Saturday, December 19, 2015

Ask Dr B: Is the multiverse science? Is the multiverse real?

Kay zum Felde asked:
“Is the multiverse science? How can we test it?”
I added “Is the multiverse real” after Google offered it as autocomplete:

Dear Kay,

This is a timely question, one that has been much on my mind in the last years. Some influential theoretical physicists – like Brian Greene, Lenny Susskind, Sean Carroll, and Max Tegmark – argue that the appearance of multiverses in various contemporary theories signals that we have entered a new era of science. This idea however has been met with fierce opposition by others – like George Ellis, Joe Silk, Paul Steinhardt, and Paul Davies – who criticize the lack of testability.

If the multiverse idea is right, and we live in one of many – maybe infinitely many – different universes, then some of our fundamental questions about nature might never be answered with certainty. We might merely be able to make statements about how likely we are to inhabit a universe with some particular laws of nature. Or maybe we cannot even calculate this probability, but just have to accept that some things are as they are, with no possibility to find deeper answers.

What bugs the multiverse opponents most about this explanation – or rather lack of explanation – is that succumbing to the multiverse paradigm feels like admitting defeat in our quest for understanding nature. They seem to be afraid that merely considering the multiverse an option discourages further inquiries, inquiries that might lead to better answers.

I think the multiverse isn’t remotely as radical an idea as it has been portrayed, and that some aspects of it might turn out to be useful. But before I go on, let me first clarify what we are talking about.

What is the multiverse?

The multiverse is a collection of universes, one of which is ours. The other universes might be very different from the one we find ourselves in. There are various types of multiverses that theoretical physicists believe are logical consequences of their theories. The best known ones are:
  • The string theory landscape
    String theory doesn’t uniquely predict which particles, fields, and parameters a universe contains. If one believes that string theory is the final theory, and there is nothing more to say than that, then we have no way to explain why we observe one particular universe. To make the final theory claim consistent with the lack of predictability, one therefore has to accept that any possible universe has the same right to existence as ours. Consequently, we live in a multiverse.

  • Eternal inflation
    In some currently very popular models for the early universe our universe is just a small patch of a larger space. As result of a quantum fluctuation the initially rapid expansion – known as “inflation” – slows down in the region around us and galaxies can be formed. But outside our universe inflation continues, and randomly occurring quantum fluctuations go on to spawn off other universes – eternally. If one believes that this theory is correct and that we understand how the quantum vacuum couples to gravity, then, so the argument, the other universes are equally real as ours.

  • Many worlds interpretation
    In the Copenhagen interpretation of quantum mechanics the act of measurement is ad hoc. It is simply postulated that measurement “collapses” the wave-function from a state with quantum properties (such as being in two places at once) to a distinct state (at only one place). This postulate agrees with all observations, but it is regarded unappealing by many (including myself). One way to avoid this postulate is to instead posit that the wave-function never collapses. Instead it ‘branches’ into different universes, one for each possible measurement outcome – a whole multiverse of measurement outcomes.

  • The Mathematical Universe
    The Mathematical Universe is Max Tegmark’s brain child, in which he takes the final theory claim to its extreme. Any theory that describes only our universe requires the selection of some mathematics among all possible mathematics. But if a theory is a final theory, there is no way to justify any particular selection, because any selection would require another theory to explain it. And so, the only final theory there can be is one in which all mathematics exists somewhere in the multiverse.
This list might raise the impression that the multiverse is a new finding, but that isn’t so. New is only the interpretation. Since every theory requires observational input to fix parameters or pick axioms, every theory leads to a multiverse. Without sufficient observational input any theory becomes ambiguous – it gives rise to a multiverse.

Take Newtonian gravity: Is there a universe for each value of Newton’s constant? Or General Relativity: Do all solutions to the field equations exist? And Loop Quantum Gravity has multiverses with different parameters for an infinite number of solutions like string theory. It’s just that Loop Quantum Gravity never tried to be a theory of everything, so nobody worries about this.

What is new about the multiverse idea is that some physicists are no longer content with having a theory that describes observation. They now have additional requirements for a good theory, like for example that the theory have no ad hoc prescriptions like collapsing wavefunctions; no small, large, or in fact any numbers; or initial conditions that are likely according to some currently accepted probability distribution.

Is the multiverse science?

Science is what describes our observations of nature. But this is the goal and not necessarily the case for each step along the way. And so, taking multiverses seriously, rather than treating them as the mathematical artifact that I think they are, might eventually lead to new insights. The real controversy about the multiverses is how likely it is that new insights will emerge from this approach eventually.

The maybe best example for how multiverses might become scientific is eternal inflation. It has been argued that the different universes might not be entirely disconnected, but can collide, thereby leaving observable signatures in the cosmic microwave background. Another example for testability comes from Mersini-Houghton and Holman who have looked into potentially observable consequences of entanglement between different universes. And in a rather mindbending recent work, Garriga, Vilenkin and Zhang, have argued that the multiverse might give rise to a distribution of small black holes in our universe which also has consequences that could become observable in the future.

As to probability distributions on the string theory landscape, I don’t see any conceptual problem with that. If someone could, based on a few assumptions, come up with a probability measure according to which the universe we observe is the most likely one, that would for me be a valid computation of the standard model parameters. The problem is of course to come up with such a measure.

Similar things could be said about all other multiverses. They don’t presently seem very useful to describe nature. But pursuing the idea might eventually give rise to observable consequences and further insights.

We have known since the dawn of quantum mechanics that it’s wrong to require all mathematical structures of a theory to directly correspond to observables – wave-functions are the best counter example. How willing physicists are to accept non-observable ingredients of a theory as necessary depends on their trust in the theory and on their hope that it might give rise to deeper insights. But there isn’t a priori anything unscientific with a theory that contains elements that are unobservable.

So is the multiverse science? It is an extreme speculation, and opinions widely differ on how promising it is as a route is to deeper understanding. But speculations are a normal part of theory development, and the multiverse is scientific as long as physicists strive to eventually derive observable consequences.

Is the multiverse real?

The multiverse has some brain-bursting consequences. For example that everything that can happen does happen, and it happens an infinite amount of times. There are thus infinitely many copies of you, somewhere out there, doing their own thing, or doing exactly the same as you. What does that mean? I have no clue. But it makes for an interesting dinner conversation through the second bottle of wine.

Is it real? I think it’s a mistake to think of “being real” as a binary variable, a property that an object either has or has not. Reality has many different layers, and how real we perceive something depends on how immediate our inference of the object from sensory input is.

A dog peeing on your leg has a very simple and direct relation to your sensory input that does not require much decoding. You would almost certainly consider it real. On the contrary, evidence for the quark model contained in a large array of data on a screen is a very indirect sensory input that requires a great deal of decoding. How real you consider quarks thus depends on your knowledge of, and trust in, the theory and the data. Or trust in the scientists dealing with the theory and the data as it were. For most physicists the theory underlying the quark model has proved reliable and accurate to such high precision that they consider quarks as real as the peeing dog.

But the longer the chain of inference, and the less trust you have in the theories used for inference, the less real objects become. In this layered reality the multiverse is currently at the outer fringes. It’s as unreal as something can be without being plain fantasy. For some practitioners who greatly trust their theories, the multiverse might appear almost as real as the universe we observe. But for most of us these theories are wild speculations and consequently we have little trust in this inference.

So is the multiverse real? It is “less real” than everything else physicists have deduced from their theories – so far.


  1. Why Nature should care for our definition of science and for what we can experimentally verify or not? Maybe we are surreal and arrogant enough to think that Nature is stupid and needs the guidance of certain theoretical physicists and philosophers to define herself?

    These people are arrogant enough to dictate the ways of the Cosmos; in practice they say: since the Multiverse is not compliant with our strict definition of Science it can't be real.

    BTW inflation and the String landscape are not independent mechanisms in that respect; they beautifully combine together to provide the reach Multiverse picture (the string vacua are populated via the inflationary mechanism) and explain this way the small value of the Cosmological Constant.

    Personally I believe indeed that the Multiverse picture is quite plausible because it has a huge explanatory power. Moreover it seems amazing to me that the two most promising theories we have for explaining Nature, when combined, they give birth in a deep and theoretically consistent way to the Multiverse picture.

  2. All in all, I think that's a lot of science fiction for no practical output.

    I like to quote Dali in this context: "tant et tant d'arrivisme our si peu d'arrivage" - excuse my French. When the unexplained is out of reach, invoking sorcery is the opposite of science. It is just ads for budget - voluntary or not.

    In practice, the existence of free parameters is a property of field theory in its present state. The multiverse assumption is firstly a manner to find an excuse to the absence of understanding of couplings. Remember what Feynman said about alpha? Now we have 19 of those in the SM (plus 6 for neutrinos).


  3. If the multiverse idea leads one to say something meaningful about the world we live in, it is a good concept; otherwise it is a useless one, even if it is real.

  4. Question - is the small cosmological constant solution in the string landscape a constructive proof, or is it a non-constructive existence proof? In particular, has it been shown that the set of string compactifications with a small cosmological constant and the set of string compactifications with a low-energy limit like the Standard Model have a non-empty intersection?

  5. Giotis,

    The 'beautiful combination' between the string theory landscape and eternal inflation would be more convincing if one could show that string theory gives rise to this type and no other type of inflation.

  6. Arun,

    Last time I looked string theorists had trouble getting a positive cosmological constant to begin with. It is my understanding that to date string theory has no explanation of the observed value of the cosmological constant. (To my knowledge the only approach to quantum gravity that comes close to having an explanation are causal sets. But then causal sets haven't yet reproduced GR, so not sure how useful that is.) Best,


  7. I have a further question - for example, is the nature of the string theory explanation of why we live in 3+1 dimensions instead of 4+1, 7+1, etc., of the same nature as the string theory explanation of the cosmological constant?

    Thanks in advance!

  8. 1) The multiverse exists.
    2) It interacts.
    3) Thermodynamics has unexpected degrees of freedom.
    4) Thermodynamics has no unexpected degrees of freedom.
    5) The multiverse does not interact.
    6) The multiverse is empirically irrelevant.
    7) Healing quantum gravitation, string theory, and standard model empirical failures is external to defective postulates' derivations (e.g., six classes of chemical experiments).
    8) Defective theory excludes external falsifying observation.
    9) Macroeconomics, psychology, political science, religion, physics...failures of application only tolerate further failures of application.

  9. Arun,

    String theory doesn't actually explain why we live in 3+1 dimensions. I mean there are some attempts to explain it, such as this or this. But I think these are quite controversial ideas. It does explain why we live in 9+1 dimensions. And, having said that, the question why we live in 3+1 is thus of a different nature as the cc question. The landscape is basically a consequence of requiring these additional dimensions to be compactified. (You would still have a multiverse without the compactification, but it would be more similar to Tegmark's mathematical universe.) The cc is a value you then have to find somewhere in that landscape.



  10. I agree that the multiverse concept is not radical. When people try to interpret it you only hear the one side regarding how may universes there are and not the other side where "the multiverse" is just another potential function.

  11. String pheno hasn't found yet the vacuum of our Universe i.e. the Standard Model embedded in a complete cosmology of a dS vacuum. This is a formidable task and when accomplished it would be big news, believe me you will hear about it :-)

    Regarding the number of dimensions: With String vacua we mean different solutions of the theory. For example Flux vacua of M-theory on Calabi-Yau four folds or on K3 or on G7 manifolds are as legit as IIB Flux vacua on CY three folds and Heterotic vacua on CY three folds (btw many of these vacua are connected via Dualities).

    Currently there is no fundamental top down stringy reason to exclude them from the landscape and thus there is no fundamental reason for a 3+1 dimensional Universe.

    Of course then the problem is if all these vacua are connected and how you can populate them all i.e. how you can jump from e.g. a four dimensional to a seven dimensional Universe.

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  13. “In the Copenhagen interpretation of quantum mechanics the act of measurement is ad hoc. [...] This postulate agrees with all observations, but it is regarded unappealing by many (including myself).”

    You don't say why you find it (and the C.I.) unappealing and what you've written above is rather confusing: a good reason to dislike the projection postulate is the fact that it doesn't agree with all observations and where the C.I. including the projection postulate does apply it's hard[er] to see anything unappealingly ad hoc about it. The C.I. might be a poor psi-epistemic interpretation but it's not a very poor psi-ontic interpretation.

  14. MarkusM: "There is little doubt that the universe continues behind the cosmic horizon, in particular as it is an apparent horizon. I.e. the level I multiverse is almost for certain."

    A big universe which continues beyond the horizon is not the same thing as a multiverse. Nor does it imply a multiverse.

    "If, however someone claims that this is not so, because the parameters do not change, then the burden of proof is on her/him, which is to show that they are all unique and fixed."

    Trust me, the burden of proof is ALL on you when it comes to the multiverse. Good luck with that one.

  15. Paul,

    I find it unappealing because it's not deterministic.

    I don't know what you are trying to say with these links. The page seems to say that there are some sorts of detectors where the standard formulation of the measurement prescription doesn't apply.

    Look, for me all measurements are scattering processes in quantum field theory. In the end you always calculate some scattering matrix. What qft does not tell me is how to get an observable out of this and this, thus one needs an interpretation of the transition amplitudes that says the elements of this thing squared are probabilties for certain processes. It's this interpretation that I think is ad-hoc, which makes me doubt it's fundamental. Best,


  16. Giotis: "Personally I believe indeed that the Multiverse picture is quite plausible because it has a huge explanatory power."

    This is a fallacy. Saying that many universes explains why the laws of nature can be different is a fallacy because it does not explain WHY the laws of nature are different in each universe - why shouldn't they be the same in each universe? We don't know how the mechanism works, so absolutely NO explanation is being provided by these hypotheses. Nothing at all is being "explained".

  17. MarkusM,

    I think you've read too much multiverse blabla. Science is about describing observations. To do this you always have to pick certain axioms for your theories. Picking a parameter is just one more axiom. There is never a justification for the axioms, that's why they are axioms. You get a multiverse if you throw out more axioms than you can afford. Then you can no longer uniquely describe observations.

    "If, however someone claims that this is not so, because the parameters do not change, then the burden of proof is on her/him, which is to show that they are all unique and fixed."

    No, the 'burden of proof' is on those who believe that they are still doing science by attempting a logical impossibility, that is to explain our observations without selecting axioms based on observations. Speak after me: it's not possible. You will just end up with Tegmark's Mathematical Universe, and then the question isn't what's the axiom, but "where are we in the multiverse?" Which is the same question as "Which axioms do we select to describe out observations." So you don't learn anything from it.

    Don't misunderstand me, it's a valuable thing to try and see whether it's possible to reduce the number of axioms, for example by finding a way to calculate some parameters. But reducing axioms by just saying I don't want to postulate this parameter, consequently all values exist is not scientific reasoning.



  18. i just read your nice column in Forbes ( and in it you refer to Dawid's "non-empirical theory confirmation". other than wondering how one gets to organize a symposium to discuss one's own ideas, i don't understand why dawid thinks that theories are ever confirmed because they're not. they may be useful or they may not and their predictions can be found to be incorrect or in agreement with experimental findings, but to say that they can be confirmed is to say that they have some sort of correspondence to reality. this conflicts with Hawking's statment that he has no idea what reality is (" I don't demand that a theory correspond to reality because I don't know what it is.") which is a restatement of the late, great comedian, Robin Williams who said "Reality... What a concept!". a better understanding of theory construction or model building (as John von Neuman said "The sciences [...] make models [that are] mathematical constructs which, with the addition of certain verbal interpretations, describes observed phenomena.) was expressed by George Box who wrote that "all models are wrong, but some are useful" .

  19. "Is the multiverse real?" Are the multiverse and MOND closely related topics? Is MOND empirically valid?
    ”Dark Matter or Modified Gravity?" - Stacy McGaugh - YouTube, 2015
    McGaugh has spent 20 years attempting to refute MOND but, so far, no refutation. I predict that Milgrom will win the Nobel prize within 5 years. The LISA Pathfinder science team seems to have totally ignored MOND — if they had not ignored MOND then I think that MOND would have been convincingly verified within 2 years. I predict that the LISA Pathfinder science team will encounter very slight and very puzzling "instrument malfunctions". Whatever explains MOND, the multiverse might be one of the leading explanatory candidates.

  20. "No, the 'burden of proof' is on those who believe that they are still doing science by attempting a logical impossibility, that is to explain our observations without selecting axioms based on observations. Speak after me: it's not possible. You will just end up with Tegmark's Mathematical Universe, and then the question isn't what's the axiom, but "where are we in the multiverse?" Which is the same question as "Which axioms do we select to describe out observations." So you don't learn anything from it."

    > Hello Sabine, I couldn't agree more with this observation.

    At the risk of sounding a little harsh (for which I apologise moderately), it leads to a partial ecape from the responsabilities researches have.

    You don't understand the causalities, ans so you decide to claim that causality is no longer needed. "It is the way it is, and in another universe it will be different."

    I detect zero science (as in scientific method) in this type of reasoning.
    Sometimes it takes 10 years to uncover the logic of a phenomenon in nature, sometimes it takes a hundred, and sometimes it takes 250 years, or even a thousand years.
    But we must never, never give up on that search.

    Yesterday's phylosophy always became today's science, and today's phylosophy will inevitably become tomorrow's science.
    A peak at history teaches us this (superstitions are lifted by science, etc).
    Precisely because we never give up, and because at some point, we always became humble enough to realise that the search must continu.
    Even the phylosophical questions surrounding Newton's first law of motion, a law we accept without any true causality, due to overwhelming epirical evidence, will one day shift from 'why' to 'how' and from 'how' to 'what happens at the smaller scales'.

    I do not think nature is absurd (excuse me Mr. Feynman) or ad hoc. We just don't have the necessary detailed information yet, to uncover the highly organised logic behind unexplained phenomena. Our lack of well aimed imagination made us underestimate the richness of the smallest and largest as yet unreachable scales. One must take such well aimed leaps of faith and then push forward towards an experiment which should at least display measurable symptoms of the leap taken.

    Such is my opinion on the matter.

    Greetings, Koenraad

    (My first name has the same characters as 'Noa Drake', we mustn't get too serious either.. )

  21. Okay, so you simply don't like indeterminism... To me that's a very alien aesthetic¹ but even if it wasn't I think I'd still be inclined to interpret quantum theory as it stands as (generalised, psi-epistemic) applied probability theory.

    ¹ To paraphrase Max Born, determinism is for the (spherical) birds.

  22. Paul,

    Yes, I am guilty. In my defense, I don't work on it. Maybe I'll get back to this when I'm retired. Then I will haunt the science blogs as a reborn crank in search of a better theory of quantum mechanics.

  23. @Paul

    I respect your view, nobody says we have to think alike. Investigating both options would be the wisest choice.
    But determinism is not exactly what I inferred. A self-organising universe does not have a particular predetermined outcome. I would recommend the work of Professor Francis Heylighen from the Brussels University VUB, a well respected pioneer on emergence and evolution of intelligent organisation, by no means to be confused with 'intelligent design', it is the opposite of that. The former developes from within the system, the latter is supposed to have been imposed by... from outside.

  24. And concerning the the interpretation of quantum theory as applied probability theory,
    i would recommend the upper half of page 196 of this paper by Gerard 't Hooft :

    And why not persue the idea that an ensemble of observed probabilities, can have a causal mechanism behind it as yet unobserved ?

    For example : Take a container full of minuscule small particles.

    Now apply a tube at the bottom which lets air in from a compressor.
    Suppose we can only observe the container and not what happens below it.
    We might conclude that the system consist purely of probabilities as far as the positions of the particles are concerned at given points in time.
    But here we know in fact that that is not the whole picture, and that there is a cristal clear cause to this ensemble of probabilities even if the individual positions cannot be predicted correctly.
    If I turn up the power of the airflow, then our ensemble of probabilities might show that on avarage the particles appear 10cm higher in the container, and that they change positions more times per second. But that's purely the consequence of being pushed up higher and moving faster due to the power being turned up.

    So arguing wether A or B is the right answer to the conundrum (determinism or indeterminism) could be to narrow a view, as one day it might turn out that C is the answer : a hybrid of both.

    Remark :
    I will not structurally impose my ideas any further then my above explanations, because I respect that this is Sabine's blog, she poses ideas, we place the occasional comment.
    But if anybody wishes to discuss things further via email, I'd be happy to, unless of course Sabine wishes to see these notions debated further here.

  25. @Noa Drake "Sometimes it takes ...years to uncover the logic of a phenomenon in nature"

    "AHA!" (James Clark Maxwell). Clarity (Oliver Heaviside). Tradition dies (50 years). 4) Implement (telephone, radio, radar, TV). Einstein, Minkwoski, 50 years, GPS and cosmology. 45 years of physics are mathematically rich and empirically sterile with a vast labor force. The multiverse makes failure a virtue.

    @David Brown Dark matter is undetected, Milgrom acceleration is unsourced. Multiverse leakage is desperation. Parts-per-billion chiral anisotropic spacetime torsion background: Baryogenesis (Sakharov conditions), Milgrom (Noetherean leakage of exact spacetime isotropy and angular momentum conservation), chiral and parity violations are diagnostics. Testable in existing equipment (violates sterile theory - forbidden).

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  27. Markus,

    Any theory is infinitely finetuned because there are infinitely many consistent sets of axioms. What is an axiom? An axiom is a definition or mathematical relation. Defining some parameter to have some value is just another axiom.

    The fact that our observations are described by only some consistent mathematics but not by other is already "utterly unlikely" and "without a reason".

    And, having said that, you should think about what it means for something to be "unlikely". Because to quantify that you need a probability distribution. Where does that distribution come from? Is it a likely distribution? How do you quantify likely again?



  28. Dear Bee,

    Let us suppose that our universe is indeed one of the metastable vacua of a string landscape with the correct sign and size of the cosmological constant; nicely described all the way to the Planck scale by string theory.

    At some distance scale much longer than the Planck scale, this string description presumably is equivalent to an effective quantum field theory, including some effective quantum field theory of gravity. This effective field theory can be used to derive lower energy effective field theories, until we integrate out any matter degrees of freedom that are relevant only at energies much much higher than the Standard Model symmetry breaking. In this series of effective field theories, doesn't the cosmological constant run? In particular, it has to cancel out the contributions of the remaining quantum degrees of freedom. That is, at the Lambda_QCD square, the effective vacuum energy density has to be order of (Lambda_QCD)^4, with the appropriate sign in order to cancel out the contributions from all the QCD degrees of freedom to the vacuum energy.

    Isn't this the problem we don't know how to solve in the first place, as to why QCD degrees of freedom seem to operate in a flat empty spacetime instead of the general relativity manifold with vacuum energy density ~ (Lambda_QCD)^4 ? That is, we still haven't understood anything?

    Thanks in advance!

  29. I guess an axiom is some low-level fundamental constant or law which you just take to be true (like an axiom in mathematics) and then you try to build your theory up from a set of axioms.

    It's clearly a good idea to reduce the number of axioms required, and it would be even better to show why your axioms necessarily take the form they have (such as the value of a constant).

  30. Sabine,

    pt. 1: How does this translate into a concrete physical example ? For instance, if one takes Maxwell's theory, what does it mean for it to be infinitely fine tuned ? Does it mean that the equations could have infinitely many other forms ?
    What does "Defining some parameter to have some value is just another axiom" mean ? Does it mean that defining the speed of light as 3*10^8 m/s boils down to an axiom ?

    pt. 2: This may be so, but this issue is related to a type IV "Tegmark-multiverse", which is not what I was referring to.

    pt. 3: That's right, the best I can do due to my sheer lack of knowledge (I am ignorant of the string landscape), is to assume that the 37 parameters of the SM live in a 37-dimensional real space and obey a uniform probability distribution.

    Best, Markus

  31. Andrew,
    "A big universe which continues beyond the horizon is not the same thing as a multiverse. Nor does it imply a multiverse." - It's all a matter of definition. Tegmark says (
    THE SIMPLEST TYPE of parallel universe is simply a region of space that is too far away for us to have seen yet. The farthest that we can observe is currently about 4 x 10^26 meters, ... Each of the Level I parallel universes is basically the same as ours. All the differences stem from variations in the initial arrangement of matter.

    "Trust me, the burden of proof is ALL on you when it comes to the multiverse. Good luck with that one." - I guess, I shouldn't have used the word proof, because that suggests that one can proof the existence or non-existence of something in a strict mathematical sense. What one can in principle do is to make a strong case for the multiverse by making a strong case for the fine tuning of the "constants" of nature for life/complexity. If you then want to reject the multiverse (and don't want to buy into a supernatural explanation) you have to show why the constants are what they are.
    Admittedly, the fine tuning argument is not a very good one at the moment because there is still a lot of controversy over it.

  32. Markus,

    For example the gauge group could be any other group, and there are infinitely many groups. It doesn't have to be Lorentz-invariant, that's another axiom. Why is it a differential equation to begin with? Why is it second order? Why is it in 3+1 dimensional space-time? Why is there a space? Why does it have a time? Why is that space-time (by assumption) differentiable? (And smooth. And has a metric on it!) There are more axioms that you need to do differential geometry as with the existence of the exterior algebra and so on (something about the triviality of the fibre bundle, the details of which I have forgotten).

    These are all axioms, most of which are never written down. But any one of these is a choice among an infinite number of axioms. Why don't we live in a 698 dimensional non-hausdorff space? Nobody knows, but we don't. Why do all our theories seem to have a Hamiltonian evolution? Why are observables never complex numbers? By assumption. These aren't mathematical conclusions, these are chosen requirements. Best,


  33. Markus,

    Re your pt 2: I don't know what you are saying with this. I am asking you what's the basis to eschew finetuning. I understand experience value. I am asking if there is anything more to it than that and I can't find anything.

    Re 3: In the space of functions a constant function is as good or bad as any other function. Easy enough too see if you make a change of basis and instead look at fourier transformations. Why not take a constant fourier transformation then? Best,


  34. Arun,

    I guess what you are saying is if you have UV/IR mixing then effective field theory arguments don't work, which I think is correct.

  35. Sabine,
    Thanks for these nice examples, now I see your point.
    Do you think there is any hope of finding out why the axioms we observe are they way they are ?
    Best, MM

  36. MarkusM, you state: "If you then want to reject the multiverse (and don't want to buy into a supernatural explanation) you have to show why the constants are what they are".

    I rather think the first step is to show "how" they are what they are. Then, multiverse or not, you have a first progress (like for the Bohr model at the beginning of all, the why is interpretation and axiomatic and it is always possible to ask more "why's". e.g: Why is angular momentum quantized?).

    A set of papers exist showing exactly this ("how?") for the known elementary particles masses and the bosons widths - all decimals are correct - plus alpha and another constant that seems related to alpha_s; and as far as I understand it seems to be "only" coherently self-maintained geometry. But apparently, nobody read. The author states it is the field "below".

    In my opinion, if the author comes close to the real thing, there is absolutely no chance to get this from field theory. (I don't know for string theory).


  37. Markus,

    Yes, it is possible that we continue to find deeper explanations for some axioms, I am actually convinced that this will be the case. I also think though it's a fallacy to assume that these explanations necessarily have to be simpler. It might very well be that the next, more precise, theory that we find is not also simpler than the one we currently have. This idea that new theories need to be more minimalistic is, in my opinion, a great hurdle on the way to progress. Yes, it would be nice and it's what you want to try first. But if it doesn't work, you have to get over it. In the history of science, the quest for more fundamental laws has not always lead to greater simplicity. (As summarized maybe by the famous exclamation "Why ordered that?") Best,


  38. Testability? This isn't really a valid critique of the multiverse. I'm sure that George Ellis and so on believe what GR tells us about the interior of black holes, though this is just as impossible to test directly as is the existence of other universes. As Tegmark points out, multiverses are not a theory, but consequences of other theories, which have been tested in other regimes.

    Giving up? This isn't really a valid critique of the multiverse. It's no more of a problem that we can't explain the exact value of various parameters from first principles than it is that we can't explain the distances of the planets from first principles. Kepler tried, but had to give up his idea when the data said something different. Those who hope to be able to explain all parameters from first principles might be like Kepler with his Platonic solids.

  39. Are there many solar systems in the world? Yes. Are they separate? No.
    Are there many galaxies in the world? Yes. Are they separate? No.
    Are there many universes in the world? Yes. Are they separate? No. There is no such thing as separate in the world.

  40. Funny is the course of mental entropy.

    Why should parameters be explained from first principles? It is exactly like quantum mechanics being explained by classical physics.


  41. Depends on the definition of "separate". Certainly some multiverses cannot causally affect others.


  42. Let´s stick to the multiverse, Phillip!
    Do you mean that some universes are not causally connected?
    I find that hard to believe. Where do they exist? In nothing?
    To me multiverse is just that there are lots of Big Bangs in the world.
    I don´t think other universes are something else, just integrated parts of an infinite unit,like everything else.

  43. Mats,

    Phillip is right. Maybe I should have been more explicit on this, but most of these multiverses are causally disconnected. In other cases, one doesn't even know what an interaction would even mean. In Eternal inflation, yes, there are lots of 'big bangs', but they are not in causal contact with our universe, and will never be. Your question "where do they exist" is rather meaningless. It's like asking When does time happen? Best,



  44. Sabine,

    How can something be causally disconnected from something else?
    It does´nt make sense! What´s in between? Nothing?
    I don´t think something else exists. Best, Mats.

  45. Mats,

    To begin with your question "what is in between" requires there to be something like a space. It's a meaningless question in most cases. What is "between" the real numbers and a left-invariant subgroup?

    But leaving aside the stranger versions of multiverses, parts of space can be causally disconnected because the speed of light is finite. We don't see everything in our own universe either, only what's inside our backwards lightcone. (Though it depends on how you define 'our own universe'). In eternal inflation that's why we never see the other universes unless they collide with ours. Best,


  46. Hello Sabine,

    So when you say causally disconnected, you mean that our observation cannot connect certain parts of space (speed of light finite, eternal inflation).
    But that notion is different from saying that certain parts of space are actually causally disconnected.perhaps that is what Mats is aiming at. Do you see a difference between the two ?

  47. Just a little clarification:

    Tegmark discusses 4 levels of multiverse. IV is his mathematical multiverse, which is not mainstream. III are the many worlds of quantum mechanics in the MWI. II are "other big bangs", i.e. other regions where inflation has stopped (as Max points out, the big bang is not where something started, but where something, namely inflation, stopped); these are causally disconnected due to the speed-of-light limitation Sabine mentioned.

    What Max calls the Level I multiverse refers to what many call the universe. Max's "universe" is what many call the "observable universe". I don't like thinking of this as a multiverse, for various reasons, but at least Max defines his terms clearly and sticks to them. This is basically that part of space from which light has reached us since the big bang. It grows with time in co-moving coordinates (it could shrink with time in physical coordinates if the universe is contracting). We can't observe anything outside our observable universe, by definition, but a) it will grow in the future (whether it will encompass the entire universe, i.e. Max's Level I multiverse, depends on the cosmological model) and b) it is like the horizon on Earth: we can't see past our horizon, but someone, say, 4 km from us would have a horizon the same size as ours, with some overlap, but could see things we couldn't and vice versa. So, this is a bit different qualitatively from the other multiverses and there is some causal connection here.

    Of course, if you define the universe to be all that exists, then by definition there are no multiverses, but that is just playing word games.

  48. Noa Drake,

    I am having some difficulty parsing your comment. You seem to be saying causally disconnected is different from being causally disconnected. So let me offer the following explanation: Region A is causally disconnected from region B if no signal from A can reach B. An example is the inside of a black hole which is causally disconnected from the outside of a black hole, but also regions of space that recede faster than light because no signal from these regions can ever reach us.

    Now when it comes to manifolds, region A can moreover be geometrically disconnected from B, which basically means the spacetime falls apart into two pieces and there simply aren't any curves that go from A to B (not even space-like ones). Regions that are geometrically disconnected are also causally disconnected. But since GR doesn't say anything about the global properties of spacetime, this possibility isn't normally taken into account. It is basically what I meant though when I asked 'where are all the other solutions to GR?'. You could, in principle, posit that any solution to GR has its own manifold which is (geometrically) disconnected from ours. As I also said above, I don't really know what one learns from this though. Best,


  49. OkSabine, I understand and accept you explanation, under the convention of you definition of 'causally connected'.I believed for example that even if a region of space were to be receding from us faster than light (no signal could reach us), that this relation of receding from us is by itself a causal connection, with or without a signal. Hence my initial confusion. Greetings.

  50. The Principal of Finite Imagination II -

    I wonder, how have things changed?:)

  51. Sabine,

    thanks for answering my question about your thoughts on axioms. You may be swimming against the "mainstream" with that approach, but I think that could be fun :-)

    Concerning pt. 2, pt 3, the more I think about the fine tuning issue, assigning probabilities, etc., the more I get confused. I think it is better to stop thinking about it for the moment.

    You are right, we should not give up trying to constrain the degrees of freedom of our theories.
    Can you give a reference to the author, who did the calculations of parameters?

    One final question:
    I was wondering if a universe within a multiverse needs to be an actual one or if the potentiality of its existence would be enough. To make more clear what I mean, a simple example: Think of a hydrogen atom as our multiverse with one orbital occupied by an electron, representing our actual universe. When the electron changes its orbital, we would have another realization of a universe within our hydrogen multiverse (but we always have only one universe (=occupied orbital) at a time). Does that make sense ?

  52. The most sensible kind of multiverse is the quilted multiverse.

  53. The way in which I interpret Mats' question:

    If you believe in the string landscape and eternal inflation combination story (I don't), then in a sense the entire Level II multiverse is an "unit".
    That is, it consists entirely of "stuff behaving as per M-Theory equations" - which is what provides the unity - with the "different universes" corresponding to specific values of constants.

    But Tegmark's Level IV multiverse would not be an unit in even this sense, as there is no "overarching entity" which manifests itself as "stuff obeying all possible mathematical equations"

    There we go, not only am I discussing angels dancing on a pinhead, I'm even classifying them. :)

  54. In his book 'Science and Hypothesis', Henri Poincaré points out something that I might interpret as a multiverse problem. It boils down to the fact that a Lagrangian can be typically interpreted as a mechanical system in an unlimited number of ways.


    Poincare points out "...Maxwell has recognised that electric phenomena satisfy the principle of least action. He was then certain of a mechanical explanation", which apparently is in Maxwell's second volume.

    But there are an unlimited number of these choices.

    "How shall we choose from all the possible explanations one in which the help of experiment will be want- optics and electricity. The day will perhaps come when physicists will no longer concern themselves with questions which are inaccessible to positive methods, and will leave them to the metaphysicians. That day has not yet come; man does not so easily resign himself to remaining for ever ignorant of the causes of things."

    Poincare notes that some will be universally rejected because of their fantastic nature, and others will be preferred because of their simplicity.


    IMO, the answer is to abandon a mechanical explanation, and keep the Lagrangian.

    Our modern multiverse problem is different, but it is some similar bias, that led that generation of physicists to keep trying to construct an aether, that we have to figure out and discard.

  55. This was, for me, a very interesting opinion piece followed by a very interesting discussion. At the risk of being a child surrounded by adults, I have a few thoughts of my own to offer.

    It strikes me that every scientific theory remains science only as long as it proves useful in conducting further science. Once it stops being useful, it becomes fantasy. Since I am not a professional physicist, I cannot judge the usefulness of multiverse speculation in the conduct of genuine science. However, whenever practical physics moves into theoretical physics (which is always a good thing), it moves onto very thin ice where insisting on absolutes carries the risk of moving the physicist from the realm of science into the realm of magic. As a writer, I like multiverse theory because it provides an easy explanation for various fictional scenarios. Even though, it does seem a bit early to consider multiverse theory as valid science. As I pointed out, it risks proving to be more magical than practical. By the same token, it is still too early to dismiss it outright. At this point in time it is impossible to directly or indirectly observe the existence of any universe but our own. This does not mean it will always be impossible.

  56. Noa Drake says: I believed for example that even if a region of space were to be receding from us faster than light (no signal could reach us), that this relation of receding from us is by itself a causal connection, with or without a signal.

    You are right in what you say there. As you surmise, also correctly, definition is partly convention.

    Whether you're a potential genius or a daft bugger is decided in convention also.

    The current convention on that would you should have checked the dictionary you daft bugger


  57. Sabine,

    the problem with your definition is that it doesn´t make sense.
    If some other universes are causally disconnected from us they can not collide with us because to do that they must be causally connected to us.

  58. Mats,

    Why don't you go do some reading on eternal inflation and bubble collisions before complaining that the problem is me.

  59. MarkusM,

    In the fields, the author is (I think) trying to "decode" the parameters from a mass equation and to find their constraints. There are several papers, the most recent I know is the following (which includes reference to the author's work. The one concerning alpha is really bizarre):

    Concerning multiverse(s), there is a recent paper from the same author in Progress in Physics which (I think) I have quoted to Sabine some time ago:


  60. Mats - I know what you're saying but a definition of something doesn't have to make sense in the way that you obviously mean, which is 'natural sense'. For words to make natural sense on a regular basis, you'd need a situation in which common parlance followed definition with high fidelity. Does your natural sense say that happens very much, not very much or almost never? Right, almost never. So it goes the other way with definitions following common parlance, common usage.

    Seen that way, the way it is, you can make sense of 'causally [dis]connected' as presented. It means what the people and communities that most had a practical use for the word, whatever was of most practical usefulness. It turns out physicists find it useful to peg causality with the physical forces acting on arbitrary pairs of objects.

    What part of that ain't sensible? :o)

  61. Brian Miller says "It strikes me that every scientific theory remains science only as long as it proves useful in conducting further science."

    No one likes a smartass Brian.

    (but you are exactly right)

  62. Maybe it's because I'm more of a philosopher than a scientist, but my problem with the multiverse concept has more to do with Occam's Razor than anything else. Clearly such a theory, along with the closely related many world's theory of Everett, is a serious violation of the principle of parsimony behind Occam's formulation. As we are reminded in a cogent online summary of Occam's principle that I often quote, "Though the principle may seem rather trivial, it is essential for model building because of what is known as the "underdetermination of theories by data". For a given set of observations or data, there is always an infinite number of possible models explaining those same data." (

    The multiverse theory provides us with an example of such a model in amusingly literal form. Not only does it imply an infinite number of possibilities, it actually insists on them. One could call it the anti-Occam theory -- i.e., if no one explanation can be found to work, then any and all explanations must be accepted.


  63. DocG,

    I think you have a problem with certain nonsense interpretations of the multiverse theory, and thats why you think it´s closely related to the Many Worlds Theory. It´s not. Multiverse is just that there are lots of universes, not unlike our, like cells in the body.
    Does it make more sense that there is one solar system than many?
    Does it make more sense that there is one galaxy than many?
    Does it make more sense that there is one universe than many?

    Are other solarsystems other worlds?
    Are other galaxies other worlds?
    Are other universes other worlds?
    Of course not. There is only one world that contains a lot of universes.
    "infinite number of possibilities", no way. Only one. Merry&Happy

  64. On December 19, Arun asked

    "has it been shown that the set of string compactifications with a small cosmological constant and the set of string compactifications with a low-energy limit like the Standard Model have a non-empty intersection?"

    For the G2-MSSM, which employs F-theory, this is argued in arXiV:0906.5359.

  65. don't believe my autocorrect, that should read "M-theory"

  66. Yes I believe Arun raised an interesting point in the evolution and geometrical understanding of the membrane surface......matched toward experimentation we see in the bubble experimentations as a play along with the ideas of poincare.

    Felix Klein had an important warning about loosing touch With regard to The abstractness of mathematics with the real world......and such relation I believe require that play along.


    Ps. Merry Christmas to you and yours and thanks for helping the public to understand. Interesting question in relation to,the bumps at LHC current.

  67. The idea of the multiverse seems to have come from a common frustration in mathematical thinking, the problem of contingency. I remember Feynman had a long dialog in one of his lectures on what it means to be moving at 30 km/hour when one only travels for five minutes. I remember one of the characters arguing: "But, if you were going to keep going at that speed for an hour, you would have traveled 30 km." There is a problem with this kind of subjunctive reasoning, and it gets worse with probabilities. There are all sorts of philosophical arguments about what it means for a coin to have a 50:50 chance of coming up heads when it is only going to be tossed once. "Yes, but if you kept tossing it enough times ... ", "Yeah, but I'm tossing it into a black hole, so you go get it and toss it again."

    Quantum mechanics, I gather, is based on probabilities, and a lot of useful calculations involve summing up all the possible cases and their likelihoods, and this often includes cases in which things can't actually happen or exist. That has got to mess with people's heads. There's a certain comfort in believing that the universe is not contingent. All those calculated cases just shouldn't go to waste. Any single coin flip must be matched by another coin flip somewhere else, perhaps in God's mind, with the opposite outcome. That desire for subjunctive comfort gets you things like multiple worlds as opposed to multiple possible worlds and multi-verses as opposed to multiple possible universes.

    Biologists seem to be much more comfortable working with contingency and probability. They see a universe of possible organisms and chemical mechanisms, but recognize that those organisms we can observe directly or indirectly are just the result of coins being tossed. Somehow this doesn't seem to bother them. We never hear about the multi-biosphere arguing that there is a real world in which prokaryotes developed higher energy metabolisms and multi-cellular organisms, at least not outside of exoplanetary speculation. I wonder if it has something to do with the strong anthropic principle that underlies biology, sort of a here we are, deal with it thing.

  68. Mats Bergenhov says:
    "Does it make more sense that there is one solar system than many?
    Does it make more sense that there is one galaxy than many?
    Does it make more sense that there is one universe than many?"

    I'm sorry but...are you seriously suggesting naïve inductive extrapolations like that carry robust knowledge we can actually use? The line of reason is provably fallacious at the categorical level. Intrinsical logics dictate we hold back infinite regress, not embrace it as you there do. Anyone else invoking multiverses also too.


  69. Lucy,

    I think it makes more sense that there are many universes, but that doesn´t mean it´s the correct answer.

  70. Is the monoverse science? Is there anything in our observations that suggests that the universe we are causally connected to (at least in part) is unique or privileged? If our best current theories suggest that the particular properties of that universe are environmental rather than fundamental, do we have any reason to conclude that they do not or cannot differ in places and times we are unable to observe? I can't see any.

    I don't know why people are crying about the death of science when this is suggested... we are clearly still very far from properly understanding the bits of universe we can observe and interact with. Even if the ultimate conclusion when we do is that it is just the local environment that makes the universe we see behave like it does, if we have pinned down exactly how and why the environment produces the observables then I think we would have reason enough to be pleased with ourselves.


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