Tuesday, April 28, 2020

No, physicists have not explained why there is more matter than anti-matter in the universe. It’s not possible.

Pretty? Get over it.
You would think that physicists finally understood that insisting the laws of nature must be beautiful is unscientific. Or at least, if they do not understand it, you would think science writers meanwhile understand it. But every couple of months I have to endure yet another media blast about physicists who may have solved a problem that does not exist in the first place.

The most recent installation of this phenomenon are loads of articles about the recent T2K results that hint at CP violation in the neutrino sector. Yes, this is an interesting result and deserves to be written about. The problem is not the result itself, the problem is scientists and science writers who try to make this result more important than it is.

Truth be told, few people care about CP violation in the neutrino sector. To sell the story, therefore, this turned into a tale about how the results supposedly explain why there is more matter than antimatter in the universe. But: The experiment does not say anything about why there is more matter than anti-matter in the universe. No, it does not. No, not a single bit. If you think it does, you need to urgently switch on your brain. I do not care what your professor said, please think for yourself. Start it right now.

You can see for yourself what the problem is by reading the reports in the media. Not a single one of them explains why anyone should think there ever were equal amounts of matter and anti-matter to begin with. Leah Crane, for example, writes for New Scientist: “Our leading theories tell us that, in the moments after the big bang, there was an equal amount of matter and antimatter.”

But, no, they do not. They cannot. You don’t even need to know what these “leading theories” look like in detail, except that, as all current theories in physics, they work by applying differential equations to initial values. Theories of this type can never explain the initial values themselves. It’s not possible. The theories therefore do not tell us there was an equal amount of matter and antimatter. This amount is a postulate. The initial conditions are always assumptions that the theory does not justify.

Instead, physicists think for purely aesthetic reasons it would have been nicer if there was an equal amount of matter and antimatter in the early universe. Trouble is, this does not agree with observation. So then they cook up theories for how you can start with an equal amount of matter and anti-matter and still end up with a universe like the one we see. You find a good illustration for this in a paper by Steigman and Scherrer with the title “Is The Universal Matter - Antimatter Asymmetry Fine Tuned?” (arXiv:1801.10059) They write:
“One possibility is that the Universe actually began in an asymmetric state, with more baryons and antibaryons. This is, however, a very unsatisfying explanation. Furthermore, if the Universe underwent a period of inflation (i.e., very rapid expansion followed by reheating), then any preexisting net baryon number would have been erased. A more natural explanation is that the Universe began in an initally [sic] symmetric state, with equal numbers of baryons and antibaryons, and that it evolved later to produce a net baryon asymmetry.”
They call it an “unsatisfying explanation” to postulate a number, but the supposedly better explanation still postulates a number!

People always complain to me that I am supposedly forgetting that science is all about “explaining”. These complainers do not listen. Nothing is being explained here. The two hypothesis on the table are: “The universe started with a ratio X of matter to anti-matter and the outcome is what we observe.” The other explanation is “The universe started with a ratio Y of matter to anti-matter, then many complicated things happened and the outcome is what we observe.” Neither of these theories explains the value of X or Y. If anything, you should prefer the former hypothesis because it’s clearly the simpler one. In any case, though, as I said, this type of theory cannot explain their own initial value.

But here is the mind-boggling thing: The vast majority of physicists think that the second explanation is somehow better because the number 1.0000000000 is prettier than the number 1.0000000001. That’s what it comes down to. They like some numbers better than others. But, look, a first grader can see the problem. Physicists are wondering why X=1.0000000001. But with the supposedly new explanation you then ask why Y=1.0000000000? How is that an improvement? Answer: It is not.

Let me emphasize once again that the problem here is not the experiment itself. The problem is that physicists mistakenly think something is being explained because they never bothered to think about what it even means to explain something.

You may disagree with me that scientists should not waste time on trying to prettify the laws of nature, alright. Maybe you think this is something scientists should do with tax money. But I expect that if a topic gets media coverage then the public hears the truth. So here is the truth: No problem has been solved. The problem is not solvable with the current theories of nature.

55 comments:

  1. As I see it the problem is often misunderstood and or overrated. In simple terms, once could say that the Big-bang is a violation of conservation of energy anyway. Matter-antimatter imbalance if often associated with a zero-balanced-big-bang-energy event, which is of course not true.

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    1. Matter and antimatter does not annihilate to zero energy.

      Delete
  2. Your post makes the unwarranted assumption that the amount of matter versus anti-matter is a conserved constant. Nobody knows for sure whether this is true, but given that black holes can be formed entirely by matter, and probably create equal amounts of matter and antimatter when they evaporate, it seems very likely that it is wrong.

    If you believe the universe was at a very high temperature at its beginning, it would have been in equilibrium. If there is no conservation law that says that the amount of matter minus the amount of antimatter is constant, then the laws of thermodynamics tell us that at this very high temperature, all particles would have been equally likely, giving an equal amount of matter and anti-matter. So if this reasoning is correct, the fact that there is more matter than anti-matter today signals that there is some asymmetry in the laws of physics. And with CP violation in the neutrino sector, physicists just found more asymmetry than they previously knew existed.

    (Now you can argue about whether we know enough about physics to say that this particular asymmetry is the one that led to the creation of excess matter. I think we probably don't)

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    1. Peter,

      "Your post makes the unwarranted assumption that the amount of matter versus anti-matter is a conserved constant."

      I am merely explaining how the standard argument goes.

      "If you believe the universe was at a very high temperature at its beginning, it would have been in equilibrium. "

      You just made an assumption about the initial condition. I don't think you understood my blogpost.

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    2. People also assume an early 'quark gluon plasma.' It is not clear where this comes from.

      For sure, it seems QM and GM were married long before the invention of evaporating black holes.

      Delete
    3. Your blogpost says “The universe started with a ratio X of matter to anti-matter and the outcome is what we observe.” The other explanation is “The universe started with a ratio Y of matter to anti-matter, then many complicated things happened and the outcome is what we observe.”

      I am trying to explain that physicists have reasons for believing "many complicated things happened." What you wrote makes it sound like Occam's razor clearly would point to the first possibility, and that only some kind of perversity on their part makes them think the second is preferable.

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    4. Peter,

      "I am trying to explain that physicists have reasons for believing "many complicated things happened."

      Yes, you tried, but you didn't.

      "What you wrote makes it sound like Occam's razor clearly would point to the first possibility, and that only some kind of perversity on their part makes them think the second is preferable."

      That's correct, that is exactly what I am saying.

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    5. The ratio of matter vs. anti-matter doesn't have to be conserved, it could evolve over time also. But if it was disparate to begin with, then just like species of animals, one might go extinct and the other not.

      If we began with 10% antimatter and 90% matter, it would not be surprising for annihilations to leave 80% of the matter as 100% of what we now find, even if both matter and anti-matter are still being produced equally by natural processes.

      Once all the creation antimatter has been annihilated, the equal production leaves the modern ratio in equilibrium; 100% matter minus a scintilla of fresh anti-matter.

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    6. Was there enough time for equilibrium to be reached? T may have been very high, but t was very small.

      Delete
    7. I see nothing wrong when physicists want to play around with the idea that there were and/or are equal numbers of particles and anti-particles. That is true even if it is not proven, based only on esthetics. It's interesting, a source of fun and games. If you do not want to play that game, fine. But some find it entertaining.

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    8. t marvell: The fun in science is discovering new things about the real world, supported by evidence and rational argument.

      People that want to have fun playing with fiction can turn to novels, screenplays and songs, they shouldn't be doing it on the job and presenting their fictions in non-fiction forums and journals as professional work worthy of serious consideration.

      I have no problem having fun in their job, but not fun at the expense of doing their job.

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    9. I disagree. Let's look at a different example: the ratio of hydrogen to helium in the universe. This ratio can be explained by saying that the universe started with a plasma of elementary particles, and as it cooled, the neutrons and protons combined to form helium. Calculations show that if you assume this, with our knowledge of nuclear physics you can show that you get the He/H ratio that is observed in the early universe.

      But we could also assume that the universe was created at a later time and a lower temperature, with the current H/He ratio. Because our astronomical instruments can't look that far back in the early universe.here's actually absolutely no way of disproving this, However, I would assert that Occam's razor says that this is very unlikely.

      If we knew enough about the laws of the universe at energies near the Planck scale, the same thing might happen. So your blanket assertion it's not possible is very misleading, if not wrong.

      I would agree that the CP violation observed in neutrinos isn't currently sufficient to explain why there's more matter than antimatter in the universe. But saying that it's impossible to explain this is just wrong.

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    10. Peter,

      What you say is correct, but you are mistaken in thinking that this example is similar to the problem I have pointed out. You can indeed make a case that one initial condition (plus evolution law) is scientifically a better explanation than another initial condition (with another evolution law) if one of these explanations is computationally simpler.

      But the point you seem to have missed is that the number 1.00000000000 is in no way any simpler than 1.0000000001 and the evolution law that you need for the former is actually more *complicated* than what you need for the latter. Eg, by your own argument, you should disfavor the hypothesis of CP violation giving you today's ratio over the idea that it just started the way it is today.

      Delete
  3. I believe people assume the big bang is analogous to particle pair production from the vacuum, thus yielding equal amounts of matter and antimatter.

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    Replies
    1. But, there is no evidence for this. The BB is not covered by current physics.

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  4. I thought all particle physics experiments produced equal amounts of matter and anti matter hence the reason for where is all the anti matter

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    Replies
    1. Well, no, that's just wrong, sorry.

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    2. If you are trying to produce a Lot of positrons fir an experiment then act of producing then produces the same amount of electrons which you don’t need I thought ?

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    3. Alan, that is not correct. While pair production from photons would indeed result in an electron for every positron produced, that isn't the only process available. Beta-plus decay is mediated by the weak force, and produces a positron from a proton (which becomes a neutron in the process). This does result in the production of corresponding matter in the form of a neutrino, just as Beta decay of a neutron to a proton producing an electron also generates an anti-neutrino. But there doesn't always have to be an electron-positron pair.

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  5. If we had perfect time reversal symmetry, we could take the universe as we see it today as an initial condition and let it "evolve" into the past. What happens to matter/antimatter ratios as this time reversed evolution takes place? Or, we could go all multiverse (sorry) and say that matter/antimatter ratios are a free parameter among possible universes. Interesting point you made, in any case.

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  6. Copy edit: Last lines; "But I expect that if a topic gets media coverage the then the public hears the truth."

    --> "the then the" --> "then the".

    Thanks for the article!

    ReplyDelete
  7. I disagree. Not necessarily, but in principle it might be possible to explain why there is more matter than antimatter.
    In the 1980s there were 3 predictions from the theory of inflation. 2 have been confirmed by now. This is evidence for
    inflation. And, as your quote says, in this theory you do
    need an explanation (i.e. mechanism) for the observed large matter-antimatter imbalance.
    Because this imbalance evolved only after the birth of the universe with inflation, this is not an explanation of an initial state!
    And in principle there might be a good explanation from a later process, of course.
    Why not?

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    Replies
    1. How is it that people do not understand that it does not remotely matter that they "disagree" with me if they have no argument?

      No, inflation cannot solve the problem because inflation, too, needs initial conditions. Of course if you didn't have matter, then this is not an initial condition for matter, but it's an initial condition nevertheless. It doesn't matter how far back in time you push your assumption for the initial condition, it will still be there, and you still haven't explained it.

      The only way to explain an initial condition would be an entirely different type of theory, one that does not rely on differential equations, but we don't currently have such a theory. At least I haven't seen one.

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    2. Look, there is some experimental evidence that there really was an inflationary phase, (independent of what intial conditions were chosen etc.). In this phase there was no matter, only scalar fields. OK? These fields eventually decayed into matter. And then you search for a quantitative explanation for the observed (matter-antimatter)/(all matter) imbalance ratio of 10(-9).
      And because one can clearly not rule out in principle that such an explanation will be found one day, the title of your blog entry is wrong.

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    3. Experimental evidence for an "inflationary phase" (if there was any, which there isn't) would not be evidence for an inflaton or for its mode of decay. And even if there was any evidence for either (which there isn't, just to make sure that this fact does not get lost) you would STILL need an initial condition for inflation. The blog title is "wrong" to the extent that it does not add "with any of the theories that we currently know of", but I explain this repeatedly in the blogpost.

      Before you repeat your mistake one more time, I recommend you first think about what I am saying.

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    4. >The other explanation is “The universe started with a ratio Y of matter to anti-matter, then many >complicated things happened and the outcome is what we observe.” Neither of these theories >explains the value of X or Y.

      Exactly in this sentence is a thinking error, Sabine.
      Yes, Y is not explained and connot be explained. But in today's leading theory of the very early universe, inflation, the asymmetry we currently observe does not depend on Y. Rather the asymmetry we observe is COMPLETELY independent of Y. Your quote of Steigmann & Scherror tells us why.

      In inflation today's value for the asymmetry is SOLELY determined by the properties of the scalar field and its decay process, that happens "long" after the Universe's initial moment.

      And when the day dawns that we understand this process fully and it yields the correct observed value then this wil have explained, not Y, but today's value of the baryon asymmetry. And SUCH an explanation Steigmann & Scherrer clearly have in mind.

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    5. Franzi,

      "Yes, Y is not explained and connot be explained. But in today's leading theory of the very early universe, inflation, the asymmetry we currently observe does not depend on Y. Rather the asymmetry we observe is COMPLETELY independent of Y."

      This is wrong. The only way to make the outcome of a process "COMPLETELY independent" of the initial state is to have an evolution law that is not time-reversible. Any theory that has a Hamiltonian evolution is time-reversible, so what you say is incorrect. Steigman and Scherrer make the usual mistake that they think the size of a number is somehow a measure for its probability. What they mean by "erase" is probably "very small" (in some sense).

      "In inflation today's value for the asymmetry is SOLELY determined by the properties of the scalar field and its decay process, that happens "long" after the Universe's initial moment."

      Nope. The process still depends on the initial condition as well on what you assume happens in the decay. Look, as I have said, the problem that I am pointing out is a general problem with the kind of theory that we are using. It is not possible to solve it by going back in time and making further conjectures about further theories that have yet again the same properties.

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    6. Inflation makes the assumption that as per initial condition in the very early universe the energy density is dominated by a scalar field. If this is a correct description today's asymmetry is completely independent ("completely" in the sense "to exponential
      precision") from the initial Y. Right?

      You write "The [decay] process still depends on the initial condition...". Why? Because the field's existence does?! Then when I explain a decay process in a nucleus today, you say "that's no explanation, because the nucleus' existence still depends on the initial condition" (which it actually does)?

      Delete
    7. Franzi,

      " ("completely" in the sense "to exponential
      precision") from the initial Y. Right?"


      "to exponential precision" is not "completely".

      "You write "The [decay] process still depends on the initial condition...". Why?"

      Because, as I have said half a dozen times already, that's a general property of the theories that we use. They are one-on-one maps. They are time-reversible. I can't fathom how this can be so hard to understand. Do you want to seriously tell me that you have never thought about what determinism means? If you need a reminder of the math, look up Stone's theorem (the one for unitary groups).

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    8. > "to exponential precision" is not "completely".

      That's what I meant, sorry I am only a physicist and not
      a mathematician ;-)

      > that's a general property of the theories that we use. They are one-on-one maps.

      Same thing: I meant "The decay process does not depend on the initial condition to an exponentially good precision". Right?
      If yes: do we then finally agree that the baryon asymmetry might have an "explanation" in the sense phycists use this term in other more recent and familiar instances?

      Delete
    9. "do we then finally agree that the baryon asymmetry might have an "explanation" in the sense phycists use this term in other more recent and familiar instances?"

      Yes, as I said, they use it wrongly in many instances, and I am really tired of having to point out the obvious: That replacing one number with another number is not an "explanation", it is merely a reparameterization. And if one of these replaces require that you make the theory more complicated, then Occam's razor says you should discard this hypothesis.

      This is why leptogenesis is not a scientific explanation (at current stand of evidence) and neither is inflation, nor supersymmetry, and so on and so forth. These are all ideas that were created to solve problems which do not exist in the first place because physicists do not understand that "explaining" something does not mean "come up with a more complicated story".

      Delete
    10. > Yes, as I said, they use it wrongly in many instances...

      LOL! What does this answer mean? "Yes as answer to your
      question [so my particular blog entry was wrong] but in
      other instances "they" [people like Steigmann & Scherrer who do not listen to me] committed the mistake that I wrongly assigned to them in this instance." Is this a correct reading?!

      Delete
    11. Franzi,

      Excuse me for temporarily thinking you had finally understood what I said. What I write in my blogpost is, needless to say, entirely correct. It is an utterly trivial point and it is frankly an embarrassment that physicists do not seem to understand it.

      Steigman & Scherrer are as wrong as most people in the field when it comes to inflation. The reason I did not go on about this in my blogpost is that, as you may have noticed, the blogpost is not about inflation. Hope that clarifies it.

      Delete
  8. So, even if CP violation gets entirely verified, we still cannot use it to prove that the universe started with a ratio of 1.0 of matter and antimatter, right? That is, for what we know, the universe could have started with more matter than antimatter regardless of CP asymmetry. Am I getting it right?

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    Replies
    1. Ruben,

      That's correct, but that wasn't my point. My point was that even if CP violation in the neutrino sector reaches the currently accepted confidence level for a new discovery, and even if you could then argue that the universe could have started with equal amounts of matter and anti-matter, then this would still not explain any more than just saying the universe started with whatever ratio happens to fit to today's observations.

      Delete
    2. I see. With such a hypothetical discovery, the only thing we can say is that the proposed one-to-one ratio might be possible, but without providing any reason to favor that possibility over any other ratios that could also evolve in the universe we observe.

      Can we go as far as to say that such discovery would only "not disprove" the one-to-one proportion of matter/anti-matter?

      Delete
  9. Modern science describes "how" and doesn't explain "why", that's really basic philosophy of science.

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    Replies
    1. Probably "what" rather than "how", as the latter still has the essence of "why" in it.

      Delete
  10. Rather glad to read this post about what physics does not really tell us. It is my many years of experience that many physicists dream up nice problems and later they and friends publish fantastical solutions to these problems. SH presents a nice example here - CP violation by neutrinos. Without reading any "serious" publication about the neutrino results I doubted any relevance. Thanks to SH I now needn't bother to read.

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  11. Thanks for that, I read the reports in news articles and I hadn't realized I had just assumed 'well of course equal amounts of matter/anitmatter' but the minute I think about it I realise I never had considered why?

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  12. This that I am going to say is only speculation; In a previous post I had said that if the proton disintegrates, the resulting positron would cancel with the electron and the problem of the difference between matter and antimatter would disappear and only a symmetric space and radiation would remain; what maybe there is no more quantity of matter than antimatter, maybe everything is misconceived. But surely I am wrong 100%.

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    Replies
    1. If you are surely wrong 100% I recommend you do not submit a comment about it.

      Delete
  13. Apparently being pro matter is an inescapable property of the world. Why? Maybe we don't have enough understanding of the resultants of rhe electromagnetic, weak and strong interactions. Moreover gravitational effects are not taken into account as yet. So I do think that saying that it is impossible to understand why is too pessimistic.

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  14. Hmm, to be fair I gave up on the comments above:-) but really professionalism is the issue here. Why is it so important to be right all the time? We should all step back and take a deep breath. The sun is still shining despite our best efforts.

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  15. I agree with a part of this and question another.

    What I agree with is this result with neutrinos is the same CP or chirality result as the Kaon problem going back to the 1950-60s, which is in a sense repeated with the CP violation result with the b quark and so called “b-machine physics.” In effect all that has been found is that chiral or CP violation is a feature of elements of quark and lepton doublets. This is a nice result, for it tells us the violation of parity by weak interactions is universal.

    I would call into question the statement this can never be understood or understood according to something more fundamental. It is the case the standard approach to physics is to impose boundary and initial conditions that give enough data to solve differential equations. However, consider the Laplace transform. This is a way of transforming a function f(t) into F(s) = ∫e^{st}f(t)dt, which is for s = a + iω is really a more general transform than a Fourier transformation. We have then the derivative of a function df(t)/dt transforms to sF(s), and solutions to differential equations can be had with polynomials. There are these pesky boundary terms that are usually ignored, at least for practical use, and these are treated according to initial and boundary condition imposed by hand. However, this is telling us something, there is in the physics what amount to integration constants that are tied to boundary terms or in effect topology. There is a possible hook here for looking at initial conditions or boundary conditions from a more fundamental ground.

    In effect these initial or boundary conditions could be understood as topological effects. These boundary terms can include cocycles, so what is topological is ker(φ)/im(φ) may be boundary conditions that have no boundary; they are determined topologically. The Laplace transform approach leads to polynomials and in a theory of rings or p-adic groups this tells us about the K-theory of these fields. I will not go further, lest I be accused of being lost in math.

    As Peter Shor points out, black holes can convert a large amount of matter into equal portions of matter and antimatter. I happen to think this information is communicated by weak gravitons or BMS symmetries that reach I^{+∞}, and this is topological information that is contained in spacetime itself. The Hurzebruch theorem for a higher order action term ∫d^4xR_{abcd}R^{abcd} is associated with ∫d^4xR_{abcd}*R^{abcd} term for * a Hodge dual. Edge states in solid state physics have Lagrangian terms EB of this form. BTW, the axion has a differential equation with this term, where the axion is considered to “carry” the CP violation of QCD.

    As a result I do think there is some very deep problems here. The origin of CP violation, or a more fundamental ground for this chirality effect, is to me a very important question.

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  16. It always seemed to me was not the claim that one set of initial parameters, like a matter universe with anti-matter speckles, versus a fifty-fifty distribution, is better than the other. The issue I thought was trying to avoid initial parameters at all, because initial parameters may as well be given by God.

    And the difficulty in avoiding arbitrary parameters came from the observation that currently physical processes that produce anti-matter---*if* I recall correctly---do in fact tend to produce matter and anti-matter more or less in equal proportion. The notion that the basic physical processes at work in the very early universe are apt to be like those at work today does tend to assume that somethings need to be explained, at least with some ideas that have more detail than God or Copenhagen. Or don't openly avow that science isn't in the business of describing reality, it just makes predictions, correlates experimental setup and outcome.

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  17. You cleared up a lot for me about this. I was always under the impression that if you extrapolated the math from our current theories backwards in time, they would show an equal amount of matter and antimatter in the early universe and that is what scientist were struggling to explain; similar to running GR backwards in time and getting a singularity.

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  18. What about statistical symmetry breaking - making equilibrium statistically repelling due to some "the more the easier" rule?
    Like for life's chirality: the more e.g. life based on D-amino acids, the more material of this type is in environment, the easier reproduction of this type of lifeforms.

    For matter-antimatter question, there would be needed some rule "the more (anti)matter, the easier to produce (anti)matter", finally leading to complete domination of one of them.

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    1. Jarek Duda: I believe that IS the argument being made, it is just a statistical argument.

      Say at creation X particles of antimatter were created, and (X+Y) particles of matter were created.

      As matter and antimatter collide, they annihilate each other. But there is more matter than antimatter, so we end up with ((X+Y)-X)=Y particles of matter, and nothing else, so 100% of what we see is matter.

      To a first approximation; some small amount of primordial antimatter may remain, having escaped meeting matter so far, and processes can create new particles of antimatter, but normal matter dominates the universe because it won the war of attrition with antimatter.

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  19. It seems to me Occam's Razor is a metaphysical principle, that no explanations that invoke unnecessary entities (as in Platonic ideals or physical laws) are in fact explanations at all. In this situation, invoking imaginary physical processes that have already produced a matter universe with anti-matter speckles, so that contemporary physical laws generally produce a fifty/fifty split is the complex hypothesis according to Occam's Razor.

    The objection that nothing is being explained forgets the covert assumption that science never explains anything, it just makes predictions.

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  20. "Truth be told, few people care about CP violation in the neutrino sector."

    Probably the understatement of the year. :-)

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  21. "1.0000000000 is prettier than the number 1.0000000001. That’s what it comes down to."

    Most believe something like this. Whether most would identify it with beauty, I don't know. The reason is that if the ratio is not exactly 1, then you have to explain why it is what it is, whereas if it is exactly 1, then there is probably a deeper underlying reason for it.

    The point is that all such numbers are not on equal footing. This is basically the same item on which I disagree with what you say in your "Screams for Explanation" paper. Now that that has been published, I have more motivation to get my rebuttal published, so I'll shut up for now and get back to work.

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  22. I'll bite ... and possibly choke on it.

    Simplified down to my level what you're saying is:
    We postulated that c (what we see) equals a plus b. Now, average 6th grader would tell us that this can not be solved. Two variables, one equation. That same grader would then probably shrug and walk away. But nobody in their right mind is going to be funding a shrug for 40 years. So, some more savvy peer of theirs might go on and study this some more. Start throwing fancy math at it, mangle poor equation until cows come home, pile assumption upon assumption, discard this and that (after all, they are practical), develop and run simulations that show same old c at different values of a and b and claim that particular (moving) picture shows how their solution to values of a and b is the correct one.
    And when some other savvy ex-6th grader, possibly more rooted in reality and less worried about finances and/or glory, points out impossiblity of presented values of a and/or b, they go for different pair. I mean, any can do so why the hell not?
    How's my Fourier transformation doing? I've set some boundary conditions and discarded some infinities, maybe some zeroes too but over the thumb, am I even in the ballpark?

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