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All celestial bodies I can think of rotate. The sun, the planets, the moon, the galaxies, clusters of galaxies, the supermassive black hole at the center if the Milky Way, accretion discs, etc. It would be very strange if they didn't. They couldn't even exist.

Are there examples of non-rotating bodies? I can find no funamental reason why such an object can't exist. Maybe a planet or two stars that have had a tangential encounter.

Deschele Schilder
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    Whilst avoiding being labelled as a duplicate by just including every object in the universe, the answer is the same: https://astronomy.stackexchange.com/questions/29366/is-it-possible-for-stars-not-to-rotate?noredirect=1&lq=1 – ProfRob Jun 27 '21 at 13:42
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    @ProfRob But are there objects that dont rotate? Or is that a meaningless question as all motion is relative? Are there objects not experiencing a centrifugal firce? – Deschele Schilder Jun 27 '21 at 13:52
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    related recent article: https://www.newscientist.com/article/2280743-enormous-strands-of-galaxies-in-the-cosmic-web-appear-to-be-spinning/ – Aaron F Jun 28 '21 at 09:00
  • Comments are not for extended discussion; this conversation has been moved to chat. – called2voyage Jun 29 '21 at 13:12
  • Supposing an object existed that was absolutely not rotating at this moment, I would think that it must be a temporary condition. If the object has volume, that would naturally mean that one side would be closer to another massive object. Gravity would have a slightly different pull on that side, which would likely cause the object to start spinning a bit. So yes, just the right kind of collision might transfer all of a body's rotational inertia to another object, eventually, and probably not too long later, it would steal some from other bodies nearby. – Seth Jun 30 '21 at 16:53

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As with any claim of possibility, it really comes down to whether we are able to measure it or not. Since we're not talking about quantum mechanics, this is not too difficult to speculate.

All celestial bodies I can think of rotate. The sun, the planets, the moon, the galaxies, clusters of galaxies, the supermassive black hole at the center if the Milky Way, accretion discs, etc. It would be very strange if they didn't. They couldn't even exist.

Indeed! There are lots of reasons to expect any astronomical object in the Universe to be rotating, e.g., because of the angular momentum it will inherit after formation.

Are there examples of non-rotating bodies?

IT is possible that an object is rotating so slowly that is is not possible for us to measure the rotation rate with empirical certainty, and so we may presume that the object is not rotating, and we'd be fine with assuming it is not rotating in our theoretical models of such an object (within that regime). I do not know of such an example, but one can exist in principle.

Here is a list of observed slowly rotating objects, i.e. asteroids and exoplanets. The asteroid with the currently known smallest rotation rate has a period of ~1800 hours, which is about 75 Earth days. As the first figure in that wiki article shows, there is no obvious correlation between diameter and period for exoplanets.

With disk galaxies, it is known that they all, regardless of difference in size, have the approximately same rotation rate.

Long period radio pulsars are rotating slowly compared to other pulsars, with periods of over 5 seconds, and they are very difficult for astronomers to observe. For example, PSR J0250+5854 has the slowest spin period when compared to any known magnetars and X-ray dim isolated neutron stars.

I can find no fundamental reason why such an object can't exist. Maybe a planet or two stars that have had a tangential encounter.

A simple answer (perhaps) is conservation of angular momentum: the progenitor's angular momentum before the object forms is not destroyed.

Daddy Kropotkin
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    It would be fun to plot a histogram of $\omega = 2 \pi/T$ for all of those together from 100 hours up to the maximum. I wonder if it would be flat? (I just don't know how to easily extract those numbers or I'd do it myself) – uhoh Jun 27 '21 at 18:21
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    That could be interesting indeed, and not too expensive to do in python with the py.corner module. However, I do not know if the list on the wiki page is comprehensive enough to be informative to make such effort worth it. – Daddy Kropotkin Jun 27 '21 at 21:42
  • Cant the progenitors have opposite angular momentum so after the encounter they have zero rotation? Can planets exist for which a day lasts as long as a year? – Deschele Schilder Jun 28 '21 at 18:46
  • @DescheleSchilder Not the point of your comment's question, but a tangential observation about the definitions of days and years: the Moon has a sidereal day equal to its "Gaian" sidereal year. This is the statement that it is tidally locked with Earth-- any planet tidally locked to its star would have this property. Of course, the moon's Gaian day (analogous to our solar day and presumably what you mean in this context) seems difficult to define, with the most obvious candidates to my mind being zero and infinity. – jawheele Jun 29 '21 at 18:28
  • Neutron stars are known to lose angular momentum via their magnetic fields through a process called "spin down". See https://en.wikipedia.org/wiki/Neutron_star, section "Spin Down". Since the rate of spin-down is constant, it follows that some neutron stars will eventually stop rotating completely. – C Teegarden Jun 30 '21 at 17:39
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Yes, there is one and only one!

The universe itself is not rotating about an axis; it is isotropic, which is actually a stronger property (meaning all degrees of freedom are equal in magnitude). For example, in addition to non-rotation, it is not stretching in one dimension more than another.

If it were to be rotating, the cosmic microwave background measurements would show spiral effects, which are not present.

You asked for an object in the universe. Whether the universe is in the universe, and whether it is an object, I leave up to the philosophers ;-)

Although you mentioned celestial objects, the actual question didn't specificy that the object had to be a celestial object, so please forgive my pedantry in sharing this very cool, fairly recent research with you!

https://www.imperial.ac.uk/news/174667/scientists-confirm-universe-direction/

Robino
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    Journal if you want to go deeper https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.117.131302 – Robino Jun 28 '21 at 08:06
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    Nice answer! But cant we say that if the universe rotates that the cmbr is rotating along? – Deschele Schilder Jun 28 '21 at 08:11
  • @DescheleSchilder Yes, we could, and the null hypothesis was that this was (one of) the case(s). If indeed this was the case, the cmbr would be travelling through spiraling/rotating space, which would affect cmbr polarity. Therefore we would expect the polarity of cmbr to be different from different parts of the universe. However it all "looks" the same. From the data, the odds that there is a difference is 120,000 to 1! – Robino Jun 28 '21 at 10:37
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    This becomes more of a "Rotating relative to what?" question. Since it's not possible to observe the universe from the outside, we can't say for certain whether or not it rotates, or whether even the concept of rotation could apply to an entire universe. – Darrel Hoffman Jun 28 '21 at 14:30
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    @DarrelHoffman In an otherwise empty universe, with no stars, dust or anything at all, you are floating (in a spacesuit) with your arms stretched out. If pulling your arms in makes you feel an acceleration, then you are rotating. Rotating relative to what? – Robino Jun 28 '21 at 15:13
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    Ernst Mach believed that you could not be rotating, as there is nothing to rotate relative to, and therefore you would always feel nothing when bringing the arms in. Intuition (at least for myself) says otherwise however and this has been the scientific communities view since the acceptance of Einstein's GR. – Robino Jun 28 '21 at 15:33
  • In answer to your question, it is rotating relative to the previous "slice" of spacetime. – Robino Jun 28 '21 at 15:36
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    This answer doesn't make much sense. It's certainly possible to have cosmological models with rotation, such as the Godel spacetime. But there is no reason to say that "Yes, there is one and only one!" The rotational frequency of the universe is something that can be measured, just like the rotational frequency of any other astronomical object. We can put an upper limit on it, just as with any other object. –  Jun 29 '21 at 00:59
  • @BenCrowell there have been models with rotation, however the research from Imperial College London and UCL state (quoting from the abstract) "Including all degrees of freedom simultaneously for the first time, anisotropic expansion of the Universe is strongly disfavored, with odds of 121 000:1 against." I linked to the paper in my first comment. I would be interested to hear your thoughts on it. – Robino Jun 30 '21 at 10:26
  • @Robino: The Saadeh paper is available on arxiv without the paywall: https://arxiv.org/abs/1605.07178 The probability you quote looks like it's a Bayesian probability, with prior distributions arbitrarily chosen for certain variables. That means it can't be interpreted as the probability that X is true. Your claim that there is something special about the universe as opposed to other classical systems -- that we can somehow measure its angular momentum to be exactly zero -- doesn't make any logical sense. –  Aug 02 '21 at 16:18
  • @BenCrowell probabilities are often quoted like that because it's more accessible to members of the public. Bets on horses are quoted as "odds" and is not to do with Bayesian probabilities. To say that a result is not true because the way the certainty about the result is published reminds you of something else is nonsensical. – Robino Aug 06 '21 at 20:18
  • For the avoidance of doubt, it is not "my claim" that the universe is isotropic, I am just sharing peer-reviewed, widely accepted, published scientific research. – Robino Aug 06 '21 at 20:27
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There are many objects in the universe. By chance, some will happen to have zero angular momentum. It is a meaningful question, because "all motion is relative" applies to linear motion, not acceleration or rotation.

If an object is changing rotation, slowing down and eventually spinning the other way, at some point it will have a rotation of exactly zero.

Very old black holes will shed angular momentum in the Hawking radiation, so they will naturally become non-rotating ... eventually (but not yet).

But there are objects that are very carefully given non-rotating status: scientific instruments. I suspect that Gravity Probe B was non-rotating (the whole thing, not the gyros held within), and an instrument that studies the CMB will point steadily while making an exposure.

I take back the "relative motion" part, slightly: GP-B was not rotating in the sense of there being no centrifugal forces on it, but it measured (very tiny) rotation anyway due to two GR effects. So what you mean by non-rotating can vary. All observers agree that there's no centrifugal forces; that is, no acceleration due to rotation. But it will change orientation relative to the CMB or another such object that's no in a close orbit, anyway, because space is not flat.

JDługosz
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  • I indeed mean no relative rotational motion between the universe and the object ( no centrifugal forces). Best answer! – Deschele Schilder Jun 29 '21 at 18:07
  • "no relative motion between very distant points in the universe and points on the surface of the object" and "no centrifugal forces" are different, not equivalent. Due to space shrinking around a massive object, a body in orbit (like GP-B) can do one or the other but not both at the same time. It will end up turning without having any angular momentum or feeling any centrifugal forces, or it can experience rotation in order to avoid moving. – JDługosz Jun 29 '21 at 18:13
  • So being at rest wrt earth (no rotation and linear motion) means no rotation? Instead the universe is rotating? – Deschele Schilder Jun 29 '21 at 18:18
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    @DescheleSchilder see https://en.wikipedia.org/wiki/Geodetic_effect No, the Universe is not rotating; rather, spacetime is not flat. Moving in a path through space, without rotating at all, and coming back to your starting position, you can end up pointing in a different direction than you started with. – JDługosz Jun 29 '21 at 18:25
  • What do you mean bý space shrinking? How can space shrink (or expand)? – Deschele Schilder Jun 29 '21 at 18:25
  • Come back with another orientation? Dont only parallel vectors do that? Or do you mean a freely falling body? – Deschele Schilder Jun 29 '21 at 18:28
  • Also, read Greg Egan's introduction to Parallel Transport. Re space shrinking: that's General Relativity. The distance around a circle (around a massive object) will be a little bit shorter than Euclid would tell you. This is famously how GR solved the puzzle of the precession of Mercury. – JDługosz Jun 29 '21 at 18:30
  • I was exactly thinking about Mercury! Thats why I wrote a freely falling body. So the circle doesnt fit for Mercury? More or less. – Deschele Schilder Jun 29 '21 at 18:35
  • So mercury rotates an extra round every time it is bak where it started (after many rotations around the sun)? – Deschele Schilder Jun 29 '21 at 18:39
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    Search for questions here and on Physics SE, and search the Web in general, to read up on Geodetic Effect. Then, if needed, post a new question (here or on Physics). – JDługosz Jun 29 '21 at 18:44
  • Yes! I always ask a bit too much... – Deschele Schilder Jun 29 '21 at 18:46
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"Not rotating" is equivalent to "zero angular momentum". In classical mechanics, angular momentum is a continuum, and so the distribution is a continuous probability distribution where, even if zero is the mode, the probability mass for any single value is zero.

In quantum mechanics, eigenvalues of the angular momentum operation are all half-integer multiples of $\hbar$. Since this gives a finite number of possible values, the probability of zero is finite, but the range of possible angular momentum is so huge compared to $\hbar$ that the probability of it being exactly zero is essentially nil for a particular object. For instance, the angular momentum of the Earth about its axis is somewhere around 75 orders of magnitude larger than $\hbar$.

The probability of an angular momentum randomly selected from a range between zero and the earth's angular momentum being zero is similar to the chances of randomly choosing a molecule of air out a room four times and getting the same one each time. In an infinite universe, we can expect some objects to have zero angular momentum, but the observable universe does not have enough planet-sized objects to expect one of them to have zero angular momentum.

If we go to a molecular level, not only is the range of possible values smaller, but the number of molecules available is larger, so at that scale, there are quite a few with zero angular momentum (again, ignoring mixed states).

Acccumulation
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A nonrotating body would need to have zero angular momentum. Not very little, not SubUltraMicroscopicallyInfinitestimal, but zero.

The chance of finding a celestial body that does not rotate at all, is about the same as finding a yardstick that is exactly one yard long. Not even one planck length more or less.

Would you consider a planet that rotates once every 10 million seconds to be nonrotating? If so, look to Venus. Which, by the way, is the most non-rotating natural celestial solid body I could find.
Nonetheless, it is still rotating.

How about something that (controlled) rotates less than about 5 milli-arcseconds over a year? For that, look to the Kepler Space Telescope. (when it was still in use, and nonrotating only while commanded to do so).
Nonetheless, it was still rotating.

Attaining absolute non-rotation is as difficult as attaining absolute zero temperature. You can get close. Very very close. But it is unreachable.

PcMan
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  • Is it the same as asking if an object has a zero linear velocity? Is rotational motion just as relative as linear motion? Or is it an absolute state of motion? – Deschele Schilder Jun 28 '21 at 08:06
  • Not quite. linear motion is purely relative between two objects. An object's rotation is relative to itself, only. A single marble in deep space, blind, would not be able to tell if it was undergoing linear motion at all, much less in what direction and how fast. But it would be able to feel the effects (centifugal "force") imparted by its own rotation. – PcMan Jun 28 '21 at 08:11
  • But the centrifugal force can also be caused by the masses rotating around the marble (frame dragging). – Deschele Schilder Jun 28 '21 at 08:14
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Because scalar fields (like the one hypothesized to drive most--but not all--versions of cosmic inflation) don't rotate, the idea that the universe (or the local "Universe", in some versions of a multiverse) doesn't rotate has become very popular, but there have been some indications (like a recent sky survey, described at https://arxiv.org/pdf/2101.04068.pdf, by Lior Shamir) to the contrary. However, non-rotating objects must exist instantaneously in some rare gravitational situations, such as rarely perfect collisions of previously-rotating objects of identical mass & volume.

For a version of cosmic inflation that actually requires rotation of each of the local universes in its multiverse, check out Nikodem Poplawski's torsion-based cosmological model, described in many 2010-2021 papers whose preprints can be found by his name on Cornell University's free Arxiv website. It's well-known but not widely-accepted, mainly because its provision of a (tiny) spatial extent for fermions requires Einstein-Cartan Theory, developed by Einstein and the mathematician Cartan in 1929, a few years after the discovery of particulate spin: Although it reduces to General Relativity in vacuum, ECT is more complicated and uses notation still unfamiliar to many physicists. (Also, Poplawski's model implies a multiverse eternal to the past as well as to the future, and such "past eternality" is contrary to creationistic beliefs widely-accepted in the most populous English-speaking country, so that familiarity with ECT is not necessarily an advantage in many of its ecclesiastical and state-run universities.)

Edouard
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