md65536

It means the path of an object in free fall in an escape orbit. My apologies, I have been speaking as if a circular orbit is at escape velocity, which I thought it was. I think Mike Smith Cosmos has been speaking of a circular orbit... however it doesn't really matter because whether oscillating at v_orb or v_esc or faster, the device will still fall to the ground.

It would not stay at a fixed orbit radius, or if it did it would exert a downward force to do so. Try this: Draw a diagram with an arc (make the arc prominent enough that it is clearly an arc, because it represents the effects of gravity, so if it's nearly a straight line it can hide it), and the device with the spring stretched to its max on that arc. Then draw force vectors representing the direction that the springs must pull the two masses, in order for them to remain on the desired orbit. Then draw equal and opposite force vectors representing the masses pulling back on the spring as their momentum is changed. Then look at the net force that the momentum of the masses pull the spring---is it zero (so device may remain stationary), or are the masses pulling the device out of its fixed position?

No, because an object in orbit is still in freefall, it is just continuously falling in a different direction (all the directions of a circle). Your device, also in freefall, falls only in the directions inward around that partial arc. It falls to the ground.

Yes it's vague and it's a puzzle to figure out what is proposed, but I think the answer is in post #2: "However the Mass Transport System, at this stage would be in a condition of Stationary Orbit ." The principle: (revised to try to explain better)... It is speculated that escape velocity provides upward force, instead of simple momentum which carries an object away from the Earth in the direction it's already going. It is assumed that a stationary object with oscillating mass has an upward force, according to the principle of escape velocity. It is used in the device with linearly oscillating mass, but the principle is also explained using a rotating mass and this is used to explain the supposed non-Newtonian effects that for awhile Laithwaite incorrectly thought occurred with gyroscopes. The idea is that speed is all that matters, and so such an object could behave as if in orbit with escape velocity, without actually needing to be in orbit: A "stationary orbit".

I think you're missing the point of the thread (as I had as well), because you've listed many practical problems, but they're irrelevant because the scientific principle behind the device is incorrect. All the practical problems offer distractions, because focusing on solving them ignores the main problem that it just won't work. The only part that travels at high speed can be made very aerodynamic and placed in a vacuum. The whole craft (and its passengers) don't need to travel fast at all---only the propulsion part needs to, like a helicopter. The practical problems can be solved and you'd still end up with a device that doesn't work. The proposed principle is to use escape velocity of a spinning oscillating mass, without letting that mass orbit the Earth. The problem is that any object that is on an escape trajectory is technically in an orbit of the escaped mass. You can't use escape velocity to escape Earth's gravity if you're not in an orbit. Yes, but the problem is Newton's third law: For every reaction there is an equal and opposite reaction. For example if you use the kinetic energy stored in the spinning wheel to launch it upward, there will be an upward force propelling the mass up, and there will be an equal downward force pressing against the ground. Say the mass breaks apart; for part of it to launch upward the other part would have to launch downward. Suppose you quickly grip the edge of the wheel and momentum carries it upward; you'll feel a downward force on the grips. The effect in the video puzzles me too... but I don't think that you can "store" reactive force and/or redirect it in the same direction as the active force. That would allow "reactionless drives". Laithwaite made a mistake here. He later figured it out and agreed that this does obey Newton's laws, and his explanations were incorrect. Still, the behavior of gyroscopes, even if well understood by some, is still puzzling and unintuitive. What you *can* do is use a "force couple" to have the equal and opposite forces parallel but not in line with each other. See http://www2.eng.cam.ac.uk/~hemh/gyroscopes/boylifts.html

Well it's clear to me that the device proposed in this thread wouldn't work, as has been explained, and it's clear that the effect demonstrated by Laithwaite in the video: ie. lifting a 40lb weight with one hand, is not a "reactionless drive" force and couldn't be used to levitate a mass without pushing down on something... but I still don't get what's happening. He uses some force to "steer" the mass, pushing it in a circle around him. What I think is happening is that he's forcing a precession of the gyro around himself, centered on himself. This induces a coupling force upward on the mass, and downward through his center. So while the mass looks and feels weightless, its entire weight is transferred downward through his center. If he were standing on a scale, there would be slight changes in weight as he changes the momentum of the mass, but while he's lifting it up at a steady rate the scale should read his weight + 40 lbs. The reason that it feels light as feather is that the usual moment or torque on his arms from holding the weight at some length from his body is not there. I suspect that though it appears even lighter than 40 lbs, it is likely as heavy as lifting the weight straight up from above, and only feels light because it would take much more effort to lift 40 lbs as he does, if it weren't spinning, due to torque. Is this correct?

He does say it's "light as a feather". He's not scamming us. The spinning weight has a lot of kinetic energy that can be used... if it hit something the right way it could fly up quite high using its own energy. Any energy used reduces the rate that it spins. Here he's converting some of that spin into upward force by slightly changing the direction that it spins??? The effect might be exploitable in a powered device that maintains the gyro's spin??? I imagine it's because the energy required to spin up the mass, giving it useful rotational momentum, could instead go into giving it upward momentum and actually propelling it where it's meant to go. Some of the energy stored in a spinning gyro would be lost. However, rockets are used because they're simple and practical, not because they're energy efficient. They have tremendous losses. Another example of using gyros to launch things would be to spin a mass at a tremendous rate and then let go of it, like the sport of hammer throw. If the mass was aerodynamic enough it should be more efficient than rockets. Anyway I'm getting off topic, but whether or not it's practical for a mass transit revolution, couldn't the effect be exploited for levitation, at the very least for a sciencey toy? -- I mean as demonstrated in the video, which is not related to escape velocity.

Oh I see... the mass orbits around itself (its center of mass), not the Earth? I totally misunderstood the point. Yes, this would not work. An object in orbit around the Earth is in free-fall. In a circular orbit it has escape velocity. Its momentum carries it away from the Earth while gravity pulls it down into a new direction, in balance. Your device would also be in free-fall but without being carried away anywhere by its own momentum, it falls just like any other object. A satellite still falls, but it falls in a circle, because the direction of gravity is moving around it in a circle, relatively, as it moves around the Earth. Your integral slices are momentarily moving at escape velocity relative to the Earth, but by moving in a tight circle they are constantly returning to the same locations, essentially keeping the direction of gravity the same. Unlike an orbiting satellite, your device falls in one direction.

and The speeds given (22,000 mph among others) are close to the escape velocity at sea level. I assume that a stable orbit is used as a levitation mechanism (though I don't see how it's feasible). With two masses connected in a stable orbit via a spring, couldn't you use potential energy in the spring to accelerate an object from rest on the ground, and then somehow capture its kinetic energy as it slows at its destination? The increased mass and decreased speed after picking up cargo could simply change its orbit maybe ? I think a good place to start criticism---unless I just plain don't get this---is that there not enough clear explanation of what's actually involved (do the masses travel through the atmosphere? or through vacuated tubes?) enough to actually do calculations to see if anything's feasible or what it would involve. However, I think that if some of the design details were ignored and some of the basic principles developed a bit more, there may be some ideas here that are at least worth contemplating. The basic idea seems to be a system of capturing the energy from "reentry" of cargo and using it to propel cargo into orbit. The energy required to change orbits of cargo could be transferred using some system of springs, could it not? I don't know how physical principles would make such a thing impossible.

I'm no expert. When thinking of adding up these series as a process, it is a process that never ends. If the series converges, it can be considered a process that "ends after an infinite number of steps". "Never" here refers to the number of steps. If you map each term to a length of time, and the series adds up to a finite sum, then it can end after a finite amount of time. Eg. Zeno's paradox. It's very much the same thing: A process that can only end after an infinite number of steps can also end after a finite amount of time if you can perform an infinite number of steps in a given time. But what we must carefully avoid is attaching incorrect meaning to either the numbers or the process of summing them. Numbers and math are abstractions, that obey certain rules, and things that have the same properties can also obey the same rules, but not everything has the same properties. These numbers are not physical things that exist. To say that a non-converging series is "equal" to a single value, has as much meaning as you give it, and is only true for things that share that meaning. For example in OP's linked video, they map the summing of 1 - 1 + 1 - 1 + ... to the process of turning a light on and off, and the duration between switches to 1, 1/2, 1/4, ... This means that the rate of switching approaches infinite for a moment. Is that meaningful? There's no answer to what the state of the light is after an infinite number of switches in a finite number of time if it's not physically possible to do that. The series, and the elusive single "answer", is applied incorrectly to something that doesn't have the same properties. The answer of "the process doesn't end and doesn't have an answer", and the different result of the analytic continuation and its answer, each appropriately apply to different things. If you're thinking about it as if numbers have a physical existence independent of whatever they might represent, and there must be a single answer to every equation, then I think you'll end up stuck with paradoxes due to having made bad assumptions.

Yes. According to a clock in the second muon's frame, during the short lifetime of the 2nd muon, the first muon ages a small fraction of its lifetime. (And vice versa.)

"The C Programming Language" aka "K&R" is probably still the de-facto C reference book, written by Kernighan and Ritchie (Ritchie invented C). It will explain all those details. You might want to google "c programming language pdf". I don't think it's the best or easiest way to start or learn programming in general, but once you know some programming basics it will tell you everything you need to know about C. Googling "c tutorial" or "programming tutorial" will probably be enough to get started.

Thanks. What I mean is I'm unable to answer many of the questions asked due to limited knowledge of the equations. I do understand, I think, that the lengths we're talking about here come from solutions to the Einstein field equations, as they apply to particular observers. In the case of Schwarzschild coordinates, what we're talking about is coordinate length as measured by an ideal observer an infinite distance from the gravitational mass in question. Certainly, someone like myself who doesn't always want to do the maths, must accept that understanding concepts in GR either comes from the maths, or is at least consistent with them. Any of the replies I'm writing, though I realize I make a lot of mistakes, are trying to interpret the meaning of what the maths are saying. There *is* something particular about the Schwarzschild radius... it's the radius at which a mass would collapse due to gravity if all its mass was contained within that radius. However that radius is a coordinate length, and not the same as the coordinate length measured by other observers, and it's not a proper length. Even though it's measured differently in different coordinates, its physical location and physical meaning remains the same... a mass is either a black hole or it isn't, right? Do all observers agree on that? I agree that to get the answers to these questions, (some)one must do the calculations. However to understand the answers, one must understand the meaning of the equations. Without understanding what the equations mean, it's easy for example to calculate the right answer for one observer, but incorrectly assign it to another observer. For example, early in the thread you wrote that A and B agree on the distance to the star in the example. This requires understanding that---I think---the distance to which you're referring is expressed in Schwarzschild coordinates, which are the same according to anyone, because they're defined using the measurement frame of an observer at an infinite distance from the mass, not according to (coordinate) measurements made at either A or B using their local coordinates and frame of measurements. This answer (which I'm not yet sure is right, so there is still more for me to understand) doesn't come from the equations, but an understanding of what the equations mean.

Fair enough, but I think it's important to differentiate between where GR doesn't make meaningful predictions (like at singularities?, or where time can "stop"), and where it might make predictions that can't practically be verified (such as inside a black hole, from which we could receive no useful information), and where it makes bizarre yet falsifiable predictions that are simply more extreme versions of what's already been verified. I don't think it's good to mix what can't meaningfully be predicted and what can, and say that both are beyond our capacity. Anyway this is beyond *my* current capacity. I've been googling some questions and came across this: "Falling Into and Hovering Near A Black Hole" http://mathpages.com/rr/s7-03/7-03.htm As an example here, the equations used in this thread break down at the Schwarzschild radius. Indeed it seems that as you approach that radius, all clocks everywhere in the universe may approach an infinite tick rate, and you would be fried by an eternity's worth of blue-shifted radiation from stars.* BUT this is the prediction for if you're hovering at that radius, and to do so would be equivalent to traveling at the speed of light or whatever... it would require infinite energy. It's not physically possible so it's not meaningful to predict what would happen if you did it. * Edit: Dammit I change my mind again, for the third time at least. Here's an interesting excerpt from the link above: The distances used in the equations in this thread are in Schwarzschild coordinates. Apparently that's not the same as the measurements in the hovering observer's local frame. And I think neither are the same as proper length. So there's many different possible measures of length, I think radar distance would be different too. Since the inch in Schrwarzschild coordinates is measured as "light years" in this excerpt, it would take years for light to cross such a distance to reach the observer in her own frame of reference, so again I think that no matter how close the observer gets to the horizon, she wouldn't be fried in an instant, because all of that radiation would still take years to arrive. Definitely confusing, I don't think I've solved it yet! I can't do the calculations. There are various things you could look up here: spaghettification etc. Falling into and hovering near an event horizon are different things. The bigger the Schwarzschild radius, the less the tidal forces... you would be stretched head to toe and squeezed sideways, but according to googled videos, you could survive falling through an event horizon of a big enough black hole (freefall, apparently you wouldn't even be able to detect the location of the horizon). So, there are a lot of different parameters and possibilities, most of which I don't know. But supposing that you're not affected by such extreme tidal forces... in a small enough "local" area everything seems normal. So supposing that a clock say at your hands ticks at roughly the same rate as the one near your eyes, then you would experience drinking the coffee at a normal rate. A local clock ticks at one second per second. It is only slow relative to *other* clocks, not itself. So you wouldn't experience the "slowing of time", the slowing of your clock that others could measure. Earth would appear brighter, blue-shifted, and aging at a fast rate.

I'm trying to answer only in terms of GR, often trying to figure it out as I go. GR is not "beyond our capacity". Yes, with a variant measure of distance, a length in GR can vary depending on observer. BTW I figure you would not observe a distant star's lifetime in a brief flash, while near a black hole. If you imagine a line of rulers between you and the star, and suppose that the star's clock ticks at a rate approaching infinity, then you'd receive all that light in an instant only if all of the clocks along the line of rulers were also ticking at a rate approaching infinity, and that wouldn't be the case here. For example with a relatively "nearby" clock that ticks at only twice your rate, the light from the star would still take 1m/c to cross its meter stick during which your clock would need to tick (half as much).

One second by our clock, but still 10 seconds according to a traveler's clock. There's not a lot of point of saying the trip takes one second, because we can't make that trip while maintaining a clock that ticks at a tenth the rate. If you brought a ruler stretching from Barcelona to NY into our extreme gravitational field, it would take 10 seconds by our clock to cross it. Well... it depends on how you compare them, ie. what definition of distance is used. The proper length of a 1m ruler is 1m according to any observer -- it is invariant. You can be sure because a clock at the ruler, anywhere, will measure light to take 1m/c to cross the ruler. There are other measures of distance..... No, it's not a mathematical consequence. It's not logical, yet math is logical. A photon doesn't have a perspective, but even if you say the universe contracts to 0 length, the photon still has 0 size and isn't "everywhere". The photon doesn't have a clock; there's no measure of time for which you can pick a moment from the photon's perspective. Meanwhile, the photon is only ever between Barcelona and NY in this example, and picking a moment using any clock will put the photon at only a single location (classically). Even if our clock slows to a stop, and distant clocks seem to tick at an infinite rate, we don't lose all sense of time, and we still know that a trip between Barcelona and NY still takes 10 seconds according to those distant clocks. I'm not sure if the appearance of this stuff would be gradual or not. If you fell into a black hole and your distant sun's clock ticked at an extreme rate, could you receive its lifetime of light output in a brief flash? I don't know how to make sense of that.

I agree with all those statements, except now you're using radar distance instead of proper distance. Using the original values, the radar distance from A to the star is 10 billion light years, and the radar distance from B to the star is 10 billion light years + 10 light seconds. A and B are not separated by 10 light seconds. Their measurements of radar distance differ. I agree with xyzt and think that including radar signals helps clarify the answers. Without it, the timing differences could be confused with a problem of simultaneity. I'll try to stay on topic.

I used a value of 2 to more easily imagine the clocks with extreme time dilation instead of a few seconds over 10 billion years. It's not very physically practical but it could be done by having B near a black hole and A far away in empty space. The distance between A and B doesn't directly affect the measurements of timing or distance of between A and the star. A's and B's clocks tick at a different rate. What do you mean by that the difference would cancel out? You don't need to care about the distance from B to the star to be able to say that B calculates a shorter duration on its clock, for a signal to travel from the star to A, than A does by its own clock. A's clock is ticking faster.

I'll modify your original example to make it easier to talk about. Imagine that observer A and the star are stationary in flat spacetime, so their clocks tick at the same rate. They're 10 billion LY apart. A burst of light from the star takes 10 billion years to cross the distance according to A's clock. Imagine that you place 10 billion rulers, each 1 LY long, end to end between A and the star. This measures the proper distance or ruler distance between the two, and all observers will agree that there are 10 billion of them between the two. You could also put a clock at each ruler, and each clock would measure that light crosses its ruler in one year. Now consider observer B in a lower gravitational potential so that B's clock is ticking at half the rate of A's. While A's clock has ticked 10 billion years, B's has only ticked 5 billion. Also, while each of the rulers' clocks ticks 1 year, B's clock only ticks half a year. Yet... B agrees that there are 10 billion rulers between the star and A, since proper distance is invariant. If you say that B observes the photons crossing a 1 LY ruler in 0.5 years, then you're comparing the distance measured by one of the distant rulers to a time measured at B, and that doesn't really matter so much, because "the local speed of light is c" means that it crosses a 1 LY ruler in 1 year according to a clock at the ruler (not that 1 LY is usually "local" but it works in this case). (There are also different measures of distance that you could use, with which A and B might not measure the same distance between A and the star.) So, B could say that it took less time by its own clock, for the light burst to travel from the star to A, but it wouldn't use that to define the speed of light.

You can speak of the simultaneity of events across all of space, but the property of simultaneity of those events only applies locally. "A local definition of simultaneity is an assignment to each spacetime event of a spacelike hyperplane that, roughly speaking, determines the events that are locally simultaneous." [E. Minguzzi. Simultaneity in special and general relativity. http://arxiv.org/abs/gr-qc/0506127] In other words, you can imagine a hyperplane through all of space being like an instant in time, and all events on that hyperplane can be considered locally simultaneous according to some observer, but that hyperplane might not apply to some other observer, for whom the same events couldn't meaningfully be considered simultaneous. However, if you keep reading the paper I cited and understand it better than I do, you'll see that the way that you'd define these hyperplanes is not unique but depends on a convention of simultaneity. The author selects such a convention, defining "[math]\bar{C}[/math]-simultaneity, as the most natural and useful in the week field limit." But that doesn't mean that there's any absolute physical meaning to the simultaneity of events defined by that.

I think the circumference of a circle that size could be calculated to the nearest Planck length using somewhere around 62 digits of pi. "Taking pi to 39 digits allows you to measure the circumference of the observable universe to within the width of a single hydrogen atom." -- http://gizmodo.com/5985858/how-many-digits-of-pi-do-you-really-need "So NASA scientists keep the space station operational with only 15 or 16 significant digits of pi, and the fundamental constants of the universe only require 32." -- http://blogs.scientificamerican.com/observations/2012/07/21/how-much-pi-do-you-need/ "Scientific applications generally require no more than 40 digits of π" -- http://en.wikipedia.org/wiki/Pi It seems whenever this argument comes up, some people are speaking of systematic reasoning, and others are speaking of intuitive reasoning, or maybe something else too and everyone's using the same word "logical". I think if one says "logic doesn't apply", or "If theory is going against logic , the theory is wrong" for that matter, one ought to explain which meaning they're using for the word "logic". Valid logical reasoning still must apply in QM, but some intuitively common-sense assumptions (which some might call logic) don't apply. Edit: That said, I'm making the same mistake of not defining what I mean... From http://en.wikipedia.org/wiki/Logic: "in particular that what physicists have learned about quantum mechanics provides a compelling case for abandoning certain familiar principles of classical logic: if we want to be realists about the physical phenomena described by quantum theory, then we should abandon the principle of distributivity, substituting for classical logic the quantum logic proposed by Garrett Birkhoff and John von Neumann." So if by "logic" one means the classical rules of logical reasoning or whatever, then with QM it's true that logic doesn't apply. http://en.wikipedia.org/wiki/Quantum_logic applies.

This is true for certain observers, for example someone at the north pole, or others similarly "stationary relative to the center of the Earth". For those observers, yes, light crosses the length of the ruler in a different amount of time depending on the direction the ruler is traveling. But that's not a measure of the speed of light, that's a measure of the change in difference of position of the ruler and the light (aka "closing speed"). Speed of light is measured relative to a stationary, non-contracted ruler. Consider the same thing from either of the observers on the equator. The observer has its own ruler, which is stationary and not contracted. Light takes 1m/c seconds to cross the ruler. Consider the other observer and you get the same result. Each considers its ruler as stationary, neither considers the ruler to be traveling toward or away from the photons.

Isn't it something like: A black hole less massive than 22 micrograms makes no sense in current theory? You've shown that despite that, measurements of mass smaller than that have *other* theoretical and measurable meaning. So you could argue that times smaller than a Planck time might have *other* meaning and may be measurable, but that doesn't prove that it is necessarily so, because there is no currently known such other measurable thing. As it relates to the topic, I think you could no more certainly say "Yes, there are precise moments of time and everything passes continuously through every moment" than "No, at the smallest scale time is like a quantum foam-like thing, and particles leap back and forth with certain statistical chances of leaping clear over a quantized moment (even backward)" and I think you could build a philosophical case around either argument, maybe even using proposed theories, but you couldn't settle it using only accepted theory. So while as you've shown, we currently don't rule out meaningful measurements of times smaller than Planck times, it's also true that we currently can't be certain of them.

Not having meaning (as I think Planck time implies according to current theory???) and not being possible (as you wrote earlier) are two different things. Smaller units of time would need a working theory of quantum gravity to make sense, and since we don't have that, we don't know what the meaning of smaller times would be. It neither makes sense to say you can keep breaking time down into smaller units, nor that it's impossible to. No accepted current theory answers that. So whether time is quantized is not answered, but treating Planck time as a quantum of time doesn't mean that time actually divides into discrete pieces, it just means that speaking of smaller pieces has no known physical meaning or measurable effect. This is based on what I think I know and I'm certainly no expert.

While I agree with everything said, I'll just add a bit more aimed at a novice who wants to make games. If you go the "programming in C++"-only route, you'll likely end up implementing small pieces of the game, like features that the designers need, or the "systems" that make up the game. Or you'll spend a long long time making a complicated game. If someone wants to just fool around with making a game on their own, you can do it nowadays with very little to none C++ programming. I'll use Unreal3 as an example cause that's all I know, but you can create a game in it using the existing base game example that comes with it, and run the editor, place a large flat surface into the world, drop an existing Unreal vehicle onto it and a spawn point, then you can play it and you already have a game where you can drive around with all the same physics and vehicle art/sounds of a basic Unreal game. Next you could add buildings or start creating a unique game with custom code. However, most of that can be done with scripting (c-like code) and you could make a pretty complex game before ever having to touch any c++. A layer of abstraction above this, instead of just using a base game of an engine, you could use an entire game and make a "mod" for it. For example you can create a Half Life 2 mod, actually I don't know exactly how but people do it... create new levels and art and stuff, script the encounters and game mechanics, and code any new behaviors and junk. This is probably the best way for an individual to "make a game" of the calibre of GTA, and often games companies hire people based on the quality of the mods that they've made. You could probably make a "cut the rope" style phone game with nothing but c++ or equivalent; even Angry Birds uses a physics engine (third party I think), but you could create your own if you were eager; you can make a bad 3d game fairly easily by using an available engine; and, you could probably make a game as good or better than GTA3 for example, using a more modern engine and existing art/sound assets and only scripting the game. To anyone really curious, I'd recommend making a bad 3d game (that is, nothing novel about it, nothing polished) starting with an engine's example games, just to get started figuring it out and having a base to start experimenting with.