Zeno's Paradoxes

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ruveyn
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05 Dec 2013, 3:12 pm

pete1061 wrote:

Actually, a photograph does have a time component, exposure time.

.

Every photograph -must- be blurred. But if the blurring is small it is not noticed.

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naturalplastic
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05 Dec 2013, 3:16 pm

A point has zero dimensions.

Therefore the time it takes to move through a point, at any nonzero velocity, is zero time. So to move through an infinite number of points is: zero multiplied by infinity which is: zero time.

So therefore not only is motion possible its MORE than possible. There should not be any such thing as 'travel time'. All speed should be infinite!

So the opposite of Xeno's paradox is the real paradox!

Last edited by naturalplastic on 05 Dec 2013, 5:13 pm, edited 1 time in total.

naturalplastic
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05 Dec 2013, 3:23 pm

TallyMan wrote:

American wrote:

There must be such a thing as "points" in space and time because there much be such a thing as the smallest possible unit of space or time. Points are infinitesimally small. Points are the smallest possible units of space or time. Points have no length or volume because, if they did, they could be smaller, and thus would not represent the smallest possible unit of space or time, which necessarily must exist if space and time exists.

Actually in the real world there are no points. The smallest length is the Planck length. 1 planck length = 1.61619926 * 10-35 metres. When distances become so small common sense notions don't apply and quantum physics is the only way to describe what is happening at such small scales. It is almost as though our universe is granular (or digital) in nature rather than analogue. So if you took an everyday length such as one metre in the real world, it doesn't have an infinite number of points along it. The metre could at most be divided into 1.61619926 * 10^35 segments, each segment being indivisible.

Could that mean that the time it takes to "walk the Planck" at the speed of light would be the shortest possible interval of time (meaning time is also granular)?

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05 Dec 2013, 3:34 pm

naturalplastic wrote:

TallyMan wrote:

American wrote:

Could that mean that the time it takes to "walk the Planck" at the speed of light would be the shortest possible interval of time (meaning time is also granular)?

See here: http://en.wikipedia.org/wiki/Planck_time

It is getting beyond the scope of my knowledge. We could do with Jono here as he has a PhD in physics and has a special interest in quantum phenomenon. I'm sure I've come across time being described as granular rather than continuous, certainly with regard to quantum phenomena but I'm at the limit of my knowledge here.

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The_Walrus
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05 Dec 2013, 3:40 pm

American wrote:

That is how we know that there is no such thing as motion.

You have this back to front.

We know motion exists, therefore Zeno was wrong.

sonofghandi
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05 Dec 2013, 4:23 pm

pete1061 wrote:

I predict that some day the plank length will be dis-proven. I can't put my finger on it, but something about it doesn't fit. Seems like just a limit to our observation capabilities. Kinda like a horizon on an additional dimension of scale. Which means that there are even more dimensions on top of that. 3 spatial dimensions + 1 time just aren't enough.

granular universe? only when observed, according to wave/particle duality.

The Planck length is much much smaller than our current observational capabilities. In physics, depending on which theory/theories you like best, there are 5, 8, or 11 dimesions. M-theory currently is the front-runner (and has the most factual support) with 11 dimensions but is far from proven.

We have gotten to the point in physics where we have suddenly realized exactly how much we have yet to learn. We now know that only around 4-5% of the universe is made up of what we consider matter.

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05 Dec 2013, 4:25 pm

I'm not an expert on physics, so never really understood how motion actually shows Zeno to be wrong.

techstepgenr8tion
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05 Dec 2013, 6:00 pm

pete1061 wrote:

I had a similar feeling - ie. it's a claim of an absolute, it worked based on a theory by Plank but things like that are taken for decades, even centuries, until new information kicks it to the curb similar to how Newton is looked at as providing generally stable rules of operations at the macro but just not at the micro. Even if we have space and time pixilated it just rephrases the Zeno question - instead of how does something move across infinite divisions its how does something move from one pixel to the next.

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05 Dec 2013, 6:08 pm

techstepgenr8tion wrote:

Even if we have space and time pixilated it just rephrases the Zeno question - instead of how does something move across infinite divisions its how does something move from one pixel to the next.

My memory is fuzzy on the details, my university days were thirty years ago, so please don't be too hard on me if I muff this... If I remember correctly a particle e.g. an electron can move from one place to another without actually being present at any time in any of the intervening space, it just spontaneously appears in the new location. I'm thinking of properties like quantum tunnelling where and electron has a finite probability of being on the other side of an energy peak... scaled up to everyday sizes it would be like a football suddenly appearing on the opposite side of a hill without it having been pushed up and over the top. Strange and interesting things happen at the small sizes involved with particles and quantum physics.

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The_Walrus
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05 Dec 2013, 6:13 pm

MCalavera wrote:

I'm not an expert on physics, so never really understood how motion actually shows Zeno to be wrong.

You've never understood how things moving disproves Zeno's thought experiments that disprove movement?

It is too late at night for me to look up the answers Jim al-Khalili provided in his book Paradox (a good read if you can get past his tone). I will try to look tomorrow.

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05 Dec 2013, 6:22 pm

My bad. I thought you were referring to the Achilles' paradox when, instead, you were referring to the arrow one. (I didn't read the OP properly until now)

MCalavera
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05 Dec 2013, 6:25 pm

Oh, wait, the others are about movement, too.

techstepgenr8tion
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05 Dec 2013, 7:14 pm

TallyMan wrote:

techstepgenr8tion wrote:

Even if we have space and time pixilated it just rephrases the Zeno question - instead of how does something move across infinite divisions its how does something move from one pixel to the next.

Right, I think my comment was just more toward the notion that things seem to be changing with respect to the observations in the scientific community at that level that what was given truth 30 years ago now is looked at as the best educated guess or theory 30 years ago. What you just stated though is part of why I'm not sure what to make of Plank's constants - whether he's right or whether he just had a very good theory based on the best available information that might fall apart over the next 100 years (if he calculated it somehow with the speed of light as bedrock he might have something but, lol, we're also looking at time itself here and questioning it's relationship to space).

As for the jumping around part - it would be a bit like, pardon my anthropomorphism of subatomic particles, but that they're more interested in what their grouping is supposed to be in material reality when they're on the clock than whether or not they're showing the same social etiquette on the micro in how they come and go as their aggregations would on the macro. I could see how new-agers might grab on to this kind of stuff for more sensible hunches than just the stoner 'woah dude!' it's-weird-therefore-mystical factor.

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05 Dec 2013, 9:09 pm

American wrote:

Ganondox wrote:

American wrote:

ModusPonens wrote:

I like them. However, calculus blew them away.

I know virtually nothing about calculus but my impression is that these paradoxes are philosophical in nature and I cannot see how math could solve them. Yes, math is logic, which philosophy, but... Can you explain more perhaps? BTW, great screename. Was modustollens taken?

Because it proved that idea the an infinite sum must be infinite to be completely false. You CAN transverse an infinite number of points in a finite amount of time.

That's logically impossible to do because no matter how many points you traverse there will always be another one and thus you can never traverse space at all. How can you finish traversing the points in space between two points when there is a never ending number of points to traverse? There will always be another point to traverse before you can move anywhere. "Traversing" an infinite number of points, even if possible, still wouldn't get you anywhere; it would not result in any motion ever. Obviously, motion appears to be possible, but that must be wrong. Simplicius said that Diogenes the Cynic got up and walked across the room upon hearing the half-way paradox in order to prove it wrong. But that doesn't satisfy me.

Take 0.9, add to it 0.09, it give 0.99. Then add 0.009, it give 0.999. Add 0.0009, you got 0.9999, and so on. In the end you got 0.999999999... with a infinity of 9. Each 9 come from a addition and still, 0.999999... equal to 1. So with a infinite number of addition you got a finite number. Which mean that with a infinite number of movement on a infinite number of points, the added infinites movements give a finite number.

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05 Dec 2013, 11:42 pm

ruveyn wrote:

pete1061 wrote:

Actually, a photograph does have a time component, exposure time.

.

Every photograph -must- be blurred. But if the blurring is small it is not noticed.

ruveyn

Exactly. Photographs have no time dimension. They simply don't capture anything other than a point in time that has no length. So think of the arrow paradox that way. That is, there is an infinite number of possible pictures of the arrow as it "moves" through space from the bow to the point when it falls or hits something and stops. And, in fact, between any two photographs you could take, there would be an infinite number of photographs. So, how does the arrow ever move anywhere?

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06 Dec 2013, 2:23 am

American wrote:

Ganondox wrote:

American wrote:

ModusPonens wrote:

I like them. However, calculus blew them away.

Because it proved that idea the an infinite sum must be infinite to be completely false. You CAN transverse an infinite number of points in a finite amount of time.

No, because you move an infinite amount of points in a segment of time which has an infinite amount of points. By your logic time can't exist either. Either a. the universe is digital and discrete, in which Zeno's paradox is irrelevant as there is a smallest level of division, or b. the universe is analogue and continuous, in which Zeno's paradox is disproven by calculus. You can't travel by a single point because that's meaningless in a continuum, there is no such thing as an adjacent point, you don't move points one at a time as that's just nothing, an instant with no passage of time, and your point is nonsense. You don't understand the math involved, so you are counterintuitively coming at an illogical conclusion.

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