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IamHungry
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time and calculus
#3217660  10/05/04 12:04 PM (13 years, 1 month ago) 


for all you math nerds (apparently NOT like me):
think of a graph of an object moving at constant velocity. the coordinate plane has distance for the x values and time for the y values. at any given point on the graph, we can derive the object's equation and find the rate of change of its velocity at that instant (d/dx mx+b= 0 ). this 0 indicates a horizontal slope since the rate of change is not changing.
is it possible to graph time in such a way? does time have a derivative? if so, does the derivative have a derivative?
plus, i dont know how many of you have heard of spacetime diagrams. theyre graphs that symbolize the absolute time and space of an event relative to a mentioned reference frame. i think this might be more suited to this example but i never heard of it before class today, so im guessing theyre not too common.
 Here comes the sun, do n do do,
Here comes the sun, and I say,
It's alright...
Edited by IamHungry (10/05/04 01:05 PM)

Letto
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Re: time and calculus [Re: IamHungry]
#3217714  10/05/04 12:22 PM (13 years, 1 month ago) 


Quote:
IamHungry said: for all you math nerds (like me): think of a graph of an object moving at constant velocity. the coordinate plane has distance for the x values and time for the y values.
This is against all physics and math conventions. Time is always the independent variable, therefore it has to be on the xaxis. If it is the way you have it, your graph won't be a function, it'll be a relationship without any significance.
"at any given point on the graph, we can derive the object's equation and find the rate of change of its velocity at that instant (d/dx mx+b= x ). it just so happens that since the object is moving with constant velocity the derivative is going to be the same at every instant (x)."
Actually the derivative will be 0 since it's moving at a constant velocity, there is no acceleration. An object moving at constant velocity will have an equation y = 2 m/s or any other number. The derivative of a constant is 0.
"but for an object that is accelerating (velocity OR direction), the graph of the derivative is not going to be a straight line"
Sure it will. An object falls at 9.81 m/s^2 from gravity. The velocity vs. time graph will be a parabola. The acceleration graph will be a straight line with the slope 9.81.
"instead of graphing an object relative to its distance vs its time, lets graph "now" relative to position vs time. so... does time have a constant "velocity?" or does it accelerate and decelerate according to your own perceptions? is it possible to find the derivative of time? if so, what is it?"
Your graph is not a function, so you can't draw these inferences.

trendal
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Re: time and calculus [Re: IamHungry]
#3217835  10/05/04 01:05 PM (13 years, 1 month ago) 


Time does not have a velocity in much the same way that distance does not have a velocity
We move through time in much the same way that we move through space. The question, then, should be "do we move through time at a constant velocity?" The answer is no...but we DO more through spacetime at a constant velocity! Can you guess what that velocity is? It is the speed of light!
Our spacetime velocity always remains the same...but the individual components of our spatial velocity and temporal velocity can and do change. Think of time and space as being at right angles to each other. Now if you are running through "spacetime" at the speed of light, the two components of spatial and temporal velocity MUST add up to exactly the speed of light. So, if you are sitting COMPLETELY still spatially, you are moving at the fastest possible speed through the time dimension. If you decide to move through space itself, you must divert some of your time velocity into spatial velocity. Thus, time "slows down" as you speed up through space and vice versa
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Logic is a threat
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IamHungry
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Re: time and calculus [Re: trendal]
#3217855  10/05/04 01:13 PM (13 years, 1 month ago) 


wow, it makes so much sense now. is it safe to assume time stops when youre traveling at the speed of light? and is that why exercising allows you to live longer? although unless youre running near the speed of light the time perception difference is negligible.
Quote:
trendal said:We move through time in much the same way that we move through space. The question, then, should be "do we move through time at a constant velocity?" The answer is no...but we DO more through spacetime at a constant velocity! Can you guess what that velocity is? It is the speed of light!
i wish you were my professor instead of this clown i have now. he might as well have been teaching in portugese.
anyway i guess i thought of the passage of time as a passive event rather than an active event (wtf?). time doesnt pass, but rather we pass through time.
but thanks trendal you really cleared it up for me.
 Here comes the sun, do n do do,
Here comes the sun, and I say,
It's alright...

trendal
tangential derivation
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Re: time and calculus [Re: IamHungry]
#3217902  10/05/04 01:32 PM (13 years, 1 month ago) 


Yes, you would cease all movement through time if you could travel at the speed of light through space. Which brings me to an interesting tidbit: light does not feel the effects of time. A photon, which BEING light travels at the speed of light, does not move through time AT ALL. There are photons flying around space right now which were emitted shortly after the creation of the Universe...they have not aged one second in the 15 billion or so years since!
No, exercising does not slow down your passage through time...it just helps keep your body in good physical condition
 The story book's been read
And every line believed
Curriculum's been set
Logic is a threat
Reason searched and seized
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IamHungry
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Re: time and calculus [Re: trendal]
#3217922  10/05/04 01:38 PM (13 years, 1 month ago) 


is there a better forum for this? im fascinated beyond belief right now.
does gravity affect time?
 Here comes the sun, do n do do,
Here comes the sun, and I say,
It's alright...
Edited by IamHungry (10/05/04 01:54 PM)

trendal
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Re: time and calculus [Re: IamHungry]
#3217962  10/05/04 01:53 PM (13 years, 1 month ago) 


I'm sure there are lots of forums around that are specific to physics and science...but I don't mind discussing such things in a philosophy forum
Yes, gravity certainly DOES affect time! Gravity, as Einstein pointed out, is a warping of spacetime. The warping has two effects: we feel a force, which we call "gravity"...and our passage through time is slowed down. This has been experimentally confirmed by placing atomic clocks at the top and bottom of tall buildings...after a while the time on both clocks is compared and the one on top of the building has run SLIGHTLY slower than the one in the basement. This has something to do with the equivalencs of gravity and acceleration (gravity is itself a form of "acceleration"...if you are in a spaceship with no windows which is accelerating at 9.8 m/s^2 you would feel NO different than you would sitting on the launch pad: the "force" of acceleration is the same as the "force" of gravity).
Now you've got my mind all warped around some of thse ideas
 The story book's been read
And every line believed
Curriculum's been set
Logic is a threat
Reason searched and seized
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IamHungry
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Re: time and calculus [Re: IamHungry]
#3218008  10/05/04 02:03 PM (13 years, 1 month ago) 


so thats why black holes are so appropriately named. i mean, ive always known that light "cant escape from black holes," but i never pictured light as particles (photons) acted upon by a force (gravity).
this is just a thought here but would it be feasible to construct a more accurate standard of time for people to use? like should we take into account the elevation of a city to see what time it is relative to a lower city, or is that difference just way to small to notice?

trendal
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Re: time and calculus [Re: IamHungry]
#3218049  10/05/04 02:10 PM (13 years, 1 month ago) 


Second question first: yeah the difference is EXTREMELY small, so there isn't much of a point in redefining our standard of time or anything. We are only JUST able to detect time dilation with our most sensetive clocks.
As for black holes, yes they are called "black" because even light cannot escape them...but gravity does not DIRECTLY effect photons in the same way it affects matter. Remember that the light is moving THROUGH spacetime? Well if you warp spacetime, then the path that the light has to travel warps as well. Light passing close to the sun is "bent" slightly around the sun because the space there is warped by the sun's mass. When you watch a sunset on Earth, you "see" the sun fall below the horizon a little AFTER it actually happens (this is not just due to the time it take light to reach us...from the horizon to you is only a BRIEF fraction of a second for light to travel). The Earth's gravity "bends" the light from the sun slightly so that even though the sun has already set, you can still see the top of it.
Another effect of spacetime warping on light is that it causes a redshift in the light's frequency (ie: the frequency drops). In effect: the light leaving a black hole becomes SO redshifted that it is no longer visible (it shifts down in frequency until it essentially "doesn't exist").
 The story book's been read
And every line believed
Curriculum's been set
Logic is a threat
Reason searched and seized
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JacquesCousteau
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Re: time and calculus [Re: trendal]
#3218847  10/05/04 05:44 PM (13 years, 1 month ago) 


Quote:
trendal said: Think of time and space as being at right angles to each other. Now if you are running through "spacetime" at the speed of light, the two components of spatial and temporal velocity MUST add up to exactly the speed of light. So, if you are sitting COMPLETELY still spatially, you are moving at the fastest possible speed through the time dimension. If you decide to move through space itself, you must divert some of your time velocity into spatial velocity. Thus, time "slows down" as you speed up through space and vice versa.
This stuff is fascinating, Trendal, but I'm having a difficult time understanding how to apply these statements practically.
For instance, take this part: "Thus, time 'slows down' as you speed up through space and vice versa."
Let's specifically pinpoint the act of speeding up through space. What is a specific example of this?
Is it like when you move from a state of meditation in which you are perfectly still to a state of simply being up and about, walking around?
Is the spatial velocity you speak of the literal movement of the human body?
Does spatial velocity increase directly in relation to our perceived speed of physical movement? (ie, if I'm moving at 50 mph, is my temporal velocity lower than it would be if I was moving at 20 mph?)
And that brings up another big question: Does physical movement caused externally from ourselves (for instance, in the car going 50 mph) "count"? Does it apply to the relationship of spatial and temporal velocity, or does that only apply to our active motion? Why or why not?
Finally, my favorite question out of all these: What can this information of relationship between temporal and spatial velocity lead us to conclude about the time dialation experienced on psychedelics?
If our perception of time slows down, we must be moving at a higher temporal velocity. Therefore, we must be moving at a lower spatial velocity, right? What does that mean, practically speaking?
I don't study into this stuff much at all, but I still find it fascinating. Last time I tried was when I read "A Brief History Of Time" by Hawking. I just couldn't get my head around the concepts most of the time, because of the way he explains them.

JacquesCousteau
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Re: time and calculus [Re: trendal]
#3218872  10/05/04 05:49 PM (13 years, 1 month ago) 


After rereading the paragraph I quoted in my last post, I concluded that this statement may actually be a very good way of describing how we "exist". Perhaps we move through time at the speed of light before we're born, but then we decide to divert some of that into spatial velocity. I mean, the only time we are COMPLETELY still spatially is before we're born and after we die. It just seems to add up.
But perhaps I'm just crazy as a loon!

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Re: time and calculus [Re: IamHungry]
#3219446  10/05/04 07:56 PM (13 years, 1 month ago) 


yeah i was wondering about this stuff as well afew months ago... this thread was pretty interesting... http://www.shroomery.org/forums/showflat.php/Cat/0/Number/2965365/page//fpart/1/vc/1
this last post reminds me of the consept of the movie 21 grams (supposedly the amount of energy of life)... life just may be enegry making use of it's potential to interact with other enegry?
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trendal
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I'll try and answer all your questions as best I can
When I say "spatial velocity" I refer to your velocity through any of the spatial dimensions (length, height, width). When you are driving down the highway you are "moving through space" at a specific velocity (which is NOT be equal to your actual road speed!) You are also moving in a circle around the Earth's center as it rotates, and you are also moving around the sun (as the Earth orbits). Beyond that, our solar system moves around through the galaxy because of the gravitational influence of our neighbouring stars...we also orbit the galaxy once every 225,000,000 years or so. All these directions of movement (vectors) add up to get your "spatial velocity" (as I use the term, here).
Does spatial velocity increase directly in relation to our perceived speed of physical movement? (ie, if I'm moving at 50 mph, is my temporal velocity lower than it would be if I was moving at 20 mph?)
Spatial velocity is physical movement, and yes your temporal velocity does slow down the faster you move through space.
Think of it this way: spatial V + temporal V = spacetime V
Your spacetime velocity is the combination of your spatial and temporal velocities, and ALWAYS adds up to the speed of light.
And that brings up another big question: Does physical movement caused externally from ourselves (for instance, in the car going 50 mph) "count"? Does it apply to the relationship of spatial and temporal velocity, or does that only apply to our active motion? Why or why not?
All motion through spacetime is the same, whether it is caused by our muscles or an external force acting on our body (ie: your car's engine moving you and the car along the road).
Finally, my favorite question out of all these: What can this information of relationship between temporal and spatial velocity lead us to conclude about the time dialation experienced on psychedelics?
Here's where things get tricky There is a very BIG difference between the perception of time "moving", and the actual act of moving through time! The perception of time's movement is purely a human conception, probably part of the way our consciousness works. Your perception of time's movement can and will change depending on your state of mind. If your perception changes, however, your actual temporal velocity does NOT change. On the other hand, if your actual temporal velocity changes...there is NO effect on your perception of time's movement!
I don't feel that I am explaining this too well, I'll try again:
Your "perception" of time is a relative thing, depending on how "fast" your thought process occurs. If you are thinking "faster" than normal, you will perceive time as slowing down...if your thoughts slow down time will "feel" like it is speeding up.
Your temporal velocity however is not a perception...it actually occurs. You cannot "feel" changes in temporal velocity however. This is, of course, dependant on the assumption that human consciousness is a product of our physical bodies (specifically: brain), but we will entertain this assumption for the sake of argument. If you move a little slower through time, your entire body moves slower through time. From an outside perspective the nerves in your brain will ACTUALLY fire at a slower rate, as will all your bodily functions slow down. If your thought process is a function of brain function, and brain function slows down, then your thought process will slow down with it. You will not "feel" any different...it's not as if you will be watching your body and everything around you move slower (remember: that only happens when your PERCEPTION of time changes).
 The story book's been read
And every line believed
Curriculum's been set
Logic is a threat
Reason searched and seized
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JacquesCousteau
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Re: time and calculus [Re: trendal]
#3219712  10/05/04 09:00 PM (13 years, 1 month ago) 


Yeah, I follow you. Two different things entirely, basically.
I had the feeling that might be the answer.

kaiowas
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Re: time and calculus [Re: IamHungry]
#3220869  10/06/04 12:30 AM (13 years, 1 month ago) 


your graph will look like y axis will be the distance, and the x axis will represent time.
so here's the equation for a line: y=m*x+b
m=slope of the graph, or in physics terms (talking about speed) it is the rate of change of distance with respect to time.
x and y are the coordinates where x=time, and y is distance. b is where the object is at x=0 (or in this case where time is zero or our starting point).
y=m*x+b is only for a line. this means the slope is constant. it is the slope we are looking at, not time when we take the derivative.
here's how math people write it
dy/dx, the d's for some reason mean "the change in".
so the slope is the change in y (distance) divided by the change in x (time).
conceptually, the derivative can be looked on as a marker to check on the rate of change between things and any instantaneous moment.
so in this case if we are talking about a car, if it is in the line format (ie y=m*x+b), the car wouldn't be changing speeds, because a line's slope is constant. it never changes. so you ask, what if we take the rate of change with respect to the rate of change, in this case it would be zero, because the car isn't accelerating, (cause it never changes speed).
I'll try units as well to clarify
the units for speed could be written as (miles per hour). in this case this means miles divided by hours. that's the rate, ie the slope of the line. taking the derivative of this is saying, ok, I wonder how fast the car is going at t=2 seconds compared to t=5 seconds. well, if we have a line, it's slope never changes, which means the speed of the car never changes. this means the car is going just as fast at t=2 seconds as it is at t=5 seconds. so therefore there is no rate of change, and the derivative is zero.
lets look at the units
take the derivative of the slope is seeing how fast the speed is changing with respect to time. this means it looks like this
mph/h
miles per hour divided by hours is the acceleration (how fast speed changes with respect to time).
so you see what I mean? you can't take the derivative of time itself, because the derivative is looking at the change of one thing with respect to the other. notice how I keep saying "with respect to" because that is what calculus is. looking at the change.
 Annnnnnd I had a light saber and my friend was there and I said "you look like an indian" and he said "you look like satan" and he found a stick and a rock and he named the rock ooga booga and he named the stick Stick and we both thought that was pretty funny. We got eaten alive by mosquitos but didn't notice til the next day. I stepped on some glass while wading in the swamp and cut my foot open, didn't bother me til the next day either....yeah it was a good time, ended the night by buying some liquor for minors and drinking nips and going to he diner and eating chicken fingers, and then I went home and went to bed.senior doobie

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Re: time and calculus [Re: IamHungry]
#3221538  10/06/04 03:54 AM (13 years, 1 month ago) 


Look here:
http://www.ac.wwu.edu/~markosia/papers/Rate.pdf
"How fast does time pass?" by Ned Markosian. The argument discussed:
(1) If it makes sense to say that time passes, then it makes sense to ask 'How fast does time pass?'. (2) If it makes sense to ask 'How fast does time pass?', then it's possible for there to be a coherent answer to this question. (3) It's not possible for there to be a coherent answer to this question. ???????????????????????????????? (4) It doesn't make sense to say that time passes.
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Re: time and calculus [Re: trendal]
#3221597  10/06/04 04:44 AM (13 years, 1 month ago) 


if you are in a spaceship with no windows which is accelerating at 9.8 m/s^2 you would feel NO different than you would sitting on the launch pad
As long as the ship wasn't rotating as it moved through space. Something about innertial frames or something...
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