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Events and the Space-Time Manifold


geordief

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An "event" is a point on the Space-Time graph where something occurs .

 

Or is it?

 

Is it a point where something may occur but may not? (Are there [x,y,z,t] s where nothing happens? )

 

 

Also, I have an (erroneous?) idea in my head that the Space-Time graph can ,if drawn in sufficiently fine detail model every macro level interaction between things in the real world.

 

Is this a misapprehension ? Is the name "event" in the Space-Time graph (or manifold) simply a description of when and where something might occur but it does not describe the occurrence in its entirety?

 

So "event " is only a partial description of what is happening?

 

If the manifold was assembled in fine enough detail (quantized?) would it possibly describe what occurs completely?

Edited by geordief
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Say event A =

<<Car hits man crossing the street at traffic light. The clock in the car shows 5:00 o'clock. The clock of the man crossing the street shows 4:35 o'clock.>>

That event is absolute: it's one and the same in all reference frames.

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If the manifold was assembled in fine enough detail (quantized?) would it possibly describe what occurs completely?

 

I know you are talking relativity here but the uncertainty prinicple inevitably comes to my mind when looking at the above question.

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I know you are talking relativity here but the uncertainty prinicple inevitably comes to my mind when looking at the above question.

Does the term "event" mean two different things in Relativity and Quantum Theory?

 

And to the extent we imagine that ,in layman's parlance an "event" can be a unit of "things happening" is that a third sense that may not even be covered by either ?

 

I say that because ,when I think about "events" I seem to be drawn to this meaning but it may have no application in either theory and so am I twisting myself in knots to no purpose?

 

Admittedly I have not got my head around the two main theories yet ,but I do not want to cloud my future appreciation of them if and when I do.

 

EDIT: Since you brought up the uncertainty principle as the manifold get more and more defined or populated does that imply that the space/time relationship could become "blurry" as more and more lines were drawn on the space time graph?

Edited by geordief
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Does the term "event" mean two different things in Relativity and Quantum Theory?

I'm not sure. I think that that your question "If the manifold was assembled in fine enough detail (quantized?) would it possibly describe what occurs completely?" implies probabilitiy therefore I'm automaticaly thinking QM (I have poor grasp of quantum theory)

 

And to the extent we imagine that ,in layman's parlance an "event" can be a unit of "things happening" is that a third sense that may not even be covered by either ?

 

I say that because ,when I think about "events" I seem to be drawn to this meaning but it may have no application in either theory and so am I twisting myself in knots to no purpose?

 

Admittedly I have not got my head around the two main theories yet ,but I do not want to cloud my future appreciation of them if and when I do.

 

EDIT: Since you brought up the uncertainty principle as the manifold get more and more defined or populated does that imply that the space/time relationship could become "blurry" as more and more lines were drawn on the space time graph?

I think so. I think "Fuzzy" is the word that the physisists dealing with this stuff use.

Edited by koti
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geordief

1)So "event " is only a partial description of what is happening?

2)If the manifold was assembled in fine enough detail (quantized?) would it possibly describe what occurs completely?

 

 

1) Yes

 

2) No

 

The choice of the word 'Event' is an unfortunate one given the usual english use of the word.

 

It simply means that whoever chose it (or translated the German?) chose to add an unnecessary word to the vocabulary of mechanics.

 

The word 'point', as in its usual geometric meaning of a collection of definite coordinate measured against some system of axes, has served faithfully for some centuries and that is the whole meaning of the word 'event' in this context.

Edited by studiot
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1) Yes

 

2) No

 

The choice of the word 'Event' is an unfortunate one given the usual english use of the word.

 

It simply means that whoever chose it (or translated the German?) chose to ad an unnecessary word to the vocabulary of mechanics.

 

The word 'point', as in its usual geometric meaning of a collection of definite coordinate measured against some system of axes, has served faithfully for some centuries and that is the whole meaning of the word 'event' in this context.

 

So does this mean (as I suspected) that in order to elaborate on the Yes & No answer to Geordief's 2 questions we have to dig into the absurdities of QM ?

Thanks for this post btw.

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If the manifold was assembled in fine enough detail (quantized?) would it possibly describe what occurs completely?

 

This is the great challenge of our age. The mathematics of general relativity requires that manifolds are continuous and differentiable. Attempting to deal with the possibility of quantised time and space is the reason for things like string theory, loop quantum gravity, etc.

Edited by Strange
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So does this mean (as I suspected) that in order to elaborate on the Yes & No answer to Geordief's 2 questions we have to dig into the absurdities of QM ?

Thanks for this post btw.

 

Not really.

 

QM and einstinian relativity address different matters, although there is some overlap in that there are versions of the equations of QM that incorporate relativistic mechanics, rather than classical mechanics.

I believe that Paul Dirac was the first to offer this.

 

There are yet remaining areas of Physics that are (fully) addressed by neither QM or einstinian relativity, for example electric Charge and number (of molecules or particles).

 

You may also not be aware that the 'uncertainty principle' also applies in classical mathematics and even in the rules of simple arithmetic of ordinary numbers, which is why we have adopted certain conventions about arithmetic to resolve this.

 

Edit +1 to Strange. I have trying to make this point for some time.

 

 

strange

The mathematics of general relativity requires that manifolds are continuous and differentiable.

Edited by studiot
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Although relativity has been successfully married to QM in some instances like QFT ( more specifically, with SR ), or Hawking radiation, the fact remains that GR ( or more specifically, the block-universe model ) remains classical/deterministic in nature.

As such, I expect the block-universe model to be one of the first casualties of any viable Quantum Gravity theory. The probabilistic nature of QM cannot be reconciled with deterministic future events.

 

I happen to like the term 'event', as it implies a time ( one of the co-ordinates ) and so makes perfect sense.

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