Ok, let's look at your comments in detail!
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Yanniru:
What I am saying is that if we accept your theorem as correct, as I do, then what it says is that the unknowable data must follow the same rules as the known data.
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That is true!
My opening definition of "unknowable data" requires it to obey exactly the same rules as the "knowable data". The ONLY difference between the two is that "knowable data" is real: i.e., our universe is a real consequence of that data, and it can not change; "unknowable data" is a function of our explanation. It plays the role of the things that scientists dream up to explain their observation. If it didn't obey exactly the same rules, it would not be "deemed to exist".
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Yanniru:
Let me give you and the rest of the readers an explicit example:
Suppose the known data only involved the collection of photons. Then the rules that apply to the known data are Maxwell's equations.
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You are making two mistakes here! First, you are ignoring my definition of "knowable data" (implying that it is the same as your "known" data; and second, you are presuming "photons" are "knowable data". From the perspective of my presentation, by identifying "photons" as "knowable data", you are assuming that the entities you call "photons" absolutely must be "deemed to exist": i.e., that absolutely no possibility exists that any theory in the future will ever declare what you call "photons" to be some other phenomena. That is an awfully big assumption!
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Yanniru:
So according to your theorem, the unknown data must be "constrained", to use your terminology, by Maxwell's equations. Then the equations derived should be Maxwell's equations.
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Again, you are confusing your concept "unknown data" with what I define as "unknowable data": i.e., the things that scientists dream up to explain their observation. Secondly, my theorem says that it obeys exactly the same rules as the things they didn't dream up (the real things, whatever they happen to be). That means the dreamed up things must obey the rules dreamed up by the scientists of the future for the things they believe exist. If they don't, the scientists of the future won't deem them to exist! Again, you are assuming that absolutely no possibility exists that any theory in the future will ever declare that Maxwell's equations are erroneous. Once more, that is an awfully big assumption.
Now, as an aside, if my theorem is correct, (and you have agreed that it is) then anything can be explained through the rule F=0 as defined in Chapter 1 of my paper. My equation 1.27 is the equation which must be obeyed if the rule is F=0. So 1.27 is the equation obeyed by everything! If you go to equation 4.24, you will discover that Maxwell's equations are an approximation for equation 1.27 when one is speaking about entities which interact with charged fermions (which are a solution to another approximation to equation 1.27).
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Yanniru:
Now in the derivation following F=0 you set the rules for your known data to have certain symmetries. Therefore the equations that you derive are consistent with those rules, which in this case are symmetries.
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I have a sneaking suspicion that you are going to interpret that to mean that the individual solutions must obey those symmetries. That is not at all what is expressed in the given symmetries. What those symmetries say is that the entire universe taken as a holistic entity in its entirety must obey those symmetries. Anytime you select out a limited piece of the universe, the character of that selection can produce all kinds of asymmetries. But I am sure you are sufficiently competent that my suspicions are groundless.
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Yanniru:
The derived equations cannot apply to any data that are inconsistent with those rules as stated by your own theorem.
For sure the derived equations do not apply to any or all sets of rules.
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I have no idea what "derived equations " or "sets of rules" you are referring to here. The rule I am talking about is F=0 and my derived equation is completely in accordance with that rule. That is how the equation was derived.
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Yanniru:
Now as before you will just say that I do not understand, or deflect the argument by some other means.
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No, I am the one who doesn't understand here. I don't have the slightest idea of what you are talking about.
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Yanniru:
But I am not concerned with what you think. The argument based on yout theorem is so straight forward that any reader on this forum will understand it's implications regarding your work regardless of what kind of a smokescreen you put up. Your own theorem proves your work is limited by the set of rules you assume.
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Of course the set of rules chosen create limits. The theorem says that if one is given the freedom to add ANY thing to that list of things whose behavior is to be explained, (i.e., if you can add anything you can dream up, so long as it obeys the rule being used) then "anything" can be explained through the rule F=0. The question of describing the universe has thus been transformed into "finding the things which exist": i.e., finding entities which obey equation 1.27. What exists defines the universe.
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Yanniru:
Now back to the photons. Your theory is able to derive Maxwell's equations but is not able to derive the behaviour of a photon. In other words your theory applies to fields but not to particles. It says nothing about how fields collapse into particles or about any of the other standard interpretations of quantum mechanics. It is quite far from being a theory of everything.
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Of course it says nothing about how fields collapse into particles. What it says is that when you go to look at the universe, you will obtain results which will be consistent with the probabilities which satisfy equation 1.27. Now look at that equation once! It has an infinite number of terms. The equation is impossible to solve. The best you can do is to make rational approximations for the terms you are going to assume unimportant to the experimental situation you are interested and solve the approximation you have generated by integrating those terms out.
The theorem essentially says that you may trade rules for items to be explained. However, I can only prove the theorem for the rule F=0. It is entirely possible that everything cannot be explained by another set of rules; however, I seriously doubt that.
Finally, it would be a fine "theory of everything" except for one difficulty: it's not a theory! It is actually nothing more than a big complex Dewey decimal system for keeping track of what we know ("knowable data") plus what we think know ("unknowable data") so we can make decent estimates of what we should expect.
A universe defined by the rule F=0 is quite different from the universe conceived of by scientists of today even if it looks just like what they see. For example, the F=0 universe does not include the rule called causality. Our scientific community considers causality to be the backbone of their world. They think it is a "real" aspect of the universe which cannot possibly be dispensed with.
What they don't realize is that causality a mental concept. What I mean by that is that causality is an element of explanation, not an element of reality. In the absence of an explanation, the word cause has no meaning. In a sense, the cause is the explanation; the sole purpose of any explanation is to lay out a cause. If you were all knowing, you would know what is and there would be but one cause: the cause would be "it exists".
Causality plays exactly the same role in modern science that gods played in ancient religions (they were the original "cause"). In ancient times, people believed that the explanation of anything required understanding the gods position in the issue. Under careful logical analysis, belief in gods began to be less and less satisfactory as a rational "cause" (explanation) of observed phenomena. Dropping that concept from the job of searching out acceptable explanations was actually quite slow to be accepted. And, as a matter of fact is not really accepted by a lot of people even today.
Above and beyond that, in a very real sense, the role played by the gods in ancient explanations is still with us in modern science. It no longer possesses the conscious will associated with the gods but it is still thought of as absolutely necessary to any explanation; we call it causality. The scientific belief in causality today is as strong as the beliefs in gods ever was, to my knowledge, no one is attempting an explanation of anything sans "causality".
However, causality is also beginning to show serious wear around the edges. The problem began with the success of Quantum Mechanics and has been seriously compromised by some of the modern experiments. If you take a step back and examine the role of the new concept "entanglement" you should be able to comprehend that its sole purpose is to provide for the retention of "causality" in the face of problems with the "collapse of the wave function" (another concept which only exists to keep causality in their theories.
Now I hold that "causality" is not a necessary component of any explanation. Of course, I am a majority of "two" (surprise, surprise there is somebody else who agrees with me) so my opinion is utterly worthless; however, my work, which depends not at all on the idea of causality is an explanation which completely justifies Quantum Mechanics with out any resort to causality at all. If I am correct, then it accomplishes two very significant things: first, it removes any concern with the problems arising from requiring causality and second, since all of standard mechanics (what we see as the ordinary world) can be derived from Quantum Mechanics, the common phenomena experienced by everyone will still satisfy all the intuitive results obtained by causality.
The world without causality is quite easy to understand: all we can really ask of reality is that whatever happens in the future must be statistically consistent with what has happened. That is, any future explanation of any phenomena must also apply to any past phenomena which qualify for the explanation. All that is required to satisfy this kind of explanation is the logical procedure required to obtain the result; if that is the case, "causality" is not an issue at all.
We are left with but one cause: why is the universe here and how come we can think about it? Well cause, just cause that's all. Hi Paul, I thought you would like that one. (I didn't answer your response to my other post because I agree with you completely.)
I am glad you are having fun Yanniru -- Dick |