Paradoxes Resolved, Origins Illuminated

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rush

74 Posts

Posted - 13 Feb 2003 : 19:19:30

Is the Planck lenght the smaller limit for the Universe? Is the Planck time the smaller limit for the passage of time or is it just the limit of our measurements? How can we be sure that there is something in a smaller scale than the Planck scale?

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tvanflandern

USA
2793 Posts

Posted - 14 Feb 2003 : 02:48:58

quote:
Is the Planck length the smaller limit for the Universe? Is the Planck time the smaller limit for the passage of time or is it just the limit of our measurements? How can we be sure that there is something in a smaller scale than the Planck scale?

According to conventional models, the Planck units are the smallest possible. According to the Meta Model, scale is infinitely divisible. IMO, the line of reasoning in chapter 1 of Dark matter... about Zeno's extended paradox for matter shows that scale must be infinitely divisible, much like space and time. Otherwise, contact would be impossible, much the way motion would be impossible if space and time were not also infinitely divisible. -|Tom|-

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Enrico

Italy
80 Posts

Posted - 14 Feb 2003 : 08:14:23

"the line of reasoning in chapter 1 of Dark matter... about Zeno's extended paradox for matter shows that scale must be infinitely divisible, much like space and time. Otherwise, contact would be impossible, much the way motion would be impossible if space and time were not also infinitely divisible. -|Tom|-"

It must be noted this is wrong interpetation of Zeno's paradoxes. They were developed to support the concept of quantized space-time and not refute it. I think I made my points clear in the topic about infinity. Motion is impossible if space-time is infinetely divisible according to the first three paradoxes of Zeno. This is because, there are infinite points to pass to complete the motion, 1+1+1+...+...

The fourth paradox of Zeno has to do with relativity and speed of light.

The extention of Zeno paradox to include mass is not appropriate. For Zeno, universe was made of a single discrete substance. That is why he insisted in quantization. In essence, Zeno's ideas fit perfectly with Plank's limits.

Extending Zeno's paradox to include mass leads to a logical contradiction in the context of Zeno's premises and any model based on that is self-contradictory.

Enrico

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tvanflandern

USA
2793 Posts

Posted - 14 Feb 2003 : 11:14:34

quote:
It must be noted this is wrong interpetation of Zeno's paradoxes.

This should read "in your opinion". I at least qualified my statement with "IMO", which means "in my opinion", and mentioned the situation in the Meta Model, not attempting to make a claim about reality. Several of your statements are declarations that appear to carry the weight of fact, when they are likewise just personal opinions.

quote:
They were developed to support the concept of quantized space-time and not refute it.

That is false. Zeno's paradoxes argue for the impossibility of motion under either premise -- infinite divisibility or a smallest possible unit of space and time. Various modern authors argue for one or another of these premises, according to their own opinions.

quote:
I think I made my points clear in the topic about infinity. Motion is impossible if space-time is infinetely divisible according to the first three paradoxes of Zeno. This is because, there are infinite points to pass to complete the motion, 1+1+1+...+...

And I rebutted that argument with the well known counterargument that we can put intervals on a line segment into a one-to-one correspondence with an infinite series having a finite sum. The series for the classical Zeno paradox is 1/2 + 1/4 + 1/8 + 1/16 + ... = 1. Using one-to-one correspondences is the only logical way we have to deal with infinities. To deny the obvious conclusion of using such logic without a good reason would not be rigorous thinking.

quote:
The fourth paradox of Zeno has to do with relativity and speed of light.

Zeno (an ancient Greek scholar) died a little before relativity was invented.

There are eight classical Zeno paradoxes. The "extended paradox" I mentioned is hypothetical #9.

quote:
The extention of Zeno paradox to include mass is not appropriate. For Zeno, universe was made of a single discrete substance. That is why he insisted in quantization. In essence, Zeno's ideas fit perfectly with Plank's limits.

Everything in this paragraph is opinion written as if fact. And these declarations are not accompanied by a logical argument. I applied reasoning identical to Zeno's (as used for space and time) to the Meta Model's fifth dimension, scale/mass. Why is that inappropriate? Why does it matter what Zeno's personal world view was centuries before the discovery of molecules, atoms, and quantum particles, and of reasons to expect elysons and gravitons to exist on yet smaller scales?

quote:
Extending Zeno's paradox to include mass leads to a logical contradiction in the context of Zeno's premises and any model based on that is self-contradictory.

Bold claims. Can you even begin to justify them as anything more than opinion? Please describe the physical properties of the hypothetical "smallest possible entity". In particular, please tell us:

** Does this unit particle spin? Does it deform under rapid spin? Does it have a spherical shape? Some other shape? Describe its degree of rigidity.

** Can two unit particles collide? Do they stick and become a double particle (depleting the unit particle supply in the universe) or do they elastically rebound (which requires shape deformation during collision)? If the latter, with what velocity does the rebound occur, and why? And what then about grazing collisions?

** Can a collision with enough energy split a unit particle?

** What density does the unit particle have? High or low? Could it be hollow? With what thickness of shell? Indeed, does it have an inside, given that its interior is apparently never accessible to the rest of the universe?

** Describe the surface of the unit particle. Note that it cannot be dented or scratched or altered in any way through collisions or spin because such details are properties of bodies that have further sub-structure.

** Why would unit particles have finite dimensions in space yet infinite domensions in time? Or do they come into and go out of existence? From and to where?

Note that I do not expect you to know the unknowable for particles that have yet to be discovered. I am asking for answers in principle for questions that appear to have no possible reasonable answers. I have long been an advocate of banishing the kind of "fuzzy think" that reasoning by mathematics encourages in today's thinkers, which has led many to abandon the principles of physics. We need to bring back physical reasoning to the field, which applies far more serious constraints on models of reality than any mathematical argument can. -|Tom|-

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Enrico

Italy
80 Posts

Posted - 15 Feb 2003 : 11:51:50

I understand my English is not good and I cannot express myself the best way, so sometimes it seems I make bold statements.

Zeno's paradoxes were constructed by Zeno to support the Monism theory of his teacher Parmenides and provide grounds for a direct refutation of Anaxagoras theory of plurality.

With that said, it is well known that Zeno claims that if distance of infinitely divisible then motion is imposible or in a better sense

1. motion cannot start or
2. motion is chaotic
3. motion is non-deterministic

Zeno's paradoxes are an assault on the concept of infinity in any way possible. After Zeno stated his paradoxes, the concept of infinity was declared "illegal" for use in mathematics and physics. That was in the time mathematics was viewed as a part of physics. In modern times, mathematics took an independent route and the concept of infinite was revived by Cantor.

We do experimental philosophy appart from studing the only proper subject of philosophy which is fromal logical analysis. I will give you and real example of the need to consider quantized space-time in every physical process. Consider a dc-motor closed loop feedback system. The feedback is realized by using an encoder mounted on the motor shaft and a light source measure the pulses generated by the encoder as the motor turns. Those pulses are used by the feedback system to command the motor to turn a certain number of revolutions.

Then, the encoder must have not only a finite number of pulses but a maximum number dictated by the physical system. If there are few holes in the encoder then the accuracy is very small. But if there are too many, there is problem when the time between two holes is less than the time constant of the motor system. If according to your opinion space can be infinetely divided then one can think of an encoder with infinite holes. Then

1. motion of the motor cannot even start because for every small distance there are infinite pulses to send which is impossible to do.

2. even if motion starts, it cannot finish since there are infinite holes to get through and this requires infinite time for sending infinite pulses.

3. Even if motor moves some way, the position will be random variable because the time contant of the motor will always be greater than the time between pulses and this means position cannot be known.

This is an example of the problems the idea of infinite divisibility creates in reality. Different physical systems require different quantization to have motion sucessfully.

Now, as far as you asking me what is the smallest particle I cannot answer this and this question has nothing to do with logical consistency in using Zeno's paradoxes. Just remember that the statement:

If things can divide infinitely then London is in England

is a always a true statement. Similarly,

If things cannot divide infinitely then Paris is in France

is always a true statement.

For both statements above to be true we do not care of the mechanisms or the size and spin of smallest particles.

I will try to find so reference for you to read on Zeno's paradox that is in English. Unfortunately, all our references are in Italia, Latin or Ancient Greek.

Enrico

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tvanflandern

USA
2793 Posts

Posted - 15 Feb 2003 : 17:07:56

quote:
[Enrico]: Zeno's paradoxes are an assault on the concept of infinity in any way possible. After Zeno stated his paradoxes, the concept of infinity was declared "illegal" for use in mathematics and physics.

Nonetheless, the five (mathematical) dimensions used to measure substances and their properties must themselves be infinite. That presents no contradiction because dimensions are not real or tangible. They are the mathematical tools by which we observe and measure the real and tangible, and they are infinite by postulate, and by the lack of any intelligible meaning to finiteness for dimensions.

The meaning of "infinite" for dimensions is simple: We cannot name any finite limit to any dimension, however large, and be assured that we will never find an example of a real, tangible substance or property that will exceed the limit. Quantities where no finite limit, however large, can be specified are infinite by definition.

quote:
That was in the time mathematics was viewed as a part of physics. In modern times, mathematics took an independent route and the concept of infinite was revived by Cantor.

The concept of infinities and the infinitesimal became more than aesthetic, becoming an essential tool for the description of reality, with Leibnitz and the introduction of his calculus. Today, we take limits as quantities approach zero or infinity without a second thought, and expect the results to describe nature well. Gamow brought forward another dimension in the physical applications of infinities with his use of one-to-one correspondences. Today's understandings of the nature of reality are built squarely on both of these usages of the concept of infinity.

quote:
I will give you a real example of the need to consider quantized space-time in every physical process. [Routine example of a Zeno-like paradox omitted.] This is an example of the problems the idea of infinite divisibility creates in reality. Different physical systems require different quantization to have motion sucessfully.

I have an entire section of chapter one in Dark Matter, Missing Planets and New Comets devoted to showing why this is wrong. The showing utilizes both types of infinities -- limits and 1-to-1 correspondences -- to argue logically that there is one and only one way for motion to be possible, and that requires infinite divisibility of both time and space. Later, we apply that same line of reasoning to contact.

The short story -- hardly self-explanatory in this brief note -- is that the ratio dx/dt (representing motion) in the limit as dx and dt both approach zero can still be finite. That is obvious in mathematics when calculus is applied. It is equally true in physics when 1-to-1 correspondences are constructed. Any alternative hypothesis leads to a host of unresolvable paradoxes of the type I listed near the end of my previous message.

quote:
Now, as far as you asking me what is the smallest particle I cannot answer this and this question has nothing to do with logical consistency in using Zeno's paradoxes.

You cannot answer my questions, nor can anyone else. We are trapped by both horns of the paradox -- motion is logically impossible either way -- unless we recognize that an infinite series or an infinitesimal ratio can still have a finite sum or quotient, and that these mathematical results correspond to descriptions of reality also.

I don't understand your claim "this question has nothing to do with logical consistency in using Zeno's paradoxes". This was the half of the paradox (which showed that motion was impossible) arguing that a smallest possible entity was illogical. However, I have no interest in a debate about history, only about current science. So if you insist that the books you read do not attribute this viewpoint originally to Zeno, fine. I am only interested here in today's status of the debate about nature. We can get the attributions straight as a side issue. Let's not interrupt the discussion of the nature of motion and contact. If Zeno had never existed, the arguments today would be the same.

quote:
Just remember that the statement: "If things can divide infinitely then London is in England" is a always a true statement. Similarly, "If things cannot divide infinitely then Paris is in France" is always a true statement. For both statements above to be true we do not care of the mechanisms or the size and spin of smallest particles.

These are trivial examples of fallacious logic. I do not see their applicability here. I have not introduced any false premises.

To advance the discussion, I redirect your attention to my list of questions at the end of my last message. If they have no possible answers consistent with the principles of physics, then the nature of motion and contact cannot involve a smallest possible particle. -|Tom|-

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AgoraBasta

Russia
234 Posts

Posted - 15 Feb 2003 : 19:49:00

Enrico,

Your example with a "motor" is totally unphysical. But that's OK, as long as you haven't studied that science. But you make there deliberate logical mistakes, like this:

quote:
If according to your opinion space can be infinetely divided then one can think of an encoder with infinite holes. Then

1. motion of the motor cannot even start because for every small distance there are infinite pulses to send which is impossible to do.

Here you presume that "infinite holes" might be made, yet "infinite pulses" are impossible to send/process. There's no reason to assume that the former should be more possible than the latter - your logical error is obvious. (and you can let both numbers together trend infinitely up, btw)

But that aside, some physics is still needed to build a logical diagram of your "setup", since you must build a realistic cause-and-effect chain. Here, right off the start, you hide all the assumptions you make of the immediate cause of motion. Thus you deliberately create a fallacy upon your gedanken-experiment.

Please don't consider it a personal attack, but let me tell you that there's a crowd of phylosophers whose ideas of physical reality are based on nothing other than hidden assumptions and zero factual knowledge of the most basic stuff of that physical reality...

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Enrico

Italy
80 Posts

Posted - 16 Feb 2003 : 06:34:23

"Your example with a "motor" is totally unphysical. But that's OK, as long as you haven't studied that science. But you make there deliberate logical mistakes.."

I appreciate Dr. Flandern's answers, he has good points to make like made by other known scientists and I'm trying to debate with him the issues of Zeno's paradox. By starting an argument by attacking both the capability and the intentions of the other party is not a good thing to do and shows a lacking of both scientific character and ability for effective communication. Good scientists never start an argument like this and when they do, everything they say is often neglected and those people never get recognition in their field but remain in the shadows of their abrasive character.

Dr. Van Flandern:

If infinite divisibility is possible then construction of an encoder with infinite holes should be possible in theory and such an encoder would prohibit motion. Zeno's paradoxes have nothing to do with time but you introduce time to resolve them. One may take all the time needed, if infinite divisibility of space is allowed then motion is impossible. By taking limit dx/dt, a process of convergence is introduced but you failed to provide a physical mechanism for that process. You trying to resolve one paradox by introducing a mathematical chaos of infinitesimals and limits when there is an asnwer much much simpler: space is quantized.

But thank you for your answers. As you know a debate like this may never end. Good luck to you.

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tvanflandern

USA
2793 Posts

Posted - 16 Feb 2003 : 10:58:54

AB: As much as I appreciate the support for my position here, and the valuable science you bring to this Message Board, in this instance I am forced to agree with Enrico that you turned the discussion personal first. That does not excuse Enrico's personal insults back to you, and I certainly wish he had shown more restraint. But if we are going to end flame wars here, we need to stop these matters at their root.

I also wish that all participants would make allowance that English is not the first language of many here, and not always jump to the conclusion that an attack was intended.

That said, accusing someone of using "deliberate logical mistakes" is hard to read in any way except as a personal attack, and certainly has no relevance to the merit of the ideas presented. Note especially how this Message Board differs about such types of communication from certain others you participate in. (I have "Bad Astronomy" in mind, which is a personal attack right from the Board name. That board allows participants to attack one another freely, and IMO is a disgrace to science.)

Accordingly, I have removed AB's second round of attack message, escalating the intemperate rhetoric. Let's please have no more of that type of message.

To ALL: Please make an extra effort to direct all your comments toward the merit of ideas, and none of them to the character, competence, motives, ancestory, or other qualities of the person representing them. Characterizing ideas is the same as characterizing their presenter. Just stick to what is right and what is wrong with the ideas, and the rest will take care of itself.

Please follow my "Orange Juice Rule": Never say anything here to another participant that might make it awkward to meet that person and sit down with him/her over a glass of orange juice and have a friendly, in-person chat about the same issues. Many thanks. -|Tom|-

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AgoraBasta

Russia
234 Posts

Posted - 16 Feb 2003 : 16:30:02

quote:
[TVF] That said, accusing someone of using "deliberate logical mistakes" is hard to read in any way except as a personal attack, and certainly has no relevance to the merit of the ideas presented.

Sorry, I can't agree with you here. It's a normal thing among philosophers to distort the physics so that it fits into the limits of their concepts and constructs. Such efforts on their part are always quite deliberate and quite often simply nihilistic towards the natural sciences, and the mistakes they make along that course are quite deliberate indeed.
It is my firm conviction that exactly such deliberate philisophers' mistakes are the root cause of dissent both in this thread and in the earlier related discussions on this board. Hence the argument can be won by the physicists only if the philosophers are forced to respect the physicality of the premises in those discussions, and all the tricks they use need be exposed and promptly dismantled.

Please feel free to remove this post if you consider it offensive or irrelevant.

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1234567890

360 Posts

Posted - 16 Feb 2003 : 20:06:46

Zeno used faulty premises to argue against motion. If Zeno were living in the 21st century, an illustration of his reasoning process would go like this : His car is parked in the garage. He gets into his car, starts the engine, sees that the garage door is down, shuts his engine off and sadly concludes driving is impossible because one can't get out of the garage.

To reach this absurd conclusion of course, he had to start from a couple false premises: 1. the garage door has to be open for you to drive through it, and 2. there's no way to open the garage door.

It sounds facetious but it's not too far off from the absurd reasoning process of his paradoxes.

What more proof of motion did Zeno expect than the fact that he was able to move his hand in space to write down his paradoxes?

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tvanflandern

USA
2793 Posts

Posted - 17 Feb 2003 : 00:34:56

quote:
[AB]: It's a normal thing among philosophers to distort the physics so that it fits into the limits of their concepts and constructs. Such efforts on their part are always quite deliberate and quite often simply nihilistic towards the natural sciences, and the mistakes they make along that course are quite deliberate indeed.

I do not agree with you on several levels. Philosophers may not be experts in physics, and may give priority to their own philosophical convictions over ones from physics they may not understand as well. This is a natural and understandable process we all engage in -- giving priority to what we are familiar with and therefore more confident of. I see nothing insidious about it.

Moreover, "deliberate" seems to imply "acting in bad faith". That is certainly not true. Among several possible explanations for such behavior, the human capacity for self-deception is virtially unlimited.

quote:
It is my firm conviction that exactly such deliberate philisophers' mistakes are the root cause of dissent both in this thread and in the earlier related discussions on this board. Hence the argument can be won by the physicists only if the philosophers are forced to respect the physicality of the premises in those discussions, and all the tricks they use need be exposed and promptly dismantled.

I don't recommend you apply for any jobs at the United Nations.

All factions in disputes tend to impute dishonest, unethical, or sinister motives to their opponents. But no true meeting of minds is possible until each side is prepared to take its opponents and their needs/interests/ideas seriously.

The first step for anyone involved in a dispute is to try to understand the other side's position. In an intellectual dispute, one needs to understand why the other side believes what it does -- to understand the issue the way one's opponents understand it. Having that true understanding is the only way one can hope to make an honest comparison of the merits of the two opposed viewpoints.

Much more than that is needed, however, if the two sides are to have a meeting of minds. One must open up one's own position, including its weaknesses, to the other side. To have any hope of being taken seriously, one must be prepared to agree that one's own position is wrong if the facts uncovered merit that. Most people are not prepared to surrender their own positions under any circumstances, so they can never be persuasive to others with a committed position. To reach agreement, each side must take the position that "If I am shown to be in error, that only means that I will be smarter tomorrow than I was yesterday."

quote:
Please feel free to remove this post if you consider it offensive or irrelevant.

All that I insist upon is that you respect the people you debate with by not insulting them or ridiculing their ideas. Stick to the merits. Accusing them of acting in bad faith is an insult. It is a bad idea under all circumstances because, if you are mistaken, you have made an enemy needlessly (perhaps of a potential future ally); and if you are right, it still shuts down discussion of the merits and allow the other side a chance to win by changing the subject away from the merits, where they would lose.

One way to "win" in any discussion of intellectual ideas is to show that the merits of your position exceed the merits of the opposed position, as judged by neutral parties. Another way to "win" is to concede that the position of the other side has more merit than your own position. That is a win for you not only because it makes you smarter, but also because your opponents have compelling evidence that you deal in good faith and are fair-minded. This opens doors for you in any and all future discussions. Almost no one trusts arguing with someone who can never admit error or back away from a clearly losing position.

Please think it over. We all have much to learn from our debate opponents. If nothing else, we learn how well we truly understand the subject ourselves, and how well we can teach it or communicate it to neutral parties. -|Tom|-

P.S. If you do not think you can show the degree of respect I request here, perhaps your talents and experience would be more successful on another Message Board. I have been amazed to see in some USENET newsgroups that even highly insulting postures sometimes have beneficial effects -- something I previously thought impossible. But this Board plans to distinguish itself by allowing all non-attacking, non-derisive, scientific viewpoints to be presented in an environment free of attack and derision from others. We'll stick to that as long as it seems to our Board of Directors to be working for us. I hope you can agree to modify your style accordingly and stay. -|Tom|-

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AgoraBasta

Russia
234 Posts

Posted - 17 Feb 2003 : 10:47:11

Tom,

It appears to me that you perceive my comments in an exclusively negative sense. Thus the positive meaning of those gets muted. So I'll reformulate once (and only once) more -

No single party in the dispute should be allowed control over premises. Single-sided tinkering with the premises should be uniformly considered as unfair tactic. Winning a dispute when the opponent controls the premises is next to impossible. And winning disputes is crucial to defending truths or even verities.
(BTW, that's why you can't win in disputes with the orthodox relativists - they simply privatize the premises and refuse to come to common grounds.)

Now on to particular case we have here -
Being caught tinkering with the premises one is accused of unfair tactics by that very fact. According to your own declarations, such accusation is a personal attack of itself. And it surely feels like that to the guilty party. So there's an option for the guilty party to claim being attacked personally, without addressing the matters in question, and that's exactly what we've seen in this thread. Thus your limitations against "personal attacks" get unfairly exploited; and that's only to be expected since fairness is not as widespread a virtue as one would like it to be.