Talking About Dark Matter and Dark Energy

Trying to keep these occasional Facebook Live videos going. (I’ve looked briefly into other venues such as Periscope, but FB is really easy and anyone can view without logging in if they like.)

So here is one I did this morning, about why cosmologists think dark matter and dark energy are things that really exist. I talk in particular about a recent paper by Nielsen, Guffanti, and Sarkar that questioned the evidence for universal acceleration (I think the evidence is still very good), and one by Erik Verlinde suggesting that emergent gravity can modify Einstein’s general relativity on large scales to explain away dark matter (I think it’s an intriguing idea, but am skeptical it can ever fit the data from the cosmic microwave background).

Feel free to propose topics for future conversations, or make suggestions about the format.

54 Comments

54 thoughts on “Talking About Dark Matter and Dark Energy”

  1. Suggestion for a future FB video or blog article:

    You are scheduled for an MIT Physics colloquium talk on Dec. 8th about “Extracting the Universe from the Wave Function.” (http://web.mit.edu/physics/events/colloquia.html) Unfortunately, unlike many universities that publicly post videos of colloquia talks, MIT apparently does not.

    From this upcoming talk’s abstract, it sounds like this might be related to your blog post on “Space Emerging from Quantum Mechanics” (https://www.preposterousuniverse.com/blog/2016/07/18/space-emerging-from-quantum-mechanics/) and possibly your FQXi talk “What Events Lurk Inside the Wave Function.” (http://fqxi.org/community/forum/topic/2682). But even if so, you might have new material to report about it.

    So since the MIT talk won’t be publicly available, it would be great if you could discuss the topic either on FB or here in your blog.

  2. Tom Clark,

    Sorry I just saw your remarks. I forgot to click the “Notify me of follow-up comments ..” box. Good point about direct and indirect observational evidence, in general.

    Almost by definition, dark matter is dark because they interact only gravitationally (“indirect in this context), and not say, electromagnetically (our usual understanding of “direct?”). Then there hopefully is no need to bring up the obvious?

    In other words, the existence of dark matter from the days of Vera Rubin (and before) are all indirect evidence. Hope I’ve not misunderstood you.

    Best,

    KC

  3. Thanks, Sean! When I saw that the subject of your talk was papers that suggest that dark matter and dark energy might not be necessary to explain an accelerating expansion of the universe, I thought that one of the things you would be discussing was a news item I saw on Facebook that claimed that (I hope I’m remembering this right) we are now aware that there are many times more galaxies than we thought there were, and that all that extra mass was enough to explain the accelerating expansion of the universe. Is that a thing, or did I dream it? 😉

  4. KC: “…dark matter is dark because [it] interacts only gravitationally…In other words, the existence of dark matter from the days of Vera Rubin (and before) [is based all on] indirect evidence.”

    That’s to say there are reasons to believe in the reality of dark matter (DM) and dark energy (DE) based on observations of ordinary matter and inferring what needs to be the case to account for those observations within widely accepted theories, e.g., of gravitation and cosmic evolution.

    What would help seal the deal on the unequivocal reality of DM and DE are observations, e.g., in the lab, that are more or less independent of, but consistent with, these theory-laden inferences. (Maybe this helps define “direct observation”: not beholden to theory.) Such observations would likely reveal characteristics of DM and DE that go beyond what’s needed to account for their gravitational effects on ordinary matter. We would get a better grip on what DM and DE are in themselves, so to speak, which would justify greater confidence in their reality.

  5. Tom Clark,
    Thanks for clarifying. Your “direct vs. indirect” are better understood.
    1) For direct observation of DM in a lab, there has been no lack of efforts. So far, they’re to no avail. May yet succeed. Please note that if DM interacts only via gravitation, and if DM is made up of particles, it is unlikely that such particles have large enough gravitational interaction to be suitable for laboratory investigation or detection. One shall see.
    2) DM and DE perhaps should not be lumped together too readily. Their darkness reflects our lack of knowledge more than any physical meaning. For example, there’s no dark E=mc² type relationship known. A favorite statement is: “Using DM to study DE is employing something we know little to study something we know even less”.

    JRDMB,
    Thank you for alerting us to the December 8 colloquium at MIT. I may be misunderstanding the title “Extracting the Universe from the Wave Function”. To me, it could suggest “GR spacetime emerging from QM entanglement”.
    If so, there are theoretical papers on the subject (Van Raamsdonk 2010, Orus 2014, Swingle and Van Raamsdonk 2014, Lin et al. 2015). Could include Susskind, 2016 (“ER=EPR”) and the Maldacena correspondence, if so desired. All papers are on-line.
    No practical scheme allowing that emergence has been proposed to my knowledge. One way to approach the subject might be to highlight the role of entanglement in any measurement. With that in mind, one could then consider: “Extracting the Universe by Measuring a QM ‘Substrate'”, (thereby branching or collapsing the wave function of the universe in that substrate).
    If such a substrate exists, it is unlikely to be physical (my October 10 comment in Sean’s September 25 “Live Q&As Past and Future”).
    For the previous statement not to be true, either a property cannot exist before measurement, or if it exists, it has to be physical. They may be more difficult to prove than detecting DM in the lab?
    Until disproved, meanwhile, I’m exploring what a non-physical substrate could possibly mean. Some “work-in-progress” ideas appeared in relationship to an article about Steven Weinberg in “Why QM might need an overhaul” in ScienceNews under “GuoZhang LEE”, the Madarin “spelling” of my name.
    In any case, looking forward eagerly to Sean’s deliberation at MIT.

    randal sexton,
    Correct me if I’m wrong, the Bullet Galaxy suggests DM does not interact even with itself (the way baryonic matter does). In a collision, they pass right through each other.

    KC

  6. Verlinde’s approach has ST emerging from entanglements. I wonder if the details of ST from that approach has an impact on the prediction of Hawking radiation at the BH event horizon, bearing on the information paradox.

  7. bostontola,

    Thanks to your question, I revisited Sean’s video yet again, this time bearing your question in mind. It seems that as long as Verlinde takes a MOND approach, his effort will be found lacking, compared to cold DM models, according to Sean.

    Sean’s explanation recalls another facet of the Bullet Galaxy (last comment to randal sexton). There is some parallel between how baryonic vs. DM acoustic oscillations in CMB behave, and how the DM component of the Bullet Galaxy ends up, after a head-on collision, further ahead of the baryonic component, since DM does not interact with anything, while the baryonic component of the galaxy does.

    Another diversion, in passing, is the way Sean describes CMB acoustic oscillations (both baryonic and DM) as a function of the size of regions involved, reminds one of fractalness/self-similarity/symmetry in general, within the CMB. These might be worth pursuing for those interested.

    Hawking radiation was not mentioned by Sean specifically. But since MOND is still GR per se, one might assume the baryonic component of a black hole remains as is, Hawking radiation or not. Whether the DM aspect, as per Verlinde, influences Hawking radiation is not obvious. The best person to answer is Erik Verlinde.

    Meanwhile, if there does exist a non-physical “QM” substrate from which GR spacetime, including black holes (and its Hawking radiation), emerge via entanglement (my last comment), and if DM could possibly be black holes (November 12 comment), DM and black holes may both have emerged from a non-physical substrate.

    If “non-physical physics” seems too far-fetched, look no further than the wave function. We’ve been using it for nearly a century. Yet, physics never has full physical access to the entire wave function.

    In case a non-physical wave function (e.g. psi-epistemic) engenders less resistance, be informed that it may provide a simpler explanation of the Uncertainty Principle. QM measurements yield uncertain results because we only have physical (classical) rulers. Using a physical ruler to measure a non-physical “object” naturally gives us uncertain read-outs. But then we’ve diverged too much.

    KC

  8. KC,
    Thanks for the thoughtful response. After reading Verlinde’s paper, I don’t regard it as taking a MOND approach per se. It predicts MOND at large scale, but it has it’s own character at micro scale. It’s the micro character of ST that I’m interested in regarding Hawking radiation and information paradox. If the micro structure impacts behavior of the horizon, it may predict effects that differ from Hawking. I’m not an expert, so I’ll be happy to wait to see.

  9. bostontola,

    Attempts at reconciling GR and QM involve “modifying” GR to some extent, whether using Milgrom’s, Verlinde’s or other approaches. I should have been less ambiguous in that regard. Thank you for the correction .

    Following up on my last comment, “non-physical” physics, if correct, could offer an exception. Similar to its explanation of the uncertainty principle, the idea is simple. It says that GR physicality, when appropriate, yields naturally to “QM” non-physicality. With that, there is no need to modify Newton or Einstein. At a black hole, for instance, Einstein’s field equations simply cease applying , rather than failing in infinities.

    Surely, that sounds absurd. In the last comment, the reminder of the non-physicalness of the wave function itself plus psi-epistemic opened a small crack. At black holes, we are reminded that Einstein himself, though he flip-flopped in 1916 and in 1939, had held essentially that black holes are not physical.

    Today’s black holes correspond largely to the Schwartzscild metric, which was endorsed by Einstein in 1915. Einstein reaffirmed that in 1939 (“On a stationary system with spherical symmetry consisting of many gravitating masses”, Annals of Mathematics Vol. 40(4): 922-936). In that paper, Einstein made two points: 1) the sphere (at the Schwartzschild radius) constitutes a place where the field is singular and 2) a clock kept at this place will go at the rate zero.

    If we take Einstein seriously (and apply his wisdom to the possibility of “non-physical” physics), at black holes, clocks stop. Without time running, spacetime can take a rest. With no GR spacetime, Einstein’s field equations need not be pressed into further duties and fail eventually.

    This is a roundabout (and unconventional) way to get to your Hawking radiation. But the answer, as in Heisenberg uncertainty, should be evident.

    KC

  10. Even though inertia and gravity may not actually be quantifiable, it seems like inertia should be thought of as being quantized, because the air resistance felt by planets, like Earth, doesn’t slow down their rotation. If someone was to add up all the air on Earth hitting the trees and added that all together, then it should create a force which would slow down the Earths rotation, but it seems like it doesn’t (along with other small scale events taking place on the surface).

    This could be due to each individual force acting on each individual tree isn’t strong enough to alter the Earths rotation by 10^-34 cm over a time period of 10^-34 sec. Then instead of energy being lost in such a circumstance into the Planck Scale (an immeasurable difference), the energy would only be dissipated in other methods at each individual tree. The wind would just hit a brick wall, in a manner of speaking. Then it could be possible that it could require a certain amount of gravitational pull in order for it to have an affect on other distance objects in a galaxy or the universe, like a scaler to the amount of force required to act on an object.

    Anyways, I think there was a women who studied under Brian Green, which developed a theory of gravity leakage through higher dimensions to explain dark matter years and years ago. I believe that it would still be the most likely candidate to explain dark matter, considering what has been recently brought up about the subject. I think it could be possible that gravity leakage would be a likely candidate to explain the dissipation of harmonic oscillations of the big bang, if you consider the possibility of there existing failed alternate universes which did not bounce back. If merging the two theories fit the data in some way, then it could provide evidence for alternate universes.

  11. bostontola,

    No physical spacetime, regardless of how coarse- or fine-grained (see below), then no Hawking radiation. But that still leaves your question about information not addressed.

    My two previous comments, together, hint that both at the GR scale and at the QM level, physicality is key. For GR, field equations fail when things get “too physical”. For QM, the Schrodinger equation (or the wave function it describes) is “not physical enough”. It lacks a clear physical understanding. Why QM works so well despite that is another topic.

    Not obvious is that physicality (GR), or lack thereof (QM), could provide one avenue to unity. Rephrased, “No matter how much one scales down spacetime toward Planck (or string) length, or scales up Hilbert space toward some classical phase space, our standard physical-only language always puts a road block on quantum gravity efforts”. Invoking a non-physical substrate, as is done here, might circumvent that road block. Incidentally, it also leads back to your question about information at black holes.

    Taking seriously the idea of spacetime emergence from QM, where “QM” is a non-physical substrate (Comment on Nov 17 to JRDMB), it is reasonable that the substrate contains information “coding” for not only spacetime but other GR items. If black holes are speculated to be part of that substrate, your question has an answer: The information that went inside a black hole could be “re-used” for subsequent GR emergence.

    A system of such information recycling has been worked out. It’s a subject for another day. Meanwhile, a non-physical (“QM”) black hole recasts both the information and firewall paradoxes. Quotation marks are used because strictly speaking, QM, as is understood, is actually that non-physical substrate, described in classical physics (physical-only) language. To confess, I do not know what that non-physical substrate should be called, in its own language. A language that tolerates non-physicality.

    Incidentally, one major road block of its own, for non-physical physics, is the challenge to come up with a traditional equation, without speaking the traditional physical-only language. Still, even though one has no name yet for a language that tolerates non-physicality, freeing ourselves from the box set by our physical-only language, and see what physics could be like beyond, seems a good idea.

    KC

  12. KC,
    Actually, if there is no Hawking radiation then it would eliminate the information paradox. Hawking radiation is treated as thermal, so the information is lost. I am wondering if the detailed structure of the event horizon affects the radiation in a way that preserves the information in a fully quantified way. If so, there may be ways to design experiments that predict different results for that geometry and say the smooth continuous GR geometry, making it a testable theory. These same details may account for the issues that Dr. Carroll calls regarding the dissipation subtleties.

  13. Bostontola, you have it completely backwards regarding the information paradox. Hawking radiation is supposed to be the cure for the information paradox, the thing that prevents it. The problem was that information is lost when an object falls into a black hole. Then information can get out of a black hole via Hawking Radiation. I just never understood why it is always the negative particle and not ever the positive particle that end up falling into the black hole, which allows it to evaporate.

    I find it odd that information or energy is conserved in such a manner. To me, the whole theory implies a causal link between random particle pair production and black holes, as if random particle pairs are leaked through spacetime from black holes (not to put words in Hawking’s mouth, really). Then I don’t think microscopic black holes could evaporate, because random particle pairs only occur about once in every cubic meter of space, so then there would be no physical interaction between the particles and the microscopic black hole, regularly. Then Hawking Radiation becomes less accurate on smaller scales.

  14. John,
    The Hawking radiation as originally defined caused the information paradox. There are a number of modifications aimed at solving it, but none have been verified. I was wondering if Verlinde’s formulation may predict one of these solutions. If you want to clarify your thoughts on the information paradox, there is a reasonable description on Wikipedia.

  15. bostontola,

    Thank you for your further thoughts including “Actually, if there is no Hawking radiation then it would eliminate the information paradox. Hawking radiation is treated as thermal, so the information is lost”. The second sentence shows why it is prudent, regardless, to have an information recycling scheme. Whereby:

    1) To the question, “Is the information of a particle lost?”, the answer is “No, it is not. That information returns to the non-physical substrate”.

    2) To the question, “Can the returned information be used to recreate a given particle?”, the answer is “Yes, but after randomization inside the non-physical substrate, one might as well regard the particle (though happened to be made from that returned information) as a new random particle, despite looking like the old particle”. It becomes a matter of preference.

    3) To the question, “Why the randomization?” The answer is, “To conform to nearly 100 years’ worth of observational evidence in QM experiments such as the double-slit. The randomization guarantees emergence will yield a random result”.

    4) Anyway, for this proposed scheme, information is better thought of as being conserved not per particle, but conserved by treating the physical GR domain and the non-physical substrate as a single mutually cooperating entity in the universe. As spacetime is among what is being recycled, if one thinks of this as a kind of quantum gravity scheme, that’s not too unreasonable.

    Surely this sounds too outlandish. So allow me to recount why non-physical physics is considered in the first place. It was not pulled out of thin air. Nor was it designed to solve the information paradox. Instead, it grew out of a thought experiment involving a “universe-size multi-slit screen”, modified from the standard double-slit experiment (Personal communications with Frank Wilczek, September 19, 2016). Its significance and utility merely “fell out”, as if from a traditional equation. The application at a black hole is just one example.

    Addressing further remarks by bostontola, a non-physical black hole no long has an event horizon (nor any geometry). Instead, there would be a sharp border where GR spacetime becomes non-physical. At that point, Einstein’s field equations stop functioning, naturally, as there is no more physical spacetime to need their application.

    Nor would a non-physical black hole need any “thermal treatment”, either via straight up entropy per Beckenstein, or with string overtones per Verlinde. But do proceed with your efforts to see if the latter offers a better resolution of the information paradox over the various existing options. The non-physical option proposed here does sound too simple and extraordinary. It will definitely require extraordinary proof.

    Meanwhile, with a non-physical model, at the risk of excommunication, the “no drama” interpretation, despite apparently countering Einstein’s own views in 1939 (yesterday’s comment), is obviously no longer in force. Again, the main advantage of a non-physical model is the removal of a physical singularity, and with it, the salvage of Einstein’s field equations from infinities.

    With no point singularity, cosmologists need not bypass it using quantum tunneling as in Gielen and Turok (“Perfect Quantum Cosmological Bounce”, Phys. Rev. Lett. 117, 021301, July 6, 2016), or in similar efforts by Rovelli and Mersini-Houghton (two references each in 2014 and 2015), just to mention a few. Nor is there as need to resort to a Euclidean spacetime involving imaginary time (Hawking, “A Brief History of Time” Bantam Dell Publishing Group, 1988).

    If all this sound too fanciful, can always trace back to the universe-size multi-slit screen thought experiment which, in principle, can be experimentally confirmed.

    KC

  16. bostontola,
    I have always thought of information and energy as being interchangeable in their description, but I guess that Hawking Radiation would allow conservation of energy without giving up information about what is inside, if that is what you mean.

    I think, if the theory of gravitational leakage through higher dimensions is valid, then Hawking Radiation wouldn’t be necessary to explain conservation of energy problems that would occur in a black hole. Gravitational energy could escape and possibly information about the mass inside of it. I think it is a shame that the theory would have to go up against such a big contender, such as Stephan Hawking, but Hawking Radiation has been debated for decades about its validity, and I don’t think theory really holds up as being accepted among the scientific community from it. Every Ph.D. which writes a book about it only mentions that scientist don’t agree on it…

  17. Your conversation just reminded me of that, because every other theory in physics which deals with conservation of energy has a casual link between the events (you can quote something if I am wrong about that). The transfer of energy requires a physical or causal link between the events. Then particle pair production was shown to create energy, and black holes showed that they could make a system lose energy. Then it was like Stephan Hawking just put together the only two concepts in physics that violate conservation. Then that really leaves the question if that was done in the correct manner, since there is no causal link described between the black holes and the appearance of random particle pairs. Then it would seem like there would have to be a causal link between the two events, since the theory is attempting to show how everything in physics is conserved from those being the last two things in it that appeared not to be. Then I am not sure if that was truly the motive of Stephen Hawking when he developed the theory, but it sure seems like it. Then there is no causal link between the gravitational pull of the universe and dark energy either, even though the numbers would suggest that they conserve each other in some way…

  18. KC,
    Isn’t a sharp border where GR spacetime becomes non-physical just a horizon? I guess you could define the discontinuity in some way differently, but then it becomes arbitrary doesn’t it?

  19. bostontola,

    1) “Isn’t a sharp border where GR spacetime becomes non-physical just a horizon?”
    You are correct. It’s similar to an event horizon. In fact, the non-physical proposal generally keeps all existing terminology (and equations, with their successes). Only the interpretation are new. Consistent with the simplicity of the non-physical scheme, I just chose the most direct way to describe that horizon.

    The name used by current physics is “event horizon”. While “no drama” is also a rather simple characterization, unfortunately, it has led to problems such as the firewall paradox. Further, there is a lack of consensus on how the event horizon should be defined. This can be illustrated just by tracking how one expert, Stephen Hawking, changed his mind over time, let alone a whole host of others.

    Not only is a sharp border of non-physicality clearly understood, and free of a firewall paradox, it has many other advantages. Not the least are salvaging Einstein’s equations and averting a singularity. Neither is offered by current physics. That certainly does not make a non-physical proposal correct. It is just one of many alternatives.

    Incidentally, one could think of “no drama” as sentencing Einstein’s equations to eventual failure. A non-physical horizon commutes that sentence to life. A life of useful application just short of the non-physical/physical horizon.

    2) “I guess you could define the discontinuity in some way differently, but then it becomes arbitrary doesn’t it?”
    Certainly. It comes down to two criteria. 1) Does it offer advantages over existing alternates? 2) Will it endure Occam’s razor?

    While on the subject of horizon, what Frank Wilczek and I agreed, that the interference bands at the observable horizons would be very thin, is not entirely correct. I’ve since realized that if we take an identical photon and repeat the experiment at one of the observable horizons, we should get identical interference bands as we did on Earth. That is, the interference bands that Wilczek and I thought would be very thin, will be thick instead, as thick as the ones found on Earth.

    What that says is the location of an experiment affects what is observed. Wilczek and I are correct if the experiment is carried out on Earth. But as one moves the experiment toward one horizon, the center of that universe-size multi-slit screen is also moving along with the experimenter. That’s why the interference band thickness will change accordingly.

    The key to a confirmatory experiment is to use the same photon on Earth as at the edge of a horizon. The end of my last comment suggests that such an experiment is in principle doable.

    A simpler way of thinking about the situation is that the observable universe moves with any observer or experimenter. The “observer” part is elementary. The “experimenter” part is usually overlooked (until we are faced with a universe-size multi-slit screen).

    Will save why this might possibly explain how we fool ourselves into thinking the LHC could show particle tracks in a bubble chamber for another day.

    KC

  20. I thought Hawking got hustled by Susskind to retract his theory, because of Susskind’s idea that the information would be stored on the event horizon and never fall inside the black holes. In SR, an object cannot detect its own time dilation. In GR, I don’t think that concept has been made perfectly clear among the scientific community, or if it has, I have been left out of that. If you assume that gravitational forces are truly equivalent to forces of acceleration, in every respect, then an object being pulled by the force of gravity should be able to detect its own time dilation, since an object undergoing acceleration would, as according to the solution of the Twin Paradox. Then both observers would just measure both of their clocks slowing down as they fell into the black hole. In other words, the person falling into a black hole would know that they are the one falling into a black hole and that their time would actually be dilated. Then I didn’t think time dilation was supposed to influence an objects forward velocity to begin with in SR or GR.

    It makes me wonder if these types of black hole solutions could be flawed, because they treat the hands of the watch as the whole watch itself. It would seem like if a watch fell into a black hole, that only the hands of the watch should slow down, not the whole watch falling itself due to time dilation. Then a watch would be spaghettified, so it would make it extremely difficult to distinguish such a difference in thermodynamic based solutions; it would seem from what I have read about them from Carroll’s book, Particle at the End of the Universe.

  21. bostontola,

    Thank you for drawing our attention to a good article on Verlinde’s entropic gravity by Wolchover. Verlinde thinks he could replace DM with DE interacting with visible matter. Right off the bat, that is explaining something we know little using something we know even less. It does not necessarily mean Verlinde is incorrect, just a point to bear in mind.

    Nevertheless, Sean’s point about the CMB is said to have been addressed, although Verlinde says his calculations are incomplete.

    Incidentally, the Bullet cluster collision, in which randal sexton had an interest, is also touched upon in the article. Verlinde explains the differential behavior of visible matter and his DE-generated spacetime by saying the latter displays less elastic gravitationl interaction. This again eliminates the need for DM.

    KC

  22. KC,
    Verlinde is deriving ST from well developed theory/math of quantum entanglement. This derivation yields DM/DE as characteristics of that spacetime. There are plenty of details to complete. If it works and predicts differentiating results, it will be testable. That would be huge. Lots of ifs.

  23. bostontola,

    Being one who is acutely aware of the downside of how “standard” (classical) physics spectacles could impair one’s ability to understand QM, I should have refrained from over-asserting the “standard” claim that using DE to explain DM may not be that good an idea. Actually, if Verlinde is correct, he might be killing two birds with one stone using his entropic gravity approach. It would certainly please Rev. Occam, at a minimum.

    On the other hand, extraordinary claims require extraordinary proofs. Assuming Verlinde could eventually square his calculations with the CMB data, the flat galaxy rotational curves, the visible to DM halo transition in galaxies Sean mentioned in his video etc., there is another possible new hurdle for Verlinde to surmount.

    Namely, if we take seriously the idea that dark matter are black holes (see Sean’s https://www.preposterousuniverse.com/blog/2016/03/10/did-ligo-detect-dark-matter/, as well as Carr et al., “Primordial Black Holes are Dark Matter”, arXiv:1607.06077v2 [astro-ph.CO] August 8, 2016, Bird et al., “Did LIGO Detect Dark Matter?”, Phys. Rev. Lett. 116, 201301 May 19, 2016 and Kashlinsky, “LIGO gravitational wave detection, primordial black holes and the near-IR cosmic infrared background anisotropies”, arXiv:1605.04023v1 [astro-ph.CO] May 13, 2016), there are quite a bit more observational data for Verlinde to explain.

    Come to think of it, if dark matter are black holes, in addition to Casimir plates, stationary and accelerating observers and black holes, I should have included dark matter as one of the tools to elicit various distinct observable “effects” from an underlying quantum field (see my Dec 1 comment in Sean’s “Gifford Lectures on Natural Theology” blog).

    KC

Comments are closed.

Scroll to Top