What\'s Ultimately Possible in Physics by Paul N Butler

Paul,

> What would you say is the greatest area where we have different views and what are yours in that area.

I cannot think now at important differences, probably because I feel great about the differences between various views. But if I would want to make a suggestion, this would be that fundamental physics can be understood better by understanding the underlying mathematics. Before this step is taken, we may think that mathematics is just the quantitative expression of physics; only after this step is taken can become clear how apparently unrelated pieces of the puzzle fit in harmony.

Cristi

Cristinel,

I have seen this concept that reality is founded upon mathematics as though there are underlying math formulas that somehow generate the reality that we observe. If we look at physics as the study of the structure of observed reality with the intent to understand its basic underlying structure and rules of behavior, we find that the most fundamental basic structure that exists in observed reality is motion. A single one-dimensional motion is a simple structure that contains only a small amount of information. It mainly possesses three pieces of information, which are position, direction, and motion amplitude level. Each of these pieces of information could be looked at as a quantity. You could number each position within the dimension so that each position would be assigned its own specific number that was different from the numbers assigned to all other positions within the dimension. You could also assign a number to the motion's direction so that one direction would be labeled direction 1 and the other direction would be called direction 2. You could also think of a specific motion amplitude as a quantity of motion with a specific value. When you actually look at a motion, you do not actually see these quantities, however. What you actually see is the motion existing at a position in space that changes in a specific direction at a rate that depends on its motion amplitude. The motion is not generated by the numbers or numeric quantities. Instead, the numbers are generated by man to allow him to quantify and study the motion's observed effects. The numbers allow man to follow the motion's information variabilities that exist as parts of the makeup of the motion. The motion is the fundamental entity. The motion's motion amplitude is a direct attribute of the motion alone. The motion's position and direction are attributes that come from the interaction of the motion with the information structures of the dimensional system that the motion exists in. All of these attributes are stored within the motion as parts of its makeup. The numbers are a step of abstraction away from the actual motion's existence. As an example, the motion amplitude is a continuously variable structure. In order for man to generate the numbers he must first divide that structure into a scale with numbers applied to various scale points in that continuous variability. This involves the creation of a unit that equals a certain specified amount or level of motion amplitude. Twice that level would then equal 2 units of motion amplitude, etc. It is still possible to see the continuous nature of the structure by using partial units, such as 9.898 units of motion amplitude, but man likes to make things simple, so actual tests and examples would more likely use whole units as much as possible, which can distract one from the continuously variable nature of the structure and make one begin to think of it more as a structure divided into discrete steps of motion amplitude. The scale and numbers are not actual attributes of the structure, but are artificial attributes imposed on the structure by man to allow him to more easily follow the effects of its variations to aid in the study of the structure. Mathematics is just a part of man's language structure and as such it contains the same types of advantages and disadvantages as any other part of man's language, but man's language that describes observed reality is not the same as the language that actually composes reality. It is at best just an image of it.

That being said, it is true that observed reality is built up from basic structural rules and understanding those rules and being able to express them in some language form can be of great help in increasing ones knowledge and understanding of observed reality. It is also true that those rules that contain quantitive relationships or aspects can often be expressed more simply in mathematical forms. Even in those cases, however, one could instead express the rules in English or other languages without the use of math. It would just possibly be more cumbersome to do so. You are right that if you express in math form those things that can be more simply expressed in mathematics, it can make it easier to see relationships between quantities than it might be if it is expressed in another form. As an example, D=RT where D=distance, R=rate, and T=time does show relationships between distance and time that can give one a good understanding of part of the nature of time. Of course, one must first understand that it is easier to replace the rate with the motion amplitude, which is basically the same thing in a different form (it is easier to see and understand this in a visual form rather than through math) to get D=MT (where M=motion amplitude) or T=D/M. This is the formula that describes how periods are generated and the period concept is considered part of the definition of time. Basically the length of a period increases with increases in distance traveled and decreases with increases in motion amplitude. A specific period is the result of or generated by a motion with a specific motion amplitude traveling through a specific distance (of course, there are many combinations of distance traveled and motion amplitude that generate the same period). This aspect of time is therefore derived from and its existence is dependant on motions traveling through distances. If all motion in the universe went away, there would be no periods of time in the universe. In addition to that, there would be no sub-energy, energy, or matter either in the universe since they are composed of motions. Conversely, this means that as long as motion exists in the world, periods of time will also exist. Periods of time are used to compare motions that have different motion amplitudes to each other. We would not really need the concept of time periods if motion only came in one amplitude level because that level could be considered the unit of motion amplitude, so that T=D/M would equal T=D/1 or T=D. This means that time and distance would be the same equivalent concept. Then if someone asked you when you would arrive, it would make perfect sense to say, "I will be there in 10 miles", which would be easily understandable by anyone who had previously traveled 10 miles.

Food For thought

These things apply to observed reality, but may not completely apply to the level of structure behind observed reality that generates it. At this time man is not yet ready to accept that level though. It is well beyond man's present maximum acceptance threshold. To get the image, think: the characters on the television screen are not ready to think about the internal workings of the television set that generates them. I won't go into that any more now. You have to wait until the time (the end of that particular period of motion through distance) for the release of basic dimensional structuring concepts to get that introduction. Don't expect that very soon though.

Sometimes observing things in detail in reality, comparing the observations of two or more things in reality, or using the visualization of things that are similar to what you are trying to understand in your mind (good when you can't actually observe the object of study) can also allow you to see how apparently unrelated pieces of the puzzle fit in harmony. Some things yield their secrets more easily in one way and others do so in another way. The real key is to be able to discern which method is most appropriate for your current investigation and to have the skills to use that (and all other) method(s) effectively. That is what structural pattern analysis is all about. Too bad that concept has not yet been understood to be important in this world (although there have been some who have figured some aspects of it out for their own use and have contributed much to man's understanding).

I will not be available to answer comments until about the last week of January 2010. Feel free to make them to me though and if I can stay in this world, I will answer them when I return to this place. If you get one in by Sunday, I may be able to answer it before I go, but no guarantee.

Peace be unto you.

Paul,

You seem to identify mathematics with numbers, which is a very limited concept of mathematics. In fact, I even warned against this mistake in my small comment. What I said is just that you can understand better some phenomena in physics by understanding some chapters of mathematics. I did not say that everything in the world should be understood by mathematics, and certainly not just by numbers.

Your intuition about the limitations of using numbers to represent coordinates is good. It is no wonder that mathematicians know it, and insist on it. If you read about differential manifolds, you can see that the coordinates are not the fundamental objects, and the true objects used by mathematicians are coordinate-free. And motion is a relation between the position (more generally in phase space or in configuration space) and time. It is mathematics.

Food For thought

To know how a foreign country really is, you have to visit it, and to spend some time there. Then, you are in a good position to discuss with a native about his country. A vacation is a good opportunity to explore new places.

Enjoy your trip.

Cristi

Cristinel,

Yes, a large part of what currently would come under the definition of mathematics has to do with the interrelationships or interactions of quantities of or numbers of things with one another. I do realize that there are branches of mathematics that can deal with things on a non-quantitative basis such as much of set theory and path flow structuring, etc. (I like to connect most of those areas more under the heading of logic than math, but that is just my personal method). I also realize that there are areas of math that deal more in the area of spatial structuring such as much of geometry, etc. Even these areas often include quantitative elements in their structure and definitions of things. For example, in Euclidian Geometry part of the definition of a triangle might be that it contains 3 straight lines that intersect to form an enclosed structure with 3 sides and 3 internal angles and that the 3 internal angles thus created total 180 degrees of rotation (one half of a rotation) on a scale where 360 degrees equals one complete rotation around a central point. Notice that there are numbers of lines and angles, and a quantity of amount of rotation involved. We both agree that some things can be easier to understand from a mathematical point of view and that there are also some things that can be understood more easily by other means.

So you won't have to believe that I am attacking your positions on things or trying to undermine you in some way let me explain some of my information gathering techniques and my reasons for using them. First my main reason for communicating with you (or even man in general) is to see if you are or can become compatible to work with, share, and hopefully enjoy together a common fellowship based on development of common understandings without mutually exclusive concepts hindering our progress. For that to happen we both need to get to understand each other's beliefs and understandings about the world and work through any disagreements or at least recognize and find ways around them. When we make statements, they are often based on much study of information, but we tend to give very minimal summaries rather than the whole understanding and often over generalize, so it is not possible to get the complete understanding of the concept that is being covered. In your statement "fundamental physics can be understood better by understanding the underlying mathematics" you do not limit the concept to just some of fundamental physics, so the natural assumption is that it applies to all fundamental physics. The concept presented is that there exists mathematics that underlies or is the basis for or possibly produces fundamental physics. The term fundamental physics would most likely refer to basic concepts in physics and I assumed that you meant that. It also could refer to concepts of any level of complexity about fundamental levels of the worlds structure studied as a part of physics, such as particle physics or the study of electromagnetic energy photons, etc. Since you did not go into the extent or depth of your meaning of the underlying mathematics of fundamental physics, I had two easy methods to get that information from you. First I could just ask you what you meant in that respect. This method can work, but tends to be slow because it can take many communication turnarounds to get much information. Secondly I could look at the whole range of belief that I have found so far in man in that concept and give one extreme or the other and then explain where my belief is in respect to it, so I pass on to you my belief and allow you to respond with a more detailed response of where you are at on the topic and whether you are in agreement with me on it or to give your reasons if you disagree in some point(s). This allows simultaneous communication to you while at the same time you would tend to think that I believed that you had the extreme position that I mentioned and give me your belief in a more detailed way (unless you actually held the extreme position). If you haven't yet seen anyone with that extreme position, it also passes the information on to you that some do believe that way. Of course, I can't work that way with everyone because some who are weak either from much rejection or just from timid personalities might be either offended or discouraged easily by it and that is not my goal, but you have shown the ability to respond effectively to it. It allows me to mention many of the concepts that I would like to know your viewpoint on in more detail and at the same time show you my understandings about them for your observation and comment. In your response you changed from "fundamental physics" to "some phenomena in physics" and from "understanding the underlying mathematics" to understanding some chapters of mathematics (which I presume to mean understanding some specific applicable types of mathematic processes or maybe also the possession of knowledge at some certain necessary levels of complexity of those processes to use them successfully to aid in the understanding of the phenomena). We agree on these things. My point about the quantitative relationships or aspects is that phenomena that involve numbers or quantities of things are more likely to be the ones that are better understood by use of mathematics. This is not to imply that there are not any that do not have anything to do with numbers or quantities that could be easier to understand by the use of some mathematical processes that do not involve numbers or quantities.

I am glad to see that you understand the problems of manmade coordinate systems. Reality is not coordinate-free, however. The fact that things exist in specific local positions in respect to each other creates natural local coordinates. Because man cannot get out of the world and look at the whole world at once from that global perspective he does not know if global coordinates exists. It is only known that no indications of such global coordinates have been observed from man's limited local perspective, but that is not very surprising. You will have to give me more information about your belief that motion is generated by position and time. Generally those who believe that time is a physical dimension tend to believe that in some way our three dimensional world and/or the objects in it travel through the time dimension (or at least that they have a motion in it) and time is in one way or another the observed result of that travel. Of course, that travel would be motion, so it seems like motion would have to generate time even in that type of system rather than the other way around, but there are a multitude of different beliefs and explanations that I have seen, so in this case I will just ask you to elaborate on how you understand it to work. Of course, position can be said to be connected to motion because motion by definition is a change in position, but even there, the position is not usually considered to cause an object in it to move or change to another position. Instead, the objects motion is considered to cause its change in position or at least to be equal to that change in position

A very long time has been spent in the foreign place and much observation has been done of the natives. The discussions are now begun. Tell me, how would you describe particle, nuclear, and atomic physics and chemistry to a native in a small village in Africa who only understands a language that does not even have words adequate to describe the basic concepts? It is an interesting problem, but not insurmountable if the native really wants to know. Of course, you have to decide whether you really want that native to have all the information needed to make a nuclear bomb, etc. Yes vacations can be very good. There are so many interesting places to see in the world and some of the more interesting ones are very new.

Thank you, I will try to enjoy it.

Paul,

I wanted to give some examples of fundamental physics, which cannot be truly understood in a non-mathematical fashion. You may read very good popular books and get the impression that you understood them, but you really understand them when you understand them geometrically. I started to compile a list, and then I realized that the list will be difficult to read, and you will pick up some details and contradict them, without trying what I say. Moreover, as you said, my statement was about fundamental physics in general. Therefore, I think that it would be better that you pick some phenomenon of fundamental physics, which is today understood, of course, and which you think that you can fully understand without mathematics. According to my statement, I should be able to show you that you can understand it better if you understand it mathematically. But the only way I can show this to you is by telling you what to study to obtain this understanding (assuming that I understand this phenomenon myself and I can guide you). Otherwise, our long discussion reduces to me telling you how good is a special recipe of ice cream, and you providing philosophical arguments supporting the idea that you will not miss anything by not tasting it.

You say "Reality is not coordinate-free, however." I disagree. A coordinate-free object doesn't remain the same by changing the coordinate, but rather it's "shape" remains the same. If you want to understand what mathematical physicists know about coordinates, and by coordinate-free objects, you can read something on differentiable manifolds, special and general relativity, and gauge theory.

About motion. Motion is change in time. Change of what? Of a state, or of a configuration. All possible states, or all possible configurations of a system, in a particular theory, form an abstract space. Motion is change of the state in time. Therefore, motion is a curve in the space of all configurations or states, parameterized by time. Any physical phenomenon which is currently understood has such a description. Can you think at a different kind of physical motion, which is not completely describable like this? For the motion, I would recommend something on Lagrangian and Hamiltonian mechanics, Schrodinger equation, and perhaps dynamical systems in general.

On your observation about time as a fourth dimension, I would say that explaining time as a moving 3D-space in the 4D-space is wrong, and this is not the way time is understood as a fourth dimension (or at least those who understand it like this are wrong). The first idea is that all the equations describing physical phenomena happening in space have as solutions fields, which can be defined equivalently as time-evolving space fields, or as space-time fields. Therefore, all the information is contained in the space-time fields. The second, and most important reason for viewing time as a fourth dimension, is due to Lorentz transformations, which rotate space components into time components and time components into space components. These two clues suggest that, at least as a representation, time as a fourth dimension satisfies all the physical needs. Mathematics explains relations. Some may disagree, but can they show a physical phenomenon which is not describable with time as a fourth dimension?

You say:

"Tell me, how would you describe particle, nuclear, and atomic physics and chemistry to a native in a small village in Africa who only understands a language that does not even have words adequate to describe the basic concepts? It is an interesting problem, but not insurmountable if the native really wants to know."

It depends on how much they want to know. If they want to have an idea, popular science books can be enough. If they really want to know, I am sorry, but they will need to learn a lot of mathematics and physics. And the mathematics is not just for being fancy, it is necessary. I respect your thoughts, this is why I did not come to you and tell you that you need to learn math. It was you who came to me and told me not to use math. I cannot show you the importance of math in physics, if you don't jump and swim. It is your choice, I don't want to insist at all. The discussion was continued because you asked me to resolve some of your doubts. But if the doubts keep coming, there is only one solution: go and see. Take a particular phenomenon and explore it. But it's up to you.

You cannot describe with words a symphony to someone, the only way is for him to listen that symphony (or you can show him the sheet, if he can read it).

Cristi

Cristinel,

I saw your comment, but don't have time to go over it in detail now, as I am getting ready to go on my trip. It looks like one thing that we have in common is the understanding that math can sometimes make it easier to understand things about the world around us. Why don't we start by taking a couple of basic concepts and explain what the math shows us about the nature of the world that we live in. Lets say we start with a simple geometry example say the Pythagorean Theorem where you can get the size of the side that is not a part of the 90 degree angle (hypotenuse) by squaring each of the other two sides and adding the 2 results together and then taking the square root of the result. In the next three weeks while I am gone you can think about it and tell me in your next comment all that you can see from the math of it that explains things about the real world and how the world works as an example of how math can be helpful in giving understanding about the real world. We might also try one a little more difficult like E=MC^2 if you have time. When I get back I will give what I see in them also and we can then compare notes and see if we can maybe add to each other's understanding or maybe you can help me to understand if I am completely wrong on it, etc. I think it would be an interesting first step together and maybe help each of us to get to know the other better.

Paul,

My claim was not that, in order to understand physics, you need to know all mathematics, so there is no reason to start with a math topic and search for applications. What I said is that "fundamental physics can be understood better by understanding the underlying mathematics". If you disagree, and consider this an "extreme position", you can pick a phenomenon in fundamental physics, at your choice, then you explain it without understanding mathematics, and I will try to show you how mathematics can make it clearer.

But perhaps you agree. Or maybe you are not interested in doing this, and that's fine, you can tell me, because I don't want to insist; we can stop our discussion at any time.

Have a nice trip,

Cristi

Cristinel,

I am not sure where you got the idea that I was implying that one would have to know all mathematics to understand physics or that I was in some way claiming that you were implying that. If that were the case, no one could understand physics because it is obvious by the existence of currently unexplainable mathematical paradoxes that man's mathematical skills are still incomplete or lacking in some areas. Moreover, if I believed that you were implying that, I would have had to ask you to present all math and then to tell me how it in total gave a better understanding of fundamental physics. I think we can agree that this is not necessary because the world is designed such that individual parts of it can be understood (at least in part) without having to understand it in total. As a matter of fact it is only by gaining understandings of such parts and assembling these bits of knowledge together that we have any hope of gaining a total understanding of the world that we live in. As I said before, I think we are in agreement that mathematics can be an aid (a useful tool) to gain understanding of some things in the world. My point is that the mathematics is best used in conjunction with observations of the world around us to help us to better understand the things that we observe in the world around us and to possibly guide us to look for things (make certain new specific observations) that may help us to see and understand the world to a greater extent or at a deeper level. It is the combination of mathematics with real world observations that truly allows us to get the best understanding of how the world works and, therefore, also gives us a better understanding of physics because (properly applied) it is a part of the study of the world and our attempt to get a better understanding of it. My reason to start with a simple geometric example (the Pythagorean theorem) was to start in an area of math that I believe you are expert in (geometry), about which we can both agree that the math can lead to a better understanding and to work together in it to see what we can understand better from the math and how we can combine the math of the theorem with other observations of how the world works to get the most out of it that we can by seeing where the math and other observations lead us. I believe that you might be better at explaining what the math tells us about the world and I may be better at combining that knowledge with other observations to arrive at a more complete total understanding of the subject and where it leads us or to see new areas of thought that the math leads us to explore. You may be the one to develop the new math to describe these new areas of thought. Of course, I may be wrong about that, but we will not know either way unless we try. I asked you to start by giving the math and what you see as the better understanding that comes from it because the math is the initial focus that leads us to specific thought patterns and observations for expansion into new understandings. This is the natural way to start if you want to show how the math leads to a better understanding of the subject because the observables and thought paths that result can be easily traced back to the beginning math source. If I, on the other hand, began by explaining in English from the dimensional viewpoint what the Pythagorean theorem tells us and why it works the way that it does, the benefits of the concise form of the math formula or the geometric expression of it might not be as apparent. In other words, I chose the subject to allow both of us to not only prove our points, but also to allow us to work together by allowing each of us to contribute to the final result according to our individual strengths and to compensate for each other's weaknesses. For me to pick an area where math would be of no or limited benefit would not be a valid choice to encourage us to work together, which is my goal, if it is agreeable to you. My viewpoint is not that the world can be best understood by either the exclusive use of math or by the exclusion of math, but by the proper joining together of math with other methods of thought expression and with observations of the world that we live in, to allow us to develop thought patterns that give us deeper insights into the structure of the world and how it works. I think that to make it easier we should limit our first discussion to the Pythagorean theorem and leave E=MC^2 for later. I would still like you to begin from the math point of view first if it is agreeable to you, but if you feel uncomfortable doing it that way; I can give it from an English description of observables first. Of course, I would need to use some numbers, etc. because there are some quantitative aspects to be understood. You can either just present it from the math perspective in your next comment or let me know if you want me to do it from the other angle first.

I am interested in doing this if you are. Just let me know how you want to proceed with it in a way that we will be working together and not against each other.

Thank you. The trip went well.

Dear Paul,

It is good to see you back, and to see that we agree so much, being in the same time different. You have interesting ideas, and it is great to see you working to improve even better your eloquence, by adding more mathematical rigor. I am very busy, being caught in several projects, but I would love to give you some references and quick answers in the areas where I am competent, if you are interested.

Best regards

Cristinel,

On the one hand it is good to hear that you have several projects to work on because that means you likely have adequate income, which is good for you in the current state of the local economy. On the other hand, although the initial compatibility test phase would not demand much of your time, the full transfer of basic fourth vector concepts, the time required for the receiver to extrapolate more advanced concepts on his own from the basics (This is a required step. Advanced concepts will not be transferred, but must be developed locally to meet minimum cooperative protocols.), and the generation of the necessary structural math models will almost surely take many man years of work on the part of the selected receiver. This could possibly be reduced if several adequate receivers who can work together are found, however. Even so, it will still likely require much long term work to complete the transfer and local development of fourth vector technology to the point that those involved will receive the great rewards that will be due to them from the local societal structure because many of the concepts are contrary to man's current scientific belief structure. It will, therefore, likely require adequate experimental proof, which will not come until the concepts are understood and developed close to the point of practical use. Your current busy condition means that you would not likely have adequate time to devote to this endeavor.

Thank you for your offer to give quick answers in the areas where you are competent. I am not sure of what all of your areas of competence are, so maybe you could let me know about them in a little detail so I will know what is acceptable to ask about from you. There are a couple of questions that I would like to get the answers to if you know them or if you don't know them, but you know someone else that would know the answers to them maybe you could refer them to me or me to them. The first is: Have there been any experiments done in which a photon of about .511MEV has been changed into an electron that is about at rest or any experiments in which an electron about at rest has been changed into a photon of about .511 MEV. If so, has any one looked at the frequency and/or wavelength of the photon before the change and then looked at the frequency and/or wavelength of the resultant electron to see if it is the same as that of the initial photon or not and if not what is the difference? The same question applies to the pre and post frequency and/or wavelength in a change from an electron to a photon. I am looking for the results of an actual experiment and not just a math calculation of what is expected by theory if possible. An experiment in which the initial photon is greater than .511 MEV and produces an electron that is not at rest or one in which an initial electron that is not at rest produces a photon greater than .511 MEV would also be of interest if it contains the pre and post frequency and/or wavelength information as described above. The second question is: What is the predominant current belief as to why the speed of light is what it is and not some other value?

It looks like they may soon close out access to these contest pages since the contest is now officially completed. If it is closed out, or if you just prefer to, you can reach me at pljb1@juno.com to give me the answers if you can get them for me and to tell me about your areas of expertise so I will know what types of questions you might be able to answer for me. Some other way for me to reach you other than by this page would also be helpful if you want to continue communication after these pages are closed.

May you be successful in your many projects. I would be interested in hearing about what they are if they are not considered secret, etc. and you would not consider it an invasion of your privacy or anything. All I know at this time is that you work as a computer programmer on computational geometry and are working on your doctoral degree in fiber bundle geometry. You also apparently do some independent research in the area of attempting to reconcile quantum theory with relativity theory per your paper. I guess these things could keep you busy. You are right that you can get around the quantum effects. They are due to certain dimensional structural and inter-dimensional interface relationships. The key is to access and understand the level of structure below these effects that generates them.