Some subtle aspects of relativity.

[Erasmus00]

I think I understand our sticking point- we have very different notions of a geometry, and I'll try to highlight the problem.

Just exactly why does the path length need to be observer independent, other than the fact that Einstein's theory says so?

Actually, its not a requirement of Einstein's theory, its a mathematical requirement for a consistent geometry. The length of lines in any geometry cannot depend on the coordinates used to describe those lines. In my mind, the fundamentally nice thing about Einstein's relativity is that its a geometrical theory- we can describe everything with geometric objects and never have to specify coordinates. A metric, by definition, must produce invariants. These are mathematical requirements. A geometry is simply a space equipped with a valid metric. Einstein interpreted by Minkowski is a metric space, yours is not.

Again, my problem isn't that your construct is WRONG, its not. Its that its not as useful. I'm not saying Einstein's is the only right solution, rather that your solution uses the utility of Einstein's.

Come on Will, take a look at another possibility. It's the relativistic transformations which are important here not the lack of existence of a preferred coordinate system.

My complain has nothing to do with a preferred frame- some geometries have preferred frames, some don't. My complaint is that coordinates don't matter (your own admission is that the coordinate system shouldn't matter, the labels are arbitrary anyway). Hence, our formalism should emphasize this fact by describing things by geometric objects, NOT objects tied to coordinates.

The utility of Einstein really only comes with Minkowski's addition to the theory- special relativity describes a very nice metric space i.e. a geometry, and so we can get rid of coordinates entirely and describe things in terms of geometric invariants.

Now, as to scale invariance, lets start with an observation:

On a large scale (mega parsecs), the universe is quite regular, and IS roughly scale invariant, see the sloan digital sky survey. However, as you zoom in, it becomes clumpy and is no longer scale invariant- the universe is only roughly scale invariant. (to be scale invariant, things must be homogenous- compare the contents of the room you are in to the contents of a pocket of space 3 light minutes away). On our telescope scales, its observationally trivial that things aren't scale invariant.
-Will

[Doctordick]

Sorry Will but I think you just have that Einsteinian brain clamp screwed on just a little bit too tight; I think it is cutting off the blood flow to your brain.

Originally Posted by Erasmus00

I think I understand our sticking point- we have very different notions of a geometry, and I'll try to highlight the problem. Actually, its not a requirement of Einstein's theory, its a mathematical requirement for a consistent geometry. The length of lines in any geometry cannot depend on the coordinates used to describe those lines.

The whole object of the issue of relativity is the transformation of measurements in one observers geometry to the same phenomena as seen in a second observers geometry. Geometry is, “the branch of mathematics concerned with points, lines, curves, and surfaces and the method of representing them”.

Originally Posted by Erasmus00

In my mind, the fundamentally nice thing about Einstein's relativity is that its a geometrical theory- we can describe everything with geometric objects ...

This is a direct consequence of that Einsteinian brain clamp.

Originally Posted by Erasmus00

A geometry is simply a space equipped with a valid metric.

You have the issue backwards if I ever saw such a thing. A metric is “a geometric function that describes the distances between pairs of points in a space”. The metric is defined by the geometry and there is nothing in the definition which says that “different representations of the same phenomena” need to yield identical value for the effective length of the path: i.e., identical metrics. The value of their metrics along the path of the entity need not be the same, they are a function of the geometry used by the specific observer.

Originally Posted by Doctordick

The path length of a cannon shot in a frame at rest with respect to the cannon is quite different from the path length of the same cannon shot in a frame at rest with respect to the x motion of the cannon shot itself.

Originally Posted by Erasmus00

Einstein interpreted by Minkowski is a metric space, yours is not.

Here's that brain clamp again. Einstein interpreted the metric to be the central issue of the physics. Without that brain clamp, the metric would be a way of measuring the path of an object in the given geometry.

Originally Posted by Erasmus00

Again, my problem isn't that your construct is WRONG, its not. Its that its not as useful.

So you manage to dismiss my work without examining it; right? I am sorry but I cannot hold that as a valid issue; how can you seriously say it is not useful without examining the consequences of such a view is beyond me. It certainly sounds like a closed mind.

Originally Posted by Erasmus00

I'm not saying Einstein's is the only right solution, rather that your solution uses the utility of Einstein's.

Now that is an outright lie. My solution makes utterly no use of Einstein's solution. My construction was designed to show that the Einstein solution was exactly the same as mine. I came up with it long before I had even a glimmer of Einstein's work. It is perhaps founded on Lorentz and Fitzgerald's work but not because I read their work but rather because the same solution to the Michelson-Morley conundrum which occurred to them occurred to me.

Originally Posted by Erasmus00

My complain has nothing to do with a preferred frame- some geometries have preferred frames, some don't. My complaint is that coordinates don't matter (your own admission is that the coordinate system shouldn't matter, the labels are arbitrary anyway). Hence, our formalism should emphasize this fact by describing things by geometric objects, NOT objects tied to coordinates.

Using a geometry to describe the evolution of structures is not “tying objects to coordinates”. In fact, “describing things as geometric objects” could much more be described as tying those objects to coordinates. Put that brain clamp aside and think about things a bit.

Originally Posted by Erasmus00

The utility of Einstein really only comes with Minkowski's addition to the theory- special relativity describes a very nice metric space i.e. a geometry, and so we can get rid of coordinates entirely and describe things in terms of geometric invariants.

"One geometry can not be more true than another; it can only be more convenient." by Henri Poincareé. Einstein's is more convenient to his perspective, mine is more convenient to an absolutely objective perspective; a perspective which presumes there are no axioms to define the “correct geometry”.

Originally Posted by Erasmus00

On a large scale (mega parsecs), the universe is quite regular, and IS roughly scale invariant, see the sloan digital sky survey. However, as you zoom in, it becomes clumpy and is no longer scale invariant- the universe is only roughly scale invariant. (to be scale invariant, things must be homogenous- compare the contents of the room you are in to the contents of a pocket of space 3 light minutes away). On our telescope scales, its observationally trivial that things aren't scale invariant.

Again, there is utterly no thought in that statement. “Belief is easy, thought is not. That is why so many people would rather believe than think.” Scale invariance on a universal scale has absolutely nothing to do with the smoothness or clumpy nature of the solution. It has to do with the solutions themselves. If you have an equation which defines the possible solutions to “the universe” and that equation is scale invariant, it means that changing the scale of that specific solution yields an equally valid solution. Use your head, if you had a complete description of the universe which satisfied a specific equation (a scale invariant equation) and you doubled every measurement in the entire description, that new description would also be a valid solution to the equation. In no way does such a thing require the solution be smooth in any way. Scale invariance and smoothness are not the same thing.

The problem here is that you are so bound up with compartmentalizing your thinking that you cannot comprehend the possibilities inherent in a total solution. The physics community is so stuck on the idea that a many body equation cannot be solved that they never even consider the possibilities represented by such an equation. Just as Ptolemaic authorities could not comprehend a dynamic solution to the motion of the planets and had to conceptually attach them to celestial spheres, modern physicists cannot comprehend that the universe might satisfy a simple many body equation and have to conceptually tie their solutions to Einsteins space-time geometry. I had proved the validity of my fundamental equation ten years before I found the first solution. During that period, I held no expectations from that equation other than "solving it might be of value". I only saw its significance when I saw the solutions.

However, if you are adamant in your belief that my attack is useless, we can just part ways; I am not going to fight your prejudices. Try taking off that brain clamp and examine my thought experiments. You might learn something.

Have fun -- Dick

[Erasmus00]

Doctordick, you wonder why you have trouble getting your ideas across, but in the last page you have responded to my criticism by telling me to take off my brain clamp, and I still feel you are missing my point. If you wish to communicate ideas to other people, you really need to try to understand what they are saying. I will rephrase my objection to your relativity framework in as clear a way as I can:

You and Einstein BOTH agree that the coordinates should be irrelevant because ultimately they are just labels. Einstein's response was to formulate a language to talk about physics that is coordinate invariant, and doesn't need coordinates at all to describe its fundamental entities.

By reparameterizing Einstein, your new relativity formalism loses this coordinate independence- so in a sense while you are asserting that coordinates are meaningless you are then defining your physics to rely on these meaningless numbers. Further, your Euclidean metric isn't actually a metric. This isn't an Einstein thing, its a MATHEMATICS thing. Metrics are properties of spaces NOT coordinates. You can't turn a Minkowski space into a Euclidean space by reparametrizing, its still a Minkowski space (just like you can't flatten a beach ball by using square coordinates on top of a mercator projections).


Now, as to scale invariance- if your equation is scale invariant your solution ought to also be scale invariant. The solution is the universe. Now, on a large scale the universe is isotropic and homogenous (see the sloan digital sky survey). However, on a small scale, the universe is extremely lumpy, i.e. it is different at a light minute scale then at a megaparsec scale. Also, I cannot think of an interaction that is scale invariant (QCD is strongly coupled at large scales, weakly at small scales. QED is the opposite, etc). What observations do you have to support your scale invariance?
-Will

[Doctordick]

Originally Posted by Erasmus00

Doctordick, you wonder why you have trouble getting your ideas across, but in the last page you have responded to my criticism by telling me to take off my brain clamp, and I still feel you are missing my point. If you wish to communicate ideas to other people, you really need to try to understand what they are saying. I will rephrase my objection to your relativity framework in as clear a way as I can:

I think I have a very clear idea as to why you have objections and that is because you have utterly no comprehension at all of what I am doing.

Originally Posted by Doctordick

Since my earlier explanations of that procedure seems to be rather unclear to most people, I will try to present the central issues here again for you.

The fundamental issue is that no one knows what reality is: i.e., your world view is acquired via an unexplained procedure. (I could waste a lot of time talking about philosophers unsuccessful attempts to attack this problem but I won't.) The philosophic world has made a rather powerful devision of the issues involved here; that division comes down to “ontology” and “epistemology” and I will make rather extensive use of that division (google the terms if you don't know what they mean). Ontology is the issue of “what exists” and epistemology is the issue of the nature of knowledge. In rather broad terms, scientific theories are epistemological constructs and scientists seldom concern themselves with ontology (sometimes they invent “new” entities). Science generally proceeds by what I call the “by guess and by golly” attack. They say, “suppose this existed” (they guess an ontology), “what kind of predictions could you make” (they look at the epistemological constructs they can make under the assumption of that ontology). They get a good answer (the experiments work out) and they say “by golly, that must be the right answer”.

A major problem with that attack is what is called “infinite regression”. There is no way to be sure that the fundamental elements of your ontology are in fact fundamental; there might be a lower level ontology which will yield (as an epistemological construct) the ontology you thought was fundamental. The fundamental problem here is the need to guess the ontology. Since the only defense of that guessed ontology is the success of the epistemology it seemed to me that some analytical analysis would be valuable. (Consider the attack used to solve the problem of black body radiation; take a bunch of unknowns and look for a solution which defines those unknowns and what do you get but the black body spectrum).

Well, let us take an arbitrary undefined fundamental ontology. (Remember, the only defense of that ontology is success of the epistemological construct based on it.) Since the ontology is totally undefined, we certainly cannot describe any element therein (without having that epistemological construct) so I will just use numerical labels to refer to those elements. For the moment, I will simply call those true elements of reality (thus defining reality). I often refer to that entire set of elements as set “A”. Now, there are two important issues embedded in that perspective. First, there is no way for me to be sure that I am even aware of all the elements of set “A” and, second, my epistemological construct may very well include hypothetical elements not in A (think philogestin). With regard to the first, my analysis must include the possibility of changes of that which I am aware. To accommodate this possibility, I will introduce set “B” which constitutes elements of “A” I become newly aware of. Since I can not be aware of an infinite number of references, changes in the set I am aware of must be finite, they can be ordered. I will use the index “t” to indicate which change I am talking about.

The entire set of ontological elements that I am aware of (and from which I build my epistemological construct) must consist of a collection of sets B_t. I will refer to the true elements in that collection as set “C” but I must admit of another component, the set of elements I think are true which are required by that epistemological construct. This second set I will refer to as set “D”. There is an interesting dichotomy here. These two sets obey different rules; the first is real and cannot change but the second is merely necessary to support the presumed epistemological construct; on the other hand, there cannot be any way (under that epistemological construct) to tell the difference between the two sets. This turns out to have some very profound consequences.

Now you need to remember, these are no more than massive sets of numbers divided into subsets indexed by t; mere references to the ontological elements which stand behind that epistemological construct. Meanwhile, exactly what purpose does that epistemological construct serve? I say that it serves the purpose of yielding to you a set of expectations which are consistent with your experiences (those true ontological elements referred to as “C”). What is important is that the set of expectations can be represented by “the probability of experiencing some supposed new set B_t”: i.e., another set of those self same references to elements of what you believe to be reality. That is, a number who's value is dependent upon another set of numbers. That is the definition of a mathematical function and that mathematical function is defined by the specific epistemological construct.

The central issue of my original proof (that any flaw-free epistemological construct must obey my fundamental equation) resides on the fact that the assignment of those numeric references has utterly no impact upon the situation at all. That is to say, if in my first description of that epistemological construct uses a specific number to represent one of those ontological elements in all sets B_t making up the sets “D” and “C” and in the functional representation of your expectations, then, using a different number in all cases cannot yield a different result. That lone fact results in some very profound consequences.

I will explain (and have explained) that proof in detail but, unless one understands the basis of that proof, explaining the proof is a total waste of time. If what I have just said makes any sense to you, I will cover the details of the proof again; however, this thread is concerned with other issues.

My proof shows that there is always an interpretation of any explanation which must satisfy my fundamental equation (which is directly cast into a Euclidean geometry).

You keep wanting to cast it in Einstein's perspective and it is just simply a very different perspective. The only purpose of that parameterization was to point out that exactly the same entities used in the Einsteinian perspective can be directly translated into my perspective.

Originally Posted by Erasmus00

You and Einstein BOTH agree that the coordinates should be irrelevant because ultimately they are just labels. Einstein's response was to formulate a language to talk about physics that is coordinate invariant, and doesn't need coordinates at all to describe its fundamental entities.

I am not even describing fundamental entities; I am intentionally leaving the issue entirely and absolutely open. My fundamental equation is valid no matter what those “fundamental entities” might be. I use geometry for one purpose and one purpose only: I use it as a mechanism to display humongous volumes of information parameterized via numerical references to ontological elements and nothing else. These “ontological elements” are totally undefined things: i.e., unknowns. I display these numerical references as points in a Euclidean geometry and I use the definition of a “Euclidean metric” as given in “Wolfram MathWorld”

Originally Posted by Erasmus00

By reparameterizing Einstein, your new relativity formalism loses this coordinate independence- so in a sense while you are asserting that coordinates are meaningless you are then defining your physics to rely on these meaningless numbers.

This is exactly what I mean by that “Einsteinian brain clamp” (you tell me what I am defining without ever even looking at my definitions). And that reference to “doing good old fashion physics”, what I mean is, take down your data, plot it and look at the implied relationships. For example, take a look at the thought problem I gave you (it is entirely non-relativistic and requires no knowledge of relativity). Work out how that would appear and then we can talk. If that is beyond your analytical abilities, I am totally wasting my time.

Originally Posted by Doctordick

I have a thought experiment you really need to perform. Suppose, for the fun of it, that I am an individual from a technologically advanced society and I meet with you to show you a couple of devices we have invented. I can't show you why it works the way it does because I, personally, don't know the science behind it; but I do know exactly what it does. The first device looks exactly like what you would see as an old fashion analog pocket watch. It has a dial with three hands which show hours, minutes and seconds, and has a knurled stem at the top which would appear to be for setting and/or winding the watch.

But I tell you it is not a watch; it is a one way time machine. When the stem is turned it will move the holder (and the holder only) into the future. When the stem is not turned, the reading on the time machine will read exactly the correct time (we won't worry about relativistic effects here, just assume that, for practical purposes, we live in a Newtonian universe). When the stem is turned, the reading on the face can be advanced. When the reading is advanced, the holder will be moved to exactly the time indicated on the face. The reverse is not possible. It is my understanding that one can not move to the past because doing so would cause paradoxes, but moving to the future will cause no such problems.

The question is, if I operate my time machine, what do you see? If you think about it a little, you should realize that, as I turn the stem, I move to whatever time is indicated on the face: i.e., I don't disappear and then reappear at the new time, I instead move through each and every time indicated on the dial. If you look at the face of the device while I am turning the stem, you will simply see the correct time as, whatever time you are at, I am there too (the second hand will appear to advance just as it did when I wasn't touching the stem). You will see me standing very still with my hand on the stem. If I advance the dial one hour while I take one breath (during the breath I turn the minute hand entirely around the face), you will see that breath as taking the entire hour. If my pulse were sixty beats a minute, you could perhaps detect my heart as beating once or twice during that hour (depending of course on how fast I personally am turning the stem). We won't worry about other effects; you could push me but I don't think either of us would like the results.

My second device is a toy we make for our children. It appears to be a standard baseball but it is not. It contains exactly the same time machine which I just demonstrated for you; however, it has no stem. Within the ball is a second device which, via internal dynamic effects enables it to know exactly where it is (remember, for practical effects of this thought experiment, we live in a Newtonian universe). When it is moved, the time machine (it and the ball within which it is contained) is advanced in time proportional to the distance it is moved. It is advanced exactly one second for every foot it is moved. Such a ball will display some rather interesting dynamic effects. (For the sake of simplicity, we won't consider rotation; the system is not designed to be rotated as rotation brings up some very complex effects.)

Consider two children ten feet apart playing catch with such a ball. From the children's perspective, how long does the ball take to cross the room? Suppose you replace the children with professional baseball pitchers? Then try firing it out of a canon. If you cannot figure out the logical consequences let me know and I will explain (and justify) the results. Another thing you might look at is tying a string to the ball and swinging it is a circle. I think you will find the consequences are quite interesting.

If you refuse to look at that problem, I will henceforth ignore your posts on the assumption that you are scientifically incompetent.

Originally Posted by Erasmus00

You can't turn a Minkowski space into a Euclidean space by reparametrizing, its still a Minkowski space (just like you can't flatten a beach ball by using square coordinates on top of a mercator projections).

But I can plot the information in a Euclidean geometry if I wish! What the devil do you think a Mercator projection is. The fact that the measurements on the Mercator projection (a Euclidean geometry) must be scaled to obtain the measurements in reality has nothing to do with the metric of that Euclidean geometry and everything to do with measurements taken from your data. Any competent physicist would recognize that fact. And their “theory” would “explain” those scaling factors: i.e., in this case the two dimensional information being represented is actually a sphere in a three dimensional Euclidean geometry and not that spherical geometry is the only geometry applicable to the situation. Likewise, Einstein's space time is a rather limited interpretation of the circumstance. A valid quantized interpretation of a four dimensional Euclidean universe (my fundamental equation) yields exactly the same results and that is the central issue here.

Originally Posted by Erasmus00

Now, as to scale invariance- if your equation is scale invariant your solution ought to also be scale invariant.

What you are totally avoiding is the issue of solving a many body equation. Your entire mental image is from the perspective of a one body problem (or at best, a two body problem). My equation is an n body equation and the solutions can be quite complex. You keep looking at those one body solutions. If you look at it from the perspective of a many body problem, the boundary conditions on that one body solution are fixed by the solution for the rest of the universe. If that solution has lumps in it, the local solutions can be quite different.

Just for the sake of argument, look at a coherent solution of an infinite surface which can support wave motion. The equation can be perfectly scale invariant and yet a possible solution could be as lumpy as you desire (think of the initial water level in an infinite pool). And the a specific micro solution in a disturbed area could be quite different from a similar micro solution in a similar disturbed area with a significantly different size. You need to learn how to do physics.

Have fun -- Dick

[Erasmus00]

Doctordick, I don't enjoy being insulted, and if your method of addressing complaints is to insult the asker, then I can see why you have trouble getting people to look at your work. I am done with this conversation, but leave you with this question: you claim the universe is scale invariant, but what empirical evidence do you have? No fundamental force we've measured is scale invariant. Every wave we've seen has dispersion, etc.
-Will

[Bombadil]

Originally Posted by Doctordick

I don't exactly know what you mean by that. It is a measure of the path length of an entity in our personal rest frame of reference, the frame in which we are describing the circumstances.

The way I understand it is that the right side of the equation is the distance in your x,y,z,tau coordinate system but this coordinate system is inside of a x,y,z,tau,t system. Now, the movement on any of the x,y,z,tau axis’s can be changed by moving along a different axis as long as the total distance traveled remains the distance changed on your t axis but is there any way to change the distance moved along the t axis or for that matter, does it even make sense to talk about the t axis for anything but a way of keeping tract of the elements in the equation?

Originally Posted by Doctordick

It is a common transformation used in quantum mechanics to change the wave function to a new function having momentum with respect to the first: i.e., the momentum operator is a differential operator and the differential of a product, , adds a term related to the function . Since the definition of the momentum operator is , setting will add the factor K to the result of application of the momentum operator. If we have n arguments we can do this n times (once for every argument and add nK to the total momentum. At that point, one is no longer in the frame of reference where vanishes.

Am I correct in saying that the only effect that adding momentum to the fundamental equation has on the derivation of the schrodinger equation is adding a waited alpha term to the function after the first integration? In fact the only effect that adding momentum appears to have on the fundamental equation seems to be adding a waited alpha term to the equation. But how I understand the alpha term, it is in a totally different vector space then the rest of the terms in the equation. So adding this should have no effect on the propagation speed of the wave which I understand to be 1/k. Although it seems that this may not be the case and that the added momentum has an effect on the value of the right side of the equation. If so, is the task to find a scaling factor that leaves the value of the constants on the right side of the fundamental equation the same no matter the momentum added?

Now, will mass and energy eventually be added to the equation in the same way only with the mass or energy operators in place of the momentum operator?

Originally Posted by Doctordick

No you would not. My equation is deduced from my definition of “an explanation” via ordinary symmetry arguments.

Since my earlier explanations of that procedure seems to be rather unclear to most people, I will try to present the central issues here again for you.

I suspect that I was not entirely clear as to the equation that I was referring to as the remainder of the post while quite interesting seems to be the basic idea for the derivation of the fundamental equation while what I was referring to was the equation

Originally Posted by Doctordick

I will explain (and have explained) that proof in detail but, unless one understands the basis of that proof, explaining the proof is a total waste of time. If what I have just said makes any sense to you, I will cover the details of the proof again; however, this thread is concerned with other issues.

What you are saying does make sense to me, previously I have managed to find some of your derivation of that equation from links that you have put in different threads although I don’t know how much of it so I would be interested in seeing the proof. But as you say this is clearly not the place to go into the issues involved so I won’t go into commenting on the remainder of your post here.

[Doctordick]

Originally Posted by Bombadil

The way I understand it is that the right side of the equation is the distance in your x,y,z,tau coordinate system but this coordinate system is inside of a x,y,z,tau,t system.

Think about that a bit. Exactly what do you mean by the phrase, “inside of a x,y,z,tau,t system.” I am not using t as a dimensional axis here. I am merely using t as an evolution parameter. How do you propose to plot the changes in a physical configuration of interest by using t as an axis and at the same time attempt to include all four physical axes (x,y,z and tau). We can only actually plot two dimensions against one another on a sheet of paper. It may be true that we can create a picture which the brain will interpret as a three dimensional image; however, even that only allows us to plot two physical dimensions against that evolution parameter. Furthermore, those three dimensional images can sometimes be difficult to interpret as illusions can sometimes arise in such a picture.

Originally Posted by Bombadil

... for that matter, does it even make sense to talk about the t axis for anything but a way of keeping tract of the elements in the equation?

For the moment, forget that equation. The issue here is keeping tract of the position of entities in the x,y,z,tau coordinate system. Those entities follow paths in that geometry and the value of t tells you where on that path the entity is at time t. I am using t as an evolution parameter in exactly the same way Newton used time.

That is one of my major complaints about Einstein's picture. He also sees objects as following paths through his four dimensional “space-time” geometry and uses the concept of time to talk about evolution of structures along those paths. In essence he simultaneously uses time as a coordinate of his geometry and as a concept of position along those paths (essentially he is confusing two very different issues).

Originally Posted by Bombadil

Am I correct in saying that the only effect that adding momentum to the fundamental equation has on the derivation of the schrodinger equation is adding a waited alpha term to the function after the first integration?

Perhaps I should not have put that issue forward in this thread as I am afraid it is confusing you (that is why I changed the title of the post to “Answers to Bombadil's questions!”. The central issue here is that my equation “is just not valid” if the total sum of all momentum of all entities being described by that equation does not vanish. However, in spite of that fact, if I do have a specific solution to that equation, quantum mechanics does provide me with a mathematical mechanism for transforming that solution to a solution where that sum is not zero (this is a subtly a very different issue). Please note my definition of momentum; there is no alpha term in the definition. A secondary issue here is that, in deriving Schroedinger's equation, I am clearly stating that Schroedinger's equation is an approximation to my fundamental equation and is thus only valid when those approximations are valid. It is a well known fact that Schroedinger's equation is not in conformance with special relativity so, technically speaking, any shift in reference frame can be seen as invalidating Schroedinger's equation: i.e., the mathematical mechanism discussed above does not technically give the correct answer; it only yields an approximately correct answer.

Originally Posted by Bombadil

If so, is the task to find a scaling factor that leaves the value of the constants on the right side of the fundamental equation the same no matter the momentum added?

The scaling factor occurs directly as a consequence of the fact that the “form of the equation” must be exactly the same in all three relevant frames even when each is moving with respect to the other. The Dirac delta functions are of no consequence in that analysis as they are not influenced at all by a scale change. Omitting them, the remainder of the equation has the time evolution of an expanding sphere. Actual events described by that equation must conform to that self same expanding sphere. The only way that can be true is if observers who go to use that equation in those different frames use a different coordinate system. The solution to that problem is exactly the same solution required to make Maxwell's equation valid in everyone's frame (they must all see a flash bulb as producing an expanding sphere). This problem was solved years before Einstein published his theory and is exactly the changes which his theory was concocted to explain. The scaling solution is simple high school algebra and I will show it to you if you wish. The problem is exactly the same in four dimensions as it was in three dimensions.

Originally Posted by Bombadil

Now, will mass and energy eventually be added to the equation in the same way only with the mass or energy operators in place of the momentum operator?

I don't understand your question at all. I have already defined the mass and energy operators in terms of the fundamental equation itself. They are not added to the equation, they are already there; I have done no more than define what aspects of the equation I am referring to when “I” use the terms “momentum”, “mass” and “energy”.

Originally Posted by Bombadil

... what I was referring to was the equation

That falls directly out of my fundamental equation and is essentially a differential description of that expanding sphere I just mentioned above.

Originally Posted by Bombadil

I would be interested in seeing the proof. But as you say this is clearly not the place to go into the issues involved so I won’t go into commenting on the remainder of your post here.

The central idea of the proof can be found in my paper, “A Universal Analytical Model of Explanation Itself” which I posted in 2006; however, a number of things I said in that paper seem to have confused people and I have made some real changes in the way I express those issues since then (including a subtle, but very important change in my definition of B_t). I think I now know a little more about how I should have put the thing but, as far as I know, I no longer have FTP access to those web pages (actually I am quite surprised to find that they still exist on the web as it seems to me they could disappear at any moment). If you want to catch up on the current situation, you might read some of the posts on the thread “What can we know of reality?”

Originally Posted by Doctordick

This is a thread started to discuss a serious problem deeply embedded in the whole fabric of philosophical thought.

Don't waste a lot of time there unless it really interests you. But, if you do get into reading that thread, I would suggest you read the opening post, referred to above, and then start with post #33 which gives essentially my background discussion with Anssi over on “physicsforums”. From that point forward I think you would hit the most important issues if you looked at the posts by “Qfwfq”, “Buffy” and “Anssi” plus my direct answers to them. That should pretty well cover most of the things people seem to misunderstand. If you have any questions, post to that thread, with a quote of the particular post you are referring to, and I will do my best to make the issues clear (there are a lot of things I could put quite differently). That is one of the reasons I think I am right; there are six ways from Sunday to attack all these things.

Meanwhile, not to put too much on your plate, you might check out the post I am composing for this thread. I have decided to expound on that thought experiment which I was trying to get Erasmas00 interested in working out. He either had no interest in the problem or found it beyond his abilities. Either way, I will present a solution for everyone's examination.

Have fun -- Dick

[Doctordick]

Sorry Will, I had no intention of insulting you; I was just trying to get you to examine the thought experiment I had set up. Since you have chosen not to pursue that issue, I will present an analysis that I think most of the people here have the insight to understand. I am of course talking about the two children ten feet apart playing catch with that magic time shifting ball.

The question was, if the ball contained a time travel device which moved it into the future one second for every foot it moved in the rest frame of the observer, how would it appear to behave. I will draw upon the old fashion Newtonian x,t diagram of the actual motion of the ball (the path it would follow if the time machine did not exist) at a velocity of 10'/sec, 50'/sec and 1000'/sec. Ten feet per second is reasonable for two children playing catch, fifty feet per second is a little slow for a baseball pitcher but was easier to draw and one thousand feet per second is pretty reasonable for a cannon shot. These are the blue, green and black lines seen at the bottom of the chart.
(Apparently you have to click on the chart to see it, and magnify it at least once to see the detail.)

Now, because of the time machine in the ball which will move it into the future, these will not be the observed paths. The time machine is set to advance the ball into the future at a rate of one second for each foot it travels in the rest frame of the observer. All one need do is add one second to the time specified to the balls position for each foot it has moved since it started on its path. Since the distance between the two points of interest is ten feet, the ball will have advanced an extra ten seconds into the future during the travel over the specified ten foot path. The lines for these apparent paths are also shown in the figure. The blue path is transformed into the aqua path where the ball appears to cover the ten feet in eleven seconds, yielding an apparent velocity of about .9 feet per second. The green path is transformed into the mint green path where the ball appears to cover the ten feet in ten point two seconds, an apparent velocity of about .98 feet per second. And, finally, the black path of the cannon shot is transformed into the gray path where the ball appears to cover the same ten feet in 10.01 seconds, which corresponds to an apparent velocity of about .999 feet per second.

It should be quite obvious to the reader that this ball appears to live in a universe where the maximum allowed velocity is ten feet per second. Let us consider the dynamics of this circumstance. If you think about the kinetic energy the children, the pitcher and the canon have applied to the ball, you should also comprehend that, to the observers playing with the ball, its apparent mass is rising precipitously (though its apparent velocity has changed by very little, the momentum to be transfered goes out of sight quickly). In fact the behavior of the ball is quite analogous to common relativistic behavior in almost every way. I find it to be a very interesting phenomena though no physicist I have ever talked to has shown even even the slightest interest. Forty five years ago, when I first raised this issue with a professor when I was a graduate student, I was told, “well of course you are right, but don't show it to any of the other students because it will just confuse them.” Being an idiot at the time, I did indeed keep it to myself.

One question which comes up with the above analysis is, “if we advance into the future because we a moving in that rest frame, why do we move into the future when we aren't moving in that rest frame?” Well, suppose we are moving in a fourth dimension, which we are unaware of, at some fixed velocity. In fact, suppose we are moving at a fixed rate through that four dimensional universe and that, when we are moving in the rest frame, that motion is only a component of our actual motion: i.e., the path length which yields that advance in time is the actual four dimensional path in that four dimensional Euclidean universe. It turns out that the correction required by that simple hypothesis yields consequences exactly (and I mean exactly) the same as those required by “special relativity”.

Now this is a rather funny circumstance. Einstein has set up a four dimensional representation of reality where entities (and that includes us observers) move along paths in that space. A space which is rather strange in that its four components do not have the same qualities. One has this quality that it is “imaginary”. He has to do this in order to make the measurements we perform come out consistent with the experimental results. (It's a tough world and sometimes one must go to extremes to get results which agree with experiment.) You should note that any rational analysis of the circumstance still requires a parameter to specify exactly where we are on that path (something the physicists don't like to talk about). Here I have added a simple dimension orthogonal to x, y and z but otherwise identical in nature and found that the consequences are exactly the same as Einstein's rather more complex scheme. I used to think simplicity was of value in physics.

We do, none the less, have a difficulty with this picture. Why can't we detect this fourth dimension? Here quantum mechanics comes to the rescue. Every experiment performed by every scientist who has ever lived has been done with equipment constructed with mass quantized entities. Not only that, they all work in laboratories constructed entirely from mass quantized entities. Suppose the kinetic energy of an entity due to the motion in this fourth dimension is what we call “mass”? If that is the case then the fact that all our equipment is built from entities with quantized mass (including the laboratories themselves), then momentum in the tau direction is almost universally quantized. The dimension canonical to that momentum would be the dimension within which that momentum is defined and, by virtue of the uncertainty principal, that dimension would become absolutely undetectable. Gee guys, that seems to me to be a rather obvious solution to the difficulty inherent in this picture.

Doesn't the way this all fits together bother you at all? I am afraid that professor I spoke to forty years ago was right; “it will only confuse them!” Doubt in one's beliefs often leads to confusion.

There is another rather important issue embedded in this perspective. The perspective (except for the addition of this fourth axis) is totally in accordance with the old Newtonian view of reality. This is very interesting because of another problem which arose after Newton proposed his theory of dynamics. In Newton's picture, one was dealing with what he defined as inertial frames (essentially defined by the fact that F=ma was to be valid; if that equation is not valid, you're not in an inertial frame). Of particular interest is what in the good old days used to be called pseudo forces. These are forces which actually don't exist but are in fact mere consequences of the fact that you are not in an inertial frame: for example, the force which tips over your coffee sitting on the dash when you turn your car through a sharp turn. There is no real force there, it is no more than the fact that your coffee would continue in a straight line if the friction with the dash wasn't there.

There are all kinds of pseudo forces which can be generated by the simple fact of working with “the wrong frame of reference”. The one fact which is almost a universal indicator that one is dealing with a pseudo force is the fact that, in all pseudo forces, the acceleration is exactly the same for all masses: i.e., the apparent force is always exactly proportional to the mass of the object. That occurs for the very simple fact that no acceleration is actually taking place; all apparent acceleration is due entirely to the acceleration of the frame of reference. Two of the most common pseudo forces well known to any physicist are centrifugal and Coriolis forces, both of which are entirely due to doing one's doing their calculations in a rotating coordinate system.

Now gravity has exactly the same quality that the apparent force (the force causing the acceleration) is always exactly proportional to mass. This thought leads any thinking scientist to the idea that gravity is a pseudo force; that gravity exists for the simple fact that the geometry used to calculate the paths of entities under the influence of gravity simply is not the proper inertial frame. Much work involving subtle changes in the geometric representation of physics problems was applied in an attempt to find a geometric transformation which would yield gravity as a pseudo force. The search was an utter failure and, in the mid 1700's, a French mathematician, Pierre-Louis Moreau de Maupertuis, proved that no such transformation existed. Physicists gave up on the prospect of finding that geometry but their work did not go unappreciated; many very important relationships had been discovered when that range of possible transformations were studied.

The search had led down paths which have become central to most all of modern physics. Out of this work we get many of the mathematical relationships accepted as fundamental to modern classical mechanics (Lagrangians, Jacobians, Hamiltonian mechanics just to name a few). In addition this work led directly to the early formulation of quantum mechanics so it was certainly not a waste of time. You may ask, why does Dick bring up this esoteric garbage? Well the answer is actually quite simple, if you examine Maupertuis' proof, you will discover that one of the central issues was the fact that objects with different velocities followed different paths. Now, if you look at what I have just presented, you will discover that, since I have identified mass with momentum in that unobservable tau direction, mass is no longer a quality of our entity but rather a statement of its dynamics (as determined by its total energy and its kinetic energy (). Everything in my picture travels at exactly the same velocity of 1/K (the free variable describing the dynamic evolution the scale, a scale which is established entirely by the analyst performing the analysis). Gee whiz; there are no “different velocities” and Maupertuis' proof entirely fails.

Add to this a rather common position held by the physics community when I was a graduate student (a position which, I believe, is taken as fact today), and a somewhat important issue is raised. According to established authority (see Adler, Bazin and Schiffer, "Introduction to General Relativity", McGraw-Hill Co., New York, 1965, p. 7), "Einstein proved that "a reduction of gravitational theory to geodesic motion in an appropriate geometry could be carried out only in the four-dimensional space-time continuum of [Einstein's] relativity theory". If that statement is true then Einstein certainly has strong support that his picture is worth the effort; but, the real question is: is it true? I think I have certainly reopened the question and the issue should certainly be reexamined; especially in view of the problems Einstein's GR has with quantum mechanics.

I have no such problems and, in spite of Erasmas00's conclusion that my picture (though correct) is useless, I would suggest that it is a very valuable attack and well worth the effort to understand. General relativity is a rather straight forward issue in my picture and I will present it to anyone who has the fortitude to follow my exposition. The approach is not at all per the current Einsteinian catechism but is rather quite solidly based on the classical physics approach to the analysis of phenomena.

Thanks to you all -- Dick

[AnssiH]

From what I can tell, that seems like a very reasonable/useful way to plot information. Especially since it ties "relativistic time evolution" and quantum mechanics under single paradigm rather nicely. I do not understand why people are so hesitant to look at it. Could it be they are little bit emotionally attached to some personal ontological view, which they see as contradictory to this treatment? (which it may or may not be)

I don't claim to understand it completely but at least I'm working on it. It is little bit frustrating that my math skills are not up to par to work on it faster (especially with having limited time to spend on the issue). It'd be nice to see other people, more competent in math, seriously taking a look at it. It's nice to see Bombadil doing it, and I'm sorry to see Erasmus getting frustrated and leaving.

Erasmus, if you are still reading this, you need to excuse DD little bit; he's frustrated by always receiving objections that are based on some feature found from some specific worldview/model. If you can appreciate the fact that any information can be mapped/modeled in many different ways, you can probably also understand that a feature that is implied by one of all those possible mapping methods, cannot really be considered "the way reality is".

About the scale invariance that was causing some confusion. It refers to scale invariance that exists to your model of reality as a whole. In a sense, you could say that if the whole reality - absolutely everything in it - was to scale up ten times suddenly, it would be undetectable. I.e. while your model of reality does assign numerical values to describe the relationships between things, scaling absolutely everything changes absolutely nothing.

So, in an ontological sense we don't know what is the "size of reality" (it is not even sensical notion), which is the specific ignorance that makes any worldview scale symmetrical (as long as it does not contain an undefendable assumption about some specific scale being ontologically true).

Do you guys understand how this all has to do with completely general properties that arise from those forced symmetries (of which "scale" is just one) to our models of reality? I.e. properties that are not really true "because reality is like that" but rather because "we are mapping information in such and such ways"?

-Anssi