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Natural Science Forum / Physics / Particle Physics / March 2006Relative Dimensionality Paradigm
By evacuating all of space and granting just two particles the context of dimensionality takes on a striking choice. If we allow for just one distance between these two particles then we might claim a one-dimensional system as in classical physics where we just work in one Cartesian dimension x for a simple problem. But is this valid? Are those particles in spacetime? Where is the additional information? If we accept that they are in spacetime and that there is one distance between the two then the other dimensions must be informationally encoded. This is the paradigm of relative dimensionality. There is a junction here between relativism and quantum theory. This is significant to the polysigned context as well, where the following angular proposition falls out more neatly. The notion that these particles are inherently granted angular information is consistent with quantum theory. A particle inherently observes an angle between itself and another particle. This angle may be interpreted as relative to a ray. This ray may be generalized to a polarized axis. The system of two particles now contains one distance and two angles. Is this sufficient? The two particles together now form a three dimensional system. Particle A may not see what particle B sees. Each may have its own angular reference and have no ability to get the other particle's angular reference. This is probably the minimal construction that allows a three-dimensional solution for a two particle interaction. There are many structural possibilities within the paradigm. The minimal construction already allows a more complex interaction than the classical model suggests. Does the two particle system exist in spacetime? -Tim $$ No SPACE between point-mass ..only LiNEs. $$ You are too confused almost to answer, professionally. $$ Firstly, ALL test-particles in GR are POiNT-particles. $$ Points have no iNside or OUTside, and no gaps between. $$ GR TEST-point-particle on a WORLD-point-SURFACE, ONLY. $$ Note that ACTiON only happens between ADjACENT points. $$ SPACE appears ALMOST empty ..caN'T see photons sideON. $$ No SPACE in all geometry, BETWEEN points ..only PATHs. $$ There's NO matter NO momentum and NO mass in GEOMETRY. $$ It's GR c WRONG.```Brian A M Stuckless, Ph.T (Tivity). Tim wrote: > > By evacuating all of space and granting just two particles the context > of dimensionality takes on a striking choice. [quoted text clipped - 31 lines] > > Does the two particle system exist in spacetime? > > -Tim Re: Relative Dimensionality Paradigm. That's highly compressed but I think I got some of the gist. I'm not sure what "It's GR c WRONG" means. These are not test particles in the situation above. These are real particles. If we don't have spacetime with two particles why would we have it with more particles? Superposition would be broken. They have to exist in natural space. I have a hard time with your granting paths but claiming no space. You've got to have something to work with as a basis. The simpler the better. It's an open problem. Criticizing existing theories is easy. Finding a clean construction is not so easy. I'll admit I'm having a hard time doing any physics in the polysigned construction. Yet it already generates spacetime. http://bandtechnology.com/PolySigned/PolySigned.html I appreciate your concept of adjacency and the polysigned numbers have something to say about that. In their lattice it is possible for a position to be adjacent to another yet the other is not adjacent to the prior. It is a unidirectional system. It's got more to it than ordinary geometry. In the directed context you can claim that d(a,b) ! = d(b,a). If a is adjacent to b we can say that d(b,a) = d(a,b) / (n-1), where n is the sign of the domain. Those d's are lattice based path length. In a continuum is another way to study the problem. There is a lot of work to do in the polysigned domain. -Tim > $$ No SPACE between point-mass ..only LiNEs. > $$ You are too confused almost to answer, professionally. [quoted text clipped - 44 lines] > > Does the two particle system exist in spacetime? > > -Tim > Re: Relative Dimensionality Paradigm. > By evacuating all of space and granting just two particles the context > of dimensionality takes on a striking choice. [quoted text clipped - 3 lines] > just work in one Cartesian dimension x for a simple problem. But is > this valid? Are those particles in spacetime? Of course they are in space-time by the very definiiton of space-time. Bill > Where is the additional information? > [quoted text clipped - 26 lines] > > -Tim > > By evacuating all of space and granting just two particles the context > > of dimensionality takes on a striking choice. [quoted text clipped - 6 lines] > Of course they are in space-time by the very definiiton of space-time. > Bill Can their solution then be one-dimensional? Are you uncomfortable with a 1D solution? The idea here is to deny the simplistic 1-D solution because it does not conform informationally to the space. The question then becomes what to endow these particles with so that they do conform informationally. The polysigned numbers suggest an angle. I think that is what quantum mechanics uses too. The polysigned numbers suggest a tatric format for the spacetime representation: a11 a21 a22 a31 a32 a33 ... each a is an unsigned number. The format represents: P1 x P2 x P3 ... Stopping the progression at P3 we would call the tatrix T3 and it is an efficient representation of spacetime. But there are six parameters. Well, the representation has a reduction that always allows a zero in each row. So that leaves three signed parameters. So spacetime has a tatrix structure. As one tries to do particle type theories over a tatrix and maintain relativity one of the easiest solutions is to maintain a constant magnitude over each level. i.e. | P1 | = | P2 | = | P3 | ... So now the singular distance between two particles is instantiated. So what makes it spacetime? At each level beyond P1 there are qualities which are the remaining degrees of freedom. at P2 it is a sign choice ( - / + ) at P3 it is an angle ( U(1) I believe is the standard notation ) at P4 we would have more angles, but its probably best to stop at P3 for now. So now strangely what should be a spacetime representation has been reduced to a magnitude, a binary, and an angle. That seems pretty weird but that is for just one particle in space. Since we need two particles to do any physics it may be a sufficient representation. Raising the tatrix by one level from T3 to T4 yields a six dimensional space which still maintains support for spacetime. (http://bandtechnology.com/PolySigned/PolySigned.html) If invariance is enforced (the singular distance as above) then rather than merely getting three additional angles we get a one of four choice. This is getting esoteric I'm sure so I'll stop there. The original point was to query whether a 1D solution that is the tradition of classical physics is valid in reality. The relative nature of a two-particle system yields an impressive choice. -Tim > > Where is the additional information? > > [quoted text clipped - 26 lines] > > > > -Tim >> > By evacuating all of space and granting just two particles the context >> > of dimensionality takes on a striking choice. [quoted text clipped - 8 lines] > > Can their solution then be one-dimensional? Of course. > Are you uncomfortable with a 1D solution? Of course. > The idea here is to deny the simplistic 1-D solution because it does > not conform informationally to the space. Your idea is silly. > The question then becomes what to endow these particles with so that > they do conform informationally. The question is for you to understand what models are. The situation requires 4 parameters for each particle ie a total of 8 parameters - but that can be plotted on the same space-time diagram. Bill > The polysigned numbers suggest an > angle. I think that is what quantum mechanics uses too. [quoted text clipped - 69 lines] >> > >> > -Tim > The question is for you to understand what models are. The situation > requires 4 parameters for each particle ie a total of 8 parameters - but > that can be plotted on the same space-time diagram. > > Bill Your solution will be nonorthogonal in 3 of the dimensions unless the particles involved have additional characteristics. You might as well pose the problem in ten dimensions and claim that it supports ten. Is that OK too? The solution will carry the same meaning and be equally reducible to two dimensions (using time as a dimension). Also within your argument I do not see 8 parameters in the problem. I see just four. So you must be invoking an origin, a point of reference that I believe should be tied to one of the particles. I'm mostly interested in this from the informational perspective, rather than quibbling over vector representations. The fact remains that we do not observe simplicial particles. They have dynamics that are very peculiar. The dimensionality relation posed here is already supported. I suppose that the argument may be dismissed as metaphysics, and it is at that level that I am hoping to discuss the problem. Should spacetime not be conserved in a two-body problem would there then be an inconsistency for a three-body system which is the superposition of its component two-body systems? Working within the 1D two-body solution paradigm a three-body problem will still only form a 2D system. At four particles we can have a 3D system and then as we add particles we should see no more dimensional increase. Just increased redundancy and dynamics but still in 3D. That's a strange pattern. I don't really see a problem with that but it would be a lot more consistent if we just started out in 3D and allow the complexity to rise but not the dimensional basis. Is there also a one-body system? Self-action would allow for it. Have you ever gotten an electron to sit still? -Tim BIg babies, stop cheating. "David opens a new plane" > By evacuating all of space and granting just two particles the context > of dimensionality takes on a striking choice. [quoted text clipped - 33 lines] > > -Tim > By evacuating all of space and granting just two particles the > context of dimensionality takes on a striking choice. If you do that, you obtain something useless. Read on. > If we allow for just one distance between these two particles Physics is about measurements. Explain how the distance between the particles is measured, WITHOUT introducing any more particles (or objects, such as fields) into the universe. No photons; those are particles, too! No clocks; those contain _lots_ of particles! No meter-sticks; those contain lots of particles, too! What's more, physics is also about predictions, and more specifically it's about predictions regarding the interactions of particles. How can your 2-particle system have any interactions (beyond, at most, one collision), WITHOUT introducing any additional particles (or objects)? > then we might claim a one-dimensional system as in classical physics > where we just work in one Cartesian dimension x for a simple [quoted text clipped - 9 lines] > > The notion that these particles are inherently granted angular The angle with respect to _WHAT_? How do you measure any angle in this system, _WITHOUT_ introducing additional particles? Define your terms! Explain exactly what "angle" you are talking about! > information is consistent with quantum theory. A particle inherently > observes an angle between itself and another particle. Observes it _HOW_? This is not a trivial, irrelevant question. Go back and look at the beginning of Einstein's 1905 Electrodynamics paper. What's he talk about first? He talks about _HOW_ you make measurements, _HOW_ velocity, time, and distance can be measured, because without specifying such things you don't have anything "physical" to talk about. So, _HOW_ does one particle "observe an angle" between itself and the other particle, without any other particles in the universe? > This angle (which remains undefined) > may be interpreted as relative to a ray. This ray may be > generalized to a polarized axis. [quoted text clipped - 12 lines] > > Does the two particle system exist in spacetime? Sure, but you can't do much with it. It's too small to be interesting.  SignatureNospam becomes physicsinsights to fix the email I can be also contacted through http://www.physicsinsights.org > > By evacuating all of space and granting just two particles the > > context of dimensionality takes on a striking choice. > If you do that, you obtain something useless. Read on. > > If we allow for just one distance between these two particles > Physics is about measurements. > Explain how the distance between the particles is measured, WITHOUT > introducing any more particles (or objects, such as fields) into the > universe. No photons; those are particles, too! No clocks; those > contain _lots_ of particles! No meter-sticks; those contain lots of > particles, too! Hi Sal. This is a theoretical two body problem. It is the only one that we know how to solve. Can we simply accept that there is a distance x between these two particles measured in meters and that the distance will vary? I have never seen anyone actually use a measuring rod on particles before. The only reference points in the system are the two particles so there is one distance x, which varies based only on these two particle's interaction and some initial conditions. If you don't want to use fields I think for this context it is OK to just use a 1/(r*r) type of force but as you will see that is what I am troubled by: I will try to make the argument by using the contrapositive. So let's assume that we have two particles containing only the property of mass. We don't give them any angle characteristic. They are directionally symmetric. We plop these two particles into spacetime. The only observable in the system is the distance and therefore the only data that these particles will ever obtain is one dimensional. To the particles they do not exist in spacetime. Instead they exist in a one dimensional space. So where is the spacetime? The original argument suggests that the system constructed here is invalid. There is an informational mismatch that is incongruent with the notion of spacetime. The only remedy to this situation is to endow the particles with additional features or try something else (e.g. strings). That part of the problem is open. I am open to this being a false paradigm. But I am using it to explore a problem and thought of it as a bridge between quantum and relativity. Informational conservation might be a useful principle. The prediction it makes is already satisfied. I think the strongest argument against the mass construction above is that should the two particles fall into an orbit, perhaps elliptical, that they will form at least a two dimensional system. They will experience oscillating distance. The hypothetical angle is an internal property that each particle has which allows it to measure the direction of the other particle. Because we accept one distance between the particles angular information is really all that we have left to work with geometrically. In the minimal construction each particle now has a two dimensional context, but the two together form a three dimensional system. The really hard part is to define the interaction as a function of both distance and these angles. I'm not able to do it yet so I am sorry that I cannot specify this part of the problem. We could make something up but would be pretty easy to shoot it down. I was thinking of qV x B and how the electon's magnetic moment is woven into that. Some radical motion is the resultant. > What's more, physics is also about predictions, and more specifically > it's about predictions regarding the interactions of particles. How > can your 2-particle system have any interactions (beyond, at most, one > collision), WITHOUT introducing any additional particles (or objects)? This is more an argument that predicts that particles should have features rather than predicting the exact interaction of those two particles. > > then we might claim a one-dimensional system as in classical physics > > where we just work in one Cartesian dimension x for a simple [quoted text clipped - 22 lines] > > Observes it _HOW_? Perhaps I should not claim the particle to be an observer. It is an experiencer. It experiences this angle by definition. It is a suppositional argument and is not critical to the problem. That is the open part of the problem. The thing I'm trying to focus on is whether or not it is valid that two particles have a 1D solution. > This is not a trivial, irrelevant question. Go back and look at the > beginning of Einstein's 1905 Electrodynamics paper. What's he talk > about first? He talks about _HOW_ you make measurements, _HOW_ > velocity, time, and distance can be measured, because without > specifying such things you don't have anything "physical" to talk > about. That's true, but he was also playing with varying the properties of distance and time based on the properties of the system so it was crucial to address these concerns. > So, _HOW_ does one particle "observe an angle" between itself and the > other particle, without any other particles in the universe? If you could come up with somethihng other than an angle it might also be productive. But in the geometrical sense if you grant a singular distance between these particles the only thing left to you is angles. This is also consistent with empirical particles. For example an electron's spin axis is intrinsic. An electron will always be able to specify an angle to another electron based on the orientation of this axis to the direction of another electron. It still doesn't fix the other electrons position in 3D. But it could be used as a source of interaction. > > This angle > > (which remains undefined) I hope not any more. But if you think it is ill defined still perhaps we could work on some more of the basics. For example the proposition holds that spacetime exists. This implies a 3D space. From one particles position we simply choose a unit vector in a random direction and call that the "Ray" Now there is also a vector connecting the two particles, for particle A we could call this X. Define unit vectors r(Ray) and x(X). The angle is just arccos( r dot x ), where dot is the vector dot product. > > may be interpreted as relative to a ray. This ray may be > > generalized to a polarized axis. [quoted text clipped - 15 lines] > Sure, but you can't do much with it. It's too small to be > interesting. Higher systems are based on the superposition of these two body systems. I really appreciate your discussion and challenge to these ideas. I've inspected your website briefly and will try to learn more about the Sagnac effect. -Tim http://www.BandTechnology.com >> > By evacuating all of space and granting just two particles the >> > context of dimensionality takes on a striking choice. >> If you do that, you obtain something useless. Read on. >> > If we allow for just one distance between these two particles > [quoted text clipped - 8 lines] > This is a theoretical two body problem. It is the only one that we > know how to solve. This isn't quite correct. The 2-body problem is the only one with an analytic (closed-form) solution. Problems with larger numbers of objects can be solved to any precision you like, and future behavior predicted to any precision you like. Their behavior can be modeled to any precision you like. That's generally taken to mean we can "solve" such problems, in a very real sense. > Can we simply accept that there is a distance x > between these two particles measured in meters and that the distance > will vary? I have never seen anyone actually use a measuring rod on > particles before. OK, I grant that you can do that. It's cheating a little, because it apparently doesn't have any physical consequences in the universe you've described, but it's at least well-defined. We can also observe that, should a radar gun suddenly materialize in the otherwise empty universe, one particle could use it to determine the distance to the other. You still have a big problem with _time_, though. How do you define it in a universe with just two particles? A radar gun measures speed, too, but it couldn't do that if it didn't come equipped with an internal clock, and once you add a clock to the universe you've added a whole pile of particles interacting in complex ways. > The only reference points in the system are the > two particles so there is one distance x, which varies based only on > these two particle's interaction and some initial conditions. If you > don't want to use fields I think for this context it is OK to just > use a 1/(r*r) type of force So we have two particles and a mutual field of some sort? > but as you will see that is what I am > troubled by: [quoted text clipped - 3 lines] > So let's assume that we have two particles containing only the > property of mass. Ah ... So, your mass tensor is nonzero and now, if you want to figure out the interaction, you need to solve the field equations to determine the curvature... Or you can use the Newtonian approximation. One way or another you have some sort of attraction operating between them. > We don't give them any angle characteristic. They are directionally > symmetric. In that case you appear to have made your universe explicitly 1-dimensional. > We plop these two particles into spacetime. The only observable in > the system is the distance and therefore the only data that these > particles will ever obtain is one dimensional. To the particles they > do not exist in spacetime. Instead they exist in a one dimensional > space. So where is the spacetime? Well, since you don't have any clocks in the universe, the "time" dimension seems to be a little lacking. But aside from that, what's wrong with spacetime with just 1 spatial dimension? It's used all the time in SR problems. > The original argument suggests that the system constructed here is > invalid. No argument I made. I just said it's too simple to be interesting. > There is an informational mismatch that is incongruent with the > notion of spacetime. [quoted text clipped - 7 lines] > relativity. Informational conservation might be a useful > principle. The prediction it makes is already satisfied. What prediction? > I think the strongest argument against the mass construction above > is that should the two particles fall into an orbit, perhaps > elliptical, that they will form at least a two dimensional > system. They will experience oscillating distance. Indeed! Conservation of angular momentum comes into the picture. Yes, come to think of it, they will behave that way. On the other hand, if you put a massless and intangible observer in this sparsely populated universe, he/she would be hard pressed to say whether these two particles are orbiting in 2 space dimensions under the influence of a central 1/r^2 force, or are oscillating in 1 space dimension under the influence of a force that looks something like k(r-r0). On the _other_ other hand, AFAIK there's no way you can get any interaction going which will reveal the third space dimension, even indirectly, in this limited situation. > The hypothetical angle is an internal property that each particle > has which allows it to measure the direction of the other > particle. But suppose the poor thing is rotating -- how would it know? A rotating particle would "see" the other particle as revolving around it, instead, unless it could figure out, somehow, that it's not, itself, stationary. If you make each "particle" complex enough so that it carries an inertial reference frame within itself -- and can determine (a) whether it's, itself, rotating and (b) identify an (arbitrary) set of up, down, right, left, front and back directions then you've got enough information to start talking about angles and a full set of three dimensional information, but you've also got a universe that's an awful lot more complex than just two elementary particles. > Because we accept one distance between the particles > angular information is really all that we have left to work with > geometrically. > > In the minimal construction each particle now has a two dimensional > context, Huh? What's this mean? Again, if you give each "particle" enough structure to have an internal "orientation" and to determine whether it is itself rotating, then each defines, in effect, a 3-dimensional inertial frame. You still have, of course, got a bit of an issue with regard to clocks. > but the two together form a three dimensional system. The > really hard part is to define the interaction as a function of both > distance and these angles. Can't you can set up the equations of motion in ordinary 4-space and then just project the results down into whatever space you like? The only problem with your 2-particle space is that there's very little you can actually, physically, measure in that space. > I'm not able to do it yet so I am sorry > that I cannot specify this part of the problem. We could make [quoted text clipped - 11 lines] > features rather than predicting the exact interaction of those two > particles. Not at all. The only such "prediction" is that featureless particles have no measurable features, not that particles _must_ have features. >> > then we might claim a one-dimensional system as in classical >> > physics where we just work in one Cartesian dimension x for a [quoted text clipped - 38 lines] >> > That's true, but he was also playing with varying the properties of "he"? > distance and time based on the properties of the system so it was > crucial to address these concerns. [quoted text clipped - 17 lines] > > I hope not any more. Do you mean you defined it by the assertion that each particle has (in effect) an internal gyroscope of some sort? > But if you think it is ill defined still perhaps we could work on > some more of the basics. For example the proposition holds that [quoted text clipped - 4 lines] > r(Ray) and x(X). The angle is just arccos( r dot x ), where dot is > the vector dot product. You've picked a random number and called it "angle". Now we can say that the two particles are at "angle" relative to some vector. "angle" may or may not vary with time, depending on whether a randomly chosen direction varies randomly or not. This doesn't seem terribly helpful. It provides no actual reference point for measuring anything. It provides no way to determine, for instance, angular velocity of the position vector of one particle relative to the other in any meaningful way. >> > may be interpreted as relative to a ray. This ray may be >> > generalized to a polarized axis. [quoted text clipped - 18 lines] > Higher systems are based on the superposition of these two body > systems. Actually the 2-body systems generally used involve numerous other bodies used for reference. Such things as fixing the difference between a 1-dimensional central force going as something like k*(r-r0) or a 2-dimensional central force going as something like k/r^2 just don't come up when one uses a universe with many complex objects in it, even when we ignore all but two of them for the purposes of understanding basic electromagnetic interactions. > I really appreciate your discussion and challenge to these > ideas. I've inspected your website briefly and will try to learn [quoted text clipped - 3 lines] > > http://www.BandTechnology.com SignatureNospam becomes physicsinsights to fix the email I can be also contacted through http://www.physicsinsights.org > >> > By evacuating all of space and granting just two particles the > >> > context of dimensionality takes on a striking choice. [quoted text clipped - 72 lines] > In that case you appear to have made your universe explicitly > 1-dimensional. This is the conclusion that is troubling about the most simplistic solution. I did not explicitly make a 1-dimensional spacetime. I explicitly stated real spacetime but out comes this 1D system. > > We plop these two particles into spacetime. The only observable in > > the system is the distance and therefore the only data that these [quoted text clipped - 52 lines] > it, instead, unless it could figure out, somehow, that it's not, > itself, stationary. This is the minimal construction. The Ray is the axis of rotation. The angle and the distance are what the particle experiences. I would not deny the vector that connects the two particles. That is a fundamental piece of information. All of the additional features you list below should not be necessary. The angle is relative. > If you make each "particle" complex enough so that it carries an > inertial reference frame within itself -- and can determine (a) [quoted text clipped - 12 lines] > > Huh? What's this mean? An angle and a distance makes two dimensions of information. > Again, if you give each "particle" enough structure to have an > internal "orientation" and to determine whether it is itself rotating, [quoted text clipped - 102 lines] > Do you mean you defined it by the assertion that each particle has (in > effect) an internal gyroscope of some sort? yes. > > But if you think it is ill defined still perhaps we could work on > > some more of the basics. For example the proposition holds that [quoted text clipped - 15 lines] > instance, angular velocity of the position vector of one particle > relative to the other in any meaningful way. I didn't mean to introduce a random component into the system. I just meant to define an angle in the simplest context I could. As these angles (each particle has one) vary the system has become three dimensional, satisfying congruence to spacetime informationally. Again this is merely a minimal construction. Can time in this system simply be an independent real variable such that the distance and angles vary as a function of it? Where is the need for clocks? So we would have x(t), a(t), and b(t). a for angle alpha of particle A and b for angle beta of particle B, and x for the distance between A and B. I don't really like this, but if you insist I will try to go there. I don't think I can deal with the radar gun you've suggested. I guess this becomes a Newtonian model. -Tim > >> > may be interpreted as relative to a ray. This ray may be > >> > generalized to a polarized axis. [quoted text clipped - 40 lines] > Nospam becomes physicsinsights to fix the email > I can be also contacted through http://www.physicsinsights.org Time to do some snipping. [Tim] >> > We don't give them any angle characteristic. They are >> > directionally symmetric. [SAL] >> In that case you appear to have made your universe explicitly >> 1-dimensional. >> > This is the conclusion that is troubling about the most simplistic > solution. I did not explicitly make a 1-dimensional spacetime. I > explicitly stated real spacetime but out comes this 1D system. I don't see the problem, really. A system consisting of 1 mass connected to a solid wall by a spring is "1 dimensional". Two masses connected by a spring but constrained to move in a line is "2 dimensional". But that's just the dimensionality of the configuration space, not the spacetime itself. You've started with two particles in an otherwise empty universe. We can ask several things about the system. 1) What parameters can be _measured_ inside this space using tools available inside the space? Answer: Not enough to be interesting, so let's drop that question for now. 2) What parameters can be _defined_ inside this system? In other words, what parameters could an intangible ghost inside the universe measure? There seem to be just two: a) Distance between the particles b) Relative speed between the particles Anything else requires introducing some additional structure. A vector which points in a "fixed direction", mentioned (far) below, seems very artificial to me -- how does our intangible ghost keep track of what direction was the "fixed direction"? 3) We cheated in (2). How does our ghost measure distance? This is not a trivial question. If this is a relativistic universe then "distance" is only well-defined between points in an inertial frame of reference. With just two particles, how do you determine an inertial frame? How do you make measurements within a particular frame of reference, when all you've got are two particles? Suddenly we seem to need a whole flock of ghosts, all carrying synchronized clocks, and the universe doesn't look so empty anymore. In particular we end up inheriting an orientation from the flock of ghosts, and the question of how to measure angles becomes trivial. Perhaps we should make this a Newtonian universe -- then we can just talk about "distance" and "time" without specifying who measured them! 4) Can we define "time" inside the universe? Answer: Yes ... sort of. As you pointed out, we can use the distance between the particles as a "clock", _assuming_ that distance is changing. But again, this doesn't work so well if the universe is relativistic, because it's distributed (it requires both particles to determine the time) -- it provides no way to define time for a particular observer at a particular point, and provides no way to determine the relative timing of spatially separated events. 5) What's the dimensionality of the configuration space of the two particles? Looks like 1 to me; again, there is no reference point inside the universe to tell you anything except how far apart they are. 6) How many space dimensions are needed to describe the motion of the particles? Answer: 1 or 2, certainly not 3. 7) Can we tell how the particles interact by watching them? Answer: No! Suppose the distance between them is fixed. Does this mean they're non-interacting, or does it mean they're in a circular orbit around a common center? Without some other point of reference the two seem indistinguishable. What's worse, if the distance between them is fixed we have no "clock" at all in the universe -- it's totally static. 8) If we already _know_ how they interact, does that help? Yes, it helps ... some. Suppose we _know_ they don't interact at all. Then, if we see them grow closer together and then move apart, and then just keep moving apart, we can say they are in constant linear motion with respect to each other. But if we have no clock in the universe except their relative motion, we can't say anything more than that, as far as I can see. With a separate clock, we can talk about how fast they're going, and we can determine, up to a reflection, what plane they're moving in. 9) What would _really_ help? Three non-interacting stationary particles arranged non-colinearly. That would provide an unambiguous inertial frame. Then, add a fourth non-interacting particle which is painted red on one side and blue on the other side. Set it spinning. Now there's a clock. But the simplicity of the 2-particle space is really lost at that point... [ snip ] >> > The hypothetical angle is an internal property that each particle >> > has which allows it to measure the direction of the other [quoted text clipped - 11 lines] > additional features you list below should not be necessary. The > angle is relative. Relative to _what_? What parameter would a ghost in the universe measure in order to obtain this angle? The ghost would need to stick a thumbtack into the fabric of space in order to provide a fixed point with which to obtain the angle, and at that point there's a third particle in the universe (the thumbtack). >> If you make each "particle" complex enough so that it carries an >> inertial reference frame within itself -- and can determine (a) [quoted text clipped - 13 lines] >> >> Huh? What's this mean? > An angle and a distance makes two dimensions of information. OK, you're talking about degrees of freedom here, or the dimensionality of the configuration space, rather than the dimensionality of the universe itself. [ snip ] >> > But if you think it is ill defined still perhaps we could work on >> > some more of the basics. For example the proposition holds that [quoted text clipped - 18 lines] > I didn't mean to introduce a random component into the system. I > just meant to define an angle in the simplest context I could. But an angle needs to be between two vectors. In simple terms, you need three fixed points to determine an angle. You've got two. What's the location of the third point determined by? You've postulated another vector, but provided no way to identify this vector, and what's more, there seems to be no way to determine if it's stationary or rotating. > As these angles (each particle has one) vary the system has become > three dimensional, satisfying congruence to spacetime [quoted text clipped - 3 lines] > that the distance and angles vary as a function of it? Where is the > need for clocks? As I said, if you just _assume_ time, then you've also just _assumed_ a Newtonian universe. > So we would have x(t), a(t), and b(t). a for angle alpha of particle > A and b for angle beta of particle B, and x for the distance between > A and B. I don't really like this, but if you insist I will try to > go there. I don't think I can deal with the radar gun you've > suggested. I guess this becomes a Newtonian model. Yes, so it appears. [snip ] >> > -Tim >> > >> > http://www.BandTechnology.com SignatureNospam becomes physicsinsights to fix the email I can be also contacted through http://www.physicsinsights.org > Time to do some snipping. > [quoted text clipped - 220 lines] > Nospam becomes physicsinsights to fix the email > I can be also contacted through http://www.physicsinsights.org I think you have made a strong case for your position. Mine is merely a position of information conservation. The spring analogy is coherent though it would require constraining the spring in two dimensions. In that regard the particles here are different. They are free in space. That they only use one dimension of it may be possible. If information is conserved then the relative dimensionality paradigm states that we will never observe the simplistic particle in spacetime. I don't know exactly what a spin-2 graviton means, but I suppose the fact that it has a spin does not put it in the simplistic category. The position of the second particle relative to the first particle is partially defined by the angle measured by the first particle to the second particle via its internal reference. Since superposition is the way that we get to higher systems the naked two body system is relevant to those systems. A big problem with the angle hyposthesis initially made is that if each particle determines its interaction by information unknown to the other particle then the possibility of destroying conservation laws arises. If each particle has its own angle that the other knows nothing about then a degree of independence arises. One would have to arrive at a consistent conclusion there. Maybe the other angle is available via a virtual photon type of construction as Ken has suggested. I appreciate your detailed explanations here. I think I'm OK putting this away for a while. Thanks for all of the advice. -Tim > > By evacuating all of space and granting just two particles the > > context of dimensionality takes on a striking choice. [quoted text clipped - 76 lines] > Sure, but you can't do much with it. It's too small to be > interesting. Tim, I'm inclined to agree with Sal's physicality take on the problem. Even two naked charges "a" and "b" need to exhibit energy by coupling, presumeable using a photon bouncing between them, good stuff to consider. Regards Ken > > > By evacuating all of space and granting just two particles the > > > context of dimensionality takes on a striking choice. [quoted text clipped - 83 lines] > Regards > Ken Hi Ken. Nice to hear from you. I hope you've read about the P4 signon (rhombic dodecahedron). Wikipedia says: virtual particles are an artifact of perturbation theory, and do not appear in a nonperturbative treatment. As such, their ontological status is questionable; however, the term is useful in informal, casual conversation, or in rendering concepts into layman's terms. (from http://en.wikipedia.org/wiki/Virtual_particle) I don't necessarily take anyones word for anything so I'll try to be open to the virtual photon, but at the same time reserve some general skepticism. I don't really see how it plays into the dimensionality of the system. I suppose in that (do we have to go to wave functions?) an electron has some 'size' it could be important. It's kind of fun to try to picture these high speed electrons with photons managing to travel from one to the other without missing. I'm so bad at this stuff. That's the kind of thing that would be nice to get rid of. Paradox after paradox. Correct me if I'm wrong. I'm sure that I am quite wrong in one context or another. Hmm, what if that virtual photon that tried to get to the electron did miss and had to chase after it? Then couldn't the 'virtual' distance between the electrons be slightly greater? Maybe even a lot greater. Maybe great enough that the electrons wouldn't have such a strong repulsion? But photons, virtual or not, aren't supposed to bend are they. We'd maybe have to let charge curve space too. Anyhow, I'm not sure how it alters the informational aspect of the two-particle system. Once we go up to this level these particles already have spin axes and the features that they should have according to the informational argument. So we get strange behaviors for them that require lots and lots of math to figure out a few special scenarios of the problem. I don't know how to do all of that stuff. They sure aren't 1D solutions. End Of Rant. -Tim |
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