The Relativity/Quantum Mechanics Conflict

[Rade]

....Without ever knowing anything about the actual structure of reality behind all this....

Hi again. AnssiH, when I think about this comment you just made, within the context that it was made in your last post, it seems to me I can take it two ways. As I understand your argument, you are saying that the approach of DD to "explanation itself" is to show how any explanation can be derived "without ever knowing anything about the actual structure of reality".

 

Now, in one way I would agree, but in another I do not--let me explain. Logically it can be claimed as an axiom that there are two ways to know some thing (1) from inside the thing (2) from outside. Do you see anything wrong with this simple logical proposition ?

 

OK, let us apply the DD approach...to explain without ever knowing anything about the actual structure of reality....to a hat :artgallery:

 

It seems to me, that the term "actual structure" refers to the inside, to make a claim of knowledge from the perspective of being inside of the hat. So sure, in this case, the DD approach works well, one can explain a hat without ever knowing anything about the actual structure [inside] of a hat. We can apply the Fundamental Equation perfectly to explain a hat from outside the hat, where it sits on Sherlock's head :smart:

 

However, where the DD approach has a major problem is when the "reality" under investigation is the Universe Itself. Unlike the hat as a type of reality, humans can ONLY know the universe from the inside, never from the outside. That is, the only type of knowledge of the universe logically possible to any human mind would be the "actual structure" [inside] of the universe.

 

So, you see, when you claim that DD has a new perspective to explanation such that it allows a human mind to explain...without ever knowing anything about the actual structure [inside] of reality..., then logically the Fundamental Equation of DD can say absolutely nothing about the "actual structure of the universe itself" :eek2: This situation will not do. If the equation is to make a claim of being fundamental it must allow for explanations of the actual structure [inside] of the universe itself. Otherwise, the entire science of Cosmology must by definition be outside explanation using the Fundamental Equation. Another example is study of the human mind, I mean, any human attempting to study their own mind from "within their mind".

 

So, I would suggest you not say that the Fundamental Equation of DD can provide explanation ....without ever knowing anything about the actual structure [inside] of reality--it only can add to confusion. If you agree, then you need to show how the Fundamental Equation of DD is applied to two different types of explanations of reality (1) knowledge gained from the inside reality (2) knowledge gained from outside reality. They are completely two different types of knowledge, and we want the Fundamental Equation to apply to both.

[Erasmus00]

Also you should be able to understand the impossibility of actually understanding how any specific explanation performs that first transformation

 

But you can figure out general features- if the probability is binary (either 1 or 0 at a given point) then no matter how you construct the mapping, the result is a binary distribution (either 1 at a point, or 0). These binary distributions can never solve the fundamental equation.

 

And most of all, such an analysis should be redundant anyway. Think about this; to find a valid counter example would mean you have found such valid interpretation for unknown data, which does not contain self-contradiction in terms of the expectations that it generates BUT it contradicts the fundamental equation.

 

Classical mechanics is just that- an explanation for a set of data that has no self-contradiction AND contradicts the fundamental equation. This is without connecting classical mechanics to reality- but rather looking at it as a mathematical system.

 

Classical mechanics is proven to be internally consistent, and there is a set of data it explains. Further, its probabilities it predicts are always 1 or 0. Dick's representation fails in his derivation of the symmetry constraints-in particular he uses a derivative but his mapping was discrete.

 

So finding a counter example would mean there is an error in the deduction of the fundamental equation! Don't you think it would be quite a bit easier to actually find that error in the algebra?

 

My point is that a counter example exists, the argument is wrong.

 

Seriously, looking for a counter example would be much like trying to disprove Newton's third law of motion by endlessly throwing different objects at each others.

 

Your logic is flawed- Dick's analysis proceeds deductively from a set of axioms. It is not empirical like Newton's law. Its like disproving Euclidean geometry by drawing a triangle on Earth and noting its angles total more than 180 degrees. Similarly, explanations might exist that do not fall into Dick's axioms.

 

For instance, I remember you made an argument about how his universal notation is not scale symmetric, which to me just rings as an instance of confusing something in the notation with something analogous in modern physics.

 

I pointed out that Dick's model IS scale invariant- unfortunately a truly surprising feature of modern physics (and reality, as far as we know) is that it is NOT scale invariant. i.e. Dick's model predicts that ALL valid explanations are scale invariant- the existence of explanations that are NOT scale invariant is another counter example.

 

Also, consider that Dick's model takes discrete data (from his set :artgallery: and constructs his representation out of it. By the time he gets to his universal representation he wants to take derivatives!

[AnssiH]

Now, in one way I would agree, but in another I do not--let me explain. Logically it can be claimed as an axiom that there are two ways to know some thing (1) from inside the thing (2) from outside. Do you see anything wrong with this simple logical proposition ?

 

Like I said before, I don't understand at all what you mean by it. Can you define what you mean by "inside" and "outside" for me?

 

So, you see, when you claim that DD has a new perspective to explanation such that it allows a human mind to explain...without ever knowing anything about the actual structure [inside] of reality..., then logically the Fundamental Equation of DD can say absolutely nothing about the "actual structure of the universe itself" :shrug:

 

Correct, the fundamental equation cannot say anything about the actual structure of the universe itself.

 

"Explanation" was defined to be something that generates valid expectations. Not necessarily "the ontological truth".

 

Look at it this way; if you take DD's universal notation, apply some universally valid definitions (=applicable for any given data), and follow the consequences imposed by the fundamental equation, then you are already looking at relationships that are also found from modern physics.

 

Traditionally those relationships are taken to be valid "because reality is built that way", i.e. because the entities defined by modern physics are believed to be fundamental building blocks of reality, i.e. believed to carry ontological identity to themselves, and that we just "found them" when we looked at reality.

 

Why is it then, that universally valid definitions together with symmetry constraints yield the same relationships? It implies that any set of data can be understood (prediction-wise validly) in terms of the same concepts. How could that be?

 

Fundamentally, your expectations are always based on inductive reasoning, no matter how you have chosen to understand the information-to-be explained. The universal validity of certain relationships means that any information can always be made to "fit that mould", i.e. you can always interpret the information in terms of entities that obey those relationships. That interpretation IS your immediate perception/comprehension of reality. You can think of the thus defined entities (including space and time) like universally valid containers for your inductively established expectations.

 

That implies strongly, that the mystifying features of modern physics are not features of reality, they are features of those "containers" we built in our minds as part of our method of handling reality in our mind (for prediction purposes). The raw information that we actually know about reality, is simply made to fit those containers. If you follow the analysis carefully, you can understand the details and consequences of this circumstance a lot better. Suddenly it makes perfect sense that quantum mechanics contain some strangely idealistic features. It's all pretty illuminating.

 

This situation will not do.

 

Why not? And on the same note...

 

If the equation is to make a claim of being fundamental it must allow for explanations of the actual structure [inside] of the universe itself. Otherwise, the entire science of Cosmology must by definition be outside explanation using the Fundamental Equation. Another example is study of the human mind, I mean, any human attempting to study their own mind from "within their mind".

 

Why? I think you may be assuming that an explanation cannot be valid if it doesn't capture the actual ontological structure of something. Remember, that by "explanation", we are referring to generating valid expectations, and nothing more.

 

-Anssi

[AnssiH]

But you can figure out general features- if the probability is binary (either 1 or 0 at a given point) then no matter how you construct the mapping, the result is a binary distribution (either 1 at a point, or 0). These binary distributions can never solve the fundamental equation.

 

I.e. when a given explanation gives binary probabilities, like newtonian mechanics? Such an explanation cannot be seen as an approximation of the fundamental equation? Why is that more than a philosophical stance implied by a given explanation? Like I said, you can't tell what the raw sensory information was, and how it translated, before we got to the interpretation called newtonian mechanics.

 

When you want to talk about newtonian mechanics as detached from reality, you are also detaching this discussion from "explanations to unknown information".

 

And I hope you are not seriously thinking that a trained physician would just miss something like that if it actually was a valid concern? Like I said;

"DD's fundamental equation is not by itself an argument of what a representation of reality must look like, or how the solutions must behave mathematically. Different kinds of approximately valid solutions can exist, as the equation itself just restricts those solutions to generate expectations in self-coherent manner."

 

And most of all, such an analysis should be redundant anyway. Think about this; to find a valid counter example would mean you have found such valid interpretation for unknown data, which does not contain self-contradiction in terms of the expectations that it generates BUT it contradicts the fundamental equation.

Classical mechanics is just that- an explanation for a set of data that has no self-contradiction AND contradicts the fundamental equation.

 

This seems to boil down to the same issue as above; either you take it as a violation of the fundamental equation if an explanation is merely an approximation of the fundamental equation, or you don't think such an approximation is possible at all?

 

Should I take it you don't see the fundamental equation as good or even valid way to represent those universal symmetry requirements, because it implies probability distributions akin to quantum mechanics? Can you think about how would you state the same symmetry requirements in terms of a differential equation then, without limiting what sorts of explanations can be thus represented?

 

This is without connecting classical mechanics to reality- but rather looking at it as a mathematical system.

 

Let's stay on topic. You could pick up pretty much any set of axioms and semantically call it explanation. Not what an explanation was defined to be in this analysis. Look ->

 

Classical mechanics is proven to be internally consistent, and there is a set of data it explains.

 

And therefore you take it to be "an explanation" even in that very limited form. I really think I understand exactly what you are saying, and why you are saying it, and it's clear to me that you are making a mistake when you ignore the symmetry constraints, the approximations, and the universally applicable definitions that lead to newtonian mechanics as an explanation to unknown information.

 

Don't forget that the argument was, that newtonian mechanics arises as an approximated solution, when generating an explanation to some unknown data.

 

Your approach is to take newtonian mechanics as an axiomatic system, and trying it for a fit. When you do that, you are also taking its defined entities as absolutely valid by themselves, without concerning those epistemological symmetry requirements at all. I.e. what actually went into generating those definitions as part of an explanation to unknown information. You are essentially skipping the topic entirely.

 

As oppose to this, if you start with the symmetry requirements, and analyze what universally applicable definitions and approximations (i.e. assumptions) are actually needed for ending up to the relationships of newtonian mechanics, you will also notice that it comes along with some subtle consequences that eventually lead to things like relativity (as a more accurate approximated solution, since at that point you would have basically dropped some approximations/assumption that were not valid)

 

That's why we've been commenting newtonian mechanics is not self-coherent, we are referring to that latter issue. We are essentially saying it's not perfectly following the symmetry requirements, but instead to get there, you must use assumptions that just are not valid. Different topic, you see.

 

Essentially your error is to equate the axiomatic form of newtonian mechanics with the newtonian mechanics that arises as an approximated solution to the fundamental equation; the end results may look exactly the same (when you cherry pick those few definitions), but in the first case you are skipping how the definitions are related to the information-to-be-explained.

 

Further, its probabilities it predicts are always 1 or 0. Dick's representation fails in his derivation of the symmetry constraints-in particular he uses a derivative but his mapping was discrete.

 

I don't understand what you are trying to say by that.

 

Your logic is flawed- Dick's analysis proceeds deductively from a set of axioms. It is not empirical like Newton's law. Its like disproving Euclidean geometry by drawing a triangle on Earth and noting its angles total more than 180 degrees. Similarly, explanations might exist that do not fall into Dick's axioms.

 

I just mean to say that the task would be humongous, as compared to trying to prove that the axioms are flawed, or the deduction is flawed.

 

I'd just view it as analogous to theoretical physics, in that theoretical physics is trying to find new relationships via not-so-obvious logical consequences to some known premise, as oppose to randomly creating different sorts of circumstances in a lab in order to experimentally find new relationships.

 

At any rate, it would be helpful if you can point out an axiom that rules out some possibilities for explanations. Because that would be an issue that needs to be looked at, as it would essentially amount to a hidden assumption of some sort.

 

I pointed out that Dick's model IS scale invariant- unfortunately a truly surprising feature of modern physics (and reality, as far as we know) is that it is NOT scale invariant. i.e. Dick's model predicts that ALL valid explanations are scale invariant- the existence of explanations that are NOT scale invariant is another counter example.

 

Sorry about my unfortunate typo, but I take it you picked up what I wanted to say.

 

His notation is scale invariant, because it contains all the information that goes into a world view. That doesn't mean the explanations must be scale invariant in the sense of what scale invariance means in physics; it doesn't mean that any sub-set of that information is scale-invariant by itself.

 

It just means that the overall global scale for "absolutely everything" is scale invariant, and that is certainly true for modern physics too. But if you are just scaling a sub-set of defined universe, of course that is not scale invariant; that is essentially the same as laying down a different circumstance. For instance, a similarly shaped object behaving differently in different sizes is just another way of saying saying that a lump of 100 atoms behaves differently from a lump of 10000 atoms. That's not at all what the scaling of information in DD's notation means.

 

I don't believe this to be such a difficult issue, I mean if you take a spacetime diagram that contains all the information about some situation, what changes in the physical statement, when you print that diagram onto papers of different sizes? Seriously, if there are other people reading this, can you tell me if you understand what I'm saying here, please?

 

Or alternatively, explain to me a situation of modern physics that is not scale invariant, and I will explain to you what aspects of that situation you failed to scale.

 

Also, consider that Dick's model takes discrete data (from his set :shrug: and constructs his representation out of it. By the time he gets to his universal representation he wants to take derivatives!

 

I just don't understand what you want to say by this. :I

 

Discrete data means that the information that went into generating an explanation, was of finite amount. The derivatives that vanish refer to unchanging expectations upon changes to such aspects of the mapping which can always be arbitrarily chosen (i.e. not related to explicit knowledge about the information). I don't understand what you are pointing at as a problem.

 

Oh well

-Anssi

[Erasmus00]

I.e. when a given explanation gives binary probabilities, like newtonian mechanics? Such an explanation cannot be seen as an approximation of the fundamental equation? Why is that more than a philosophical stance implied by a given explanation? Like I said, you can't tell what the raw sensory information was, and how it translated, before we got to the interpretation called newtonian mechanics.

 

Ignore Newtonian mechanics for a second- can we agree that if a given explanation predicts something with either 100% certainty or 0% certainty, then the resulting [imath]\psi[/imath] function (no matter how you map it) must be strongly peaked? i.e. its essentially 1 at one point, and 0 everywhere else?

 

How can we take a derivative of this? Further, is there ANY strongly peaked function that can solve Dick's equation? I contend the answer to the second question is no.

 

When you want to talk about newtonian mechanics as detached from reality, you are also detaching this discussion from "explanations to unknown information".

 

The universal equation, as described, it doesn't matter where the information comes from. Its totally unknown. ANY explanation for ANY data set should conform to the analysis. Maybe Newtonian mechanics has confused the issue by implying physics information, how about the data set "the digits of pi." I can provide an equation that will allow you to predict with 100% certainty what the nth digit of pi is. This is clearly an explanation of the set {digits of pi} in the sense that Dick wants.

 

This seems to boil down to the same issue as above; either you take it as a violation of the fundamental equation if an explanation is merely an approximation of the fundamental equation, or you don't think such an approximation is possible at all?

 

No approximation of the fundamental equation will yield classical mechanics, as I've said many times.

 

Should I take it you don't see the fundamental equation as good or even valid way to represent those universal symmetry requirements, because it implies probability distributions akin to quantum mechanics?

 

Its not invalid because it implies probability distributions akin to quantum mechanics- its invalid because it assumes you can take that derivative, and there are plenty of distributions where the derivative is ill defined. Hence, it automatically restricts the equation to the set of continuous, smooth distributions.

 

That's why we've been commenting newtonian mechanics is not self-coherent, we are referring to that latter issue. We are essentially saying it's not perfectly following the symmetry requirements, but instead to get there, you must use assumptions that just are not valid. Different topic, you see.

 

But your assertion is wrong- Newtonian mechanics has all the same symmetries that Dick imposes. Its translation invariant, etc. You have made many assertions that simply aren't true- I think because you have never studied classical physics, and you've never studied classical physics as an axiomatic system.

 

So maybe the digits of pi example above will be easier- we don't need a formal system to understand it.

 

I just mean to say that the task would be humongous, as compared to trying to prove that the axioms are flawed, or the deduction is flawed.

 

Only if I tried to exhaust everything. Instead, its really clear to see that any discrete, binary probability distribution will never solve Dick's equations, no matter how you remap it. Classical mechanics is just one such example.

 

It just means that the overall global scale for "absolutely everything" is scale invariant, and that is certainly true for modern physics too.

 

No, it is NOT true for modern physics. Thats the problem- you are assuming you know what modern physics says because you can't imagine the world not working the way you want! Modern physics is NOT scale invariant- if you change the scale of absolutely everything you get different physics! Obviously, we can never measure this, but we can take the theory, change the scale of everything, and see what happens in the explanation.

 

Or alternatively, explain to me a situation of modern physics that is not scale invariant, and I will explain to you what aspects of that situation you failed to scale.

 

Change the scale of literally everything by a factor of about 10^16 and quarks will no longer be bound together as protons.

 

Discrete data means that the information that went into generating an explanation, was of finite amount.

 

Actually, no. Discrete data means its not continuous. You cannot fill a continuous space with even an infinite amount of discrete data.

[Doctordick]

I am sorry Anssi, but I don’t think you will ever reach Erasmus as he has utterly no idea as to what we are talking about and he makes that fact quite clear with every post he makes.

But you can figure out general features- if the probability is binary (either 1 or 0 at a given point) then no matter how you construct the mapping, the result is a binary distribution (either 1 at a point, or 0). These binary distributions can never solve the fundamental equation.

Notice here that he wants to view the binary distributions as “solutions” and not as the data points the solution is to fit. Those two concepts are violently different things. Solutions to my fundamental equation yield probability distributions consistent with data given (which essentially constitute boundary conditions). Binary distributions are perfectly consistent with such probability distributions; a fact he would rather ignore.

Classical mechanics is proven to be internally consistent, and there is a set of data it explains.

Again with the internal consistency of classical mechanics. That consistency is only obtained by ignoring a great many important issues. The “data” an explanation is explaining must include “all” necessary data and I don’t think Erasmus even begins to understand what the word “all” in that statement means.

My point is that a counter example exists, the argument is wrong.

As you (and any rational person) well know, the problem here is quite simple, one cannot present a counterexample to something they do not understand.

Your logic is flawed- Dick's analysis proceeds deductively from a set of axioms.

Have Erasmus provide you some explanation which does not use the axioms of logic or point out an axiom I use which is not either an axiom of logic or an axiom of mathematics (which, by the way, Feynman asserted was the essence of logic). As I say, Erasmus simply does not comprehend what you and I are talking about.

I pointed out that Dick's model IS scale invariant- unfortunately a truly surprising feature of modern physics (and reality, as far as we know) is that it is NOT scale invariant.

Again it should be clear to you that Erasmus has no comprehension of what we are doing as he presumes a scale dependence is required without even thinking about how one could possibly establish the validity of such a theory. He just wants to ignore that issue: i.e., he simply does not comprehend that my fundamental equation is a constraint on one’s expectations which absolutely all valid theories must obey.

By the time he gets to his universal representation he wants to take derivatives!

Now Anssi, you know that is part of the induction thing and has practically nothing to do with the data being explained; it is a consequence of the human tendency to put continuity into their explanations. We are talking about “expectations” and to presume that a continuum of possibilities does not exist is simply ignoring a great many possible theories.

 

Erasmus just continues to demonstrate his total lack of understanding of what we are discussing with his latest post.

Maybe Newtonian mechanics has confused the issue by implying physics information, how about the data set "the digits of pi." I can provide an equation that will allow you to predict with 100% certainty what the nth digit of pi is. This is clearly an explanation of the set {digits of pi} in the sense that Dick wants.

Again Erasmus is ignoring the essence of the problem I have solved by equating a specific case of defined results with explaining undefined data. He brings up pi as if it is the only correct explanation of some stream of data. As if obtaining what his theory concludes is 3.141 implies the next digit will be “5” with 100% accuracy. Sure, there is a significant probability that the next digit might very well be “5” but that same result is perfectly consistent with the theory that the sequence is random. Obtaining a “2” would disprove his theory but not the theory that the sequence being received is totally random. My equation is a constraint on the probability distribution consistent with “all” possible valid theories; something totally beyond his comprehension. My retort to his example isn’t even valid because it makes the presumption that the data being received is “digits”; another un-defendable theory.

 

You and I know that that what he is talking about is totally off subject but he doesn’t know that because he has no concept of what the actual subject is. For example, even before beginning to talk about “pi”, one must first explain geometry: i.e., the “data” to be explained must include “all” the raw information from which geometry is to be deduced. Before explaining geometry one must first explain English: i.e., the “data” to be explained must include “all” the raw information from which the meanings of the symbols involved may be deduced.

 

Exactly the same arguments go to all of his other complaints. He is simply not concerning himself with the issues we are talking about basically because he cannot even comprehend such an endeavor.

No approximation of the fundamental equation will yield classical mechanics, as I've said many times.

If Erasmus has any understanding of modern physics at all, he is fully aware of the fact that all results of classical mechanics are fully consistent with quantum mechanics so long as the appropriate approximations required to hide the errors in classical mechanics are made: i.e., there exists no classical result which can be used to disprove quantum mechanics.

 

Furthermore, when he claims classical mechanics is an internally consistent system, he is making the assumption that measurements implied by standard classical mechanics can be made: i.e., classical mechanics is based upon a great many underlying assumptions which are presumed to be valid without analysis. When I say it must be consistent with “all” information, I mean nothing at all may be presumed. Erasmus consistently wants to talk about compartmentalized problems which involve a collection of supposed understood information. That is just not what we are talking about.

Change the scale of literally everything by a factor of about 10^16 and quarks will no longer be bound together as protons.

That is a totally idiotic statement as, if absolutely “everything” was scaled by a factor of 10^16 how could one possibly know that such a scaling factor had been imposed? Erasmus’s assertion is obviously based upon some theory he is presuming to be correct.

 

Erasmus has utterly no interest in discussing the problem I have solved as he is firmly convinced that solving that problem is impossible. As far as he is concerned, the only way to attack the problem of explaining anything is through compartmentalized thinking. So long as he sticks to his prejudices, talking to him is a total waste of time.

 

Have fun -- Dick

[AnssiH]

Well DD just posted a reply when I was about to. I thought it was pretty much to the point, and I hope you don't take it as an insult this time. I have to say it is little bit bothersome to receive comments that are clearly arising from confusion about what the subject is. I'll still give it a stab myself.

 

Ignore Newtonian mechanics for a second- can we agree that if a given explanation predicts something with either 100% certainty or 0% certainty, then the resulting [imath]\psi[/imath] function (no matter how you map it) must be strongly peaked? i.e. its essentially 1 at one point, and 0 everywhere else?

 

Yes, according to my understanding that would be the case.

 

I.e. if a given explanation assumed determinism (i.e. held a philosophical stance over and beyond induction, which is what all the definitions are fundamentally based on).

 

But I do not understand why the fundamental equation expressing the constraints on [imath]\psi[/imath] that way means that no explanation taking that deterministic stance could be seen as being in agreement of those constraints? I do not understand why do you take it as impossibility that a given explanation could make some appropriate approximations/assumptions in its definitions, which imply deterministic predictions?

 

I am under the impression this has got something to do with mathematical behaviour of the concepts DD is using, as you seem to be commenting here;

 

How can we take a derivative of this? Further, is there ANY strongly peaked function that can solve Dick's equation? I contend the answer to the second question is no.

 

but I don't understand that very well either. I think DD's reply on this issue might be more useful for you. Or not...

 

Anyway, what I really wanted to say;

 

The universal equation, as described, it doesn't matter where the information comes from. Its totally unknown.

 

Yes.

 

ANY explanation for ANY data set should conform to the analysis.

 

No. We are talking about explanations to unknown data, not "any data", for instance, not data whose meaning is pre-defined at the statement of the problem. Which is the case in the axiomatic newtonian mechanics.

 

Maybe Newtonian mechanics has confused the issue by implying physics information, how about the data set "the digits of pi." I can provide an equation that will allow you to predict with 100% certainty what the nth digit of pi is. This is clearly an explanation of the set {digits of pi} in the sense that Dick wants.

 

No, it is completely off-subject, exactly what he does not want. "Explaining unknown data" is not the same thing as "explaining pi". Your statement is starting with the knowledge that you already know what is being explained.

 

The subject is about explaining information whose meaning is unknown; such task means build an idea of what is it that you are looking at in the first place, in the attempt to start predicting the data. (We are interested of generating expectations)

 

(See the parallels with building a world view about reality, and of how you can never obtain explicit knowledge about it?)

 

That also means you can't set up a problem even with the premise that you are receiving "numbers", as you would have already pre-defined these are indeed "numbers" we are looking at.

 

Likewise, you can't set up a problem with the premise that you are receiving data points, that would also be a pre-defined statement.

 

The discussion of the issue in terms of "data points" is just to refer to a representation of "some data". We are being very careful to NOT imply anything about the actual behaviour of those data points (as that would mean an assumption has been made about the nature of the data)

 

Think of it rather as building a world view based on some patterns of some sort, and obviously doing so via inductive reasoning. The definitions of your world view are essentially containers for the patterns; via those definitions you are taking a stance about what something is supposed to mean (in your opinion).

 

No approximation of the fundamental equation will yield classical mechanics, as I've said many times.

 

I'm sorry, but having followed the derivation of Schrödinger's equation (and thinking about the approximations involved), and knowing that newtonian mechanics can be seen as a further approximation of it, is slightly more convincing than you saying many times such a thing cannot be done.

 

What it means to me, that those approximations yield newtonian mechanical relationhsips, is simply that the definitions of newtonian mechanics can be seen as arising from the necessity to wrap those recurring patterns into terminology of persistent objects, in self-coherent manner, i.e. the form of comprehension of those persistent objects that obey newtonian mechanics, can be seen as an epistemological issue entirely.

 

But your assertion is wrong- Newtonian mechanics has all the same symmetries that Dick imposes.

 

Obviously you should not equate the symmetries represented by the fundamental equation, with the (similar looking) symmetries of newtonian mechanics in such a straightforward manner. There are quite a few issues to consider before you get from infinitesimal dust-mote representation with flattened [imath]\tau[/imath] dimension to the definitions of newtonian mechanics.

 

I think you are viewing this issue with far too much haste to have made that interpretation... Look, I don't mind if you don't feel like spending the time to really think about it, but as long as you don't, making these seemingly random comments from left and right is not that appreciated...

 

No, it is NOT true for modern physics. Thats the problem- you are assuming you know what modern physics says because you can't imagine the world not working the way you want! Modern physics is NOT scale invariant- if you change the scale of absolutely everything you get different physics! Obviously, we can never measure this, but we can take the theory, change the scale of everything, and see what happens in the explanation.

 

Change the scale of literally everything by a factor of about 10^16 and quarks will no longer be bound together as protons.

 

Oh my god are you serious...?

If you change the scale of absolutely everything, there is nothing to detect any change. Of course this is true for modern physics, and for any given description of anything.

 

I know what they typically mean by "scale invariance" of various things in physics. And obviously they mean the idea of scaling SOME aspects of something, while leaving the rest of the universe intact. Like speed of light or some properties of space etc.

 

And the quarks not being bound together; did you remember to scale the speed of light, and everything that gives you the definition of lengths? Look at whatever equation describes that situation, and scale everything associated with that equation. How would you imagine getting any different predictions?

 

Come on, there must be other people reading this and doing a facepalm right now? Right?

 

EDIT: I'm thinking you may be assuming that the [imath]x,y,z,\tau[/imath] space somehow contains a definition for lengths in its own definitions, and scaling information in it would thus mean scaling everything except those aspects that are used to define/measure lengths? This may be related to the same confusion as what makes you refer to all sorts of defined data as "unknown data"... Think about this a bit, the [imath]x,y,z,\tau[/imath] space contains the representation of ALL the information that is your world view, and it is that information that gives you the meaning of lengths. Different world views define it differently, after all.

 

Discrete data means that the information that went into generating an explanation, was of finite amount.

Actually, no.

 

Actually yes, that is exactly what it means, you made a knee-jerk comment without understanding the subject once again, and it's bothersome. I would think if you were actually interested, perhaps you would ask a question instead of voice the first random thought that pops into your mind.

 

The representation of the "unknown data" is seen as discrete, under the fact that any explanation of anything is always based on finite amount of information.

 

That is, we know that information can be represented as a discrete set of data points. We know it would be invalid to represent it as continuous.

 

Hence; "Discrete data means that the information that went into generating an explanation, was of finite amount."

 

-Anssi

[Erasmus00]

Once again, you and Dick have missed the point by thinking you understand what I am getting at, without really considering what I'm saying. Instead of assuming I'm making a horrible mistake and don't know what I'm talking about, please take a moment to read. Consider that not even once have I felt my concerns have been directly addressed- this is why I keep restating myself.

 

I think the problem ultimately is, AnssiH, that you don't have a clear understanding of the mathematical operations Dick is using, so when there are serious constraints implied by the mathematics he is using, you don't notice. If you are familiar with the idea of a derivative, please do me a favor- sit down with a grid, and plot out some deterministic probability distributions (either 0, or 1 at a given point in space). Now, what will the derivative look like?

 

Further, by trying to use (in my mind) familiar examples such as classical mechanics, I seem to have brought some baggage with the terms. When I say classical mechanics, I mean a set of mathematical axioms disconnected from a physical interpretation. These axioms make predictions in a mathematical space (x,t) space. There are no definitions about what these objects mean, simply a set of recipes to create predictions. When you hear classical mechanics, you apparently think of the set of rules that relate physical objects to these mathematical rules- this has a further set of axioms, etc. With one small exception, I recommend we drop this discussion and switch to digits of pi.

 

My last bit on Newtonian mechanics:

I'm sorry, but having followed the derivation of Schrödinger's equation (and thinking about the approximations involved), and knowing that newtonian mechanics can be seen as a further approximation of it, is slightly more convincing than you saying many times such a thing cannot be done.

 

Newtonian mechanics is NOT an approximation of Schroedinger's equation. You need additional assumptions to move from Schroedinger's equation to newtonian mechanics- you need what is known as the measurement postulate of quantum mechanics. This is not contained in Schroedinger's equation.

 

 

Anything can count as a set of data, and any known set of data can become an unknown set of data simply by removing context. In this case, take the first few digits of pi, 31415. Dick points out, rightly, that there are many explanations to this set of data. Thats fair and I agree. However, at least one explanation, (the digits of pi explanation) has probability distributions that are binary. Each point in representation space will have a 100% or 0%. The digits of pi explanation IS valid, but DOES NOT solve Dick's equation. Therefore, Dick's equation does not contain every explanation- at best it contains explanations that generate continuous probability distributions!

 

If you change the scale of absolutely everything, there is nothing to detect any change. Of course this is true for modern physics, and for any given description of anything.

 

This is a philosophical assumption you bring to the table- my argument is that there are explanations, such as QCD, in which there is no dimensionful parameter involved in the theory, but the theory itself naturally generates one. Changing all the length scales in the problem will not change the naturally generated scale. This is fundamentally related to the fact that a point charge cannot scale in size (it exists at one point).

 

As far as we know, the universe works this way, but that isn't important- what IS important is that Dick's equation cannot capture such behavior.

 

The representation of the "unknown data" is seen as discrete, under the fact that any explanation of anything is always based on finite amount of information.

 

That is, we know that information can be represented as a discrete set of data points. We know it would be invalid to represent it as continuous.

 

Two things- first even an infinite amount of discrete data leads to a discrete distribution. This was the point I was making. Look at the counting number {1,2,3,4,5...} there are an infinite number of them but they are discrete.

 

Now, finally- we come to the heart of all of this classical mechanics/digits of pi/etc. you say (repeating for emphasis):

 

That is, we know that information can be represented as a discrete set of data points. We know it would be invalid to represent it as continuous.

 

The operation Dr. Dick takes to enforce his symmetry constraints is a derivative which can only act on a continuous distribution. IF IT IS INVALID to represent this as a discrete set of data points, it is invalid to take a derivative, and Dick's equation is invalid.

[Rade]

...we know that information can be represented as a discrete set of data points. We know it would be invalid to represent it [information] as continuous.

AnssiH---I do not understand how the fundamental equation of DD requires that it is invalid to represent information as being continuous ?

 

While it is true that one can represent information as a discrete "set" of data points (such as the set [1,2]; [0,1]; [2,5]..etc) it is also true that information can be represented as a continuous sequence of individual datum.

 

Take for example the "bit" computer code, which is a binary digit code, where a "bit" is an individual 1 or 0 in a binary numeration system. If you select some code format to represent a sequence of "bits", such as ASCII, you can form a representation of information that can be the basis of some interpretation or explanation. Thus the continuous ASCII binary code sequence ...11100101110010001110001111000...if expanded to 38,804,992 bits, in one and only one sequence (a single finite number), represents the song 'Toxic' by Britney Spears when played on your MP3. However, if you take the exact same bit sequence and format it as a JPEG file, it will have a completely different explanation--perhaps a picture, not a song. In fact, because there are an infinite number of imaginary file format codes that can be used to operate on those specific 38,804,992 bits of information, there are an infinite number of explanations possible for them--and not a single 1 or 0 needs to be moved out of sequence.

 

My point being, your comment suggests that it is invalid to represent "information" as a continuous sequence (which is clearly false), thus suggesting that any continuous sequence of bit information does not apply to the fundamental equation of DD, which also seems like a false statement, for the simple reason that the equation would then not be fundamental--DD could not explain how the voice of Britney could emerge from a continuous sequence of binary information. I mean, we need DD's equation to at least in theory be able to explain Britney--correct ?

 

What am I missing in my understanding (or lack of) your comment ?

[AnssiH]

Once again, you and Dick have missed the point by thinking you understand what I am getting at, without really considering what I'm saying. Instead of assuming I'm making a horrible mistake and don't know what I'm talking about, please take a moment to read. Consider that not even once have I felt my concerns have been directly addressed- this is why I keep restating myself.

 

Don't worry, I'm trying to understand what you are trying to say, I'm confident we are talking past each others because of holding different unvoiced assumptions.

 

One such problem is definitely that in your mind "unknown information" appears to refer to something very different than what is meant in the analysis. That could explain almost every problem we have had in our communication, and it is certainly important issue to get absolutely right.

 

I think the problem ultimately is, AnssiH, that you don't have a clear understanding of the mathematical operations Dick is using, so when there are serious constraints implied by the mathematics he is using, you don't notice. If you are familiar with the idea of a derivative, please do me a favor- sit down with a grid, and plot out some deterministic probability distributions (either 0, or 1 at a given point in space). Now, what will the derivative look like?

 

There are no derivatives, or at most they could be seen as 0? Is that what you are getting at, I mean I get that part. I don't understand why that means there could not exist explanation that takes the philosophical stance of determinism.

 

Remember two things, it is always an extra assumption (or approximation) on what can be known inductively, and second, we are explicitly talking about explanations that generate expectations for information that is totally undefined at the get-go. We are not talking about a small set of definitions associated with pre-defined information.

 

Further, by trying to use (in my mind) familiar examples such as classical mechanics, I seem to have brought some baggage with the terms. When I say classical mechanics, I mean a set of mathematical axioms disconnected from a physical interpretation. These axioms make predictions in a mathematical space (x,t) space. There are no definitions about what these objects mean, simply a set of recipes to create predictions. When you hear classical mechanics, you apparently think of the set of rules that relate physical objects to these mathematical rules- this has a further set of axioms, etc. With one small exception, I recommend we drop this discussion and switch to digits of pi.

 

Sure.

 

Newtonian mechanics is NOT an approximation of Schroedinger's equation. You need additional assumptions to move from Schroedinger's equation to newtonian mechanics- you need what is known as the measurement postulate of quantum mechanics. This is not contained in Schroedinger's equation.

 

In my mind approximation and assumption is the same thing, at least that is the case with the approximations involved between fundamental equation and Schrödinger's equation. I.e. it contains the types of assumptions, that certain circumstances produce such a negligible effect that they can be ignored.

 

One approximation/assumption involved with getting from undeterministic probabilities to deterministic probabilities would be that having seen one circumstance to lead to another circumstance every time thus far, means it will do the same thing every time from this point on also. That is obviously undefendable assumption, i.e. a philosophical stance.

 

I know what you are thinking though, the assumptions that lead from Schrödinger's equation to newtonian mechanics make assumptions about what the data itself is. That question remains, but it needs to be thought quite carefully through, because it is not at all clear what aspects are actually related to the nature of the data (require it to be of specific kind) and what aspects are related to that transformation from unknown events to defined persistent entities. So far in the analysis very many physical quantities have shown to be related to the transformation, not to the data.

 

Anything can count as a set of data, and any known set of data can become an unknown set of data simply by removing context. In this case, take the first few digits of pi, 31415. Dick points out, rightly, that there are many explanations to this set of data. Thats fair and I agree. However, at least one explanation, (the digits of pi explanation) has probability distributions that are binary. Each point in representation space will have a 100% or 0%. The digits of pi explanation IS valid, but DOES NOT solve Dick's equation. Therefore, Dick's equation does not contain every explanation- at best it contains explanations that generate continuous probability distributions!

 

Essentially your argument is that if the underlying data is based on some ontological/metaphysical rule, and if one manages to guess that rule, then he holds an explanation that does not necessarily obey the fundamental equation?

 

First comment I have is that upon building that explanation, at no point there exists explicit information that the data is based on the digits of pi, and assuming so is undefendable. I.e. high degree of confidence that this is the case, is different from making the "philosophical" assumption that the data is and always will be ontologically pi. So even then I would take the expectations to be non-binary, apart from making that assumption/approximation in undefendable sense.

 

Second comment is that I think it's dangerously close to off-topic to consider the possibilities of "accidentally" guessing the ontological nature of the data being explained. The important part to focus onto is that there are certain symmetries that your explanation must obey as long as you are NOT making undefendable guesses, and that as long as they lead to the same relationships as modern physics, what does that say about modern physics.

 

This is a philosophical assumption you bring to the table- my argument is that there are explanations, such as QCD, in which there is no dimensionful parameter involved in the theory, but the theory itself naturally generates one. Changing all the length scales in the problem will not change the naturally generated scale.

 

I assume by "naturally generates scale", you mean it is a consequence of other parameters. Can you analyze where those parameters are coming from, and whether they are properly scaled?

 

It would be very difficult for me to tell how QCD translates to [imath]x,y,z,\tau[/imath], but I don't have to because it's very simple issue if you look at it from the other angle. The [imath]x,y,z,\tau[/imath] mapping is just mapping everything that exists in the situation in terms of a given explanation, while the actual coordinate space of [imath]x,y,z,\tau[/imath] is completely immaterial notation system. If an explanation was not scale invariant, it would mean it is a function of the actual coordinate values of [imath]x,y,z,\tau[/imath], i.e. it would contain undefendable assumption (and by chance the reality happened to be staged against an actual [imath]x,y,z,\tau[/imath] that contains observable properties to itself, etc...)

 

I.e. we are talking about exactly the same issue as shift symmetry inside [imath]x,y,z,\tau[/imath] being totally immaterial. Of course it is, we just arbitrarily chose the size and origin of the [imath]x,y,z,\tau[/imath] space in the first place, that space itself doesn't have any properties having any effect on the information being mapped.

 

I don't see this as a philosophical assumption, as it is pretty much the same as saying, "it makes no difference whether I draw this diagram on the left side or on the right side of this paper".

 

In that sense, your argument about QCD, if it was valid, it would mean QDC gave different results when you printed the same graphical representation of it onto papers of different sizes. I'm quite confident each print still had the same expectations to it, surely we are talking past each others here?

 

This is fundamentally related to the fact that a point charge cannot scale in size (it exists at one point).

 

If it doesn't have a defined size, then it cannot have any consequences to other things being scaled either can it?

 

Two things- first even an infinite amount of discrete data leads to a discrete distribution. This was the point I was making. Look at the counting number {1,2,3,4,5...} there are an infinite number of them but they are discrete.

 

Yes, but I don't understand at all why you are pointing that out.

 

Now, finally- we come to the heart of all of this classical mechanics/digits of pi/etc. you say (repeating for emphasis):

That is, we know that information can be represented as a discrete set of data points. We know it would be invalid to represent it as continuous.

The operation Dr. Dick takes to enforce his symmetry constraints is a derivative which can only act on a continuous distribution. IF IT IS INVALID to represent this as a discrete set of data points, it is invalid to take a derivative, and Dick's equation is invalid.

 

"if it is invalid to represent this as continous data, it is invalid to take a derivative" I'm sure you meant to say.

 

I think you would already know the answer to this if you were interested of actually thinking this issue yourself, instead of trying to find an apparent reason to not look at it at all.

 

First, we know the information underlying the world view can be represented as discrete set.

 

That does not mean at all that a specific world view could not assume continuous aspects to the data (i.e. it would always be an extra assumption, not explicitly known from the information-that-was-explained)

 

Nor does it mean that the expectations produced by an explanation must be binary.

 

The derivative expressing the symmetry constraints yields universal requirement, whose violation essentially means changing expectations upon arbitrary changes to the representation of the data. A specific explanation making philosophical stances over and beyond universal necessities, does not mean it cannot be seen as an approximation to the fundamental equation. You just have to make those same approximations when working them out. Right?

 

Like I said before, the fundamental equation itself is not a constraint on how the solutions need to work mathematically. I asked you before if you can think of another way to express the same universal requirements, in the attempt to make you think about the fact that making an assumption of binary probability distribution is ALWAYS a specific assumption, not a universal fact.

 

AnssiH---I do not understand how the fundamental equation of DD requires that it is invalid to represent information as being continuous ?

 

It is just to say, that the information that an explanation is based on, is of finite amount, always.

 

It doesn't mean that a specific explanation could not represent information as continuous. I.e. make an assumption that there is more going on in reality than what is "explicitly known".

 

-Anssi

[Rade]

It is just to say, that the information that an explanation is based on, is of finite amount, always. It doesn't mean that a specific explanation could not represent information as continuous. I.e. make an assumption that there is more going on in reality than what is "explicitly known".

OK, thanks--you are talking about "an explanation", not "explanation itself". However, "explanation itself" (in general) is possible if the underlying information is infinite--correct ? I mean, the only requirement here is that, given that the information available for "explanation itself" is infinite, that all attempts to make a "specific explanation" would change over time as more unknown underlying information was added to that already under consideration--correct ?

 

First, we know the information underlying the world view can be represented as discrete set

How do we know this ? It would help if you use the Britney Spear song example I posted above. So, from that example, what is the "world-view", (is it the song 'Toxic' as a whole ?) what is the "underlying information", (the words of the song, the voice, the music notes on a page, the {1,0..} bits of computer information ?), what is the "discrete set", and finally, what do you mean "we know". Do we know with 100% certainty or is there some uncertainty in what we know about how we "represent" the underlying information ? Sorry, I ask this in a simple minded way but a clear example of how the words you use to a visual example using "bits" of information and set {} notation would help me better understand the words. Thanks.

[AnssiH]

OK, thanks--you are talking about "an explanation", not "explanation itself". However, "explanation itself" (in general) is possible if the underlying information is infinite--correct ? I mean, the only requirement here is that, given that the information available for "explanation itself" is infinite, that all attempts to make a "specific explanation" would change over time as more unknown underlying information was added to that already under consideration--correct ?

 

Uh... it is just to say that whatever information "was under consideration" when a given explanation came to be, was of finite amount.

 

If by "underlying information" we refer to the information that was taken into account, then no that cannot be seen as of infinite amount, since you can't take infinite amount of information into account.

 

If by "underlying information" you instead refer to some hypothetical amount of information, "ultimately available inside reality" (so to speak), then you could say that can possibly be of infinite amount, but that hypothesis has got no consequences that need to be taken into account for universal analysis about explanations, as there's no need to consider an explanation that actually has taken infinite amount of information into account. That is logically impossible.

 

First, we know the information underlying the world view can be represented as discrete set

How do we know this ?

 

In that sentence "information underlying the world view" was referring to the former idea, "whatever information has been taken into account".

 

It would help if you use the Britney Spear song example I posted above. So, from that example, what is the "world-view", (is it the song 'Toxic' as a whole ?) what is the "underlying information", (the words of the song, the voice, the music notes on a page, the {1,0..} bits of computer information ?),

 

The "underlying information" refers to a form that cannot be actually represented; it is the information in undefined form (undefined, as in, you cannot define a representation form). So it is not words, voice, notes nor bits.

 

We cannot actually picture or think about the underlying information at all, as to do so would be to define it some way.

 

Only facets of that "undefined form" we can represent at all are:

 

1. A finite amount of the aspects of "underlying reality" were considered upon building an explanation for it (thus, we are not concerned by the possibilities of continuous nature for the "information actually underlying a world view")

 

and

 

2. A valid explanation for that information does not contradict itself; the expectations it gives for specific circumstances are always the same for that specific circumstance; the expectations do not change arbitrarily (or upon immaterial changes to the representation of that circumstance).

 

We don't know what those circumstances are or how they are supposed to be mapped, nor do we know what those actual expectations are. We just know about the expectations not changing arbitrarily. I.e we know the fundamental equation applies to the explanation of the data, without knowing anything about the data itself.

 

Very many people try to ask questions about this by asking for examples of already defined things, which is just them going off-subject. There are no objective arguments to be made about those already defined things, I could only argue about the aspects of those specific definitions. You are supposed to view the universal symmetry requirements of expectations, not specific mappings of information.

 

what is the "discrete set", and finally, what do you mean "we know". Do we know with 100% certainty or is there some uncertainty in what we know about how we "represent" the underlying information ?

 

I trust the above gave you an answer to this.

 

Sorry, I ask this in a simple minded way but a clear example of how the words you use to a visual example using "bits" of information and set {} notation would help me better understand the words. Thanks.

 

And to this.

 

There's no reason to agree upon a specific mapping of information, as long as the reader understands the argument is about unchanging expectations upon immaterial changes to ANY mapping. The argument is not about any specific mapping.

 

-Anssi

[Erasmus00]

In my mind approximation and assumption is the same thing, at least that is the case with the approximations involved between fundamental equation and Schrödinger's equation.

 

Approximations act on the equation to change it. However, to get classical mechanics we need the additional axiom "when someone takes a measurement, the system stops evolving based on the Schroedinger equation." Since the content of Dick's analysis is based on his equation, you cannot consistently make an assumption that it is invalid.

 

 

Essentially your argument is that if the underlying data is based on some ontological/metaphysical rule, and if one manages to guess that rule, then he holds an explanation that does not necessarily obey the fundamental equation?

 

Not quite. Lets look at it this way: if there exists ANY self-consistent explanation of some data that doesn't solve the fundamental equation, then Dick's equation is wrong. In this case ONE possible explanation of {3,1,4,5..} is the digits of pi. This explanation can't solve the fundamental equation, but IS a valid explanation. Regardless of whether that explanation is justified, it is valid.

 

I assume by "naturally generates scale", you mean it is a consequence of other parameters. Can you analyze where those parameters are coming from, and whether they are properly scaled?

 

No, if it was a consequence of the other parameters, then obviously the theory would be scale invariant.

 

I don't see this as a philosophical assumption, as it is pretty much the same as saying, "it makes no difference whether I draw this diagram on the left side or on the right side of this paper".

 

In that sense, your argument about QCD, if it was valid, it would mean QDC gave different results when you printed the same graphical representation of it onto papers of different sizes. I'm quite confident each print still had the same expectations to it, surely we are talking past each others here?

 

Yes, that is exactly the implication. If you routinely blow up the theory on different sizes of paper, and do calcuations it will make different predictions.

 

If it doesn't have a defined size, then it cannot have any consequences to other things being scaled either can it?

 

Because the point charges have no size to scale, they can create effects that won't scale with the system- its a mathematically possible feature of explanations that the "fundamental equation" will never show.

 

Yes, but I don't understand at all why you are pointing that out.

 

The point is that even with an infinite amount of data taking, you can never create a continuous representation with Dick's mapping. It is never valid to take derivatives.

 

First, we know the information underlying the world view can be represented as discrete set.

 

That does not mean at all that a specific world view could not assume continuous aspects to the data (i.e. it would always be an extra assumption, not explicitly known from the information-that-was-explained)

 

So then Dick's equation does not produce ALL possible explanations, it produces those explanations that take the specific worldview that there are "continuous aspects to the data." This is a completely different claim.

 

Like I said before, the fundamental equation itself is not a constraint on how the solutions need to work mathematically. I asked you before if you can think of another way to express the same universal requirements, in the attempt to make you think about the fact that making an assumption of binary probability distribution is ALWAYS a specific assumption, not a universal fact.

 

I agree, its a specific assumption- my point is not that the universal equation is never valid, my point is that SPECIFIC EXPLANATIONS fail to fit it! I'm talking about binary probability distributions not because I think they are universal, but because they are the specific case that breaks the analysis!

 

Also, yes, the fundamental equation IS a constraint on how the explanations need to work mathematically- if an explanation fails to make Dick's "continuous" assumption, it can never solve the equation, and in that case, what is the point of the fundamental equation?

[Doctordick]

Erasmus, I will direct this post to you though I fully expect you to ignore the thing entirely. Although Anssi’s comprehension of what I am doing is far in excess of yours, his knowledge of physics makes it quite difficult for him to argue with your ridiculous complaints. And, if you understood what the problem I have solved was, the ridiculousness of your complaints would be clear to you. I don’t think you are a stupid person.

Approximations act on the equation to change it. However, to get classical mechanics we need the additional axiom "when someone takes a measurement, the system stops evolving based on the Schroedinger equation." Since the content of Dick's analysis is based on his equation, you cannot consistently make an assumption that it is invalid.

First, the content of my analysis is based on the definitions behind my equation.

It is then clear, at this point, that the problem of finding [imath]\vec{\Psi}[/imath] is one of interpolation. We need to find a function which fits the known circumstances (known for specific t indices) and use that function to express the hypothetical probabilities for all circumstances outside those known circumstances.

My equation does not change; however, the data which the solution is required to fit changes every time the underlying data changes: i.e., new data is obtained. This is essentially exactly what happens when the solutions to Schrodinger's equation “collapse”: i.e., one’s expectations for the future are changed. So long as no measurements are made, the distribution of probabilities consistent with all valid explanations are given by the specific solution consistent with the known data (which, of course, can be seen as “evolving” because of that “t” parameter). Note that the “present” is defined to be a change in the known data thus this “evolving” only happens “out of sight” so to speak.

 

The issue here is prediction of one’s expectation. The solution of my fundamental equation yields probability distributions for the future (where the future is defined to be what is not known) consistent with the “finite” amount of data upon which those expectations are based. The solution changes every time the data changes. It should also be clear to you that the data which the solution is required to fit is often a discrete thing. In fact, that data would be non discrete only if there were uncertainty in the actual nature of that underlying data.

 

The fact that classical mechanics is not a valid representation of all possibilities should be obvious to anyone who has ever run into one of those “series” problems in an intelligence test. The solutions to those “series” problems are base on the assumption that the missing element is exactly in accordance with the given pattern: i.e., there is absolutely no information missing. The fundamental error is the required use of induction. My equation is based on deduction only. The equation is no more than a constraint that the “inductive” result (the actual specific theory) must fit the known data exactly. As such, no valid solution can result in a discrete probability distribution unless it happens to be an eigenvalue of that equation. On the other hand, in the absence of eigenvalues the solutions can still be highly localized to specific values which approximate discreet values.

Not quite. Lets look at it this way: if there exists ANY self-consistent explanation of some data that doesn't solve the fundamental equation, then Dick's equation is wrong. In this case ONE possible explanation of {3,1,4,5..} is the digits of pi. This explanation can't solve the fundamental equation, but IS a valid explanation. Regardless of whether that explanation is justified, it is valid.

Why do you keep saying that “the digits of pi” is a solution to my equation? “The digits of pi” is an explanation of nothing if it is standing alone! You have simply omitted all of the data necessary to make that comment meaningful. Suppose I asked you for an explanation of “pdigle”. Would you give me 3,1,4,5 based upon that request? Surely you must comprehend that “pdigle” could possibly be translated into “the digits of pi” in some hypothetical language. In order to give you the proper problem to explain, there is one hell of a lot of other information which needs to be specified. You are apparently addicted to compartmentalization of the problems you want to analyze: i.e., in every example you give you insist on presuming valid information outside your specified example exists.

 

Furthermore, you don’t seem to comprehend that “an explanation” has been defined (for the purpose of this presentation, to be a procedure for assigning probabilities to unknown information and your assertion that discrete results violates that equation presumes “eigenvalues” solutions for definable operators can not possibly exist. That is a somewhat ridiculous presumption.

The point is that even with an infinite amount of data taking, you can never create a continuous representation with Dick's mapping. It is never valid to take derivatives.

The data amounts to specific results which must be members of the probability distribution implied by [imath]\vec{\Psi}[/imath]. There is no connection between the continuity of the data and the continuity of [imath]\vec{\Psi}[/imath]. All you are doing here is demonstrating your complete lack of understanding of the character and meaning of my equation.

I agree, its a specific assumption- my point is not that the universal equation is never valid, my point is that SPECIFIC EXPLANATIONS fail to fit it! I'm talking about binary probability distributions not because I think they are universal, but because they are the specific case that breaks the analysis!

It appears that you have no understanding of what is ordinarily called “eigenvalues”. Discreet values for defined operations under specific boundary conditions (think known data) in no way imply the solution to the equation ([imath]\vec{\Psi}[/imath]) can not be continuous.

 

Anssi, believe me, this person has utterly no concept of what we are talking about; he is simply throwing up unthoughtout cavils in an attempt to discourage people untrained in physics from thinking about my presentation. As far as “scale dependence” goes, there has to be some kind of scale dependence in the presumptions of the theory in order to violate universal scale symmetry: i.e., Erasmus is omitting to present all the underlying presumptions, i.e., he insists on compartmentalizing once more. The real problem here is the fact that compartmentalization is universal aspect of any theory in any modern science and trained scientists simply can not comprehend the existence of an absolute holistic solution to any really complex problem.

 

I pretty well prove that in my demonstration that any three dimensional distribution of points (think of the entire universe we find ourselves in) can be seen as the projection of an n dimensional object on a three dimensional manifold. See my post, “A simple geometric proof with profound consequences”.

I am of the opinion that the following proof is of great significance when one goes to consider "emergent" phenomena and the complexity achievable from simple constructs. The proof concerns a careful examination of the projection of a trivial geometric structure on a one dimensional line element.

A corollary extending that proof to three dimensions can be found at the end of that post. The issue of scale is clearly immaterial in that proof.

 

Have fun -- Dick

[Erasmus00]

My equation does not change; however, the data which the solution is required to fit changes every time the underlying data changes: i.e., new data is obtained. This is essentially exactly what happens when the solutions to Schrodinger's equation “collapse”: i.e., one’s expectations for the future are changed.

 

This is the problem is the subtlety that in quantum mechanics measurements can correlate. This means that measurements that Bobs make can effect events in Alice's future even if Bob doesn't communicate with her. I fail to see how this "psi adjusts with data" approach can model that.

 

The fact that classical mechanics is not a valid representation of all possibilities should be obvious to anyone who has ever run into one of those “series” problems in an intelligence test. The solutions to those “series” problems are base on the assumption that the missing element is exactly in accordance with the given pattern: i.e., there is absolutely no information missing. The fundamental error is the required use of induction.

 

But this alters what you are claiming- instead of representing any possible explanation, you seem to now claim your solution represents some sort of probabilistic ensemble of potential explanations- this is a different claim.

 

The equation is no more than a constraint that the “inductive” result (the actual specific theory) must fit the known data exactly. As such, no valid solution can result in a discrete probability distribution unless it happens to be an eigenvalue of that equation.

 

Why? What part of your solution gives an interpretation that involves eigenvalues? To get quantum mechanics to yield reasonable predictions we make the additional assumption that a measurement can only return an eigenvalue, but this is an assumption. Why do eigenvalues have any special importance in your explanation-model?

 

There are certainly inductive results that DO fit data sets that yield discrete distributions.

 

Why do you keep saying that “the digits of pi” is a solution to my equation? “The digits of pi” is an explanation of nothing if it is standing alone!

 

No, I'm saying that if you have a data set that is {3,1,4,...} one such explanation is that these comprise the digits of pi. Its not the ONLY explanation, but it is one. Digits of pi can be formalized by saying its the spigot formula for digits of pi Bailey–Borwein–Plouffe formula - Wikipedia, the free encyclopedia. No other information is needed only the set of unknown data {3,1,4,1,5,9...}. Another explanation is that it is random- I also fail to see how a random (or pseudo-random) number generator can solve your non-stochastic equation. I fail to see how I'm requiring any information other than the set of numbers to be explained.

 

Furthermore, you don’t seem to comprehend that “an explanation” has been defined (for the purpose of this presentation, to be a procedure for assigning probabilities to unknown information and your assertion that discrete results violates that equation presumes “eigenvalues” solutions for definable operators can not possibly exist.

 

It is my understanding that psi represents the probability amplitudes for a given data set. Even if its an eigenvalue for your operator, the probability (eigenfunction) for any given data point is still continuous.

 

There is no connection between the continuity of the data and the continuity of [imath]\vec{\Psi}[/imath]. All you are doing here is demonstrating your complete lack of understanding of the character and meaning of my equation.

 

I agree, but there are clearly many explanations of discrete data that are themselves discrete. My point is that an explanation yielding discrete probabilities won't solve your equation, and SOME explanations will yield discrete probabilities (an explanation of a set of only integers should produce a zero probability for a non-integer)

 

Anssi, believe me, this person has utterly no concept of what we are talking about; he is simply throwing up unthoughtout cavils in an attempt to discourage people untrained in physics from thinking about my presentation.

 

I honestly don't care if other people read your presentation- I'm trying to figure out what you are tying to say, and raising objections as I see them. Consider the amount of time I've clearly spent trying to get at what you are talking about.

 

As far as “scale dependence” goes, there has to be some kind of scale dependence in the presumptions of the theory in order to violate universal scale symmetry: i.e., Erasmus is omitting to present all the underlying presumptions, i.e., he insists on compartmentalizing once more.

 

No, I'm not, this is again your philosophical bias- you don't understand how a universal scale symmetry can fail, so you claim its impossible. In a system where a scale is generated dynamically by point particles, scaling won't change that dynamic scale (the point particles don't scale, as points don't scale). There is no scale dependence in the theory (the lagrangian is, in fact, scale invariant). I'm not talking about scaling some subset of everything, I'm talking about scaling literally everything.

[AnssiH]

I decided to reply out of order, simple things first;

 

In that sense, your argument about QCD, if it was valid, it would mean QDC gave different results when you printed the same graphical representation of it onto papers of different sizes. I'm quite confident each print still had the same expectations to it, surely we are talking past each others here?

Yes, that is exactly the implication. If you routinely blow up the theory on different sizes of paper, and do calcuations it will make different predictions.

 

I'm absolutely certain we are talking past each others; The only way that I can make sense of your comment is if by "scaling everything" you mean scaling things in terms of some definition of lengths (I suppose that is the only way "scale everything" makes sense to you; you are not thinking of this from the point of view of undefined information).

 

What I am referring to is the same as just scaling a picture that contains the statements of lengths in itself, i.e. when scaling "everything", I mean you'd be scaling the 1 meter reference grid as well.

 

I'm saying that because the [imath]x,y,z,\tau[/imath] does not carry the definition of lengths, it is the information itself that does (picked up via generating appropriate definitions). So whatever numbers you have chosen to lay down in that coordinate system is entirely immaterial. I.e. the scale on the numbers that you use to refer to that space, is arbitrarily chosen. I.e. your expectations cannot be a function of that number, because you did not get that number from the information-to-be-explained. If you choose to change that scale of your choice later on (universally), you are essentially just choosing to refer to what used to be one number, with another number. Sort of analogous to choosing to refer to "1 meter" as "3.28 feet" instead.

 

If you pick up on what I'm saying, I can't believe you'd have any objections to it.

 

Next, the most important point to clear out (nothing in the analysis makes sense if this part isn't understood properly);

 

if there exists ANY self-consistent explanation of some data that doesn't solve the fundamental equation, then Dick's equation is wrong. In this case ONE possible explanation of {3,1,4,5..} is the digits of pi. This explanation can't solve the fundamental equation, but IS a valid explanation. Regardless of whether that explanation is justified, it is valid.

...you don’t seem to comprehend that “an explanation” has been defined (for the purpose of this presentation, to be a procedure for assigning probabilities to unknown information...

 

"Explanation" was defined to be a procedure for assigning probabilities to unknown information, and by unknown we are referring to information whose meaning is not known at all, i.e. it is "undefined". This is extremely important point to get right, because the symmetry arguments rest on the very idea of the meaning of the information being unknown. (think about where the symmetry arguments came from, obviously they don't apply with pre-defined information)

 

That means that your example, where the information is set to be "numbers" (of pi) at the get-go, does not refer to "an explanation" as its been defined.

 

Look at it this way; when the meaning of the information is unknown, your expectations of it are based on familiarity of recurring patterns (exclusively on patterns, not "individual data points" in any sense), and the chosen definitions for the patterns, and their mapping onto a coordinate system with their associated expectations, cannot be a function of that coordinate system itself. The coordinate system was just a made up thing to contain the information in a specific form, which we call "our worldview".

 

If your expectations cannot be a function of the coordinate system, it means you are mapping information and expectations in it in accordance of shift symmetry (and scale symmetry).

 

But if you start a problem by stating what the explained thing is, the symmetry arguments do not apply. When you suggest a problem like that, you are not even on the topic of generating explanations for unknown things. (And that's the fundamental problem of trying to come up with a counter-example with small set of defined things, and considering it to be "an explanation")

 

Basically your objection is based on mis-representation of the analysis, just like twin paradox is an objection to relativity only when relativity is being mis-represented.

 

I think if you understand the above, it should also answer quite many of your questions already.

 

Approximations act on the equation to change it. However, to get classical mechanics we need the additional axiom "when someone takes a measurement, the system stops evolving based on the Schroedinger equation." Since the content of Dick's analysis is based on his equation, you cannot consistently make an assumption that it is invalid.

My equation does not change; however, the data which the solution is required to fit changes every time the underlying data changes: i.e., new data is obtained. This is essentially exactly what happens when the solutions to Schrodinger's equation “collapse”: i.e., one’s expectations for the future are changed.

This is the problem is the subtlety that in quantum mechanics measurements can correlate. This means that measurements that Bobs make can effect events in Alice's future even if Bob doesn't communicate with her. I fail to see how this "psi adjusts with data" approach can model that.

 

I do see it, and in fact I would go so far as to say that this is the first satisfying explanation as to why Bob's measurements appear to affect Alice's measurements, even when those measurements are separated by space-like distances. At least "satisfying" as long as one is not insisting on knowing the ontological structure of reality (I think it is sort of invalid to even ask for that). This is a bit tricky to explain without going through the actual analysis in detail, but I can always try.

 

Think about it this way; the symmetry arguments arise from immaterial aspects of the mapping of some information, and together with few universally applicable definitions, they lead to relationships that appear in modern physics too. Thus we can say something about what sorts of circumstances in the mapping are perceived as some familiar defined objects, such as "a photon" (and some other elemental things, with or without "mass").

 

Obviously, prior to generating any definitions for some information, it is not possible to refer to any "space" either in any meaningful way. After generating some definitions, those defined elemental things appear to contain persistent identity to themselves (since we conceive them in the sense of something moving from one location to another), but epistemologically we are talking about two different observations of similar patterns. The patterns themselves cannot be said to exist inside a space (or to "move" in any sense), but if you can generate definitions that encapsulate those patterns into defined "persistent things", then there can be apparent motion to them, which in turn gives you the means to meaningfully refer to "space" (properties of which are related to the properties of your other definitions).

 

I.e. the definition(s) of space arise from man-made definitions, and are related to the same epistemological requirements as the definitions of the entities inhabiting that space (they are sort of the flip sides of the same coin). As oppose to being tied to actual explicit knowledge about any ontologically real "substances" or "volumes" or "identities" out there.

 

That is an epistemological issue entirely, which is not to argue reality is idealistic at all. It is to argue something about how reality is meaningfully handled in our minds; Perhaps its easier to view this analysis as something commenting on how the information about reality can be comprehended and tracked in terms of some (semi)stable things existing inside some space, while ontologically you can't say what is the cause of the stability behind those things. Ontologically it could be an illusion of persistence, and epistemologically it most certainly IS an illusion, in that it is not based on explicit knowledge of anything.

 

Now, the symmetry arguments always validate quantum mechanical expectations, not because reality is quantum mechanical, but because those symmetries arise from the immaterial aspects of the mapping of the information (i.e. any information can always be mapped accordingly, as long as that information is indeed ENTIRELY UNDEFINED at the get-go).

 

That leads to our case; there are circumstances in the mapped data, where a specific pattern has been taken as evidence of some "stable thing" existing in the situation, while out expectations for its future are still based on inductive expectations for that familiar pattern; our expectations still evolve via wave-like routes (remember, the definition of that thing and its expectations are a result of inductive reasoning from patterns, not a result of explicitly knowing there are such elements that actually move from one location to another in reality).

 

One example of such a circumstance would be any ordinary double-slit experiment, with any defined objects whose definition meets the appropriate criteria for observable interference pattern (a photon, an electron, a buckyball). (That something actually moved in the experiment is an extra assumption to what we know)

 

Another example of such circumstance is any expectations connected via entanglement of any sort, including Bob and Alice making measurements with space-like distances. We don't know what the underlying information was, which gave us the idea that there is (e.g.) "a photon of a specific polarity" in one place. But having uncovered the epistemological requirement of the validity of quantum mechanics, we know that seeing the circumstance that means "a photon of a specific polarity", can (and must) have a very non-classical effect onto our expectations about some other measurement, regardless of where that measurement is in our defined space (and time). Nothing propagates "immediately" through the universe when a measurement is made, but we know that our definitions for (and associated with) the elemental entities are related to each others in ways that our expectations collapse "through the universe" in such an unintuitive manner, in a so-called entanglement situation.

 

Einstein et al bringing up the EPR paradox was basically just them saying that if quantum mechanical relationships are indeed valid as they have been represented, then as a consequence "spooky action at distance" must also occur. Well, it is paradoxical only if quantum mechanics are mis-represented; only if QM definitions are mixed together with some assumptions that are undefendable aspects of a classical world view.

 

Note here that it doesn't matter at all which quantum mechanical interpretation one uses to explain that result to oneself in intuitive terms; as far as the "what we actually know" goes, every single one is equally (in)valid. What matters is that the classical intuitions, which make this result seem odd or paradoxical, are KNOWN to be invalid for epistemological reasons alone; they can't fit together with the quantum mechanical definitions (and it is always possible to generate valid QM definitions/mapping).

 

I would say that the classical intuition which is at odds with "what we actually know", is to assume that the comprehension of "space" and the stable things inhabiting it, is being caused by actual ontological identity to those defined elemental things. For all we know, they don't carry identity apart from what we place onto the patterns representing them, and if you can wrap your head around the idea of those elemental things as being merely references to certain recurring patterns (i.e. the apparent persistence to them being a result of specific definitions), it should make a whole lot more sense to investigate quantum mechanical entanglement as an epistemological feature of our comprehension of reality.

 

And if you can do that, then you should also be able to understand just where all those seemingly idealistic features of quantum mechanics arise (think of various delayed choice quantum eraser experiments, for instance).

 

Now the whole thing above applies to relativity just as much. I.e. why is it, that reality as we have defined it, obeys relativistic length and time definitions. Of course everybody understands the universe can't be said to actually contradict in length when you accelerate into a different frame. But much can be said about the epistemological reasons for our definitions of lengths behaving that way; why there must be that connection between our definition of "motion" and "length".

 

Well, it's very hard to find unambiguous words here! But perhaps you can pick up on how important it is to understand that the information-to-be-explained is indeed unknown at the get-go, since we are working with the symmetries that are a consequence of not knowing the explicit meaning of the information.

 

-Anssi

[Erasmus00]

What I am referring to is the same as just scaling a picture that contains the statements of lengths in itself, i.e. when scaling "everything", I mean you'd be scaling the 1 meter reference grid as well.

 

I understand exactly what you mean- take a picture, and blow it up. Take your theory, or representation, or what have you, and xerox it on to a larger piece of paper, etc. I'm telling you that there exist explanations where blowing up the image DOES change the predictions. You seem to be insisting thats impossible.

 

What about flipping things in a mirror (i.e. swapping left and right hands)? This is also a symmetry of Dick's explanation that is not a symmetry of modern physics.

 

If you pick up on what I'm saying, I can't believe you'd have any objections to it.

 

I've understood what you are saying, I think you aren't comprehending what I'm saying- there are explanations where the scaling you want to do DOES change the predictions. Its surprising, I know.

 

"Explanation" was defined to be a procedure for assigning probabilities to unknown information, and by unknown we are referring to information whose meaning is not known at all, i.e. it is "undefined".

 

I understand that. Any set of numbers, however, is unknown information as soon as context is removed. i.e. {3,1,4,1,5,9...}. This is unknown information- there are several explanations of this unknown information. One is that the digits are random. Another is that these are the digits of pi.

 

Also, its worth pointing out that Dick's model only works if the information is a set of numbers.

 

That means that your example, where the information is set to be "numbers" (of pi) at the get-go, does not refer to "an explanation" as its been defined.

 

But if you start a problem by stating what the explained thing is, the symmetry arguments do not apply. When you suggest a problem like that, you are not even on the topic of generating explanations for unknown things.

 

You have completely and totally missed my point. I'll reiterate as clearly as I can

 

Here is a set of undefined information {3,1,4,1,5,9..}

 

According to Dick's analysis, ANY CONSISTENT EXPLANATION MUST SOLVE HIS FUNDAMENTAL EQUATION.

 

Here is one explanation: these are the digits of pi (there are many others, including the digits are random).

 

Here is the problem- the explanation "digits of pi" can't solve Dick's equation because the probabilities they give are either 1, or 0 (this character, probability either 1 or 0 cannot be changed by any mapping). Hence, the derivative is an undefined operation, which means Dick's equation cannot apply.

 

Dick in his last post seemed to indicate that this is because his equation applies to ensembles of explanations, but that is clearly not the original claim .