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jelliott

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  1. jelliott

    Orbital Decay and You

    By jelliott,

    (You, of course, indicating its impact on the Earth and not necessarily you on a personal level.)

    By essentially sapping energy from an orbital system, gravitational radiation makes orbits more circular and continuously decreases their radii. Overall angular momentum decreases, as this too is essentially stolen by radiation. The decrease in the radius of orbit is given by the following equation:

    Substitution of the Earth's and Sun's masses for m1 and m2 tells us that the rate of our orbit with the Sun is decreasing by the second: 1.1 * 10^-20 meters per second, to be exact. Not to freak you out or anything, but we're getting closer and closer to the Sun as you read this. In exactly 365 days (that's a year in math terms), we will be MUCH closer to the Sun than we are now. About 1/300 of the diameter of a hydrogen atom. Now that's a bafflingly huge number, but I'm sure we have a few years left under our belt before we collapse into the Sun and die fiery deaths.

    This equation can tell us the lifetime of an orbit as well, before this collapsing occurs. However, since the rate of change depends on the radius and not time, integration of the equation is necessary. So the lifetime of an orbital radius is brought to you by this guy here:

    Again, substituting in the Earth's and Sun's masses, we find our orbit to be about 1.09 * 10^23 years. Seems pretty massive, especially considering this is 10^13 times larger than the age of the Universe itself.

    Well, I hope you learned something, and I'll see you next quarter.
  2. jelliott

    The Observer Effect

    By jelliott,

    The observation of interactions is basically the foundation of science and physics, but often times this observation directly alters the phenomena being observed. This concept is aptly named the observer effect.

    In circuits, the voltage and current can be measured by the use of voltmeters and ammeters, respectively. However, the placement of these devices into the current alter the actual voltages and currents of these circuits. This is why voltmeters are very high in resistance and wired in parallel, and ammeters are very low in resistance and wired in series. This is to minimize the essential error or alteration they are causing, and since there is really no "zero" or "infinite" resistance, these errors will just have to be diminished by improving technology, though obviously we have come very far in this respect.

    There are other examples, such as measuring temperature with a thermometer. The thermometer slightly changes the temperature of the liquid it is placed in. Also, electrons are detected by using photons, and this interaction alters the path of the electron.

    This is often confused with Heisenberg's uncertainty principle in quantum physics, so I'll mention that briefly. Basically, the precision of a pair of physical properties of a particle (complementary variables) can be expressed as an inequality.

    Here, x and p are position and momentum. As the precision of one gets higher, the precision of the other gets lower, and this relationship can be expressed as a fundamental limit using inequalities.
  3. jelliott

    Gravitational Waves

    By jelliott,

    Relativity, as we know, explains the intimate connections of space and time, since they are essentially components of one larger entity, the spacetime continuum.

    One of the more elusive byproducts of this theory is the concept of gravitational waves. To explain, first understand that the spacetime continuum has curvature, and this curvature is directly affected by the mass of an object. For instance, large masses like planets will actually cause spacetime to "bend" around it.


    And gravitational waves are like any other waves, in that they are ripples that travel outwards from the source - these in particular, though, are ripples in spacetime, which travel away from the source carrying energy in the form of gravitational radiation. Again, this is just a theory by Einstein, but I'd keep an open mind about it. Because, you know, he's Einstein.

    So what objects produce these waves? Well, they have to be accelerating. But more than that, this motion cannot be spherically or cylindrically symmetrical. Gravitational waves HATE symmetry.

    For people like myself who love seeing equations related to things, here is the power developed due to gravitational radiation in a system of masses m1 and m2:

    Just by looking at these numbers (G^4)/(c^5) these are extremely small numbers we're dealing with. For instance, the Sun-Earth system gives off a whopping 200 watts - absolutely paling in comparison to the electromagnetic radiation emitted by the Sun (3.86 * 10^26 watts).

    Tune into my next post (which will be in about 10 minutes) and I'll discuss gravitational radiation's implications on orbits n' stuff.
  4. jelliott

    Chaos and its Creations

    By jelliott,

    My previous blog post took a look at the far future - a timeline of events predicted to occur in our known universe assuming it exists infinitely (no Big Crunch).

    Well, if it exists for an infinite amount of time, there will logically be an infinite number of physical occurrences/interactions. So theoretically, though seemingly improbable, there could potentially be the formation of what's known as a Boltzmann brain.

    Entropy is increasing in our universe as it expands - chaos - and according to this particular hypothesis, it is possible that a self-aware entity could emerge from all of this disorder. Random quantum fluctuations can result one of these brains floating into existence, complete with thoughts, memory/data storage, etc.

    As a matter of fact, there's a slight paradox going on here. It would seem as though the probability of us, self-aware entities existing within an organized environment, is far less likely than those of single, dispersed entities existing in thermodynamic "soup" - again, another term for chaos and entropy.

    So our evolved brains are technically pretty unlikely compared to a Boltzmann one - feel special, you've earned it.

    How did he even come to this conclusion? Well, our observable universe is fairly low in entropy - lower than it seems it should be. So it's possible that we inhabit some bubble of lower entropy. After all, entropy is constantly fluctuating, though it's generally on the "up" trend, as the universe slowly tends towards heat death. Yay!

    Not to creep anyone out, but I'll end with a question. What if you were merely one of these Boltzmann brains, imagining yourself in a physical body that doesn't really exist? And what if everything we see in our observable universe is nothing but a hallucination?

    No, that's silly. Now if you'll excuse me it's about time to dissipate back into the void.
  5. jelliott

    Event Horizons

    By jelliott,

    We humans are drawn to the unknown and the mysterious. And what's more mysterious than black holes? Not much.

    An event horizon (a.k.a. a point of no return) is a boundary in spacetime where an outside observe cannot be affected by anything beyond it. In other words, a gravitational pull is so strong that nothing can possibly escape it. Light emitted from beyond the black hole's event horizon can never reach an observer outside of the horizon.

    If you, an observer, are looking towards one of these horizons, an object approaching it from your side will never quite reach it - it will appear to slow down as it approaches nearer. However, to the traveling object, no strange effects are felt - it passes through the horizon in a finite time (0.0001 seconds for a black hole of 30 solar mass). This time is proportional to the mass.


    So, as said before, from an observer's perspective an object approaching a horizon will never appear to reach it - it will just appear to slow down. Interestingly enough, for an object near to horizon to appear stationary to the observer, a force must be applied - and as the object gets nearer and nearer the event horizon, this necessary force increases without bound, becoming infinite.

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