Archive for the ‘Uncategorized’ Category

A Variant Geometry for Spacetime

September 18, 2017

There are a lot of odd characteristics of existing spacetime physics, creating a lot of questions that are difficult or impossible to answer, such as, “Why is the speed of light approximately 300,000 km/s?” or “Why can’t you go faster than the speed of light?” or “Is there such a thing as a tachyon?” Or, “If you can’t go faster than the speed of light, how is it possible to age only 4 months due to time dilation while traveling 4 light years?” I hope to offer an alternate geometry to provide some reasonable answers to these questions.

Let’s start with some fundamental concepts about photons. It’s generally believed that photons are their own antiparticles, and also that the speed of light is the ultimate speed past which nothing can travel. Also, in a photon’s frame of reference, the distance from source to destination appears to be zero, and it takes zero time to travel that distance. This led me to speculate that light might, in fact, travel at an infinite speed, and that somewhere out there, there is a geometry in 4D space-time where that makes sense, where, when we try to measure it, we see light ambling along at a tedious 300,000 km/s. It would also explain why you can’t travel faster than the speed of light; the speed is, in fact, infinite. It’s really hard to go faster than that. The difficulty lies in finding that geometry. My second supposition regarding photons is that they are always emitted perpendicular to the path of travel (through time) of the originating particle. In a standard space-time diagram, assuming a velocity of c, this leads to the light cone diagram. In the new geometry, assuming an infinite photon speed, the picture is a little different, but still leads to the well-known equations we are used to.

Figure1

Looking at Figure 1, the vertical line A represents the source of photons a and b, which travel instantaneously to the observer on line B. Line B observes the two events a and b separated by time ct2, and from B’s perspective, the object has moved away a distance x, which equals a-b. In A’s proper time, the time between the two events is merely c time t, and the distance is zero, so the interval is s=ct1. From B’s proper time, the duration is ct2 and the distance A has traveled away from him is x, so the measured interval between the two events is s=√(ct22-x2), which should be familiar to everyone.

Figure2

In Figure 2, we see what happens as B gets closer to the X axis. But it still produces the common formula for the interval. What the diagram does not explain is why the speed of light appears to be roughly 300,000 km/s.

However, what Figure 1 can do is allow us to derive the standard time dilation formula:

∆t1=∆t2/√(1-v2/c2)

How do we get there?

Note the velocity of B away from A is

v=x/t2

 So x2=(vt2)2

From before, we had s=ct1 in A’s reference frame and s=√(ct22-x2) from B’s perspective. Set the two equations equal, and we get

(ct1)2=(ct2)2-x2

Substituting for x2 we get

(ct1)2=(ct2)2-(vt2)2

 Divide it all by c2 and pull the t2 out of the two terms on the right gives us

(t1)2=(t2)2•(1-v2/c2)

Or, ∆t1=∆t2•√(1-v2/c2), which should be familiar to a lot of you out there. It’s the standard formula for time dilation due to relative velocity.

So Figure 1 works out that if the line is at a 45 degree angle, then v=c/√2, which shouldn’t be a surprise. And as v gets closer and closer to c, then the graph gets flatter and flatter. But this graph is based on the idea that c is infinite. Why is it that when we measure it, it’s always 300,000 km/s? Clearly, if you set up an experiment that bounces light back and forth between mountain tops, and c=∞, then your test should show that light moves instantaneously. Not 300,000 km/s. And yet, we always measure c at the same boring 300,000 km/s (yeah, I know this isn’t exact value-it’s 299792.458 km/s. Get over it-this is easier to type).

So what is it that makes an infinitely fast photon measure as a finite number in all frames of reference? Is it the expansion of spacetime? Is it the curvature of spacetime due to gravity affecting the value of c that we measure? Is it that this theory is just wrong? I don’t know yet – this would obviously have to be resolved before this model made any sense, and may or may not appear in a later entry. Any speculations about this are welcome.

 

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A Fool’s Physics

September 18, 2017

I’ve read a lot of physics in my life and have a lot more to read, a lot more to learn. It’s hard to read any general physics text without stumbling across some interesting tidbit that makes me sit back and ponder how that tidbit fits in with my mental model of the universe. Some things make sense, some don’t. When I heard of the Unruh effect, I was dumbfounded (to my understanding, this is the emergence of energy out of a vacuum relative to an accelerating object). When I learned that photons are their own antiparticles, I was confused. When I realized that the time component in the spacetime interval produces a hyperbolic curve in the formula, it was an enlightenment years in the coming. When I read that antiparticles are just regular particles going backward in time (Feynman, I think), that, too, messed with my mental models of the universe. To say nothing of dark matter, the accelerating expanding universe, and so on. So, I try to organize all this hodge-podge of apparently related information into a single model that makes sense. As most physicists will tell you, it is an insurmountable task. But, I am not a physicist, really. I have a Masters in Astronautical Engineering, and as Sheldon Cooper would tell you, I’m really just an engineer. I create mental models that make sense to me, but may not have any practical use or truth in the larger sense of things. But we all have to start somewhere. I’ll keep reading, and revise the incorrect bits as I go along.

In this log of ramblings, I’ll offer up a bunch of foolish ideas on physical reality. I’m a big fan of determinism, so be forewarned. I also think of time as an actual, physical dimension. If you happen to join me on this warped (!) journey of speculation, I’d love for you to tear my arguments apart, tell me what’s wrong, and perhaps help shape the speculations into something that makes a coherent sense of reality, or assure their demise.

Causality Paradox? What causality paradox?

September 11, 2017

I can’t call this real physics, this is just pure and wild speculation. I had a funny idea today about whether or not you can go back in time and shoot your grandfather, thus keeping yourself from ever being born. Ethical questions aside, I thought of a possible solution to the whole “paradox” issue.

First, if you aren’t familiar with the Grandfather Paradox, you can read up on the subject at Wikipedia at https://en.wikipedia.org/wiki/Grandfather_paradox.

Start with the idea that we are always travelling at the speed of light. You, the Sun, the Earth, your brother Bob, everything is travelling at the speed of light through the time dimension, all going the same direction so your relative speed is zero. This is a pretty common concept in modern physics, so I’m not going to expand on that here. Just more physics weirdness.

So, let’s say I get the dubious urge to go murder my grandfather at some time in the past, before I was born. Using some fantastic time machine, I go back in time to when Grandpa was just a young fella and shoot him. What happens then?

Well, imagine that space and time are a 4-dimensional matrix, but that changes made in the matrix can only propagate forward at the speed of light. Remember, that’s how fast we move through time. Eventually, the change (where I no longer exist) reaches the point where I would have gone back in time, but the particles that would have made up my body go shooting forward past that point and never go back. Well, they aren’t “shooting forward” so much as redirecting the world line of their old path at the speed of light. Now, instead of making a U-turn and heading toward their fate with my grandfather, the bullet-magnet, they continue forward in time. The old worldline going backwards collapses/disappears at the speed of light and eventually catches up to where Granddad is, and lets him live. I’m born again! And I foolishly decide, again, to go back in time and kill my granddad.

What does this result in? An oscillation. The world line shifts back and forth between the two realities, carrying the data from both possible realities, like a sine wave on a current. Just as a single electrical sine-wave can contain positive and negative values as it propagates through a wire, so can events toggle on a worldline as that worldline propagates through time. Even past the point where I made my fateful decision, the world line is toggling back and forth; both realities are true, taking their turn as the decision I made causes both of them to be real. The duration of this toggling or oscillation would be twice the duration of the time from when I went back in time to when I snuffed Gramps; the duration of the whole loop.

It’s my belief (not necessarily shared by many others) that we live in a four-dimensional space time that exists perpetually as a 4D matrix, and that what we perceive as our consciousness exists at each point along that worldline. There is the version of you that you perceive now, and the version that existed when you kissed your wife for the first time, savoring the moment you’ve forgotten. Kind of a repetitive immortality.

But what I’m suggesting above is that multiple realities can exist on a single worldline; you don’t need multiple universes dividing every time a critical decision is made or a quantum observation collapses a wave function, or a bit of antimatter goes back in time and changes an existing chemical configuration. Both events occur and exist on a changing, fluctuating, dynamic 4D worldline. There’s the version of you that remembers killing your Grandfather, and the version that never existed, propagating through time, one behind the other forever on the oscillating world line.

The normal view of a 4D worldline is of a static deterministic universe, bound by the future and past configuration of an unchanging worldline. Another view is that every decision, human or quantum, splits the universe into a multiverse, a crowded infinity of infinities. This version allows us to stick with one universe, but to modulate our worldline to allow multiple realities to exist along a single timeline.

Possibly, an outside observer could interface with either version of your reality, based on where he encounters your worldline from his own worldline. Could that be the “collapse of the wavefunction” we talk about? Good grief, that would make the Schroedinger’s Cat conundrum actually possible. Dead and alive! I always thought of it as complete nonsense.

One issue with this model is that each worldline, as it moves from one reality to another, may have to move instantaneously from the collapsed worldline to the new worldline. I think. No real way to test it, that I can imagine. Mmm…maybe pick a subatomic decay process that can have multiple durations, then have someone record the decay time data, then take off (with that data) somewhere at high-speed so your worldline is no longer in sync with the experiment’s original timeline, fast enough that the time separation is greater than the decay time variance. Then, come back and see if the recorded time is the same as it was before; you’ll have two sets of readings of the duration of a single decay, and they might not agree. Wouldn’t that be something?

 

Conservation of Linear and Angular Momentum

September 11, 2017

Some Simple Physics; Conservation of Momentum

There are no strange ideas in this entry. In fact, I might call this a boring entry. If you want to read the weird stuff, read one of my other entries.

I was sitting around reading a primer on particle physics (L.B. Okun) today, and got thinking about the conservation of linear and angular momentum.

Conservation of linear momentum means that, when you chuck something out the rear end of your spaceship, then your spaceship moves the opposite direction, so m1v1 = m2v2 . So, if you toss out a small mass of propellant from one end at a really high velocity, then you move the much larger mass the opposite direction at a much slower velocity (along with your remaining propellant). This is an exponential relationship, but that’s not what this blog is about today, so you can forget learning about that useful tidbit of knowledge.

Anyway, to increase your velocity, you have to chuck part of your mass the opposite direction. Pretty basic. If you just move stuff around inside your ship, the ship won’t move at all (except incrementally for the duration that you move around in the ship, but you won’t acquire a continuous velocity). Anyone who’s been on one of those playground spinners and tried to throw your body one way or the other knows how that works. You throw your body forward a foot, and the disk rotates a foot and stops.

So you can’t change the momentum of an object by moving stuff around inside. Not even if you have the rocket inside an enclosed sphere. The sphere won’t move.

I was recently (foolishly) wondering if that was true of angular momentum, too, if you had a rotating planet or moon, is there some way you can get energy out of the rotation by diddling around with the insides, somehow tapping the angular momentum of the planetoid for energy. Ultimately I realized you cannot in a closed system, but it should have been obvious to me all along. However, as with a rocket, you can change the angular momentum by ejecting part of the object. You can even speed up the spin a lot or slow it down.

Satellites do this sort of thing all the time. Usually they have spin they want to get rid of, and they call the technique “momentum dumping”. Two methods known to me involve extending tethers (like ballerina arms) to slow down the satellite’s spin, then releasing the tethers, or spinning up a high-speed gyro in the opposite direction of your spin (potentially dumping the core of the gyro, though I’m not certain any spacecraft does that – usually they use the gyros to turn the spacecraft both ways, hoping the overall effect will cancel out, and when the spin in one direction gets to be too much, they finally use propellant to dump the angular momentum). These are called Control Moment Gyros, or CMGs, and they usually have a minimum of three on board to cover the 3 axes.

Carrying this concept one step further, since you can eject propellant from a ship to make it go faster in a straight line, you can similarly spin up a chunk of mass from your planetoid in the opposite direction of your planetoid’s spin to make the planetoid spin faster, then eject that spinning mass into space. What amused me about the idea is that it’s essentially the same as a rocket ejecting propellant linearly to increase linear momentum, but here you are ejecting an object with accelerated angular momentum to increase the angular momentum of your planetoid. The difference being, you don’t ever have to eject the mass; it’s rotating in place, like a CMG.

That’s it. Not really that interesting, I guess. The equivalency of the two systems and the idea of “rotational rocketry” just struck me as amusing.

Trying to Accelerate an Infinite Mass

August 29, 2017

Short entry today; an easily digestible bit of physics.

A number of times in physics books and articles, I’ve come across people stating that “as an object approaches the speed of light, its relativistic mass increases, so it’s harder and harder to accelerate the steadily increasing mass, thus, you can’t speed up.”

I’d like to call bullshit on this argument. As your ship’s mass increases, so does the mass of your propellant in equal parts. If your mass doubles, so does the propellant mass being ejected out of your rockets, and you’re still obeying the law that for every action there’s an opposite and equal reaction. It’s just as easy to accelerate as it was before. You still can’t measurably reach the speed of light, but that’s for another entry I’m working on.

See? Easy peasy.

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 orbital 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 gravitation 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).

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

Welcome to my blog. Hope you find something interesting here.