md65536

Nobody technically disagrees. They can all measure certain aspects of the same phenomena differently (time, distance, etc -- while other aspects which are invariant would be measured the same by anyone). But all the different measurements are consistent with each other. They do not fail to correspond; by definition they don't disagree. You can say they disagree on the values of 2 measurements made from different frames if you want. Another way of saying that is "the measurements are relative." Also... while everyone may see things slightly differently, they all agree on what each other should see.

I've abandoned the cylinder idea. I'm simulating an oscillating point in one dimension along a line on which is a gravitational mass. I still haven't dealt with flat geometry or curvature properly. I tend to do things the hard way. :/ I try to figure things out for myself, come to the conclusion "that doesn't make sense", and then try to learn the proper way of doing it. It's not the best way to learn. Yes, learning the math would be the smart way to start.

So far I've learned that I have no idea about the things I've been talking about! I have mental ideas of what curvature means, but then if I try to do calculations based on that, I'm stuck. Which means my "understanding" is not usable, which means I don't really understand curvature. I really need to learn the math. But of course that didn't stop me. I found a post on another site which said that the curvature caused by Earth is in the range of 1mm. As a guess I figured the effects of this curvature might be inversely proportional to r (I also tried 1/r^2 but 1/r seems to work better... not perfect though). I was going to describe the calculations I'm using but I realize it must be wrong because it doesn't have a property of local flatness. So I think I must be overestimating the effects of curvature. Which is unfortunate because to get results close to Newtonian gravity, I had to use a curvature of 17.6mm instead of 1. But when I tweak values, I can get results that are close to Newtonian. It is tempting to try to get them to match (eg. I wonder if I can make it match by including the effects of time dilation etc), but that's a red herring if I'm not even using curvature even remotely right. Another problem to address is numerical error. I'm adding tiny values (the difference in x after leaping back and forth a very small distance) to very large ones (x is around the radius of the earth). I'm surprised I got values at all. I may be able to mitigate this by separating big variables from small, and making sure no variable includes both big and small. For example, I would have 2 variables for x... one for its position ("big") and another for the distance it traveled since the beginning of the simulation (small, at least to start with). Also I'm using mainly Euler method. Also I'm using a huge leap distance of 0.1m (otherwise I'd have to simulate billions of oscillations without getting anywhere)... I have to find a way to approximate a few billion tiny oscillations in a single calculation, while making sure the errors are kept small. Implementing this forced me to figure out a way that acceleration plays a part. The best I have so far, is this: Suppose a particle leaps 1 unit in one direction, and then 1 unit in the opposite direction, but due to changing measurements of distance, say it is 1 trillionth of a unit away from its initial position. The time that it has taken to make these leaps at a speed of c is t = d/v = 2/c. It has moved 1 trillionth of a unit in a time of 2units/c, which I'm treating as a tiny change in velocity that the particle gets to "keep"... if it leaps once, it acquires a tiny additional velocity and keeps moving with that velocity while continuing to oscillate. That would mean that after a trillion (an arbitrary example number here) oscillations, it would approach a significant fraction of c (I'd have to include time dilation and length contraction if the velocity gets large). So in summary: Don't know what I'm doing yet, but I can fudge this in several ways to force some results. At this point I don't expect it to work if I make some reasonable corrections, but I'll try to figure out some corrections.

Well, if you compute the answer (whether the computer is electronic, or your brain, or water logic gates or anything) you'd use a computer. If you say had a huge lookup table of binary numbers with one-bit add results (a sequential list of numbers?) you could find the answer without computing it. But I think what you're asking for is an algorithm to work out the answer by hand or in your head. A simple algorithm for adding numbers can be the same for binary or decimal. When you add a 1 to an arbitrary decimal number, you are using an algorithm. For example, a typical way for people to add 2 arbitrary numbers is this: 1. Add the least significant digits together. If it exceeds the maximum value of a digit, then carry the one to the next least significant digit. 2. Add the next least significant digits plus the carry. Again carry the 1 if there is one. 3. Repeat step 2 for all digits. For binary numbers the only other information needed is to know how to add 2 bits plus a carry: 0 + 0 = 0 0 + 1 = 1 + 0 = 1 1 + 1 = 0 with carry 0 + 0 + carry = 1 0 + 1 + carry = 1 + 0 + carry = 0 with carry 1 + 1 + carry = 1 with carry This is typically how humans add: Memorize a table of one-digit addition, and use a loop and simple rules to compute arbitrarily large numbers. Computers use logic that doesn't require the loop or "cascade". For adding just a single bit, there are simpler algorithms. http://www.wikihow.com/Add-Binary-Numbers might explain it simpler.

Is this a "free energy" device/perpetual motion machine? Why is it called The Unified Theory?

I don't think this would be practical. Assuming you had a stable orbit (orbiting in the opposite direction that the moon orbits relative to Earth might work?), then extracting energy would involve some net force between the moon and "alternator", which would quickly pull it out of a stable orbit. Unless it's possible to extract energy from the process of returning to a stable orbit? Eg. every orbit might involve "sling shotting" around the moon and then extracting energy while slowing down. I don't know if that's possible but I can't imagine it being practical compared to other possible methods, given the complications and the relatively low power output I'd expect.

I'm thinking I should try simulating this on the computer, unless anyone knows why this might be a waste of time. What I would simulate is this: On a one-dimensional line, have a mass at x=0 with some familiar value (such as Earth's mass) and a test particle at some arbitrary x0. Calculate distances on this line using some kind of spacetime equations (which hopefully I can find on wikipedia!), set up with curvature based on the mass. "Leap" the test particle back and forth along this line by some fixed distance in the particle's frame, at a speed of c. Edit: Somehow accumulate and apply the test particle's velocity. Plot the location of the test particle over time. Questions to answer: How does the leap distance matter? Does a random speed < c and/or random leap distance give better results? If so how quickly does the result converge? A successful outcome would involve fully accounting for gravity when using real-world constants, within some reasonable error. A failed outcome would involve no definitive acceleration in the test particle. A possible outcome according to replies to this thread would be that any simulated acceleration is negligible compared to g0. If such an experiment would be valueless, I might avoid trying to do it. Would the results of a simulation matter?

The force of gravity is proportional to mass, which is relative and depends on relative velocity. I don't think gravity is absolute in any sense. Edit: I just read some posts in the original thread and it looks like this reply is completely wrong.

Perhaps "the result is symmetrical" would be more precise than "the same"? I think that to be exactly "the same" with respect to the sign of t, means the process doesn't depend on the direction of the arrow of time, which would be a more specific case of T-symmetry? Eg. constant velocity would be T-symmetrical (reverse time and you reverse the movement), while zero velocity (ie relatively at rest) is not just T-symmetrical, but also "the same" regardless of whether time is going forward or backward. I'm also confused more generally... Is a process T-symmetrical if and only if it is reversible? By reversible I mean able to return exactly to a previous state. I haven't been precise with my wording, but with the conjecture that gravity works "the same" under time reversal I mean that it is an attractive force either way, which would mean that it is not T-symmetrical. If gravity is T-symmetrical, then reversing time would mean reversing gravity, and just like playing a movie in reverse, it would appear to be a repulsive force. The conjecture is based on other conjectures. I accept that I can't claim anything meaningful or provable at this point.

If you had an arbitrary vector (βr,βphi,βtheta), could you not apply a rotation matrix to rotate it onto the r axis, then apply the boost matrix for the Cartesian x axis, using r instead of x (they should be equivalent if the axises are aligned), and then apply an inverse of the rotation matrix to get it back to your original direction? Multiply these 3 matrices to calculate a general boost matrix? My maths ain't so good, but I'm curious... would that work?

I thought about this some more and I think I see what you're saying... In my example, in the launcher's frame, light from M2's launcher seems to be moving somewhat forward to catch up to M1. Meanwhile from M1's frame, that same light is moving toward M1 totally perpendicularly. This is why everything in the launcher frame appears slanted to the moving M1; light that appears to be coming from behind M1 according to one frame, appears to be coming from the side in another frame. But then... isn't it true that according to the launcher's frame, gravitons would also "approach M1 from behind and slow it down"? The answer is... no, the paradox resolves itself exactly the same way. Just as from M1's frame, everything in the launcher's frame appears slanted, everything in M1's frame appears slanted according to an observer in the launcher's frame (the launcher frame can be considered moving relative to M1's frame equally validly as M1's frame can be considered moving relative to the launcher's frame). So now... sorry for the complication... consider this... Imagine another observer in the "middle of the football field", equidistant from M1 and M2, which observes them passing by in the middle of their "race". Imagine also a ruler connecting M1 and M2. Since the M1+M2 frame is moving relative to the Middle observer, the ruler will appear bent to her. It would be the same as if the Middle observer were moving toward the midpoint between M1+M2 while M1, M2 were at rest. The middle of the ruler would appear farthest forward in the race according to Middle, while the M1 and M2 edges would slant back toward the launcher positions. Now if you imagine photons or gravitons emitted from M1 or M2, as seen by Middle, they would appear to always travel along the ruler. They would travel in a straight line according to Middle (or according to anyone), but different parts of the apparently bent ruler would coincide with that straight line at different times, because the ruler is moving. Any observer would see M1 and M2 being pulled by each other in the direction of the ruler, even if that ruler is bent according to some observers. It's weird but it's consistent. So M1 and M2 converging would be essentially involve the ruler shortening. The direction of the ruler represents M1's "side" in any frame. So, weirdly, you might say that Middle sees photons from M2 approaching the moving M1 from behind, but they hit M1 on the side, even though Middle sees that side slanting forward! This is only possible because M1 is moving forward while colliding with the photons. Any additional details can make it more complicated, but it should always work out perfectly.

Yes, you might think of it that way, but remember that in M1's frame everything off to its side in the Launcher frame appears to be slanted forward (along a line that is angled slightly forward of perpendicular). The point on the Launcher frame that is "less distant from M2's launcher" is also offset forward in M1's frame by exactly the same distance, making that point appear perpendicular in M1's frame. You can prove that it works out "magically perfectly" simply by considering that light moves relative to each and every inertial frame, and imagining the path of a photon relative to M1. Remember that a photon in M1's inertial frame will behave as if this is a rest frame. If you consider M1's frame to be moving forward relative to the launcher frame, then all the photons in M1's frame must also be considered moving forward or "dragged along with the frame" -- it's less confusing simply to treat it as a rest frame with any other frame moving. Since M1 doesn't "leave the photons behind" as it moves, the lateral delayed images never appear to be from behind. Just to further clarify that point: All photons can be considered to "be in" every inertial frame. You can consider the launcher frame at rest and imagine photons relative to that frame, and then switch to a different frame and consider the same photons relative to that other frame... the same photons behave as if any inertial frame they are considered from is at rest. All of the SR "paradoxes" I've seen so far are similar: 1. Relativity seems weird, and you can imagine weird situations. 2. Describe that situation without considering relativistic effects, and you deduce impossible situations. 3. Consider ALL applicable relativistic effects (time dilation, length contraction, lack of simultaneity, etc), which seem like further complications, and everything ends up working out perfectly. They're all puzzles and this one's a good one. It's not due to coincidence that relativistic effects happen to make everything work out by just the amount you need. They are essential to the consistency of the scenario.

The aberration occurs between the moving rockets' frames, and the "launcher" frame. Think of it like 2 (very fast) runners on a (very large) football field. Due to aberration, the yard lines would not appear perpendicular to the runners, but instead slant forwards. This is crucial to this example because each of the traveling objects appears in their own frame to have a head start. During the head start, the other object appears to be in the launcher/football field frame; during the head start there is relative motion between each object and the other (from their own frames of reference). But due to aberration (a form of length contraction), they only appear to be catching up to a perpendicular line to each other, rather than appearing to have left the other behind. During the head start, the start line (including the other object) appears slanted forward. When they are at the same speed, there is no relative motion, and they are perpendicular to each other from either object's view point (or any viewpoint on the football field equidistant to each). But they still never appear to be at the same yard line, from either of the object's viewpoints. The yard lines do not appear perpendicular to them. Further, this allows for each object to appear to themselves to always be ahead in the race relative to the launcher/football field frame (which must be the case due to the delay of observations of the other object), and yet remain neither ahead nor behind the other in their own frame where the other is relatively stationary. This is the solution to the paradox. You can't ignore lack of symmetry from the objects' perspectives, so you can't ignore relative motion at the start of the "race", and so you can't ignore length contraction and still expect it all to work without problems (which also means that if you're doing the numbers, you can't ignore time dilation either).

So a geodesic is the same path, passing from t -> -t? I think that implies that spacetime curvature is the same for t as for -t? Or at least, there is no inversion of the curvature that would make time-reversed gravity into a repulsive force. If you send a signal to the moon and time-reverse the process before it gets there, it will reverse course and return to you. If you drop a neutron off a building and time-reverse the process before it lands, it will continue to fall (I speculate). Admittedly, this depends on some of my own interpretation, which is not accepted science. As you say, there is no clear interpretation. Ignoring whether my examples describe practical or possible realities, figuring out the theoretical implications can be useful in figuring out what is possible in the universe and hopefully ultimately how it all works. Large-scale T-symmetrical time reversal is probably impossible (this very thread speculates one of several reasons why), and certainly impossible in any universal way that requires the existence of a fictional concept of "universal time", but it's useful in very small scale interactions such as those described by Feynman diagrams.

owl, you are a fool. You are a pigeon, crapping on the chessboard that is this forum. Since you don't understand analogy, I don't expect you to understand metaphor, so I apologize for my inaccurate insult. Philosophy of science is fine and it has its place, but you are using it to discredit GR. This is a Relativity forum, not a philosophy forum; hence the pigeon analogy and now metaphor. If you can prove that GR is wrong using philosophy in a way that is generally accepted, then those philosophical arguments are relevant here. But around here, GR is generally accepted science that has not been refuted in any accepted way, regardless of any "hot debate". You have a LONG WAY to go to disprove GR using philosophical arguments. Until it is generally accepted, THOSE ARGUMENTS DO NOT BELONG HERE. If you wish to try to refute GR using arguments that are not already accepted science, do it in the speculations forum. There's another choice: 3) Stop posting. I'm a fool myself. But I'm trying, Ringo. I'm trying real hard to number 3.

I believe that my post fully resolves the paradox but no one has acknowledged or refuted it. If two rockets are separated by one lightsecond and are launched at the same time in their rest frame, they will each see themselves start to move one second before the other does. But length contraction will make perpendicular lines that are in the launchers' frame appear to curve forward. The other rocket will appear ahead of me (on one of those curved lines) until I catch up to it exactly at the point where it reaches the same speed as me. While traveling with the same velocity they are relatively at rest, and will be exactly perpendicular to each other, even though they each witnessed having a head start over the other. In short: The effects of length contraction ensure that nothing impossible happens. My previous post explains more. The principle is essentially this: http://en.wikipedia.org/wiki/Aberration_of_light I'm assuming that gravitons and photons behave identically.

If the universe were thought of as an expanding (inflating) ball... (it might not be valid to do this)... Yes, I think you could define a changing measure of distance, such as "one unit = radius of the universe". Then using that measurement, the universe remains a ball with radius of one unit, and everything inside it shrinks and contracts into "patches" of greater density. You might be able to reconcile gravitational acceleration with the equivalence principle, in that a frame under the influence of gravity is equivalent to an accelerating frame. Perhaps something like... the strength of a gravitational field is related to the rate at which it contracts. Everything shrinks relative to the size of the universe, so it always seems like there is more room in the universe... it appears to be expanding relative to everything. Upon re-reading your post, I don't think this is what you're talking about. When you say "expand a vacuum within the atmosphere", do you imagine pushing everything else out of the way, so that the atmosphere (analogous to the universe) remains the same size, and everything outside of the vacuum gets pushed together (analogous to gravity)? Or do you imagine that the atmosphere is being pulled larger, and everything in stays where it is, so that the distance between things remains the same but those distances diminish relative to the increasing size of the atmosphere? If you mean the latter, then no I don't think that the expansion of the universe explains the effect of gravity. One interesting side-effect of imagining the size of the universe being fixed and the size of everything else changing relative to that is this: If the universe started out as a singularity, couldn't it be considered to still be a singularity?

t only shows up squared, so the equation has the same value whether it is positive or negative. ??? It makes sense that a particle traveling along a geodesic would travel in the opposite direction along the same geodesic if time were reversed.

Gravitationally accelerated test particles do not move along a single geodesic. If a black hole were time reversed and "became a white hole", yet we at an external perspective were not time reversed, the white hole would continue to gravitationally attract us. What I'm not sure of is whether the particles inside that white hole would follow full reverse paths and appear to be gravitationally repelled from the white hole, or if they would only follow reverse geodesics, and remain gravitationally attracted to the white hole. Only the latter makes sense, because (I assume) the spacetime curvature of the time-reversed black hole would remain the same as before, and that curvature is what dictates the gravitational acceleration. But then again, like you said we don't have a good notion of space and time. I'm mistakenly thinking of curvature only as spatial curvature, so time reversal might imply changes to spacetime curvature that I can't clearly imagine.

But how do you accelerate the objects at the same time according to all observers? You can't. If I have a viewpoint from which the 2 objects are symmetrical, and I synchronize the start of their acceleration, then they'll always be symmetrical to me. But each of the objects will see that they appear to have had a head start vs the other. Assuming gravity waves behave exactly like light, an object's gravitational pull on me will always appear to come from exactly where the object appears to be. So let's restate the problem with a different example: Imagine 2 objects P and Q at the start of a race. Imagine a very long start line, many light seconds long, with the objects separated by 1 lightsecond. A light signal equidistant to P and Q starts the race. Suppose P and Q instantly accelerate to some significantly fast speed (so we consider only 2 inertial frames: at rest relative to the start line, and moving relative to it). From P's perspective, it started the race 1 second ahead of Q. P won't see Q start the race for 1 second, and vice versa. The resolution to the paradox is this: If we imagine any photons moving through space, we can imagine them moving along with whatever inertial frame we choose to consider, correct? So, imagine photons emitted from Q a fraction of a nanosecond after Q starts to move (assume it is essentially at the starting line) and traveling along the start line, perpendicular to the velocity of P and Q. From P's moving inertial frame, these photons will "move along with P" and remain incoming from a perpendicular direction. This must mean that the start line appears to curve "forward" according to P. When it switches frames, it sees the start line stretching out to the side but now stretching slightly forward of perpendicular. It appears as if Q is "already ahead" of it. After 1 second, it appears to catch up to Q laterally at the same time that Q appears to start moving. They would remain "side by side" except for that first second (and if they stopped at the end line, Q would appear to be behind P for only that last second). I read in Carl Sagan's Cosmos that traveling near the speed of light would warp things so that things that were behind you would squish into your forward cone of vision, but I never really made sense of that until now.

I came across a definition of a white hole as a "time-reversed black hole." I assume that a white hole would only let light out. However, this doesn't make sense to me. If you have a curved geodesic contained within a black hole event horizon, wouldn't light travel along the same path whether it was going forward in time or backward in time? It seems to me that spacetime curvature would determine whether light etc would be confined to a space, or unable to enter that space. A time-reversed black hole would be gravitationally identical to a black hole. Perhaps its spin would be reversed or something, but essentially its influence on the universe would be the same??? A white hole then would be a "spacetime inversion of a black hole", where the curvature is inverted or negated or something. Extrapolating, it seems clear that gravitational attraction is independent of the direction of the arrow of time (it's probably still dependent on the rate of time or the magnitude of the arrow, if that makes sense). Gravitation is a one-way process, regardless of whether or not time is. ??? Or would a time-reversal of a black hole allow light to escape along the same paths that let it in?

No, I agree everything's relative. I just think the additional dimensions are important. Since you reduced location to distance, I assumed you were talking about spherical coordinates while considering only the distance dimension. Your example of orbiting the sun is not the best example, because the sun is essentially the same in any orientation. But if instead you were orbiting Earth, and say you wanted to land, then yes your relative distance is important, but if it mattered where on Earth you landed, and whether you landed on your head or on your butt, then relative orientation also matters. But this is all beside the point because as soon as you add a third point that's not collinear, an angle dimension becomes relevant, and if you add a fourth point that's not coplanar to the other 3, a 3rd dimension becomes relevant. With 4 non-coplanar points, I don't think your example of choosing an arbitrary axis and origin where you can ignore a dimension, will work. Certainly, the distinction between whether locations are considered relative or absolute is relevant to the thread, and I hadn't considered it in the original post. But I think that any theory that attempts to describe reality would have to consider locations to be relative.

You're describing relative location in terms of only distance, implying that one dimension is enough to define the relative location between 2 points exclusively. The other spatial dimensions (representing orientation) are irrelevant -- do you mean in general, or as it pertains to this thread? I don't think I agree. I don't think the most elementary particles are one-dimensional, and the relative orientation of 2 particles might be important especially when it comes to light, or velocities. As it pertains to the conjecture, I'd say that the size and the shape of a particle's "spatial range" is what matters (the range perhaps defined by a probability wave that specifies the possible locations of the particle and the probability of it being in any particular location. A "larger wave" would mean less locational precision, which I'm suggesting corresponds to lower energy). Unless the possible range is isotropic (ie. it's shape would need to have spherical symmetry?), then the orientation would be important. Yes... this seems to be in direct contradiction to my conjecture. It would seem that the location of the particle (the electron?) is less precisely defined in a higher energy state. Unless there's some other property that shrinks and allows greater precision, the conjecture does not account for electrons and must be wrong. Electrons ruin all my ideas! Are you sure we have to consider their existence at all???

Potential energy depending on location fits the conjecture better than velocity does. Is it a general case? Does any change in relative position involve some change in potential energy? I can't actually imagine how kinetic and/or potential energy relates to the idea. I shouldn't have mentioned it.

This probably refers to the one built by Aldo Costa: http://en.wikipedia.org/wiki/Aldo_Costa_(inventor) "However, as with other devices of this kind, the energy created by the unbalanced weights falling is merely equal to what's required to lift them to become unbalanced in the first place." Videos of it here: http://www.blueman.name/Des_Videos_Remarquables.php?NumVideo=2274#NAVIGATION Some explanation here: http://www.besslerwheel.com/wwwboard/messages/241.html "his wheel stalls"