How Much To Fill In A Pool With Concrete Math The Nature Of Grab-Ity (Gravity)

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The Nature Of Grab-Ity (Gravity)

Say you drop something and it falls, as you’d expect, vertically to the ground. A routine happening! You can easily explain what happened (and where and when), but can you explain how it happened, or why that something fell vertically down and not in some other direction? You probably can not.

Gravity is associated most strongly with two physicists – Newton and Einstein. Post Newton, gravity just had something (mathematical) to do with how massive objects are and how far apart they are. There was no real explanation of why or how. Gravity was just the way it was, and Newton’s Laws of Gravity were mainly predictive, not explanatory. [At least the ancients had an explanation. Objects (air, earth, fire and water) sought their natural place in the ordered scheme of things – as if they had minds of their own obeying cosmic laws. Thus, solids were at the bottom and rocks fell down because their place was with solids; water fell down but sat atop of solids; air rose to sit above water; and fire wanted to rise above the air to be with the sun, an obvious ball of fire in the sky.]

Post Einstein, gravity was just a phenomenon that was attributed to joint interactions between mass and space-time. Gravity was a property of the geometry of space. Mass distorts the shape of space-time, and so other objects move in accordance with that warped shape just like moving objects on the surface of the Earth follow the contours – the warps.

Today, physicists are trying to absorb gravity (which is a continuous phenomenon) into the now well established realm of quantum physics (which is not continuous). So far, no dice, but it’s not for lack of imaginative trying. The basic reason for trying to merge the two is that there are several things in nature that can only be adequately explained by unifying the two – primarily the singularities at the heart of Black Holes and the Big Bang.

So what exactly is gravity? Well, at first glance, gravity is obviously a force – it forces you to fall downwards or conversely, you have to apply a force to overcome it.

Traditional physics texts list four known forces at work in the Universe – gravity, electromagnetism, and the strong and weak nuclear forces. Unfortunately, gravity is pretty much now the exclusive property of Einstein’s General Relativity Theory while the other three are based around quantum physics. Physicists have as a first Holy Grail the desire to link as one the three quantum forces, or GUTs (Grand Unified Theories), and have just about succeeded – at least in combining convincingly the weak nuclear and the electromagnetic forces – electroweak theory. The second Holy Grail is to link all four into a TOE – a Theory of Everything, or in more common physics language, finding a quantum theory of gravity or quantum gravity as mentioned above.

Alas, despite intense effort (over several generations by theoretical physicists), no such link has ever been experimentally shown. The only thing to date that has achieved this TOE is the solely mathematical theory of strings, which, alas, has no experimental runs on the board some thirty years on. Even so, it takes string theory to require some ten or eleven spatial dimensions to achieve this, again something for which there are no experimental (and no common sense) evidence. It’s proving an interesting area for nerdy thinkers, but it (string theory) remains, 30 years on, theory, Theory and more THEORY!

What if one assumes the opposite (for a refreshing change)? So perhaps it just isn’t possible to relate or link gravity (hence General Relativity) to the other three known (quantum) forces. TOE is not only elusive, it’s impossible. Gravity and the other three forces can’t be combined any more than one can turn an apple into a pear. [“Heresy, heresy” I hear you cry!]

So how is gravity different? Perhaps gravity is just so different that it not only stands alone, it must stand alone.

Gravity is different #1: Unlike the other three forces, gravity has an opposite – anti-gravity, or in today’s cosmology, ‘dark energy’ which is causing the Universe’s expansion rate to ever increase or accelerate. You’d be hard pressed to come up with a concept of an anti-strong or anti-weak nuclear force, or an anti-electromagnetic force! What would an anti-magnetic field be? Could you have anti-light? Such concepts only induce headaches!

Gravity is different #2: Two of the three quantum forces operate over atomic (or sub-atomic) lengths. Both gravity and electromagnetism (EM) can, in theory, extend their influences to infinity. But, while EM can be blocked (at least for a while) by placing an object or insulator in front of the EM source, gravity can’t be. No known physics can block gravity. Place a sheet of metal in front of a lamp, and you block the light. Place the same sheet between you and the Earth, and you won’t start floating upwards!

Gravity is different #3: What can gravity do that quantum forces can’t – bend light – that’s a pretty neat trick! [See below for more details.]

Gravity is different #4: Of all the four known forces, gravity is by far and away the weakest of the weak. If gravity were on the beach, gravity would get sand kicked in its face! Now you may not think gravity is all that weak while in freefall from a 12 story building roof heading for the concrete sidewalk far below, but it is – relative to the rest. [In fact it’s the electromagnetic force that terminates your 12 story fall, and presumably you!] I mean it is easier to lift up a paperclip from your desk with the entire mass of the Earth trying to stop you, than it is to separate that same paperclip from a reasonably strong magnet. In fact you could use that magnet to pick the paperclip up in the first place. Magnet one; Earth’s gravity zero! And you certainly would have to use a lot more force trying to walk through brick walls, or other solid objects, so the electromagnetic forces acting between the atoms and molecules holding them together as a solid must be pretty strong. And don’t even think about trying to pull apart the nucleus of an atom or to separate the quarks that make up a proton or neutron. No, we may think of gravity as a giant force, but it’s still the smallest of the four giants, sort of like a gnat compared to elephants.

Gravity is different #5: If string/membrane (brane) theory is right, then gravity alone of the four known forces can ‘travel’ off our brane (actually termed a braneworld) to another braneworld (and vice versa) through what is termed ‘the bulk’. The other three forces are stuck to our braneworld, and presumably, those three forces would also be glued to another braneworld. Thus, relative to the other three forces, gravity is diluted and thus is experienced as being a weaker (the weakest) force. It also explains how two braneworlds can attract one another and collide. Such a collision results in a Big Bang for each braneworld, but a Big Bang that occurred in pre-existing space and time. [Look up ‘Ekpyrotic Universe’ for the nitty-gritty details.]

Gravity is different #5 (continued): Invoking the braneworld concept and associated forces further helps to explain ‘dark matter’, which one recalls has positive gravity, yet is invisible or ‘dark’ (apparently it has no association or interaction with electromagnetic energy). Anyway, the idea is that ‘dark matter’ is in fact just ordinary matter, but on another braneworld (or in another universe – part of the Multiverse). We feel ‘dark matter’s’ gravity cause gravity can travel through ‘the bulk’ or leak between braneworlds, but we can not see ‘dark matter’ because electromagnetic energy can not travel across ‘the bulk’ that separates braneworlds. (String theory may still be, thirty years on, only pure mathematics and theory, but it can explain some real physics phenomena! Now if only someone could figure out how to slot ‘dark energy’ into this scenario, they’d be a candidate for the Nobel Prize!)

Presumably for there to be gravity there has to be mass (or matter), so an electron has gravity; you have gravity; the Planet Earth has gravity – and so on. But a photon, that ‘particle’ that carries the electromagnetic force, doesn’t have gravity since it can’t have any mass (because it travels at the speed of light and only something without mass can do that).

So gravity can deflect the electromagnetic force. We’ve all read about that famous experiment where the positions of stars were pinpointed that should be very near the limb of the Sun during a solar eclipse. The starlight from those stars was deflected by the Sun’s gravity and thus, during the eclipse, the stars seemed slightly out of position in the sky. This was in accordance with Einstein’s General Relativity predictions and the merger of theoretical prediction and observational reality elevated the physicist from that of a scientist known and respected by colleagues to that of international superstar known to the masses – the scientist who overthrew Newton’s Theory of Gravitation. There’s another astrophysical effect of the deflection of electromagnetic radiation by gravity, and that’s known as gravitational lensing. While predicted by Einstein, he felt it would never have any practical applications. But today’s astrophysicists have used the phenomena – that of massive (high gravity) objects in space deflecting and focusing the light (like a lens) from more distant objects behind them – to study same. It’s by this technique that the presence of ‘dark matter’ has not only been confirmed, but mapped, as ‘dark matter’ has gravity and can act as a gravitational lens!

Can gravity deflect gravity? In Newtonian physics, the gravitational force travels instantaneously. If the Sun were to somehow vanish now, we’d feel the Earth orbital effects, now. In Einstein’s Special Theory of Relativity, gravity travels at the speed of light, and thusly gravity and EM (of which light is a part) share a common bond. Thus, if the Sun were to somehow vanish now, it would be eight minutes before we’d notice Earth’s orbit being perturbed. Experiments have to date only proved gravitational influences travel at very close to light speed, but as yet, not an exact match. Close, but no cigar. Of course it’s only fair to point out that these experiments are incredibly difficult to carry out, and the final verdict is still far off.

All the four forces have particles associated with them – particles that convey the force from Point A to Point B. In the case of the electromagnetic force, it’s the mass-less photon. The strong nuclear force has the gluon. In the case of gravity, the assumed theoretical particle (it hasn’t been actually detected yet) is the graviton.

If the particle assumed to carry the gravitational force (the graviton) travels at light speed, it should be mass-less, and with analogy with the photon, be deflected by another gravitational field. If a photon passes near a Black Hole (a high gravity object), its pathway will be bent. If a graviton (say part of a gravitational wave – something predicted by Einstein’s General Theory of Relativity) were to pass near the same Black Hole, its pathway should be equally bent. If a graviton has some mass and thus travels at somewhat less than light speed, that too will show up as a change in its pathway as it passes close to a Black Hole. Equally, a graviton, if there is such an animal, should be sucked into a Black Hole if it hits the Black Hole’s bulls-eye.

It might be surprising that if gravity can deflect gravity as well as radiation, then how can gravity ‘escape’ from a Black Hole and radiation* can’t? Of course gravity is an intrinsic property of mass, and there’s certainly lots of mass in a Black Hole, so obviously a Black Hole has gravity and it’s not as if it were escaping or leaking out. Of course one could, perhaps should, argue that gravitational waves are just ripples in space-time geometry, and gravity is just geometry, and geometry can’t be sucked into a Black Hole the way matter/energy can be. Translated, gravity again is just different – it’s not a force like the other forces, it shares no commonality with electromagnetism or the strong and weak nuclear forces, its just geometry in which case there might be no need for a gravitational force particle.

An interesting side question is can light deflect light? Unfortunately, light doesn’t stand still, but what if, as a thought experiment, one fired a laser beam in one direction and another laser beam at right angles to it, but say just a fraction higher (so the two beams don’t make contact). Would the pathways of the two laser beams alter as they crossed? Would two laser beams fired off in parallel slowly be drawn together and eventually merge? How about two laser beams fired head on towards each other? I suspect the two beams would just pass through one another. To the best of my knowledge, light only interacts with light as wave phenomena, not as particle phenomena, causing constructive or destructive interference. So, two beams at right angles, or fired in parallel, wouldn’t display any particle sorts of properties – that is, deflections. Again, the photon is mass-less so shouldn’t have any sort of deflection influence on other photons. That’s my guess anyway. So…

John’s musings one: gravity is a quantum phenomenon; gravity is not a continuous phenomenon; there is a unit of gravity that can not be subdivided; the graviton is the fundamental particle that conveys the force we feel as gravity. There will eventually be an experimentally verified TOE.

John’s musings two: gravity is a consequence of geometry. Mass distorts space-time’s geometry (which would be absolutely flat in the absence of any mass) which in turn distorts how mass moves (which would be in a straight line in the absence of any geometry other than flat space-time geometry). Gravity has bugger-all to do with quantum physics and just can not be reconciled with it. There is no fundamental unit of gravity and no need for a gravity-bearing particle.

Now this mass/space-time dynamic is very interesting. Mass tells space-time how to curve or warp (which determines the geometry); space-time geometry tells mass how to move, movement which in turn alters the geometry, which in turn alters the motion, and so on, and so on. Very dynamic! It’s also very circular, sort of like the chicken and egg question.

How exactly does space-time affect the motion of mass? Well, that’s pretty straight forward – I think. It’s one of the fundamental axioms of physics that an object once set in motion, stays in motion, and travels in a straight line – unless acted on by an external force. If you hit a hockey puck across the ice, it keeps on going on (if you ignore friction) in the direction you hit it. If some other player then hits the puck, the puck (probably) changes both speed and direction. But, what if, instead, the puck hits a slight slope in the ice. The puck will change direction. Geometry has affected the motion of a mass. Geometry has mimicked a force. Or, take the unfortunate S.S. Poseidon sailing along on a smooth sea until a sudden rogue wave rudely alters her course and speed in real quick-smart time. The sea’s geometry changed, resulting in, in this case, a good cinema experience!

So how exactly does mass warp space-time? I don’t know exactly (in case you were expecting a revelation at this stage). You might think the entire concept crazy. I mean we’ve all seen the Sun and the Moon, and the Apollo astronauts have seen the Earth from afar, and we know these objects have mass and hence gravity, but have you, or the astronauts, seen any warping of space-time in the vicinity of the Sun, Moon and the Earth (unlike that – by analogy – the bowling ball on the rubber sheet illustration beloved in all physic’s texts)? Okay, there’s noting apparent to the naked eye that anything is warped, there’s no psychedelic effects apparent, no distortions, etc. The Moon doesn’t appear as a shimmering now-you-see-it-now-you-don’t object. But then, we do have that starlight defection experiment verified during solar eclipses (tick to Einstein). Perhaps these worlds aren’t massive enough to imprint their distortions on our retinas. The more the mass, the more dramatic would be the result, and anyone who has seen long duration time exposure photographs of massive galactic-sized objects, the gravitation lens at work, witnessed the formation of Einstein’s Rings (or arcs), has certainly seen space-time warping or the pathway of light deflected by mass (tick to Einstein).

I suspect the answer as to how exactly mass warps space-time is probably straight forward. As the Earth travels in its orbit around the sun, space (or space-time) has to give way to accommodate our planet. Or, if you toss a ball through the air, the air is displaced as the ball passes through. The air has been slightly, and briefly, warped. Or, back to the S.S. Poseidon, her sailing along on calm seas causes displacement in the ocean and generates bow waves causing the ocean’s geometry to change. The bow waves, radiating outwards (like gravity waves?) hence cause a rocking of a small rowboat far away.

So, experimental conclusions (to date): Einstein one; quantum physics/string theorists zero.

In matters of theoretical physics and accompanying mathematics, one must temper the ‘thought experiment’ results with liberal does of healthy common sense – attention string theorists. In matters of observational and verified experimental physics, healthy common sense must take a back seat to confirmed results. Despite gravitational lensing, etc. gravity (the how and the why) still seems to reside largely in the theoretical realm, and I’m sure we’d all like to see this very mysterious force emerge in the light of total understanding based on a lot more experimental data. In the meantime, in the here and now, string theorists, and those proposing models of quantum gravity, better get their experimental act together!

A further recommended reading about gravity:

Schutz, Bernard; “Gravity from the Ground Up: An Introductory Guide to Gravity and General Relativity”; Cambridge University Press, Cambridge; 2003:

*Actually theoretical astrophysicist Stephen Hawking showed that Black Holes weren’t entirely black; some radiation can escape from them, know known as Hawking Radiation. It’s actually a now and then quantum phenomena. Normal everyday electromagnetic radiation can’t escape from a Black Hole once trapped behind the Black Hole’s event horizon. However, the energy associated with a Black Hole, via Einstein’s famous equation relating mass and energy, can morph into virtual particles outside the Black Hole’s event horizon – that region and below of no escape.

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