md65536

Thank you! It's nice to see someone else as excited about the theory as I am! I am unfamiliar with the university of Bellevue but if they have an Advanced Timeology team in their physics department, then I'm sure it would be beneficial to have me speak to someone from there. I've been developing this theory in isolation. It would be nice to finally get some help.

Time consists of energy that oscillates 90 degrees out of phase with spatial energy, in the form of particles called chronotons. These chronotons can be positively charged (representing time that hasn't happened yet, IE. the future) or negatively charged (which is what the past is made up of). Positive chronotons react with particles of the present, called immediatons, to create negative chronotons and other particles called effectons. There are immediatons present in all elementary mass particles. The more mass an object has, the more chronotons it needs to react with, which is why larger things are slower. Once positive chronotons are "used up", an object will basically slow to a halt. This explains why the moon has stopped turning some time in the past. However, negative chronotons can be turned back into positive chronotons through Big Bangs and also supernovae. The sun emits positive chronotons at a fairly constant rate, which is why time appears to flow at a fixed rate for all observers. I don't really have any evidence other than common sense. I've been working on this theory for awhile now and it seems to work.

Are you saying that frame-dragging etc warps space-time differently for gravity vs light? Or that light and gravity waves propagate along different geodesics or at different speeds? If so, that's something I don't understand. If you are not saying that, then I stand by what I said. To use a particle metaphor, one might say that photons and gravitons from a point on the gravitational mass arrive at the same time from the same direction (their path is the same geodesic across space-time warped by any number of phenomena). The result is that the gravitational mass "feels" (according to the pull of gravity) at any moment to be exactly where it appears to be at that moment.

Perhaps my arguments were unfair. I apologize. I've also realized that speaking of scientists and non-scientists in general based on a few posts, let alone based on all people who post to science forums, is a gross overgeneralization. However I don't want to hijack this thread so I won't argue semantics. Back to the original topic... in another thread by the same poster, I basically said in this post in the Speculations forum that the main mystery for me on this topic is how mass/energy in one place can affect the length of measurements at distant locations around it. If that could be explained, then I believe I could piece together a very loose, very speculative explanation of how energy/mass effects (as in "brings into existence") space-time, whose curvature dictates the path of energy (which includes matter), wherein the path of mass energy in an inertial frame manifests as gravitational acceleration. I was looking up "frame dragging", and I found this: "Static mass increase is a third effect noted by Einstein in the same paper. The effect is an increase in inertia of a body when other masses are placed nearby." Could static mass increase explain space-time curvature? If it explains how the presence of one quantity of energy affects the measurements of another quantity of energy, it would mean (to me at least) the missing piece to the puzzle. Unfortunately, I can't quickly find much info on it, and the wikipedia "talk" page says "I'm pretty sure this was shown by Carl Brans in 1962 to be a coordinate effect, and not fundamental." So it's more likely that static mass increase is an effect of space-time curvature, rather than a cause of it. Can anyone speak to this?

This thread i think is a good example of the problem dividing scientists and non-scientists, and the resistance of each to the other. Scientists: Obviously ProcuratorIncendia was wondering HOW mass and spacetime are related, but rather than saying "No one really knows, exactly," you argue semantics and say that the question is not really important. If he instead had asked "Why does an apple fall?" you would have answered "gravity" and maybe even explained it. I'm certain no one would say "Well that's not science!" I assure you, if you had a simple answer for a causal connection between mass and spacetime, you would think that it is science, and you would think that it is important. ydoaPs: "'Why?' is a question regarding the intention of a causal agent with respect to the effect said agent caused." -- I'm sorry but "cause and effect" DOES fall in the realm of science. "Why" can refer to both "what causes the effect" and "what is the predetermined reason for wanting the effect" or whatever. If you had an answer to either, you would give it. Instead, you argue semantics. This "That which I do not understand is not important" attitude will hold back science if you all take on that stance. Non-scientists: ProcuratorIncendia: You say "I don't like equations...Try to not use them.", and "i'm not buying a book". What I'm hearing is "Explain this to me and I don't want to put in any effort." You might as well be asking "Explain science to me, without talking about any science." Or, "Make me understand, but I don't want to do any thinking." Or more to the point, I think you are asking that people simplify the explanation of some scientific aspect for you, rather than making it simple by understanding all of the related science (including math) behind it. I'm sorry for this rant and it's nice to see each side indulging the other to a degree, but I think a change in attitude would be helpful. Scientists: The simple fact is that not everything can be easily explained because we don't understand everything yet. That is an opportunity, not a problem to brush aside. Non-scientists: If you want to understand something that is on or beyond the boundary of mankind's understanding, you must go to that boundary and push it. If you want someone to bring the understanding to you on a platter, you must patiently wait for someone else to figure it out completely for you and write a "for dummies" book*. * That's just a joke by the way. Everyone in this thread is obviously well above average intelligence. Thank you.

I have a fairly solid understanding of why the speed of light is a cosmic speed limit, but as for the value of c itself, I have no idea. Is this value connected in any way with other fundamental constants? Are the fundamental constants of the universe pretty much arbitrary? c is based on measurements of time and length, but would it work equally well if it was a different ratio? I don't see why not. There are theories involving infinite universes each with different values for the fundamental constants. People ponder questions like "Which would support the formation of galaxies? Which would support life?" and stuff. Personally, I would think that if we finally found a Unified Theory of Everything, that all of the fundamental constants could be derived from each other. However, I've seen no evidence that that is true. I've never found a plausible explanation of why the speed of light is the value that it is. Though... you can get around this by using units of distance and time so that c=1, which is the sensible thing to do when dealing with light. Eg. instead of m/s, express it in lightyears/year. This defines distance in terms of the speed of light; you could also do the opposite and define a unit of time based on a unit of length. Then to make sense of the value of the speed of light, you would need to find a significant, non-arbitrary unit for either length or time. The Planck length is the only one I can think of, but that itself is based on light. Perhaps this line of reasoning could lead to an explanation, but the only sense I can make of it is that it just comes back to "an arbitrary value."

As gravity waves and light both propagate at a speed of c, you pretty much have that a mass is attracted to where another gravitational body appears to be at that moment. I've tried imagining a mass catching up to it's own "wake" and I'm pretty sure that it must involve it traveling at superluminal speeds, which is impossible for good reason. I think this idea is similar to something like "Imagine the orbiter catching up to its own delayed image, and seeing multiple copies of itself... can it crash into itself?" The answer is no; all three of the ideas in that sentence are impossible.

I never really figured out the details, but doesn't the left side of the brain control the right side of the body, and vice versa? And the left side of the brain is more analytical, while the right side is more creative and junk. I wouldn't doubt that the motor control parts of the brain are quite separate from the thinking/reasoning parts of the brain, but the left-brain motor control stuff might have better connections to the analytical parts of the brain which might make it better for precise control. Then left-handedness might indicate something to do with the intrabrainial connections... perhaps a stronger connection between the hemispheres, which overrides the left-brain advantage, or perhaps some deficiency that reduces fine motor control in the left-brain. I myself am "mostly righthanded" but have less right-handed fine motor control, and I write with my left hand. I wouldn't doubt that some slight deficiency gave my right hand an abnormal disadvantage, and then years of practice in writing strengthened and honed the left-hand advantage.

Okay I wrote up a perfectly wonderful response along the lines of everyone else and then spotted a source of confusion. Yes, an exterior observer would "observe the light reaching the back of the traincar first" as that end moved forward to meet the light signal that is moving backward. The situation you describe requires that the LED switch device is causally connected to the "light hitting the sensors" events. This means that the LED switch event must happen long enough after the sensor event, that information from the 2 sensors can travel to the switch. The sensor can't know instantly when a sensor was triggered; this information reaches it at best at the speed of light. An example setup might have the LED switch in the middle of the train, connected by wires of the same length to each sensor. The hobo (assumed) on the embankment with his perfect observation device "observes" the light hitting the rear of the train quickly, but then observes the signal from the sensor taking longer to reach the switch (as both are moving forward). Meanwhile he sees the light take longer to reach the front sensor (as the front sensor is moving away while the light travels), but then observes the signal from the sensor taking less time to reach the switch. Regardless, the sensor/switch setup is "causally connected", and no matter how you calculate it, I guarantee that no observer is going to see the order of any 2 causally connected events to be reversed from what another observer sees.

I don't think this is true when relativity comes into play. Specifically I think that the inside of a black hole is "bigger" than the outside. But regarding the original question... Here are some concepts that I think are interesting when trying to understand infinity: - Infinity is not a value (infinity + 1 etc). If you treat it as a value, I think it's possible to say that infinity^2 == infinity. Google "infinite hotel" for seeing how you can expand an infinite value and not change its value. Or whatever. - There's a difference between countably infinite and uncountably infinite. The real numbers are uncountable but the rational numbers are countable (to my great surprise when I learned it). When speaking of infinite variability (such as the idea of multiple universes for every possible reality) the pigeonhole principle is also interesting. Example puzzle: If you have an infinite long string of digits that never repeats, will you eventually find any given finite string of digits within it? - An infinite number of things does not necessarily need to take up an infinite amount of space. Consider the infinite sum 1/20 + 1/21 + 1/22 + 1/23 + ... = 2. An infinite sum of positive numbers can be finite and in fact quite small. So an infinite number of monkeys could fit in a small room if the first monkey was normal sized and each next monkey was half the size of the previous monkey. Ask, or just google, for more info on the concepts. Probably the most fun way to understand infinity is to work through the puzzles and paradoxes involved, and build up not just one universal understanding of "infinity", but a whole set of tools for rationalizing about infinite values or quantities.

What branch of science satisfies all of these criteria? Chemistry is not a science because we've never directly observed parts of one atom interacting with parts of another. Sure, you put baking soda and vinegar together and you get school project lava, but there's no evidence that the baking soda and vinegar turned into lava because we can't see into atoms as they interact. What is the next step? Prove that science is not science?

Is black hole evaporation equivalent to heat death? I'm stuck on the idea that a black hole and a "universe seen from the outside" are essentially the same thing.

Around 9:30 to 11:06 in the video is a good demonstration of how an expanding universe would make different locations seem "like the center". If you inflate a beach ball and you know exactly where its surface is then you can find the center. We don't know where the surface (or edge) of the universe is, or what its shape is.

Personally I think that trying to reason past "quarks have gravity" is like trying to figure out what is beyond the edge of a flat earth. You can imagine anything you like as an answer, but if you skip way past the edge of your knowledge or understanding, then there's nothing real and known to compare against, to use to evaluate new ideas. Personally I don't think that gravity is a "thing" that can be "had". It is similar to inertia. You wouldn't say that things stay at rest because of particles called "nonmovitons" that are like little monsters that pin stuff down to the rubber sheet of space. Similarly I don't think you need gravitons to understand gravity. Gravitons might be real... perhaps any aspect of reality that can be measured over a volume can be described in terms of particles (perhaps not). So this leads to a suggestion for another way to develop your ideas. Break them down into smaller ideas, and work backward instead of forward, trying to understand the ideas that you are building on. Wikipedia is fairly good for that. If it talks about something you don't understand, it will likely link to it, and you can keep working backwards until you have enough of the fundamentals figured out. You can skip over as much as you want (math or stuff that's too hard to understand) but the less you skip the more you'll understand it. I also think that it's good to simultaneously accept that everything that has been discovered so far might be right, AND that everything that doesn't fully make sense might be wrong. That way you can work with new ideas using existing ideas that many others have put a lot of work into, but you can also keep your mind open to completely new ideas. It lets you not get stuck thinking that any one idea (existing or new) is the only solution. Well let's see... I don't think that space-time is a thing or stuff, either. The grids you and others draw in spacetime diagrams are just measurements. Space might be described as a measurement of length. Spacetime curvature refers to things like length contraction and time dilation. Space then can be said to be a measurement of the size of matter and of the emptiness between parts of matter. That is... the curvature of space affects the observed size of objects within that space uniformly (scaling matter and the space between matter equally). Matter is equivalent to energy, and it is also "mostly empty space". It might be that energy doesn't really have a "size", and that a scaling of matter is equivalent to a scaling of the emptiness between quantities of energy that make up that matter. So, space curvature is a scaling of all distances between energy within that space. Mass then is quantities of energy. The "force of gravity" and the spacetime curvature from which it is effected, is a measurement of energy densities or something. ??? goes here. Matter is made up of oscillating energy. As this energy oscillates it follows the same curvature that light follows, which makes it accelerate towards the mass that has curved its space. Light appears to curve because it is following the shortest path through spacetime, which isn't a straight line from our observational reference frame. In a sense matter being affected by gravity could be said to do the same thing. As it oscillates, the curved path toward the mass is slightly shorter than staying put or moving away from the mass. It might be that the object is becoming slightly smaller as it accelerates into spacetime that is curved more by mass. The opposite (growing bigger; moving away from gravitational mass) would mean the oscillating energy is moving farther on each oscillation, and it would require added energy to do so. Okay so this is crackpot speculation, by the way. Just rambling, confusing ideas. It's all beyond my understanding. The missing ??? part is beyond my reasoning. For some reason, the presence of energy in one place, affects the measurements of length in distant locations all around it. Does any of that suggest something worth exploring further?

I don't see it that way. Rather, I think that mass defines the curvature of space-time, and that oscillating energy behaves in curved space-time exactly as a stationary object (or oscillating energy that otherwise has no motion relative to some frame of reference) behaves in "flat" space-time. I believe that because gravity is classically understood as a "pulling" force, we try to describe it that way (pulling on space-time, or pulling on light, or whatever). But I think it can be explained without speaking of "pulling" at all. In your original post you speak of "gravity acting on spacetime". I think this may be a confusing notion. I would say that mass acts on or affects (or even effects) spacetime; gravity is the observed result. The real question for me (which I can't answer) is this: How or why does mass define the curvature of space-time? To try to answer your question, it seems to me that mass seems to expand or "puff up" space-time around mass energy, in a way that can't be seen. For example, in your image the squares of the grid have more area around the gravitational mass, but since there's no visible grid in space, we don't actually observe that. You may have to restate your ideas in a new way in a new thread... I fear I may have derailed your thread by mixing in my own ideas. My hope was to suggest ways forward where our ideas overlap. I have no further ideas for you at the moment. Is there anyone else who can help? Where our ideas conflict I'll have to stick to believing what I currently do, unless someone compels me to think about it differently. Your idea about light refraction doesn't conflict with any of my understanding, and is worth consideration. For me the question is: "Does 'matter' define a curvature of space-time that on one scale (atom-scale) explains refraction (and possibly other things like electromagnetic force or strong force) and on another scale (planet-scale) explains gravity?" My previous understanding of refraction is that it involves light being absorbed and re-emitted by matter, but now I wonder if it can be completely explained by space-time curvature on a very small scale. Good luck with discovering and refining more ideas!

Does it have to have a human time-scale? If not, why not accept the limit of c in the simplest way? If stars are tens of lightyears apart, then a single thought might take thousands of years. It would be like discovering a giant that is hidden in plain sight due to it being inconceivably large, and so slow that its movement is undetectable. In a human lifetime it would be like the brain is paused mid-thought. Humans might need to do some kind of computer simulation to discover "what thought is the galaxy currently thinking?" The buildup to an answer could be quite interesting! Where the space between "neurons" is growing too fast, this could represent "individuals" that are disconnected from each other and have independent thoughts. On the other scale, it might be discovered that tiny quantum fluctuations on such a small scale might represent the equivalent of billions of years. Perhaps in the brief flashes of an LHC collision, a universe is born, and it appears tiny only from the outside, yet inside it billions of years seem to pass, and galaxies form, and intelligences evolve and try to figure out the meaning of their universe... yet to us it all appears and disappears in a flash as their universe suffers heat death and becomes just a bug on the windshield of the collider detectors.

The relevance is that gravity in some way is similar to light. Special relativity is based on the invariance of c, meaning that from any reference frame, light travels at c. Neither moving relative to a light source, nor experiencing time dilation and/or length contraction, will change the observed speed of light. So I assume nothing will change the predicted observed speed of gravity waves. That's not the same as saying it's "unaffected by time", but I think it'd be possible to make some kind of argument like that, if you were careful with your wording and especially clear about what frames of reference you're speaking of. Frames always trip me up. Well, it sounds wrong in exactly the opposite way. GR sounded preposterous but the math said it was right. Your idea sounds reasonable (at least once GR is accepted), but I can't think of any math to support it. Well, within that analogy I'd say I can't see the person clearly enough to get a good shot with any weapon. How to strengthen it: More math. Expressing the ideas more precisely relative to existing accepted ideas. I also can't think of how to strengthen the ideas, but I could quickly go over my own theories or understanding of how it all works... (Disclaimer: I am currently technically a crackpot!) - Time is literally equivalent to distance and both are observational effects. I would say "there is no objective time or distance" rather than just "there is no time". I think the universe can be described consistently without time and distance (instead, with chronology and order, respectively). It might be described "non-observationally" as a singularity with topology but not geometry, while geometry is a product of observations of the universe. - The force of gravity falls off inversely proportional to r2, while the surface area of a sphere increases proportionally to r2. To me this means that the total force of gravity exerted by a mass can be "spread evenly" in a sphere around the mass and the total sum of that force will be the same at any distance r (it will just be spread thinner the farther out you go). Also note that the visible area of an object (the moon for example) is also inversely proportional to r2. This means that if the sun and the moon (which look roughly the same size) were discs of the same depth and density, they would have the same gravitational pull on us. As it is, the sun is much less dense but much much much "deeper", and so has a much stronger gravitational attraction. -- I don't think this has anything to do with how it works, I just think it's interesting. - Because geometry is an effect of observation, we can conceptualize warping space to make it look different from a different (possibly non-observational) point of view. For example you could imagine warping space so that all the possible spheres concentric with a gravitational mass actually have the same surface area. From that point of view, the force of gravity would be the same at any distance from the mass, but all matter and objects would get smaller the farther they are from the gravitational mass. This, by the way, is an example of a vague and underdeveloped idea! Imagine a mass such as a spherical black hole, and draw lines like rays from its center. From our point of view, we see the rays diverging as they extend farther away from the mass. You might imagine turning the black hole "inside out" such that the lines diverge the closer you get (and converge to a point approaching an infinite distance from the black hole, where its gravitational attraction approaches 0). This might be what a black hole "looks like" to light. On the off chance that any of that made sense, it still doesn't answer your question: Why would mass make space appear differently curved in different frames of reference? I don't know. I think though that length contraction is a necessary means of maintaining consistency of observations. - Finally, if we imagine all matter as oscillating energy (traveling at c), then we might say that nothing is ever really "at rest". If you imagine a particle as energy constantly moving back and forth, but while it's doing this each trip back and forth is curved slightly exactly as the path of light is curved due to gravity, it takes on a trajectory that accelerates toward the gravitational mass. Then, the "time" aspect of the particle's acceleration can be expressed in terms of the number of times it oscillates back and forth, or alternatively as the total distance it travels in all its oscillations. This is all speculation. I think it would take 10 years (possibly 100) to develop these ideas satisfactorily. I'm still working on the first one, and it's a lot of work and maybe 90% of my ideas so far turned out to be wrong (but the math really does shine a light on it all). Wikipedia says of Einstein: "In 1907, beginning with a simple thought experiment involving an observer in free fall, he embarked on what would be an eight-year search for a relativistic theory of gravity." So it might take some time, for any ideas by any of us! Sorry I can't be more directly helpful with your ideas.

Well, to be honest I skipped over idea 1 because I don't understand it. After reading it quite a few times, I think what you're saying is... Ignoring time, the gravitational force of a mass is the same everywhere. For example, the sun's pull on Mercury is the same as the sun's pull on Earth, except that since Mercury is experiencing slower time, and since gravity is not affected by time, it accelerates toward the sun faster. Using gravitons just for the sake of analogy, one might say that Earth and Mercury are receiving gravitons at a time-independent "universal rate", which in Mercury's slower time it appears as if more gravitons are received per unit of time. Is that what you're saying? As for the math... the force of gravity is inversely proportional to the square of the distance between 2 masses, so to simplify things imagine something at say Earth's orbital distance from the sun. Another object twice that distance will experience 1/4 of the gravitational force. However, they will experience very little difference in gravitational time dilation. I can't think of any way to explain the difference in force as an effect of time dilation. (Actually I think using Gm/r2 is a Newtonian approximation that ignores relativistic effects, but if you can predict the orbits of planets while ignoring relativistic effects then I think it's unlikely that relativistic effects like time dilation can fully account for the orbits on their own.) As for saying that gravity may be free from the effects of time... General relativity predicts gravity waves that travel at c. I assume these waves would obey the same relativistic laws as light, and so "the speed of gravity" would not be affected by a mass's relative velocity. So in some sense gravity is time independent........... unfortunately the meaning and possible significance of this is whooshing over my head. Anyway just cuz I don't get it doesn't mean it's wrong. Also... it sounds wrong!, but even it if is that doesn't mean it can't be corrected and remain an important and good idea. For example instead of explaining the motion of the planets, it might explain the just the difference between Newtonian and General relativity's predictions of orbital motion... I dunno!

I like this idea and it's intriguing. I think it needs much more development though; how is space-time like a medium? How are the two alike, to make refraction and gravitational lensing the same mechanism? Figuring out the math should show what's right or wrong about the idea, and open up a ton of new directions to explore. I'm not intrigued enough to try to do this myself. I'm pessimistic about the chances of non-scientists like us explaining their underdeveloped ideas and having scientists "get it" with the same intuition that you have that tells you it's an idea worth exploring. If you can, and if you care, keep working on your ideas and developing them as best you can. And keep writing about them! Even if you no one develops your ideas directly, perhaps someday someone will be working on related ideas and gain insights from yours. But... there are so many crackpots out there, that undeveloped ideas tend to be lost in a sea of crackpot theories, and no one has the time to read them all, think about them all, and separate the good ones from the bad. Also... it's usually easier to explain why a new idea is wrong (even if it's a good idea) than it is to explain why a new idea is right, so don't worry if people focus on that. A good idea can be modified until it's right.

I'm (still) not a physicist, so take this with salt: A geodesic is the shortest path between 2 given points in curved space. In Euclidean geometry, a geodesic is a straight line. With curved spacetime, the shortest distance is not always a straight line. In fact, geodesics will appear to have different curvature, depending on the observer. I have a feeling that if you were to travel along the path of light as it curved through a strong gravitational field, it would appear to you that you were always following a straight line (though you would see space warping around you as you change between weak and strong gravitational fields), while an observer in a weaker field would see you travel a curved path. Using the rubber sheet analogy, imagine that from your perspective you always see the rubber sheet as flat, even though someone else might describe it being deformed by a large mass pulling it into a "bump". The shortest path would not be straight over the bump, but would be to go around it somewhat, with a curvature that depends on how deep the bump is. With a typical bump, you would never see the shortest path across the bump being a full circle. For a really steep bump, the limit would probably be a semi circle. So, mass does not pull light or the "lines of space" into it the way that gravity pulls matter. It curves space, the way pushing into a rubber sheet might. Suppose you want to describe a geodesic from point A to point B, that is nearly a full circle, around a planet or a black hole or something. What you are describing is that the shortest path between A and B goes all the way around the circle. So it must be no longer than the straight line distance between A and B. To do this, you would need to stretch the space that exists between A and B into a circle. Or another example: Suppose you are describing some gravitational phenomenon that allows you to shine a flashlight in your hand towards some planet-sized blackhole-like object, and have the light curve along a geodesic around the object that brings it back to your eye. Then the geodesic from flashlight to eye describes the shortest path between the two. This would only go "around the object" if you could take the spacetime between your flashlight and eye, and pull on it and wrap it around the object. If that were possible to observe, any observer that still saw the object as planet-sized would probably see your arm being at least planet-sized (most likely many many times larger). I didn't quite express what I intended to there, at least not very clearly. Another analogy might be if you imagine placing a ruler along a geodesic. If you travel along the ruler it will appear to be straight. If the ruler is 1m long and straight according to one observer, yet another observer sees the same geodesic as a planet-sized near-circle, then what they will see is the ruler and surrounding space stretched into a planet-sized circumference. I doubt this describes anything realistic, however I believe that warping of similar scale (or larger or even infinite?) occurs with black holes. To us, a black hole may seem like a small sphere. To light that cannot escape it, the same distances seem infinite. --- Must edit... since I totally went on a tangent from the original post. Yes, something horizontal on earth that we see as pretty flat appears flatter to us than it would be observed by a distant observer in weaker gravity (they would see it being slightly/unnoticeably curved). However, since the earth is sphere it's pretty much always going to be round. A distant observer will observe length contraction due to the curvature of space, so they would see the earth slightly/unnoticeably smaller than we would observe it. This is pretty much the same as saying it's less flat: a given surface area on a larger sphere is flatter than the same surface area on a smaller sphere.

Here's an example of how you can visualize time slowing down, using the diagram. Imagine 2 trains traveling at the same speed on 2 different lines on the drawing, one which is curved more than the other. The train on the curved path will appear to take longer because on the drawing it has longer lines to travel along. However, these lines represent straight lines in space, so (assuming no acceleration of the trains due to gravity) the train on the "curved" path in the drawing would appear to be moving slower across the same distance as the other train. Similarly you can imagine a train spanning the long curve underneath that orange ball in the picture. Then picture that curve and the train mapped vertically onto a straight line, and it will be shorter than the curved train. This illustrates length contraction. Yes, this diagram is not perfect and probably only makes sense if you already understand some basics of GR. The picture doesn't teach GR. One problem is that the vertical dimension (time?) doesn't represent the same thing as the horizontal dimensions (space), so the diagram illustrates a concept, not a visual observation.

These are guesses based on a limited understanding of general relativity: It would not be observed to be the same size. Yes, the entire mass of a black hole keeps everything in it small, not just (or at all?) because it compresses matter against other matter, but because it curves space and length-contracts everything (the size of any matter and the empty space between it). Using the bag of sugar as a prototypical 1kg, let's just say that you're inside the black hole next to this bag of sugar, and then you and the sugar are transported to Earth. You would experience the same change in observed lengths as the bag of sugar, so from that point of view the size would not appear to change. How is it conceivable to be in a black hole next to a bag of sugar? If space is contracted so much that what we see as a "small" black hole has length contraction so severe that the bag of sugar and you are infinitesimally small, then the infinitesimal space between you and it can fit comfortably in the black hole along with rooms or planets or an entire universe, making it seem like the inside of the black hole is mostly empty space. The way to figure out what you'd expect to see is through math, and I don't know black hole math. I may be way off on what the math says, and I may be way off on the interpretation.

Then I should change the wording... something like: So there must be 2 years of Earth aging corresponding to the contraction in distance between Earth and rocket, but the full 2 years of aging will only be observed over time as the rocket moves, and any yet-unobserved portion of that expected aging can disappear (or be wiped out by another simultaneity correction or something) if the rocket doesn't maintain its velocity.

Suppose rocket twin is at rest 4 light years away and Earth twin is sending a pulse every year. You might have a situation where there are 4 pulses "en route" that till take respectively 4, 3, 2, and 1 years to reach rocket twin. Then suppose rocket twin accelerates toward Earth such that gamma = 2 for a negligible duration. The space "occupied" by the pulses contracts, so the pulses are now .5 light years apart, and will take 2, 1.5, 1, and 0.5 years to reach the rocket. If the rocket returns to rest the pulses will return to taking 4, 3, 2, 1 years to reach the rocket. Is this correct? I'd somehow assumed that invariance of c would mean that the light pulses would remain the same distance apart (oops) and that they'd be 2, 1, 0, and 0 years away (the last 2 compressed into a "burst" of aging the Earth appears to experience). If the rocket is at rest 4 light years from Earth and instantly accelerates so that gamma = 2, then without the rocket having to move anywhere yet, it is now 2 years away by light signal. So the Earth must have gone through 2 years of aging during that rocket-time. I'd (incorrectly I guess) assumed that the rocket would observe that aging during the instant acceleration. If I now understand correctly, we might say that the 2 years of aging applies to Earth's present ("now" on Earth according to the rocket is 2 years away whereas it was 4 years away only moments ago), which the rocket won't observe for some time. I see now why wikipedia says the frame switch is more of an update to simultaneity than a literal aging. If the rocket remains at that velocity (about 0.866c so that gamma = 2), then it will observe those 2 years of Earth's "extra" aging spread over some time as it makes its way back. Is this also correct? Further, if the rocket is 2 light years away and goes from gamma = 2 to gamma = 1, it is now 4 light years away, and the "update to simultaneity" means Earth's present (according to the rocket) is earlier than it was a moment ago, but no "negative time" will be observed because the rocket is no longer traveling. The expected observation that was less than 2 years away a moment ago is now 4 light years away. I will have to update my calculations and see what I can salvage from them. When I feel I understand some part of it, the twin paradox seems like the greatest math and logic puzzle I've ever attempted. The other 95% of the time it's the worst.

Short version: Can a space traveler ever observe Earth time appearing to go backward? I claim "no" but under that claim I keep coming around to an inconsistency where more distant things will age more than nearer things. Where am I going wrong? Long version: I'm trying to figure out what is observed by the traveling twin during an extremely fast deceleration + return acceleration phase in the twin paradox. This is also described as the rocket undergoing a frame switch. According to my understanding of what I've read, the traveling twin will see the Earth twin age a large amount in that very short period of rocket time. What happens if the rocket "frame-switches" several times while far from Earth, by coming to a stop and accelerating toward Earth, then stopping and accelerating away from Earth again (involves multiple switches between 2 frames: outbound, and return)? What happens if it repeats this, "shaking" back and forth, reaching high velocity each time, over a very little duration of rocket time? Solution 1 (no good): My calculations show that the Earth twin will continue to age rapidly during these frame switches (specifically, she will age much as length contraction takes effect when accelerating in each direction, and age not at all as length contraction is released when decelerating). However, it also is apparent that the distance that the rocket is from Earth will determine how much the Earth twin ages when the rocket does this little trick. This leads to inconsistency... Suppose the rocket has traveled to Planet X which is stationary relative to Earth, and then "shakes" for awhile. The Earth twin will age a lot relative to the rocket twin, but a Planet X twin will age only slightly faster than the rocket twin. This makes no sense because the Earth twin and Planet X twin should not age differently relative to each other. Solution 2: When the rocket switches from outbound to return frame, the Earth twin will age relatively fast, but when switching from return to outbound frame, the aging difference will be undone. One way for this to happen is for one twin to age fast and then the other twin to age fast. But if the rocket can shake many times in a short period of time, it should age only that short period of time. So if the Earth twin ages a great amount during one frame switch, it must un-age on the other frame switch. This means the rocket can observe earth time going backwards. I hope that this is NOT the case, because it punches a huge hole in my theory of how time works, and my understanding of observable reality. Solution 3: The time periods in which the Earth twin seems to age greatly actually overlap, so that if the rocket shakes for awhile, the rocket twin observes only one aging period on Earth (possibly fluctuating between fast and slow aging as the rocket shakes?). Solution 4: Not all frame switches have the same observed relative aging? Solution 5: Something I've missed? Some way in which time dilation compensates? Or a maximum possible acceleration rate?