Open thread: ask a relativist

Solving Einstein’s field equations is my day job, so I’m happy to take any questions about relativity, black holes, gravitational waves, or the like.

Regular posting will hopefully resume next week.

56 Responses

  1. Besides Doppler shifting due to metric expansion, are you aware of any competing theories to explain the observed red-shift of distant galaxies in every direction?

  2. I’m not aware of any viable theories. Dust absorption can redden starlight, but not shift spectral lines. The redshifts are too strong to be from local gravitational sources.

    I suppose one could ask if it could be regular motion-induced doppler shifts. But then each spot would have a different definition of simultaneity, and ours would be suspiciously special in making the universe look isotropic. This has just occurred to me, though, so I might be overlooking something.

  3. I’m fine with our (or, more particularly, the Incarnation’s) spot being “suspiciously special.”

    Any thoughts on the potential relationship between the metric of spacetime and what we take to be universal constants? What might be the impact in our observations if, say, c (or G or ε0) was in some way dependent on that metric (and therefore increasing in value with the expansion of the universe)?

  4. That’s a fun topic, not that I know much about it. I once heard Freeman Dyson give a talk on constraining how the fine structure constant might have been evolving with time. I remember that one of the best constraints came from a natural fission reactor–lots of radioactive stuff just happening to be stuffed together enough to sustain fusion for over a billion years.

    (Incidentally, an important part is framing the question properly. Of course it would be possible to rescale all the fundamental constants together in a way that would just be equivalent to changing units. Things like the fine structure constant are dimensionless ratios that correspond to “real” change.)

    Of course, we see light from distant sources that was emitted long ago, and I’m sure that can be used to put some constraints, but it’s tricky. Stars are messy objects; old stars really are different from newer ones because of the subsequent chemical enrichment of the universe; and if some distant star looks off, there’s usually a much more boring possible explanation. Black holes, on the other hand, are probably too simple, because everything scales with G. We would just mismeasure the mass.

  5. Why (as in, what is the logical justification for it) is it believed that the universe is expanding? I assume it’s that certain ways of measuring distance yield different results than others?

  6. In every direction we look away from Earth, we can see that every distant galaxy appears to be receding from Earth, and that there is a linear relationship between the distance from Earth and the speed of recession. The speed is measured by the Doppler-induced redshift of the spectral emission of the stars in the galaxy.

    So, either our observation point happens to be at the center of the universe, from which all other objects are receding, or the whole universe is isotropically expanding.

  7. “We would just mismeasure the mass” — so if G were not the universal constant we currently believe it to be, but was in some way dependent on time, degree of localized spacetime expansion, or who knows what else, might we mis-measure the mass of the universe by, say, a factor of six?

  8. I phrased that wrong. Why is it believed that the expansion is accelerating is what I meant.

  9. In astronomy, mass is primarily measured by gravity (watching how fast things orbit the object), so lowering G is like dialing down masses. In a cosmological context (in the Friedman equations), changing G is exactly like changing the mass density of the universe. The density would appear to be changing at something other than its expected rate, which would leave an imprint on how Hubble’s constant evolves with time, although it might be difficult to measure. (And, of course, if G changes with time, then our understanding of gravity is incomplete and Friedman’s equations might have other modifications.)

  10. Hi ArkansasReactionary,

    This inference comes from the relationship Josh mentioned being not exactly linear. Faster expansion means a steeper slope for velocity v vs distance d in Hubble’s Law. If the expansion used to be slower, then if we look far enough away, we will see epochs of the slower expansion where the slope is shallower. Basically, v(d) appears to flatten out a bit at high distance/redshifts.

    What could call this measurement into question? It depends on our ability to use type 1A supernovae (exploding white dwarfs) as standard candles. If, for instance, white dwarfs in the early universe were different, the observed relation between luminosity and duration might not apply.

  11. Ok, but how do we know what the distance is, if dv/dd isn’t constant?

  12. Are there many 1A supernovas to use in the first place?

  13. That’s where “standard candles” are needed. You’ve got to have some source whose luminosity you actually know. For instance, if every star had the same luminosity, you could tell how far away each star is by just looking at it. The dimmer ones would be farther away; the brighter ones would be closer. Nature doesn’t appear to have anything line this, but there does seem to be the next best thing: sources whose luminosity appears to be a function of their period or duration–features of their light that one can always measure. Then, you just need enough of those sources close enough to detect their distance in other ways (e.g. parallax) so you can establish and calibrate the function. Then assume the relationship still continues to hold farther away where you can’t confirm it. Ideally have several standard candles as a check.

  14. > Are there many 1A supernovas to use in the first place?

    Enough, anyway. They’re rare in any particular galaxy, but bright enough to be seen from many, many galaxies.

  15. Ok, but shouldn’t we see redshift based on the current expansion rate of the universe? So shouldn’t that coincide with the SC measurement?

    This isn’t an area I understand well.

  16. It’s easier when you’re told that the cosmological redshift isn’t really a Doppler shift. It’s better to think of the galaxies standing still while space expands between them. (“Space expanding” meaning that the Pythagorean theorem has a time-dependent scale factor attached: distance^2 = a(t)^2 [dx^2 + dy^2].) What’s going on with the redshift is that photons expand with the universe as they travel. If the universe gets 2 times bigger (meaning a(t) doubles), between emission and observation of a photon, that photon’s wavelength doubles. Interestingly, it doesn’t matter how fast the universe is expanding at the precise moment of emission or observation. (That makes it different from a Doppler shift.) All that matters is the accumulated difference in the size of the universe (meaning scale factor a(t)). When we see different redshifts at different distances, we’re really seeing different cosmological scale factors at different times in the universe’s history. The slope of the line gives us information about how quickly scale factor growth is accumulating with time around the era of emission.

  17. “What’s going on with the redshift is that photons expand with the universe as they travel. If the universe gets 2 times bigger (meaning a(t) doubles), between emission and observation of a photon, that photon’s wavelength doubles”

    This is incredibly interesting, and not something I’d heard explained before. Thanks!

  18. In SR, as momentum approaches the speed of light, wouldnt mass approach infinity as well since they are directly proportional and velocity will asymptotically approach c? I dont understand how physicists make mass invariant to escape this condition?

    Also is there a way to travel into the past so that I can have more time to study for my E&M exam coming up this week?

  19. Bonald, are you aware of the work of Robert Sungenis who, among other things, debunks Einstein theory of relativity? – http://galileowaswrong.com/buy-the-book/

    Do you personally find any conflict between your traditional Catholicism and field of study?

  20. Hello catodisapproves,

    Mass and momentum are proportional, but in special relativity the equation changes from
    p = m v
    to
    p = m v (1-v^2/c^2)^(-1/2)
    Even with m constant, this blows up as v approaches c because of that third term.

    Now, you might ask where that third term comes from. Basically, it’s because the covariant generalization of
    p = m dx/dt
    is
    p = m dx/dtau
    where tau is the proper time, i.e. time measured in the frame of the moving object. (Time according to the object under study is the only time singled out by the problem, after all.) Because of time dilation, time is passing more slowly for the moving object, so less tau passes for a given change in x. Hence momentum being bigger than it would be in the Newtonian definition.

  21. Can you summarize for me what his argument is for geocentrism?

  22. If I wanted to be a geocentrist, I’d be pretty happy with general relativity. The whole universe revolelves around the earth every 24 hours.

  23. Caveat: I didn’t buy or read Sungenis’s whole book on the matter; but from his writings elsewhere, at least one fundament of his argument is that current theory does not at all refute, and is in fact consistent with, a view that Earth is the center of the universe.

    Josh said the same thing above:
    “So, either our observation point happens to be at the center of the universe, from which all other objects are receding, or the whole universe is isotropically expanding.”

    From what I can gather, Sungenis argues that “our observation point happens to be at the center of the universe.”

  24. @Bonald

    Ok, that makes it much easier to understand.

    But another question, if X is the age of the universe, and space has been expanding, then there should be objects that are presently slightly more than X light years away, but which we can see because the distance the light had to travel would have been less than X, no?

    And if that’s so, shouldn’t we get SC distance measurements of greater than Xc?

  25. Re Robert

    Does he actually argue that the sun revolves around the Earth, or does he just claim that the Earth enjoys a unique place in the universe?

  26. ArkansasReactionary, Dr. Sungenis does believe that the sun revolves around the Earth while it stands still. Years ago, when I first learned about his geocentrism, he offered $1,000 to anyone who disproved it empirically. But no one has won the money.

    I think he’s a young earth creationist, too.

    Sungenis’s website lives at (http://www.catholicintl.com).

  27. Here’s a video where someone interviews Dr. Sungenis.

  28. “Does he actually argue that the sun revolves around the Earth, or does he just claim that the Earth enjoys a unique place in the universe?”

    You’re misunderstanding; of course the sun revolves around the Earth. Has nothing at all to do with Sungenis. NASA’s “Astronomy Picture of the Day” just had a demo pic of the two black holes captured by LIGO “revolving around each other.” In common parlance we often say that the body with lesser mass “revolves around” the body with greater mass; but note that astronomers don’t quite see it that way.

    Sungenis’s purpose in all of this is to try to establish a much wider and deeper range of truth-invariance to long-standing ecclesiastical teaching, particularly papal teaching. That teaching, Sungenis shows, also often included or assumed teaching about the truth-nature of these pronouncements, and their seriousness. He’s strenuously objecting to the idea that one can overturn what he sees as constant magisterial teaching over centuries, by using some exterior standard (that we’ve just now come up with). And showing that (for instance) ‘modern science’ does not in fact overturn the centuries-long Church teaching that the Earth is the center of the universe, helps Sungenis’s case.

    Anyway, Bonald at least, now has enough to go on re Sungenis; that having happened, I’m signing off on this topic.

  29. Nearly forgot to comment that I heartily enjoyed the title of this post: “Ask a Relativist.” Pretty good pun on yourself, Bonald; I liked it a lot.

    Fr. Stanley Jaki, of course, remarked somewhere (I can’t track it down at the moment) on the blatant absurdity of Einstein’s naming of the Special Theory, since it all depended, not on ‘relativity’, but on the absolute invariance of the speed of light.

    I did find Jaki more generally discussing Einstein’s own ‘relativism’:

    http://stanleyjaki.blogspot.com/2015/09/the-absolute-beneath-relative.html

  30. Pace josh above, I also don’t understand why relativity isn’t a complete vindication of the Church in the Galileo affair.

    That is, why can’t I say that if every frame is as good as every other frame (from the POV of physics), then the rotating frame of some guy standing on the surface of the Earth is the best frame (because if physics abstains, some other voter gets to make the decision, like, say, the Bible)?

    Does A revolve around B or does B revolve around A is a question which implicitly supposes an inertial frame, does it not?

    It seems even better than this, though. Physicists routinely use whatever frame makes their calculations in the problem at hand most convenient. Isn’t this exactly the Church’s position in the Galileo affair? Somewhat anachronistically: the geocentric frame is the best frame, but if you want to use other frames to do calculations because that’s more convenient: have a party.

    The attempts I’ve seen to dodge this line of argument have struck me as either lame or incomprehensible (I don’t rule out the incomprehensible-to-me ones being right, of course).

  31. And, ironically, it was Galileo who started the whole idea of velocity being relative.

    It’s true, one frame is as good as another. When we say that the Earth revolves around the sun and not vice versa, we just mean that the coordinate system that shows the former is an inertial coordinate system (asymptotically Minkowski) while the latter isn’t. (Even that isn’t exactly true.) I tend to agree with my discipline’s prejudice that inertial frames are superior, and of all such frames that of the cosmic microwave background has the best claim to being special, but it is still a prejudice.

  32. I understood that the Church had the right of it in the Galileo affair because she was rightly defending the established Ptolemaic system against Galileo’s insufficiently proven new theory. Have I got it wrong?

  33. Google “great Ptolemaic smackdown”

  34. Remember, guys, we’re not obliged to think that the Church (or, more specifically, the Roman Inquisition) was right in this case at all. The issue is certainly more ambiguous than is commonly perceived (Galileo’s arguments were wrong and his treatment not particularly harsh), but it still strikes me as an unfortunate use of ecclesiastic authority. I see no need to condemn a theory just because it’s insufficiently proven.

    Anyway, I don’t buy the idea that geocentrism is in the Bible. I talk about the sun rising and setting all the time, for example, without intending to endorse geocentrism.

  35. Forgive me if this is a bit OT, but we see or infer the presence of really dense stellar remnants supported by electron degeneracy pressure (white dwarfs) and neutron degeneracy pressure (neutron stars). Why don’t we see anything supported by proton degeneracy pressure, or other weird hyper-dense stellar remnants?

  36. @Peasant

    At degeneracy pressure, protons and neutrons take up far less space than electrons. So So in order to make a proton degenerate gas, you would need to take an electron degenerate gas and move all of the protons to the center. The EM force is so much more powerful than gravity that this is not possible.

    Neutrons are unstable on their own, and tend to decay into protons and electrons (and antineutrinos). But they are only slightly unstable, having a half-life of several minutes. Because they are only slightly unstable, the extremely high potential in the nuclues of an atom (resulting from the strong force) creates a situation where it would be less energetically favorable for them to decay (since protons attract each other more weakly than neutrons), thus rendering them indefinitely stable in most atomic nuclei.

    Neutrons stars are similar, except based on gravity rather than the strong force. Because the decay of a neutron star’s neutrons would cause it to expand to be many times bigger (and thus have less gravitational potential energy), it is more energetically favorable for the neutrons to not decay, and they are thus rendered indefinitely stable.

    But neutrons are unique in this regard. All other unstable subatomic particles are much more extremely unstable, to the point where they would have to be heavy enough and small enough to create a rather large black hole before they could stably exist at degeneracy pressure.

  37. Hello,

    I see ArkansasReactionary beat me to it, but here’s the answer I was composing.

    There will be proton degeneracy pressure in a cold neutron star, but it’s less important than degeneracy pressure from neutrons just because high density matter has many more neutrons than protons (by a factor of 8, for the simplest equation of state). Ultimately, the reason high density matter tends to favor neutrons in the lowest energy state is because, to maintain charge neutrality, one must have an electron for each proton, so one “pays” the energy of both a proton Fermi gas and an electron Fermi gas for having protons.

  38. Geocentrism as medievals understood it involved the idea that there is a unique up-and-down direction in the world. While heliocentrism is happy with many local up-and-down directions. Since, we have been to Moon and have felt the local up-and-down direction, the medieval geocentrism is definitely disproved.

  39. Up and down flip for Dante when he passes through the center of the Earth, but I suppose it’s true that the medievals presumed a unique center point toward which everything fell. Arguably this was out when Galileo recorded the phases of Venus. My own definition of geocentrism would be that the Earth motion is inertial compared to an average of the stars in our neighborhood of the galaxy or to the Hubble frame as measured by the CMB. Both of these can be easily ruled out with Doppler shifts. However, since this is probably not what the medievals meant, so disproving it doesn’t mean anything one way or the other.

  40. @mikvet

    There are two questions. Was the Church right, given the available knowledge at the time, in the Galileo affair? This question is boring. Obviously, the Church was right. The Ptolemaic system was at the time and remains the most successful scientific theory of all time. By Galileo’s time, it had been chugging along producing correct predictions for 1000 years. It still produces correct predictions. Copernican heliocentrism was worse than the Ptolemaic model in that its predictions were worse. It was also worse in the sense that it predicted the parallax, and the parallax was not forthcoming. It was also new which is always a bad-making thing in a scientific theory. Finally, as pertains to geocentrism, everything Galileo said which was original was wrong, pretty much.

    The second question is was the Church right, given our current state of knowledge. As I say above, I think it was.

  41. @vishmehr24

    “Geocentrism as medievals understood it involved the idea that there is a unique up-and-down direction in the world. ”

    Really? How did they explain the fact that Chinamen’s feet stuck to the ground?

  42. @Bonald

    I don’t think the case was ambiguous at all. Galileo was wrong, and the Church was too mild with him.

    ” I see no need to condemn a theory just because it’s insufficiently proven.”

    Huh? The Church did not condemn Copernicus. The Church did not condemn the various Copernicans, including Galileo, for being Copernicans. The Church was, if anything, pleased with Copernicus.

    The Church did not condemn heliocentrism because it was insufficiently proved. Germany did not outlaw the swastika because it is aesthetically unpleasing. Before Galileo, heliocentrism was licit. Before the Nazis, the swastika was licit.

    The Church condemned heliocentrism because it was Galileo’s flag. The Church rightly recognized that Galileo’s attitude towards the Church’s authority was defective, that he was schismatic in fact if not in theory, that he was some kind of semi-Protestant. And She recognized the danger of letting him continue to run around saying the things he was saying.

    Galileo articulated the view that the Church did not have the authority to judge scientific theories, that it’s ambit was limited to airy fairy spirity stuff inside people’s heads. The Galileo affair was kind of a reprise of the Condemnations of 1277. When the Church told him to cut the crap, he went on a demented rampage in which he openly mocked the Church’s authority.

    The Church did Galileo the great kindness of taking away from him the thing which was leading him into heresy and rebellion.

  43. Does GR implies the B-theory of time? Or does it depend on what interpretation of the equations is used, as with wave-function collapse in quantum mechanics?

  44. DrBill,
    Medievals knew that the Earth was spherical. The unique up-and-down direction is radial, toward the center of Earth.

  45. I think you have a very broad understanding of the concept “disproved.” Geocentrism, read as the theory that the Earth is at the center of the universe, can survive the falsification of the auxilliary assumption that gravity points everywhere towards the center of the Earth.

    The fully articulated Ptolemaic theory, complete with crystal spheres, is falsified by comets. Medievals knew about them or at least enough about them to understand that they were problematic.

    Given that the geocentric and heliocentric theories were about evenly matched in terms of predicting what they were supposed to predict (the movement of the heavenly bodies), the contest was comets vs parallax.

    Heliocentrism says there should be stellar parallax, and there was none. A determined heliocentrist could say that the lack of measured parallax occurs because the stars are so far away (and therefore huge) that the parallax was swamped by measurement error. This is one of the signature arguments of cranks. It turns out to be right here, of course.

    Geocentrism, as articulated by Medeivals, leaves us wondering how comets move around the heavens, since they should be bashing into the spheres. This problem is fixed by getting rid of the spheres. Getting rid of falsified auxilliary assumptions like this to preserve the core theory is a hallmark of non-crank science.

    Anyway, the Bible passage which was taken to favor geocentrism doesn’t require anything about the direction gravity points or whether or not there are spheres and etc. It just requires that the sun go around the Earth.

  46. @Bill

    Regarding the reference frames being equal argument, that only applies to inertial reference frames. If the sun revolved around the Earth, it would involve huge violations of conservation of momentum.

  47. @AR

    That’s not what Bonald says above, nor is it my understanding.

  48. Well, you can work in rotating frames of reference if you’re willing to live with Coriolis forces, a non-Minkowski asymptotic metric, and the like. The laws of physics (expressed in the properly covariant way) will work fine, but such a coordinate system is bound to seem unnatural except near Earth.

  49. You’re right, the conservation laws would still work if it were assumed that space itself were rotating.

    But that seems excessively ad hoc to me.

  50. Me too. I guess DrBill’s point is just that what I find a natural coordinate system depends somewhat on criteria I get to choose, but saying Church officials got involved in a dispute over coordinates makes them sound even more boneheaded than saying they got involved in a dispute over science.

  51. DrBill said:
    > The Church condemned heliocentrism because it was Galileo’s flag. The Church rightly recognized that Galileo’s attitude towards the Church’s authority was defective, that he was schismatic in fact if not in theory, that he was some kind of semi-Protestant. And She recognized the danger of letting him continue to run around saying the things he was saying.

    It occurs to me that I’ve been far more disrespectful of a sitting pontiff than Galileo ever was.

  52. saying Church officials got involved in a dispute over coordinates makes them sound even more boneheaded than saying they got involved in a dispute over science.

    Let me know if you ever meet such a one, and we can have a good laugh at his expense.

  53. It occurs to me that I’ve been far more disrespectful of a sitting pontiff than Galileo ever was.

    As Zippy is wont to point out, you’re just obediently making a lio.

  54. This seems the most reasonable place to ask: Do you know how astronomers can describe the material makeup of asteroids we’ve never been to? Do you have some resources that you can point me at so I can get a basic understanding?

  55. Spectroscopy is the main tool. One can look at the sunlight reflected by an asteroid and see what wavelengths got absorbed. For some asteroids, the mass (and therefore density) can also be inferred from the effects of the asteroid’s gravity.

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