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Author Topic: OCTOBER DISCUSSION:  (Read 4519 times)
eurekabruce
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Ehhh . . . What's up, Doc?


« on: October 09, 2006, 03:16:25 PM »

For October, I'm going to talk about Quantum Mechanics vs. the concepts of Minkowski, and distortion inherent between the two.  An acquaintance of mine (who remains incognito at the moment) has brought forward the idea that the spacetime we perceive is only apparent due to our interpretation thereof.  Looking at matters from the Minkowskian perceptive, there seem to occur unperceived specetime intervals and unrealized energy exchanges.  This is his concept:

------------------------------------------------

Visualising proper Interval Locality

A space-time diagram is a graph showing position as a function of time. Conventionally, time runs up the diagram with the past at the bottom and the future at the top. Position is the horizontal (X axis, represented by one dimension). Events can be reasonable visualised using this devise but it has a fundamental weakness in that the interval between events is necessarily distorted. Diagram 1 illustrates this difficulty



The space-time diagram allows to visualise position as a function of time, but the price we have to pay is a distortion of the proper interval between events. (A consequence of trying to depict the Minkowski geometrical relationship between space and time on a sheet of paper characterised by Euclidian geometry.) However for any single event we can create a coordinate transformation that allows us to graphically represent the magnitude of the proper interval between the event and any other set of coordinates in space-time.

In diagram 1 let (X2-X1)2 + C2(T2-T1)2 = H2 ; if (X2-X1)2 > C2(T2-T1)2 then
(X2-X1)2 - C2(T2-T1)2 = S2 and if (X2-X1)2
The change in equation representing the change from space-like to time-like intervals.


Now let event 1 be positioned at the origin of the space-time diagram. So that X1 = 0 and T1 = 0.

We can use the coordinate transformation x = (S/H)X and t = (S/H)T to visualise the interval from the origin to an event at (X, T).


In diagram 2; point A represents the coordinates of position and time relative to a given frame of reference. The distance from the origin to Point B now represents the proper interval from the origin to event 1. The proper interval will be fore-shortened unless for space-like intervals T is 0 or for time-like intervals T is infinite.
Now let us extend the coordinate transformation to the gridline (1, T)



Diagram 3

Diagram 3 shows the proper interval transformation for the gridline (1, T). Note here C is set at 1.

We see the plot of the gridline transformation touches the origin twice, when T = 1 and when T = -1. That is for these two events the proper interval joining them to the origin has collapsed to zero. According to the principle of proper interval locality the world states at (1, 1) and (1, -1) are therefore not independent of the world state at the origin. More specifically a quantum system experiencing event (0, 0) can receive momentum from a quantum system at (1, -1) and donate momentum to a quantum system at (1, 1).




Diagram 4

In diagram 4 the coordinate transformation is shown for the gridlines (-1, T), (-2, T), (-3, T), (1, T), (2, T), (3, T), (X, -1), (X, -2), (X, -3), ), (X, 1), (X, 2) and (X, 3). It is important to remember that this gridline transformation is unique to the event (0, 0). Superimposed on the diagram are the world lines of two quantum objects Q1 andQ2. Q1 is initially at rest relative to our inertial frame of reference and placed at X = 0 Whilst Q2 is in relative motion and its path passes through the event (2, 2). The Proper interval between events (0, 0) and (2, 2) has zero magnitude, the two quantum objects are touching in space-time and therefore the can exchange energy. An interaction is indicated by the change in direction of the objects at (0, 0) and (3, 3). The curved white plot is the proper interval between event (0, 0) and the world line of quantum object Q2. Note that this object passes through event (3, 0) the distance and the proper interval between this event and the origin have the same magnitude.

So, what do you folks think of this little brain-stretcher?  I hope to get Mr. X to put out more material on this subject.

Regards,

Eureka Bruce
Loc/Sec
« Last Edit: October 09, 2006, 03:18:19 PM by eurekabruce » Logged
maags
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"Uplifted" by Max D. Standley


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« Reply #1 on: November 14, 2006, 05:37:15 AM »

OK, I can see that I don't (and maybe won't ever) get much of this.  Shocked

But, just to really show my ignorance, could you tell me why you don't refer to the line representing position "P" instead of "X" the way you do here? You call the line representing time "T" which makes sense to me.   Roll Eyes


How's that for an ignorant question? Now that a really ignorant question has been asked, everyone else can ask their ignorant questions without fear of being thought silly.   Wink
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Avatar artwork by Max D. Standley.
ScubaMark
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... if a frog had sidepockets ...


« Reply #2 on: November 14, 2006, 04:37:47 PM »

... could you tell me why you don't refer to the line representing position "P" instead of "X" the way you do here? You call the line representing time "T" which makes sense to me.

Actually, that is a good question.  The best answer is likely not very satisfying....  It is simply a "convention" or accepted practice.   One good reason for not calling it P is because "position" is described differently depending upon which global and local coordinate systems you choose and requires multiple variables to do so.  In a typical 3 dimensional Cartesian coordinate system the three "directions" are referred to as X, Y, & Z.  Where X is directly in front of you, Y is the directly to your left, and Z is straight up.  The convention is (typically) to just use X & Y for two dimensions and if you are only concerned with or only need one dimension to describe the phenomena, then only X is used.
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eurekabruce
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Ehhh . . . What's up, Doc?


« Reply #3 on: November 14, 2006, 09:27:50 PM »

Hey, ScubaMark, glad to see you jump in, here!

Just like everybody else, I'm doing my best to wrap my poor fried brain around this different way of viewing spacetime.  I could post what I think, but in so doing I could well distort the concept.

My gut instinct is to post our British Mister X's name and e-mail address so folks can ask the 'horse's mouth' directly:

William Robert Ormerod

englishdales@googlemail.com

If you manage to get in touch will Robert, please fill us in.

Regards,
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maags
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« Reply #4 on: November 16, 2006, 06:41:40 AM »

... could you tell me why you don't refer to the line representing position "P" instead of "X" the way you do here? You call the line representing time "T" which makes sense to me.

Actually, that is a good question.  The best answer is likely not very satisfying....  It is simply a "convention" or accepted practice.   One good reason for not calling it P is because "position" is described differently depending upon which global and local coordinate systems you choose and requires multiple variables to do so.  In a typical 3 dimensional Cartesian coordinate system the three "directions" are referred to as X, Y, & Z.  Where X is directly in front of you, Y is the directly to your left, and Z is straight up.  The convention is (typically) to just use X & Y for two dimensions and if you are only concerned with or only need one dimension to describe the phenomena, then only X is used.

OK, thanks. I thought I was missing something, but it appears I was not.  Smiley

Now that that little detail is settled, I am going to go back and see if I can get more out of it.  33

P.S. LOVE the frog avatar with the little scuba tank on it!!!!   Grin

I used to have a business selling watergarden supplies called Frog Heaven Watergardens. There is a huge soft spot in my heart for frogs and toads... heck. all amphibians and other water creatures!   thumbs up 
« Last Edit: November 16, 2006, 06:48:07 AM by maags » Logged

Avatar artwork by Max D. Standley.
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