Saturday, April 10, 2021

Does the Universe have Higher Dimensions? Part 1

[This is a transcript of the video embedded below.]

Space, the way we experience it, has three dimensions. Left-right, forward backward, and up-down. But why three? Why not 7? Or 26? The answer is: No one knows. But if no one knows why space has three dimensions, could it be that it actually has more? Just that we haven’t noticed for some reason? That’s what we will talk about today.

The idea that space has more than three dimensions may sound entirely nuts, but it’s a question that physicists have seriously studied for more than a century. And since there’s quite a bit to say about it, this video will have two parts. In this part we will talk about the origins of the idea of extra dimensions, Kaluza-Klein theory and all that. And in the next part, we will talk about more recent work on it, string theory and black holes at the Large Hadron Collider and so on.

Let us start with recalling how we describe space and objects in it. In two dimensions, we can put a grid on a plane, and then each point is a pair of numbers that says how far away from zero you have to go in the horizontal and vertical direction to reach that point. The arrow pointing to that point is called a “vector”.

This construction is not specific to two dimensions. You can add a third direction, and do exactly the same thing. And why stop there? You can no longer *draw a grid for four dimensions of space, but you can certainly write down the vectors. They’re just a row of four numbers. Indeed, you can construct vector spaces in any number of dimensions, even in infinitely many dimensions.

And once you have vectors in these higher dimensions, you can do geometry with them, like constructing higher dimensional planes, or cubes, and calculating volumes, or the shapes of curves, and so on. And while we cannot directly draw these higher dimensional objects, we can draw their projections into lower dimensions. This for example is the projection of a four-dimensional cube into two dimensions.

Now, it might seem entirely obvious today that you can do geometry in any number of dimensions, but it’s actually a fairly recent development. It wasn’t until eighteen forty-three, that the British mathematician Arthur Cayley wrote about the “Analytical Geometry of (n) Dimensions” where n could be any positive integer. Higher Dimensional Geometry sounds innocent, but it was a big step towards abstract mathematical thinking. It marked the beginning of what is now called “pure mathematics”, that is mathematics pursued for its own sake, and not necessarily because it has an application.

However, abstract mathematical concepts often turn out to be useful for physics. And these higher dimensional geometries came in really handy for physicists because in physics, we usually do not only deal with things that sit in particular places, but with things that also move in particular directions. If you have a particle, for example, then to describe what it does you need both a position and a momentum, where the momentum tells you the direction into which the particle moves. So, actually each particle is described by a vector in a six dimensional space, with three entries for the position and three entries for the momentum. This six-dimensional space is called phase-space.

By dealing with phase-spaces, physicists became quite used to dealing with higher dimensional geometries. And, naturally, they began to wonder if not the *actual space that we live in could have more dimensions. This idea was first pursued by the Finnish physicist Gunnar Nordström, who, in 1914, tried to use a 4th dimension of space to describe gravity. It didn’t work though. The person to figure out how gravity works was Albert Einstein.

Yes, that guy again. Einstein taught us that gravity does not need an additional dimension of space. Three dimensions of space will do, it’s just that you have to add one dimension of time, and allow all these dimensions to be curved.

But then, if you don’t need extra dimensions for gravity, maybe you can use them for something else.

Theodor Kaluza certainly thought so. In 1921, Kaluza wrote a paper in which he tried to use a fourth dimension of space to describe the electromagnetic force in a very similar way to how Einstein described gravity. But Kaluza used an infinitely large additional dimension and did not really explain why we don’t normally get lost in it.

This problem was solved few years later by Oskar Klein, who assumed that the 4th dimension of space has to be rolled up to a small radius, so you can’t get lost in it. You just wouldn’t notice if you stepped into it, it’s too small. This idea that electromagnetism is caused by a curled-up 4th dimension of space is now called Kaluza-Klein theory.

I have always found it amazing that this works. You take an additional dimension of space, roll it up, and out comes gravity together with electromagnetism. You can explain both forces entirely geometrically. It is probably because of this that Einstein in his later years became convinced that geometry is the key to a unified theory for the foundations of physics. But at least so far, that idea has not worked out.

Does Kaluza-Klein theory make predictions? Yes, it does. All the electromagnetic fields which go into this 4th dimension have to be periodic so they fit onto the curled-up dimension. In the simplest case, the fields just don’t change when you go into the extra dimension. And that reproduces the normal electromagnetism. But you can also have fields which oscillate once as you go around, then twice, and so on. These are called higher harmonics, like you have in music. So, Kaluza Klein theory makes a prediction which is that all these higher harmonics should also exist.

Why haven’t we seen them? Because you need energy to make this extra dimension wiggle. And the more it wiggles, that is, the higher the harmonics, the more energy you need. Just how much energy? Well, that depends on the radius of the extra dimension. The smaller the radius, the smaller the wavelength, and the higher the frequency. So a smaller radius means you need higher energy to find out if the extra dimension is there. Just how small the radius is, the theory does not tell you, so we don’t know what energy is necessary to probe it. But the short summary is that we have never seen one of these higher harmonics, so the radius must be very small.

Oskar Klein himself, btw was really modest about his theory. He wrote in 1926:
"Ob hinter diesen Andeutungen von Möglichkeiten etwas Wirkliches besteht, muss natürlich die Zukunft entscheiden."

("Whether these indications of possibilities are built on reality has of course to be decided by the future.")

But we don’t actually use Kaluza-Klein theory instead of electromagnetism, and why is that? It’s because Kaluza-Klein theory has some serious problems.

The first problem is that while the geometry of the additional dimension correctly gives you electric and magnetic fields, it does not give you charged particles, like electrons. You still have to put those in. The second problem is that the radius of the extra dimension is not stable. If you perturb it, it can begin to increase, and that can have observable consequences which we have not seen. The third problem is that the theory is not quantized, and no one has figured out how to quantize geometry without running into problems. You can however quantize plain old electromagnetism without problems.

We also know today of course that the electromagnetic force actually combines with the weak nuclear force to what is called the electroweak force. That, interestingly enough, turns out to not be a problem for Kaluza-Klein theory. Indeed, it was shown in the 1960s by Ryszard Kerner, that one can do Kaluza-Klein theory not only for electromagnetism, but for any similar force, including the strong and weak nuclear force. You just need to add a few more dimensions.

How many? For the weak nuclear force, you need two more, and for the strong nuclear force another four. So in total, we now have one dimension of time, 3 for gravity, one for electromagnetism, 2 for the weak nuclear force and 4 for the strong nuclear force, which adds up to a total of 11.

In 1981, Edward Witten noticed that 11 happened to be the same number of dimensions which is the maximum for supergravity. What happened after this is what we’ll talk about next week.


  1. Describing a phenomenon with mathematical spaces doesn’t mean that those spaces are physical spaces. All variables can be expressed as dimensions in an abstract mathematical space to solve various problems. It is the case not only in physical sciences but also in social sciences. I don’t see why being able to add dimensions to get electricity and magnetism would make them dimensions of the physical space.

    1. I didn't say anything about "physical spaces" and don't know what you mean by that. Of course any system has a configuration space.

    2. Paps57,

      Well, then my reply goes to you too. Why you want to agree with a statement after I just explained that it makes no sense is beyond me, but that's my life: having to cope with people who refuse to take answers from me.

    3. Sabine, the physical space I referred to is the same as the space you mentioned in the following: " they began to wonder if not the *actual space that we live in could have more dimensions". I wanted to emphasize a clear distinction between the *actual space that we live in and the mathematical space composed of geometrical dimensions that, I agree, can also accurately represent the interactions between particles of our universe.

    4. One of the theories is that in one of you past lives you were a ruthless Mongol Khan and squashed way too many skulls in your raids. So that now you have to listen to all those voices to process karma.

    5. Paps57,

      It's not my "opinion" that I didn't say anything about "physical spaces", it's a fact.

    6. Bertrand,

      Just because you believe there is a clear distinction doesn't mean there is one.

    7. Well, I have no idea about higher-dimensional physics but maybe an analogy helps. We often describe electromagnetic fields with complex numbers not because we think that imaginary fields exist but because it's much easier to do it that way than by mucking about with trigonometric functions.

      Likewise it may well be that a theory describes some effect perfectly when you do your calculations with 11-dimensional vectors but that doesn't prove that eight rolled-up dimensions actually exist. You need some other way to prove (or disprove) that.

      NB, I have no idea how to think of rolled-up dimensions or the corresponding vector space. Like, at all. Perhaps somebody could explain in simple terms what a space with two normal and one rolled-up dimension would look like?

    8. @smurfix: a good example is a water hose. Seen from a distance, it looks like a 1D object. But if you get closer, you see that there are actually 2 more dimensions curled up at the scale of the hose diameter. If the diameter were much smaller, say 1 micron, you'd never notice that the other two dimensions even exist.

    9. @Sabine, Bertrand, Paps57: perhaps the misunderstanding with Bertrand comes from your phase space example. The phase that the phase space is 6D is indeed a mathematical artifact of Hamiltonian theory. Newtonian mechanics is 3D and so is its Lagrangian version. Hamiltonian mechanics takes the positions and momenta to be independent variables, and thus invents a 6D "phase space". This is very useful of course, but only as a mathematical trick. It is fundamentally different from the 10 spatial dimensions that you discuss in the erst of this post.
      PS: "phase space" requires no hyphen

    10. Why is phase space a "mathematical artifact"? It has a sympletic structure, alright, but that doesn't make it an artifact. And in any case, I am not talking about phase spaces in my video. So, yes, if that was the confusion Bertrand and Paps57 had, thanks for sorting it out.

    11. @Paps57, smurfix

      Hi, I was imagining the rolled-up dimensions as something like cannelloni pasta but that doesn't help anyone.
      I've looked up many physics and geometrical objects online and there might be some nice pictures but usually everything is equasions and mathematics, and lots of terms I also need to look up, then look up the terms to describe those terms, then at the end of that I have a vague idea and the fervent wish I'd started studying physics last decade.
      I think the short answer is, 'it probably looks like math'.

      @opamanfred Thanks for that analogy.

    12. @Vadim
      I envision Dr. H as also having been a warrior-mystic fighting the ravaging hordes to preserve sacred knowledge. These days, it's fighting with science and logic instead of shield and sword.
      The men in her head talking are all those physicists going on about String Theory, MWI, etc instead of hallucinations from fungus-contaminated bread. :)

  2. I've long thought that pure mathematics might turn out to be mostly practical after all, in some way or other. I can't say if that statement is at all accurate, of course.

    1. Maths, in this case multiple dimensions can be considered in simplest way as "just" a tool to help solve problems.If that end is achieved, then is that not enough? Why must the math (or physics for that matter) be physical to be useful? But it must be potentially useful on human scale of space/time.
      Maybe the issue arises as an unstated and not quite explicit pushback against excessive science/math promotion (budgets).
      Multi dimensional view of material properties does not disturb anyone.

    2. Hi Morris,
      I mean, things that seem like pure mathematical or topological invention may well turn out to have a physical counterpart in some process or phenomenon, or to be useful for practical purposes originally not realised. I don't mean that pure math is a bunch of puzzle pieces that need to be fitted in place.

      I absolutely agree that concepts such as extra dimensions are useful tools in any case, bar when they're done to death with no practical results.

      Anyone who complains about funding these is yet to understand how developing concepts brings real-world advantages, similar to objecting to having a budget for NASA fails to take into account technological advances they make that are useful on Earth.

      This field is fascinating. (One of my favourite such things is the tesseract but we can only approximate them physically.)

    3. I think that the funding question is not as simple as you present.A more objective view is one of prioritizing effort given the limit of (public) resources. So does SETI or multiverses even appear on a list of worthwhile pursuit on a relative basis? I think I am rational in asking who pays and who benefits and should there be reasonable correlation.
      Consider that much of the discussion in whatever field is self promotion.

    4. I did over-simplify the funding question. I agree with you on that correlation.
      I would say that multiverse studies shouldn't get funding and SETI is questionable at best.
      I'm only familiar with what is reported via YouTube channels and mainstream media, for the most part. Self- promotion seems to involve making things as 'whizz-bang' as possible, not how useful.

  3. The unstable nature of the Kaluza-Klein compactified region is solved by making them Ricci flat. This is a basis of Calabi-Yau theory. This Ricci flatness means the Hamilton equation ∂g_{ij}/∂t = -2R_{ij} is zero and the metric is static. In string and M-theory this means wrapped strings or D-branes do not uncontrollably grow in size. Of course curvature is defined for dimensions 2 and larger, so this does not help with the one dimensional circle.

    String and M-theory probably have no direct bearing on the universe we observe. Even the lack of proton decay suggests that SU(3)×SU(2)×U(1), may hold all the way to the quantum gravitation or Planck scale. If so, there are no GUTs. However, I would not commit the GUT, Kaluza-Klein, string theory books in your library to the fire, or used book sale counter, just yet. There may turn out to be a role for all of this, Kaluza-Klein, strings etc, in spite of this.

    One thing I found interesting is how with the Levi-Civita or Christoffel connection coefficients Γ^a_{bc} defined with terms ∂^ag_{bc} that by imposing the condition that for a = 5, the additional dimension, that ∂^5g_{ab} = 0 one gets ∂^a_{5c} - ∂^b_{5b} and this is formally the same as the definition of the gauge field F_{bc}. This is the covariant electromagnetic field that shares the same level with the non-covariant gauge-like potentials of gravitation, In a non-metric form of relativity this can be “fixed,” where Yang-Mills fields emerge on the same level as covariant curvatures.

  4. It is a bit of mathematics, but the bosonic string as a topological continuation that eliminates redundancies and this computes out to be 26 dimensions. Then if the bosonic string is supersymmetrized this reduces to 10 or 11 dimensions.

  5. [1 of 3 on 2021-04-10]

    “… it was shown in the 1960s by Ryszard Kerner, that one can do Kaluza-Klein theory … for any similar force … [by adding] a few more dimensions. For weak … two … [for] strong … four.”

    Slow, neuron-based human brains necessarily and unavoidably navigate reality using hierarchies of assumptions. These assumptions range from fish-in-the-water level assumptions that are so deep and implicit that it can be tough even to perceive their existence to such fleeting assumptions as to which cup the ball is under in the cup and ball game. These assumption hierarchies enable the rapid elimination of otherwise insurmountably large numbers of alternative interpretations that would overload our cognitive capacities.

    In most situations, a well-adapted, reality-based assumption hierarchy is a remarkably efficient way to process information. Most of us (thankfully) do not worry overly about being unwitting players in The Truman Show, not because such a situation is completely impossible, but because our cognitive assumption hierarchy tells us the possibility is so remote that it’s not worth wasting time on.

    One of the hallmarks of human-type intelligence is that our assumption hierarchies are dynamic and can change over time. Unfortunately, changing such hierarchies is a tricky business indeed since each change leads to a new interpretation of reality. By simple combinatorics, most such changes, especially at the base levels of the hierarchy, lead inevitably to insanity, the inability to make future reality estimates that match what unfolds in the real world. Notice that analyzing the past is just part of improving the future estimation since the only estimation paths open to us reside in the future. From a cognitive data structures perspective, the entire concept of a “past” is simply part of how we achieve better estimates of the future. As historian David Christian has noted with remarkable crispness and insight, only a relatively narrow middle space of conceivable universes possess a sufficiently rich balance of structure and change to enable a richly diverse and exciting future. Outside of such just-right universes, the concept of “past” quickly diminishes in value for understanding and estimating the future.

    Creating accurately predictive dynamic assumption hierarchy is far more of an art than a science. Those who are exceptionally good at applying it to the costly and psychologically deeply unsettling deeper levels of an assumption hierarchy are called geniuses. Einstein did it twice. The first time was in his miracle year of 1905, in which by his statements, the 1700s views of philosopher David Hume powerfully impacted his willingness to revise deep assumptions about the absoluteness of space and time. Einstein did it again a decade later with General Relativity, in which he made even more radical revisions based on the profoundly geometric and decidedly non-Hume insights of his former instructor, Hermann Minkowski.

    One of the deeper assumptions of current theoretical physics is reductionism in terms of particles. While there was some sincerely motivated and data-driven questioning of this assumption back during the pre-quark “particle zoo” period of the late 1960s, the remarkable success of quark theory and the Standard Model solidly erased any concerns on this point. For good reasons, the assumption that the number of particles grows smaller as you move deeper remains a profound component of physics’ deeper assumption hierarchy levels.

    Regarding dimensions, this kind of reductionism (let’s call it dimensional reductionism) is, alas, far less prevalent.

    The emergence of a dimensional zoo is a genuine risk in the absence of the assumption that new dimensions are costly, uncommon, and avoided if possible. In the comment after this, I give one highly unexpected (for me at least) example of how dimensional reductionism might be relevant to Kaluza-Klein theories.

  6. [2 of 3 on 2021-04-10]

    The simplest definition of dimensional reductionism assumes one should always use the lowest number of dimensions possible to represent a given situation. For example, restricting a physics model to six-dimensional phase space — holographic phase space — rather than exploding it exponentially with every particle added is a straightforward example of using dimensional reductionism.

    A deeper level of dimensional reductionism requires transforming the definition of a dimension. Emergent dimensionality (my phrase; I’m not sure if there is an exact literature phrase for it), for example, is the idea that dimensions are nothing more than mathematical relationships between absolutely conserved mass-energy units. Taking that idea seriously further implies far from being absolute, dimensions are both malleable and finite in precision. Such thinking was instrumental in the emergence of S-matrix theory, in which notable figures including Heisenberg and Wheeler asserted that the concepts of space and time largely fell apart below the scale of nucleons. Quark theory and asymptotic freedom annihilated the S-matrix assumption hierarchy, but similar thinking later unexpectedly reemerged at the Planck scale in the form of quantum gravity and string theory.

    Dimensional reductionism gets particularly interesting when it includes the idea that there are relationships between dimensions in the emergence process. Along those lines, Mark Transtrum (BYU) and his team developed one approach to interrelational dimensional reductionism that certainly surprised me.

    Transtrum noticed from modeling data in both biology and physics that the hypergeometric concept of hyperribbons (his term) helps explain why so many types of data in models collapse with unexpected ease, provided only that one allows some minor noise or “sloppiness” along certain degrees of dimensional freedom. A ribbon is very short in its first dimension (thickness), much longer in the next one (width), and again much longer in the next one (length). Transtrum hyperribbons generalize this exponentially-increasing-width concept to four or more dimensions.

    The hyperribbon idea is relevant to Kaluza-Klein models — blame me for this assertion, not Transtrum — due to what happens after applying dimensional reductionism as viciously as possible to the Standard Model. The most data-efficient dimensional model for representing the experimentally observed spectrum of electric, weak, and strong charges fermions in the Standard Model is not the 1+2+4=7 dimensions of an extended Kaluza-Klein model, but 3. This 3-space has units matching those of the total charges of the three red-green-blue down quarks, with each color charge, each merged with -⅓ of electric charge to create three mutually orthogonal “chromoelectric” axes.

    To the best of my knowledge, Glashow was the first to notice this quirky data reduction in a throw-away side comment he made back in 1980 on how to remember the charges of neutrinos, down quarks, up quarks, and electrons. Glashow’s mnemonic cube only works if one cannot separate color charge from fractional electric charge. However, since all experimental data indicates just that, the Glashow mnemonic cube works.

  7. [3 of 3 on 2021-04-10]

    In a dual holographic universe model with dimensional reduction, the resulting charge relationships form a hyperribbon correlated to the distribution of the forces in spacetime. Neutrinos with weak-only interactions form the first and shortest dimension of this force-range ribbon. Quarks with chromoelectric charges form the ribbon’s second nucleon-scale force range, although to be precise, that is a two-step range in which down quark charges are fundamental and up quarks charges are composite. Finally, electrons with “pure” (actually 3-part composite) electric charge form the final and infinite-scale force range.

    After only recently encountering Transtrom’s work, I was genuinely astonished to see what appears to be a hyperribbon lurking in the depths of the Standard Model. While I was familiar with the dimensional reduction aspects of the Glashow cube mnemonic, the idea that some deeper and still (to me) opaque reason for the geometry of that space to have ribbon-like qualities is unexpected. Suppose the fermionic ribbon embedded in the Standard model is more than just a quirk. In that case, it suggests that hyperribbons in physics and biology result from a dimensional composition process in which more robust, longer-range dimensions emerge by adding and partially canceling shorter-range emergent dimensions.

    So, after all of that, here is my bottom line on dimensionality:

    Rather than getting rid of the extra dimensions of the intriguing Kaluza-Klein models by curling them, perhaps Transtrom has a better idea: Implement those less conspicuous dimensions as the lower elements in the scale hierarchy of the corresponding compositional hyperribbon, of which there would likely be multiple types. The resulting structures might very well provide new insights into why, for example, the astonishing effective but complicated Standard Model is the way it is.

    1. Hi Terry. Would it not be easier for dimensional reductionism to just have one field and a Single Stuff that creates everything in the field/universe? Just have 3 dimensions + time and no curvature? Would it not be great if all of physics could be constructed from this single stuff? It would seem so much simpler, especially than rolled up dimensions or those exotic ribbons.

    2. Terry, you yourself wrote so insightfully about those 'who are exceptionally good at applying it to the costly and psychologically deeply unsettling deeper levels of an assumption hierarchy'! Einstein was able to get on board by artistically understanding how the early twentieth century scientific community was prepared to cope with its costly and psychologically deeply unsettling anxiety about time and space. This does not mean that there are no alternative ways of constructing SRT, sharply differing in their philosophical content. For example: through 4-dimensional space, as the Kantian a priori form of consciousness (look in my blog for the corresponding construction). But the intellectual fashion is changing, and now it is no longer as fashionable as at the beginning of the twentieth century to talk about space and time as material entities capable of 'bending' or even 'curling up into a tube'. So is the fashion for additional dimensions: it is gradually disappearing. Physics will try to solve the same problems in a different way, with a greater meaning of 'subject' and 'consciousness'. Of course, this is not forever too.

    3. Peter, Igor, thanks for your interesting thoughts and kind remarks. I'll be busy elsewhere this week, but I should get back to your comments and any others later this week.

    4. Identity: the possibility of uniquely identifying objects is a "classic" emerging property, there is no identity for quantum objects, now measurements are impossible without Identity and without measurements we can't define space, hence space is another classic emerging property.
      Even Mathematics is not possible without Identity.

  8. Hi Sabine,

    This is my favorite video from you so far.

  9. A supersolid is a special quantum state of matter where particles form a rigid, spatially ordered structure, but also flow with zero viscosity. This is in contradiction to the intuition that flow, and in particular superfluid flow with zero viscosity, is a property exclusive to the fluid state. But a rigid supersolid lattice of a bose condensate can flow through the smallest hole yet still maintain its rigidly solid nature. I can't help but wonder if there might be extra dimensions enabling this unique behavior.

  10. Hi Sabine. Is your comment “no one has figured out how to quantize geometry without running into problems” the same as the problem of quantizing GR?

  11. Love your videos. Okay this is probably a dumb question but it is driving me nuts.
    On the double slit experiment, why does gravity not collapse the wave function as a "detector"?  Could the answer be that there is no quantum gravity, that there is a minimum energy (mass) threshold to gravity? Gravity on the small scale I know is tiny and unmeasurable, but has it been considered that it could be zero (i.e. the answer to quantum gravity is no gravity)?
    Could it be that when the 'particle' as a wavefunction passes through the slit it has too low an energy density that there is no gravity and it gets to completely act as a waveform until striking the wall? But with a detector you  "add" energy to cross a threshold, the particle "gains" gravity and then the waveform collapses and you have a particle with a center of mass (and decoherence and losing superposition is the result of being confined by gravity/space-time)?
    I am aware gravity per GR is the geometric spacetime so how could an object 'float' above the curvature? This seems intuitive to me that I rejected the thought apart from some strange idea that perhaps there is a 'buoyancy' to gravity you must overcome which is the minimum gravitational energy? This video on extra dimensions however - perhaps if the object is of insufficient energy/mass it is too small to interact with gravity?
    Maybe then in the centre of a black hole you would ionize a particle to where gravity doesn't apply, a waveform transformation occurs and then your particle can by probability not end up in the centre that you avoid a singularity.
    Could the "dark energy" pushing the galaxies away be the particles leaving the galaxy lowering in energy (mass) density to the point of losing gravity, the "loss" of gravitational interaction causing negative gravity?

    1. Craig,

      In standard quantum mechanics/field theory that's just because gravity is too weak. It just wouldn't happen quickly enough. However, Penrose has argued that quantum mechanics needs to be changes so that gravity indeed causes the collapse (or reduction) of the wave-function. There's no evidence this is correct, but the idea is being experimentally tested.

    2. My speculative intuition, which has now been superseded, was that for an interaction to reduce wave-behavior to discrete particle behavior, that interaction had to measure a relevant property of the wave behavior, e.g., changed particles exchange photons which measure their polarity. ("Measure" is probably not the right word, but there has to be some correspondence between the interaction and the wave-nature that is affected, is what I was intuiting.) Whereas gravitons only "measure" the mass property, which does not affect other wave properties.

      I guess there must be some evidentiary benefit from hypothesizing that any interaction works but that gravity takes a long time, but at the moment I can't imagine a mechanism for that. Gravitons (if they exist) are thought to move at the speed of light, or close to it. Also, we know (I think) that in experiments in which an entangled electron-positron pair are produced, their polarities are reduced roughly instantaneously, but their spins are not. This would imply to me that charge-force photons reduce polarity but not spin, just as I had assumed gravitions would not reduce different properties than mass. (Or perhaps the consensus notion is that charge-photons do reduce spin but also weakly over a long time.)

    3. I know it sounds counter intuitive but could the answer be that gravity isn't weak at the quantum level is zero? Already in a particle accelerator you could never hope to detect the impact of gravity, could this be not because it is weak but because the impact is not there below a minimum mass/energy?
      To the make the case for zero gravity below a minimum particle mass/energy density, if there is any gravity the center of the mass changes based on which slit the particle goes through - thus any gravity ends up potentially a detector. That any graviton needs a position. I've always just assumed the answer was that the center of the mass ends up being the centre of the mass for the probabilities, but really if there was NO centre of mass the experimental results would be exactly the same.
      Can the answer not be that any particle needs a minimum mass/energy for gravity to apply? That gravity then acts as the detector assigning a centre of gravity and you lose your wave-function?
      To prove it is tough because no gravity is hard to detect given we pretty much detect no gravity.
      I suppose the no gravity theory would predict that there could be energy added to a wavefunction particle that does not meet the requirement for detection but would still result in wavefunction collapse - this would be the minimum energy/mass density for gravity to apply to a construct. But doesn't that happen anyway, that there is a power level where your electrons will collapse the waveform regardless of if you use a detector or not?
      Alternatively in a particle accelerator could you have it where for the collision to occur every time you must have real-position vs. superposition but you do it an energy level below detection energy but above the minimum energy/mass-of-a-particle gravity threshold?
      Alternatively can do you do an experiment where you fire electrons below this minimum energy/mass through something really large (Earth and the Sun) to a satellite opposite where the arrival time predicted with gravity and without gravity would be measurable (and far in excess of the time impact of detection/waveform collapse)?
      The other prediction of a zero gravity I suppose is that for conservation of energy I assume there is some "negative energy" / "negative gravity" given you are 'losing' gravity and 'gaining' gravity' - where would the energy go of moving on/above the curvature of space-time?
      Is this obviously wrong or is it worth trying to read up and come up with these experiments / calculations/ some kind of theoretical reason for this minimum gravity applicable particle energy/mass density?

    4. It's bugging me so some more thoughts:
      #1) If gravity applies to particles below a minimum-gravity-applicable-mass/energy-of-a-particle(MGAMEOFP?) than in a blackhole everything would fall into the singularity and the blackhole would stay the same size as mass reduces to infinitely small. But if there is no gravity when the size reduces below a minimum-gravity-applicable-mass/energy-of-a-particle (MGAMOAP?) then the particles compressed at the center could cross this threshold and get to waveform out the centre. Then you get some cool magnetohydrodynamics as these particles blink into existing outside of the centre which regardless will cause the blackhole to expand with more mass.

      SIDE THOUGHTS - Would this lead to a constant release of energy from gravity, but would it balance out with the revival of gravity when the particle winks back and interacts with particles in place? Hmm. But what about the Pauli exclusion principle - do you end up pushing out the probability way out there?!!? How do you jump that particle out of superposition if everything around you is in realposition and you can't occupy the same space?

      #2) Virtual particles. Virtual particles coming in and out of the universe if gravity applies will have gravity and thus potentially infinite gravity, but if virtual particles are below a minimum-gravity-applicable-mass/energy-of-a-particle (MGAMOAP?) there is no gravity and no problem.

    5. To beat my dead horse a bit more, in the Stern-Gerlach experiment particle spin about one axis relative to an applied magnetic field is reduced, but not the other two directions. So it does seem that only relevant interactions reduce wave properties.

      If so, than a a graviton does not interact differently with electrons of different spins, nor with particles of the the same mass but different charge polarity, so it should not reduce those properties.

      However (as I now realize), it does affect momentum, but only very weakly, and that is the mechanism of the weak effect. The effect has to be strong enough to overcome the uncertainty in a particle's momentum, which (in any two-slit experiment on Earth) it is not. A very massive object, such as a baseball (relative to the photons typically used, or even a C60 molecule) would be affected, which is why we don't see quantum wave-behavior in baseball games.

      In inter-galactic-structure regions of space, perhaps even baseballs would have wave-behavior.

    6. Sabine and Jim,
      Thanks to your responses, posts and videos I could not sleep and found "Does space-time torsion determine the minimum massof gravitating particles?" (Bohmer, Burikham, Harkol and Lake, 2017).
      Note: "a torsion-induced minimum mass to the spin-generalized strong gravity model for baryons/mesons, and show that the existence of quantum spin imposes a lower bound for spinning particles, which almost exactly reproduces the electron mass."
      No extra dimensions required!
      Doesn't that make sense then if it is slightly above that of an electron? Your detection then adds energy to the particle that it crosses this threshold and gravity takes hold forcing the move from superposition to realposition.
      The oversimplified analogy I think I have is that imagine the space time bowl as filled with a superfluid (of virtual particles?). If you don't have enough energy/mass you get to float and you aren't in free fall - i.e. no gravity. If you get above the mass/energy density of an electron boom, you sink down and hit space-time curvature and gravity now applies to you.

    7. Ah.. one more post.
      Read Arndt, Markus; Nairz, Olaf; Vos-Andreae, Julian; Keller, Claudia; Van Der Zouw, Gerbrand; Zeilinger, Anton (1999). "Wave–particle duality of C60 molecules". Nature. 401..
      Note in their experiment they IONIZE the atom at high temp.
      I think that's the cheat for larger particles, if you put in enough energy and heat you ionize and then your energy/mass density actually drops. I wonder if the only waveform they see is those particles with the density below that of the electron.
      A cool thought, if it were true at the big bang where everything is so hot there would be no gravity and then gravity emerges as you cool and you cross that density. Wish I was smart enough to calculate when that happens to see if it would match predicted inflation models.

    8. Craig,

      You have submitted some comments about your personal theory of something. Please read the comment rules. This comment section is to discuss what I wrote. If you want to discuss your ideas, please set up your own blog.

    9. Apologies Dr. Hossenfelder, got carried away.
      I did love your video, first one where I actually got into a discussion on the more than 4 dimensions concept (outside one on how gravity waves didn't show more dimensions than the 3D+1).
      Usually I find videos on the topic uninteresting as so abstract and un-linked with reality (one of the reasons why I watch your videos is that I loved your book Lost in Math: How Beauty Leads Physics Astray.

    10. Thanks for the reference to the 1999, first C60-fullerene diffraction experiment. As I read it, the ionization occurred after the diffraction, as part of the detection mechanism. I noticed also that there was detectable gravitational deflection in the C60 trajectories, but it did not come into play as long as it was aligned with the diffraction grating (vertical grating, vertical deflection). So I remain satisfied that only relevant interactions produce decoherence.

      Further experiments have been done. I found the following one interesting also:

      "Quantum interference of large organic molecules"

      Nat Commun. 2011 Apr; 2: 263.
      Published online 2011 Apr 5. doi: 10.1038/ncomms1263

      "Our experiments prove the quantum wave nature and delocalization of compounds composed of up to 430 atoms, with a maximal size of up to 60 Å, masses up to m=6,910 amu and de Broglie wavelengths down to λdB=h/mv≃1 pm. We show that even complex systems, with more than 1,000 internal degrees of freedom, can be prepared in quantum states that are sufficiently well isolated from their environment to avoid decoherence and to show almost perfect coherence."

      "Collisions with residual gas molecules [in the vacuum chamber], the emission of heat radiation and the absorption of blackbody radiation are among the most important decoherence mechanisms for interferometry with massive particles."

      (None of which are detected by conscious observers, I add for Keith Gill's benefit.) (He may respond that everything is conscious, but that is not the current definition of consciousness.)(And I apologize for beating this horse again, and will find a charity to donate to as a fine payment.)

  12. The danger with the idea's of extra dimensions , is that it is a mathematical concept, and is not a property of nature. Hence we may get confused and use mathematical descriptions which could detach from nature's true working forever (S-theory?).

    1. The difference between mathematical concepts and properties of nature is not so clear. According to Galileo, the book of nature is written in the language of mathematics. :-)

    2. - Certainly in the days of Galileo mathematical concepts where derived from observing the physical world. The problem is that in the post S-theory area , we started doing the reverse and required nature to respond to 'strange ideas' as extra dimensions.

  13. The reason for the three equally nondependent dimensions can be linked the fact that 1-lines between positions can target each other freely only in geometry with mimimum three independet degrees of freedom. Via interactions degrees doubled to dimensionality.

  14. Some decades ago, I read the article from W. Büchel where he shows that in a world with more than three dimensions the orbits of the planets are not stable and a clear communication with waves is not possible in this world. At least not if the extra dimensions have the same properties as the first three.
    Why is Space Three-Dimensional? Based on W. Büchel: “Warum hat der Raum drei Dimensionen?,” Physikalische Blätter 19, 12, pp. 547–549 (December 1963): American Journal of Physics: Vol 37, No 12 (

    1. Henning Flessner,

      First, thanks for the excellent reference. You have successfully tempted me to break my promise not to get distracted until later in the week. :)

      The issue of why our universe exhibits not just three fully isotropic spatial dimensions but also three equally isotropic rotational symmetries is a deeply fascinating one. One and two spatial axes are not sufficient to enable life; four and above start getting very dark very quickly. V. Balakrishnan argues persuasively that for wave propagation, odd is better, but three is best.

      However, there is one issue (noted in passing by Feynman in his Lectures) for which 3-space is genuinely unique: It is the only space for which there is a one-to-one mapping between all spatial and rotational axes.

      One might well say, “yes, but so what?” Consider that the simplest form of 3-space is non-rotational. This simple 3-space occurs in three-dimensional arrays and crystallography, e.g., in cubic salt crystals. Such 3-space are not equipped de facto with isotropic rotational symmetries. One must add those symmetries, and from an algorithmic complexity perspective, this addition of isotropic rotational symmetries is anything but trivial.

      I suspect from this that the very existence of isotropic rotation in 3-space is one of those fish-in-the-water topics for which our universe deceives us. An alternative assumption is that spatial isotropy and rotational isotropy are the tightly interlocked sides of the same spatial emergence coin. Suppose a resolution-limited dual holographic universe model is viable. In that case, one of its implications in this area is that the most fundamental and resolution-limiting mass-energy units involved in the emergence of “smooth” spacetime are the spins of real (not virtual) fermions and bosons. Vector bosons, indeed.

  15. "...You can however quantize plain old electromagnetism without problems."

    Dirac would like a word; and Feynman would love to listen in on your answer to Dirac.

    By the way, an English improvement in your 8th graf: "...they began to wonder whether the actual space that we live in..."

  16. I think it was the Finnish physicist, Gunnar Nordstrom, that first had the idea of higher dimensions.

    Personally, I prefer to think of space as having internal degrees of freedom rather than it having more dimensions of spacetime.

    I mean, suppose each point of space could rotate, then we would bump of the dimension of spacetime by 3 and so have a 7 dimensional spacetime.

    Is there some way of dinstinguishing internal and external degrees of freedom?

  17. We may be living in a crack in a 4d space. Can't escape as our energy is very very small compared the 4d space.

    Only quantum tunneling or a great explosion would allow an escape.

    Explains renormalization. We see the large energy but just have to cancel it out.

  18. Amazing that 11 matches with the string theory 11.

  19. bee

    what about physics of higher-dimensional time ?

    1. Sorry, the coincidence.

      If you postulate one spatial and three temporal dimensions, you can think there is only one propagating light-like action curving fort and back in every time dimensions forming the physical continuum but spatially always only internally forward in its space. :)

    2. @neo:

      I came across a reference to a two time theory years ago. I think that is a theory in search of something to explain. Personally, for me, physical causality imposes a single time dinension. It's not readily apparent how one is to think of two dimensions of time.

    3. Connes does a great job of deriving the classical standard model from his spectral action. This is basically the Hilbert-Einstein action in non-commutative geometry. He also requires a space that has a classical dimension of zero, a point, but which has a non-classical dimension of 6d. Now 6d+4d =10d, the spacetime dimension for a superstring to vibrate in! This to me feels like a significant coincidence.

      I also want to add that from a philosophical perspective we talk about the electromagnetic field as though it is distinct from spacetime. But has anyone ever been able to separate it from spacetime? No, of course not. So why should we think of the electromagnetic field as distinct from spacetime? We really ought to think of it as another aspect of it, if we can't separate it. And this nicely dovetails with the whole Kaluza-Klien idea.

      Personally, whilst I can believe in curled up space. It remains to be proven or demonstrated as plausible that space has extra dimensions. This means that there has to some energy regime where space uncurls. The natural place to look for somethimg like this is in the very early universe, just after or at the big bang. But if there is no evidence that the curling up has a physical aspect to it, I don't see why ontologically speaking we should then talk of curled up space as this suggests uncurled space and extra dimensions. It's not enough that the mathematics can be made to work, we also have to show that there is some physical referent.

    4. Two-dimensional time is near imaginary time concept.

      But one a very interesting setting is a pair of 2-dimensional manifolds of Klein bottles which defines electromagnetism in the modified spirit of Kaluza-Klein. I see it pssible to think that there is a time and space dimensions in the both manifolds, so two time dimensions! The fifth degree cares the connection from time to time as tangential connection between manifolds.

      Disclaimer: The description is a glimpse out of the content from the very preliminary study. Just imagine and enjoy!

    5. Hi Eusa,
      That is truly bizarre.
      Are the 2 times running in tandem, or what?
      I'm trying to picture this and not sure if I'm imagining it correctly.

    6. Hi C Thompson,
      Yes, you got it right - tandems are a good analogue. Those 2 times correspond with electric charge states, 2 spaces correspond with parity states and tandem connections care of nonlocal correlations i.e. entanglements.

    7. @neo:

      I spoke too soon. Apparently there are such things as hyperbolic metamaterials where light travels as though it is in a universe with two time dimensions.

      It looks like that theory in search of something to explain can stop searching!

  20. Step 1: Every dimension has an observer.
    Step 2: "An observer watches something" happens in Zero dimension,

    Step 3: "An observer watching an observer" happens in One dimension,

    Step 4: "An observer watching an observer watching an observer" happens in Two dimension, . . . . . Step n: it can go on till the n dimension.

    Let's twist the rule to itself.

    An observer (zero dimension)

    An observer watching itself, (one dimension)

    An observer watching itself observing, (two dimension)

    An observer watching itself observing itself, (three dimension)

    An observer watching itself observing itself,.................. (n dimension)

    And there can be any level of observer,

    so there can be any level of dimensions.

  21. You don't get to define dimension as you like. Please open a math book.

  22. Dr. Hossenfelder,

    You always pick the best topics! And the comments have been very enlightening for me. Personally, I am a huge proponent of multi-dimensional unfolded space as with a little imagination you can find explanations for so many things we currently do not understand or have not taken the time to question. But rather than start a debate I have a question: if we can have simulation theory, Holographic and Anti-deSitter space, and one of my all time favorite things, Spontaneous Symmetry Breaking, why can't unfolded multi-dimensional space also be a theory?

    I am looking forward to part 2, and thanks for the info about Caley as I have always given Reimann credit for 'n' dimensional space due to is 1864 or 66 paper.

  23. Back when I was very interested in superstring theory, there was a website created and maintained by Patricia Schwarz that was absolutely fantastic. It addressed the subject at both the layman and expert levels, so attracted a broad audience. I guess with the dearth of evidence for such tightly curled up higher dimensions in the form of exotic particles or higher energy Kaluza-Klein excitations of Standard Model particles, she may have decided to close the site down, as I searched for it several times. But there are screen captures for the website at the "Wayback Machine-Internet Archive" back to 25 January 1999. And, to my surprise there were screen captures as recently as 7 April 2021, but with the message "This site is temporarily unavailable". So maybe it is still running and down for maintenance. If so, I will check it out as soon as it is back up.

  24. Part 1 of 2

    Nobody had ever expected to see quantum effects coming out of a cavitating cleaner. But amateur physics experiments performed at home have most likely done it. This breakthrough in amateur experimental methods is so much unexpected and might open the door to the discovery of how multiple dimensions of a quantum system functions. Also this method could form the basis of an experimental platform for string theory.

    When a static system is doing multiple concurrent activities, there is a chance that the system's dimensionality exceeds that of space time. To my eye, this multi functionality seems to be the case with a caveating cleaner eroding a sheet of aluminum foil.

    There is an excellent chance that the cavitator is producing a Bose condensate at room temperature. The usual method used to produce such a condensate is to lower the temperature of a collection of special atoms to near absolute zero. The usual method is an experiment requiring the use of a $million worth of low temperature equipment.

    The cavitating cleaner is producing Bose condensation by just turning the unit on. This condensate can be studied in real time. This process is also 100% reproducible and these micro based experiments can be performed using real time microscopic inspection methods as well as high frame rate video examination. Just turn on the cavitator, and the Bose condensates springs to life.

    There are over 70 different kinds and counting of Bose condensates currently characterized. It is not clear what flavor of condensate that is being generated in the cavitator.

    The indications that a Bose condensate is being formed by the cavitator is the appearance of a Mexican hat structure impressed into the aluminum within a blackened duplex microcavity. The number eight shaped duel cavity begins its formation as a dipole but when the duel cavity is fully formed, only one side of the duplex cavity remains active. The other inactive member of the dipole is ill formed and stunted. What marks the soliton as active is a vortex of water that is ongoing inside and above the cavity which is rotating at a fearsome rate. This vortex of water has been observed on video at 120 frames a second but the vortex still looks like a amorphous cloud even at 8 millisecond resolution. The direction of rotation and its violence becomes apparent when some detritus moves close to the water vortex. The water vortex looks like a cloud hovering over the aluminum sombrero as the rotational rate of the vortex is so very great. The vortex of water is centered on the crown of the Mexican hat structure that has been impressed into the aluminum.

  25. Part 2 of 2

    The rotation of water above the condensate in the cavity is extreme. That rate of rotation is directly proportional to the magnetic field strength of the vortex tubes projecting out of the soliton. It might be possible to calculate this field strength of the vortex tubes of the condensate by determining the rotation rate of the water and correlating that rotational rate against the known magnetic strength of a rare earth magnet. Because the rate of water rotation is so great, a very expensive high rate video camera is required to do this rotational counting, however.

    I also see the aluminum foil break apart and float in the roiling water currents atop the surviving duplex structures. On some of these fragments, the Mexican hat structures are still impressed into the material of the fragment. On occasion, an active water vortex is still active on the surface of these fragments.

    Some of these active fragments remain active and continue to generate a water vortex even after the power to the cavitator is turned off.

    Without exception, the duplex structures have only one rotating water vortex ongoing. The other conjoined cavity in the duplex structure is inactive and its Mexican hat structure is ill formed. It appears that the rotating vortex cavity has transferred its energy to the counter vortex cavity structure. The direction of water vortex rotation is counterclockwise which indicates from the right hand rule that the magnetic effect producing the water vortex is a North Pole magnetic monopole field.

    The color of the surface of the duplex cavity is black except for the Mexican hat deposition which appears to rise out of the centered base of the cavity. The Mexican hat formation has an iridescent jewel like nature, is now highly magnetic. When a magnet was placed in the water, a fragment of this formation was found to have affixed itself to a magnet placed in the water. The magnetic particle looks like the central core or crown of one of the sombrero structure that has had parts of the brim of the Sombrero missing. This structure of the fragment has assumed a hexagonal shape and must have been formed by a supersolid lattice field.

    As the foil is ripped apart, most if not all of the resulting aluminum fragments were coated with some black stuff. Any position change of the fragments did not change the color of these fragments as they floated and tumbled in the water currents of the cavitator. This lack of change of color of the fragments prompt me to consider this black color coating as a chemical, contaminant, or new element that is permanently coating and affixed to the duplex cavities.

    The Mexican hat configuration looks identical to a petal Bose polariton condensates which are described in associated articles with the petals located on the rim of the hat and a peak at its center.

    I noticed unexpectedly that when a blue laser was used to illuminate one of the sombreros, the laser light of a spot near the crown was down shifted by the active soliton to shine in an intense white slightly orange tinted light.

    A bubble of gas is seen to exit the Bose condensate soliton when the power to the cavitator is turned off. This bubble might be matter that is being carried in the condensate when the condensate is active. The termination of the condensate might be releasing the gas upon its termination. This activity might be a sign of multi-dimensional activity over and above the four dimensions of space time is at play.

  26. Good morning Sabine,

    yes, that is a very interesting question: "How many dimensions does our world have?"

    In your video you show the three dimensions partly with your hand
    or with the graphic in the background.

    You can, as we all know, move a small steel ball in three directions in space and position it as you like.

    You can't do that with a single electron, as we all know.
    Are you sure that in this range there are also 3 dimensions?
    Can you imagine that in the range below approx. 1µm the three dimensions start to disappear?

    Give me a call if you like the question.

    Have a nice day

    By the way: It is snowing here...

    1. Hi Stefan,
      Wouldn't an object of that ultra-small size simply move in a much smaller X,Y,Z space still,
      unless there's some phenomenon that prevents that movement I'm unaware of?

  27. The most important problem is how do I get a grant to study the multiverse theory?

    1. Become a theoretical physicist then write catchy papers.

  28. Hello C. Thompson,

    the problem is, below about 1µm the objects become blurred and transparent.

    If you look at blood under a microscope, you can see red blood cells.
    These are about 8µm in diameter and about 2µm thick.
    But we don't see sharp edges, we see stripes, so-called interference interference fringes.

    You can now take X-rays or electron beams and observe cells, for example.
    Google(cell images electron microscope)
    Then you can see structures of about 10nm resolution.
    But you need the smathed cell structure for these images.

    You can take a scanning tunneling microscope or a scanning force microscope and make atoms visible. But you need a macroscopic basis for that.
    In the case of individual atoms and molecules, it's the crystal in which the atoms are
    or on which the molecules sit.
    Google(atomic force microscope images)

    You can do experiments with single C60 fullerene molecules.
    By classical reckoning, these are 2nm in size. But if these
    molecules fly through a grating of 100nm line spacing, interference fringes form behind them.
    Obviously, the C60 molecules see the 100nm dash-spacing grating.
    So I think the C60 molecules are much larger than 2nm.
    Google("Wave-particle duality of C60" Nature 401, 680-682, 14.October 1999)

    You can do scattering experiments with electrons in accelerators.
    And the physicists of our world calculate an electron size of 10^-18m or smaller.
    You can find this value in Wikipedia and Particle Data Group.
    But remember: the detectors are several metres away from the scattering centre.
    And to get to 10^-18m, you have to do some maths and assume,
    it's the only explanation for the detector events.

    So I wonder if the assumption of homogeneous space (and dimensions etc) is a good assumption for micro-objects.

    BTW, if you want to draw the line at 10nm, that's fine too. I wouldn't argue.

    Best regards

    1. Thank you for that answer, regards to you too.

    2. So I wonder if the assumption of homogeneous space (and dimensions etc) is a good assumption for micro-objects

      There have been numerous experiments attempting to show that space is not continuous, but they have all failed.

    3. Hello Scott,

      which experiments are you referring to?


  29. Hi, I went to look up R. Kerner's proposal. I wondered if there is a reference establishing the +4 dimension requirement for the strong interaction. Somehow I would have thought that +3 would have been enough as a 7D spacetime can accommodate all the SM symmetries AFAIK.

  30. Is the meaning of "dimension" different in physics from applied mathematics? For instance, if I wanted to characterize the items in a rooms, I might use a table with one row per item. The columns would represent dimensions, like the x, y and z of the spatial location of each object's center of gravity. Then, I could also have columns with many other dimensions, like object mass, color, material, function, etc. How are these emerging dimensions different from dimensions in physics?

    1. "Is the meaning of "dimension" different in physics from applied mathematics?"

      No, but there are different definitions of dimension already in mathematics. The one I'm referring to is the dimension of the manifold which you can determine from the dimension of the tangent space which is a vector space, so then it comes down to linear independence -- it's really straight forward and similar to what you have in mind (number of independent coordinates necessary to parameterize the space, up to singular points maybe). Since these are all metric spaces it's the same as the Haussdorff dimensions. However, there are other ways to define "dimension". For example if you have a network rather than a manifold then the Haussdorff dimension doesn't help you much, you'd use the spectral dimension instead. There are more ways to define the dimension of math things, all of which I was not talking about.

  31. In the terms that this conversation has taken, I have to ask: Do we really know what a 'dimension' actually is? Certainly, it is a type of degree of freedom of motion, but the way physicists are talking about them, it almost sounds like they are a type of particle. In the concept of dimensional compactification, the 'extra' dimensions are shriveled up into small entities, which can affect how forces and fields are expressed. This sounds like a dimensional particle to me... To carry the analogy further, since most particles in the universe are not fundamental structures, then perhaps a spatial dimension is not a fundamental thing either. If dimensions are in fact composite structures then perhaps we don't really know what a dimension is after all. If true, it could certainly explain all the trouble theorists are having...

  32. "Space, the way we experience it, has three dimensions. Left-right, forward backward, and up-down. But why three? Why not 7? Or 26? The answer is: No one knows. ... "

    I know the answer. We experience three spatial dimensions because our ancestors lived in trees (human beings come from apes). Our ape-like ancestors had to be fearful because their natural predators could hunting them coming from any spatial direction.They were always watchful. Conversely, antelopes only experience two spatial dimensions. They live in a nearly 2-D universe. They just expect their natural predators could hunting them in the Kintengala African Plain, mostly through that infinite flat. Furthermore, worms might be experiencing just one spatial dimension, because they only follow the direction of their guzzler mouths, they don't need more spatial dimensions to survive. The problem with this hypothesis is that physicists believe spatial dimensions is something real, something that exists out there, not in here. They think the space we experience is something outside of our minds.  But, the truth is we experience three dimension the same way we experience three primary colors, (red. green, blue). Why three? Why not four?. Well, bees see four primary colors, they can see in the ultraviolet spectrum. So yes, it all evolutionarily depends of our survival needs. The light spectrum is nearly continuous, but it seems we experience it quantised, because we have three kinds of cones in our eyes. (a cone is a type of photoreceptor cell in the retina). Spatial dimensions may be infinite or none, whatever. But, we experience only three because our emergent minds have a discrete structure. 

    Regards, “Bee” Hossenfelder :-)

    1. Hi Albert, this is a minor point, but humans are a type of ape.

  33. The recognition of the possible operation of extra dimensions in the life cycle of quasiparticles can reveal unrealized important phenomena. It may be possible for coherent metastable quasiparticles to exist in a state of superposition and can become dormant for and indefinite period of time. Being coherent, they naturally are predisposed to form large extended condensates. Also being in a state of superposition implies that their existence and activities are not apparent to an interested observer.

    These quasiparticles are hybrid waveforms that are comprised of two or more fundamental waveforms which can include both fermions and bosons which reconfigure into bosons at formation and can therefore form condensates. A hundred or more such composite waveform combinations are possible and all there various types are metastable and can become dormant.

    One possible path to the formation of this class of composite particles is the application of an energy pulse that conforms with an associated unique profile. This pulse provides a framework around which the quasiparticle forms. The unique energy pulse can be viewed as a key that allows the particular quasiparticle to forms. The framework of the formation process is enabled by extra dimensions that are particular to the type of quasiparticle. Once formed, the quasiparticle exists in a metastable state and if not properly stimulated by a energy background of a particular keyed format, the quasiparticle becomes dormant, metastable, and remains coherent in a state of superposition.

    These condensates can exist in a dormant state within space time in any form: solid, liquid, gas, plasma or vacuum made possible by their unique set of extra dimensions consistent with their formation.

    If the host medium is properly stimulated with the correct energy format, the dormant condensate will reactivate and continue its growth process defined by the extras dimensions in which they exist and which controls their life cycle.

    Lacking the particular energy format to feed any given quasiparticle, large amounts of these particles accumulate over time and aggregate to form vast condensates called dark matter. This dark matter can be comprised of many and varied of these dormant quasiparticle types. These clouds of condensates will grow if exposed to the matching energy format and consistent with the dimensionality that they exist within. These condensates exist in a state of superposition and are not observable. They also do not respond to energy unless that energy is consistent with their formation energy profile which also includes the formation profile mapped by their unique set of extra dimensions.

    In sum, the existence of dark matter is made possible by extra dimensions of space time.

  34. With reference to the post that I contributed to this blog a few days ago regarding how multiple dimensions could underpin unobservable processes during cavitation, I now continue as follows:

    Beginning a few days ago, an opportunity afforded itself whereby an scanning electron microscope (SEM) analysis of the magnetic fragments produced by the cavitating cleaner was attempted and completed today. The magnetic particles were characterized and turned out to be a collection of random shaped element alloy mixtures comprised of a wide range of various elements. Since there was no attempt to avoid contamination of the tap water, the element mix that was found is to be expected. But in all cases, the alloys always included iron as the magnetized element.

    The surprising result was the shape of these alloyed particles: in one singular case, a perfect formed sphere with a crenellated surface that resembled the surface of the brain. In this singular case, an absolutely pure iron micro sphere with a brain like crenellated surface was formed instantly in water without any heat. How such a singular object can form in a low energy environment is inexplicable.

    One advantage of this cavitation based experiment is that it is 100% reproducible, and dirt cheap to perform... that is if you have access to a SEM.

    If you are interested in pursuing a challenging science based mystery story, the cost of participation in time and money is less than trivial. What will be hard is discovering the reasons that underpin this mysterious result.

    I have no clue about how these strange particles can form and I would sure like to get an explanation of how such a perfect crenellated sphere can form so rapidly and what could possibly be the template that directs the shape of this formation... could extra dimensions be involved?

  35. Sabine,

    “…the state-space of quantum mechanics is an infinite-dimensional function space.”

    This statement is from the Wiki article, “Dimension.” I am wondering if this it true and, if so, why there is the need for a careful accounting of dimensions on one hand when quantum theory has them in such abundance.


    1. Dear Don,

      interesting and good question.

      I looked at the Wiki article.
      It mentions many spaces but explains little.
      Let me try to shed some light on this.

      In our normal 3-dimensional spatial space, many things are described with vectors.

      From these vectors you can determine many things, e.g.
      - their length (size)
      - their direction
      - whether two vectors are perpendicular to each other
      It is interesting that any vector can be represented by 3 selected vectors by linear combination.
      These selected vectors are called basis. And yes, a 3-dim. space needs 3 vectors as basis,
      a 2-dimensional space needs 2 vectors, and a 387-dimensional space has a base of 387 vectors.

      This concept can also be applied to functions and is visible in quantum mechanics.
      If one solves the Schrödinger equation, for example, for a Coulomb potential (hydrogen atom), one obtains the following.
      Psi functions (abbreviation):
      2s, 2p
      3s, 3p, 3d
      5s, ...
      For these functions you can also determine a "length", calculate if they are perpendicular to each other
      and as you probably already guessed, there are an infinite number of them.
      This is called a function space because the vectors are functions.
      And the base contains an infinite number of functions, which is why it is infinitely dimensional.

      You can read about this very nicely here:
      Jump to "Motivating Example ..."
      and then to "History". The integral gives you an idea of how to determine whether functions are perpendicular to each other...

      Sabine's talk focused exclusively on the question: "Are there more than 3 SPATIAL dimensions?"
      ... and had nothing to do with function space, which I tried to introduce.
      The function space is also called Hilbert space, after the mathematician David Hilbert,
      who lived for many years in Göttingen, where I did my PhD thesis.

      Was that a little helpful?

      @Sabine: I hope you feel comfortable with my explanation.

      Many greetings

  36. Stefan,
    I thank you for taking time to answer my question. I believe I understand the distinction. The infinite dimensions of quantum theory are simply a part of its mathematics and not a statement about the dimension of the underlying space, but I confess to having only a Braille-like appreciation of the mathematics. I am not comfortable with its level of abstraction. In a manner of speaking, I am not able let go of the shovel, some physical reference.

    I wonder about the depth of distinction between entities in relativity and quantum mechanics, their degree of independence. From the Wiki commentary on Geometry:

    “One of the oldest such discoveries is Gauss' Theorema Egregium (remarkable theorem) that asserts roughly that the Gaussian curvature of a surface is independent from any specific embedding in an Euclidean space. This implies that surfaces can be studied intrinsically, that is as stand alone spaces, and has been expanded into the theory of manifolds and Riemannian geometry.”

    Am I correct in inferring that the mathematics of relativity and quantum mechanics are fundamentally at odds with regard to their depth of distinctions between entities? In the realm of shovels it seems like the most notable events take place at the boundaries between things.

  37. I believe that the universe is much larger than we see it in the most powerful telescopes. Moreover, we cannot look at the universe from the side in real time. Since we see that galaxies are flying with acceleration, there must be an expansion front for galaxies. We do not know the width of this front and its curvature. This expansion front should be spherical and it looks like a rubber shell whose thickness we do not know. This is a consequence of Einstein's theory and this fact was pointed out by other scientists.

    Inside this spherical expanding shell is the visible region of the Universe. The visible part of the Universe is located inside this spherical expanding shell. Therefore, we perceive our universe as flat and homogeneous. It seems astronomers have already measured the curvature of the universe. But the main thing is that if we are inside the visible region of the Universe, which is much smaller than the spherical front of expansion, then galaxies should have different speeds and different acceleration of expansion.

    Then we can have a map of the expansion of galaxies with vectors of the expansion rate of galaxies. Next, we can calculate from this map the curvature of the universe, the width of the expansion front and the direction to the center of the expanding universe and our position on this map. This work must begin to be done. It seems astronomers have already established that galaxies are expanding at different speeds. Then this fully confirms the spherical shape of our universe inside the spherical front of the expansion of which there are galaxies. It is like a rubber shell of a ball and inside this shell are galaxies. Therefore, we observe that all galaxies move away from each other when such a shell expands.

    I am repeating that this is the generally accepted model of an expanding universe according to Einstein's theory. We have to make only one addition, that the visible area of the spherical universe is much smaller than its actual size.


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