Planck limits

<BLOCKQUOTE id=quote><font size=2 face="Verdana, Arial, Helvetica" id=quote>quote:<hr height=1 noshade id=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?<hr height=1 noshade id=quote></BLOCKQUOTE id=quote></font id=quote><font face="Verdana, Arial, Helvetica" size=2 id=quote>

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 <i>Dark matter...</i> 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|-

"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

<BLOCKQUOTE id=quote><font size=2 face="Verdana, Arial, Helvetica" id=quote>quote:<hr height=1 noshade id=quote>It must be noted this is wrong interpetation of Zeno's paradoxes.<hr height=1 noshade id=quote></BLOCKQUOTE id=quote></font id=quote><font face="Verdana, Arial, Helvetica" size=2 id=quote>

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.

<BLOCKQUOTE id=quote><font size=2 face="Verdana, Arial, Helvetica" id=quote>quote:<hr height=1 noshade id=quote>They were developed to support the concept of quantized space-time and not refute it.<hr height=1 noshade id=quote></BLOCKQUOTE id=quote></font id=quote><font face="Verdana, Arial, Helvetica" size=2 id=quote>

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.

<BLOCKQUOTE id=quote><font size=2 face="Verdana, Arial, Helvetica" id=quote>quote:<hr height=1 noshade id=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+...+...<hr height=1 noshade id=quote></BLOCKQUOTE id=quote></font id=quote><font face="Verdana, Arial, Helvetica" size=2 id=quote>

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.

<BLOCKQUOTE id=quote><font size=2 face="Verdana, Arial, Helvetica" id=quote>quote:<hr height=1 noshade id=quote>The fourth paradox of Zeno has to do with relativity and speed of light.<hr height=1 noshade id=quote></BLOCKQUOTE id=quote></font id=quote><font face="Verdana, Arial, Helvetica" size=2 id=quote>

Zeno (an ancient Greek scholar) died a little before relativity was invented. <img src=icon_smile.gif border=0 align=middle> There are eight classical Zeno paradoxes. The "extended paradox" I mentioned is hypothetical #9.

<BLOCKQUOTE id=quote><font size=2 face="Verdana, Arial, Helvetica" id=quote>quote:<hr height=1 noshade id=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.<hr height=1 noshade id=quote></BLOCKQUOTE id=quote></font id=quote><font face="Verdana, Arial, Helvetica" size=2 id=quote>

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?

<BLOCKQUOTE id=quote><font size=2 face="Verdana, Arial, Helvetica" id=quote>quote:<hr height=1 noshade id=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.<hr height=1 noshade id=quote></BLOCKQUOTE id=quote></font id=quote><font face="Verdana, Arial, Helvetica" size=2 id=quote>

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|-

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

<BLOCKQUOTE id=quote><font size=2 face="Verdana, Arial, Helvetica" id=quote>quote:<hr height=1 noshade id=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.<hr height=1 noshade id=quote></BLOCKQUOTE id=quote></font id=quote><font face="Verdana, Arial, Helvetica" size=2 id=quote>

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.

<BLOCKQUOTE id=quote><font size=2 face="Verdana, Arial, Helvetica" id=quote>quote:<hr height=1 noshade id=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.<hr height=1 noshade id=quote></BLOCKQUOTE id=quote></font id=quote><font face="Verdana, Arial, Helvetica" size=2 id=quote>

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.

<BLOCKQUOTE id=quote><font size=2 face="Verdana, Arial, Helvetica" id=quote>quote:<hr height=1 noshade id=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.<hr height=1 noshade id=quote></BLOCKQUOTE id=quote></font id=quote><font face="Verdana, Arial, Helvetica" size=2 id=quote>

I have an entire section of chapter one in <i>Dark Matter, Missing Planets and New Comets</i> 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.

<BLOCKQUOTE id=quote><font size=2 face="Verdana, Arial, Helvetica" id=quote>quote:<hr height=1 noshade id=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.<hr height=1 noshade id=quote></BLOCKQUOTE id=quote></font id=quote><font face="Verdana, Arial, Helvetica" size=2 id=quote>

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.

<BLOCKQUOTE id=quote><font size=2 face="Verdana, Arial, Helvetica" id=quote>quote:<hr height=1 noshade id=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.<hr height=1 noshade id=quote></BLOCKQUOTE id=quote></font id=quote><font face="Verdana, Arial, Helvetica" size=2 id=quote>

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|-

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:<BLOCKQUOTE id=quote><font size=2 face="Verdana, Arial, Helvetica" id=quote>quote:<hr height=1 noshade id=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.<hr height=1 noshade id=quote></BLOCKQUOTE id=quote></font id=quote><font face="Verdana, Arial, Helvetica" size=2 id=quote>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 <b>together</b> 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 <b>immediate</b> 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...