Posts Tagged ‘relativity’
gravitational mysteries 2 – it’s not a force, but…
this has something to do with it all…
So I mentioned in my previous post that the Moon is tidally locked to the Earth, keeping the same face to us, presumably for eons. I left it there, without an explanation from Dr Google or anyone else. Does it have anything to do with that gravity thing?
There’s an answer on Eos, an Earth Sciences magazine I’ve shamefully never heard of, so thanks to Caroline Hasler:
A tidally locked object rotates around its axis exactly once during its orbit around a host planet or star. This physical quirk affects many planets and moons, including Earth’s Moon…
This tidally locked state is a consequence of gravity. As the Moon orbits Earth, Earth’s gravity tugs at it. This force deforms the Moon, reshaping it from a perfect sphere into something a little more akin to an American football: slightly squashed at the poles, with a bulge at its equator facing Earth and another on its far side. The same sort of deformation manifests itself in Earth’s oceans, where the Moon’s tidal forces produce watery bulges that travel around Earth as it rotates, leading to alternating high and low tides.
So gravity, this curvature of space-time, deforms the moon, and presumably the oblate spheroid that is the Earth, and billions of other bits of flotsam and jetsam spewed out by our messy universe. Interestingly, though, Hasler describes gravity as ‘this force’, while so many others, such as Veritasium and the PBS SpaceTime presenter, insist that it’s not a force… the point being that it’s hard, it seems, even for those who understand the physics of gravity (though I sometimes wonder if anybody really does), not to describe it in forceful terms. Anyway it’s this gravity spacetime curvature that ‘forces’ the Moon to be locked into facing the Earth without ‘turning away’. And yet the Earth isn’t tidally locked to the Sun. This is partly because the Earth is too far away, and partly because it’s already tidally locked to the Moon.
Exoplanets have been found that, due to their closeness to their stars, are tidally locked to them. Mercury is apparently ‘semi-tidally locked’ to the Sun at present (it has what they call a 3:2 spin-orbit resonance, rotating 1.5 times for every orbit) but presumably this tidal locking will gradually unlock as Mercury spirals away from the Sun over time – an awful lot of time. Which suggests that planets like Earth are getting further from their stars, very very gradually. And so eventually the Moon will gradually unlock itself from the Earth. As to why this is happening, I don’t know – as yet. In the planets’ case, it’s probably because the Sun is gradually losing mass. You can’t get energy out of nothing.
I’m watching Leonard Susskind’s online lectures on special relativity – or rather, I’m watching the first lecture, and I’m already lost. I’ve also bought and had a go at Susskind and Friedman’s book, Special Relativity and Classical Field Theory: The Theoretical Minimum, but haven’t got very far. I’ll keep trying, I think, and then I’ll die. It’s the maths that tends to trip me up.
So let’s go with the book, which is easier to continually refer to. It starts by telling me that special relativity is all about reference frames.
In general, reference frames are about perspectives. Everybody’s perspective is different, due to the time and place of their birth, their upbringing, which has decisively affected their neural development and so forth. All very complex, so we’re narrowing the term to refer to location in time and space. In the Cartesian sense, we have spacial co-ordinates on three axes, x, y and z, as well as an origin from which we can measure distances. And then there’s a t axis for time. So at this stage we have to imagine that time is synchronised for everyone – same starting point and same rate.
So these reference frames, in terms of space, vary individually (we can shift them around) and from other reference frames. They can be moving or (relatively!) stationary. Time, though, seems a bit trickier:
The assumption that all clocks in all frames of reference can be synchronised seems intuitively obvious, but it conflicts with Einstein’s assumption of relative motion and the universality of the speed of light.
Susskind & Friedman, Special Relativity and Classical Field Theory, p5
So we have coordinates to pin down events. The laws governing those events are apparently the same in all inertial reference frames (IRFs) – i.e in which a body, subject to no forces, moves in a straight line with uniform velocity. So, in a fast moving plane, you will be subject to the same laws as you’re subject to on the (rotating) ground, as long as your velocity is uniform. Everything’s in movement, one might say, but if your movement is uniform, then it’s as if you’re at rest. You’re in an IRF.
Now I want to jump, if it’s a jump, to Lorentz transformations, which I’ve been trying unsuccessfully to understand. Here’s how Wikipedia clarifies the matter:
In physics, the Lorentz transformations are a six-parameter family of linear transformations from a coordinate frame in spacetime to another frame that moves at a constant velocity relative to the former. The respective inverse transformation is then parameterized by the negative of this velocity.
I’ve taken out all the links, which, if followed, might enlighten me further, but clearly this is v complicated stuff, which I need to understand for an understanding of special relativity. I expect to fail, valiantly, so first I will say that Hendrik Lorentz was an intellectual giant in what became the transformative physics of the early 20th century, making vital contributions to the understanding of electromagnetism, electrons, the aberration of light and much much else.
Lorentz transformations are transformations within inertial reference frames. What about non-inertial reference frames? They would include accelerating and decelerating motion (obviously non-constant velocity), and, apparently, a rotating reference frame. But isn’t the Earth’s rotation something we don’t feel because of the constant velocity of that rotation? But then, doesn’t the Earth, or a ball, rotate at different rates around the axis of rotation? Isn’t it obvious that a person on the equator is moving at a faster pace than someone close to the rotational axis? Apparently, the cognoscenti define this as ‘a special case of a non-inertial reference frame that is rotating relative to an inertial reference frame’.
Actually, there are times when I really do wish I was a bonobo.
I’ll stop here for now, having so far avoided the mathematics. Maybe next time, or maybe not, but I must add here something consoling I read today in Richard Dawkins’ most recent book, Book do furnish a life:
… practising scientists do need years of training. But you can enjoy music, appreciate music even at quite a sophisticated level, without being able to play a note. Similarly, I think you can appreciate and enjoy science at quite a sophisticated level without being able to do science. I want to encourage people to treat science in the same kinds of way they would treat music or art or literature: as something to be enjoyed, not at a superficial level, but at quite a deep level, without necessarily being able to tell one Bunsen burner from another or integrate a function.
R Dawkins, Books do furnish a life: reading and writing science, 2021, pp 109-10
References
Tidally Locked and Loaded with Questions
Why are planets not tidally locked with the sun?
byu/Neotheo inaskscience
Richard Dawkins, Books do furnish a life, 2022 (paperback edition)
the ever-fascinating herr einstein
‘I am truly a “lone traveller” and have never belonged to my country, my home, my friends, or even my immediate family, with my whole heart; in the face of all these ties, I have never lost the sense of distance and a need for solitude – feelings which increase with the years. No doubt, such a person loses some of his innocence and unconcern; on the other hand, he is largely independent of opinions, habits, and judgements of his fellows and avoids the temptation to build his inner equilibrium upon such insecure foundations.
Albert Einstein, 1931
Currently reading a book called Einstein & Oppenheimer: the meaning of genius, a slightly grandiloquent title, and the book is at times rather dourly ponderous, but fascinating, especially about that remarkably self-contained solitary, Einstein. Solitary but not too solitary, for the list of his correspondents is daunting. My own correspondence, even with the whole internet to assist me, is paltry by comparison, and I know that comparing myself in any way to Einstein is – well, cheeky to say the least. But since I compare myself with everyone else, why not with him?
This book treats of the theoretical work of Einstein in some detail and with apparently great proficiency [I’m in no position to judge], but though I really do try to get my head around the idea of a unified field theory, quantized general relativity and the whole concept of a gauge theory, I’m more interested in his temperament, his basic nature, and the associations I keep making with my own.
One interesting association was Schopenhauer. I read a collection of his writings in my early twenties. Probably the first philosopher I read after Nietzsche, and before the more tamed, academic philosophers of the Anglo-American tradition. Schopenhauer was a dour, dignified pessimist, a kind of modern Stoic, whose writings could nevertheless provide much consolation for solitary types, as for example this passage, which much influenced Einstein:
What a person is for himself, what abides with him in his loneliness and isolation, and what no one can give or take away from him, this is obviously more essential for him than everything that he possesses or what may be in the eyes of others… for one’s happiness in this life, that which one is, one’s personality is absolutely the first and most essential thing.
Reading passages like this, when you’re young but yet not so young that you haven’t already experienced years of solitude, is of course only partially consoling. It’s also hard, very hard. We don’t want to face the reality of our own nature, even when that nature – its cogitations, its imaginings, its memories – has given us such pleasure and sustenance over the years. We constantly hope for some kind of self-transformation, a hope deferred that makes the heart sick. But to return to Einstein, he obviously had other consolations, a brilliance and a focus well beyond the best of my imaginings and application. And the extraordinary results of that brilliance and focus were surely enough to allow him to feel well satisfied with his solitary self.
Clearly, in his quiet way, Einstein was a man of enormous self-confidence. Of course, being recognized, from 1915 until his death, as by far the most transformative scientist of the twentieth century will have had some effect upon his ego, but in fact his self-confidence was manifest well before he presented his theory of general relativity. Silvan Schweber, the author of the book I’m reading, illustrates this in ingenious fashion.
Einstein, under the early influence of Schopenhauer, went on to read various Hindu philosophico-religious texts [another association: after reading Schopenhauer, I went out and bought copies of The Upanishads and The Bhagavad-Gita, but I didn’t get very far with them]. It was apparently under the influence of Vedic philosophy that Einstein developed a curious habit of holding his thumb and forefinger together, in what is called the vitarka gesture, especially when he posed for photographs. This gesture, often presented in images of Vishnu and Buddha, is a sign for compassionate teaching, and in a later Buddhist teaching it symbolized the union of method and wisdom. There are at least four extant pictures of Einstein using this gesture, shown below. It might seem pretentious almost, but I find it powerful in its quiet assertion.
Solvay, 1911. Einstein second from left
Solvay 1913. Einstein standing, centre
Solvay 1927. Einstein is now the central figure
1942