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Background Gravity – Time Dilation in a Flat Field

August 11, 2017

I got into an argument with a physics buddy not that long ago (a year, maybe), about gravity. We have an intermittent arrangement where we go drink beer and talk about physics at two or three pubs in San Luis Obispo. Usually, the physics becomes a little less coherent as the evening wears on.

One of the discussions centered on whether there is a “background field” of gravity or not, or whether it’s even sensible to discuss such a thing since, in an infinite field of equally distributed mass (or gas, or 1 atom per cubic light year, whatever), all the forces around you seem to cancel out. The mass of the universe to your left is equal in size to the mass of the universe on your right; you feel a net acceleration of zero. I argued that even though the field was “flat”, there was still a field there. He argued that a field implied a gradient; there is always a force.

We did not come to a satisfactory conclusion. It might merely have been the fact that we were defining the same terms in different ways in our heads. I’m not sure. I thought my argument was rock-solid.

So, here is my side of it.

Some of you are probably familiar with Newton’s Shell Theorem. It’s in his Principia Mathematica, and if I remember right, he solved it without using calculus. Basically, what it says is this; if you are inside a spherically symmetric shell of mass, then you feel no gravity pulling you any direction. It’s a bit non-intuitive. Let’s say the Earth is hollow, and the entire planet’s mass has been compressed into a thin spherical shell a few centimeters (or meters, it doesn’t matter) thick. If you are floating around in your Nike Space Suit inside this shell, you will not be pulled toward the center, or the inner surface of the shell, or anywhere else inside the shell. Wherever you are put, you will remain.

Personally, I think this is one of the coolest theorems ever.

It’s also true that if you are outside the surface of a spherically symmetric planet, then it doesn’t matter how dense it is, at a given radius you will feel the pull of a certain amount of gravity. If you are in orbit above the Earth, and the Earth suddenly becomes a black hole of the exact same mass, you will remain in orbit, totally unaffected by that change. That’s pretty cool, too. Given that the gravitational force is based on F=GMm/r2, this should be kind of obvious. Neither your mass (m) or the mass of the Earth (M) has changed, your orbital radius is the same, and G is the gravitational constant. Ergo, the density of the object you are orbiting at a radius “r” from the center of the object is irrelevant.

So, that was me drifting from the actual subject. Shell Theorem—let’s get back to that.

As you might know, the clock of anyone in a gravity field runs slower than that of a clock outside of that gravity field. This is called gravitational time dilation (and is equal to ∆t’ = ∆t √(1-2MG/rc2) for a non-rotating sphere). A person on Earth actually ages slower than a person in deep space, according to relativity. This was verified with clocks flying around the Earth in the Hafele-Keating experiment. Before you ask, yes, they took into account Earth’s rotational speed, the speed of the airplane (in both directions relative to Earth’s rotation) with regard to Special Relativity’s time dilation due to velocity. It was a nice experiment.

Let’s say we’re using a hollow Earth from Newton’s shell theorem. As you get closer to the Earth, you are in a deeper gravity well, and the outside observer sees your clock slow down. There’s a small hole in the planet, and you pass into the planet, where everything is pulling you in opposite directions equally, so you seem to feel no force. And yet, your time dilation effect does not suffer a discontinuity, jumping suddenly to that of the outside observer. You are in a denser gravity field, but a flat gravity field. [to the physics majors out there, for god’s sake, if my terminology sucks, please correct me]. Your time dilation will be just the same as if you were standing on the surface of the planet.

So now you have a flat gravitational field (no “force” pulling you in one direction, that is, all forces pulling you equally in all directions). And yet, even in this apparent lack of gravity, where you can’t actually tell that you’re in a gravity well, your time runs slower than the time of someone far from the planet.

I extended this argument to the rest of the universe. If mass was distributed equally around you, even though you felt no force one way or the other, there would still be a background gravitational field. Gravitational time dilation implies a gradient; for time dilation to be relevant, you need someone in a weaker gravitational field measuring your time. However, both the measured and the measurer can be in locally flat gravitational fields.

Does a flat gravitational field curve spacetime by itself? Or is it only the gradient between two different gravitational fields that curves spacetime? My general opinion is that you don’t need the gradient for the curvature of spacetime. If you have an infinite universe with equally distributed mass, then from some arbitrary center, it will appear to curve spacetime until it closes the dimensions of universe into closed loops, like the inside surface of an event horizon (though other arbitrary centers will have different, yet overlapping event horizons – a subject I will touch upon another day). Likewise, if you have a large, thin flat sheet of soapy water in the air, fluctuations are going to cause it to form bubbles, closing up the edges. In spacetime, there may be a similar tension (gravity?) that closes the edges together into a 4D hypersphere.

How would you test the curvature of space inside a shell? I’m not entirely sure. I think the universe we have is a good test case, however.

Silicon Based Lifeforms vs Creationists

July 23, 2010

Ever since the ground-breaking experiments of Urey and Miller, who proved it was possible for amino acids to spontaneously arise out of a laboratory-controlled “primordial soup” of inorganic chemicals, scientists have been racing to take the next step and find out just how the amino acids can become self-replicating organic strings. The importance of this is obvious. This would give us a continuous lineage from rocks to humans. Evolution in a nutshell, a complete package end-to-end with which to torment creationists.

Unfortunately, lacking this final detail in the string of continuity, mutation, and speciation, creationists will cling to this last vestige of their delusion like a drowning man rubbing a rabbit’s foot. Of course, they will do that anyway, even with absolute proof that evolution can stand on its own, and continue to perpetuate the lie that evolution is still grounded in Lamarkian concepts. Anyone who’s ever been on the receiving end of a Jehovah’s Witness tract knows just what I’m talking about – their sum total knowledge of evolution comes from the latest theories of the 1880s and the rants from their apparently uneducated pastors.

Even if scientists complete the experimental foundations of the RNA World, there will still remain skeptics who will blame the results on contamination from external sources, unless, of course, the carbon-based replicating organism is completely alien to anything that currently exists. But the odds of that are considered low; carbon compounds like to react with other carbon compounds in very specific ways that restrict the options available.

But why go this route? Why not select a version of life that can’t possibly be contaminated by Earthly life forms? For example, silicon (versus carbon) based life? Something that will provide incontrovertible proof that life can arise spontaneously in some of the nastiest conditions the universe can lob at us.

I’ve read a bit about the possibility of silicon-based life forms. Most people don’t think it’s possible, usually based on speculation about how silicon bonds with oxygen and can’t properly build long, strong chains like carbon does (not completely true – look up polysilanes). Most of these articles assume certain things; that oxygen, carbon, hydrogen and other low-level atoms are still going to be around for silicon to bond with, and that the temperature of the silicon-based chemistry will have to be about the same as our own. Silicon doesn’t do well at this temperature. Too hard, too short a chain, blah, blah, blah.

But to create a true silicon analog of the carbon based world, we have to eliminate the whole top line of the periodic chart (barring lithium – we need that). This might seem to be a crazy task until we look at Venus, which at a mere 600 degrees C, and with the aid of ultraviolet rays, has lost most of its hydrogen and oxygen into space. It has very little water left. However, for a silicon analog to exist, with no carbon, hydrogen, oxygen, nitrogen or helium to pollute its atmosphere, we would need a fairly small planet with a surface temperature of over 1000 degrees C. Taking a look at the next row down on our periodic charts, we can see that the analog to H20 would be Li2S, oceans of dilithium sulfide (not to be confused with dilithium crystals, which are used in starships). This happens to melt at about 950 degrees C. The second row in the chart below nitrogen is phosphorus. P2 gas forms from P4 at over 800 C, which works just great for us as our analog to N2 in our own atmosphere. An atmosphere consisting mostly of phosphorus might be hard on us humans, but it’d likely be just fine for the siliconites. The analog to C02 would be SiS2, silicon sulfide.

I’m not sure how silicon would do as a chain at 1100 degrees if it was isolated from lower-level chemical elements. Probably not as well, after all, you are dealing with a valence shell that’s one shell further away from the nucleus than carbon. But once you eliminate all these reactive impurities, who’s to say?

What I’d love to do is build a nicely insulated ceramic chamber, dump a lot of these second-level elements into it, heat it up to 2000 degrees to vent off the light elements, then let it cook for a few years around 1100 degrees. Make a “freezing side” of the box at 900 degrees, and a hot side at 1150 to give it a nice thermal gradient. Add a spark-gap generator. Then watch and see what grows. Repeat Urey and Miller’s 1-week experiment, but on silicon. Would we get analog-silicon amino acids? I’d bet on it. Analog RNA? Analog life? Who knows? But it would sure be cool to find out.

Hi, Folks.

January 16, 2010

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