Thread: It's a small world, after all.

Originally Posted by Brafil

That means, the object travels in infinitely fine time/space steps. Or any existing object would travel at the same speed.

But that's not possible. Then the distance between any two objects must be infinity, or the object wouldn't move according to Newton.

Sorry, but I do not understand your argument.

EDIT:

Originally Posted by Mario F.

You mean Zeno's Paradoxes of Motion?

Right, but that is independent of Newton's first law of motion, if I recall both correctly.

Originally Posted by Brafil

Or I am wrong in some way.

Probably Brafil

There are very fine time/space steps, that is what atomic physics is about -- but they are finite.

Time is actually a property (or consequence) of atomized matter, which it is possible to conceive of matter which is not atomized, ie. pure substance, which would relate to space but probably not time, so neither Newton's nor Einstein's laws would apply to it (the logical properties of substance vs. atomic matter is an interesting one).

The concepts of the "event horizon" and black holes play into this. It could be that in extremely dense regions of space, there would be no space left at all -- something denser than a neutron star, something that would have *absolute* density, the same way *absolute* zero is a specific point at which movement ceases completely. The normative laws of physics are considered to break down in proximity to such a potential object, since the laws of physics are about atomized matter and not really about substance itself (which is binary: the two possible states of 3D space are "substance" and "no substance").

I hope that clears things up a bit.

Originally Posted by laserlight

Right, but that is independent of Newton's first law of motion, if I recall both correctly.

If for no other reason, at least because the paradoxes use the notion of infinity which immediately drags them into the Uncertainty Principle. Or in other words, it's the paradox that suddenly becomes questionable and not the law it tries to question.

But esssentially the paradox rules out any possibility of motion, so had it not been resolved already, it could be used to question the 3 laws, I guess.

EDIT: Brafil however introduced the paradox into his argument has if it was some kind of law: "That means, the object travels in infinitely fine time/space steps.". That's just low

Originally Posted by Mario F.

it's the paradox that suddenly becomes questionable and not the law it tries to question.

the Heisenberg uncertainty principle states that certain pairs of physical properties, like position and momentum, cannot both be known to arbitrary precision.

I have never seen it defined in exactly this way -- so that it applies to objects of any size. Interesting.

>> If space could be divided infinitely, any object would need infinite time to move from one position to the other. The same with time.

But the division of space or time (or anything, for that matter) can only be done in finite steps. If one could divide something into an infinite amount of pieces then the very concept of a "piece" becomes meaningless.

>> the Heisenberg uncertainty principle states that certain pairs of physical properties, like position and momentum, cannot both be known to arbitrary precision.

Moreover, it asserts that this is not merely due to some limitation in measurement, but that it is in fact an intrinsic quality of nature. I'm sorry, but that's just nonsense. The uncertainty exists simply because we cannot know the complete state of the system* a priori, and NOT because it is governed by probablistic functions and "collapsing wave-functions". I'm not saying that quantum mechanical calculations aren't useful, just that they shouldn't be confused with "the thing itself".

*Since all matter in the universe exerts a force that propagates everywhere, you would indeed need to factor in all these forces to achieve a "perfect" calculation.

Originally Posted by Sebastiani

Moreover, it asserts that this is not merely due to some limitation in measurement, but that it is in fact an intrinsic quality of nature. I'm sorry, but that's just nonsense. The uncertainty exists simply because we cannot know the complete state of the system* a priori, and NOT because it is governed by probablistic functions and "collapsing wave-functions". I'm not saying that quantum mechanical calculations aren't useful, just that they shouldn't be confused with "the thing itself".

LOL Sebastiani. Sorry, mate but I need to ask:

And you are...?

Originally Posted by Brafil

If space could be divided infinitely, any object would need infinite time to move from one position to the other. The same with time.

You may be able to divide space infinitely, but you cannot do so with atomic matter, which would be the measure of space WRT objects. And you cannot do it with time at all except in a naive sense. The reason time compression and dilation take place is because "time" is a dimension of atomic reality and subject to laws -- it is not an independent phenomenon, like a objective clock in the background that would grind monotonously on even if nothing existed.

Originally Posted by Sebastiani

>> the Heisenberg uncertainty principle states that certain pairs of physical properties, like position and momentum, cannot both be known to arbitrary precision.

Moreover, it asserts that this is not merely due to some limitation in measurement, but that it is in fact an intrinsic quality of nature.

Actually, the phrase is "the nature of the system itself" which might have a somewhat different meaning.

Originally Posted by Sebastiani

Moreover, it asserts that this is not merely due to some limitation in measurement, but that it is in fact an intrinsic quality of nature. I'm sorry, but that's just nonsense. The uncertainty exists simply because we cannot know the complete state of the system* a priori, and NOT because it is governed by probablistic functions and "collapsing wave-functions". I'm not saying that quantum mechanical calculations aren't useful, just that they shouldn't be confused with "the thing itself".

*Since all matter in the universe exerts a force that propagates everywhere, you would indeed need to factor in all these forces to achieve a "perfect" calculation.

Just checking, since I am not well studied on this: are you saying that physicists generally now believe what you have stated, or are you presenting your opinion on an issue that is still widely open to debate as fact?

Originally Posted by Brafil

If you were able to divide space infinitely, any object would have to move inf/inf units from point A to B.

You could have a thought experiment like that, but atomic objects do not move that way (they do not coast independently thru space, except in a pragmatic, Newtonian realm).

The point of Zeno's paradox is that it is a logical aporia; it's about the artificiality of thought and not intended to be taken seriously altho, perhaps, it often has been...

Originally Posted by laserlight

Just checking, since I am not well studied on this: are you saying that physicists generally now believe what you have stated, or are you presenting your opinion on an issue that is still widely open to debate as fact?

The general consensus is probably that the Uncertainty Principle is correct (at least most sources I've read seem to present it as a fact). But I think the matter is certainly debatable. Statistics is indeed a useful tool for analysing systems, but does it really model reality? I think not. It "works" because it simplifies an infinitely complex problem, and as long as we understand it as such then there is no harm done. But what Heisenberg and others have done is to essentially assert that these probablistic terms of the equation are *in fact* undeniable aspects of nature. This is a terrible mistake! Any observation is going to record a measurement that falls within a certain minima/maxima simply because it is impossible to integrate the infinite number of factors that influence the system. The *only* reasonable solution is to use statistical functions to obtain results that agree with the calculations. That is not a rejection of determinism, but an acceptance of the limitations of our knowledge and understanding of the complexity of the system.