Godel and The Philosophy of Special Relativity

[bobc2]

Burton Feldman, in his book "112 Mercer Street" (Einstein's address during his tenure at Princeton) tells of a comment that Einstein made to a friend: "...when he felt old and his own work no longer meant much, he came to the Institute mostly for the privilege of walking home with Godel." Godel of course was a giant among mathematicians, but he turned his interests toward physics and philosophy in later life.

Wouldn't you have loved to have listened in on those conversations between Godel and Einstein. Perhaps some of those conversations played a role in the development of Godel's ideas about what came to be known as the "Block Universe." I've found reference to the "Block Universe" in Wikipedia articles and other places. But so far I've really not found much detail. The description would seem to be that of a 4-dimensional universe populated by 4-dimensional objects (I'm using object in the sense of Bertrand Russell's "The Problems of Philosophy."). However, I can't be sure that he does not have in mind idealistic 4-dimensional things, more in the sense of Berkely or Leibnitz.

Roger Penrose presents the example of two people walking past each other and then considering the two different Special Relativity 3-D worlds they each live in at the instant they pass each other. One individual's world extending out to the Andromeda Galaxy has the aliens in that galaxy pondering whether or not they should attack earth. The other individual's 3-D world extends out to the galaxy where locally the time is several days later, and the aliens have already launched their attack. This situation certainly implies that the bodies of the aliens along with their space ships, etc., are 4-dimensional objects--and very likely (in Penrose's view) in that same Bertrand Russel sense.

Putnam has argued very convincingly for the 4-dimensional universe populated by 4-dimensional objects ("Time and Physical Geometry." Journal of Philosophy, 64:240-7).

So, could any of you expand on the philosophy of Godel with regard to the interpretation of Special Relativity?

Also, could you make any observations about possible implications of his philosophy (relating to time and/or consciousness, for example)?

 

[ThomasT]

Have you read this?
Contributions of K. Godel to Relativity and Cosmology by G.F.R. Ellis
http://projecteuclid.org/DPubS/Repo...d.lnl/1235417013&view=body&content-type=pdf_1

 

[bobc2]

Have you read this?
Contributions of K. Godel to Relativity and Cosmology by G.F.R. Ellis
http://projecteuclid.org/DPubS/Repo...d.lnl/1235417013&view=body&content-type=pdf_1

No, I have not. But, I will now. Thanks very much!

 

[Maui]

The description would seem to be that of a 4-dimensional universe populated by 4-dimensional objects (I'm using object in the sense of Bertrand Russell's "The Problems of Philosophy."). However, I can't be sure that he does not have in mind idealistic 4-dimensional things, more in the sense of Berkely or Leibnitz.

There are no 4-dimensional 'things'(worldlines) and the fundamental shift in our understanding of reality is(and will be) towards moving away from the idea that things exist, towards the notion that 'things' occur. Demanding that there be solid objects with properties in absolute space is a recipe for disaster as far as physics is concerned.

 

[FlexGunship]

Demanding that there be solid objects with properties in absolute space is a recipe for disaster as far as physics is concerned.

Meh. Works well for most calculations.

 

[Maui]

Meh. Works well for most calculations.

"Works well for most mundane calculations"

that do not include high speed, high gravity, any kind of high precision or any idea of what truly is happening out there. Basically, in the philosopher's viewpoint, it's worthless.

 

[bobc2]

There are no 4-dimensional 'things'(worldlines) and the fundamental shift in our understanding of reality is(and will be) towards moving away from the idea that things exist, towards the notion that 'things' occur. Demanding that there be solid objects with properties in absolute space is a recipe for disaster as far as physics is concerned.

Then, would you explain how different observers experience different cross-sections of space-time?

And please explain how absolute space is a recipe for disaster?

Two observers living in different spaces is a disaster if you cannot account for it with something like a 4-dimesional universe--whether that universe is external "objective" space or "ideal" space.

 

[Maui]

Then, would you explain how different observers experience different cross-sections of space-time?

Applying Lorentz transformation would be a good start.

And please explain how absolute space is a recipe for disaster?

The absolute space is part of your imagination/misunderstabding/misapprehension of reality. This a stone-cold, experimentally verified fact.

Two observers living in different spaces is a disaster if you cannot account for it with something like a 4-dimesional universe--whether that universe is external "objective" space or "ideal" space.

You misunderstand the notion of 4-d universe and what led to it.

 

[bobc2]

Applying Lorentz transformation would be a good start.

Yes, that would be an excellent place to start. So, let's derive the Lorentz transformation to obtain the time, t'', for an observer at rest in the double prime coordinates, as computed using the coordinates of another observer at rest in single prime coordinates. We set it up with a symmetric space-time diagram in which a red rocket and blue rocket speed away from each other with the same speed as shown in an unprimed rest system (black coordinates). The advantage of the symmetric view is that lines drawn in the sketch have the same calibration for the red guy as for the blue guy.

The orientation of the blue and red coordinates in the upper left diagram follow directly from the fact that the speed of light is constant for all observers, regardless of their relative velocities. This means that the green photon world lines must always bisect the angle between X4 and X1, X4' and X1', X4'' and X1''.

So, we are depicting the ontological 4-D space (supressing X2 and X3) with the 4-D spaceship objects (objects in the sense of Bertrand Russel), abreviating their 4-D orientations with the world lines, X4' and X4''. Having established the 4-D objects in 4-D space, we can now identify a right triangle and show directly the relationships between X4'', X1', and X4'. They are manifestly related by the Pythagorean theorem equation as shown with the sketches below. Simple high school algebra is then used to solve for X4'' and thus, t'', which is the Lorentz transformation (rotation) for time. Yes, indeed, this is a good place to start. At face value it implies an ontological 4-space.

Notice the two different cross-section views of the red guy and blue guy in the upper left diagram. These views establish a NOW for each observer's instantaneous 3-D world.

The lower left indicates the well known length contraction as well as time dilation. In the blue guy's instantaneous 3-D world the red rocket is much shorter than his own. Also the clock in the red rocket would be showing a much earlier time as viewed by the blue guy.

The absolute space is part of your imagination/misunderstabding/misapprehension of reality. This a stone-cold, experimentally verified fact.

I would respectfully disagree with your stone-cold, experimentally verified fact. Perhaps I misunderstand where you are coming from.

You misunderstand the notion of 4-d universe and what led to it.

I think my Lorentz transformation derivation above makes it pretty clear the notion of a 4-D universe. Could you explain the fault in that presentation.

 

[Maui]

Yes, that would be an excellent place to start. So, let's derive the Lorentz transformation to obtain the time, t'', for an observer at rest in the double prime coordinates, as computed using the coordinates of another observer at rest in single prime coordinates. We set it up with a symmetric space-time diagram in which a red rocket and blue rocket speed away from each other with the same speed as shown in an unprimed rest system (black coordinates). The advantage of the symmetric view is that lines drawn in the sketch have the same calibration for the red guy as for the blue guy.

The orientation of the blue and red coordinates in the upper left diagram follow directly from the fact that the speed of light is constant for all observers, regardless of their relative velocities. This means that the green photon world lines must always bisect the angle between X4 and X1, X4' and X1', X4'' and X1''.

So, we are depicting the ontological 4-D space (supressing X2 and X3) with the 4-D spaceship objects (objects in the sense of Bertrand Russel), abreviating their 4-D orientations with the world lines, X4' and X4''. Having established the 4-D objects in 4-D space, we can now identify a right triangle and show directly the relationships between X4'', X1', and X4'. They are manifestly related by the Pythagorean theorem equation as shown with the sketches below. Simple high school algebra is then used to solve for X4'' and thus, t'', which is the Lorentz transformation (rotation) for time. Yes, indeed, this is a good place to start. At face value it implies an ontological 4-space.

Notice the two different cross-section views of the red guy and blue guy in the upper left diagram. These views establish a NOW for each observer's instantaneous 3-D world.

The lower left indicates the well known length contraction as well as time dilation. In the blue guy's instantaneous 3-D world the red rocket is much shorter than his own. Also the clock in the red rocket would be showing a much earlier time as viewed by the blue guy.

Nice diagram and nice way to demonstrate that the relationships you are trying to establish across 2 or more FOR, do not represent in any way an absolute, immutable spacetime and immutable objects with fixed properties. A transition from 'objects' to 'relationships' is mandatory, unless and until i see a better proposition(I haven't so far).

I would respectfully disagree with your stone-cold, experimentally verified fact. Perhaps I misunderstand where you are coming from.

Length contraction, time dilation and spacetime curvature are verified facts that demonstrate that space is not absolute(actually spacetime is not absolute, but since space and time have been united in GR the statement as it is is correct).

I think my Lorentz transformation derivation above makes it pretty clear the notion of a 4-D universe. Could you explain the fault in that presentation.

Your Lorentz transformation is just a calculation and the 'picture' behind it is insane. It says that your body doesn't have specific fixed properties but ones that vary depending on how and where you measure. This is where i am coming from - things are the way they are(or seem to be) only from the very specific point of view that i hold at the moment. Deriving what and how the universe is(a sort of god's view), from this misleading POV, is a disservice to logical thinking.

As a sidenote, nobody really understands the 4D universe of GR, so this talk will lead to nowhere(nowhere close to what we experience as a 3D universe)

 

[bobc2]

Length contraction, time dilation and spacetime curvature are verified facts that demonstrate that space is not absolute(actually spacetime is not absolute, but since space and time have been united in GR the statement as it is is correct).

This statement is quite puzzling to me. I thought my derivation of the length contraction and time dilation demonstrated that these phenomena were consistent with the concept of a 4-dimensional objective universe (Godel's "Block Universe"). Could you explain the fallacy of my logic. I'm not claiming that this is proof, but rather that the 4-D concept is consistent with the phenomena. So, how is it not consistent?

Your Lorentz transformation is just a calculation and the 'picture' behind it is insane. It says that your body doesn't have specific fixed properties but ones that vary depending on how and where you measure.

But this is the whole point of requiring a 4-D universe, that is to avoid the insanity of having bodies that do not have fixed properties. It is precisely because the 4-D objects have fixed properties that one would embrace a 4-D object concept. Different observers (having different relative velocities) would have different impressions of my body, but using their knowledge of the 4-D universe, they would all agree on the fixed 4-D properties of my body. Having just a 3-D world is what leads to the bodies without fixed properties.

This is where i am coming from - things are the way they are(or seem to be) only from the very specific point of view that i hold at the moment. Deriving what and how the universe is(a sort of god's view), from this misleading POV, is a disservice to logical thinking.

I recall during my doctoral physics program taking the course on The Philosopy of Physics. There were four of us physics students along with my Quantum Mechanics professor and one PhD philosophy student. On the last day of the class the philosophy professor shared his world view. He said that the class room next door did not exist until he stepped out into the hallway and opened the door. Is this the same as your 3-D world view? We physics students looked at each other, puzzled--the philosophy student was smiling and nodding her head.

As a sidenote, nobody really understands the 4D universe of GR, so this talk will lead to nowhere(nowhere close to what we experience as a 3D universe)

I think you are certainly partially correct on that. Godel used one particular solution of Einstein's equations to investigate the notions of time. It was a fruitful investigation, and while his model did not correctly represent some of the key observed properties of the universe, it became a springboard for developments in cosmology and philosophy.

 

[bobc2]

Have you read this?
Contributions of K. Godel to Relativity and Cosmology by G.F.R. Ellis
http://projecteuclid.org/DPubS/Repo...d.lnl/1235417013&view=body&content-type=pdf_1

ThomasT, I read the paper over the weekend. Very very interesting and informative. I'll try to get back to relate some of the ideas presented. Thanks again.

 

[Maui]

This statement is quite puzzling to me. I thought my derivation of the length contraction and time dilation demonstrated that these phenomena were consistent with the concept of a 4-dimensional objective universe (Godel's "Block Universe").

What do you think a 4-dimensional block universe is? It seems you think it's something similar to the familiar 3-d universe.

Could you explain the fallacy of my logic. I'm not claiming that this is proof, but rather that the 4-D concept is consistent with the phenomena. So, how is it not consistent?

A block universe is ... a collection of worldlines. The familiar objects of daily life are worldlines, they are not objects per se, they are extended 'objects' in time. The worldline of the object 'dog' is the dog being everywhere that it will be in it's life simultaneously. My human body is represented as me being everywhere from Shanghai to California simulataneously(places I've been to). This representation and understanding of reality resists an objective picture. There is none. The 'picture' that could be built upon it is not objective.

But this is the whole point of requiring a 4-D universe, that is to avoid the insanity of having bodies that do not have fixed properties. It is precisely because the 4-D objects have fixed properties that one would embrace a 4-D object concept. Different observers (having different relative velocities) would have different impressions of my body, but using their knowledge of the 4-D universe, they would all agree on the fixed 4-D properties of my body. Having just a 3-D world is what leads to the bodies without fixed properties.

I don't see what you are saying. You are referring to a 4-D universe in a SR thread(your thread), so i assume you are talking about our relative 4-D universe, not some special cases or some exotic idea of a preferred frame of reference.

I recall during my doctoral physics program taking the course on The Philosopy of Physics. There were four of us physics students along with my Quantum Mechanics professor and one PhD philosophy student. On the last day of the class the philosophy professor shared his world view. He said that the class room next door did not exist until he stepped out into the hallway and opened the door. Is this the same as your 3-D world view? We physics students looked at each other, puzzled--the philosophy student was smiling and nodding her head.

I wouldn't argue with the philosophical position that biology could be fundamental, and not physics.

I think you are certainly partially correct on that. Godel used one particular solution of Einstein's equations to investigate the notions of time. It was a fruitful investigation, and while his model did not correctly represent some of the key observed properties of the universe, it became a springboard for developments in cosmology and philosophy.

Time is what keeps those worldlines from happening all at once.

 

[bobc2]

What do you think a 4-dimensional block universe is? It seems you think it's something similar to the familiar 3-d universe.

Yes. In the model for reality that I've been discussing here the 4-D universe object is not unlike the 3-D object universe--it just has the additional 4th dimension. The objects populating the overall universe object have the interesting characteristic of extending great distances (millions of miles) along the 4th dimension (X4) as compared to many inches, feet or miles along the X1 dimension. The neurons of brains have interesting properties, exhibiting fractal properties extending a few inches along X1 relative historical geometric properties extending into observed X1 space (the fractals are replete along X4).

A block universe is ... a collection of worldlines. The familiar objects of daily life are worldlines, they are not objects per se, they are extended 'objects' in time. The worldline of the object 'dog' is the dog being everywhere that it will be in it's life simultaneously. My human body is represented as me being everywhere from Shanghai to California simulataneously(places I've been to).

No. The worldlines extend through a 4-dimensional space. We can compute the distance moved along the world line by taking readings from a clock and multiplying c x dT (or integrating as required for curved world lines).

This representation and understanding of reality resists an objective picture. There is none. The 'picture' that could be built upon it is not objective.

But, we have already shown how the continuous sequence of 3-D pictures can be understood in the context of a 4-D universe model such that we now have 4-D objects without contradictions. We have already shown that Special Relativity exposes conflicts between different observers experiencing just sequences of instantaneous 3-D objects. The 4-D space clearly resolved the perceived paradoxes associated with a universe restricted to three dimensions. I don't understand how you can turn that analysis on its head. Perhaps you have a more complete explanation of that.

I don't see what you are saying. You are referring to a 4-D universe in a SR thread(your thread), so i assume you are talking about our relative 4-D universe, not some special cases or some exotic idea of a preferred frame of reference.

The 4-D universe would not single out anyone observer's 3-D cross-section view of the 4-D universe as being special. Our particular frame of reference on Earth would not be special in that sense.

I wouldn't argue with the philosophical position that biology could be fundamental, and not physics.

Does that mean that you would embrace the world view expressed by my philosophy professor (...the room does not exist until I open the door.)?

Time is what keeps those worldlines from happening all at once.

It might be that your psychological impression of the way time works keeps you from imagining how a 4-dimensional object could happen all at once.

I'm still searching for a more detailed account of Godel's ideas about time. At this point I get the impression that both he and Einstein had the notion of time simultaneously flowing in every local neighborhood of the 4-dimensional universe. Godel made a statement to the effect that if you are to relativize time you must destroy previous notions of time. (I'll try to find the exact quote)

 

[Maui]

Yes. In the model for reality that I've been discussing here the 4-D universe object is not unlike the 3-D object universe--it just has the additional 4th dimension. The objects populating the overall universe object have the interesting characteristic of extending great distances (millions of miles) along the 4th dimension (X4) as compared to many inches, feet or miles along the X1 dimension. The neurons of brains have interesting properties, exhibiting fractal properties extending a few inches along X1 relative historical geometric properties extending into observed X1 space (the fractals are replete along X4).

Then you are not discussing the relative spacetime of SR, which is radically different from any conceivable 3-D model of the universe.

No. The worldlines extend through a 4-dimensional space.

...also called Spacetime. Spacetime is the collection of events that define its existence, i.e. its worldlines. All the events(worldlines) define what spacetime is(i've always found this a particularly useful analogy). Same way a collection of dots both represents a line and IS actually the line.

But, we have already shown how the continuous sequence of 3-D pictures can be understood in the context of a 4-D universe model such that we now have 4-D objects without contradictions.

Objects that vary their defining properties across referential frames can not be objects. They can be events or relationships, but not objects. You are no longer talking about a universe, but of a reality or personal experience.

We have already shown that Special Relativity exposes conflicts between different observers experiencing just sequences of instantaneous 3-D objects. The 4-D space clearly resolved the perceived paradoxes associated with a universe restricted to three dimensions.

I don't understand what you are saying, but there are no perceived paradoxes in the Newtonian limit, which is adequate for the mundane human perception. It's only when one pushes for true knowledge and inquires about the big philosophical questions that we have to leave the cosy world of confused and imperfect perception.

The 4-D universe would not single out anyone observer's 3-D cross-section view of the 4-D universe as being special. Our particular frame of reference on Earth would not be special in that sense.

Are you able to sketch a simple drawing of a 4-D universe(block universe)? Why would you call that universe? Is a photon that extends from the BB all the way to the heat death of the universe really a photon(a photon that's spatially extended for hundreds of billions of light years)?

Does that mean that you would embrace the world view expressed by my philosophy professor (...the room does not exist until I open the door.)?

There is what i am certain of and there is what i believe. The unobserved things and events are things i am forced to believe(and not be certain of).

I'm still searching for a more detailed account of Godel's ideas about time. At this point I get the impression that both he and Einstein had the notion of time simultaneously flowing in every local neighborhood of the 4-dimensional universe. Godel made a statement to the effect that if you are to relativize time you must destroy previous notions of time. (I'll try to find the exact quote)

I can't follow what you are saying here. Maybe someone else will like to comment.

 

[bobc2]

I'm still searching for a more detailed account of Godel's ideas about time. At this point I get the impression that both he and Einstein had the notion of time simultaneously flowing in every local neighborhood of the 4-dimensional universe. Godel made a statement to the effect that if you are to relativize time you must destroy previous notions of time. (I'll try to find the exact quote)

I've made a serious blunder in attempting to recall the Godel quote. It was actually, "The concept of existence...cannot be relativized without destroying its meaning completely."

I found this quote in an article titled, "Being and Becoming in Modern Physics" - Stanford Encyclopedia of Philosophy

The article addresses the questions, "Does time flow or lapse or pass? Are the future or the past as real as the present? An introductory statement asserts that, "...These metaphysical questions have been debated for more than two millenia, with no resolution in sight," and "Does the special theory of relativity, for example, show that there is no passage or that the future is as real as the present?"

So, Maui, how are we doing? Do you think we have a shot at settling these issues? Thanks for the expression of your ideas. The dialog has been informative for me.

 

[bobc2]

"Works well for most mundane calculations"

that do not include high speed, high gravity, any kind of high precision or any idea of what truly is happening out there. Basically, in the philosopher's viewpoint, it's worthless.

Going back over some of your earlier posts I noticed this one and felt it required a response, because on this point you are certainly factually incorrect. Countless calculations have been made for processes involving relativistic speeds and also for processes that must take Einstein's general relativity theory into account. Muons would never make it to the Earth from the high atmosphere cosmic ray collisions (for which precise calculations have been performed using special relativity theory), and GPS devices commonly used require very precise position calculations that include general relativity theory corrections.

 

[bobc2]

Meh. Works well for most calculations.

FlexGunship, I just wanted to second your comment and emphasize that it holds up for very precise calculations at relativistic speeds as well as for applications that must take into account general relativity theory. I spent a lot of time in grad school working through the problem of calculating the precession of the orbit of the planet Mercury using general theory (just one second of an arc per century). You are right--works well for most calculations. Thanks.

 

[ThomasT]

ThomasT, I read the paper over the weekend. Very very interesting and informative. I'll try to get back to relate some of the ideas presented. Thanks again.

Ok, glad you enjoyed it.

 

[Maui]

Going back over some of your earlier posts I noticed this one and felt it required a response, because on this point you are certainly factually incorrect. Countless calculations have been made for processes involving relativistic speeds and also for processes that must take Einstein's general relativity theory into account.

You misunderstood. My reply -

"Demanding that there be solid objects with properties in absolute space is a recipe for disaster as far as physics is concerned."

was directly targeted against the outdated Newtonian notion of objects with fixed properties existing in absolute spacetime. Because neither spacetime is absolute, nor do solid 'objects' exist in time(they occur in all interpretations, whether by collapse or apparent collapse). The quoted statement above takes into account both SR, GR and QM so you are essentially repeating what i said.


See if rephrasing my statement makes it more clear:

Works well for most mundane calculations"

that do not include high speed, high gravity, any kind of high precision or any idea of what truly is happening out there. Basically, in the philosopher's viewpoint, it's(the Newtonian worldview) worthless.

 

[bobc2]

You misunderstood. My reply - was directly targeted against the outdated Newtonian notion of objects with fixed properties existing in absolute spacetime. Because neither spacetime is absolute, nor do solid 'objects' exist in time(they occur in all interpretations, whether by collapse or apparent collapse). The quoted statement above takes into account both SR, GR and QM so you are essentially repeating what i said.

Thanks for giving us more clarity on your position. Keep in mind your notions do not represent the thought of all philosophers, neither past nor present. Putnam, for example, argues forcefully for external 4-dimensional objects.

So, it would appear that you would side with my philosophy professor's view that the class room next door does not exist until he goes out into the hallway and opens the door into the neighboring class room. Am I correct in drawing that conclusion?

So then, how do you escape from solipsism? Do you accept Berkely's view, Leibnitz, Whitehead, ..., or with whom of the idealist philosophers would you identify yourself? Or, do you bring a new philosophy?

When you include the "collapse" term, I assume you are referring to the quantum mechanics wave function collapse. In my view it is difficult to identify the wave function as having existence, although Penrose definitely assigns more reality to the wave function than the eigenstate resulting from the wave function collapse. On Penrose's side of the argument you can at least acknowledge that there is no uncertainty in the wave function itself.

By the way, on a personal note, I really don't claim to understand past, present, future, time, or existence, ... or reality generally, whether from the standpoint of ontology or epistemology. For me these issues are shrouded in mystery, perhaps more mystery than humankind will ever be able to unravel. But, it is still interesting to me to pose a model and investigate the implications of such a model.

 

[Maui]

So then, how do you escape from solipsism? Do you accept Berkely's view, Leibnitz, Whitehead, ..., or with whom of the idealist philosophers would you identify yourself? Or, do you bring a new philosophy?

Solipsism doesn't claim that reality doesn't exist, it only says that that reality exists in a different way than anticipated. Since it will continue to exist, a better knowledge about it can only further help us better understand the situation. So even if solipsism is true, this doesn't change much the way i feel about reality. I don't think i can identify with any of the philosophers you listed, it's very dubious if any human being understands reality at this point(the most knowledgeable people on this site all seem to entertain some exotic worldview, but it's apparanetly so wild that most don't bother to share it; it may even be against the forum rules to do so in an informal manner).

When you include the "collapse" term, I assume you are referring to the quantum mechanics wave function collapse. In my view it is difficult to identify the wave function as having existence, although Penrose definitely assigns more reality to the wave function than the eigenstate resulting from the wave function collapse. On Penrose's side of the argument you can at least acknowledge that there is no uncertainty in the wave function itself.

I don't claim to know if wavefunctions have objective existence, that's not the point i was making in this thread. Even if they do, it's still much weirder than what common people in the street would expect about the world. But there seems to be some relationship(this seems to hold in most cases for the greatest physicists too) between how much time you dedicate to contemplating these issues and the idea that the way we experience space, time and matter must be, in some way, interrelated with mind.

By the way, on a personal note, I really don't claim to understand past, present, future, time, or existence, ... or reality generally, whether from the standpoint of ontology or epistemology. For me these issues are shrouded in mystery, perhaps more mystery than humankind will ever be able to unravel. But, it is still interesting to me to pose a model and investigate the implications of such a model.

No knowledge is always better than false knowledge.

 

[PhysDrew]

Wow this thread has opened my eyes to my own ignorance. I only knew Godel for his work on his incompleteness theorems. This is good news to me, I've got another topic to read through, thanks!

 

[Max™]

I would have to point out that if YOU are a solipsist, then it matters greatly to the way which I observe the world in relation to you, as I am reduced to little more than an artifact of your sensorium.

As for the philosophical implications of special relativity, they are simple: you and I are not in the same "now", we can at best locate ourselves in roughly adjacent slices of the universe, and say they are close enough to agree on simultaneity for our purposes.

If we are moving rapidly, this becomes ever more obvious, as bobc2 pointed out, and the slice of events which rocket A calls "now" differs dramatically from the slice which rocket B calls "now", as illustrated by this gif:
[URL]http://loveisscience.files.wordpress.com/2010/01/relativity_of_simultaneity_animation.gif[/URL]

If you want to speak of a broadly universal definition of reality, you need to step completely outside of the observer/spacetime sort of construct into something more like a configuration space, which an author I'm fond of put rather eloquently:

“Imagine there is no time. Imagine there is no space…” In the still cold of Callisto, as she described extraordinary ideas, Luru’s voice was a dry rustle.

“Take a snapshot of the universe. You have a static shape, a cloud of particles each frozen in flight at some point in space.” A snapping of fingers. “Do it again. There. There. There. Each moment, each juggling of the particles, gives you a new configuration.

“Imagine all those snapshots, all the possible configurations the particles of the universe can take. In anyone configuration you could list the particles’ positions. The set of numbers you derive would correspond to a single point on a mighty multidimensional graph. The totality of that graph would be a map of all the possible states our universe could take up. Do you see? And that map is configuration space.”

“Like a phase space map.”



“Like a phase space, yes. But of the whole universe. Now imagine putting a grain of dust on each point of the map. Each grain would correspond to a single point in time, a snapshot. This is reality dust, a dust of the Nows. Reality dust contains all the arrangements of matter there could ever be…”

Slowly, as Luru explained and Nilis tried to clarify, Pirius began to understand.

Configuration space was not Pirius’s world, not his universe. It was a map, yes, a sort of timeless map of his own world and all its possibilities, a higher realm. And yet, according to Luru Parz, it was a universe in itself, a place you could go, in a sense. And it was filled with reality dust. Every grain of sand there represented an instant in his own universe, a way for the particles of his universe, atoms and people and stars, to line themselves up.

But this was a static picture. What about time? What about causality?

If you lined up reality dust grains in a row you would get a history, of a sort, Luru Parz said. But it might not make sense as a history; nothing like causality might emerge, just a jumble of disconnected snapshots one after another. But the sand grains attracted each other. If they came from neighboring points in the greater configuration space, the graph of all possible instants, the moments they mapped must resemble each other. And so the grains lined up in chains, each line of grains representing a series of instants which, if you watched them one after another, would give you the illusion of movement, the illusion of time passing — perhaps, if the grains were similar enough, even the illusion of causality.

This is a 2+1D block universe:
[PLAIN]http://www.ipod.org.uk/reality/reality_block_time2.jpg

As opposed to a presentist version where the portions beyond the 2D space aren't "real":
[PLAIN]http://www.ipod.org.uk/reality/reality_block_time1.jpg

(from: http://www.ipod.org.uk/reality/reality_block_universe.asp )

Naturally it is absurd to claim that the universe stops existing when you aren't looking at it, who made you the king of observing things? No, our awareness simply orders information in a manner which was useful in an evolutionary sense, being able to perceive time as a whole wouldn't help us pass on our genes, so we don't have that capacity. We can fake it though.


As for Godel, he worked out that if you construct a universe in such a manner that it is rotating, you can follow timelike paths which loop back on themselves, allowing time travel without any particularly stringent requirements like FTL, wormholes, or whatnot.

http://en.wikipedia.org/wiki/Gödel_metric

 

[Chestermiller]

I have an alternate interpretation of an object's or particle's continuity into the time direction that may help to resolve some of the controversy.

I envision an army of clones marching through a field in rank and file formation. Each row of clones is older than the row behind it, and the rows are equally spaced. It is night time, and the field is pitch black. But there is a strobe light that flashes on each time a row of clones moves into the position previously occupied by the row in front of them. The differences in age between adjacent rows of clones is exactly equal to the time between flashes. Therefore, when the strobe light flashes, there is no apparent change in the picture one sees.

The field is analogous to “absolute” hyperspace, and the clones are analogous to objects at rest in a single frame of reference. All the clones in a given column of the formation (i.e., file) actually represent the existence of a single object in the reference frame at various proper times during the object’s existence (i.e., travel into the time direction).

This description is the discrete representation of the continuous existence of an object moving through hyperspace. Only if we adopt such a model is it possible in a typical 1D motion problem (e.g., usual train example) for each and every object in one reference frame to encounter each and every object in a different reference frame during their interactions. Otherwise objects from two different frames can only encounter each other in discrete pairs.

 

[bobc2]

I have an alternate interpretation of an object's or particle's continuity into the time direction that may help to resolve some of the controversy.

I envision an army of clones marching through a field in rank and file formation. Each row of clones is older than the row behind it, and the rows are equally spaced. It is night time, and the field is pitch black. But there is a strobe light that flashes on each time a row of clones moves into the position previously occupied by the row in front of them. The differences in age between adjacent rows of clones is exactly equal to the time between flashes. Therefore, when the strobe light flashes, there is no apparent change in the picture one sees.

The field is analogous to “absolute” hyperspace, and the clones are analogous to objects at rest in a single frame of reference. All the clones in a given column of the formation (i.e., file) actually represent the existence of a single object in the reference frame at various proper times during the object’s existence (i.e., travel into the time direction).

This description is the discrete representation of the continuous existence of an object moving through hyperspace. Only if we adopt such a model is it possible in a typical 1D motion problem (e.g., usual train example) for each and every object in one reference frame to encounter each and every object in a different reference frame during their interactions. Otherwise objects from two different frames can only encounter each other in discrete pairs.

Chester, You might try out this idea on the physicists in the physics forum as well as the philosophers here.

 

[bobc2]

I would have to point out that if YOU are a solipsist, then it matters greatly to the way which I observe the world in relation to you, as I am reduced to little more than an artifact of your sensorium.

As for the philosophical implications of special relativity, they are simple: you and I are not in the same "now", we can at best locate ourselves in roughly adjacent slices of the universe, and say they are close enough to agree on simultaneity for our purposes.

If we are moving rapidly, this becomes ever more obvious, as bobc2 pointed out, and the slice of events which rocket A calls "now" differs dramatically from the slice which rocket B calls "now", as illustrated by this gif:
[URL]http://loveisscience.files.wordpress.com/2010/01/relativity_of_simultaneity_animation.gif[/URL]

If you want to speak of a broadly universal definition of reality, you need to step completely outside of the observer/spacetime sort of construct into something more like a configuration space, which an author I'm fond of put rather eloquently:




This is a 2+1D block universe:
[PLAIN]http://www.ipod.org.uk/reality/reality_block_time2.jpg

As opposed to a presentist version where the portions beyond the 2D space aren't "real":
[PLAIN]http://www.ipod.org.uk/reality/reality_block_time1.jpg

(from: http://www.ipod.org.uk/reality/reality_block_universe.asp )

Naturally it is absurd to claim that the universe stops existing when you aren't looking at it, who made you the king of observing things? No, our awareness simply orders information in a manner which was useful in an evolutionary sense, being able to perceive time as a whole wouldn't help us pass on our genes, so we don't have that capacity. We can fake it though.


As for Godel, he worked out that if you construct a universe in such a manner that it is rotating, you can follow timelike paths which loop back on themselves, allowing time travel without any particularly stringent requirements like FTL, wormholes, or whatnot.

http://en.wikipedia.org/wiki/Gödel_metric

Nice post, Max.