Archive for the ‘relativity’ Category
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)
gravitational mysteries – part one, maybe
what happens when you fall for gravity…
I don’t understand gravity, and I doubt that memorising equations will be of much help.
Gravity, I’m told, is a killer. If I fall from a high cliff, or a multi-storey building, onto hard ground below, I’ll most certainly die, due to gravity (and carelessness, because I know what falling onto hard ground, even just from a standing position, can do to a person). So gravity should be treated with gravity.
But then, gravity has benefits. It keeps us on the ground, prevents us from flying away. In fact, gravity has essentially formed our bodily structure. We have muscular legs which with some small effort we can lift from the ground and plonk down in another place in a tiny ongoing battle with gravity, which we’ll eventually lose.
So I suppose it could be said that gravity is a given. An essential element in the development of all living things that creep over the earth and even fly in the sky just above it. We just have to deal with it.
And yet, I hear things about gravity that don’t make much sense to me. I hear that gravity pins humans to the Earth, but also pins our planet to the Sun, and pins the Moon to our planet. And yet it doesn’t. The Moon hasn’t fallen to the Earth in the way that my body would fall to Earth from a tall building. It circles the Earth. In fact it is spiralling slowly away from the Earth. Something else must be happening, surely?
So what do I do when I don’t know? I consult people who claim to know. And what do they say? Well, in terms of the Moon’s spiral, it’s about velocity. Here’s an explanation designed for children, or children at heart like me:
From Earth, it might look like the moon is stationary, meaning it is not moving, but in reality, each year the moon gets 3 cm [further] away from Earth. Without having the force of Gravity from earth [the] moon would have just floated away from us. The moon’s velocity and distance from Earth allow it to make a perfect balance between fall and escape.
In case the velocity of rotation of the moon was a little bit faster, it would have escaped the Earth’s Gravity. On the other hand, if it’s a little bit slower, it would have fallen on Earth. That’s why the moon doesn’t fall on Earth.
So that’s a good start, but why is the Moon revolving around the Earth at just such a speed that it keeps at (almost) the same distance? Isn’t that just too convenient? I also hear that the Moon is ‘tidally locked’ to the Earth, keeping the same ‘face’ to us all the time. That means it rotates on its axis over the same time-frame as a single orbit around Earth. Or nearly so, because the Moon’s orbit isn’t perfectly circular, which seems to be the case with every other orbit we know of. I suppose a precisely circular orbit would be a wonder, but then again…
Anyway, our Earth isn’t precisely globular either, and I’m betting it’s the same for the Moon, and every other planet and moon out there. I’m beginning to sense a pattern in this lack of a pattern. Or this approximation of a geometric pattern which doesn’t quite get there with the purity of mathematics.
Not that this is a bad thing. I’ve written previously about Milankovic cycles, variations in the eccentricity and tilt of Earth’s orbit around the Sun, which add spice to our planet’s climate. It’s like we use mathematics to understand the universe’s endless play with mathematics.
But getting back to that cliff fall. I’ve more than once heard the tale that Einstein’s ‘happiest thought’ was of such a scenario. Nothing to do with sadism or masochism, nothing to do with the landing. It occurred to him that, though the falling fellow might feel the force of the air swishing by him, he would not feel any ‘force’ of gravity. In a vacuum he wouldn’t feel any force at all. He might as well be stationary. Gravity, according to my good mate Wiki,
… is most accurately described by the general theory of relativity, proposed by Albert Einstein in 1915, which describes gravity not as a force, but as the curvature of spacetime, caused by the uneven distribution of mass, and causing masses to move along geodesic lines.
Which all sounds pretty radical, especially for 1915, when Fokkers had only just become a thing. So I get that mass is very unevenly distributed. At night we see clumps of stars here and there, with lots of apparently blank space in between. And though we can see for miles and miles and miles, this messy distribution of matter and space extends way beyond what we can see, perhaps even with our most inventive gadgetry. But ‘curvature of space-time’ still smacks of science fiction after all these decades.
Einstein had of course come up with this marriage of space and time 10 years earlier with his very special theory of relativity. So there are three dimensions of space and one of time. But are there? What exactly is dimensionality? Is it more than a human invention? In looking this up I’ve come up immediately with an essay ‘The invention of dimension’, on the naturephysics website. So that answers that question. Or does it? Here’s a quote from the start of the essay:
The modern concept of dimension started in 1863 with Maxwell, who synthesized earlier formulations by Fourier, Weber and Gauss. In doing so he added a nuance that we acknowledge today whenever we refer to the dimensions of, say, g (≈ 9.81 m s−2) as distance over time squared, rather than just the dimensional exponents (1, −2). By referring to the dimensions of a quantity, Maxwell seemed to imply that real things have natural dimensions. In the same spirit he designated units of mass, length and time as ‘fundamental units’.
Distance over time squared is a formula for constant acceleration, which again takes me back to gravity. When we fall from a cliff or a plane we constantly accelerate (leaving aside prevailing winds etc) until we hit the ground, but until that moment we’re not feeling any force upon us, according to Einstein. So acceleration isn’t a force? Apparently not. Is it the result of a force – the effect of a causal force? Well it can’t be an effect of gravity, because gravity isn’t a force.
So our acceleration in the above example is caused by a distortion of space-time which in turn is caused by the mass of planet Earth. But if we had fallen not from a plane but from a spacecraft much much further away, say the distance of the Moon from Earth, what would happen? Would we fall at all? We have satellites and a space station up there (I’m not exactly sure where), so would we just go into orbit like they do? Or are they carefully put into orbit by exquisitely precise mathematical calculations?
But, returning to Einstein’s not-so-happily falling fellow. The only thing he has to worry about is the landing. But the landing, and the force of the landing, is caused by the Earth’s mass. Presumably if we lived on a life-sustaining planet with the mass of Jupiter, which Dr Google tells me is over 300 times that of Earth, we’d be falling, or accelerating at a much faster rate (I’m tempted to say 300 times faster, but the mathematics is always more complicated). But then we couldn’t even live on Jupiter because our weight would be 300 times greater than that on Earth, just as the twelve men who walked on the Moon weighed, for a few days, only one sixth of what they weighed at home. So for life to have evolved on a planet like Jupiter (mass-wise) it would have to be made from very different stuff, molecularly. None of those heavy bones and dense tissues, like brains. An elephant’s brain weighs about 6 kilograms, and on Jupiter it would weigh 1800 kilos. So I suppose it’s important to think about planetary or lunar mass when we’re looking for extraterrestrial life, or alternatively, to think about different building blocks….
Anyway, it’s fascinating to note where thinking about gravity can take you, even when you know virtually eff all about the science. But I do want to learn more, and I’ll keep plugging away at it….
References
https://www.vedantu.com/physics/why-doesnt-the-moon-fall-into-the-earth#
https://en.wikipedia.org/wiki/Tidal_locking
aspects of climate change – Milankovic cycles