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bibhas
This thread has its origins in some concepts of Physics I don't understand. These are those that frequent discussions on the origin of the universe. The following post from the "Determinism & Free Will" thread in Chit-O-Chat will serve as the starting reference.

QUOTE(hits @ Aug 31 2005, 03:03 PM)
QUOTE(bibhas @ Aug 31 2005, 12:53 PM)
QUOTE(hits @ Aug 31 2005, 11:13 AM)
My opinion on the question of the existence of an absolute scale is that it depends on what YOU are. If you define yourself to be the entire physical universe, sure there is an absolute frame of reference. If you are a Vivek or Hithesh, then there are 2 possibilities -

1) You know the exact boundaries of the physical universe
2) You don't.

In case 1, there can be an absolute scale, and time can be unidirectional. In case 2, not so much. Remember though, I am strictly referring to the physical domain here.

Hits
*


My turn to play the "'I am stupid" card.
Someone please explain what an "absolute scale" is and how it is related to the uni-directionality of Time. Also, is it being implied that time can be multidirectional in a non-absolute scale ? How so ?
*



Bibhas,

I'll explain what I meant in my post -

An absolute scale is just another term for an absolute frame of reference. As you will know, in expressing a "transformation" or physical movement in terms of units of dimensions, it becomes paramount to fix the position of zero. Depending on where "zero" is with respect to you, the observer, your answer may look different (although they are the same).

So, the presence of an absolute scale would solve that problem. Every entity in the physical domain will know precisely where "zero" is, and where they lie in relation to "zero". Trouble is, if you don't know the extent of the physical domain, it becomes difficult to start assigning an "absolute scale". But that's fine, because "non-absolute scales" will do the job just fine (you just need to remember that they are not absolute).

Now, as you will see, the flow of time will vary depending on how you assign the scale. This can get complicated quickly, as we are slowly digressing towards the first lecture on the Theory of Relativity! I can get into that in a different thread if you want me to.

A final point - Time can be multidirectional even on an absolute scale. One just doesn't see it happen in our physical lives.
*



Hithesh,
I am still confused about why one needs to know the complete extent of the physical domain in order to have an absolute frame of reference. Also confused about the flow of time in both non-absolute and absolute scales.
Bibhas
hits
Bibhas,

Have you started on Hawking's book?

Hits
visuja
Me did Hitesh sad1.gif ..but lost myself in the first few pages and then didnt have the drive to move forward. As I said, I need lots of time to digest new info and being as impatient as I am, I'm still stuck with rudimentary questions in many areas. (Shaayad umar ke saath saath patience bhi aa jaaye unsure.gif :sigh:)

Since Shivani mentioned a few things on 'strings", Shivani -- could you explain what are "strings" ? And how does its definition help in unifying ('tying up' !) all theories together ?
anurag
For all the questions being posed here, may I suggest the recent book by Roger Penrose "The Road to Reality". Some of you may have heard about his earlier popular book titled "The Emperor's New Mind" in which he discussed the inadequacy of the laws of physics in explaining consciousness.

In his new book, String theories and the more recent version of string theory, known as M-Theory have been augmented with his newly proposed twister theory.

In my opinion, this is a fantastic and a very gentle reading on a Sunday afternoon over oodles of coffee. I assure you that you'd be enlightened. Not too expensive either.

anurag
QUOTE(bibhas @ Aug 31 2005, 03:23 PM)
Bibhas,

I'll explain what I meant in my post -

An absolute scale is just another term for an absolute frame of reference. As you will know, in expressing a "transformation" or physical movement in terms of units of dimensions, it becomes paramount to fix the position of zero. Depending on where "zero" is with respect to you, the observer, your answer may look different (although they are the same).

So, the presence of an absolute scale would solve that problem. Every entity in the physical domain will know precisely where "zero" is, and where they lie in relation to "zero". Trouble is, if you don't know the extent of the physical domain, it becomes difficult to start assigning an "absolute scale". But that's fine, because "non-absolute scales" will do the job just fine (you just need to remember that they are not absolute).


If I may add my less than two cents:


Like Bibhas, I am not too sure of the dependence of extent of the physical domain on the notion of an absolute frame of reference. But then what is the extent? Is it the infiniteness or the unboundedness? If it is bounded but infinite, then that would keep things simpler than they would be if the universe was infinite and unbounded as well.

However things may not have to get complicated or unsolvable with changes in the frames. There are frame-invariant properties that would answer all of our questions and the properties which would not be frame-invariant would be useless anyway. To give a simple example, when a runner runs on tracks, depending on where the viewer in the stadium is, the runner's apparent position to the viewer would change but the runner's inherent properties of motion, such as velocity and acceleration would n't change.

PS: I wish that these and a few other threads had come about a bit earlier.
visuja
Nice to see you Anurag. The books that you mention --- are they in a simpler language than Stephen Hawkin's book ? Though I understand it might be difficult to explain these concepts in non-technical terms. I'll try and look for the books in my univ library.

I think it is easier to understand the effect of frames of reference when they are applied to spatial dimensions. But it is the unidirectionality of time (with respect to our frame of reference) that bothers me. If I can udnerstand the reversibility of time in another frame of reference, then probably I'll be better able to understand a few posts in other threads. I'd love to discuss on that, but that would take us into discussions on theory of relativity (and there are already many threads at HF which require deep thinking from my side sad1.gif)

I wish I had a better understanding of analytical math without having to relate mathematical equations to physical reality. It does a great job at doing away with physical reality and in a way, is a great tool in analysing these 'unknown' dimensions.

Vivek

PS : Please do bring out any implict assumptions that I may be making in my comments. Hits has been doing a great job at that smile1.gif
shivani
sigh!
I wish there was a way to do without maths.. but seems ther eis no other option.
Visu.. am on your side.. only much behind.
lets say.. "chad ja beta sooli pe bhai karenge Ram" and try to learn.
I would try to make a post on Strings, as I have understood it.
About the book Anurag has suggested.. well.. would leave it for sunday.
shivani
My understanding of String theory :-

Through the mathematics of quantum mechanics and experimental observation, it was deduced that all known particles fell into one of two classes: Bosons and Fermions Bosons are particles that transmit forces. Many bosons can occupy the same state at the same time. This is not true for fermions, only one fermion can occupy a given state at a given time, and this is why fermions are the particles that make up matter. This is why solids can't pass through one another, why we can't walk through walls -- because of Pauli repulsion -- the inability of fermions (matter) to share the same space the way bosons (forces) can.

Why string Theory - Particle physics interactions can occur at zero distance -- but Einstein's theory of gravity makes no sense at zero distance.
Relativistic quantum field theory has worked very well to describe the observed behaviors and properties of elementary particles. But the theory itself only works well when gravity is so weak that it can be neglected. Particle theory only works when we pretend gravity doesn't exist. So to speak it is applicable only on very small particles.
General relativity only works when we pretend that the Universe is purely classical and that quantum mechanics is not needed or applicable in our description of Nature. ( eg. stars)

If there were a good quantum theory of gravity, then the particle that would carry the gravitational force would have zero mass and two units of spin. This theorized particle is called the graviton.
Now, a graviton can be added to quantum field theory by hand, but the calculations do not match. This is because particle interactions occur at a single point of spacetime, at zero distance between the interacting particles. For gravitons, the mathematics behaves so badly at zero distance that the answers just don't make sense.
String theory suggested that each particle is actually made of "strings" : a wiggling tiny thread. Think of a guitar string that has been tuned by stretching the string under tension across the guitar. Depending on how the string is plucked and how much tension is in the string, different musical notes will be created by the string. These musical notes could be said to be excitation modes of that guitar string under tension.
In string theory, as in guitar playing, the string must be stretched under tension in order to become excited. However, the strings in string theory are floating in spacetime, they aren't tied down to a guitar. Nonetheless, they have tension. The string tension in string theory is denoted by the quantity 1/(2 p a'), where a' is pronounced "alpha prime"and is equal to the square of the string length scale.
If string theory is to be a theory of quantum gravity, then the average size of a string should be somewhere near the length scale of quantum gravity, called the Planck length, which is about 10-33 centimeters, or about a millionth of a billionth of a billionth of a billionth of a centimeter. These particles cannot be observed by any experiment. Then comes the question, if the string can only constitute bosons ( particles that transmit forces) or fermions, too (particles that make up matter)? Open ended or Closed ended? Both.
Different String theories are classified according to whether or not the strings are closed loops, and whether or not the particle spectrum includes fermions. If fermions are included, there must be a special kind of symmetry called supersymmetry, which means for every boson (particle that transmits a force) there is a corresponding fermion (particle that makes up matter). So supersymmetry relates the particles that transmit forces to the particles that make up matter, and these are called superstrings.
Now how does quantum mechanics apply to strings? For bosonic strings, this question is only answered in the affirmative if the spacetime dimensions number 26. For superstrings it comes down to 10. How we get down to the four spacetime dimensions we observe in our world is another story.
If we ask how to get from ten spacetime dimensions to four spacetime dimensions, then the number of string theories grows, because there are so many possible ways to make six dimensions much much smaller than the other four in string theory. This process of compactification of unwanted spacetime dimensions yields interesting physics on its own.
This period in string history has been given the name the second string revolution.
And now the biggest rush in string research is to collapse the table above into one theory, which some people want to call M theory, for it is the Mother of all theories.

I will try to make another post soon on how the the other 6 dimensions are collapsed into known 4 dimensions. Meanwhile if someone else volunteers for it.. great :-)
bibhas
QUOTE(hits @ Aug 31 2005, 05:54 PM)
Bibhas,

Have you started on Hawking's book?

Hits
*


Yes I have. And this time around, even Harry's "Half-Blood Prince" (which my wife finished reading just as I started Hawking) didn't sway me away, at least not yet laugh.gif

Bibhas
p.s. It would take me a long while to make sense of Anurag's, Vivek's and Shivani's posts, so I am going to take the rest of the day off to practise the special Desh Bandish that Guruji taught me yesterday.
visuja
Make sense of my post !! headbang.gif maine aisa kya keh diya ? blab.gif mujhe to shivani ka post dekhkar hi darrrr lag raha hai...and she's supposed to post more !!! doh.gif (And to think I had asked her to post on 'strings') Ayyoooooo !!!!! doh.gif Aur hits ne to shuruaat bhi nahin ki hai blab.gif
bibhas
QUOTE(visuja @ Sep 1 2005, 12:27 PM)
Make sense of my post !! headbang.gif maine aisa kya keh diya ? blab.gif  mujhe to shivani ka post dekhkar hi darrrr lag raha hai...and she's supposed to post more !!! doh.gif (And to think I had asked her to post on 'strings') Ayyoooooo !!!!! doh.gif  Aur hits ne to shuruaat bhi nahin ki hai blab.gif
*



It takes one to be really poor to understand what poverty really means ! Mere physics ke level kya hai, yeh tum nahiin jaante.

Mandrake
Need help birthday boy? wink2.gif

I simply llllove physics! thumbs-up.gif
bibhas
QUOTE(Mandrake @ Sep 1 2005, 12:42 PM)
Need help birthday boy? wink2.gif

I simply llllove physics! thumbs-up.gif
*


Yeh bhi koi poochne waali baat hai aindrajaalak ? madad chaahiye tabhi to thread shuru kiya.
visuja
Yes Mandrake. Some help would be great on what Shivani posted. Poora bouncer gaya sad1.gif (hehe I can dump all my astronomy queries onto you biggrin.gif) Woh black hol;e waala thread bhi achha tha... kb4u is apparently a physics student... would be great to have him here in this discussion too...

QUOTE(bibhas)
It takes one to be really poor to understand what poverty really means !
Haan ye baat to sahi hai. Isliye me lagbhag absent at following threads: D&FW, Mythology, Legends, RR, Photography, Shayari, dabble in regional threads blab.gif Ek biowaala thread hota to wahaan bhi gaayab rehta wink2.gif

Me always hang around in chit-o-chat .... rollf.gif blab.gif Me crossed 700 posts in < 2 months doh.gif

Hope to hear more form you Anurag. Your posts on Math and dimensions at another thread intrigued me. Would like to learn more on that, especially on its application to visualising other dimensions. Good to have a variety of ppl here, each comfortabloe in their own field and dabbling in all other fields (tongue.gif ..main apni baat kar raha tha smile1.gif)

mandrake, cud u throw some light on 'your' time ka funda ? (trust us .. baby.gif)
shivani
sad1.gif and I thought atleaast this time what I have writtenis simple and understandable..
maybe it needs to start with Relativity and Quantam mechanics as well..
or maybe I just need to sit aside and learn more. (better approach..hint taken.. onto it from nowon)
hits
QUOTE(anurag @ Aug 31 2005, 09:46 PM)
For all the questions being posed here, may I suggest the recent book by Roger Penrose "The Road to Reality". Some of you may have heard about his earlier popular book titled "The Emperor's New Mind" in which he discussed the inadequacy of the laws of physics in explaining consciousness.

In his new book, String theories and the more recent version of string theory, known as M-Theory have been augmented with his newly proposed twister theory.

In my opinion, this is a fantastic and a very gentle reading on a Sunday afternoon over oodles of coffee. I assure you that you'd be enlightened. Not too expensive either.
*



Good references Anurag. Folks, I would still suggest soaking in Hawking's book first, as he eases you in to the concept of the curvature of time better than any written body of work I've come across. However, for someone who is comfortable visualizing space and time as extensions of the same construct, the first few chapters may be a tad repetitious.
hits
QUOTE(anurag @ Aug 31 2005, 10:10 PM)
If I may add my less than two cents:


Like Bibhas, I am not too sure of the dependence of extent of the physical domain on the notion of an absolute frame of reference. But then what is the extent? Is it the infiniteness or the unboundedness? If it is bounded but infinite, then that would keep things simpler than they would be if the universe was infinite and unbounded as well.


You may have identified the source of the disconnect Anurag. The basic issue here is around both these points - the boundedness and the infiniteness of the universe. An assumption either way is exactly that - an assumption. When an absolute frame of reference is assigned to a space, certain intrinsic assumptions are made regarding point zero. The first, of course, is that point zero belongs to the space (otherwise, you need to define the space point zero resides in, and ....okay, not going there unless required). Now, it may be possible under unbounded and infinite conditions to actually uncover information that says this - The initial assumption that point zero belongs to the said space is invalid!

An absolute reference frame, by definition, should never be subject to such a contradiction. Hence the general practice in any post-General Relativity theory to not assign absolute scales to spaces that are not defined as bounded and finite (Note that we also don't know if the universe is unbounded and/or infinite!).

Okay, the good news, as Anurag alludes to below, is that this doesn't matter and shouldn't deter us from seeking our answers. Relative frames of reference work just as well. Just be sure to "transform" one frame to another when required.

Hits

QUOTE(anurag @ Aug 31 2005, 10:10 PM)
However things may not have to get complicated or unsolvable with changes in the frames. There are frame-invariant properties that would answer all of our questions and the properties which would not be frame-invariant would be useless anyway. To give a simple example, when a runner runs on tracks, depending on where the viewer in the stadium is, the runner's apparent position to the viewer would change but the runner's inherent properties of motion, such as velocity and acceleration would n't change.

PS: I wish that these and a few other threads had come about a bit earlier.
*

bibhas
Hithesh and Anurag,
Can you define "unboundedness" and "infiniteness" in simple layman, i.e., my level terms ? As I see it, they appear one and the same to me.
Bibhas
hits
QUOTE(bibhas @ Sep 2 2005, 07:58 AM)
Hithesh and Anurag,
Can you define "unboundedness" and "infiniteness" in simple layman, i.e., my level terms ? As I see it, they appear one and the same to me.
Bibhas
*



I am sure Anurag was referring to the mathematical definition of a bound. Bibhas, I am desperately "short on time" (chuckle!) today (have a flight to catch), and won't be able to delve into it much. I'll leave you with this - Any space has certain basic properties that define its extent. Consider these 2 examples -

1) The space defined by all points that are generated by the expression 1/n, where n goes from 1 to infinity. There will be infinite points in this space, but it is bounded. You know that the maximum value the expression can attain is 1 and the lowest is close to 0. So, the space is bounded, but infinite.

2) Now consider the same expression, but with n going from 0 to infinity. This space has a lower bound of 0, but the upper bound doesn't exist, as the expression blows up, when n gets progressively smaller than 1. So, the space is both infinite and unbounded.

The above is a very non-purist way of describing bounds. There are a few nuances involved, and under those circumstances, my statements above will not hold true. However, I hope you are able to see the difference between unboundedness and infiniteness.

Thank you
Hithesh
visuja
Have a nice trip Hitesh smile1.gif

Thanks for clarifying them. So 'bound' is the extent of a function, while 'infinity' is the number of points / values that function can take within the extents (if any) ? In that case, any function should contain 'infinite' points within its bounds, I suppose ? Does 'unboundedness' imply 'infiniteness' ? unsure.gif

Aarrgh.... I asked for it doh.gif ---- discussing abstract mathematical terms sad1.gif (no wonder I HATE thermodynamics cry.gif)
anurag
QUOTE(hits @ Sep 2 2005, 10:21 AM)
QUOTE(bibhas @ Sep 2 2005, 07:58 AM)
Hithesh and Anurag,
Can you define "unboundedness" and "infiniteness" in simple layman, i.e., my level terms ? As I see it, they appear one and the same to me.


I am sure Anurag was referring to the mathematical definition of a bound. Bibhas, I am desperately "short on time" (chuckle!) today (have a flight to catch), and won't be able to delve into it much.
<snipped>



Bibhas and Vivek


Hits has given an example of unboundedness and infiniteness in terms of mathematical sets. Here is one more from geometry (in the context of the extent of the universe) to help you understand and visualize the difference between the two.

Infiniteness is in terms of stretching the space forever, while boundedness is being able to define the boundaries of the space.

Imagine a mathematical flat plane, if you draw a line on the plane, the line would continue going in either direction. And, you would n't be able to set the "edge" of this line either. The former is "infiniteness" of the plane, while the latter is "unboundedness".

Now draw a line on a sphere (like, on the surface of the Earth), the line would wrap on itself since the line on the sphere is the geodesic (the shortest path between two points) or the great circle. You already know that this is how the airlines decide the path of flying between two cities barring some commercial and practical considerations. So, the line did n't really continue to infinity but you'd be hard pressed to say that there is a certain "edge" or the boundary of this great circle. This is true for any given line on this surface, therefore, the surface of a sphere is finite but unbounded.

Now, if you assume that the space of the universe (I say the "space" since just sayng the universe can mean other things as well -- such as the totality of energy and matter existing in the universe) is like the surface of a sphere of higher dimensions, then it is finite but unbounded but the real answer is unknown yet. Jury is out on that one.

So, as you see from this example Vivek, "unboundedness" does not imply "infiniteness", nor the viceversa. These are two independent notions.
visuja
Sorry Anurag, u'll have to come down lower to teach us the 1,2,3's of the math sad1.gif.
QUOTE(anurag)
The former is "infiniteness" of the plane, while the latter is "unboundedness".
This is understandable in context of the plane and line example. A plane (like z=0 or the x-y plane), by its definition is 'infinite' in all (x,y) directions, and hence any line (again by its definition) contained in that plane will be 'unbounded'. So 'finiteness' is a property of x, while 'boundedness' is a property of f(x) ?? Am I right in saying then that any f(x) will be 'bounded' in a 'finite' range of x ? I suppose thats not necessarily true given Hitesh's example. smile1.gif

But I dont see the analogy in your sphere example.
QUOTE(anurag)
, the line did n't really continue to infinity but you'd be hard pressed to say that there is a certain "edge" or the boundary of this great circle. This is true for any given line on this surface, therefore, the surface of a sphere is finite but unbounded.
The sphere to begin with is 'finite' since its surface area is fixed for a given radii. But the line on the sphere surface is 'unbounded' by its definition ?? (that a line basically extends to infinity in both directions). And what we call the circumference transcribed by that line is actually the length of the segment that circumscribes the sphere once ?

Also, please clarify what do 'domain' and 'range' mean. I remember learning one is for x and the other for f(x), but always got confused sad1.gif

Sorry bibhas if it got too technical. I promise wont ask so many technical details henceforth baby.gif
bibhas
QUOTE(anurag @ Sep 4 2005, 12:28 PM)
Infiniteness is in terms of stretching the space forever, while boundedness is being able to define the boundaries of the space.

Imagine a mathematical flat plane, if you draw a line on the plane, the line would continue going in either direction. And, you would n't be able to set the "edge" of this line either. The former is "infiniteness" of the plane, while the latter is "unboundedness".

Now draw a line on a sphere (like, on the surface of the Earth), the line would wrap on itself since the line on the sphere is the geodesic (the shortest path between two points) or the great circle. You already know that this is how the airlines decide the path of flying between two cities barring some commercial and practical considerations.  So, the line did n't really continue to infinity but you'd be hard pressed to say that there is a certain "edge" or the boundary of this great circle. This is true for any given line on this surface, therefore, the surface of a sphere is finite but unbounded.


Anurag,
That was awesome, nothing like being able to visualize a concept to understand it ! clap1.gif Thanks for that. Can you also make me "visualize" an entity that is bounded but infinite ?
Bibhas

p.s. Hithesh, I understood the difference between "boundedness" and "infiniteness" as well as the mathematical difference between "bounded & infinite" and "unbounded & infinite" (Thanks to you & Anurag). I'm just trying to visualize this difference so I can relate it to reality and hence resolve it in my mind.
bibhas
QUOTE(hits @ Aug 31 2005, 03:03 PM)
An absolute scale is just another term for an absolute frame of reference. As you will know, in expressing a "transformation" or physical movement in terms of units of dimensions, it becomes paramount to fix the position of zero. Depending on where "zero" is with respect to you, the observer, your answer may look different (although they are the same).

So, the presence of an absolute scale would solve that problem. Every entity in the physical domain will know precisely where "zero" is, and where they lie in relation to "zero". Trouble is, if you don't know the extent of the physical domain, it becomes difficult to start assigning an "absolute scale". But that's fine, because "non-absolute scales" will do the job just fine (you just need to remember that they are not absolute).

Now, as you will see, the flow of time will vary depending on how you assign the scale. This can get complicated quickly, as we are slowly digressing towards the first lecture on the Theory of Relativity! I can get into that in a different thread if you want me to.

A final point - Time can be multidirectional even on an absolute scale. One just doesn't see it happen in our physical lives.
*


Hithesh,
Now that I think I have a resonable handle on absolute and non-absolute scales (thanks to you, Anurag and Hawking {Before you ask, No I haven't finished it yet but I am just getting into the Quantum Mechanics chapter now}), can we get back to my original question (in red). Can you give me some analogies that'll make me see the variation in time flow in relation to the frame of reference ?
Bibhas
shivani
I am reasonably lost sad1.gif
would someone be please kind enough and explain it to me .. bibhas/ visuja ???
hits
QUOTE(bibhas @ Sep 6 2005, 09:12 AM)
Hithesh,
Now that I think I have a resonable handle on absolute and non-absolute scales (thanks to you, Anurag and Hawking {Before you ask, No I haven't finished it yet but I am just getting into the Quantum Mechanics chapter now}), can we get back to my original question (in red). Can you give me some analogies that'll make me see the variation in time flow in relation to the frame of reference ?
Bibhas
*



Let's start that off with a thought experiment. Let's say there's a star a few million light years away from the earth. Your objective is to try and evaluate the details of the life of the star, by sitting in various frames of reference. Try thinking through these scenarios -

1) You are seated on the earth, and have powerful telescopes to observe the light on the star. So, your frame of reference is the earth.
2) You are seated on the star, and that's your reference frame
3) You are seated at the edge of the light beam that the star is throwing, and that's your frame.

Think through how you'll perceive the star's life seated on these reference frames. Remember a few cardinal points as you think through - None of the reference frames are in motion, with respect to you. However, to an observer on the earth, you may be traveling at the speed of light in scenario 3. Similarly, to an observer on the star, you'll be in motion (alongwith the earth), in scenario 1.

bibhas
QUOTE(shivani @ Sep 6 2005, 01:43 PM)
I am reasonably lost sad1.gif
would someone be please kind enough and explain it to me .. bibhas/ visuja ???
*


Shivani,
I don't think I can put it in words even though I have resolved it in my head. Just ruminate on Anurag's earth/geodesic wala paragraph. Think of it this way: a sphere has a finite area/volume/whatever but has no boundary, right ? You won't be able to find and mark its boundary, hence it is finite but unbounded.
Similarly, a line can keep growing as long as you can draw it, has no ends and is also infinite, so infinite and unbounded.
The third is where I have trouble- an infinite entity whose boundary can be found ! In my mind, a bounded entity would be finite by definition simply because we can get to its edges to measure it. Now Anurag might say that a stretchable membrane could be bounded but be stretched to infinity (in theory) but as long as we can find a boundary, it is finite at that point. confused.gif
hits
QUOTE(bibhas @ Sep 6 2005, 12:19 PM)

The third is where I have trouble- an infinite entity whose boundary can be found ! In my mind, a bounded entity would be finite by definition simply because we can get to its edges to measure it. Now Anurag might say that a stretchable membrane could be bounded but be stretched to infinity (in theory) but as long as we can find a boundary, it is finite at that point. confused.gif
*



Bibhas,

How about a Kalpataru? The tree's dimensions are well defined, correct? However, there's infiniteness associated with it, because "stuff" keep's comin' out!

In more real terms, you could have a well bounded entity, but in measuring the constituents within this entity, you may have to end up counting to infinity. It's almost like a rock that breaks into 2 when you try to measure it, and then into 4, and so on, endlessly. Sure, you can argue that the number of quarks within that rock is finite. But what's to say Quantum Chromodynamics revises that assumption tomorrow? It's here that a mathematical interpretation may help - You can continue to split a point further down into infinite points. How may real numbers exist between the well defined bounds of 0 and 1? Infinite.

Hithesh
bibhas
QUOTE(hits @ Sep 6 2005, 02:27 PM)
It's almost like a rock that breaks into 2 when you try to measure it, and then into 4, and so on, endlessly. Sure, you can argue that the number of quarks within that rock is finite. But what's to say Quantum Chromodynamics revises that assumption tomorrow? It's here that a mathematical interpretation may help - You can continue to split a point further down into infinite points. How may real numbers exist between the well defined bounds of 0 and 1? Infinite.

Hithesh
*


clap1.gif clap1.gif clap1.gif

Got it Hithesh.
bibhas
QUOTE(hits @ Sep 6 2005, 01:53 PM)
Let's start that off with a thought experiment. Let's say there's a star a few million light years away from the earth. Your objective is to try and evaluate the details of the life of the star, by sitting in various frames of reference. Try thinking through these scenarios -

1) You are seated on the earth, and have powerful telescopes to observe the light on the star. So, your frame of reference is the earth.
2) You are seated on the star, and that's your reference frame
3) You are seated at the edge of the light beam that the star is throwing, and that's your frame.

Think through how you'll perceive the star's life seated on these reference frames. Remember a few cardinal points as you think through - None of the reference frames are in motion, with respect to you. However, to an observer on the earth, you may be traveling at the speed of light in scenario 3. Similarly, to an observer on the star, you'll be in motion (alongwith the earth), in scenario 1.
*



1) The star as I see today is what it was 5 million years ago ( I put a number on your "few").

2) The star I see today is its current state, i.e., 5 million years into earth's future.

3) This is the tricky one. I wanna say Time keeps continuously changing (is this what you call "flowing" ?) and I see everything from the star's "today" to its past "five million years ago".
So essentially I've travelled into its past, i.e., Time is not uni-directional ?
shivani
thanks a lot Bibhas and Hits..I think even I got it. (though I might come back with same Q again sometime in future)
so next have to try to visualize the three cases hits noted above.
(wish mil was here sad1.gif it all would have been so simple)
also .. can there be a better examples from physics rather than maths for bounded but infinite ?? not kalptaru.. as that is a magical thing
bibhas
Great Shivani !

Ok, here are some questions that popped into my head while reading Hawking's book and I'd be glad if anyone can answer these for me. (for those of you who haven't read it but want to, I have a pdf file of this book).

1. Is microwave radiation (observed by Penzias & Wilson as well as COBE) the only experimental evidence for Big Bang ?

2. How can Friedmann’s third model be extrapolated to state the universe to be flat ?

3.“The mass of the sun curves space-time in such a way that although the earth follows a straight path in four-dimensional space-time, it appears to us to move along a circular orbit in three-dimensional space.”. Yeh kuch samjha nahiin. Any visual analogies ?

4. Can you give an example of a particle with a spin=1/2 (no, not an electron ), i.e., one that requires a 720 degree rotation to look identical ?. Matlab, the way Hawking uses a dot for s=0, an arrow for s=1 and double-headed arrow for spin=2.

Bibhas
p.s. How can theoretical physicists live with the fact that all they do is propose theories which may never be validated exptally ? How can someone live with that kind of uncertainty within them ?
shivani
Bibhas
Can you please send me the pdf ?? send on my mail id. and which one is it ??
currently am reading his Brief history of time... and paperback version is gonna take eons.
bibhas
QUOTE(shivani @ Sep 6 2005, 02:51 PM)
Bibhas
Can you please send me the pdf ?? send on my mail id. and which one is it ??
currently am reading his Brief history of time... and paperback version is gonna take eons.
*


Shivani,
actually it is Brief History of Time and can be downloaded from:

www.churchofsatan.org/pdf/stephen_hawking_a_brief_history_of_time.pdf

Bibhas
shivani
thanks Bibhas : )
visuja
Thanks for the link bibhas. I had left my book back at home, so this should be useful.

As for the 3 scenarios, I essentially agree with bibhas. My analysis / observations assume that relative motion between the frame of reference and the star is generally small / negligible compared to speed of light. I presume the spectral shift / Doppler effect can be corrected for to arrive at the 'true' information for that frame of reference.

1. Earth as frame of reference: Any information that we can collect about the star in observation is limited by the 'time' factor --- and the finite speed of light. So essentially what we 'see' is the star's past (ranging from 8 minutes to millions of years). A far fetched idea, but in theory, we can at the most have all information from the star's birth to its 'apparent' age as seen from the earth. ---- all info at a phase lag of the 'time difference' in question.

2. Star as the frame of reference: Essentially u live with the star. So u should have all information right from the star's birth to its current age. This would be the most accurate and up-to-date info that one could gather about the star.

3. Edge of light beam as frame of reference: Ah ! Talk of immortality ! The star would seem 'immortal' to you because you would be seeing an unchanging, unmoving star all the time. So even after millions of years on leaving the star, even if the star has ceased to exist, one would always see the star in exactly the same state as it was when the light beam left the star millions of years ago (provided one had powerful enough telescopes to view over such large distances). This is somewhat similar to scenario 2 where one 'sees' the star even if the star does not actually exist as of today. Only difference is in this scenario, the star will continue to exist till eternity (whatever that means).

Let me conduct a similar thought experiment. Now still in scenario 3, if the light beam was travelling exactly towards the earth, then on one hand we see the star as it 'was' when we left it, while regarding our perception of the earth, we would be seeing the earth 'evolve' at 'double the speed', since we'll be moving at twice the speed of light relative to the light reflected off the earth (which carry the 'info' about the earth). If the light beam we are on happens to move in an exactly opposite direction away from the earth, then this scene is exactly like scenario 3, except that now we'll be seeing both the star and the earth in exactly the same 'state' as at the instant we left the star. Our perception of the earth will be between these two scenarios for any other direction.

I hope I made some sense here unsure.gif. Its only when the speed barrier is broken that my thought experiments also collapse sad1.gif.
QUOTE(bibhas)
How can someone live with that kind of uncertainty within them ?
bow.gif u steal words of my mouth smile1.gif. I wonder the same about all the abstract sciences ...math, physics, thermodynamics !! (how do people even conjure up things like entropy and free energy ? headbang.gif) The fact that they validated these terms later is bow.gif ...but to come up with these things is even bow.gif bow.gif sad1.gif
QUOTE(bibhas)
.“The mass of the sun curves space-time in such a way that although the earth follows a straight path in four-dimensional space-time, it appears to us to move along a circular orbit in three-dimensional space.”
Cant help with your other queries bibhas, but lemme try and explain the way I understood it.
Given the masses of the earth and the sun, I think the 'straight line' in space-time implies that the distance at which the earth revolves around the sun and the time taken for one revolution (or the sped of revolution) are optimum for the sun-earth system. I'm not quite sure how this optimum is defined though. My feeling is any closer to the sun, the earth would have plunged into the sun, while any farther away, the earth might drifted away from the sun's gravitational influence. Similarly any slower revolution would have spiralled it inward, while any faster would have caused it to drift away. But going by my 'theory', the planets should have been arranged in the order of increasing mass from the sun, which isnt the case. So obviously I'm missing something here. Visual analogies would be very very helpful smile1.gif.

I remember a program on discovery which showed an analogy to the space-time fabric. An elastic rubber sheet was held at its corners ('reasonably tightly') and steel balls of various sizes and weights were placed at various places on the sheet. The balls caused some depression in the sheet and depending on if one ball came in the 'influence' of another depression, two balls would roll into one another and so on.

I also forget why almost all orbits are elliptical and not circular ? unsure.gif (Now I'll have to start reading up Kepler's works before moving onto Einstein and Stephen Hawkings doh.gif)

Vivek
shivani
QUOTE(bibhas)
.“The mass of the sun curves space-time in such a way that although the earth follows a straight path in four-dimensional space-time, it appears to us to move along a circular orbit in three-dimensional space.”

QUOTE(visuja)
Cant help with your other queries bibhas, but lemme try and explain the way I understood it.
Given the masses of the earth and the sun, I think the 'straight line' in space-time implies that the distance at which the earth revolves around the sun and the time taken for one revolution (or the sped of revolution) are optimum for the sun-earth system. I'm not quite sure how this optimum is defined though. My feeling is any closer to the sun, the earth would have plunged into the sun, while any farther away, the earth might drifted away from the sun's gravitational influence. Similarly any slower revolution would have spiralled it inward, while any faster would have caused it to drift away. But going by my 'theory', the planets should have been arranged in the order of increasing mass from the sun, which isnt the case. So obviously I'm missing something here.


umm.. I could not understand the answer you were trying to give here Visu, instead found another question - Is there an order to planetary arrangement, in terms of the distance between a planet and its sun ??

QUOTE(Visuja)
I also forget why almost all orbits are elliptical and not circular ? unsure.gif (Now I'll have to start reading up Kepler's works before moving onto Einstein and Stephen Hawkings

This is explained in Hawkings itself.. I think first chapter ( thats all ive read so far)

QUOTE(Visuja)
3. Edge of light beam as frame of reference: Ah ! Talk of immortality ! The star would seem 'immortal' to you because you would be seeing an unchanging, unmoving star all the time. So even after millions of years on leaving the star, even if the star has ceased to exist, one would always see the star in exactly the same state as it was when the light beam left the star millions of years ago (provided one had powerful enough telescopes to view over such large distances). This is somewhat similar to scenario 2 where one 'sees' the star even if the star does not actually exist as of today. Only difference is in this scenario, the star will continue to exist till eternity (whatever that means).

Did not understand sad1.gif
QUOTE(Visuja)
Let me conduct a similar thought experiment. Now still in scenario 3, if the light beam was travelling exactly towards the earth, then on one hand we see the star as it 'was' when we left it, while regarding our perception of the earth, we would be seeing the earth 'evolve' at 'double the speed', since we'll be moving at twice the speed of light relative to the light reflected off the earth (which carry the 'info' about the earth). If the light beam we are on happens to move in an exactly opposite direction away from the earth, then this scene is exactly like scenario 3, except that now we'll be seeing both the star and the earth in exactly the same 'state' as at the instant we left the star. Our perception of the earth will be between these two scenarios for any other direction.

Ditto!! Did not understand.
QUOTE(Visuja)
I wonder the same about all the abstract sciences ...math, physics, thermodynamics !! (how do people even conjure up things like entropy and free energy ?

Maybe things are clearer to them the same way as your posts are clear to you.. while atleast I am getting so lost!!

people pardon my ignorance and dumbness here sad1.gif. The patience you guys are showing is much appreciated. bow.gif
bibhas
Hey Vivek, thanks for that post. I realize I goofed up scenario # 3, it makes much more sense that the star would look unchanged for whatever length of time you observe it from the edge of the light beam. So then, even though Time has moved ahead, it would look like it stood still. So essentially a single moment would stretch to infinity ?
I am still unable to see how a straight line path in 4D space-time would appear to be a circular (or elliptical) path in 3D. Looking for answers to this and the other Qs I posed.
shivani
QUOTE(hits)
3) You are seated at the edge of the light beam that the star is throwing, and that's your frame.


QUOTE(bibhas)
3) This is the tricky one. I wanna say Time keeps continuously changing (is this what you call "flowing" ?) and I see everything from the star's "today" to its past "five million years ago".
So essentially I've travelled into its past, i.e., Time is not uni-directional ?


This Q /scenario I did not understand. What am I when I am trying to observe the life of star here? where exactly am I on the light beam.
Also what I could understand is.. I am constantly moving away from the star, as the beam is travellign in some direction.. or am I stationary (x-y-z only t changing?)

bibhas
QUOTE(shivani @ Sep 7 2005, 12:51 PM)
QUOTE(hits)
3) You are seated at the edge of the light beam that the star is throwing, and that's your frame.


QUOTE(bibhas)
3) This is the tricky one. I wanna say Time keeps continuously changing (is this what you call "flowing" ?) and I see everything from the star's "today" to its past "five million years ago".
So essentially I've travelled into its past, i.e., Time is not uni-directional ?


This Q /scenario I did not understand. What am I when I am trying to observe the life of star here? where exactly am I on the light beam.
Also what I could understand is.. I am constantly moving away from the star, as the beam is travellign in some direction.. or am I stationary (x-y-z only t changing?)
*


Shivani,
The way I see it, you are you and you are on the edge (say leading edge) of the light beam, you're sitting on the first photon to come out at the given time. You are constantly moving away from the star at the speed of light and I made the assumption that the light beam is travelling towards the earth (to tie it up to scenario #1). In such a scenario, the star would appear unchanged throughout the length of your observation, i.e. time would appear unchanged to you with respect to the star under observation.
Bibhas
shivani
QUOTE(bibhas @ Sep 7 2005, 10:33 PM)
Shivani,
The way I see it, you are you and you are on the edge (say leading edge) of the light beam, you're sitting on the first photon to come out at the given time. You are constantly moving away from the star at the speed of light and I made the assumption that the light beam is travelling towards the earth (to tie it up to scenario #1). In such a scenario, the star would appear unchanged throughout the length of your observation, i.e. time would appear unchanged to you with respect to the star under observation.
Bibhas
*


help me understand this Bibhas.. the star would seem unchanged to me because I would have only A set or The set of information about star, when I left it. I would not be observing it ever again?? Is that assumption correct or am I somehow able to sense the changes that might be happening to the star, as I am travelling away.
If former, than yes the state is always unchanged, if later.. then.. dont know
visuja
You are right Shivani. Since you are travelling alongwith the light wave, u essentially are limited to the info carried by that wave ...ie how the star looked at the instant the light beam (and you) left the star. So u'd basically be seeing the star for all eternity at the same position.

oh good.. hits is here. He'll give a few pointers in a short sentence.. and then leave us to fill another page of our rambling tongue.gif sad1.gif
hits
QUOTE(shivani @ Sep 7 2005, 11:10 AM)
QUOTE(bibhas @ Sep 7 2005, 10:33 PM)
Shivani,
The way I see it, you are you and you are on the edge (say leading edge) of the light beam, you're sitting on the first photon to come out at the given time. You are constantly moving away from the star at the speed of light and I made the assumption that the light beam is travelling towards the earth (to tie it up to scenario #1). In such a scenario, the star would appear unchanged throughout the length of your observation, i.e. time would appear unchanged to you with respect to the star under observation.
Bibhas
*


help me understand this Bibhas.. the star would seem unchanged to me because I would have only A set or The set of information about star, when I left it. I would not be observing it ever again?? Is that assumption correct or am I somehow able to sense the changes that might be happening to the star, as I am travelling away.
If former, than yes the state is always unchanged, if later.. then.. dont know
*



Let me point out an interesting constraint here as we discuss this - The powers of human observation are limited, for the most part, by the speed of light. Let's remember this (if and) when we shuttle back to the thread on "Weird Dimensions" (Determinism thread by Shivani).

The star is changing constantly. If you are still with respect to it, you'll know what happened to it when the light beam hits you (which will be sooner, if you are closer to the star). Now, if you are moving away from the star at or greater than the speed of light you will soon break out of the light beam thrown by the star and then lose the ability to know what's happening to the star (assuming you start your flight from the star after it started emitting light). When you are far enough from the edge of the light beam, suppose you turn around in your little contraption and ride back. Now you are going to re-live the star's "past", and progressively move towards the "present"! Ain't that interesting?!!
hits
Bibhas,

I owe you responses to your questions. In time...

Hits
bibhas
QUOTE(hits @ Sep 7 2005, 01:29 PM)
Let me point out an interesting constraint here as we discuss this - The powers of human observation are limited, for the most part, by the speed of light. Let's remember this (if and) when we shuttle back to the thread on "Weird Dimensions" (Determinism thread by Shivani).

Why not all the time ?
QUOTE(hits @ Sep 7 2005, 01:29 PM)
When you are far enough from the edge of the light beam, suppose you turn around in your little contraption and ride back. Now you are going to re-live the star's "past", and progressively move towards the "present"! Ain't that interesting?!!
*


Awesome (although I had to draw out a little light cone on my pad to figure that out) ! I finally realize why Einstein chose to call time as an extension of space and merged them together into spacetime. Now, someone just tell me how I can fly at the speed of light ? camera.gif

bibhas
QUOTE(hits @ Sep 7 2005, 02:00 PM)
Bibhas,

I owe you responses to your questions. In time...

Hits
*


Not if I figure out how to travel faster than the speed of light into the future !
visuja
QUOTE(hits @ Sep 7 2005, 01:29 PM)
When you are far enough from the edge of the light beam, suppose you turn around in your little contraption and ride back. Now you are going to re-live the star's "past", and progressively move towards the "present"! Ain't that interesting?!!
*

Isnt this similar to the earth example I gave in scenario 3 unsure.gif As we travel towards the earth (sitting on the star's light beam), we would basically encounter light beams from the earth on our way (@ twice the rate) and hence would be able to track the earth's past upto its present 'state' when we reach the earth.
Whats fascinating now is that from this instant of 'present' when our 'star light beam' passes the earth, basically we'll now be sitting on a light beam that carries info about both our original star as well as the earth that we passed !! And from that 'present' instant, we will be able to see the earth only as an eternal object !!

Now if we went faster than the speed of light, we wud catch up with 'earth waves' and essentially revising the earth's past (which we had observed on our way to the earth !).

But the whole point here in going into the past is to reach a point from where we can turn back and that in itself involves travelling >= speed of light.

After all this..do u see stars !?? unsure.gif I sure do ! planet.gif
shivani
QUOTE(hits @ Sep 7 2005, 10:59 PM)
The star is changing constantly. If you are still with respect to it, you'll know what happened to it when the light beam hits you (which will be sooner, if you are closer to the star). Now, if you are moving away from the star at or greater than the speed of light you will soon break out of the light beam thrown by the star and then lose the ability to know what's happening to the star (assuming you start your flight from the star after it started emitting light). When you are far enough from the edge of the light beam, suppose you turn around in your little contraption and ride back. Now you are going to re-live the star's "past", and progressively move towards the "present"! Ain't that interesting?!!
*


am sorry.. this is just a repetition , but I need it to know, what I have understood is correct.
I am in path of a beam of light emerging from a star and can move back or forth in same direction as beam, and thus would be able to see the state of star depending on the particle am observing in the beam. that is am able to see present, past and future ( could nto understand how future) of the star.
and the motion perpendicular to direction of beam would put me in/out of my frame of reference.
correct??
and only particles with no mass( or rather infinitesimal) can travel with speed faster than light... that is why we cannot.
shivani
QUOTE(visuja @ Sep 7 2005, 11:48 PM)

But the whole point here in going into the past is to reach a point from where we can turn back and that in itself involves travelling >= speed of light.

After all this..do u see stars !?? unsure.gif I sure do ! planet.gif
*


sigh
timeout!!
before am able to understand something completely .. there is more coming along.
visuja
QUOTE(shivani @ Sep 8 2005, 02:27 AM)
I am in path of a beam of light emerging from a star and can move back or forth in same direction as beam, and thus would be able to see the state of star depending on the particle am observing in the beam. that is am able to see present, past and future ( could nto understand how future) of the star.
and the motion perpendicular to direction of beam would put me in/out of my frame of reference.
correct??
and only particles with no mass( or rather infinitesimal) can travel with speed faster than light... that is why we cannot.
*
Shivani try this. U'd know how ripples are formed on the water surface i na conentric manner. Now consider a space which has many spheres one inside the other and the light source to be at the centre of the sphere. Each sphere would represent the time that light (or photons) has travelled from the centre. Thus each spherical surface carries a time-stamp of the light source --- info regarding the source at the time the light / photon was emitted by the source.

Now as long as you sit on this photon, u'll be able to see the same star at the same place always, because that is the only information that u have. You will have to move to the next outer spherical surface to gain info about the star's past. But since you are moving with the photon, u'll need to move faster than 'your' photon to catch up with the photon on the next outer spherical surface ---- this basically means that u'll need to travel faster than light to observe the star's past.

Was this of any help ? unsure.gif
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