Wednesday, November 20, 2019

Can we tell if there’s a wormhole in the Milky-Way?

This week I got a lot of questions about an article by Dennis Overbye in the New York Times, titled “How to Peer Through a Wormhole.” This article says “Theoretically, the universe may be riddled with tunnels through space and time” and goes on to explain that “Wormholes are another prediction of Einstein’s theory of general relativity, which has already delivered such wonders as an expanding universe and black holes.” Therefore, so Overbye tells his readers, it is reasonable to study whether the black hole in the center of our Milky Way is such a wormhole.

The trouble with this article is that it makes it appear as if wormholes are a prediction of general relativity comparable to the prediction of the expansion of the universe and the prediction of black holes. But this is most definitely not so. Overbye kind of says this by alluding to some “magic” that is necessary to have wormholes, but unfortunately he does not say it very clearly. This has caused quite some confusion. On twitter, for example, Natalie Wolchover, has put wormholes on par with gravitational waves.

So here are the facts. General Relativity is based on Einstein’s field equations which determine the geometry of space-time as a consequence of the energy and matter that is in that space-time. General Relativity has certain kinds of wormholes as solutions. These are the so-called Einstein-Rosen bridges. There are two problems with those.

First, no one knows how to create them with a physically possible process. It’s one thing to say that the solution exists in the world of mathematics. It’s another thing entirely to say that such a solution describes something in our universe. There are whole books full with solutions to Einstein’s field equations. Most of these solutions have no correspondence in the real world.

Second, even leaving aside that they won’t be created during the evolution of the universe, nothing can travel through these wormholes.

If you want to keep a wormhole open, you need some kind of matter that has a negative energy density, which is stuff that for all we know does not exist. Can you write down the mathematics for it? Yes. Do we have any reason whatsoever to think that this mathematics describes the real world? No. And that, folks, is really all there is to say about it. It’s mathematics and we have no reason to think it’s real.

In this, wormholes are very, very different to the predictions of the expanding universe, gravitational waves, and black holes. The expanding universe, gravitational waves and black holes are consequences of general relativity. You have to make an effort to avoid that they exist. It’s the exact opposite with wormholes. You have to bend over backwards to make the math work so that they can exist.

Now, certain people like to tell me that this should count as “healthy speculation” and I should stop complaining about it. These certain people are either physicists who produce such speculations or science writers who report about it. In other words, they are people who make a living getting you to believe this mathematical fiction. But there is nothing healthy about this type of speculation. It’s wasting time and money that would be better used on research that could actually advance physics.

Let me give you an example to see the problem. Suppose the same thing would happen in medicine. Doctors would invent diseases that we have no reason to think exist. They would then write papers about how to diagnose those invented diseases and how to cure those invented diseases and, for good measure, argue that someone should do an experiment to look for their invented diseases.

Sounds ridiculous? Yeah, it is ridiculous. But that’s exactly what is going on in the foundations of physics, and it has been going on for decades, which is why no one sees anything wrong with it anymore.

Is there at least something new that would explain why the NYT reports on this? What’s new is that two physicists have succeeded in publishing a paper which says that if the black hole in the center of our galaxy is a traversable wormhole then maybe we might be able to see this. The idea is that if there is stuff moving around the other end of the wormhole then we might notice the gravitational influence of that stuff on our side of the wormhole.

Is it possible to look for this? Yes, it is also possible to look for alien spaceships coming through, and chances are, next week a paper will get published about this and the New York Times reports it.

On a more technical note, a quick remark about the paper, which you find here:
The authors look at what happens with the gravitational field on one side of a non-traversable wormhole if a shell of matter is placed around the other side of the wormhole. They conclude:
“[T]he gravitational field can cross from one to the other side of the wormhole even from inside the horizon... This is very interesting since it implies that gravity can leak even through the non-traversable wormhole.”
But the only thing their equation says is that the strength of the gravitational field on one side of the wormhole depends on the matter on the other side of the wormhole. Which is correct of course. But there is no information “leaking” through the non-traversable (!) wormhole because it’s a time-independent situation. There is no change that can be measured here.

This isn’t simply because they didn’t look at the time-dependence, but because the spherically symmetric case is always time-independent. We know that thanks to Birkhoff’s theorem. We also know that gravitational waves have no monopole contribution, so there are no propagating modes in this case either.

The case that they later discuss, the one that is supposedly observable, instead talks of objects on orbits around the other end of the wormhole. This is, needless to say, not a spherically symmetric case and therefore this argument that the effect is measurable for non-traversable wormholes is not supported by their analysis. If you want more details, this comment gets it right.


  1. Minor grammar fixes: “ wormholes are very, very different to the predictions” should be “ wormholes are very, very different than the predictions”.

    And “paper will get published about this and the New York Times reports” should be “paper will get published about this and the New York Times will report it”.

    No need to post

    1. "different from" in the USA or "different to" in the UK. NEVER "different than".

    2. for instance: A is different from B; C is different from B; But C is more different than A.

  2. Shaking my damn head, which is sending out ripples in spacetime :)

    Thanks for fighting the good fight Sabine!


  3. Perhaps cryptozoology would be a very close science analogy. Yes, it is theoretically possible that Bigfoot, Sasquatch or Mokele Mbembe exist, but discussing methods how to detect is not really mainstream biology.

  4. > it is also possible to look for alien spaceships coming through, and chances are, next week a paper will get published about this and the New York Times reports.

    The New York Times has already reported on (suspected) alien spaceships.

  5. Quote:
    Wormholes are another prediction of Einstein’s theory of general relativity, which has already delivered such wonders as an expanding universe and black holes.”

    Q: Is it true, that "General Relativity" predicted the expansion of the universe? I thought that it was discovered afterwards by Edwin Hubble ....

    1. It can accommodate it.

      The intial neglect of this possibility is the famous "greatest mistake".

    2. Hubert R,

      Yes, this prediction was made by Lemaitre. Einstein famously didn't like it, which is why he introduced the cosmological constant to prevent this expansion.

    3. Sabine, Einstein introduced the CC almost immediately after the initial theory, to have a static universe. The blunder was not in the introduction of the constant, rather, that the resulting system of equations was unstable, like a pencil balanced on its tip. So the stasis was illusory. It was a math error.

      Lemaitre's work first appeared in 1927, 10 years later.


    4. The reference to the CC paper is

      Einstein, A. - Kosmologische betrachtungen zur allgemeinen relativitätstheorie, Sitzungsber. Preuss. Akad. Wiss. Berlin, 1917, 142–52.


    5. Of interest perhaps - the CC actually first appeared in a footnote of the original 1916 GR paper, when considering 2nd rank tensors whose covariant divergence vanishes. That it is a footnote suggests Einstein did not wish to revise the main development at that late stage in publication. This last-minute discovery of an ambiguity in his field equations must have vexed him sorely.


    6. This is, by now, exceedingly well documented:

      Slipher noted that most galaxies have redshifts.

      Einstein developed field equations without Lambda (although he could have included it from the beginning, and some argue that he should have, on purely mathematical grounds) and finds no static solutions.

      Einstein introduced Lambda with a specific value to allow a static universe, because he, like almost everyone else at the time, believed that the universe was static on large scales.

      De Sitter found an expanding solution (though not immediately recognized as such, due to the coordinates used) with Lambda but no matter.

      Friedmann looked at the full range of solutions, with positive, negative, or zero Lambda and positive, negative, or zero curvature, finding expanding and contracting solutions.

      Lemaitre actually calculated a value for the Hubble constant in the French version of his paper, but he left it out when he translated it into English, saying that it was "of no actual interest", by which he meant "no current interest" ("actuel" is French---and "aktuell" is German---for "current", hence a common mistake among French (or German) speakers with less than perfect English.

      Hubble published a relation, with a value for what is now known as the Hubble constant not far from Lemaitres, making use of uncredited redshifts from Slipher. (Hubble regularly downplayed others' contributions to increase his own fame). He published a relation between redshift and apparent magnitude. He was very careful not to interpret this as evidence for the expansion of the universe.

      Most scientists accepted the expansion of the universe as having been demonstrated observationally.

      Together with de Sitter, Einstein publishes a mathematically simple model without Lambda, suggesting to use the simple model just for convenience as long as it is not ruled out observationally.

      Much, much later, Gamow writes that Einstein said that introducing Lambda was the biggest blunder of his life.

      With regard to the last item above: Gamow was not always a reliable narrator. Even if the quote is accurate, did Einstein mean introducing Lambda at all or not recognizing that, had he left it out (OR INCLUDED IT WITH SOME OTHER VALUES), he could have predicted the expansion of the universe (though, with hindsight, Slipher had already observed this)? Einstein certainly preferred a universe without Lambda after he accepted the expansion, though perhaps for reasons of simplicity. (Rather than the flat Einstein-de Sitter universe, which makes things easy to calculate, he actually personally favoured a spatially closed universe, to avoid the problem of boundary conditions at infinity.)

      Between about 1930 and about 1990, Lambda was sometimes invoked to explain observations (some of which turned out to be wrong) difficult to explain without it. Many, but far from all, set it to zero if there was no conflict with what they were looking at.

      At the beginning of the 1990s, many people pointed out that a model with Lambda fits the data better, though there was no one test which, alone, required it.

      The magnitude-redshift relation for supernova was the first observation which, alone, required Lambda.

      Almost everything works better with Lambda.

      CMB observations are now precise enough that they alone indicate Lambda.

      Use Google to help you find books detailing the history, buy them, and read them. Some suggestions: The Book of Universes by John D. Barrow, Discovering the Expanding Universe by Nussbaumer and Vietri, Origins of the Expanding Universe (proceedings of a conference about Slipher), In Search of the True Universe by Martin Harwit (mainly about other topics, but with a very good summary of the first few decades of modern cosmology).

    7. "The blunder was not in the introduction of the constant, rather, that the resulting system of equations was unstable, like a pencil balanced on its tip."

      I'm not so sure. Yes, Eddington published a paper pointing out this instability. The solution is an unstable fixed point, which means that, if perturbed, it will evolve away from where it is in parameter space. But since the universe is all that there is, there is no way to perturb it from outside. Of course, the real universe is not completely homogeneous, so a real universe with Einstein's value of Lambda would be unstable. But it is not a mathematical error.

      Interestingly, the Einstein-de Sitter model is, mathematically, an unstable fixed point, but that was rarely used as an argument against it. Rather, it was used as an argument for it, since if the universe weren't described exactly by this model, then it would already have evolved away from it (this is part of the largely misunderstood flatness problem). What killed Einstein's original static model is the fact that the universe is not static.

    8. "Yes, this prediction was made by Lemaitre. Einstein famously didn't like it, which is why he introduced the cosmological constant to prevent this expansion."

      Yes, Lemaitre predicted this, but also Friedmann. Yes, Einstein didn't like it at first, but this was not in response to Lemaitre, whose work on this came 10 years or so later.

    9. Cormac O'Raifeartaigh (son of Lochlainn) has published a series of papers on the history of Einstein's brush with cosmology. Blunder or no, it was something he deeply regretted as a basic flaw in his theory. In some ways, all his later work was dedicated to being rid of it for a better reason than beauty. It hovers over all the later work (distant parallelism, asymmetric g_mn, connection transforms etc.) Here are O'R's papers..


  6. Your text has the right ArXiv number but the link in the HTML source goes to a quantum paper. Correct link:

    1. That's what happens when you have too many browser tabs open... Thanks for noticing, I have fixed the link.

  7. I respectfully disagree with a blanket statement such as this: "But there is nothing healthy about this type of speculation. It’s wasting time and money that would be better used on research that could actually advance physics." I inquire: why should we "throw the baby out with the bathwater" ? First, the 1987 American Journal of Physics article, by Morris and Thorne, is an excellent pedagogic tool to introduce general relativity to undergraduates (you learn that "remarkably, wormholes as objects of study in mathematical relativity predate black holes"). Then, read Matt Visser(1995): "wormholes are described by 'plausible' physics" and "wormholes are certainly strange and peculiar objects, but they do not seem to violate basic physical principles." (page 5, Lorentzian Wormholes). It seems impossible to say how money should be used to "actually advance physics."

    1. Gary,

      As I have explained in my video, writing down the mathematics for something doesn't tell us anything about whether that something actually exists. The world of mathematics is full with remarkable stuff that does not describe the universe.

      Yes, I know that a lot of physicists today do not seem to understand that mathematics does not equal physics. That's why my book is called "Lost in Math."

      I have explained here that the history of physics tells us pretty clearly what kind of research leads to breakthroughs and what we should therefore pursue.

    2. Matt Visser concludes: "A topic as seemingly limited in scope as Lorentzian wormholes,because it forces us to come to grips with fundamental issues regarding quantum gravity,can still teach us a lot...the successful marriage of quantum physics with gravity is a major theoretical issue, an issue that confronts both particle physics and gravity physics." (1995, page 371). Apologetically, I admit I have not secured a copy of your book, Lost in Math, but it is on my reading list !

  8. This is a bit facetious, but the ridiculous scenario you presented in medicine is actually not so far from the truth. I think (could easily be wrong here), for example, the discovery of retroviruses came from people convinced to look for something the mainstream judged to be too speculative.

    1. Imagine a room with 1,000 people flipping coins. $2 per flip, and if you flip heads 10 times in a row, and you win a car (using the $20,000 acquired in the meantime).
      One person accomplishes this task. Is that anecdotal achievement vindication of the efficiency of this method of personal financial improvement?

    2. Well, the discoverers probably tell that story, 45 years after fact :)

      Retroviruses, like most discoveries in life sciences, came about because of observations that didn't fit with theories of the day, combined with advances in analytical chemistry and biology that eventually supported a new model.

      I work in this domain and should add that there are plenty of similar, current examples. For example, there are anti-cancer drug candidates developed to interact with a specific biomolecular target, that are effective in cells, animal models and are currently in human clinical trials, but a new technology, CRISPR, has shown that the ostensible "target" is irrelevant to the progression of the disease! So in terms of chemistry and biology, we have an effective intervention, but can't explain why it works.

      The math and physics that Sabine writes about is far over my head, but fwiw, from where I stand the basic problem of how to do science is the same.

  9. Sabine, I'm a big fan of this blog and I totally get the general principle of what you are trying to say, even if the mathematical detail often escapes me. However...

    Aren't you arguing against your own central message here? You are concerned that theoretical physicists are conjuring whole universes into existence on the basis of mathematics rather than empirical observation - and especially you are concerned that these physicists make predictions which are utterly untestable, and then use that untestability as an excuse to build ever bigger and more expensive machines...

    Well, here is a piece of mathematical physics where the researchers are suggesting very specifically that there *is* a way of testing something. I haven't read the paper, so I could be wrong - but isn't the essence of what they are saying, "So, loads of people make wacky (math-driven) predictions based on relativity or quantum mechanics. Most of them are untestable - but here is one we can test. *IF* wormholes are possible, and *IF* one exists within Saggitarius A* - *THEN* we might observe x,y,z. Therefore, if we don't observe x,y,z it seems likely that there is no wormhole within SagA*.

    It's not a proof (or disproof) of the existence of wormholes per se; but it is a testable null-hypothesis with a meaningful (if very specific) result.

    What am I missing? Why is this crazy-talk rather than an opportunity to remove an otherwise-open possibility from the scientific discussion?

    I'm sure you're right - but from what you've written, I can't see why.

    1. Richard,

      The world of mathematics is large. There are literally infinitely many hypotheses that you can put forward and then spend money on trying to test them. This is not a promising strategy. You have to select carefully what hypotheses to test or otherwise you will waste your limited resources on experiments that teach you nothing new. This is basically the reason why there has been no progress in the foundations of physics for 40 years: Careless selection of hypotheses to test, followed by experiments that only get null-results.

      As I have explained previously, just because it's falsifiable doesn't mean it's scientific.

      Of course theories that are entirely untestable shouldn't be pursued in science, but this isn't the major issue. The major issue is the overproduction of unmotivated hypotheses on the tests of which we keep wasting money (and people). Here is an example of this. And trying to look for wormholes is another example.

    2. Thanks Sabine. I do understand your point. But surely in this instance (and again, please note that I haven't read the paper), the aim is not to create some new (and expensive) experiment; surely, SagA* is being extensively observed already. in which case, maybe all the writers are saying is, "Guys, wacky and unlikely though it may be, it is worth keeping an eye out for this specific kind of anomaly in the data you are already collecting."

      Or do I have this wrong?

    3. Richard,

      This is correct. The concern in this case is not a costly experiment. The concern is here that we are wasting time on useless speculation while there are better things to do.

    4. [nitpick] It's SgrA* (in the constellation of Sagittarius), not SagA* - which does not exist as far as I know - in the constellation of Sagitta ("the arrow") which is informally "Sag", but has the formal IAU abbreviation Sge [/nitpick]

  10. Dear Sabine,

    Let me clarify some things that I thought we already clarified in our email exchange.

    You complain about our remark that even non-traversable wormholes can leak gravity. If you look at the scalar field case that we study, you see that the scalar field shuts off as R->r_g (wormhole mouth approaches the gravitational radius of a black hole). If did not shut off, it would directly violate the scalar no-hair theorems for black holes. However, when you look at gravitational perturbations you see that this does not happen. There are no gravitational no-hair theorems for black holes, anyway we were also puzzled by this. But we believe that this is ok. No information travels from within the horizon out. But the source of perturbations perturbs the horizon, and a test object propagating in vicinity of the horizon on the other side feels these perturbations. Just like you have two black holes merging (or a neutron star and a black hole). The merger process perturbs the horizon, and information about perturbations is sent around in the form of gravitational waves. In our case there not gravitational waves per se but they are gravitational perturbations. Within the approximations in our paper, it is not 100% clear what happens. One would have to do a full time-dependent analysis for a sequence of wormhole geometries as R->r_g. It is not excluded that one would find some suppression factors as R->r_g, but at least in our approximation there are no suppression factors.

    However, the main point of the paper are traversable wormholes. For them, there is no problem of gravitational perturbations passing through. We mentioned behavior of gravity in the limit of R->r_g as a peculiar thing we noticed.

    About the Comment written by Krasnikov, you say it gets it right, but you actually just said that you do not agree with it. The Comment argues that even out traversable wormhole case is unobservable, while your words (correctly) imply it is observable.

    Anyway, Krasnikov’s confusion perhaps stems from the fact that our Eq. (36) is a result of a monopole perturbation.
    However, in section V of our paper, we clearly say that we consider an elliptic orbit of a star located on the “other side”. An elliptic orbit cannot be represented
    with only one monopole, and can be viewed instead as a sequence of monopoles. We estimate the effect in our
    Eq. (37) by using two monopoles, one for a perigee and another for an apogee. Thus our Eq. (37) represents an acceleration
    variation in the motion of the star S2 due to an elliptic (and thus non-spherically symmetric) orbit
    of the star on the other side perturbing the metric. This time-dependent acceleration variation is
    in principle distinguishable from the original acceleration coming from the central object.

    In the language of symmetries, we do assume a spherically symmetric background, but the perturbations coming from the elliptic orbit ruin this symmetry. Birkhoff's theorem cannot be applied to our perturbed universe anymore.

    I hope this helps.

    Best wishes,


  11. Quantum tunneling is a fun phenomenon. More than once I've had folks ask me whether such odd things really happen. I would inform them that yes, quantum tunneling is quite real, and that quantum theory even provides mathematical tools for calculating the precise odds of me disappearing from my office by quantum tunneling to the other side of the planet.

    My point was always that just because a mathematically precise and well-proven theory say that something can happen does not necessarily mean it will happen. I would then explain how scale means everything in the quantum world, so that even though large objects don't behave like this, tunneling becomes very significant at small enough scales. For example, tunneling is the basis of certain (relatively rare) types of commercial transistors.

    I would always end by pointing out that the odds of me simply exploding were astronomically larger. Sometimes it worried me a bit when that was the part that made them smile... :)

  12. Assuming wormholes are realizable, could it be like in Klein bottle: non-orientable, so object going through it would undergo P or T symmetry?

  13. Sabine,

    it is disingenuous of you to claim that studying wormholes is "just mathematics". Wormholes are not postulated out of purely mathematical constructs. They are a possible consequence of a very well-tested physical theory, namely GR. We have strong reasons to believe that GR is the best theory of gravity at our disposal. Then, why should be accept some of its consequences, but not others? Based on what? Personal taste? You just can't cherry-pick the solutions you like and throw away the others!

    Of course wormholes have not been observed (yet), but neither were black holes, which were initially dismissed for the very same reason of being too fancy solutions, but are now universally accepted.
    Or are you seriously suggesting that we should only believe theoretical predictions that we already observed ? (there would never be any "predictions" then...). Would you say that if I predict a fancy effect in condensed matter based on a consistent mathematical solution of Schrodinger's equation, we should call it science fiction and dismiss it only because it is hard to believe? Long-distance entanglement is hard to believe, but nevertheless real. As I said, you can't cherry pick from a well-tested theory. If you do, you could just as well throw the theory in the dustbin.
    All this, of course, has nothing to do with "mathematics", as long asthe solutions are mathematically correct.

    1. Opamanfred,

      As usual, you managed to entirely miss the point. I have explained above why we have no reason to think that wormholes are possible. What about my explanation is it that you do not understand?

    2. If GR has zillions of solutions (like string theory) one should not be surprised if one or two turn out to describe something.

    3. @Sabine,
      I just meant that one cannot a priori rule out solutions to a well-established theory. Of course, a posteriori, you can rule out many things, but you need physical reasons for that. Perhaps your negative energy condition is a good reason, I can't judge. I guess that the authors of the paper would disagree, but that's just normal scientific discussion.
      What I object to is calling wormhole solutions "just math" and dismissing them for this.

      @Greg Feild. You do not understand the difference between a theory coming in many different versions and a theory having many solutions. Classical mechanics, quantum mechanics, electromagnetism, all have "zillions of solutions" (observing distant stars and switching on you dishwasher both imply a solution of Maxwell's equations...). Actual solutions are determined by boundary and initial conditions. Nothing mysterious here.

    4. General relativity is really just Riemannian geometry with a 4-dimensional Lorentzian metric and some constants such as G and c. The system has loads of solutions, and some have closed timelike curves. One of these interestingly is the Taub-NUT solution that is analogous to a black hole, but instead of the horizon occurring at a radial distance it does so at a time. This horizon separates regions with closed timelike curvas from a future regions without them. The anti-de Sitter spacetime (AdS) has closed timelike curves as well, and often analysis is done in a conformal patch that exclused closed timelike curves.

      The spacetime we exist in is such that it appears to obey restrictions from these situations. These restrictions are the Hawking-Penrose conditions that T^{00} >= 0, the weakest or more general form, with a number of other more restrictive restrictions. The AdS spacetime may have some physical role, but it is not the spacetime we directly observe. The interior region past both horizons of Kerr black holes has closed timelike curves as well, but one can't send a signal out to report on this.

      It is clearly not a waste of time studying curious spacetimes, such as wormholes, for these solutions and how they are obstructed against in the observable universe may tell us a fair amount. The relationship between the dS spacetime we observe and an AdS with closed timelike curves is that this will be able to solve NP-complete problems. Quantum gravity may be NP-complete it is an extremization of entanglement of states juxtaposed with isolated states. However, it is probably not a good use of one's time trying to figure out if wormholes and warp drives can exist with various hyper-spacetravel ideas in mind.

    5. Classical physics has zillions of practical applications.

  14. Hi SABINE !!!

    I hope your day is going well.

    I have,at the moment,
    so much to say...
    and so little time
    - except to say

    Thank You for Your Work.

    more later ,

    Love Your Work.

  15. Wormholes are mathematical speculations, even more 'artefactual' than black holes. We have many more really serious topics to discuss...

    1. Note that in today's understanding black holes are considered as very real and or 'established reality'.

    2. How you observe for example difference between Black hole (BH) vs Exotic compact object(ECO)? And do you see the value of an effort to measure it?

    3. Eusa,

      Please read the 6th point here (better still, read them all). For more details, read this (and the paper mentioned there). Oh yes, and please remember this information and stop repeating false statements about black holes, thank you.

    4. Are you a little prejudiced about me?

      I made questions not false statements. If event horizons once will be directly observed, I'll be happy with many answered questions.

      About an observing dilemma. First we see the guy fallen in the black hole with her image frozen in the horizon. Then we ourselves fall after her and look at her image continuously. What developement of her image will we see until we achieve the horizon? If only the frozen image stay there and we will go through it?

    5. Eusa,

      You wrote above "Wormholes are mathematical speculations, even more 'artefactual' than black holes" which is bluntly wrong. This has nothing to do with "prejudice" but I have noticed similarly bold and uninformed statements in your previous comments. I suggest you stop commenting on topics you clearly know very little about.

    6. Agreed. But could you kindly answer my easy questions with at least something substantive in addition to your valuable meta-discussion? The frozen image question is quite well defined, I think. I know the image cannot be there any more because of acceleration of the proper time of us falling into the more curved part of spacetime. We will see the developing image. The next question is: will the EH keep any absolute position or only a relative one in respect to the falling observer? What is the horizon function of observers falling in a row? Is there a connection to Kerr solution with multiplied horizons?

      This scenario didn't include in my courses of the relativity theory. Via the Kerr solution we come to the topic of wormholes and the possible observational evidence of them.

      What I want to say is that the nervousness over wormholes can rise from the fears that there might be something unexpected in speculations on black holes too...

    7. Before discussing how one could detect a wormhole consider the black hole. The Event Horizon Telescope imaged last April a black hole in M82, as I recall the Messier number. This image really is of the shadow, which is an optical exclusion due to the black hole. We really never observe the event horizon. The event horizon is a congruent set of null rays that bound a causal region. Nothing then ever leaves the horizon to serve as a signal. This is a bit different than the stretched horizon that is a quantum surface a Planck or string length above the horizon. The stretched horizon can send signals out, but extremely red shifted.

      There are a number of wormhole metrics. The usual one is similar to the Schwarzschild metric, but with something funny near where the horizon would exist. There is some region of exotic quantum field that instead of generating a positive curvature and a focusing in of geodesics, this generates a negative curvature that then induces hyperbolic or defocused geodesic motion. This can't occur outwards, so it does so in some other region. This then defines two 2-spheres in different regions of spacetime with points identified at synchronized clocks or time. So one passed across one of these 2-spheres and you emerge out the other. So if one were observing a wormhole it would be observing one of these openings.

      I appreciated the movie Interstellar for having pretty spot on physics, though the theme of the narrative about leaving Earth for new worlds “out there” I found difficult to entertain. The physics was not the usual Star-Trekkie sort of nonsense, and it got the Penrose physics of traveling near a Kerr black hole right. At the point the characters reached the wormhole opening near Saturn there was a numerical simulation of its optics. This is to be compared to the numerical simulation of the super-massive black hole (SMBH) near their destination. The wormhole looked a bit like a lens of sorts with an image of the other region. Depending on the extent of the gravity field of the wormhole, which in some metrics is considerable, there may be a shadow region as well. However, since the wormhole is a handle in this multiply connected topology there could be optical rays passing through. Given a gravity field to the wormhole there could then be various optical caustics. So a wormhole at a distance may have a shadow similar to that of a black hole, but with optical signatures, maybe caustics or focused rays, coming from the center of this shadow. So the shadow would not be a black disk, but more of a black annulus.

      So as astronomers observe SMBHs in other galaxies and the moderate-MBH in this galaxy this would be something to look for. If these sorts of optical signatures appear then we do have to open up gravitation physics to wormholes. It would make an already difficult problem of quantum gravitation far more difficult if not impossible. A galaxy may be a sort of shooting gallery with so called rogue black holes, which can come close to a star or system of planets. That is a somewhat uncomfortable thought, though asteroids in the solar system are more likely to thump us. So if there should turn out to be a black hole passing within .01 light years or so we might just be able to send a space probe there to take a close look.

    8. Just what the M87 (not M82) nucleus image is (or represents) is actually very complicated. A great many of the explanations are either downright wrong or missing some key aspects.

      Matt Strassler, a particle physicist without special expertise in either GR or astronomy, took quite some time to dig into the details. You can read about the many challenges in a couple of his blog posts, especially this 14 June one:

      Some quotes: "Over the last few weeks I’ve spent some time studying the mathematics of spinning black holes, talking to my Harvard colleagues who are world’s experts on the relevant math and physics, and learning from colleagues who produced the `photo’ and interpreted it. So I think I can now clearly explain what most journalists and scientist-writers (including me) got wrong at the time of the photo’s publication, and clarify what the photo does and doesn’t tell us."

      "One note before I begin: this post is long. But it starts with a summary of the situation that you can read quickly, and then comes the long part: a step-by-step non-technical explanation of an important aspect of the black hole ‘photo’ that, to my knowledge, has not yet been given anywhere else."

    9. Strassler's main point appears to be that this image does not separate out the accretion disk image from the photon ring where photons arc around the BH. That is due to the “fuzzy camera” and we know the photon ring is somewhere in the annulus region of photon detection, probably close to where the dark center is. So the estimate of the size of the BH, say a computation of the ADM mass, is very approximate. Also for the BH rotating the Kerr metric generates frame dragging of the photon path to adjust the size downward. For a completely extremal black hole a = m, for a = J/mc, the black inner region would completely disappear. The extremal BH has no gravity!

      I actually never read any of the EHT papers. I figured the investigators ran their date through various computer programs to make these estimates. I would hope of course that they included estimates of the rotation of the M87 BH, which I think is a = .9m and is considerable. There were statements about releasing images of the Sgr-A* BH in the galaxy center, where the image may have some of that “eye in the sky” appearance. So far I have not heard of this.

  16. A lot of theoretical physics (like wormhole theory and string theory*) is more a subject of pure mathematics -- more exciting to pure mathematicians than it should be to physicists. But the tendency to talk about pure mathematical entities as being physical realities in nature is bizarre.

    * Mathematicians Chase Moonshine’s Shadow: Researchers are on the trail of a mysterious connection between number theory, algebra, and string theory.

    "Physicists are also excited about a highly conjectural connection between moonshine [-- the unexpected connection between the monster group M and modular functions --] and quantum gravity."

    1. This is fascinating work, and a lot of it stems from Witten's observation on the role of Jacobi θ-functions and the Klein invariant or J-function along with the Langland's conjecture. I however, think it is not complete, for the problem with pursuing ever larger algebraic structures is that one is also imposing more degrees of freedom. It seems to me a fundamental theory of quantum gravitation will have few DoFs.

  17. Dear Dr. Hossenfelder
    While there are certainly a lot of things that are not worth the time and money, who is going to decide? That is the same problem as with common sense. Whose common sense? My personal common sense is quite different from your common sense. While they may overlap in some areas, they will not in others. Do you or anybody feel competent to decide, which subject in physics is worth pursuing? I am certainly not. I am sure that in many cases the decisions would be perfect valuable and most (!) would agree but in the majority cases it would be very very difficult. I think, that we can not deny anybody to think even about the to most crazy things. You said yourself, theoretical physicist are cheap. So why not let them do that stuff? We can not predict, if something useful comes from it. It might be, that this paper triggers something in somebodies head and that will save the world. Not very likely, but who knows. But that does not mean, we should not discuss and be extremely critical about these ideas. Debunk them in any way possible, but never deny anybody to come up with an idea and write a paper about it (and if that space ship suddenly pops out of Sagittarius A*, we look very stupid).
    From my perspective, one big problem in science is the current currency. Papers are the way value is measured, even just numbers of papers, without even assessing the content. That's wrong. With current technologies in collaboration software AND organisations, we could wring out ideas much faster and much more efficiently than with the current system of writing papers, peer review, publication. Terry Bollinger once wrote in one post, that techniques we use in software development do not work in science. I think they do, but that would imply to kill the current currency and way of thinking and start collaborating in a different way.
    (By the way, I think we will start to work as a highly efficient team, as soon as we realize, that we run out of time to save our planet. We are just not there, yet. In our minds that is. It is already very late.)
    I can't be mad at the NY Times for that article. It's fun. It makes people talk about physics. It lets them dream about meeting other sentient live forms. What's bad about that? For centuries people looked at the stars and asked themselves, if there is somebody out there (SETI). Even today, every time an exoplanet with just a hint of oxygen is discovered, peoples imagination goes all bonkers, if that is that second earth we are so desperate to find. We need that. Fantasy is one of the best qualities we have. Do not deny the time and money for using fantasy. Even if 99.999% of all the ideas are utter c***. Sometimes there is a gem.

    1. @Christian Tillmanns
      -- Quote: It makes people talk about physics. --
      The problem what I see here is that normal people could see in "wormholes, string theory, parallel universes" more than there truly is.

      A normal person like me associates with the term "physics", the technical/biological part of "physics" which has created my computer and my living body. This kind of "physics" has proven its correctness millions and millions of times. Therefore I associate with "physics" something very different from the kind of "physics" that lies behind "speculations" about wormholes, etc.

      My suspicion:
      Lots of speculations were sold as solid physics in order to get higher recognition and of course money from the normal people.

      If I am correct in my suspicion, than this kind of "marketing" could damage the basis of trust between recognized science and normal people, as normal people could start to see some kind of "interest driven dishonesty" behind the term 'science/physics" and their theories/speculations
      For example: climate-change theory(true) or speculation(false)?

      kind regards,

    2. „If I am correct in my suspicion, than this kind of "marketing" could damage the basis of trust between recognized science and normal people“
      Well, that ship might have sailed for some people, but it wasn’t the fault of the science community who tries really hard to make the message heard. Unfortunately science communicator almost always tell their story with some uncertainty and rightly so. The average anti-vaxxer, flat earther, climate change denier and moon landing hoax believer is absolute sure to be right. And they deliver conclusive and easy to understand explanations, as hair rising they may be logically and scientifically. Easy and conclusive is what the „normal“ people (I have to say this, but I think we are all pretty „normal“) want (and need) and that is why science also must deliver their message in this way. Otherwise it is just too freaking complicated. With the result, that oversimplifying sometimes makes the message almost wrong. We call these oversimplified explanations „lies to children“. In the last 100’000 years so many things have changed and so many ideas have been proven wrong, I don’t think the normal people are affected by this. Those who are interested in science just follow on that path and sometimes it is a dead end. Next time one reads something, there is another opening. So, why not speculate about a worm hole in Sagittarius A*? It is what we do and what we are. Curious, often wrong, sometimes right. Not telling the general public about the latest ideas would be a horrible mistake. Science would be only for the gifted and worthy. Do you really want this? I don’t think so. And it does not matter, if it is applied physics like in your phone or theoretical physics. Make it open, make it available, try (hard) to explain it to as many as possible and even if it is proven wrong over time, not telling would be worse and it is the only weapon the science community has against the anti-vaxxer, flat earther, climate change denier and moon landing hoax believer.

    3. @Hubert R
      To some extent , I agree with you. Too much popularization focuses on unsettled issues in physics. I guess it gets magazines sold more easily. And I also agree that this may undermine the laypersons' trust in scientists.
      But Sabine's blogging can have a negative effect too: just read weristdas' comments below (by far not an exception), who puts the universe expansion (very well tested) on a par with wormholes, despite Sabine having clearly said the opposite. That's why physicists should always be very honest when talking to the public.

    4. @Christian Tillmanns "The average anti-vaxxer, flat earther, climate change denier and moon landing hoax believer is absolute sure to be right. And they deliver conclusive and easy to understand explanations, as hair rising they may be logically and scientifically. "

      And "Make it open, make it available, try (hard) to explain it to as many as possible and even if it is proven wrong over time, not telling would be worse and it is the only weapon the science community has against the anti-vaxxer, flat earther, climate change denier and moon landing hoax believer."

      I find there is a somewhat curious dichotomy: some of these people are believers in magic ... there is essentially no role for logic or the scientific method.

      However, many of the anti-vaxxers etc do appear sincere in their insistence on logic and even the scientific method. And some - a very few - do realize that they lack some very basic knowledge (e.g. how vaccines work, biologically, or how to calculate orbits using Newtonian mechanics). That said, I cannot comprehend the sort of conspiracy theory like Moon hoax lander.

      For those whose assumptions include a denial of Relativity (Special or General), I find it ... curious that they do not recognize the disconnect involved in their use of GPS, smartphones, the internet, etc.

  18. Sabine is right I think about this. However, it must be remembered that early on the idea of black holes or gravitational waves was exotic. However, wormholes have some issues that make them physically problematic. A simple wormhole can be found in the metric

    ds^2 = c^2dt^2 - dr^2 - (r^2 + a^2)dΩ^2,

    where a is a factor that increases the area on a sphere of radius r beyond 4πr^2. We might think of this parameter a as varying a(r) = A/r. If you work through the Riemann curvatures you find there are nonzero Ricci curvatures that are negative. This corresponds to some source of the spacetime curvature with a negative stress-energy and T ^{00} < 0 that violates the Hawking-Penrose energy condition T^{00} ≥ 0. This condition enforces chronology protection and its violation is also a problem given that the stress-energy is computed from a Lagrangian for a quantum field. For ⟨ |T^{00}| ⟩ < 0 this means the eigen-spectrum of the field is not bounded below. This means in effect the vacuum state can be an infinite well-spring of radiation, which is something Dyson pointed out as a pathology in QED under certain unphysical assumptions.

    It can be pointed out from the perspective of the most elementary mechanics how wormholes lead to problematic issues. We have with the elementary Galilean equations of motion v' = v + at, for acceleration a, there is also the average velocity v_ave = ½(v' + v) = x/t, which corresponds to the time t and displacement x of this motion. Put this together and you get ½(v'^2 + v^2) = ax, where the multiplication by the mass gives the work-energy theorem of elementary mechanics. However, a wormhole could mean the mass travels through a wormhole short-cut without the displacement x. Through the wormhole we could have for y << x a shorter distance the velocities above given by a force through a different displacement. This is then an ambiguity. Further, given that physics has a conjugate property between position and momentum there is then no reason to think the same ambiguity could occur with momentum.

    A wormhole could connect not just regions of space, but time as well. So one could duplicate or clone a quantum state, where a closed timelike curve takes that quantum state back in time to where it exists now as a copy. One has to after receiving the copy through the original version into the wormhole. Cloning a quantum state is not a unitary process, but with a wormhole constructed from some quantum field we expect this should be the case. It is not hard to then see that

    no wormhole ↔ no cloning of quantum states

    Similarly we can argue that

    no warp drive ↔ non-signalling

    and so forth. In some ways the chronology protection. So while this may throw away lots of science fiction ideas of hyper-space travel, these conditions may mean that quantum gravitation has at least some level of sanity to it.

    I wrote a post like this yesterday on a friend's laptop that was logged in elsewhere. So far it has not shown up, and this version is preferred over yesterday's.

  19. Hypotheses build on hypotheses build on hypotheses build in hypotheses ...

    Nobody ever seen directly black holes, worm holes, space expansions, ... today, science is more fictional than scientifically. Let's come down from the shoulders of alleged giants and get down to the ground.

    1. "Nobody ever seen directly [...] space expansions".



      However, by ~2060-2080 or thereabouts papers will likely be published reporting exactly that.

      I know, mind-blowing, how could that possibly be true?!?

      With a 42m optical telescope (the EELT), cool quantum-based technology (laser frequency combs), and frequent observations of hundreds/thousands of z>2 quasars, that's how. Details? You have only to ask ...

    2. "Nobody ever seen directly black holes"

      True. But what - to you - would constitute a direct observation of a black hole?

      How about what is often called a silhouette? If so, what do you consider the work of the EHT (Event Horizon Telescope) consortium? In April this year they published what the general press called just that, for the super-massive black hole at the heart of the nucleus of the elliptical galaxy M87.

      Wikipedia article:

  20. Arkani-Hamed: “There is a giant Truth — with a capital T — of the world out there that physics is constantly working towards, that is also somehow enlaced with a giant Truth — with a capital T — of the mathematical world" and "We don’t actually know what reality is about. We are still learning, and we have to go into it with an open mind. Often, what we predict or assume something to be, can more easily be proven wrong than proven right.” (November 2019, Newspaper of Northwestern University).
    Matt Visser: "Sometimes fiction gives a good window into reality."
    (What is Fundamental ? arXiv 1805.06617).
    Brandon Carter: "Because of the scanty nature of the experimental evidence in its favor, the acceptability or the unacceptability of Einstein's theory must depend largely on whether its theoretical predictions seem reasonable or not." (1968, Physical Review, Global Structure of the Kerr Family of Gravitational Fields).

  21. Opamanfred's argument is very good: "Then, why should be accept some of its consequences, but not others? Based on what? Personal taste? You just can't cherry-pick the solutions you like and throw away the others!"

    My PhD research was essentially about finding better reasons to throw out nonsense like wormholes and time machines - that is, energy conditions. GR says as much about what reasonable metrics are as F=ma says about reasonable trajectories, that is, nothing. And the conditions are hard to come by - Sabine said negative energy density is required, but you can actually achieve local bits of negative energy density with things like the Casimir effect, but fortunately we can articulate even stronger requirements.

    It's silly to say there can't be wormholes or time machines because they'd be too weird - physics surprises our notions of weirdness all the time. But bounds on stress tensors in quantum field theory are not mere matters of taste.

    And it's really a sad state of affairs if folks like weristdas get the impression that black holes and worm holes are on equal footing. They are very much not!

    1. I think it's worth some effort to understand where folk like weristdas are coming from.

      If you read some of the comments on the YouTube version of this blogpost you'll likely quickly conclude that some are pure trolls, others are linkspamming to increase traffic to their own websites, yet others are diehard crackpots (pet "theories" immune from refutation), ... and some are just ignorant (but looking for help).

      As astronomy is - to first order - the detection and analysis of photons/electromagnetic radiation (EMR), a good first step may be to understand if an assumption early in a causal chain is the disconnect. For example, if GAIA's data is acceptable, then General Relativity (GR) must be acceptable.

      Then there's a feeling for numbers ... stars are very much further apart than are planets (excl binaries), yet relatively the distance between galaxies is much less.

      And misremembering high school (or undergrad) physics, e.g. that refraction is chromatic, but GR lensing is not.

      I feel there's no point even trying in YouTube comments (unless you're a masochist!), but here it is (my opinion, YMMV - your mileage may vary).

  22. As usual , thanks for keeping our feet on the ground Sabine, the only thing I had today was a hole in my plastic milk bottle which my cat named Schrodinger drank from a hole in the kitchen floor :-)

  23. Thanks, Doug. That's exactly what I meant, and your comparison with F=ma is spot on. Some solutions of GR may, for whatever reason, turn out to be unphysical. But one should not rule them out a priori as mathematical artifacts.
    Your last paragraph is very true as well, unfortunately.

  24. Dear Sabine,

    You wrote:
    Yes, I know that a lot of physicists today do not seem to understand that mathematics does not equal physics. That's why my book is called "Lost in Math."

    I fully agree. The whole reason why I was interested in physics was because it was about the world. It seems like a lot of physicists have forgotten about that. We ought to remind ourselves of the physical in physics.

    It's easy to get side-tracked considering the amount of mathematics in physics. I got side-tracked myself by studying mathematics myself in my first degree - my excuse was that I was running away from a racist school and mathematics seemed an easy way out then (Now, I think I should have just punched them - it would have been simpler).

    I can't say that I have anything intelligent to say about the Einstein-Rosen bridge except it was another one of those carrots used to seduce us into studying physics when we were already interested. I'd add though, that Walchover is wrong about saying that gravitational waves are 'another wild, crazy idea'. It's an emininently reasonable expectation - which is why William Clifford said as much, and this well before GR was proposed.

    Speculation is important in physics - otherwise how do we come up with new ideas - but it isn't license to think that every wild idea has the same bearing to reality as already well grounded science.

  25. You could have stopped after " article in the New York Times.." One doesn't go to the mall foodcourt for fine dining.

  26. "It’s one thing to say that the solution exists in the world of mathematics. It’s another thing entirely to say that such a solution describes something in our universe"

    Hi Sabine,

    I've been meaning to send this to you as I thought of you while reading it.
    From Alain Badiou's Immanence of Truths Chapter 24: "The Power of the Letter: The Sciences" (my translation):

    "what mathematics grasps as its real is nothing other than the total of the possible forms of the multiple...being as being is only multiplicity...[however] mathematics shows nothing of the real multiple, it inscribes the possible forms. The experimental demonstration, as to the real, not a possible form...begins with physics....Mathematics does not "verify" anything, it inscribes formal truths which it has demonstrated, within itself and by its own means, a possible existence. Under the condition of the mathematical theory of possible existences, physics...verifies that some of them are real....physics finds in reality a part of what mathematics thinks is possible."

    The difference between mathematics and physics being pure multiplicity (in our thought) and real multiplicity (in our reality).

    He also discusses the not-oft discussed concept of scientificity, contrasting "the possible vs. real couple" or "possible forms vs. real laws."

    As a set-theorist/philosopher he has a profound respect for mathematics as pure thought ( see In Praise of Mathematics) , but this respect is grounded by the understanding that all of the infinite pure thought, is not real. This is the job of physics to decipher.

    As always, I enjoy your commentary.

  27. What makes someone a "physicist today" ?

    Surely, we should require more than a PhD and some government funding before calling someone a Theoretical Physicist.

  28. FWIW, topological wormholes seem to have been a discussion topic at least as far back as the Nineteenth Century. The idea was the basis of an HG Wells short story ("The Remarkable Case of Davidson's Eyes"), which seems to have been published in 1895.

    " Explanation there is none forthcoming, except what Professor Wade has thrown out. But his explanation invokes the Fourth Dimension, and a dissertation on theoretical kinds of space. To talk of there being "a kink in space" seems mere nonsense to me; it may be because I am no mathematician. When I said that nothing would alter the fact that the place is eight thousand miles away, he answered that two points might be a yard away on a sheet of paper, and yet be brought together by bending the paper round. "

    Riemann, Gauss, Clifford & co were all playing around with variations on "curved space" geometrical physics long before Einstein came along.


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