this reason we like to put black holes in AdS spacetimes. It is the perfect theoretical box to hold a black hole. Now all of those geodesics in that tessellation get deformed by the black hole curvature. The quantum information on the horizon of the black hole is equivalent to the quantum information on the boundary of the AdS. Is this fact contained in the deformed tessellation as a quasicrystal? For a black hole that is large enough, the quantum information is a partition function quantum bits on its horizon, which holographically is equivalent to the qubits in the tessellation volumes. This for various reasons, but no proof, should be a quasicrystal.

        The following essay might prove interesting along these lines:


        Ken Ono quotes from it and cites this as a motivating essay for his insight into the proof of the integer partition function.


    2. @LC

      I am sure you have a few thoughts on the possibility of gravimetric variations in gravity waves (when we find them that is) and some shifting around of those variations based on distance from detector to the origination area, i.e., longer distances cause greater or lesser depth to the wave or closer spacing in the wave (just to place this into terms understandable and familiar to us all).

      Although we have no current power value or frequency shift for the gravitation wave or detected fields these might well exist in the measured data we would chart (when we actually get some values to chart that is). What might those values constitute? This is of course sheerest speculation on anyone’s part. But please, speculate anyway.

      Might there be some material which, like a prism does to light waves, splits any components which are intrinsic parts of the gravity wave into a spectrum of sorts. We have no such material at present of course but what would this material be composed from, what comes to mind for you.

      Would we have comparable units as in the EMT or might they be more often comparable within the QMT — might they be totally different in fact, and for us, unmeasurable and inexpressible, in any terms shy of hyper dimensional mathematical theories.

      “I had wandered for many years on the plane of reason till reason departed and speculation became my companion.” anonymous Italian alchemist lab wretch circa 1450 CE (translation not quoted but remembered, maybe poorly)

      Mike C

      1. @Mike: Gravity waves do not have dispersion like electromagnetic waves do. Any form of matter they encounter is equivalent, no matter its composition.


  6. Am i right to understand that this theory suggests that the observed increasing expansion rate is actually an optical illusion stemming from the projection of the large scale 4 dimension space on our familiar 3 dimensions?


  7. @JJ: In a word, no. Perhaps you should (re)read the article which clearly posits that the rapid expansion of the universe may be explained by the addition of new dimensions, and hypothesize that a fourth dimension may already exist at large cosmological scales. Even with my limited exposure to physics I was able to extract this much in the way of an explanation. Optical illusions play no part in the matter.

  8. Though the subject matter is a bit beyond my ken, the (short) paper by Mureika and Stojkovic was an interesting read: http://arxiv.org/PS_cache/arxiv/pdf/1102/1102.3434v2.pdf

    However, a paper critical of this work has been posted: (http)://arxiv.org/PS_cache/arxiv/pdf/1104/1104.1223v1.pdf

    From the paper:

    “It has been recently claimed that quantum gravity models where the number of dimensions reduces at the ultraviolet exhibit a potentially observable cutoff in the primordial gravitational wave spectrum, and that this is a “generic” and “robust” test for such models, since “(2+1)-dimensional spacetimes have no gravitational degrees of freedom”. We argue that such a claim is misleading.”

    Are they on to something?

  9. I join to the skeptics. Without yet having read the critical paper (thanks, Jon!) I’ll jot down some weaknesses in some haste:

    – This is a quantum gravity paper with all its weaknesses:

    — Quantum gravity is assumed to resolve both gravity and standard model. That isn’t the simplest assumption. (Though I admit to using entropy to embed the outstanding point is a good trick!)

    — QG has adopted a funny set of standards of physics which “are not”, for example claiming that absence of a minimum energy level or dynamics (making simple harmonic oscillators for start) are acceptable when they aren’t.

    Here they throw in the as I understand it erroneous claim, as also QG causal dynamical triangulations and causal set theory adopts, that random distribution of geometry in the light-cone of special relativity avoids violation of Lorentz invariance.

    It does not, and I think LBC wrote something on that long ago which I may take time to find later. If not I think I described that, while I was up to speed on it, somewhere.

    – I took one of those papers they claim support “planar events in cosmic ray experiments”; it does not, it presents _a negative_ result unless I’m mistaken!

    “Geometric structures in hadronic shower cores at ob-
    servation level are particularly interesting, as one expects
    QCD jet production to lead to secondary hadrons being
    naturally aligned to form line shape patterns [7]. Similar
    alignment structures might result from exotic hadron
    production processes [8].”

    “The measured 4 distribution and the fraction of aligned
    events of high-energy hadrons are well reproduced by the
    simulations. Moreover, the data follow the expectations
    from randomly distributed hadron azimuth angles. No
    significant dependence on the primary energy was observed.
    Within the statistical uncertainty, no correlation
    between 4 and hadronic interaction features such as jet
    production was found.

    These results are not necessarily in contradiction to
    possible alignment excesses in other shower observables,
    at different observation levels, or in a different primary
    energy range. However, the absence of an alignment excess
    in the present analysis might be used to constrain
    attempted alignment explanations.”

    – A fourth large scale dimension must be interpreted in the cosmological sense that they are discussing. However it is well known that the reason we observe only 3 large scale dimensions is because otherwise there would be no cellular observers. 4 spacetime dimensioned systems have all kind of problems.

    Specifically EM theory doesn’t work [Wikipedia] – so how come they claim that we should be able to see photons from such volumes? (Probing Airy rings to see effects.)

    – They assume expansion from a small volume. That isn’t a safe assumption in the standard cosmology, and again not the simplest in such a cosmology.

    1. Well, haste: “4 spacetime dimensioned systems” should be “4 large scale dimensions” (for space).

    2. Aspects of this theory can’t be accepted. In particular the idea that spatial dimensions emerge with time is highly problematic. As you point out there are problems with electromagnetism and in fact with gauge theories in general. There is the field tensor in spacetime F_{ab} = &_bA_a – &_aA_b (& = partial derivative and A_a the 4-dim vector potential). This rank 2 tensor in four dimensional space or spacetime is such that there is a self-duality. The electric fields are E_i = F_{0i}, 0 = time index and i = spatial index, and the magnetic fields are determined by the spatial bi-vector forms B_i = F_{jk}, for i perpendicular to the directions j and k. For instance B_1 = F_{23}. The self-duality means that F_{01} is dual to F_{23}, and F_{02} is dual to F_{31} and so forth, which in a sourceless region is equivalent to the duality in the Maxwell equations. There are some very deep mathematical physics results due to this. If spacetime was at an earlier epoch two space dimensions plus one time this structure is lost. In particular equations such as curl A = B involves a duality between the bivector curl A and a vector B, but B must point in the time direction in 2 + 1 spacetime.

      It is of course interesting to ponder whether quantum information exists on low dimensions, where these qubits are projected to high dimensions by entanglement and holography. This reduces the number of degrees of freedom. In one sense this is why string theory is mathematically so successful. Why spacetime is four dimensional and the other 10 and 11 dimensions in supergravity are compactified involves some deep issues with the bases from which symmetries can be consistently assigned. That is a bit beyond the scope of a UT post. However, if this paper were correct it would imply that compactified dimensions are reduced and uncompactified dimensions would increase with time. However, this does lots of damage to the structure of Yang-Mills gauge theory.


  10. Q: What is the meaning an origin of the zeroth dimension, here?
    Does it have any real meaning if it somehow it manifests one dimension (then onto multiple ones)?

    1. I am just waiting for the EU dimensions and Plasma Dimensions, they are bound to come at one point or another :).

  11. Avid Reader, never posted before
    Just had to express my feelings after reading these comments…

    Gosh there are some smart people on this site…

  12. To the SYSTEM GALAXIES Big Bang is SERIOUSLY WRONG SCIENCE. They talk in terms of Star Plasma and moving it about within their System Galaxies safely.
    Big Bang and evolution as sciences are used,with certain other locks as a POWER LOCK OUT.
    Text cut and withheld.

  13. maybe we still ARE in a 1 dimensional dimension and our 1d brains fool us in thinking that there are 3 dimentions out there but in fact we are trapped, trapped in a very tiny 1d box….ahhhhhhh

  14. The article states that smaller spaces are associated with fewer dimensions. What does that mean at the Planck Scale?

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