Relativity says that 2 observers can each see relative length contraction when observing the other.
In other words, I could see that I could fit your house inside my house, and you could see that you could fit my house inside yours. Practically it would be hard to do... with special relativity, it would require the houses to be moving very fast relative to each other. Parking houses is a difficult manoever at near-c speeds. With general relativity it might be possible with some weird gravity thing that I don't understand. Maybe it involves being on opposite sides of an event horizon. However, is it even possible? Or does topology give a reason why it isn't?
Seems to me, if you have one thing topologically "inside" another thing, but you have control over space so that you can compress one part of space to an infinitesimal length, and inflate another to infinite length, you should be able to turn the whole thing inside out (and even treat it as simply a change in point of view, if you had that power), without changing the topology of the set of 2 things.
So could we not then have universes inside our universe? Possibly black holes are entire universes that we see only as something infinitesimal. Perhaps even, just like 2 houses each inside the other, perhaps we are topologically inside these black hole universes. Could we be inside each of the black hole universes that are each inside of us? It's not that we're some tiny dot within the tiny speck that is a black hole singularity, each recursively within a larger version of the other, but rather we're both inside and outside of each black hole depending on which side you turn out... like a reversible jacket with billions of insides and maybe just one "outside" that one can see at a time. Your universe, whichever it may be, is always seen as the outside in the normal perspective of life.
Perhaps falling through an event horizon feels like that, like a reversibile universe turning itself inside out, so you fall into the "outside" of a different universe, and the universe from whence you came turns into an "inside", and becomes a black hole that resides within your new universe. Of course, you'd probably feel a lot like Hawking radiation, and uh... be it... which would probably put a damper on your ability to look around and contemplate how much like a jacket the multiverse seems.
They should teach topology in grade school. Then by first year of university, kids would probably know the answers to these questions.
Tuesday, September 21, 2010
Saturday, September 4, 2010
This thing all things devours
I'm in the middle of a horribly tedious rewrite and have had a crushing thought: I don't think my definition of time jives with my meaning of light being "instantaneous". Again I get that feeling that everything I'm talking about is exactly the same as what's been known for the last 100 years, and anything different is nothing more than poor wording.
I've been completely wrong in the science, the math, the language. The only thing that endures is the idea. Will it be boiled down until it's nothing more than a repetition of what I've read? Or will it be polished till it gleams, like a beautiful delicate golden turd?
Yet more contemplation and rewriting.
If time is distance, then a moment in time with 0 duration is a single point. That is not light.
If light is not a moving thing, then what is it? It is not a single instant, because it spans time (distance). Yet it is at all points along that distance simul... simul-what? It spans time but it does not move through time. Does it bridge time? No, it does only exist at a single time value, but that time value is different for different observers. And does it not actually exist as a line of energy, observable along its entire length as single points of light by different observers, but rather exists only at its source and its destination? One cannot "see" a light signal unless it is intercepted, and though you can intercept signals all along light's path if there are enough signals (like a laser through a smokey room), it is still only observable at source (as a loss of energy) and destination (as a gain).
Perhaps then light is simply a teleportation of energy. It slips out of existence in one observation-defined location (and time), and shows up elsewhere. Yet, the path is important because it determines where the destination will be. Energy teleportation makes sense within the idea of a singularity, but how is geometry and the difference between matter and space represented within a singularity? And is the singularity idea really needed, when there is no way to observe a light transmission occurring in a single instant?
Or something.
I've been completely wrong in the science, the math, the language. The only thing that endures is the idea. Will it be boiled down until it's nothing more than a repetition of what I've read? Or will it be polished till it gleams, like a beautiful delicate golden turd?
Yet more contemplation and rewriting.
If time is distance, then a moment in time with 0 duration is a single point. That is not light.
If light is not a moving thing, then what is it? It is not a single instant, because it spans time (distance). Yet it is at all points along that distance simul... simul-what? It spans time but it does not move through time. Does it bridge time? No, it does only exist at a single time value, but that time value is different for different observers. And does it not actually exist as a line of energy, observable along its entire length as single points of light by different observers, but rather exists only at its source and its destination? One cannot "see" a light signal unless it is intercepted, and though you can intercept signals all along light's path if there are enough signals (like a laser through a smokey room), it is still only observable at source (as a loss of energy) and destination (as a gain).
Perhaps then light is simply a teleportation of energy. It slips out of existence in one observation-defined location (and time), and shows up elsewhere. Yet, the path is important because it determines where the destination will be. Energy teleportation makes sense within the idea of a singularity, but how is geometry and the difference between matter and space represented within a singularity? And is the singularity idea really needed, when there is no way to observe a light transmission occurring in a single instant?
Or something.
Friday, August 20, 2010
Special Theory of Everything
Nuts to general relativity. I'mma return to wild speculation about whatever. I still have most of 10 years to figure it all out.
Theory: All forces are an effect caused by the warping of space.
Evidence for: When you move relative to something, it gets warped. When you move relative to everything, everything gets warped. We can say, "space gets warped." This is special relativity.
Conventionally, we say "When you apply a force to an object, it moves, and its velocity causes a warping of observed space."
Instead we could say "When you warp space, you move through it." Occam's Razor favors the latter.
Not that we know how to warp space by will alone. Nevertheless, we do it all the time, simply by moving. We don't know how forces work but we use them all the time. We don't know how space warping works but we use it all the time.
Evidence against: Ain't none but tired old convention.
Theory: The universe is a singularity
Evidence for: Distance and time are observer-dependent. The shape and size of the universe is different for different observers. It seems as if shape and size, and time too, is defined by an observer. If you try to envision how a spherical light wavefront "sees" the universe under Time Relativity, you see the universe shrunk to a single point: a singularity. Without observers, there appears to be no time, and no distance, and no chronology of events or causality. Observations define the observed universe; without those observations it seems to best make sense as a singularity.
Evidence against: The above description of a universe as a singularity is an attempt to describe an observation of the universe without an observer, but still using that mathematical language of an observer. It seems more likely that it exists in some different way, with different dimensions that only appears as a singularity to our common understanding of observations. But an observation of such a universe wouldn't appear as a singularity; it would appear as the universe appears to us.
Perhaps though it is possible to describe how the universe is shaped (IE. a singularity) without being able to describe how that shape might look.
Theory: All forces are an effect caused by the warping of space.
Evidence for: When you move relative to something, it gets warped. When you move relative to everything, everything gets warped. We can say, "space gets warped." This is special relativity.
Conventionally, we say "When you apply a force to an object, it moves, and its velocity causes a warping of observed space."
Instead we could say "When you warp space, you move through it." Occam's Razor favors the latter.
Not that we know how to warp space by will alone. Nevertheless, we do it all the time, simply by moving. We don't know how forces work but we use them all the time. We don't know how space warping works but we use it all the time.
Evidence against: Ain't none but tired old convention.
Theory: The universe is a singularity
Evidence for: Distance and time are observer-dependent. The shape and size of the universe is different for different observers. It seems as if shape and size, and time too, is defined by an observer. If you try to envision how a spherical light wavefront "sees" the universe under Time Relativity, you see the universe shrunk to a single point: a singularity. Without observers, there appears to be no time, and no distance, and no chronology of events or causality. Observations define the observed universe; without those observations it seems to best make sense as a singularity.
Evidence against: The above description of a universe as a singularity is an attempt to describe an observation of the universe without an observer, but still using that mathematical language of an observer. It seems more likely that it exists in some different way, with different dimensions that only appears as a singularity to our common understanding of observations. But an observation of such a universe wouldn't appear as a singularity; it would appear as the universe appears to us.
Perhaps though it is possible to describe how the universe is shaped (IE. a singularity) without being able to describe how that shape might look.
Wednesday, August 18, 2010
Force of ignorance
Einstein and Newton are my heroes, but if any scientific convention leads us astray, even one established by the most intelligent players in the game, it must be ignored or corrected (or my misunderstanding must be rectified).
List of junk that I don't like in science
List of junk that I don't like in science
- A frame experiencing gravity is indistinguishable from an accelerating frame
Observers in each of these frames will observe a warping of space around them. A linearly accelerating frame will observe a cartesian warping, where "lines of length contraction" are parallel. Under gravity, a frame will observe a polar warping, where lines converge at the center of gravity. Across the "height" of the frame of a person standing on Earth, there will be a gravitational differential (gravity should be measurably stronger at your feet than at your head, even if the difference is minuscule).
A single point of observation would still not be able to tell the difference between a linear acceleration (that can change in magnitude as the point changes position), and the force of gravity. Again, as with Time Relativity, there is the suggestion that an "inertial frame" that contains "stuff" where there is distance between the stuff, can not be consistently described as a single entity. Different points within an inertial frame will experience phenomena differently.
Update: Einstein thought of this. I think they're expressing the same idea when they say "in mathematical terms, it is the geodesic motion associated with a specific connection which depends on the gradient of the gravitational potential. Space, in this construction, still has the ordinary Euclidean geometry. However, spacetime as a whole is more complicated." (IE. it's all curved up, yo.)
- Inertia: A body at rest tends to stay at rest
To claim that the natural state of an object at rest is to remain at rest, requires one to consider the object in the absence of gravity. This requires one to consider it independent of any other matter, because otherwise there will be gravitational forces. But then you lose all definition of "at rest" verses "moving", because movement is relative. To say that the object is at rest implies that it is not moving relative to some other object. You cannot compare it to "the frame of space", which doesn't exist in relativistic physics. This object that you are considering independent of all other matter, has no way to distinguish whether it is moving or at rest compared to other things it can't observe, and its inertia or momentum is undefined.
If you add another mass into the picture, then we must have that a body at rest will tend to accelerate toward other masses. To cling to the old definition of inertia, we're compelled to treat gravity as a constant force which is something that is "additional" to the underlying natural state of things. But gravity is the underlying natural state of things. Bodies that obey a more natural definition of inertia will tend to attract each other.
This almost suggests that an object in free fall is not observing a "force" so much, but rather just being inert within the relative space around it. That is roughly how it feels, to the observer. Another observer that is overcoming gravity is the one who employs or experiences forces.
Update: Einstein thought of this. "This suggests the definition of a new class of inertial motion, namely that of objects in free fall under the influence of gravity."
Perhaps trying to unify the "force" of gravity with the other fundamental forces is like asking "what kind of apple is this navel orange?"
Sunday, August 1, 2010
Foundation for a Unified Theory
The double-slit experiment immediately makes slightly more sense under the TDR model, because it allows all possible paths for the light to be evaluated in a single instant.
Single-slit and double-slit experiments are cases of light being curved. Let us consider that light appears to travel at c along this curved path. Suppose that a photon appears to travel a curved distance of d and hits a screen. The time value at the screen along the curved path is the same time value at the sender. However, due to 1/c invariance, from any perspective I will see the time difference between sender and screen according to straight-line distances. That means that the length-time that I observe or measure between sender and receiver is smaller than it is measured along the "instantaneous" curved light path. In other words, the photon has shifted into a slightly different time than the one I can observe.
However, this also suggests that I wouldn't see any photons hitting the screen, because any curved path would mean a slight shift in time. This suggests that the light event is not instantaneous after all, but has a small duration. So, though many photons appear time-shifted, those that are shifted only slightly are still visible. An interference pattern becomes apparent, as photons are shifted out of visible time to form dark spots, and others are shifted into visible time to form brighter spots.
A natural correlation between the energy and duration of a light event is that the duration of the event would be proportional to its energy. The apparent frequency of light might be illusory. An explanation of redshift or the appearance of it would need to be provided in accordance with TDR. Note that the appearance of a sinusoidal aspect of an apparent "light wave" may mean that a light event occurs similarly sinusoidal. That is, it is a "flash" of light energy that begins "dark", increases in intensity until a maximum amplitude is reached (would the amplitude be the same for all different energies of light?), and decreases back to "dark". If a light event is said to occur at a specific time, it would likely make sense that the moment of maximum intensity would be that time. Note: Several questions come up that cast doubt on this interpretation of frequency effects of light. Does that mean that part of a light event can happen before the official time of the event? Wouldn't it make more sense if higher-energy light stretched it across space (width, for example) rather than time? Either would allow wider bands for higher frequencies to be visible in the slit experiments, but the opposite effect is apparent. Therefore these ideas need to be revisited.
The effect of "which path" observations on the slit experiments destroys the appearance of interference. A couple possible explanations come to mind:
Revisiting the Time-shift explanation for interference patterns...
Consider conservation of energy as it relates to number of photons. We would think that any photons that "disappear into another time" would be replaced by an equal number that appear from another time. However, a single-photon light-event will always be detected. So something is wrong.
The model of a single light event is a line (possibly curved). But the double-slit experiment suggests that light propagates as a spherical wavefront.
It could be that light does indeed propagate along that entire round wavefront, and in fact interacts with the entire area it "sees". However, every location that it interacts with exists in a different time, while any observer only exists in a single time. An observer will see light interact with only a single point at which its observed time matches the light event's time. An observation from the exact location of a light sender, could "see" that that light in fact hits everywhere, and not just a single point. This reinstates the instantaneousness of light.
It also suggests an experiment which may predict that observers in frames that have relative movement will see a different diffraction pattern, because each observer will have different measurements between the light source and locations on the screen. However, it could instead be that the pattern is defined by the ratio of curved-path distance to straight-path distance, which might be the same for any observer.
There must be something that was missed or incorrect in all this speculation.
The above describes single-slit interference, but doesn't cover double-slit.
One last wild speculation: What if time is meaningless to a light event? The "time" at which it occurs depends on a definition of time, which is time-frame location dependent. Perhaps the light event exists as a wave through all of time, and we only see the single location and time of that event that matches our observed time-frame's time definition of that event. In this case, when a single photon follows a curved path, we see it shifted in time depending on location and straight-line distance between sender and receiver. So with less curvature, we observe events similar to if they were straight-line light events, and at locations involving more curvature, a photon appears to disappear into another time, and elsewhere we see more or less (depending on location) that the photon is visible as it appears due to it having been sent at a different time value than the one that our time frame says it was sent at.
Confusing.
Single-slit and double-slit experiments are cases of light being curved. Let us consider that light appears to travel at c along this curved path. Suppose that a photon appears to travel a curved distance of d and hits a screen. The time value at the screen along the curved path is the same time value at the sender. However, due to 1/c invariance, from any perspective I will see the time difference between sender and screen according to straight-line distances. That means that the length-time that I observe or measure between sender and receiver is smaller than it is measured along the "instantaneous" curved light path. In other words, the photon has shifted into a slightly different time than the one I can observe.
However, this also suggests that I wouldn't see any photons hitting the screen, because any curved path would mean a slight shift in time. This suggests that the light event is not instantaneous after all, but has a small duration. So, though many photons appear time-shifted, those that are shifted only slightly are still visible. An interference pattern becomes apparent, as photons are shifted out of visible time to form dark spots, and others are shifted into visible time to form brighter spots.
A natural correlation between the energy and duration of a light event is that the duration of the event would be proportional to its energy. The apparent frequency of light might be illusory. An explanation of redshift or the appearance of it would need to be provided in accordance with TDR. Note that the appearance of a sinusoidal aspect of an apparent "light wave" may mean that a light event occurs similarly sinusoidal. That is, it is a "flash" of light energy that begins "dark", increases in intensity until a maximum amplitude is reached (would the amplitude be the same for all different energies of light?), and decreases back to "dark". If a light event is said to occur at a specific time, it would likely make sense that the moment of maximum intensity would be that time. Note: Several questions come up that cast doubt on this interpretation of frequency effects of light. Does that mean that part of a light event can happen before the official time of the event? Wouldn't it make more sense if higher-energy light stretched it across space (width, for example) rather than time? Either would allow wider bands for higher frequencies to be visible in the slit experiments, but the opposite effect is apparent. Therefore these ideas need to be revisited.
The effect of "which path" observations on the slit experiments destroys the appearance of interference. A couple possible explanations come to mind:
- The detection of light anywhere along the path changes the light event from a single curved-path event, "splitting" it into multiple straight-path light events.
- The detection of light involves an interaction with matter. That matter has size, which means the interaction takes time. This time might be random enough that it removes the otherwise precise correlation between time and locations on the screen.
Revisiting the Time-shift explanation for interference patterns...
Consider conservation of energy as it relates to number of photons. We would think that any photons that "disappear into another time" would be replaced by an equal number that appear from another time. However, a single-photon light-event will always be detected. So something is wrong.
The model of a single light event is a line (possibly curved). But the double-slit experiment suggests that light propagates as a spherical wavefront.
It could be that light does indeed propagate along that entire round wavefront, and in fact interacts with the entire area it "sees". However, every location that it interacts with exists in a different time, while any observer only exists in a single time. An observer will see light interact with only a single point at which its observed time matches the light event's time. An observation from the exact location of a light sender, could "see" that that light in fact hits everywhere, and not just a single point. This reinstates the instantaneousness of light.
It also suggests an experiment which may predict that observers in frames that have relative movement will see a different diffraction pattern, because each observer will have different measurements between the light source and locations on the screen. However, it could instead be that the pattern is defined by the ratio of curved-path distance to straight-path distance, which might be the same for any observer.
There must be something that was missed or incorrect in all this speculation.
The above describes single-slit interference, but doesn't cover double-slit.
One last wild speculation: What if time is meaningless to a light event? The "time" at which it occurs depends on a definition of time, which is time-frame location dependent. Perhaps the light event exists as a wave through all of time, and we only see the single location and time of that event that matches our observed time-frame's time definition of that event. In this case, when a single photon follows a curved path, we see it shifted in time depending on location and straight-line distance between sender and receiver. So with less curvature, we observe events similar to if they were straight-line light events, and at locations involving more curvature, a photon appears to disappear into another time, and elsewhere we see more or less (depending on location) that the photon is visible as it appears due to it having been sent at a different time value than the one that our time frame says it was sent at.
Confusing.
Monday, July 26, 2010
Gravity
I had an idea about gravity that turned out to be complete crap after struggling with the math for awhile. I'd written a couple pages about it, but they were lost in a fire when I tripped on the cord and the computer shut off. No sense repeating the theory or explaining how the math schooled my ass. But I'll try to retell the parts I want to keep.
[Well I'll mention the theory in a nutshell, for the sake of... I don't know what. The theory was that gravity wasn't due to some force acting from afar, but rather due to the difference of the apparent "force" of gravity across some fundamental constant distance. This idea basically describes gravitational gradients, which by the way is what causes tides. So rather than being pulled by something an astronomical unit away, we are pulled (or pushed) by some difference say between one side of a neutron and the other. My hope was that calculations based on existing measurements would produce an alternate formula for gravity, with a new constant analogous to G but which would have to be much much greater (to produce the same forces that the existing formula calculates for r2, but for the much much smaller delta r2). If the resulting constant was similar in value to the other fundamental force constants, that might suggest some exciting new hidden relationship. Unfortunately, the math shows that while gravity is inversely proportional to the square of the distance from a mass, the gradient is roughly inversely proportional to the cube. Fairly simple geometry can show why. In other words the calculations differ depending on which r you choose, so no such constant can be found. Or, the "fundamental constant distance" would need to grow proportionally to r. A good candidate for an idea that needs to be abandoned when shown to be wrong.]
The force of gravity exerted by a mass at a distance of r, is inversely proportional to r2. The magnitude of the force is the same at all the points on a sphere with radius r centered on the mass. Interestingly, the area of a circle with a radius of r is also inversely proportional to r2. This suggests that the force of gravity can be "spread evenly" across that sphere, making the "total force" on the sphere the same for any different value of r. As when blowing up a balloon, its radius increases and the latex is spread thinner, but the total amount of latex remains the same. If you imagine a gravity wave propagating like an expanding bubble ;) from the mass, it is similar to sound (pressure) waves, whose energy across some fixed area also is inversely proportional to r2. This is because the total energy of a single pressure wavefront remains the same, but gets spread evenly over the total area of the wave's expanding sphere. As a side note, I think this requires the wave to move at a constant speed (c for gravity waves; the speed of sound for pressure waves)... otherwise, a slowing bubble expansion might allow energy to build up, or allow the wave to be compressed laterally and compensate with an increase in amplitude.
So, gravity gets weaker as you move farther from a gravitation body, as its force gets spread across a larger area. I'd drawn a bunch of triangles to show the ratios involving a slice of a sphere around a gravitational body, and another body (a spaceship, say) that is affected by it. I realized that the force would be the same for any r, if the spaceship grew in size relative to r... in 2 dimensions that is. Then, the spaceship at r would cover the same area relative to a sphere of radius r, as the different-sized spaceship at r1 would cover relative to a sphere of radius r1. And so it would experience the same gravitational force at the different distances. A conical "slice" of gravity shares the same total gravitational force across the (curved) base of the cone, for any cone height. This is a consequence of simple ratios.
The idea occurred to me to try to visualize a spaceship that expands as it moves away from a mass, in a way that keeps the apparent size of the spaceship the same, by warping space so that lines that radiate away from the mass become parallel. In such a view, a "normal" spaceship would appear to decrease in size as it moved away from the mass. At this point I felt that now-familiar feeling that things were getting too abstract to be conceivable. Another idea came to mind of modifying gravity by somehow warping its field this way possibly through some sort of gravity lens (a lens that warps gravity, not the more familiar lens that warps light using gravity).
An interesting idea that comes out of this is that a spaceship decreasing in size as it moves away from a gravitational mass, is exactly what appears to happen to the object when viewed from the gravitational mass. The apparent area that an object takes up relative to my entire field of view, is once again inversely proportional to r2. This suggests a theory that the gravitational force on an object is related to how that object is "seen" by the mass. Interestingly, all of these ideas may be converging on some Theory of Everything that centers around the effects of observation as the core mechanism for describing physical interaction. Things affect me relative to how much I am aware of them.
Note that I'm not talking about simple visual observation. You can't hide from the sun's gravity by ducking behind a planet. The mass can "see" through matter, and can "see" the various layers or depth of matter (so a long rocket with the same visual area as a short rocket will not experience an equal force), and it can "see" the density of the matter.
As an example, consider the Sun and the Moon. From Earth, they appear to be roughly the same size. The Sun is about 400 times as far away as the Moon is, and also has a radius about 400 times the Moon's (anything that appears the same size should have the same proportion). However, it is about 0.42 times as dense. So, compensating for density, the Sun has approximately 400*0.42 = 167 times the gravitational "depth" as the Moon. Since they occupy roughly the same area in the sky on Earth, we would expect the Sun's gravitational pull to be roughly 167 times the Moon's, which it is (The actual factor is about 178).
Final Thought
I've been working on some things that make you go hmmm involving defining time in terms of distance (of which the apparent speed of light propagation is a side-effect) and may one day relate it back to this gravity stuff. One idea to explore is this: perhaps the increase in mass experienced in objects traveling at relativistic speeds, is some consequence of length stretching, which makes the object appear "larger", as far as gravity is concerned. It may even involve removing mass from one time (where it appears smaller) and moving it to a time where it appears larger, or being relative to the "rate of time", but either way obeying some "conservation of mass over time" law.
[Well I'll mention the theory in a nutshell, for the sake of... I don't know what. The theory was that gravity wasn't due to some force acting from afar, but rather due to the difference of the apparent "force" of gravity across some fundamental constant distance. This idea basically describes gravitational gradients, which by the way is what causes tides. So rather than being pulled by something an astronomical unit away, we are pulled (or pushed) by some difference say between one side of a neutron and the other. My hope was that calculations based on existing measurements would produce an alternate formula for gravity, with a new constant analogous to G but which would have to be much much greater (to produce the same forces that the existing formula calculates for r2, but for the much much smaller delta r2). If the resulting constant was similar in value to the other fundamental force constants, that might suggest some exciting new hidden relationship. Unfortunately, the math shows that while gravity is inversely proportional to the square of the distance from a mass, the gradient is roughly inversely proportional to the cube. Fairly simple geometry can show why. In other words the calculations differ depending on which r you choose, so no such constant can be found. Or, the "fundamental constant distance" would need to grow proportionally to r. A good candidate for an idea that needs to be abandoned when shown to be wrong.]
The force of gravity exerted by a mass at a distance of r, is inversely proportional to r2. The magnitude of the force is the same at all the points on a sphere with radius r centered on the mass. Interestingly, the area of a circle with a radius of r is also inversely proportional to r2. This suggests that the force of gravity can be "spread evenly" across that sphere, making the "total force" on the sphere the same for any different value of r. As when blowing up a balloon, its radius increases and the latex is spread thinner, but the total amount of latex remains the same. If you imagine a gravity wave propagating like an expanding bubble ;) from the mass, it is similar to sound (pressure) waves, whose energy across some fixed area also is inversely proportional to r2. This is because the total energy of a single pressure wavefront remains the same, but gets spread evenly over the total area of the wave's expanding sphere. As a side note, I think this requires the wave to move at a constant speed (c for gravity waves; the speed of sound for pressure waves)... otherwise, a slowing bubble expansion might allow energy to build up, or allow the wave to be compressed laterally and compensate with an increase in amplitude.
So, gravity gets weaker as you move farther from a gravitation body, as its force gets spread across a larger area. I'd drawn a bunch of triangles to show the ratios involving a slice of a sphere around a gravitational body, and another body (a spaceship, say) that is affected by it. I realized that the force would be the same for any r, if the spaceship grew in size relative to r... in 2 dimensions that is. Then, the spaceship at r would cover the same area relative to a sphere of radius r, as the different-sized spaceship at r1 would cover relative to a sphere of radius r1. And so it would experience the same gravitational force at the different distances. A conical "slice" of gravity shares the same total gravitational force across the (curved) base of the cone, for any cone height. This is a consequence of simple ratios.
The idea occurred to me to try to visualize a spaceship that expands as it moves away from a mass, in a way that keeps the apparent size of the spaceship the same, by warping space so that lines that radiate away from the mass become parallel. In such a view, a "normal" spaceship would appear to decrease in size as it moved away from the mass. At this point I felt that now-familiar feeling that things were getting too abstract to be conceivable. Another idea came to mind of modifying gravity by somehow warping its field this way possibly through some sort of gravity lens (a lens that warps gravity, not the more familiar lens that warps light using gravity).
An interesting idea that comes out of this is that a spaceship decreasing in size as it moves away from a gravitational mass, is exactly what appears to happen to the object when viewed from the gravitational mass. The apparent area that an object takes up relative to my entire field of view, is once again inversely proportional to r2. This suggests a theory that the gravitational force on an object is related to how that object is "seen" by the mass. Interestingly, all of these ideas may be converging on some Theory of Everything that centers around the effects of observation as the core mechanism for describing physical interaction. Things affect me relative to how much I am aware of them.
Note that I'm not talking about simple visual observation. You can't hide from the sun's gravity by ducking behind a planet. The mass can "see" through matter, and can "see" the various layers or depth of matter (so a long rocket with the same visual area as a short rocket will not experience an equal force), and it can "see" the density of the matter.
As an example, consider the Sun and the Moon. From Earth, they appear to be roughly the same size. The Sun is about 400 times as far away as the Moon is, and also has a radius about 400 times the Moon's (anything that appears the same size should have the same proportion). However, it is about 0.42 times as dense. So, compensating for density, the Sun has approximately 400*0.42 = 167 times the gravitational "depth" as the Moon. Since they occupy roughly the same area in the sky on Earth, we would expect the Sun's gravitational pull to be roughly 167 times the Moon's, which it is (The actual factor is about 178).
Final Thought
I've been working on some things that make you go hmmm involving defining time in terms of distance (of which the apparent speed of light propagation is a side-effect) and may one day relate it back to this gravity stuff. One idea to explore is this: perhaps the increase in mass experienced in objects traveling at relativistic speeds, is some consequence of length stretching, which makes the object appear "larger", as far as gravity is concerned. It may even involve removing mass from one time (where it appears smaller) and moving it to a time where it appears larger, or being relative to the "rate of time", but either way obeying some "conservation of mass over time" law.
Sunday, July 25, 2010
Metapost
Dear diary,
I've wondered about my willful choosing of ignorance over research, the choice to contemplate ridiculous ideas about junk rather than trying to understand what science has already determined about said junk. Part of this is a fear that any idea I have will have already been thought of and disproved, thus robbing me of any feeling of creativity unless I ignore what's out there. Part is a fear that I won't understand what I read about, and I'd rather feel smart than struggle to actually be so. I've also recently heard of the belief that creativity requires that you don't know too much about a topic, basically because you will be lead far down the path of existing knowledge, and miss some possible new and hidden branch somewhere way back on the path.
At best thinking and figuring stuff out yourself might be good practice. Also, you can think of something until you get stuck, and then look it up for enlightenment, and your brain should be more willing to accept new knowledge than it would be if you just tried to force-feed it all in without the puzzling curiosity. However, this approach can be futile; Imagine trying to figure out the cosmos by watching the night sky and ignoring all of humanity's existing astronomical knowledge. You might not get past something like,"the stars appear to be fixed on a sphere that rotates around the earth".
But this is a blog, not a textbook. So it will be stupid at times (hopefully about average as far as blogs go), and incorrect too. It is about my exploration of the realms of metaphysics, and as much about the struggle to understand, or about bad ideas, or good, as my experiences with each warrant.
One of the basic tenets of science goes something like this: an idea, no matter how good it is, must be abandoned if it is proven to be wrong. Trying to fit all ideas to one central idea or belief = timecube.com. And so stupid ideas will come and go, and be revisited now and then, and conflicting ideas will get mixed up and others resolved, until I either get that nobel prize on my shelf, or give up, or go mad.
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