Ronald Hyde

Not really arrogant, but very self confident, I know what I have and will explain it all in time. Just hold onto you hat and be calm. <3> says that everything that happens in Nature can be expressed as a function of time. If F is a function that describes something in Nature, it is always F(t). If F = F(t,x,y, z) then ultimately x = x(t), y = y(t) and z = z(t), so that anything that happens in the World is strictly always a function of time. Expressed in that unit the age of the Universe is about 10^41, slightly more. Take the logarithm of that to the base 2. Does that number look familiar? That's one reason. I'm very interested in this, I haven't used that many definitions, so it should be pretty easy to do, and maybe point me to a web resource where I could find out more. I'd really appreciate it. Thank you.

Then why did you say that all mathematical operations could NOT be defined over the natural numbers? Because I'm not a conventional person. I read whatever I can find on the subject, then I start reasoning about it myself, I look at things in original ways, I re-arrange things until I see that they are related to other things, so concepts get merged with other concepts we already know about. I can invent notation, systems of notation are very important in understanding. That is the process of developing new insight, which people who don't develop new insight don't and perhaps can't understand. Insight is the process of finding that many things have the same name, or that one thing has many names. Planck time is something someone pulled out of a hat. I have reasons beyond any stated that support the value I gave as the 'natural unit of time', but I will make it all clear in time. You shouldn't believe everything you read in a textbook. Some of it may be just plain wrong. Like it was before Planck discovered the Quantum. In the meantime keep reading my original post until you understand every word of it. I think I made it quite clear how everything that happens is function of time alone, and that time us just a number, and you will see that it all leads to a logically consistent description of the World we live in.

It's that value because observation supports that value, or approximately that value. It seems to be the minimumamount of time that it takes an interaction to happen. We have to go with what Nature tells us, not what our philosophers think it should be like. As for why it's limited to integers, consider that people have been using the notion of continuous time to describe Nature since Newtons days, but about year 1900 that notion started breaking down, when the quantum was discovered. And it's still breaking down. Because it's inherently wrong it causes problems. In describing the strong interaction the notion of 'lattice spaces' has been introduced, and calculations with them work very well, the notion of lattice space includes the idea of discrete time, so consider that there may be something to what I am saying. But the real reason for discrete, i.e. incremental time is that it makes the Universe into a structure which is logically consistent, as well as consistent with observation.

Not in the least does it invalidate it, since the basic unit of time is about 10^-25 seconds you can approximate that reaction rate very closely indeed in one minutes time.

You can start with a zero and a one, 0 & 1, if you wish they can be expressed if binary form. You also start with the basic mathematical operation of addition. You can make a new number by adding 1 to 1, and you can continue that indefinitely to make all of the natural numbers. You can define an inverse operation to addition, which is subtraction. You can define another operation which is multiplication and an inverse operation to multiplication, which is division. So just starting with 0 & 1, or even only with 1, you can define all the operations over all types of numbers, fractions, real numbers, you can extend the expressions to complex and imaginary numbers, ect.. So you can, by construction and definition build ALL of mathematics, including reflection, etc. , from just 1 and/or 0 and the basic operations of math. I much prefer the definition of a set that is used in group theory, a group is a set with defined rules of combination. It can always be considered a 'member of itself' without any contradiction, it may have subgroups, which are members of it, and it may be a member of a larger group. In fact, it's very hard to define a group, perhaps impossible, which is not a member of a larger group. To me Russels paradox has always been a non-starter. PS: This is why I know that time is a number; There are other operations such as counting, which can be defined as putting into one to one correspondence with N, which are certainly defined over the natural numbers, but cannot be applied to all mathematical objects, some are uncountable. If it weren't the world would be a completely chaotic and disorderly place.

All the states of a photon are superpositions of other states, that's the way it is, all the time. If we separate it into a particular state of one kind of polarization, it's still a superposition of the other kinds of polarization. To find what state it was in we have to detect it. That's the crazy way that QM works.

Sorry, I'm not trying to be condescending, but I think things through very carefully, so I don't appreciate it when I feel that someone is being glib or dismissive. I know about this larger definition of Godels proof, but I wasn't trying to write a book about it. Our notion of a 'formal system' began with the mathematicians of the Arabian Golden Era, who added the decimal point and zero to the Indian system of positional notation, so that the basic operations of arithmetic could be performed by simple written procedures. They called these procedures 'algorithms', a word which we use today. They also found that they could substitute x, y, z etc. for the actual numbers in an algorithm, perform operations with them and replace them with the actual numbers at the end of the operations. This method of formal substitution is where we get the notion of a 'formalism'. All the operations of mathematics are defined over the 'natural numbers', i.e. the integers. They also gave us the word Algebra which is a system of formal procedures for solving problems and expressing results. So everything that I've said, and that you've said about Godels proof is true. Oh, it's you, you love to play the devils advocate, don't you. Consider a line from Porgy and Bess, "They been tellin' all you chillun, that the devil is a villun, but it ain't necessarily so". I've read lots of textbooks, I have my own collection, including the wonderful Feynman Lectures. If the textbooks are all right why don't we have a complete description of the world? Obviously there are some kind of shortcomings in the textbooks. And yes, I know about physical quantities and dimensional relationships, all those kinds of things, so I'm going to tell you right now that the three are right, and if the text books differ they are wrong! We live in a very strange world, a world where a billion people can be wrong and one person can be right. If he comes along and shows them the error of their ways, he may become the hero of the hour, or he may have his head chopped off for heresy. That's the way it works.

You do realize that that is what I said? That measurement destroys the state that it was in, and makesa new one that is determined, or simply destroys it. A really good model of all these ideas is in the polarization states of the photon as they pass through filters that separate them into plane and circular polarization states. A plane polarized state is a superposition of circular polarized states and vice versa. But to actually measure whether a particular photon was in a particular state it has to be detected in some way, running it through filters only selects its state, detecting it destroys it, so the statement is only meaningful in the past tense.

The electron isn't a good place to start. It will take quite a few steps, levels of abstraction if you will, to get to the electron. Better places to start would be using the Heavisides Unit Step Function and treat the Universe as an initial value problem, or to build the Lorentz group up from more elementary groups and use it to construct a model. Ideally it would be nice to have a model that could be run as a computer simulation, so that you could view, as it were, the first moments of Existence.

No, that's not what it says. It says that any finite procedure cannot prove everything about relations among the natural numbers ( integers ), that there are always things that are true, that can only be proven in a larger system. So there is an infinite hierarchy of logical systems related to relations between the natural numbers. So it fits into this scheme very well, thank you! http://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_theorems And thank you for replying. I hate it when someone says something and has no intention of supporting it.

That statement is only meaningful in the past tense. If an observation, or measurement, is of a particular state of the system (e.g. you measure/observe the energy), then it must have been in one state. Measurement either destroys the state, or makes a new one with different observables.

That really doesn't say anything. If you have a line of reasoning and some facts, please let us all know. What do you think that Godel proved?

Do you know what Godel proved? He proved that any formal system is contained in a larger formal system. That proof fits this view of the world to a T. It would mean there is only one Universe, the one described by these principals, and it contains everything that could ever happen.

I'm not worried much by what the textbooks say, I'm worried by the fact that people keep making posts about the 'collapse of the wavefunction', Schrodingers Cat, and other silly and misleading ideas.

This is a comment you made on a very recent post: The collapse is not instantaneous. Moreover you are assuming that the system was not prepared in an eigenstate of the observable, in whose case there is not collapse. You seem to believe that all wavefunctions are 'real'. Quote: QM does not "depend on pictures". Answer, but people do, so they treat the wavefunction as reality and not a mathematical device. Only the results we calculate using the wavefunction are real, the transition rates, etc.

This is a very good question. It represents the probability that you will receive photons, and the fact that that reception is synchronized with the voltage variation of the antenna. It was James Clerk Maxwell who discovered that the wave equation fit into the theory of electromagnetism, and at the time that theory was purely classical, no one had any idea that light in all its forms was quantized. Now we know better than that, we know that the 'wave' is really just a calculational device associated with the discrete photons.

We make a postulation: That in some deep sense the World is made of mathematical relationships. We state three laws: <1> Every mathematical relation permitted by Logic must occur. <2> Time is just a number, an integer. <3> Everything that occurs in Nature is a function of Time. <1> says that the World is a mathematical-logical construct, that any mathematical relationship permitted by logic must occur in Nature. Logic is simple Boolean logic, which can be applied to mathematical expressions. <2> says that time is just an ordinary integer, its value is about 10^41 at present and increasing by about 10^25 per second. <3> says that everything that happens in Nature can be expressed as a function of time. If F is a function that describes something in Nature, it is always F(t). If F = F(t,x,y, z) then ultimately x = x(t), y = y(t) and z = z(t), so that anything that happens in the World is strictly always a function of time. This is all that we need to build a valid picture of the World, the rest is just deduction and the application of logic, which is Boolean logic and mathematics.

You'd be surprised at how many people regard the wavefunction as a 'thing', including far too many theorists. Just read all the nonsensical posts aboutthe collapse of the wave function, and it's supposed philosophical importance. By what methods of measurements can you separately determine the properties of the electron and proton in a bound hydrogen atom, without unbinding it? Can you for instance tell us the separate positions of them? If you can't, then your statement that they separately exist is unproven.

The wave-function doesn't represent a concrete thing in Nature, it's a mathematical device used to calculate certain things about the Hydrogen atom, such as the energy levels, transition rates, etc.. They can be calculated in other ways, e.g. Heisenberg matrices, or Feynmans path integral method. So when the wave-function 'collapses' it is of no significance whatever, because the system has changed in a way that requires a new wave-function to describe it. The Electron doesn't hide in a 'probability cloud' around the Proton, when it's bound to the Proton, they both cease to exist as single entities and a new entity is formed, the Hydrogen atom, which has excitations which can be deduced using the wave-function, among other methods. If you use the 'probability cloud' model to perform calculations you will get errors.

You're very close to getting it right. Unitarity and Boolean logic go together, and should be part of every ones thinking about physics. Unitarity can be derived from Boolean logic in a very straightforward manner. If an occurrence is allowed by logic it has a probability of one of happening, if it's not allowed it has a probability of zero, if its allowed under some conditions and not others, it may have a probability between zero and one in general.

Post reply Jul 27 (3 days ago) I've decided after much thought, that to integrate Gravity with QM you have to get rid of General Relativity. Combining GR with QM is just not a viable possibility. Space-time has to be the flat space-time of Special Relativity. Now every successful theory to data has involved some sort of unitary representation, SO(2), SU(1), SU(2), SU(3). SU(4). and even higher for QM in general. All of them are some sort of Lie, division and/or Clifford algebras. So when Gravity gets merged with the rest of physics, it has to be in that form too, whether it's considered to be quantized or not. And there's a sensible reason for that, because any other kind of theory leads to expressions of probabilities of greater than 1 or less than 0, which we know is a logical absurdity. Now GR was developed because Einstein believed that a theory of Gravity had to satisfy the principal of equivalence for acceleration and Gravity, but acceleration is only equivalent to Gravity to first order, acceleration has no equivalent for tidal forces, which gravitating bodies produce. It's entirely possible to formulate Gravity so that it occurs in flat space-time. When an atom emits light from the Sun, it's explained that the light is red-shifted because it has to move in curved space-time, but you could also just say that electrons near a massive body are lighter than electrons away from one. And it also satisfies the conservation of Energy this way. Of course much has to be changed, but that's the name of the game, make the needed changes to make a viable theory. GR not only introduces the superfluous notion of curved space-time, it also massively complicates the bookkeeping, ours and Natures. It also leads to the somewhat absurd notion, that to quote chicken little, the sky is falling. Whereas a model with flat space-time would only have matter falling. To start constructing such a theory, you could start with the Poincare' group, which isn't really a proper group as such, it's two groups of different dimensionality put in the same 4 X 4 box, but that's easily corrected.