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Is the block universe just a whole bunch of world lines (from the elementary particles)?


34student
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25 minutes ago, 34student said:

Like you mention here, I want to chat more about this in philosophy.

I think if you want folks to participate you will need to put more in yourself.

I don't see much acknowledgement in the form of chat about my input here.

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23 minutes ago, studiot said:

I think if you want folks to participate you will need to put more in yourself.

I don't see much acknowledgement in the form of chat about my input here.

Well, no, you said that I am learning and I agreed.  What more do you want.

As for your post, I am not sure what you are talking about. 

And you seem to contradict yourself (read in bold).  I just don't know what you are getting at. 

2) Spacetime is not the being, becoming or reality. It is a working model that has some characteristics the same as what we observe.
We can use that model to extract predictions about (only) some what we observe and also to explain some observations that earlier theory failed to predict.

3) Spacetime has at least one characteristic not possessed by observations (reality ?)
In order to have 'world lines' it's grid system imposes an orientation constraint, not inherent in the stucture of observational reality is models.

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3 minutes ago, 34student said:

Well, no, you said that I am learning and I agreed.  What more do you want.

As for your post, I am not sure what you are talking about. 

Why no ?

If you don't put in you won't get out.

The more I 'want' is exactly what you wrote following this, say you did not understand and offering what you didn't understand.

4 minutes ago, 34student said:

And you seem to contradict yourself (read in bold).  I just don't know what you are getting at. 

2) Spacetime is not the being, becoming or reality. It is a working model that has some characteristics the same as what we observe.
We can use that model to extract predictions about (only) some what we observe and also to explain some observations that earlier theory failed to predict.

3) Spacetime has at least one characteristic not possessed by observations (reality ?)
In order to have 'world lines' it's grid system imposes an orientation constraint, not inherent in the stucture of observational reality is models.

(2) says that spacetime is not reality

Hopefully that is simple enough.

If it is not reality then I offered a comment on what it is.

Spacetime is a working model of reality.

This is just as Engineers have working models of say beams structures.

These models may be actual physical models or they may be mathematical models  (often on a computer these days).

But just as the Engineers models of beams have characteristics that do not act in the same way as all real beams

(For instance plane sections remain plane on bending and the span to depth ratio is much greater then 50 to 1 or that stress is proportioanal to distance from the neutral axis)

So Spacetime constrains the orientation of linked events because it involves the use of coordinate systems, just as drawing a triangle by coordinates on graph paper fixes the orientation of the triangle in a way that drawing the same triangle by scribing the lengths of the three sides does not.

So (3) says that Spacetime does something that reality does not.

Does this help ?

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2 hours ago, 34student said:

Size, maybe, but shape, no.

Perhaps I should have been a bit more precise - it’s measurements of length that are relational, and the relationship depends on angles and orientation in spacetime. In practice that means that length contraction is observed along the direction of motion, but not perpendicular to it. Thus, for example, the initially spherical gold ions in the RHIC become flattened disks in the lab frame - and physically behave like flattened disks at the point of collision.

So no, shape also depends on the observer.

If you want to know about properties that do not depend on the observer, you need to consider all four dimensions of spacetime, and not just 3D measurements. For example, the train you previously mentioned would trace out a (4D) hypervolume in spacetime between two given events; this would be a quantity all observers agree upon, even if they don’t agree on isolated measurements of space and time. Thus, ontologically there are covariant and invariant quantities - but only in 4D. You always need to consider both space and time. It’s only our cognitive habit of separating these that creates confusion and misconceptions.

Edited by Markus Hanke
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11 hours ago, Markus Hanke said:

So no, shape also depends on the observer.

And also the method of observation, as pointed out by Penrose and Terrell.

Observation can be direct, as in Penrode and Terrell, or indirect ie deduced from other observations and or calculations.

Furthermore different observers have different interactions with a given object so it should not be suprising that they deduce different observations.

I would say that is the philosophy of Relativity for you.

I would completely agree with the rest of your post however.

 

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Also, this discussion has pointed out the difference between a world map and a world picture.  A picture is what the world looks like.  A map is how the world is arranged outside your view.

before I take a trip I like to look at where I am going on Google Earth

I like to have a picture in my mind to compare against the picture I see while I am driving.

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An elementary particle has just one worldline, never a bunch. Unless you're considering something in the way of Feynman's path-integral approach to quantum mechanics, in which a particle 'feels around' for possible paths with its wave function. Is that what you mean, @34student?

On the other hand, even from the classical point of view, an elementary particle can be considered to have a bunch of field lines (infinitely many) coming from the particle.

I'm not sure what the OP really means, but I think it would save everybody a lot of time if they clarified what they mean.

(Emphasis marking up literal expressions in OP that could be relevant.)

Just another observation: In physics, worldlines (or worldsheets, in string theory) don't necessarily represent observers. They are theoretical constructs to represent classical histories.

Feel free to keep ignoring my attempts to clarify the question.

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17 hours ago, studiot said:

 

So (3) says that Spacetime does something that reality does not.

What does it do that reality does not do?

 

17 hours ago, Markus Hanke said:

Perhaps I should have been a bit more precise - it’s measurements of length that are relational, and the relationship depends on angles and orientation in spacetime. In practice that means that length contraction is observed along the direction of motion, but not perpendicular to it. Thus, for example, the initially spherical gold ions in the RHIC become flattened disks in the lab frame - and physically behave like flattened disks at the point of collision.

So no, shape also depends on the observer.

If you want to know about properties that do not depend on the observer, you need to consider all four dimensions of spacetime, and not just 3D measurements. For example, the train you previously mentioned would trace out a (4D) hypervolume in spacetime between two given events; this would be a quantity all observers agree upon, even if they don’t agree on isolated measurements of space and time. Thus, ontologically there are covariant and invariant quantities - but only in 4D. You always need to consider both space and time. It’s only our cognitive habit of separating these that creates confusion and misconceptions.

Hmmm, are you saying that the universe is a unique 4d structure?   

3 hours ago, joigus said:

An elementary particle has just one worldline, never a bunch. Unless you're considering something in the way of Feynman's path-integral approach to quantum mechanics, in which a particle 'feels around' for possible paths with its wave function. Is that what you mean, @34student?

 

I never said that one particles has multiple world lines.  My OP says "universe", not "particle".

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4 hours ago, 34student said:

Hmmm, are you saying that the universe is a unique 4d structure?   

Well, the universe is a 4D structure, yes. But my main point was that in order to find quantities that all observers can agree on (ie that are independent of reference frame), you need to always go into 4D. So, length (3D) and time (1D) depends on observer, but hypervolume (4D) does not, for example. So the ontology of objects in spacetime is 4D.

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2 hours ago, Markus Hanke said:

Well, the universe is a 4D structure, yes. But my main point was that in order to find quantities that all observers can agree on (ie that are independent of reference frame), you need to always go into 4D. So, length (3D) and time (1D) depends on observer, but hypervolume (4D) does not, for example. So the ontology of objects in spacetime is 4D.

But how can that be?  Clearly the 4d shape of the universe is different for a photon than for a human.

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9 hours ago, 34student said:

But how can that be?  Clearly the 4d shape of the universe is different for a photon than for a human.

Shape is a very difficult concept to tie down.

I don't know of any way to define it without involving boundaries.

So far as we know, the Universe has no boundaries.

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8 hours ago, 34student said:

Why not?

It has no inertial frame of reference. As beecee notes, it has no rest mass, so photons travel at c. You can't use the Lorentz transforms to go between an inertial frame an a photon frame; the equations diverge.

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7 hours ago, studiot said:

Shape is a very difficult concept to tie down.

I don't know of any way to define it without involving boundaries.

So far as we know, the Universe has no boundaries.

Ok, but my point was that the 4d hypervolume does not seem to be the same for all observers.

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16 minutes ago, 34student said:

Ok, but my point was that the 4d hypervolume does not seem to be the same for all observers.

In what way ?

I am not sure of what use the hypervolume is to anyone anyway ?

Edited by studiot
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1 hour ago, studiot said:

In what way ?

I am not sure of what use the hypervolume is to anyone anyway ?

Because of length contraction.  For one observer a cubic structure is rectangular, for another it is a cube.  The hypervolume of an object very much seems to depend on the observer.  This is in contrast to what Markus Hanke says a few posts up.

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6 minutes ago, studiot said:

But a structure cube or whatever is not a point.

I know it isn't.  I do not know what you are getting at.

11 minutes ago, studiot said:


Do you understand why the other axis has to be ct ?

No, I only learnt that it was a t axis

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3 hours ago, 34student said:

No, I only learnt that it was a t axis

No worries, perhaps these sketches will help.

Starting with only 2 dimensions and comparing two different figures.

There are no volumes in 2 dimensions, only areas and lengths.

In figure 1 one side is measured in seconds the other in metres.

The region enclosed by the axes and the dashed lines is not an area.

In figure 2 both sides are measured in metres and the shaded figure is inded an area.

Moving up to 3 dimensions we now have areas and volumes (and lengths).

In fig 3 we have two side lengths measured in metres and one side measured in seconds.
This figure is not a volume.
The base and top of the figure are measured in metres times metres ie is an area but the other faces are measured in metres x seconds, which is not an area.

In figure 4 we have all three side lengths are measured in metres so the figure is a volume and is measured in metres x metres x metres.
Also any of the faces are measured in metres x metres so all faces are areas.

units1.thumb.jpg.6e94072a7fa91907e2dc82a4045af9a5.jpg

 

I can't depict 4 dimensions on a piece of paper, but the idea is the same and as you rightly say the next step up is a hypervolume.

But the progression has the same characteristics.
 

You can only have a hypervolume if all the sides are measured in metres and all the 'faces' are (3D) volumes.
If one of the sides is measured in anything else then the result is not a hypervolume.

So we can't use time directly.

So I have ended with the observation that if we multiply time by a speed the times cancel and we 'convert' the time axis into a distance axis.

Newton just used any old speed.
Einstein introduced the idea of a special speed, c, the speed of light.

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4 hours ago, 34student said:

Because of length contraction.  For one observer a cubic structure is rectangular, for another it is a cube.  The hypervolume of an object very much seems to depend on the observer.  This is in contrast to what Markus Hanke says a few posts up.

In 4D, you account for both space and time. If a boundary is contracted in space, it is expanded in time by the same factor, leaving the overall volume in spacetime unchanged.

Or to put it more technically - the volume element in 4D is an antisymmetric tensor, so any volume constructed from it by integration will be a covariant quantity.

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2 hours ago, studiot said:

No worries, perhaps these sketches will help.

Starting with only 2 dimensions and comparing two different figures.

There are no volumes in 2 dimensions, only areas and lengths.

In figure 1 one side is measured in seconds the other in metres.

The region enclosed by the axes and the dashed lines is not an area.

In figure 2 both sides are measured in metres and the shaded figure is inded an area.

Moving up to 3 dimensions we now have areas and volumes (and lengths).

In fig 3 we have two side lengths measured in metres and one side measured in seconds.
This figure is not a volume.
The base and top of the figure are measured in metres times metres ie is an area but the other faces are measured in metres x seconds, which is not an area.

In figure 4 we have all three side lengths are measured in metres so the figure is a volume and is measured in metres x metres x metres.
Also any of the faces are measured in metres x metres so all faces are areas.

units1.thumb.jpg.6e94072a7fa91907e2dc82a4045af9a5.jpg

 

I can't depict 4 dimensions on a piece of paper, but the idea is the same and as you rightly say the next step up is a hypervolume.

But the progression has the same characteristics.
 

You can only have a hypervolume if all the sides are measured in metres and all the 'faces' are (3D) volumes.
If one of the sides is measured in anything else then the result is not a hypervolume.

So we can't use time directly.

So I have ended with the observation that if we multiply time by a speed the times cancel and we 'convert' the time axis into a distance axis.

Newton just used any old speed.
Einstein introduced the idea of a special speed, c, the speed of light.

Oh cool.  Thanks a lot for that.  

1 hour ago, Markus Hanke said:

In 4D, you account for both space and time. If a boundary is contracted in space, it is expanded in time by the same factor, leaving the overall volume in spacetime unchanged.

Or to put it more technically - the volume element in 4D is an antisymmetric tensor, so any volume constructed from it by integration will be a covariant quantity.

Interesting, thanks, that will help.

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19 hours ago, 34student said:

Oh cool.  Thanks a lot for that.  

Glad it was helpful.

21 hours ago, Markus Hanke said:

the volume element in 4D is an antisymmetric tensor, so any volume constructed from it by integration will be a covariant quantity.

To put things more simply I think Markus was referring to building one of your structures with his elements like building a brick or block wall with one brick stacked on top of another.

Each brick corresponds to a 'volume element'.

 

However I am concerned with apparent suggestion that you can string together any old set of axes and multiply coordinates on them to form a volume.

Here is a simple example of the nonsense that could produce.

Let there be 3 space axes, the Mercator projection grid lines and plot the coordinates of the capitals of the world on two of these axes.
On the third space axis plot their respective elevations above sea level.

Now introduce an axis measured in seconds  ie a time axis.

Plot on this axis the half lives of all the radioactive isotopes (in seconds).

All these points will result in a 4D space for which the concept of hypervolume, or integration over some region of the space, has no meaning.

 

Sometimes when you multiply two or more quantities together you get a new quantity with some significance in the physical world.

Area and volume and work and energy are such products.

But multiplying temperature by distance has no real world significance that I am aware of.

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1 hour ago, studiot said:

However I am concerned with apparent suggestion that you can string together any old set of axes and multiply coordinates on them to form a volume.

I didn’t mean to suggest that. Of course this needs to be done according to the proper rules and procedures of differential geometry in spacetime - the language of exterior calculus naturally lends itself to this. I remember MTW has a section that shows the proper procedure to construct volume integrals on semi-Riemannian manifolds; it’s that I was thinking of.

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