"a Universal Representation Of Rules"

[Rade]

The modern conflict between relativity and quantum mechanics does not exist in my representation and I am of the opinion that the actual reason for that conflict is that Einstein's theory of General relativity is an invalid explanation.

Hello. To help with understanding your important claim:

 

1. Could you please explain what you believe the modern conflict represents.

2. Exactly what is General Relatively of Einstein an invalid explanation of ?

[Rade]

DoctorDick, one further question comes to mind.

 

In your way of thinking, what exactly is the difference between a "representation" and a "theory". An important question because you claim that your presentation is NOT a theory but a representation.

[coldcreation]

[...]

The modern conflict between relativity and quantum mechanics does not exist in my representation and I am of the opinion that the actual reason for that conflict is that Einstein's theory of General relativity is an invalid explanation. That is exactly why I am considered a crackpot as only a crackpot would consider thinking a genius like Einstein could be wrong.

 

I have pretty much the same, or similar, question as Rade.

 

a. Formulated differently, Dr. Dick, according to your representation of the constraints implied by the definition of an explanation where did Einstein go wrong?

 

b. Is your complaint that only general relativity is wrong (and if so, with which theory of gravity would you replace it), or that other discoveries made by Einstein are also wrong, e.g., special relativity, mass-energy equivalence, theory of Brownian Motion, Bose–Einstein statistics, his work on Unified Field Theory, or the photoelectric effect (pivotal in establishing quantum theory, and for which he received the 1921 Nobel Prize in Physics)?

 

 

CC

[AnssiH]

I thought I'd give a little different kind of response too, just in case it is helpful;

 

But why would we think that all of the elements that we are interested in can be classified into “symmetric/antisymmetric“ elements.

 

It's not about what kinds of elements we are "interested of", it is about how our defined elements can be associated with undefined events (or what universal limitations there exists to our possibilities to define elements/rules).

 

Actually in my mind, it is a bit of a misnomer to refer to the constraint "[imath]\sum_{i\neq j} \delta(\vec{x}_i-\vec{x}_j) = 0[/imath]" as "a rule". I prefer to view it rather as the universal constraint that arises from the existence of any rule/object definitions (any idea that there are elements with persistent existence; any idea of world lines of elements at all).

 

What the constraint states is that, no matter what those rules/element definitions are, they cannot be such that in a single circumstance there are two defined indivisible elements, who are observationally indistinguishable form each others. I.e. it is not logically meaningful to consider the same exact observable state to stand as evidence for two different defined elements.

 

A small subtlety related to all this is that the undefined events represent "whatever information that stands behind the defined elements that a particular explanation uses". It is entirely possible that there exists information that your explanation simply ignores as noise, while other explanations use that information as part of their meaningful element definitions. Either way, once you have some defined elements, you can't have definitions according to which a single element is observationally exactly the same as multiple elements.

 

The whole discussion about bosons refers to the fact that none of that prevents us from having defined elements whose unobservable behaviour is defined as such that they are taken to pass identical states. But such an idea is still only implied by some observable states, and our particular explanation about what led to those observable states.

 

I hope this answers to some things that you have in your mind...

 

-Anssi

[AnssiH]

Well DD probably won't bother responding to these because they are issues that are pretty hard to communicate and understand in different from than via understanding his actual presentation, but I'll just make a few hand-waving comments here, maybe you'll find them interesting;

 

Hello. To help with understanding your important claim:

 

1. Could you please explain what you believe the modern conflict represents.

2. Exactly what is General Relatively of Einstein an invalid explanation of ?

 

1.

QM and GR can both be derived from DD's fundamental equation, but those derivations consist of a different set of assumptions/approximations. They both may contain patently false approximations, but just the fact that they require different assumptions, can lead to a situation where the required assumptions are collectively conflicting; they cannot be logically combined.

 

It is not exactly a straightforward thing to point out which assumptions exactly conflict and in what way, but one clear point of difference is in the assumptions regarding continuity. My perspective on it is that the information behind our explanation is always of finite amount, and thus it should always be possible to find a quantified way to represent that information. To take the information as continuous, is always an undefendable assumption, that can lead to subtle difficulties (and one of those difficulties was ultraviolet catastrophy, that led to QM).

 

What DD's comment refers to is that QM appears to be more accurate representation of the world in terms of expectations, in that it is missing some approximations/assumptions that exists and lead to difficulties in GR, and as a consequence QM is simply more generally valid (more accurate in larger collection of circumstances). That is not to say that QM wouldn't contain invalid approximations too; most probably it does.

 

2.

If you look at DD's OP about deriving General Relativity, you can see what approximations he makes to derive it, and to what degree his derivation is different from the standard definition. The difference is subtle, but it appears to be at least to the same direction as the observational anomalies are. That being said, it is well beyond my capabilities to properly analyze that part of the analysis. All I can say is that it would not surprise me the least bit if it turned out to be valid.

 

It is not very easy to establish all the approximations that exist in the standard derivation of GR because some of the approximations exist in that "unconscious" part of the translation process that we talked about in the other thread (and what those approximations are, have an effect on the consequent approximations). Nevertheless, it seems those approximations are almost equivalent to the approximations that DD makes.

 

DoctorDick, one further question comes to mind.

 

In your way of thinking, what exactly is the difference between a "representation" and a "theory". An important question because you claim that your presentation is NOT a theory but a representation.

 

What he was saying was that he is not making an argument about what reality is like. The fact that he is talking about general relativity and quantum mechanics being valid or invalid has to do with their degree of accuracy or generality to express expectations. Whereas you can view his work as an analysis about the impact of different sorts of approximations. In that sense, it is an analysis to what sorts of approximations stand behind QM representation or GR representation of reality.

 

I have pretty much the same, or similar, question as Rade.

 

a. Formulated differently, Dr. Dick, according to your representation of the constraints implied by the definition of an explanation where did Einstein go wrong?

 

It's hard to point out exactly which approximation leads to what kind of error in the expectations, but one of the most obvious differences in DD's derivation of GR is that time is not represented as a "flexible" dimension, and it is possible that the difference in the expectations can be traced in large part to that difference.

 

Either way, the main difference between GR and QM is in their assumptions related to continuity, and while it is not possible to really defend the ontological correctedness one way or another, the collection of approximations that leads to QM, appears to be simply more generally valid.

 

b. Is your complaint that only general relativity is wrong (and if so, with which theory of gravity would you replace it),

 

I don't think he much cares which theory should replace it or if we should just add some kind of correction to GR (that would proably lead to excessively complex view though).

 

A valid quantum mechanical representation of gravity would probably be something very close to the current idea of gravitons, but the actual issue he is referring to is simply that it is possible to establish a collection of approximations whose consequences lead to expectations that are equivalent to GR, apart from small difference that would appear as anomalous acceleration in the kinds of circumstances where we do now observe just that. That being said, it is not a trivial thing to really examine the validity of that part of his argument, but I personally find it very interesting that such a thing would show up in his derivation.

 

I don't think you should read too much in the above paragraph though, without first understanding his derivation of GR.

 

-Anssi

[Doctordick]

I have received a private message from Anssi which suggests some confusion on some very important issues. I am posting this to clarify the fundamental underlying issues.

Per Anssi's note:
 

First thing that comes to my mind is that it can be a bit confusing to refer to the this bit "representing rules mathematically". Maybe that constraint should be referred to as the universal constraint that arises from the existence of any defined rules and their associated defined elements (or something along those lines), but it should not be referred to as "rule".
 

[math]\cdots[/math]

people find it confusing that on the other hand, you are trying to make sure you are not representing any rules, and here you are arguing about the existence of a rule, or at least it's easy to get that impression.

 

The fact that you see it that way implies you have missed some very important issues having to do with exactly what I am doing. First, all explanations inherently imply and exploit rules so any representation of “an explanation” must be capable of representing those rules: i.e., the explanation, as part of its definition, invariably constrains one's expectations. If each and every specific explanation can be represented by a specific mathematical function then the associated rules, the ability to control what can and cannot be observed, must exist as a mathematical constraint on that function. Otherwise, representing the explanation as a mathematical function must fail. You should be able to comprehend that a one to one mapping between the two categories of entities is, in that case, simply not a possibility.

Of course, the constraint just referred to is a direct component of the explanation to be represented and not a specific constraint “embedded in the definition of an explanation”. However, there is another rather similar rule which is embedded in the definition itself. That is the fact that the explanation must be consistent with the “known information” it was designed to explain. This rule has exactly the same character as the constraint embedded in any of the specific explanations to be represented: i.e., it must yield a non-zero probability for the circumstances which the explanation is designed to explain. What is different is that rule says absolutely nothing about the circumstances which are not part of the “known information”.

On the other hand, my arguments put forward the idea that every explanation yields expectations of some sort. This idea is entirely equivalent to yielding a probability associated with each and every conceivable circumstance. If circumstances are to be represented by a collection of numerical labels and probability is to be represented by a number bounded by zero and one, that is exactly the definition of a mathematical function. What is significant here is that, for a valid explanation (i.e., one which is not disproved by the known information), that function must yield a non-zero result for the arguments which represent the known circumstances.

The above is exactly the reason any proper scientific analysis uses the word “theory” for any proposed explanation. A proposed explanation may explain all the relevant known information but the real question is, does it explain all possible relevant information. This is the exact reason for interest in experimentation. The explanation (being equivalent to a specific mathematical function) yields expectations for all relevant circumstances and one certainly cannot assert that they know exactly the correct expectations for all relevant circumstances.

I need to point out here that the only thing proved by any specific experiment is that the probability of seeing a particular outcome is either zero or non-zero. Obtaining probabilities via a collection of experiments (or presumed multiple outcomes internal to that experiment) essentially arise only via logic under the presumption the explanation is correct. Consider the "What is" is "what is" explanation. It is absolutely valid and yields no estimate of probabilities other than the fact that they are all equal. From the perspective of my equation, the "What is" is "what is" explanation is the quite obvious function [math]\vec{\Psi}=0[/math].

Examining relevant unknown circumstances is exactly the purpose of experimentation and is done to assure one that the “theory” is not invalid. (Please note the important subtle fact that proving a theory is valid is not possible.)

In the above, I have underlined relevant because it is a very important issue in my analysis. Confining their explanation to relevant issues is an assumption that the person knows what is and is not relevant. This process is commonly referred to as “compartmentalization” and is used throughout the sciences for the very simple reason that it removes a great many complications. However, compartmentalization is itself a constraint on an explanation outside the definition of “an explanation”. Thus it cannot be used within my analysis.

I am looking for constraints on an explanation due to the definition of “an explanation” and nothing more; it follows that I can not presume the existence of irrelevant information. Qfwfq apparently cannot comprehend that, if an explanation requires “compartmentalization” in order to prove it is valid, it is certainly possible that it is false and thus cannot be used as a counter example to my presentation. This is the exact problem with every one of his counter examples.

One of the consequences of the above is that no possible collection of numerical labels can be omitted from the representation of known circumstances. This is the underlying fact which moved me to represent a circumstance as a collection of points on a line (the line represents all possibilities and the points represent what is known). That is a very convenient representation; however, it has one very serious flaw: it does not conserve the information represented by the numerical labels. A circumstance may contain a given element (identified by a specific numerical label) more than once and both cases will map to the same point on that line. That fact essentially amounts to loss of information and thus cannot represent all possibilities.

This was exactly why the (totally hypothetical) tau axis was introduced: in order to allow multiple representations of identical “x” labels with the “point on a line” representation. A second (totally hypothetical) “t” axis was introduced in order to represent the entire possible set of known circumstances. Thus it is that the known circumstances to be explained became represented as a set of points in a (totally hypothetical) three dimensional (x,tau,t) space. A specific explanation defines the probability of absolutely every circumstance representable in that (x,tau,t) space. The function

 

[math]
\vec{\Psi}(\vec{x}_1,\vec{x}_2,\cdots,\vec{x}_n,t)
[/math]

 

corresponding to that explanation is defined for every possible projection of its arguments on the x axis (all possible representable circumstances). The issue of compartmentalization is quite simple to handle: for any specific explanation, irrelevant circumstances are simply ignored (we simply do not concern ourselves with the probabilities of circumstances we deem irrelevant). One of Qfwfq's major problems is that, in every counter example he presents, he wishes to bring in information which he himself has essentially deemed irrelevant (the issue of understanding the communication language being the single issue he most often neglects to consider).

Sorry for the long introduction but, at this point, we can examine Anssi's issue: the way I present and defend the constraint

[math]
F=\sum_{i\neq j} \delta(\vec{x}_i-\vec{x}_j) = 0.
[/math]

 

There are actually six ways from Sunday to defend that assertion. Perhaps the simplest way to defend that fact is to note that, if the numerical labels “x” are allowed to include each and every point in that entire (x,tau) plain, every point associated with the known circumstances to be explained must yield zero for that sum. This fact is entirely a consequence of the purpose and use of that hypothetical tau axis: no two points in the entire set can be represented by one point in that space.

Can such a relationship fix the collection of known numerical labels to a specific set. The answer is of course yes! If one adds hypothetical entities for every point in that space not required by by the known labels, F=0 will constrain the known numerical labels to exactly the known set. (Being hypothetical the added points play no part whatsoever in the known information to be explained other than confining them to "what is".) This is a clear consequence of the fact that the complexity of the rules required by an explanation is a direct function of what the explanation allows to exist.

Does it also vanish for the unknown circumstances? It does for the "what is" is "what is" explanation but for other explanations the issue is simply not known; however, after an experiment checking some “unknown circumstance”, that circumstance is no longer “unknown” and thus (together with its hypothetical tau index) it thus becomes “known” information. If it is impossible to come up with a tau value which makes that sum zero, the explanation must be invalid.

It is important to note that, in the infinite limit (and my proof must be valid all the way to the infinite limit or it is false), the proposition that all [math]\vec{x}[/math] points are different (there is no information loss in the representation) is undefendable; however, the assertion that the function [math]\vec{\Psi}[/math] is required to be antisymmetric will accomplish exactly the same result.

That fact brings up two very interesting consequences. First, we have constrained the function representing our explanation to an antisymmetric function and all possible functions (all possible explanations) are no longer represented. Secondly, the tau axis was created to prevent loss of information and that constraint simply does not apply to loss of hypothetical information. By the way, that would be information not recoverable from experiment without presuming the explanation is correct. Note that, within the field of modern physics, all bosons fall into that category.

It follows directly that, so long as one cannot prove that all possible explanations of a collection require each and every presumed element, there can exist elements not constrained by that “loss of information” problem. This fact solves both of the apparent difficulties above. Since any function can be shown to be a sum of an antisymmetric and symmetric part, all possible functions are returned to the collection and thus there exist (hypothetical) elements which can explain probability distributions not possible to provide via a universe of antisymmetric elements.
 

It is not explained anywhere at all, why is it necessary to represent the circumstances in such manner that the "t" index is recoverable.

 

Actually, I think the issue is quite simple. The index “t” is totally hypothetical (a creation for representational convenience only). As such, the ordering of the circumstances is of no significance with regard to explaining them: i.e., a different explanation might order them in a different manner. On the other hand, any specific explanation (most known explanations in fact) may very well require ordering these circumstances in a particular way. This implies that the ordering required is part and parcel of the explanation itself and thus must be known once the explanation is understood. If this ordering is part and parcel of understanding the explanation, the information required to know that ordering must be recoverable from the the underlying information on which that understanding is based: i.e., if the “t” index is not recoverable from the explanation, the explanation is not understandable.

Think of the problem this way. If, in the underlying information upon which your understanding of the explanation is based, there exist two absolutely identical circumstances, how do you know there are two. In order for you to conclude there are two, there must exist some information within the explanation to resolve that issue.

As a side issue, one of things I require is that all explanations of interest must be communicable (if you can't communicate it, we cannot discuss it). You have to keep in mind the fact that what I need is a way of representing any communication in general (the definition of “an explanation” separates communications which can be categorized as explanations from those which cannot). The first assertion of my proof has to do with the fact that all communications consist of identifiable parts (which I refer to as “circumstances”). What these identifiable parts “are” is of utterly no interest to me. (Note that, to know what they are requires an explanation of them and that is the very issue under discussion.) But what I do need is a way of representing these parts without knowing what they are.

The issue of “t” resolves down to ordering these circumstances. If the explanation requires two circumstances to be ordered with regard to one another, they must be different circumstances. If the order is insignificant, the two circumstances can be combined into one. Thus it is that for any specific explanation, all circumstances of interest can be ordered.
 

Still I'm not sure why in your notation that would lead into a situation where multiple individual circumstances could not contain identical observable state (as long as they are not consequent circumstances of course).

 

I never said they couldn't. Avoiding the problems of representing such a state is exactly the reason for the tau axis. I also comment that your presentation of the difficulty relies on the concept of “compartmentalization”.
 

Actually, this is related to a related question I have in my mind, which might resolve my difficulty. A single individual circumstance means that it contains information regarding the momentum of defined entities, right?

 

No it doesn't. If you review my presentation, “momentum” is a characteristic of the explanation, (the partials of [math]\vec{\Psi}[/math] with respect to the arguments) whereas the “circumstance” is the collection of arguments themselves.
 

I.e. the collection of information that is referred to as "a circumstance" is not just the position information of elements; knowing the previous circumstance is not necessary to know the velocity of the elements?

 

Your problem is that you are attempting to present my picture as a consequence of your understanding of reality (essentially the perspective which presumes that physics is correct explanation). It is the reverse of that problem which is significant: presenting modern physics explanations as a consequence of my proof (a perspective which presumes my proof is correct).

This same issue also leads directly to the problem my presentation has with Einstein's theory of General Relativity.
 

a. Formulated differently, Dr. Dick, according to your representation of the constraints implied by the definition of an explanation where did Einstein go wrong?

 

I think the fundamental problem Einstein had was the fact that Newton had produced an almost unassailable picture of reality as a time evolving three dimensional entity. Einstein held that picture as fundamental. In order to blend special relativity into that picture, Einstein used two contradictory definitions of time (defining time as being at the same when interactions between entities occur and defining time as the reading on a clock). Everyone should note that my proof contains but one. I can not exactly reproduce his result because I don't have the option of switching between the two; however, I get very close to the experimental results they use to defend the validity of his theory implying his theory is very close to being valid.

I don't believe your second question has any bearing whatsoever on my presentation; that question only comes up if you are attempting to understand my presentation from the position of accepting the common picture of reality as correct. I say again, I am not presenting a theory; I am presenting a proof.

But back to Anssi's problems:
 

Here, similarly it is a bit shrouded in mystery as to why is it necessary that we are able to recover any single index as a function of the rest of its individual circumstance... ...I have been thinking about this quite a bit going back and forth in different ideas as to how you mean it, and much of it also boils down to that question about whether or not a circumstance is also a representation of momentum of elements.

 

This also is a direct consequence of your attempt to present my picture as a consequence of your understanding of reality. It is not “necessary that we are able to recover any single index” associated with the communications on which our understanding was based (the exact reference intended by the source communicating the explanation). What I show is that it is always possible to conceive of hypothetical entities (which need to be indexed) such that all indices required by the explanation (in my representation) are recoverable. Of course, these entities being hypothetical requires that any calculation of expectations must include the consequences of all possibilities.

That final issue produces consequences analogous to what are commonly referred to as “fields” in modern physics.
 

The whole discussion about bosons refers to the fact that none of that prevents us from having defined elements whose unobservable behavior is defined as such that they are taken to pass identical states. But such an idea is still only implied by some observable states, and our particular explanation about what led to those observable states.

 

Anssi appears to comprehend the issue here. Electro-magnetic fields are the theoretical consequences of an uncountable number of boson interactions. They are thus, under my proof, hypothetical entities required by the explanation and not “real” entities requiring explanation. Try finding an experiment which proves a photon exists without using electro-magnetic theory (and the consequent implications of resultant macroscopic phenomena) to justify that existence. They are hypothetical entities required by the explanation presented.

One difficulty everyone seems to have is comprehending that what I present is a proof and not a theory. By insisting on seeing it as a theory, they invariably view all the above issues from the wrong perspective. And I am sorry Anssi but you also occasionally look at the thing from that perspective and that is the source of your problems in the logic.

Have fun -- Dick

 

Edited May 27, 2014 by Doctordick

[Rade]

One difficulty everyone seems to have is comprehending that what I present is a proof and not a theory. By insisting on seeing it as a theory, they invariably view all the above issues from the wrong perspective. And I am sorry Anssi but you also occasionally look at the thing from that perspective and that is the source of your problems in the logic.

Thank you for the clarification DD. OK, what you present is "a proof", not a scientific theory nor a representation, as thought by AnissH. Here then is the common sense understanding of what you present as a "proof", seeing that you do not define what type of proof you present:

 

http://mathworld.wolfram.com/Proof.html

 

From this Wolfram mathematical definition of "proof", we also read why few if any modern physicist would have any interest in your presentation. You mentioned in another thread that you thought R. Feynman might have interest in your proof based presentation, but the quote from Feynman suggests that your presentation based on proof, and not theory, would not have impressed him.

 

Now, in your defense, it is possible (and please do correct me) that what you really mean to say is that your presentation is based on what is known in mathematics as a "proof theory"...see this link:

 

http://en.wikipedia.org/wiki/Proof_theory

 

If what you present is a "proof theory" then your presentation is within the set of propositions of being a type of theory, and not as you claim above.

 

Einstein used two contradictory definitions of time (defining time as being at the same when interactions between entities occur and defining time as the reading on a clock). Everyone should note that my proof contains but one. I can not exactly reproduce his result because I don't have the option of switching between the two

I see you caught yourself and removed the word "time" after "same". But, your sentence makes no sense unless it reads "...as being at the same TIME when interactions".... But then, it would be a nonsense claim that Einstein defined time using the words "same TIME", one does not define a word using the word.

 

The fact of the matter is that Einstein DID NOT have two contradictory definitions of time. Your "first" Einstein definition of time is what Einstein directly defined as the concept "simultaneity". The reason you cannot exactly reproduce his results, as neither could Newton, is that you confuse his concept of "simultaneity" with his concept of "time".

 

As to how Einstein defined time and simultaneity, let us read what Einstein had to say in 1920 on the topic:

 

http://www.bartleby.com/173/8.html

[Qfwfq]

Dick, you keep making unsupported claims about me.

[phillip1882]

i guess i don't understand the OP. the way to tell if rules are consistant or not is not through some mathematical operation, but through analizing the wording and application of them.

for example. the basic rules of go are this.

two players take white and black stones, place them on intersections of the board, and try to surround empty space.

each player may also capture his opponents stones by surrounding them.

no repitions are allowed.

the second player gets a free 6.5 points.

the game ends when players pass consecutively.

 

would your mathematical equation define these rules as being logically consistant?

for example, wouldn't passing your turn repeat the board state?

can both players play stones of either color? or is it one color per player?

what qualifies as "empty space"? how do you score it?

etc.

obviously these rules need to be clarified.

[Doctordick]

obviously these rules need to be clarified.

 

Yes, obviously they do! You are omitting all the information necessary to understand the language you are speaking: i.e., you are operating from a compartmentalized perspective (presuming English is an understood mechanism of communication) and omitting all other possible interpretations of your post. Can you not comprehend that an intelligent person, a thousand years from now, would need much more information far beyond the binary code submitted for your post in order to comprehend what you are talking about? I am discussing ALL POSSIBLE EXPLANATIONS not specific explanations of any kind.

 

As I said above,

 

Your problem is that you are attempting to present my picture as a consequence of your understanding of reality (essentially the perspective which presumes that physics is correct explanation). It is the reverse of that problem which is significant: presenting modern physics explanations as a consequence of my proof (a perspective which presumes my proof is correct).

 

What I have proved is that all explanations must satisfy my equation (where no relevant information is omitted). Now true or not true, that comment alone is a pretty worthless assertion beyond being an abstract proof of interest to some intelligent people who like to think along abstract lines. The only thing which should be of interest to the scientific community (that is, if they were truly open to intelligent discussion) is the fact that under some very simple assumptions (in fact, exactly those assumptions commonly used in modern physics) that almost all of modern physics is nothing beyond an approximate solution to that equation.

 

That fact implies that modern physics is a tautology. That my friend is a rather astounding conclusion; something worth seriously thinking about. Your example has utterly nothing to do with what I am talking about at all. In fact, the explanation of the game you are bringing up is, without a doubt, a tautological construct designed solely for entertainment. To suggest it is not a solution to my equation is to suggest it violates modern physics in some manner. I am sure that was not your intention when you made the post.

 

Dick, you keep making unsupported claims about me.

 

Qfwfq, I can find a quote of you to support every last comment I have ever made concerning your complaints about my presentation. It is just not worth the effort as you make it quite clear that you never going to make a serious effort to understand a single thing I say anyway. You would rather be little more than a Troll. You continually put yourself, over and over again, in exactly the same category as phillip1882 has above. You just like to think in a compartmentalized state. Seeing the big picture is apparently something simply beyond your abilities.

 

You have, on a number of occasions, made it quite clear that you had no interest in understanding the proof. You have explicitly stated that your interest was in the validity of the conclusion not in the proof. Without understanding the proof, the conclusion can not be understood. If you had any real interest in what I am talking about, you would look carefully at the proof.

 

Have fun -- Dick

Edited May 27, 2014 by Doctordick

[AnssiH]

Ah, I think I figured out what caused my difficulties. I'll comment to your post to make sure I understand what you mean;

 

...the explanation, as part of its definition, invariably constrains one's expectations. If each and every specific explanation can be represented by a specific mathematical function then the associated rules, the ability to control what can and cannot be observed, must exist as a mathematical constraint on that function. Otherwise, representing the explanation as a mathematical function must fail. You should be able to comprehend that a one to one mapping between the two categories of entities is, in that case, simply not a possibility.

 

So when you say "the two categories of entities", you are referring to

1. The entities defined by an explanation

2. The entities representing a constraint that limits the possibilities to those entities defined by an explanation.

 

And when you say one to one mapping does not exist, you refer to the fact that having the "2", does not mean you could recover the "1"?

 

On the other hand, my arguments put forward the idea that every explanation yields expectations of some sort. This idea is entirely equivalent to yielding a probability associated with each and every conceivable circumstance. If circumstances are to be represented by a collection of numerical labels and probability is to be represented by a number bounded by zero and one, that is exactly the definition of a mathematical function. What is significant here is that, for a valid explanation (i.e., one which is not disproved by the known information), that function must yield a non-zero result for the arguments which represent the known circumstances.

 

The above is exactly the reason any proper scientific analysis uses the word “theory” for any proposed explanation. A proposed explanation may explain all the relevant known information but the real question is, does it explain all possible relevant information.

 

Right so the reason you say "non-zero result for arguments which represent the known circumstances" instead of requiring "1" is the idea that any collection of arguments representing "a known circumstance" may omit information that was relevant to the appearance of that collection?

 

Alright, here we go;

 

Sorry for the long introduction but, at this point, we can examine Anssi's issue: the way I present and defend the constraint

 

[math]

F=\sum_{i\neq j} \delta(\vec{x}_i-\vec{x}_j) = 0.

[/math]

There are actually six ways from Sunday to defend that assertion. Perhaps the simplest way to defend that fact is to note that, if the numerical labels “x” are allowed to include each and every point in that entire (x,tau) plain, every point associated with the known circumstances to be explained must yield zero for that sum. This fact is entirely a consequence of the purpose and use of that hypothetical tau axis: no two points in the entire set can be represented by one point in that space.

 

So, that is close to how I convinced myself of the validity of the constraint the first time around. I say "close to" because I viewed it from a slightly different perspective than intented. I viewed it directly from the perspective of possible entity definitions, instead of from the perspective of viewing the constraint itself as an expression of "constraining entities".

 

The same thing was also why I felt like I am not really picking up something relevant to your defense; it became increasingly difficult to interpret some things you were saying.

 

Can such a relationship fix the collection of known numerical labels to a specific set. The answer is of course yes! If one adds hypothetical entities for every point in that space not required by by the known labels, F=0 will constrain the known numerical labels to exactly the known set.

 

Right so this sounds like you are indeed talking about the constraint itself as being represented by a collection of entities.

 

I think I need to think little bit about what kinds of subtleties my earlier perspective has caused to my interpretation of the consequential arguments. I suspect they are small, but I already know some were significant.

 

About recovering "t"

 

Think of the problem this way. If, in the underlying information upon which your understanding of the explanation is based, there exist two absolutely identical circumstances, how do you know there are two. In order for you to conclude there are two, there must exist some information within the explanation to resolve that issue.

 

Right that is pretty straightforward. The ordering of the circumstances is a function of the explanation, so whether or not two "t"'s are consequent or not is not relevant from the point of view of the notation; the value for "t" had to appear from the explanation categorizing the information one way or another.

 

The issue of “t” resolves down to ordering these circumstances. If the explanation requires two circumstances to be ordered with regard to one another, they must be different circumstances. If the order is insignificant, the two circumstances can be combined into one. Thus it is that for any specific explanation, all circumstances of interest can be ordered.

 

That I think is pretty clear way to put it and should perhaps appear somewhere in the presentation. Right now it just goes directly to the issues having to do with recovering the "t". I think there are ways to interpret the meaning of the notation where the recovery issue would not be so apparent, and thus it should be useful to have that clarification there.

 

Hmmm, on the other hand, maybe it's not useful to spend the time in tweaking the current presentation right now...

 

Your problem is that you are attempting to present my picture as a consequence of your understanding of reality (essentially the perspective which presumes that physics is correct explanation). It is the reverse of that problem which is significant: presenting modern physics explanations as a consequence of my proof (a perspective which presumes my proof is correct).

 

I had a subtle difficulty in my mind having to do with loss of information in representing circumstances, and the idea that the information behind so-called "momentum" would have to be embedded into a circumstance (as per your definition of "circumstance") was an attempt to resolve that difficulty. But I have to re-think this from the perspective that you are using to actually defend the constraint.

 

So, actually I wouldn't characterize my difficulty as being a case of trying to fit this thing into my idea of reality, it appears that my difficulty arose from having a wrong perspective towards how you were defending the constraint, and trying to solve that via the idea that perhaps I did not have the correct idea as to what you mean by "a circumstance" exactly. I was viewing any reference to "entities" as a reference to entities defined by an explanation, not as a reference to an entity-wise representation of an universal constraint.

 

Also my questions and comments about it being necessary to recover a specific x index had to do with that perspective, that you are referring to possible entity definitions of an explanation, instead of the idea of viewing the constraint as being represented by entities.

 

Anyhow, does it sound like I am interpreting you more correctly now? If I am, I think my comments above should prove useful in understanding one potential difficulty in the presentation.

 

-Anssi

[AnssiH]

I see you caught yourself and removed the word "time" after "same". But, your sentence makes no sense unless it reads "...as being at the same TIME when interactions"....

 

Or rather "defining time as being at the same value when interactions between entities occur and defining time as the reading on a clock".

 

This issue is far more subtle than you seem to think, but you should take notice that the difficulties that arise when switching between the two are incredibly subtle. If they were obvious, Einstein if anyone would have been careful enough to avoid them, don't you think? The fact that this switching exists is quite obvious, whether or not it leads to difficulties, is not.

 

The fact why DD does not directly refer to what those difficulties are in the traditional route to GR is that the existence of such a difficulty is only being implied by the facts that 1. there are two different definitions that have different meaning, being switched back and forth as per needs, 2. In DD's notation only one of the meanings is used, and the results are subtly different.

 

The fact of the matter is that Einstein DID NOT have two contradictory definitions of time. Your "first" Einstein definition of time is what Einstein directly defined as the concept "simultaneity". The reason you cannot exactly reproduce his results, as neither could Newton, is that you confuse his concept of "simultaneity" with his concept of "time".

 

The notions of simultaneity have to do with events that are space-like separated, and their supposed simultaneity.

 

Time as a concept related to interactions has to do with the idea of "physical contact". Objects cannot "come together" from two different "times". Clocks who show different readings, can. That is not to imply Einstein thought otherwise. It is to imply that much care must be taken when switching between two meanings of the concept.

 

Don't expect to understand what the difficulty is without understanding the steps in DD's derivation of GR.

 

-Anssi

[Qfwfq]

No Dick, you are again making false statements. You can talk about your claims regardless of my own humble little opinion, but you should not make false statements about me.

 

If you had any real interest in what I am talking about, you would look carefully at the proof.

I already have looked at your claimed proof and it was no use dicussing its shortcomings with you. I understand what you claim, you keep repeating this and other excuses.

 

P. S. Besides, your criticism against me showed that you don't even get your logic straight about counterexample vs. universal proposition.

Edited October 22, 2011 by Qfwfq
post scriptum

[Doctordick]

So when you say "the two categories of entities", you are referring to

1. The entities defined by an explanation

2. The entities representing a constraint that limits the possibilities to those entities defined by an explanation.

 

No, when I referred to “the two categories of entities” in that post, I was referring to “explanations” as the first category of entities I was talking about and “mathematical functions” as the second.

 

And when you say one to one mapping does not exist, you refer to the fact that having the "2", does not mean you could recover the "1"?

 

No, I was referring to that one to one mapping between explanations and functions.

 

Right so the reason you say "non-zero result for arguments which represent the known circumstances" instead of requiring "1" is the idea that any collection of arguments representing "a known circumstance" may omit information that was relevant to the appearance of that collection?

 

Not quite. I said “non-zero” for the probability of the known circumstances for a very real but subtle fact apparently ignored by most everyone. Just because a certain circumstance is a member of the set of known circumstances does not mean that the probability of obtaining (or seeing or being aware of or whatever ...) that circumstance is one. All you really know is that, if it is part of the collection of known circumstances, the probability of it occurring is non-zero. In fact, the “what is” is “what is” is a valid explanation of anything. As I said, that explanation is directly represented by [math]\vec{\Psi}=0[/math].

 

Other than that you seem to have a handle on the thing.

 

I already have looked at your claimed proof and it was no use dicussing its shortcomings with you.

 

I have no memory of you ever bringing up a single complaint with regard a single one of my logic steps. As far as I can tell, your complaints are all generalization which imply to me that you have no idea as to what I am talking about.

 

P. S. Besides, your criticism against me showed that you don't even get your logic straight about counterexample vs. universal proposition.

 

I don't think you have any concept of what my “universal proposition” constitutes. At least you have given no evidence of understanding even the first part of it.

 

Why do you keep bothering me? As far as I can see you show no interest in understanding the proof.

 

Have fun -- Dick

Edited May 27, 2014 by Doctordick

[Qfwfq]

Why do you keep bothering me?

Why do you keep saying things about me? No point in you complaining about me.

 

Have fun -- Dick

Exactly, I've more important things to do, even though I would hardly call them having fun.

[Rade]

Or rather [Einstein is] "defining time as being at the same value when interactions between entities occur and defining time as the reading on a clock".

AnssiH. Einstein would never add the word "value" after the word "same" in any attempt to define time in the way you claim.

 

Why do you accept as a truth statement the above interpretation used by DD without doing your homework ? Please post the publication by Einstein, with page number, where he defined time using the two different definitions of time exactly as worded above. Note: I do ask you to ask DD to reword his false claim, I request you show me in the scientific literature where Einstein defined time as you (and DD) claim. Otherwise, this thread may as well be placed into the "strange claim" area of the forum, if we will allow words to be assigned to Einstein of all people without documentation.

 

Well, let me also ask any of the forum physicists...please post the publication page numbers (and exact definition text) where Einstein defined time using the two different definitions claimed above by DD and AnssiH.

[coldcreation]

AnssiH. Einstein would never add the word "value" after the word "same" in any attempt to define time in the way you claim.

 

Why do you accept as a truth statement the above interpretation used by DD without doing your homework ? Please post the publication by Einstein, with page number, where he defined time using the two different definitions of time exactly as worded above. Note: I do ask you to ask DD to reword his false claim, I request you show me in the scientific literature where Einstein defined time as you (and DD) claim. Otherwise, this thread may as well be placed into the "strange claim" area of the forum, if we will allow words to be assigned to Einstein of all people without documentation.

 

Well, let me also ask any of the forum physicists...please post the publication page numbers (and exact definition text) where Einstein defined time using the two different definitions claimed above by DD and AnssiH.

 

 

I think what AnssiH and DD refer to is the (1) notion of simultaneity based on Einstein's definition, and (2) the actual reading of clocks (the notion of time at different locations).

 

(1') In the cosmological context of GR, inherent in certain interpretations of the Einstein field equations, there is the notion of cosmic time, the time coordinate commonly used in big bang models, i.e., cosmic time is the standard time coordinate for specifying the Friedmann–Lemaître–Robertson–Walker solutions of Einstein's equations. All clocks are synchronized according to a time when a homogeneous universe has the same density everywhere. Time in this case is the same everywhere, regardless of where the observer is located.

 

(2') The concept of time according to the second view depends on, or is defined by, the actual reading of clocks at different locations, which depends on the spatial reference frame of the observer.

 

 

This is basic relativity and is well documented.

 

 

CC