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 undergrounder
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 Scale and the 5th dimension... 
#8353706 - 05/02/08 12:52 PM (15 years, 11 months ago) |
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Scale impacts on the way things work in a massive way. ex:
- Living things that are large have slow matabolisms and live longer, things that are small have very fast matabolisms and live a lot shorter lives.
- Large things essentially experience time slower then small things.
- Tiny things on a Planck scale level work completely differently to things on a subatomic level which in turn are different again to the Newtonian physical laws of big things.
Now if i exist with my centre at point x,y,z and at time t, and i am fairly large like an elephant, then life for me in every way, including the very nature of how my basic physics works, will be completely different to if i exist with my centre at point x,y,z and at time t but i'm only the size of a Planck scale quark.
Doesn't that mean that scale is like a 5th dimension? I understand 'scale' is just a composite of x,y and z, but there are differences there that can't be explained by length, width and breadth alone.
P.S. I'm not a physicist or a mathematician so go easy on me if this sounds like a stupid idea.
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Bigger and bolder and rougher and tougher in other words sucka there is no other...
   
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 DieCommie
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Re: Scale and the 5th dimension... [Re: undergrounder]
#8353833 - 05/02/08 01:24 PM (15 years, 11 months ago) |
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I think you are over emphasizing the 'perception' of time as it scales with the size of an organism, to the actual passage of time.
No matter how your brain perceives time, quickly or slowly, basic physics is not completely different.
Quote:
I understand 'scale' is just a composite of x,y and z, but there are differences there that can't be explained by length, width and breadth alone.
I dont get what you mean. How about an example. What is a difference that can't be explained by length, width and breadth alone?
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HagbardCeline
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Re: Scale and the 5th dimension... [Re: undergrounder]
#8353931 - 05/02/08 01:59 PM (15 years, 11 months ago) |
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You're incorrect in your statement about equating an organism's size to it's metabolism and it's lifespan.
Box turtles are quite small and can live well over 100 years. Some species of Parrots can live to 80. Koi can live to be nearly 100 and there have even been goldfish surive to 50.
On the other end of the scale you have whales, most of which live to a maximum of 90 (Bowheads being the major exception which may live longer than even the Galapagos turtles) and the longest recorded life of an elephants is around 90 (some debate on it) but closer 70 on average.
I won't even touch on the main argument.
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I keep it real because I think it is important that a highly esteemed individual such as myself keep it real lest they experience the dreaded spontaneous non-existance of no longer keeping it real. - Hagbard Celine
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Seuss
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Re: Scale and the 5th dimension... [Re: undergrounder]
#8354373 - 05/02/08 04:02 PM (15 years, 11 months ago) |
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> Doesn't that mean that scale is like a 5th dimension?
Nope, scale is simply a modifier, or multiplier, or attribute of a shape.
Think of dimensions as shapes, (called rho) and scales as multipliers (attributes) of the shape (called iota). The vector rho defines a shape while the scaler iota defines the size of rho. You are touching on a very complex bit of mathematics.
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DieCommie
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Re: Scale and the 5th dimension... [Re: Seuss]
#8354594 - 05/02/08 05:04 PM (15 years, 11 months ago) |
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What are you talking about man? Topology?
Ive never used an iota in my life. (A good line to remember maybe  )
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Seuss
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Re: Scale and the 5th dimension... [Re: DieCommie]
#8354868 - 05/02/08 06:14 PM (15 years, 11 months ago) |
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> What are you talking about man? Topology?
Very close. Numerical methods for massively parallel computation; basically a formal method to define problems such that they can be mapped, with formal validation, to various computational topologies. My description above isn't super accurate. Iota is actually an operator in the calculus (based on lambda calculus) and behaves much like the APL iota operator.
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johnm214
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Re: Scale and the 5th dimension... [Re: undergrounder]
#8354923 - 05/02/08 06:26 PM (15 years, 11 months ago) |
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I get what you're saying I think.
If you look at various equations and mechanisms for the living being, you'll notice that they don't progress linearly as the scale changes.
As an example I used to shoot down the folks claiming that size is illusary and therefore the universe could be a living organism, with solar systems being atoms composing a cell, take a look at the equations for surface area compared to volume of a sphere.
4/3¶r^3= volume of sphere
4pr^2= surface area of sphere
so you'll see the differential of the sphere volume w/ respect to radius is greater than the differential of the surface area w/ respect to the radius, and this means that the volume increases too fast and eventually diffusion will not be an effective means of transport for the cell. This is why fast growing cells are generally small, and larger cells generally grow slower, i.e. plants
You'll find that as the radius increases that the surface area increases slower than the volume, which means less of the cell is available at any given time to the membranes on the cells "wall". This means metabolite export, protein export, and all sorts of other things are dramatically slowed as the cell increases in size, as most rely on simple difusion to transport the stuff from the cell to the membrane "wall" and thus it will take increasingly longer as the cell grows in size.
This is why you cannot have a cell as we know be the size of a person, the surface area would be way too small compared to the contents, and the cell would starve and be utterly useless to the organism. So in this way size IS real. All things are not relative, there is a difference between a bunch of universe sized cells compared to a bunch of small cells.
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undergrounder
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Re: Scale and the 5th dimension... [Re: johnm214]
#8356501 - 05/03/08 01:18 AM (15 years, 11 months ago) |
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Quote:
I dont get what you mean. How about an example. What is a difference that can't be explained by length, width and breadth alone?
I don't pretend to know a thing about quantum mechanics, but for instance the physical laws change between the normal world scale, the subatomic scale and the tiny tiny Planck scale, yes?. If you shrunk me down from my current size to that of a quark, then the world around me would be fundamentally different in every way. The very laws of physics have changed yet all that's happened is my length, breadth and width has become smaller.
Quote:
You're incorrect in your statement about equating an organism's size to it's metabolism and it's lifespan.
Box turtles ... whales ... elephants etc.
I know the experience isn't directly corellated, but comparisons within family groups is more appropriate, for instance an elephant lives a lot longer than a human (before humans discovered medicine etc.) which in turn lives longer than a mouse. Similarly, the metabolisms of each are slower to faster according roughly to scale. The same can be seen in birds, a hummingbird flaps its wings faster, its heart beats faster, it lives faster (and its perception of time may well be much slower) than say an eagle, whose wings and heart beats slower and it lives a lot longer. And a dragonfly lives faster again than a hummingbird. A crocodile lives longer, moves slower than a goanna, lives longer/slower than a skink etc. etc.
But what i think i was meaning is better described by what johnm214 explained in reference to cells and how large animals are slower than small animals and therefore WHY matabolism changes more or less with scale.
but you're right i was getting confused over perception vs. time actually changing, i was confused with how gravitational fields change actual time and therefore things that are necessarily big would exist in a different gravitational field. In a similar example, one human twin who lives in the space station will age faster and experience time slower than his twin who lives at sea level for the same amount of time. For him time IS different, if he kept an accurate watch then when the two twins compare the time after X years, the astronaut's watch will be faster and he will be older. But yeah that's unrelated, and that's where i got confused.
And Seuss's explanation makes sense, especially how the three/four normal dimensions exist relative to eachother, but scale is just a multiplier of the previous dimensions, not its own dimension (if i read that right). And come to think about it if a dimension is meant to measure only a single linear change, scale makes changes on more than one front.
Thanks
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RIP
Bigger and bolder and rougher and tougher in other words sucka there is no other...
Edited by undergrounder (05/03/08 08:15 AM)
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Stein
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Re: Scale and the 5th dimension... [Re: undergrounder]
#8356688 - 05/03/08 03:29 AM (15 years, 11 months ago) |
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Your question sounds pretty complex you should wait for buddhahoodlum to chime in and make sense of it all for everyone to take awe in.
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Seuss
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Re: Scale and the 5th dimension... [Re: undergrounder]
#8356744 - 05/03/08 04:31 AM (15 years, 11 months ago) |
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> And come to think about it if a dimension is meant to measure only a single linear change, scale makes changes on more than one front.
Yep. In math, we represent scale as a matrix of numbers with each number in the matrix being the scale of a single dimension. To scale a 3D 'thing' a matrix with three numbers would be used (one number would scale x, one would scale y, and one would scale z).
> Your question sounds pretty complex you should wait for buddhahoodlum to chime
Not at all. The OP has legitimate questions and is trying to learn. I don't care what level of education a person has, if they are trying to learn, they have my respect.
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DieCommie
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Re: Scale and the 5th dimension... [Re: Stein]
#8357266 - 05/03/08 11:06 AM (15 years, 11 months ago) |
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Quote:
Stein said:
Your question sounds pretty complex you should wait for buddhahoodlum to chime in and make sense of it all for everyone to take awe in.
Its all clear is you just watch youtube dude!!
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DieCommie
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Re: Scale and the 5th dimension... [Re: undergrounder]
#8357409 - 05/03/08 11:45 AM (15 years, 11 months ago) |
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.
Edited by DieCommie (11/13/16 10:06 AM)
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undergrounder
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Re: Scale and the 5th dimension... [Re: DieCommie]
#8360347 - 05/04/08 03:45 AM (15 years, 11 months ago) |
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OK so the physics stays the same, but the laws we use to describe it changes, yes? I think i'll leave the QM talk there, don't want to get too deep.
Thanks again
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RIP
Bigger and bolder and rougher and tougher in other words sucka there is no other...
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HagbardCeline
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Re: Scale and the 5th dimension... [Re: undergrounder]
#8364568 - 05/05/08 10:48 AM (15 years, 11 months ago) |
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In a similar example, one human twin who lives in the space station will age faster and experience time slower than his twin who lives at sea level for the same amount of time. For him time IS different, if he kept an accurate watch then when the two twins compare the time after X years, the astronaut's watch will be faster and he will be older. But yeah that's unrelated, and that's where i got confused.
Wouldn't it be the opposite? The astronaut would would age less because of the speed he was traveling at was closer to that of light.
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I keep it real because I think it is important that a highly esteemed individual such as myself keep it real lest they experience the dreaded spontaneous non-existance of no longer keeping it real. - Hagbard Celine
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deimya
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Re: Scale and the 5th dimension... [Re: HagbardCeline]
#8365136 - 05/05/08 01:57 PM (15 years, 11 months ago) |
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To blatantly quote wiki's article on the Twin paradox
Quote:
In physics, the twin paradox is a thought experiment in special relativity, in which a person who makes a journey into space in a high-speed rocket will return home to find he or she has aged less than an identical twin who stayed on Earth. This result appears puzzling, since the situation seems symmetrical, as the latter twin can be considered to have done the travelling with respect to the former. Hence it is called a "paradox". In fact, there is no contradiction and the apparent paradox is explained within the framework of relativity theory, and has been verified experimentally using precise measurements of clocks flown in airplanes.
What lifts the paradox is that the situation is not symmetrical since the space traveling twin is the only one to experience the force needed to make the spaceship do a U-turn back to Earth. Forces implies accelerations and special relativity is not valid when taking accelerated frames of reference into account. General relativity is needed to make sense of this result.
The other funny and unintuitive thing, this time simply in the framework of special relativity, is that before and after making this U-turn, that is when no force are in play but only a relative constant speed between them, both twins see each others' pace as slowed down. Indeed there is no absolute frame of reference so they both are in the same situation relative to the other.
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deimya
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Re: Scale and the 5th dimension... [Re: deimya]
#8365194 - 05/05/08 02:19 PM (15 years, 11 months ago) |
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Concerning OP's topic, scale is indeed something important with a very real effect when looking at interacting systems. In physics, the importance of scale and the way behaviors change from one to the other is understood in the context of the renormalization group theory, which has also found numerous applications in other fields like sociology, biology, urban development, etc.
The basic intuition of the renormalization group, or simply renormalization for short, is that whenever you are measuring or observing something, you are doing so with a certain "ruler", that is at a certain scale, and thus all effects taking place at much smaller scale might affect the outcome of your measurement without you knowing so. Said otherwise, what you measure at a certain scale gets additional contributions from the average of things going on at a scale you have no access of given the size of your "ruler". In physics, the formalization of this intuition, renormalization, is carried out by integrating (or tracing out, or averaging) over fast acting degrees of freedom, and so degrees of freedom measured at a certain scale get corrected by this averaging.
This process enables one to -partially- understand how the physics at small scale influence, or give rise to the physics at large scale. The interesting thing is that it is possible to show that different small scale physics, different microscopic descriptions can give rise to the very same large scale physics. In the jargon this effect is called universality. That is whether your building blocks for your model are atoms, quantum chocolate fudge, straws or legos, each with their how description and interactions, it is very possible to recover the same macroscopic physics and behaviors between two or all of these models if they fall in the same universality class.
This is still an active area of research in condensed matter physics and high energy physics and the implications and technicalities have not all been worked out yet.
So, yeah, scale has a very real effect.
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maggotz
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Re: Scale and the 5th dimension... [Re: deimya]
#8366119 - 05/05/08 07:06 PM (15 years, 11 months ago) |
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Quote:
The other funny and unintuitive thing, this time simply in the framework of special relativity, is that before and after making this U-turn, that is when no force are in play but only a relative constant speed between them, both twins see each others' pace as slowed down. Indeed there is no absolute frame of reference so they both are in the same situation relative to the other.
could you explain this a bit more?
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DieCommie
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Re: Scale and the 5th dimension... [Re: maggotz]
#8366664 - 05/05/08 09:20 PM (15 years, 11 months ago) |
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Its the twin paradox. Each twin is older than the other, which cant happen.
Form the traveling twin's point of view, the earth is moving away at high speeds and the earth's inhabitants are also moving away at high speeds. So, from the astronaut twin's point of view the time on the earth has slowed down. So the astronaut twin calculates that he is older.
From the stay at home twin's point of view, the space ship is moving away at high speeds and the the space ship's inhabitants are also moving away at high speeds. So, from the stay at home twin's point of view the time on the space ship has slowed down. So the stay at home twin calculates that he is older.
They are each older than the other - paradox. The situation is symmetric, each calculates the same thing.
However, the situation is not truly symmetric because in order to accelerate up to high speeds, force is required. So the space ship has to have a force applied to it and the earth does not (or maybe vise versa in some crazy way).
Maybe that clears it up for you a bit. Hopefully he will chime in with a good explanation.
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deimya
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Re: Scale and the 5th dimension... [Re: DieCommie]
#8367802 - 05/06/08 03:31 AM (15 years, 11 months ago) |
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I think your explanation is clearer. But yeah, the symmetry of the situation is broken by four stages of acceleration: initial acceleration from rest to cruise speed, deceleration from cruise speed to a stop, then acceleration back to cruise speed in the opposite direction and final deceleration from cruise speed to rest. The other twin on Earth feels none of these forces, thus the asymmetry of the problem.
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HagbardCeline
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Re: Scale and the 5th dimension... [Re: deimya]
#8367931 - 05/06/08 06:17 AM (15 years, 11 months ago) |
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Just so I'm clear, the astronaut will have aged less though, correct?
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I keep it real because I think it is important that a highly esteemed individual such as myself keep it real lest they experience the dreaded spontaneous non-existance of no longer keeping it real. - Hagbard Celine
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deimya
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Re: Scale and the 5th dimension... [Re: HagbardCeline]
#8368027 - 05/06/08 07:45 AM (15 years, 11 months ago) |
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Yes indeed.
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maggotz
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Re: Scale and the 5th dimension... [Re: DieCommie]
#8371997 - 05/07/08 06:18 AM (15 years, 11 months ago) |
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thanks.
now i'm clear as to why the situation is not symmetric but i'm still not sure why there is an age difference. i know it has to do with speed but why?
why and how does approaching c affect time? also, it affects time itself, right? not just the perception of time. i'd appreciate any links to info.
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undergrounder
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Re: Scale and the 5th dimension... [Re: maggotz]
#8372114 - 05/07/08 07:33 AM (15 years, 11 months ago) |
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*grabs 'Stephen Hawkings - A Brief History of Time'*
*blows the dust off*
*opens up to page 3, where the bookmark still is*
ahem..
Time is not absolute. Each individual has his own personal measure of time that depends on where he is and how he is moving. Space and time are dynamic quantities. When a body moves or a force acts, it affects the curvature of space and time -- and in turn the structure of space-time affacts the way in which bodies move and forces act. Space and time not only affect, but are also affected by everything that happens in the universe.
Time is localised. It exists at a point in space, because it is tied to space -- the space time continuum. This means that just as you and i differ in our locality in terms of space, in the same way we differ in terms of time.
Now take this very real experiment that happened in 1962: Two clocks were placed one at the top of a tower and the other at the bottom. The clock at the top is moving faster through space relative to the one at the bottom. This is because it is sitting further away from the centre of the earth. And just as you move faster at the edge of a wheel than at the centre, so things that are at high elevations in the earth are moving faster than things at sea level - relative to eachother. Now back to the experiment, the clock at the top was found to run faster than the one at the bottom, in exact agreement with the theory of relativity. Both clocks were perfectly the accurate.
It's the same with physiological clocks. If you were to sit at the top of the tower and your exact twin at the bottom, you would become older than your twin - your heart would have pumped itself more times.
The effect is miniscule when talking about clock towers, an astronaut orbiting his twin on earth would age only a matter of seconds older over a year. But at speeds approaching c, the effect is much greater.
(Paraphrased and added to for relevance)
*Closes book*
Does that help?
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RIP
Bigger and bolder and rougher and tougher in other words sucka there is no other...
Edited by undergrounder (05/07/08 07:38 AM)
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undergrounder
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Re: Scale and the 5th dimension... [Re: undergrounder]
#8372150 - 05/07/08 07:44 AM (15 years, 11 months ago) |
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P.S. If you wave your right arm about like a madman, i guess it is moving through time faster than your left arm. Isn't that cool?
... Every time your husband/wife/girlfriend/boyfriend travels on a train while you're getting stoned on the couch, they are getting older than you.. suckers..
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RIP
Bigger and bolder and rougher and tougher in other words sucka there is no other...
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HagbardCeline
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Re: Scale and the 5th dimension... [Re: undergrounder]
#8372551 - 05/07/08 10:26 AM (15 years, 11 months ago) |
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I'm having a hard time understanding why Hawking would write that. It doesn't make sense. Why would the traveling person age more?
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I keep it real because I think it is important that a highly esteemed individual such as myself keep it real lest they experience the dreaded spontaneous non-existance of no longer keeping it real. - Hagbard Celine
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DieCommie
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Re: Scale and the 5th dimension... [Re: HagbardCeline]
#8373228 - 05/07/08 01:57 PM (15 years, 11 months ago) |
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Thats part of the theory of relativity. Its called time dilation, time progresses slower for moving things than stationary ones.
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deimya
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Re: Scale and the 5th dimension... [Re: DieCommie]
#8373486 - 05/07/08 03:02 PM (15 years, 11 months ago) |
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Also the language might be misleading. It is not really that the person ages more as if the aging process was accelerated but rather that there was more time to age normally.
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HagbardCeline
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Re: Scale and the 5th dimension... [Re: DieCommie]
#8373555 - 05/07/08 03:21 PM (15 years, 11 months ago) |
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I understand that, but his quote from Hawking says the opposite. He said the clock at the top of the tower was faster and likewise the astronaut would age more than his stationary sibling.
I'm reading that as saying time speeds up for moving objects and that isn't correct. Either he's misquoting Hawking or Hawking made a huge error in that book.
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I keep it real because I think it is important that a highly esteemed individual such as myself keep it real lest they experience the dreaded spontaneous non-existance of no longer keeping it real. - Hagbard Celine
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maggotz
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Re: Scale and the 5th dimension... [Re: deimya]
#8373624 - 05/07/08 03:40 PM (15 years, 11 months ago) |
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Quote:
deimya said:
Also the language might be misleading. It is not really that the person ages more as if the aging process was accelerated but rather that there was more time to age normally.
that makes more sense to me.
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HagbardCeline
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Re: Scale and the 5th dimension... [Re: deimya]
#8373630 - 05/07/08 03:41 PM (15 years, 11 months ago) |
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Huh? "More time to age normally" would mean you experienced time faster than the stationary person. That's still saying that the person would age more and that would have to mean that time was experienced faster for the traveling person.
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I keep it real because I think it is important that a highly esteemed individual such as myself keep it real lest they experience the dreaded spontaneous non-existance of no longer keeping it real. - Hagbard Celine
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deimya
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Re: Scale and the 5th dimension... [Re: HagbardCeline]
#8373651 - 05/07/08 03:47 PM (15 years, 11 months ago) |
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The thing with the tower is a bit misleading since locally both the tower and the ground are immobile relative to each others. It has more to do with acceleration effect since the top of the tower is further from the Earth's center and thus feeling a weaker gravitational acceleration. It is not an effect between inertial frames of reference, that is frames with a simple relative constant speed. So here the funny thing is that two frames might have zero relative speed but non-zero relative acceleration, which also entails time dilatation. But what Hawking says is somewhat true, or at least not entirely false.
Edited by deimya (05/07/08 03:53 PM)
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deimya
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Re: Scale and the 5th dimension... [Re: HagbardCeline]
#8373666 - 05/07/08 03:51 PM (15 years, 11 months ago) |
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A more accurate way of saying it is that for two observers zooming past each others (or distancing themselves) at constant speed, both will see the other's watch as ticking faster, but both will see their own watch ticking at the same speed. There is no absolute frame of reference so there's no way of telling if you're moving or not, only that you are moving relative to something else. After all you are always immobile relative to you, and so you always age the same from your perspective.
Hawking is speaking of accelerated frames of reference effects as I said in my previous post.
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HagbardCeline
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Re: Scale and the 5th dimension... [Re: deimya]
#8373966 - 05/07/08 05:11 PM (15 years, 11 months ago) |
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Ok, I can understand that then for the watch in the clock tower, but that still doesn't explain the astronaut. I understand that while the trip is going on that it would appear to both that hey have slowed down, but when the astronaut gets back home and goes to have dinner at his brother's house, he should be younger.
Why does Hawking say that he would have aged more?
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I keep it real because I think it is important that a highly esteemed individual such as myself keep it real lest they experience the dreaded spontaneous non-existance of no longer keeping it real. - Hagbard Celine
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HagbardCeline
Student-Teacher-Student-Teacher
Registered: 05/10/03
Posts: 10,028
Loc: Overjoyed, at the bottom ...
Last seen: 1 month, 30 days
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Re: Scale and the 5th dimension... [Re: deimya]
#8374062 - 05/07/08 05:34 PM (15 years, 11 months ago) |
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And here we have it. undergrounder's paraphrasing wasn't all that accurate. 
Quote:
Another prediction of general relativity is that time should appear to slower near a massive body like the earth.
This is because there is a relation between the energy of light and its frequency (that is, the number of waves of
light per second): the greater the energy, the higher frequency. As light travels upward in the earth’s
gravitational field, it loses energy, and so its frequency goes down. (This means that the length of time between
one wave crest and the next goes up.) To someone high up, it would appear that everything down below was
making longer to happen. This prediction was tested in 1962, using a pair of very accurate clocks mounted at
the top and bottom of a water tower. The clock at the bottom, which was nearer the earth, was found to run
slower, in exact agreement with general relativity. The difference in the speed of clocks at different heights
above the earth is now of considerable practical importance, with the advent of very accurate navigation
systems based on signals from satellites. If one ignored the predictions of general relativity, the position that
one calculated would be wrong by several miles!
Newton’s laws of motion put an end to the idea of absolute position in space. The theory of relativity gets rid of
absolute time. Consider a pair of twins. Suppose that one twin goes to live on the top of a mountain while the
other stays at sea level. The first twin would age faster than the second. Thus, if they met again, one would be
older than the other. In this case, the difference in ages would be very small, but it would be much larger if one
of the twins went for a long trip in a spaceship at nearly the speed of light. When he returned, he would be
much younger than the one who stayed on earth. This is known as the twins paradox, but it is a paradox only if
one has the idea of absolute time at the back of one’s mind. In the theory of relativity there is no unique
absolute time, but instead each individual has his own personal measure of time that depends on where he is
and how he is moving.
So it had nothing to do with the clock at the top of the tower traveling faster but that the clock at the bottom as nearer a massive body which caused time to slow. And just I thought, the astronaut would age less.
Hawking is still a genius and all is right with the world. Except undergrounder, you need to quote from now on. Your paraphrasing privileges have been revoked.
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I keep it real because I think it is important that a highly esteemed individual such as myself keep it real lest they experience the dreaded spontaneous non-existance of no longer keeping it real. - Hagbard Celine
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undergrounder
fluffy bunny
Registered: 11/10/06
Posts: 1,394
Loc: Sydney
Last seen: 1 year, 10 months
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Re: Scale and the 5th dimension... [Re: HagbardCeline]
#8376425 - 05/08/08 03:28 AM (15 years, 11 months ago) |
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 I enjoyed my paraphrasing priveleges... it made me feel smarter than i am..
I was leaving out the gravity thing specifically to make it relevant to the space ship example, which was you guys' example, although like i said earlier I was always referring to the gravitational effect.
Anyway i realised i was mixing the two up with that example after i wrote it (at 4am last night), and was coming back right now to clear it up and lo and behold you smart cookies were already on it. Go team 
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RIP
Bigger and bolder and rougher and tougher in other words sucka there is no other...
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