Re: RMT Linear time

Angleochoas

Angleochoas

Quantum Scribe
If time is linear, then why does its passage slow non-linearly as the observer approaches the speed of light? The vibratory frequency that we live within and that our senses respond to tell us that time appears to be linear. Yet Einstein's equations tell us otherwise as v-->c.
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Perhaps it is a linear function further coupled with gravity to give it's "shape"?
It would seem from more than one area that gravity manipulates the line, and perhaps pulls it into a distorted "sphere" under the right circumstance; though are we speaking of one singular force (time) or a shared aspect of something larger? IE; (time+gravity)
 
If time is linear, then why does its passage slow non-linearly as the observer approaches the speed of light? The vibratory frequency that we live within and that our senses respond to tell us that time appears to be linear. Yet Einstein's equations tell us otherwise as v-->c.
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First "the observer" isn't the person who is approaching the speed of light. The person who feels the force of the acceleration, the observed, is approaching the speed of light. The observer is watching. Each will observe his/her counterpart's clock and measuring rod change but will notice no change in his own frame of reference. That's half of the reason that our senses tell us that our personal (proper) time is linear. The other half of the answer is that we have no current ability to accelerate massive objects like grains of sand or people to even 100 km/sec let alone to near the speed of light. We sense what we have experienced and we simply cannot experience situations involving near light velocity.

Perhaps it is a linear function further coupled with gravity to give it's "shape"? It would seem from more than one area that gravity manipulates the line, and perhaps pulls it into a distorted "sphere" under the right circumstance; though are we speaking of one singular force (time) or a shared aspect of something larger? IE; (time+gravity)
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Yes, from the inertial observer's frame the rate of the flow of time is a function of relative velocity, gravity and the degree of seperation between the observer and observed. That is experssed in Special and General Relativity. Gravity distorts spacetime.
 
Taking time and gravity into context then...
this must get alot more complicated when one looks at the universe like an infinite number of cogs in a gigantic clock...with varying gravitational waves eminating from various fields.
(stars, planets, etc).
 
this must get alot more complicated when one looks at the universe like an infinite number of cogs in a gigantic clock...with varying gravitational waves eminating from various fields.
(stars, planets, etc).
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Hence why the "N-body problem" really is an honest to goodness problem! :D
RMT
 
Hi ruthless,

Hope you are recovering! Why did she run you over???

its not that big of a deal if you work it one cog at a time
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That would be valid if the universe were static. But the problem is that it is a dynamics problem... the "cogs" (bodies) are always in motion, and the motion of the bodies cause them to warp different areas of spacetime as they move. So even if you could take the time to solve the forces acting on a single body ("cog") the solution would no longer be valid once you have it because all the other bodies would have moved and the correct solution would now be different. This is why the "N-body problem" is so difficult... it requires the simultaneous solution of a large number of coupled differential equations. The math to just solve a 3-body problem is mind-blowing. And no one has, as yet, solved a 4-body problem.

it becomes rather simple then, in my opinion.
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I can understand how you might think so. This is another case of where the universe is a lot more complex than we would like it to be. :D Check out this wiki:

http://en.wikipedia.org/wiki/N-body_problem

<font color="red"> The n-body problem is the problem of finding, given the initial positions, masses, and velocities of n bodies, their subsequent motions as determined by classical mechanics, i.e., Newton's laws of motion and Newton's law of gravity.[/COLOR]

You should also note immediately that this is dealing with classical mechanics only (i.e. Newtonian). That means even if you could solve the N-body problem classically it still does not include the effects of relativity which need to be taken into account with the near-light-speed case discussed by Angleo in his OP. That introduces even more complexity. We are talking some of the most complicated calculus problems ever!

RMT
 
hey ray,

Hope you are recovering! Why did she run you over???
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im about 80% right now. i dont figure itll take me too much longer. the first few days were pretty rough though.

i tried to get out of the car, i was upset. it was the first time we have been that close to each other in two years. we were both pretty upset and didnt want to be around each other.

so i opened the door to get out, she tried to speed up, thinking i wouldnt try to get out. i jumped out and tried to run, but my leg got caught under the tire. i slammed on my back, bounced, landed on my feet and kept walking, terminator style. my leg got ran over and my arm got ran over, and my back looks like jesus' back in the passion of the christ lol.

im making light of it now, but it really is some dysfunctional stuff. anyways, onto more interesting things. its been a long time since i have had an intelligent conversation...

about the n-body problem:

would it be possible to use autocad software with standard x,y coordinates, make gravity equal for all coordinates, then differentiate mass based on its same position within the universe?

this would in effect solve the n-body problem by saving your work, while being able to work on the individual cogs while they are in the x,y coordinate you are looking at.

thats off the top of my head. ill give it some more thought today.
 
Then you raise another question:
At what margin of error does the data render itself purely indicative rather than conclusive?
Remember the original subject topic was in regards to "linear time";
not chasing circles ^^
 
Hi ruthless:

about the n-body problem:

would it be possible to use autocad software with standard x,y coordinates, make gravity equal for all coordinates, then differentiate mass based on its same position within the universe?
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The n-body problem is not really a software tool problem. It is a pure mathematics problem based on Newtonian physics. That being said, autocad is really just a drawing package and not really useful for dynamics analysis. There are tools that satellite and planetary probe designers use that employ iterative solutions of the 3-body problem to plan missions (to Mars, and other heavenly objects). Satellite Tool Kit is one of the most popular. But again, even this tool cannot solve the n-body problem. It solves for trajectories with 3 bodies at a time and then iterates those solutions across several of the most important heavenly influences (i.e. earth, the sun, the probe, and the target planet/moon). Fun stuff to work on!!!

this would in effect solve the n-body problem by saving your work, while being able to work on the individual cogs while they are in the x,y coordinate you are looking at.

thats off the top of my head.
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Not sure I understand, but as I say above it would be an enormous challenge to try and use any existing software tool to "solve" the n-body problem. Explore the effects of multi-body problems, yes, but not solving the dynamics of an arbitrary number of bodies and their effects on each other.

The mathematics of infinite series expansions (Taylor Series) is a foundation for understanding problems like the n-body problem. This is typically second-year calculus in an undergrad engineering program. Go back and look at the n-body wiki link I provided above and look at equation #1 under the "Mathematical Formulation of the n-body problem" heading. That is similar to an infinite series expansion because it is a summation of terms. It effectively becomes an infinite series when you seek for "n" to be equal to all the bodies in the universe! :eek:

RMT
 
Then you raise another question:
At what margin of error does the data render itself purely indicative rather than conclusive?
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The answer to this always depends on what you are trying to do with the solution. (Back to intention!) /ttiforum/images/graemlins/smile.gif What I mean by this can be explained with an example from airplane navigation (my favorite topic!):

A standard GPS navigation solution on an airplane is more that good enough (has a small enough error band) to fly around in the "up and away" airspace above 18,000 feet (called IFR airspace). In general that error band is about 6 meters laterally (Latitude and Longitude) and can be as large as 10-20 meters vertically (Altitude). This is good enough to keep two airplanes from crashing into each other. But now if my intention is not only to navigate "up and away" but to actually navigate for takeoff and landing, we can see that the errors stated above are going to be problematic! If I was 6 meters off the runway centerline when I am going to land (best case), that is not very much margin on runway which have a total width of only 50 meters. But the vertical is the real problem!!! If I am even 10 meters off in my knowledge of my vertical position with respect to the ground that could lead to one VERY hard landing!

So my point is, again, to show that "indicative vs. conclusive" for something like the n-body problem cannot be determined absolutely. It must be couched in terms of what you are trying to do with the knowledge.

Remember the original subject topic was in regards to "linear time";
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Linear time is nothing more than a fabrication of the human mind. Nothing in the universe is truly linear. But a great many things can be approximated as linear within a given range of applicability. In fact, the biggest barrier to mankind achieving a comprehensive understanding of the universe is that we always tend to want to linearize everything just because it makes it easier to understand! As amazing as the human brain is, it is still VERY bandwidth-limited! /ttiforum/images/graemlins/smile.gif

RMT
 
The n-body problem is not really a software tool problem. It is a pure mathematics problem based on Newtonian physics. That being said, autocad is really just a drawing package and not really useful for dynamics analysis. There are tools that satellite and planetary probe designers use that employ iterative solutions of the 3-body problem to plan missions (to Mars, and other heavenly objects). Satellite Tool Kit is one of the most popular. But again, even this tool cannot solve the n-body problem. It solves for trajectories with 3 bodies at a time and then iterates those solutions across several of the most important heavenly influences (i.e. earth, the sun, the probe, and the target planet/moon). Fun stuff to work on!!!
Click to expand...

all the software tool would do is act as a universe simulator. it wouldnt have to be an exact copy.
even if you only get 1 frame every 15 years, mankind can eventually figure it out. easy as pie.

from what i have read, and have come to understand is that there is not enough cpu power.

lets use a pool table as an example. when a cue ball strikes a ball, even the tiniest of cpu's can accurately determine the balls trajectory, but when you add another ball into the equasion, even the worlds most powerful supercomputer has trouble determining accurately where they will go.

so, from that i say, use autocad software to map a universe, and test things to apply to the real world. you only use the autocad software to design the universe. you would have to liscense a sandbox- style engine with the most realistic physics model possible. you would then be able to look at a node using the standard x,y coordinates, and save your work. you can then focus onto one body, and know that the other bodies are in your equasion without having to map them all at once.

people can then safely work theories that may someday apply to the real world.
 
google rules all...

...and i must not be as stupid as ah' look! :D

The Millennium Run, also called the Millennium Simulation because of its size,[1][2] is the name of a computer N-body simulation which was run in order to investigate how matter in the Universe evolved over time. It is used by scientists working in physical cosmology to compare observations with theoretical predictions.

A basic scientific tool to test theories in cosmology is to evaluate their consequences for the observable parts of the universe. One piece of observational evidence is the distribution of matter, including galaxies and intergalactic gas, which are observed today. Light emitted from more distant matter must travel longer in order to reach Earth, meaning looking at distant objects is like looking further back in time. This means the evolution in time of the matter distribution in the Universe can be observed.
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The Millennium Simulation was run in 2005 by the Virgo Consortium, an international group of astrophysicists from Germany, the United Kingdom, Canada, Japan and the United States. It starts at the epoch when the cosmic background radiation was emitted, about 379,000 years after the universe began. The cosmic background radiation has been studied by satellite experiments, and the observed inhomogeneities in the cosmic background serve as the starting point for the corresponding matter distribution. Using the physical laws expected to hold in the currently known cosmologies, the initial distribution of matter is allowed to evolve, and the formation of galaxies and black holes in the simulation are recorded.
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http://en.wikipedia.org/wiki/Millennium_Run

http://en.wikipedia.org/wiki/N-body_simulation
 
Aren't these still two different things?
A simulation can be of anything, some more accurate than another, but I've never heard of them referred to as a proof of anything?

Take those simulations on A&amp;E of dinosaurs fighting sabre tooths, etc
If those simulations are based upon the theoretical probability of behaviours - does that give proof? I think not, however it does give more insight into theory, and maybe that leads eventually to the proof? Who can say?

Interesting points though.

Reading their official site there's alot of simulation in regards to dark matter.
I think that speaks volumes in this context. We've only proclaimed proof of it's existence in the last few years, and admit mostly we still have no clue what it is, so any speculation of long term observation to provide statistical data is out of the question obviously.
 
...and i must not be as stupid as ah' look!
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That is never been in dispute! /ttiforum/images/graemlins/smile.gif Why do you think Darby and I have constantly encouraged you to go back to school?


But Angleo has it right. It seems we have a terminology disconnect between us. A simulation of the N-body problem is not solving the N-body problem. So perhaps what you were talking about all along was simply simulating N-bodies, and I can accept that. But as I said, solving the N-body problem is nothing but math, and it has not been achieved and prospects to achieve it right now still look dim.

But simulations can get you close... depending on what you wish to use the knowlege for.
RMT
 
It's Saturday &amp; I'm having a beer, hence this comment.
In context to our conversation, I believe in another timeline if Def Leppard had never existed, RMT would never have worked for Northrop.
(Not to mention the implications this draws to future diet pepsi commercials).

Cheers lol.
 
Pass a beer down this way and share with a brutha, will ya? :D

Just try to think of a timeline where TTI does not exist! :eek: What would we be doing with our spare time in that timeline???

RMT
 
its not that big of a deal if you work it one cog at a time. it becomes rather simple then, in my opinion.
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Unless the 'problem' revisits a 'problem'.
Meaning, just as you 'figure' out 'one cog' and move on, you must always revisit the earlier calculation and revise it's properties.
Almost a 'time machine' in itself and very complex.
A certain integer comes starkly to mind in this context.
 
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