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Author Topic:   Time, a brief history
Son Goku
Inactive Member


Message 46 of 62 (298400)
03-26-2006 6:13 PM
Reply to: Message 30 by sinamatic
03-23-2006 12:53 PM


Spacetime Geometry
Space-time was thought-up to make equations work.
Introduction.
The equations, as nwr said, worked regardless of whether spacetime is considered real or not. Einstein himself didn't use the idea of spacetime, instead using ideas functions of velocity for empirical results. Later however it was found that relativity is more naturally (in a mathematical sense) a theory of a four-dimensional geometry called Minkowski geometry.
The four dimensional space described by this geometry is called Minkowski space, or as it is more commonly called by the public "spacetime".
However one might ask, what does a physicist mean when they say space and time are unified into one entity?
2-D basics.
Let's start with a two dimensional geometry, of the kind most people are familiar with.
This is a 2-D plane labelled by the x axis and the y axis.
Any point can be labelled by any two numbers x and y.
(Like the point (1,2) or (2,3), e.t.c.)
Now let us say we have two points on this plane:
How far away are they from each other?
Well we can draw a triangle from point one to point two as such:
And we find that the distance between the two points is (using Pythagoras' theorem):
ds^2 = dx^2 + dy^2.
Where dy is the difference in the y values (y2 - y1) of the two points, dx is the difference in the x values (x2 - x1) of the two points and ds is the distance between the two points.



Now let's jump to four dimensions.
This is a 4-D plane with not just a x axis and y axis, but also a z axis and a w axis.
So any point can be labelled by four numbers x,y,z,w.
(Such as (1,3,4,2), e.t.c.)
What the distance between two points in four dimensional space then?
Well it's:
ds^2 = dx^2 + dy^2 + dz^2 + dw^2
Where,
dx is the difference in the x values,
dy is the difference in the y values,
dz is the difference in the z values,
dw is the difference in the w values,
and ds is the difference between the points.
(As an example the points (1,3,1,2) and (9,7,5,4) are a distance of 10 apart.
dx = 8, dy = 4, dz = 4, dw =2.
So,
ds^2 = dx^2 + dy^2 + dz^2 + dw^2 = 100.
If ds^2 = 100, ds=10.)




Time for a change.
However this is just 4-D space. Every dimension is a space dimension.
Lets change one of them to a time dimension.
Now we have a 4-D plane with a x axis, y axis, z- axis and a t-axis.
Any point can be labelled with four numbers (x,y,z,t)
So far this is the same as when every dimension is a spatial one.
Now what is the distance between two points in this plane.
It turns out to be:
ds^2 = dx^2 + dy^2 + dz^2 - dt^2.
Where dt is the difference in the time values.
Compare this with the distance formula for four spatial dimensions above:
ds^2 = dx^2 + dy^2 + dz^2 + dw^2.
So time is just like a spatial dimension except you take away the square of difference in time values of two points, instead of adding it, when you are trying to find out the total distance between them.
Nearly all of special relativity falls out if we just assume the distance between points in the universe is governed by:
ds^2 = dx^2 + dy^2 + dz^2 - dt^2.
So we say the universe is "A 4-D plane with the above formula as the rule for distances".
Formally, we call "A 4-D plane with the above formula as the rule for distances" a Minkowski space or sometimes spacetime, because you use both space and time in the formula for distance.
This message has been edited by Son Goku, 03-26-2006 06:15 PM
This message has been edited by Son Goku, 03-26-2006 06:45 PM

This message is a reply to:
 Message 30 by sinamatic, posted 03-23-2006 12:53 PM sinamatic has replied

Replies to this message:
 Message 48 by sinamatic, posted 03-27-2006 3:19 AM Son Goku has not replied
 Message 50 by Posit, posted 03-27-2006 7:21 AM Son Goku has replied

  
sinamatic
Member (Idle past 4144 days)
Posts: 67
From: Traverse City, MI usa
Joined: 03-10-2006


Message 47 of 62 (298516)
03-27-2006 3:12 AM
Reply to: Message 45 by sidelined
03-26-2006 11:35 AM


Re: Time to discuss theories
Regardless, you now see by this statement of yours the inseperabilty of spacetime in describing an event.This is direct contradiction of your earlier statement{Post # 23} that space and time are different.
The only thing you have proved is that space and time are directly equvilent in mathamatical formulas. This does not make them the same though they are reliant on each other for calculation. Time is not always used to measure space or velocity. They are different

This message is a reply to:
 Message 45 by sidelined, posted 03-26-2006 11:35 AM sidelined has replied

Replies to this message:
 Message 49 by Phat, posted 03-27-2006 3:29 AM sinamatic has not replied
 Message 55 by sidelined, posted 04-08-2006 1:54 AM sinamatic has not replied

  
sinamatic
Member (Idle past 4144 days)
Posts: 67
From: Traverse City, MI usa
Joined: 03-10-2006


Message 48 of 62 (298519)
03-27-2006 3:19 AM
Reply to: Message 46 by Son Goku
03-26-2006 6:13 PM


Re: Spacetime Geometry
Formally, we call "A 4-D plane with the above formula as the rule for distances" a Minkowski space or sometimes spacetime, because you use both space and time in the formula for distance.
I understand, thanks for the explanation.

This message is a reply to:
 Message 46 by Son Goku, posted 03-26-2006 6:13 PM Son Goku has not replied

  
Phat
Member
Posts: 18262
From: Denver,Colorado USA
Joined: 12-30-2003
Member Rating: 1.1


Message 49 of 62 (298521)
03-27-2006 3:29 AM
Reply to: Message 47 by sinamatic
03-27-2006 3:12 AM


Speaking of Time....
Its now time to redefine and redirect this topic that you started...way back about 48 posts ago. You said then:
Brokenpride writes:
I have a little theory on time that I feel leans towards the existance of God. Please give it some thought and I would love to hear your replies.
It was clarified and explained that since you chose Cosmology---a scientific way of exploring the universe--that God was not the topic to be explained. Rather, the Universe and its origin were our focus...right?
I guess what Im trying to say is if you feel ready to redefine the topic and ask a fresh set of questions and/or express your current state of mind philosophically please do so! (P.S. Son Goku is very scientific and articulate, don't you think? I always learn something from his posts! He is like a Professor! )
This message has been edited by Phat, 03-27-2006 01:31 AM

This message is a reply to:
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Posit
Inactive Member


Message 50 of 62 (298548)
03-27-2006 7:21 AM
Reply to: Message 46 by Son Goku
03-26-2006 6:13 PM


Re: Spacetime Geometry
Son Goku writes:
Now we have a 4-D plane with a x axis, y axis, z- axis and a t-axis.
Any point can be labelled with four numbers (x,y,z,t)
So far this is the same as when every dimension is a spatial one.
Now what is the distance between two points in this plane.
It turns out to be:
ds^2 = dx^2 + dy^2 + dz^2 - dt^2.
Where dt is the difference in the time values.
Compare this with the distance formula for four spatial dimensions above:
ds^2 = dx^2 + dy^2 + dz^2 + dw^2.
Very interesting. Of course, you left out the little detail of units.
What do you get when you subtract 10 seconds from 2 meters?

This message is a reply to:
 Message 46 by Son Goku, posted 03-26-2006 6:13 PM Son Goku has replied

Replies to this message:
 Message 51 by Son Goku, posted 03-27-2006 7:42 AM Posit has replied

  
Son Goku
Inactive Member


Message 51 of 62 (298556)
03-27-2006 7:42 AM
Reply to: Message 50 by Posit
03-27-2006 7:21 AM


Re: Spacetime Geometry
If we measure time with a different set of units than space (as humans naturally do, although we don't sometimes in cosmology) we need to know how much meters is a second worth.
It turns out (using Foucault's method basically, but there are more developed ones) that a second is equivalent to 300,000,000 meters.
So in essence if I had a ball located in the middle of a room at twelve o' clock its coordinates in spacetime are (0 0 0 0) let us say.
The clock one second into the future has the coordinates:
(0 0 0 300,000,000).
A second is 300,000,000 meters in the temproal direction.
(It's actually 299,792,458 meters, but you get the idea.)

This message is a reply to:
 Message 50 by Posit, posted 03-27-2006 7:21 AM Posit has replied

Replies to this message:
 Message 52 by Posit, posted 03-27-2006 8:14 AM Son Goku has replied
 Message 57 by ramoss, posted 04-18-2006 8:03 AM Son Goku has replied

  
Posit
Inactive Member


Message 52 of 62 (298568)
03-27-2006 8:14 AM
Reply to: Message 51 by Son Goku
03-27-2006 7:42 AM


Re: Spacetime Geometry
So two events occurring 300,000,000 meters distant and one second apart have zero distance between them, even though they are at different points in Minkowsky space?

This message is a reply to:
 Message 51 by Son Goku, posted 03-27-2006 7:42 AM Son Goku has replied

Replies to this message:
 Message 53 by cavediver, posted 03-27-2006 8:31 AM Posit has not replied
 Message 54 by Son Goku, posted 03-27-2006 9:06 AM Posit has not replied

  
cavediver
Member (Idle past 3643 days)
Posts: 4129
From: UK
Joined: 06-16-2005


Message 53 of 62 (298575)
03-27-2006 8:31 AM
Reply to: Message 52 by Posit
03-27-2006 8:14 AM


Re: Spacetime Geometry
So two events occurring 300,000,000 meters distant and one second apart have zero distance between them, even though they are at different points in Minkowsky space?
You'll make a relativist yet

This message is a reply to:
 Message 52 by Posit, posted 03-27-2006 8:14 AM Posit has not replied

  
Son Goku
Inactive Member


Message 54 of 62 (298587)
03-27-2006 9:06 AM
Reply to: Message 52 by Posit
03-27-2006 8:14 AM


Re: Spacetime Geometry
That is exactly correct.
Now lets look at light. Light travels 300,000,000 meters in one second.
So the starting point and ending point of a light beam after a one second journey are one second and 300,000,000 meters apart and so, as you concluded, they would have zero distance between them even though they are in different points in Minkowski space.
This is why light doesn't experience time and distance, because even though it can occupy many points, there is no distance between them.

This message is a reply to:
 Message 52 by Posit, posted 03-27-2006 8:14 AM Posit has not replied

  
sidelined
Member (Idle past 5908 days)
Posts: 3435
From: Edmonton Alberta Canada
Joined: 08-30-2003


Message 55 of 62 (302272)
04-08-2006 1:54 AM
Reply to: Message 47 by sinamatic
03-27-2006 3:12 AM


Re: Time to discuss theories
Brokenpride
Time is not always used to measure space or velocity
Really? Try to make a measurement in the absence of a time component. How would this be accomplished since without time an action of measurement cannot take place. Velocity is defined as a displacement in space over a set time period {meters per second, miles per hours}.
To make it actually correct we must also include a direction in dealing with velocity.

This message is a reply to:
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Bashier Ahmed
Inactive Member


Message 56 of 62 (304910)
04-18-2006 7:22 AM
Reply to: Message 8 by sinamatic
03-21-2006 8:13 PM


Re: God has not to pay anyting to be liberal
I don't agree with "Anything made up of matter can not be infanate". Neither I support the concept of Infinite. Actually more research only would answer this issue. For my perception the God has infinite capability in infinite dimensions; our universe is just a small portion of it. If we assume that God has created the universe (and many more other things) then from my perception a single particle could come into existance from nothing. In other words 1 originated from a null or zero for simplification. Thus 0 equals to 1. If 0=1 then simply 0=infinite (I mean infinity of cosmos has also a high probablity as much as finite cosmos).
I many times tried to visualise time, the forth dimension; and I believe that there must be some way to visualise time either in our mind or on a paper (could be as simple as we see a 3D table). I have searched on the web for the same but I did not get satisfactory results. Any body who reads this message is welcome to flash a light on this.
This message has been edited by Bashier Ahmed, 04-18-2006 07:26 AM
This message has been edited by Bashier Ahmed, 04-18-2006 07:32 AM
This message has been edited by Bashier Ahmed, 04-18-2006 07:37 AM

This message is a reply to:
 Message 8 by sinamatic, posted 03-21-2006 8:13 PM sinamatic has not replied

Replies to this message:
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ramoss
Member (Idle past 612 days)
Posts: 3228
Joined: 08-11-2004


Message 57 of 62 (304917)
04-18-2006 8:03 AM
Reply to: Message 51 by Son Goku
03-27-2006 7:42 AM


Re: Spacetime Geometry
That basically is saying that photons, which are moving at the speed of light, do not experiance time, correct??
If so, what about photons that are beign slowed down, by glass for example??

This message is a reply to:
 Message 51 by Son Goku, posted 03-27-2006 7:42 AM Son Goku has replied

Replies to this message:
 Message 58 by Son Goku, posted 04-18-2006 10:16 AM ramoss has not replied

  
Son Goku
Inactive Member


Message 58 of 62 (304942)
04-18-2006 10:16 AM
Reply to: Message 57 by ramoss
04-18-2006 8:03 AM


Re: Spacetime Geometry
That basically is saying that photons, which are moving at the speed of light, do not experiance time, correct??
Yeah, pretty much.
If so, what about photons that are beign slowed down, by glass for example??
They aren't actually slowed down. They're just continuously absorbed and emitted by the material in the glass.

This message is a reply to:
 Message 57 by ramoss, posted 04-18-2006 8:03 AM ramoss has not replied

Replies to this message:
 Message 59 by sidelined, posted 04-18-2006 11:11 AM Son Goku has not replied

  
sidelined
Member (Idle past 5908 days)
Posts: 3435
From: Edmonton Alberta Canada
Joined: 08-30-2003


Message 59 of 62 (304960)
04-18-2006 11:11 AM
Reply to: Message 58 by Son Goku
04-18-2006 10:16 AM


Re: Spacetime Geometry
Son Goku
ramoss writes:
That basically is saying that photons, which are moving at the speed of light, do not experiance time, correct??
If light from another galaxy does not experience time does the information it carries also not experience time?

This message is a reply to:
 Message 58 by Son Goku, posted 04-18-2006 10:16 AM Son Goku has not replied

Replies to this message:
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cavediver
Member (Idle past 3643 days)
Posts: 4129
From: UK
Joined: 06-16-2005


Message 60 of 62 (305007)
04-18-2006 1:41 PM
Reply to: Message 59 by sidelined
04-18-2006 11:11 AM


Re: Spacetime Geometry
If light from another galaxy does not experience time does the information it carries also not experience time?
Hmmm, yes and no. By talking about another galaxy you are introducing GR effects into what was originally a question based on SR. Say the info is coded into the frequency of a photon. Although the photon experiences no time as it travels from the transmitter to the receiver, it is red-shifted. The frequency reduces by an amount related to the time passage of the photon as measured by comoving observers in the respective galaxies.
But if we take a nearby Local Group galaxy that we assume is stationary wrt us in the Galaxy, then yes, the information will not experience any real measure of time.
When you look at a star, the photon emission of the electron in the star and the photon absorption by the electron in your pupil* have no distance between them. We are so connected to the rest of the universe
(* assuming a free path through the atmosphere)

This message is a reply to:
 Message 59 by sidelined, posted 04-18-2006 11:11 AM sidelined has not replied

  
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