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  #1  
Old 12-03-2008, 07:14 AM
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about Minkowski diagram

You all know what a Minkowski diagram is.
At first sight, it is a simple space/time diagram.
Take a sheet of paper.
Draw a vertical axis. Put an arrow directed up, call this axis "time".
Draw an horizontal axis. Call this axis "x". Or call it "space".
You have already obtained a space/time diagram.

A Minskowski diagram involves a third thing, the Speed of Light, or "c".
C is the speed of a photon. Speed means motion in space and in time. In a Minkowski diagram, the speed of a photon is represented by a line at 45 degrees, at the intersection of both axes. In other words, the Minkowski diagram is a relativistic space/time diagram. (it is not a "simple space/time diagram")

Let's stop here. No intention to go into more complicated considerations
A Minkowski diagram looks like this:
http://en.wikipedia.org/wiki/Image:M..._causality.png
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  #2  
Old 12-03-2008, 07:27 AM
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That was for introduction.

Do you have your sheet of paper?
take a pencil.
Put your pencil upon the horizontal axis (the space axis).
Did you do that?
What is your pencil representing?
It represents space at a certain time.
When we say it is "space", we mean it is "every event in space". In other words, your pencil is representing the entire universe.
In fact, for representing the entire universe, you should take a very long pencil, but this is only a matter of scaling in the diagram. You can say that 16 cm on your paper (about 6 inches) represent 20 billions light-years of distance.
Take your pencil in hand.
You have the entire Universe in your hand.
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  #3  
Old 12-03-2008, 07:35 AM
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Now, where is the observable universe?

In a non-relativistic diagram, a "simple space/time diagram" (i.e. without the diagonals), the entire half-below of the diagram is the observable universe, including your pencil.
Indeed, All that we are observing belongs to the past.

In a Minkowski diagram, the observable universe is in the low triangle, called "the past".
In other words, following Relativity, there is a difference between what belongs to space (your pencil) and what belongs to the observable universe. That's the meaning of Relativity, showed in a Minkowski diagram.
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  #4  
Old 12-03-2008, 07:49 AM
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The lowest triangle is the observable universe. It is the universe that is represented by the laws of physics. But not only.
Put back your pencil on the horizontal axis.
Slide your pencil up on the diagram, about 1 inch parralel to itself.
You just made the universe older.
Make a new triangle from the new intersection.
The new triangle of the new observable universe looks bigger than the old one. This new triangle is also represented by the laws of physics.
If you slide your pencil till the upper part of your paper, and out, the triangle will include the entire sheet. So that the laws of physics will represent the entire universe.

Put back your pencil upon the horizontal axis, the space-axis, in the middle of the page.
We understand that the pencil is the Universe. O.K.?
We understand that the lower triangle is what we are observing. O.K.?
Put a positive sign at what we are observing.
............
O.K.?

Last edited by Michel; 12-03-2008 at 07:52 AM. Reason: miising letter
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  #5  
Old 12-03-2008, 08:36 AM
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Wrote this (your post was obviously on my mind) under another topic; provides clues! ?

There is a really cool book on this called "The Uses Of Argument" by Stephen Edelston Toulmin

I could figure this out by simplifying...

an "argument" is e.g. "an argument in favour of going to the film early is that the next bus arrives after the film starts"...

The backing of the argument is that the next bus arrives too late; what warrants the argument is the desire to get to the film on time. These ideas "warrent" and "backing" I recall being mentioned in S.E.T.'s book.

If one was 'philosophical' about getting to the film on time, one would be 'just letting events play out' and not rushing too hard to catch the next bus? Or one may have missed the 'next bus'; and be 'constantly re-balancing the argument' about getting/ or even the desireability of getting, to the film on time?

Philosophy then is a space-time diagram; a philosophical argument is a "Minkowski" (a double metric 'tensor' i.e. an Einstein field ("a space metric": a way of measuring SPACE; a comparison, a photon (alternative ways of grouping alternatives; so 'mass AS energy' ?)

Physics is "Natural Philosophy": a natural lay-out of things; so physics is "true by definition" because physics IS 'definition' (a maximum minimum space measurement: an error margin in Nature itself: a definitive description of 'your space'... ?)
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Old 12-03-2008, 08:42 AM
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A "Minkowski diagram" is then "a triple metric (field) tensor"; so 'a photon SPACE', a 'line charge' i.e. linear variability i.e. 'a type of sketch 'pad''; a neutral density bias
hey DoctorDick will know this: "a potential well" ("negative mass-energy" i.e. factorisation options, so 'a constant 'subdividing' of space' )
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  #7  
Old 12-03-2008, 03:09 PM
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After putting the + sign where the past is.......
Let's put the opposite sign to the opposite of the past......
So let's put the - (minus) sign onto the future.
The diagram will look like this:
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  #8  
Old 12-03-2008, 05:00 PM
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The past is positive.
In the past we find everything. Everything we see belong to the past. We can measure only things that belong to the past.

The present is on the horizontal axis. We cannot measure anything in the present. But the universe unique, and belongs to the present. outside the horizontal axis, there is no universe: there was, there will be, but there is not.

The future is exactly the opposite of the past. If the past is positive, the future must be negative.

Negative does not mean "strange", it simply means "the opposite".
We use to consider what we see, what we measure, as positive things. But it is simply a convention. We could easily reverse the convention and say that what we are observing is negative, and what we are not observing is positive. It's just a matter of point of vue.
So, when a physicist encounter an equation with negative result, such as negative energy, or negative mass, there is no need to be upset. Negative may simply mean "something in the future".
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  #9  
Old 12-03-2008, 05:29 PM
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Back to our pencil.
The pencil, on the horizontal axis, represents the present, and also represents the entire universe.
More exactly, it is a sort os "screenshot" of the universe. The universe at a certain time.
It is a view of the simultaneity prohibited by Relativity.
Physically, this simultaneity does not make much sense, because for your pencil to stay rigid, there should be interactions that act at speed much higher than C. (remember that your pencil has a length of about 20 billions light-years).
But, it is good representation of what we use to call "present". The more accurate "present" that we can observe sits on the diagonals of the Minkowski diagram.
Of course, in a Newtonian diagram, we can see the present. But the past remains positive. And the future, as supposed, negative.

Anyway, the present acts exactly as the surface of a mirror. The physical properties of events on both sides of the mirror must be the same, only with a reverse sign.

Last edited by Michel; 12-03-2008 at 05:34 PM. Reason: deleting nonsenses
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  #10  
Old 12-03-2008, 05:56 PM
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For those who know about:
When Dirac asked himself about negative energy, he had a problem. A particle always tends to go to the lowest energy level (a principle introduced by Maupertuis).
Following this principle, a particle should sink into the abyss of negative energy, and never exist. It was the end of the universe.
In respond to this problem, he introduced the idea that all the negative levels of energy where fullfilled in a "sea" of negative energy, so that there was no place anymore to sink. The positive particles where a kind of sea foam.
Now, if instead of negative energy, you think about future energy, things are completely different. Instead of a sea of negative particles, you get the sea of future events.
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  #11  
Old 12-03-2008, 05:57 PM
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Enough for today.
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  #12  
Old 12-03-2008, 08:51 PM
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sea of future events = the now

sea of negative energy = sea of negative alternatives = one step backwards = floating parameters

= "an electron"

if add the pattern "electron" to this you get "anti-space" or "the Dirac equation for an electron"
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  #13  
Old 12-04-2008, 02:43 AM
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velocity = directed distance per time

a "directed distance": distance is from point "A" to point "B" or vice-versa ?

"directed distance" = definitely e.g. to point "B" from point "A" so must allow some difference (some space) between them so 'parallax' ? That is, a base-line at "A" to allow 'lining up' of point "B" (seeing point 'B' from two reflecting angles?)

"directed distance per time" = 'space per time' ? =velocity = speed of light ?

How put 'space per time' on a space/time diagram?

It is already space/time; so you would need to repeat the whole diagram?

But if the diagram's scales are made of interchangeable units ('ones'); then the diagram is already repeated (as a grid of squares of 1x1 units)...?

On the diagonals, there is a 1:1 space to time; so the diagram 'un-repeats' (becomes 'neutral' along the diagonal (looking only at the positive quadrant where space and time are positive).

If you want to place 'speed of light' on the diagram then an 'invisible line' along the diagonal would do it- allowing a rotation of that line in 4 directions (echoing the grid of square units)- or just extend the x and y axes into negative and you can use real diagonals and the diagram is nowhere and everywhere at once ?


Two sets, 'elephants' and 'zebras', intersect at 'ears'.

The distance between 'elephants' and 'zebras' is here the direction 'ears'....
This is 'specification' (magnetism).

A 'relative specification':

Three sets: 'elephants', 'zebras', and 'cats', intersect at 'ears';

this is "electro-magnetism" or 'know the difference" you 'know' the difference between 'elephant ears' and 'zebra ears' by if you are a cat with cat ears...

(?)

velocity = directed distance per time = space per time? = vibration per time = flip?

i.e. 'inside out; outside in"

time -> space
space->time

e.g. 10mph to L.A. is a velocity; the hour is subdivided over where you are to L.A. (time-> space)(it has to be in one direction for that to work minimally subdividing the hour ?)(Mandelbrot set ?)(constantly adding fractals?)(the 'left-overs' are all added in one direction to get a 'time limit on defining 'space' i.e. a 'space time differential' or "Planck mass/distance")...

The miles are subdivided over the hours;

both gives 'a spinner' (or uncertainty in defining time in space/ space in time ) ?


= 'self' kind-of ?

is 'velocity' like 'self' ('know your limits'); 'acceleration' like 'self aware' ('know your limits in space') ? ? ?

? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?

mobile self-aware = acceleration/deceleration = constantly tripping up = 'out of it' (human like)?

an 'angel' (a floating angle)?

parallax relativity?

?
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  #14  
Old 12-04-2008, 08:45 AM
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Good morning. Here I am again.
Did you kept your diagram?
And your pencil?

Let's say that we are today. We are putting ourselves as an observator in the center, at the intersection point of the diagram. In fact we are always there, since it is quite impossible to go out of the 3 dimensions of space (= the pencil= the x axis).
To observe the universe, we are obliged to look at the past. this comes not from the diagram, but from our experience.
So, we are looking at the past.
We are looking at the universe as it was. (and not as it is).
We are looking at another pencil as it was some time ago.
Let's put our pencil in the past. Parralel to the x axis, in the green portion of the diagram, the past.
As much as your pencil sits in the bottom of the diagram, it gets bigger.
It looks like this:
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  #15  
Old 12-04-2008, 08:51 AM
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I may be wrong, but I think that this is the expanded universe that we are observing through Relativity.
Getting bigger as much far in the past.

Remark: in a Newtonian diagram, where there are no diagonals, the universe is not expanding in the past.
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