Block Time vs Q. Indeterminacy

[nitsuj]

Why not?

Simply because I can't picture it.

I could from the point of veiw of there being only 2 spatial dimensions and one time. Said differently that the sum of individual "Now Slices" make up 3D (and only because time "plays out" / distance).

Now that I can picture the Spacetime diagram from 1 space dimension through to the 3 there are, I cannot see how the block universe [STRIKE]"plays out" in time[/STRIKE] has three spatial dimensions.

The "present" moment surrounds me as a sphere. There is no "this direction future" that "direction past". Perhaps from a conscious perspective it could be thought of as future is out there (outside what ever one would define as the present moment sphere) and the past is merely the memory. Ah, the future "comes in" / "falls onto" the observer from all directions, there's no "room" for the past lol.

I may be wrong with my understanding of block universe, among a number of other things :)

EDIT: I guess I'm not buying the block universe concept moslty because of the spatial dimensions. I don't see three spatial ones in the block universe. I am going to read some more about it to try and see how it is 3 spatial dimensions and a time one, but I don't think it's there. Just can't see how.

 

[PeterDonis]

Simply because I can't picture it.

Obviously you can't picture a 4-dimensional thing with a mind that's only able to visualize 3 dimensions. What does that have to do with the physics?

EDIT: I guess I'm not buying the block universe concept moslty because of the spatial dimensions. I don't see three spatial ones in the block universe. I am going to read some more about it to try and see how it is 3 spatial dimensions and a time one, but I don't think it's there. Just can't see how.

One of the reasons we invented mathematics was to be able to reason in areas where we can't trust our intuitive capacities, such as "visualizing" things. Mathematically, 4-D spacetime is just 3-D spacetime (2 spatial plus 1 time), which you have said is perfectly OK, with one more spatial dimension added. Adding the one more spatial dimension creates no problems at all, mathematically; the model is still perfectly consistent and the tools for dealing with it still work perfectly well.

To make things as simple as possible, try starting with plain flat Minkowski spacetime, the full 4-D ("3+1") version. The metric is:

d\tau^{2} = dt^{2} - dx^{2} - dy^{2} - dz^{2}

The corresponding "2+1" version is:

d\tau^{2} = dt^{2} - dx^{2} - dy^{2}

What's the problem with adding the - dz^{2}?

 

[nitsuj]

Obviously you can't picture a 4-dimensional thing with a mind that's only able to visualize 3 dimensions. What does that have to do with the physics?

Nice tone peter. In that sense, what does physics have to do with reality then?

When you say we can't visualize a 4 dimensional thing 'cause we're only able to visualize 3 dimensions, leads to the point of confusion over time as a dimension. I don't think a dimension (specifically time) is necessarily spacial. So with that being said...

I can easily visualize the 3 spatial dimensions and another for the interval between me and whatever else I see. Or that whatever I see, it will always be cause first, then effect no matter how fast I move to try and exceed my present moment.


My comments are regarding intupreting the block universe visualy as being a 4D spacetime continuum. I can't see it. I dislike the concept more then before. But I still want to read more about it. But not from PF threads, too heated/biased.

 

[PeterDonis]

My comments are regarding intupreting the block universe visualy as being a 4D spacetime continuum. I can't.

Yes, I can't visualize all four dimensions at once either. If that's all you are saying then I'm confused about why you said the block universe concept "doesn't pass the smell test", since that implies that you think it's not valid physics, not just that you can't visualize it.

I can easily visualize the 3 spatial dimensions and an other for the interval between me and whatever else I see.

If by "interval between me and whatever else I see" you mean "interval between the 3 dimensional slice I call 'now' and some other 3 dimensional slice from which the light I am seeing 'now' was emitted", then I don't think this is any different from the 4-D "block universe", except insofar as some people who talk about the "block universe" talk about it as though any concept of 4-D spacetime required complete determinism, which it doesn't.

 

[nitsuj]

Yes, I can't visualize all four dimensions at once either. If that's all you are saying then I'm confused about why you said the block universe concept "doesn't pass the smell test", since that implies that you think it's not valid physics, not just that you can't visualize it.



If by "interval between me and whatever else I see" you mean "interval between the 3 dimensional slice I call 'now' and some other 3 dimensional slice from which the light I am seeing 'now' was emitted", then I don't think this is any different from the 4-D "block universe", except insofar as some people who talk about the "block universe" talk about it as though any concept of 4-D spacetime required complete determinism, which it doesn't.

Oh I see now, my comment about it not passing the smell test is far from an interpretation of the block universe from the perspective of a seasoned physicist. Is it valid physics? In this sense I haven't the slightest clue how to determine what is valid physics and what isn't.

Seems too strange to be able to say litteraly, the start of the universe is on one side of me, the future of it, on the other side of me. Any hoo, ima read more about block universe, since I don't doubt your belief in the block universe.

 

[stglyde]

Nice tone peter. In that sense, what does physics have to do with reality then?

When you say we can't visualize a 4 dimensional thing 'cause we're only able to visualize 3 dimensions, leads to the point of confusion over time as a dimension. I don't think a dimension (specifically time) is necessarily spacial. So with that being said...

I can easily visualize the 3 spatial dimensions and another for the interval between me and whatever else I see. Or that whatever I see, it will always be cause first, then effect no matter how fast I move to try and exceed my present moment.


My comments are regarding intupreting the block universe visualy as being a 4D spacetime continuum. I can't see it. I dislike the concept more then before. But I still want to read more about it. But not from PF threads, too heated/biased.

Just imagine 4 dimensional space and time as absolute. Only time and space are relative. If you are stationary in space, all energy is allocated for time so your time moves fast. If you now move in space, some of the energy for time is allocated for space so time slows down. Now block time is simply cutting the absolute 4D spacetime in different angles. This is one good quick way to visualize spacetime.

 

[nitsuj]

Just imagine 4 dimensional space and time as absolute. Only time and space are relative. If you are stationary in space, all energy is allocated for time so your time moves fast. If you now move in space, some of the energy for time is allocated for space so time slows down. Now block time is simply cutting the absolute 4D spacetime in different angles. This is one good quick way to visualize spacetime.

Is that all that's meant by block universe? I completely agree with that description. Seems to be the way it is. (leaving out things like "energy is allocated for time..." idk what that means, but am aware of the term 4 velocity, and leaving out 4D space, i think it's only 3D and spacetime 4D)

I thought block universe also implied that the future and past are equally as "real" as the present. And from there things like traveling to the past come up, and that's why I [had] disliked the concept.

When I pictured a light cone as a sphere, it really made it clear only the future is out "there" lol, so that's why i said block universe doesn't pass the smell test.

Out of future, past, present & time, the past seems to be the only thing that's an "illusion". I guess for me that's what really muddied the water trying to understand what time is. There's future and present / cause and effect, but no "past". (the past spacetime is still there of course)

Oh lol, that's why it's called a continuum right? cause-effect-cause-effect...

 

[PeterDonis]

I thought block universe also implied that the future and past are equally as "real" as the present. And from there things like traveling to the past come up, and that's why I [had] disliked the concept.

That's what I was trying to clarify, what you thought didn't pass the "smell test".

I think of it this way: a "block universe" is a mathematical model that describes a *possible* 4-D spacetime. But to correlate this model with the real world, we have to divide it, conceptually, into three portions.

(1) A portion of this 4-D spacetime is already known to correspond with the real world; that's the part we call the "past". This is the portion that's in the past light cone of the point in the model that corresponds to where we are here and now. This portion of the model cannot change, in the sense that it specifies a single set of conditions that must be fulfilled by *any* possible 4-D model of the complete spacetime. But what's in our past light cone is not sufficient to pick out a single unique 4-D model for the entire spacetime, so we have to consider a number of "possible" models.

(2) Another portion of this 4-D spacetime is the part that we can affect, causally, from here and now. This is the part we call the "future", and decisions we make here and now can "change" it, so we think of it as not being fixed. But in order to "change" it, we have to change the conditions here and now, and that means the model changes; we have to re-compute what the future will be from the changed conditions, and that gives us a *different* 4-D spacetime, which is now our "best estimate" of what block universe is the "real" one (out of all the "possible" ones that are consistent with our knowledge up to now).

(3) The third portion of this 4-D spacetime is not known by us, here and now, to correspond with the actual world, because it's outside of our past light cone; but we also can't affect it causally, because it's outside of our future light cone. The only thing we can do is to compute, based on what we know of our past light cone, what this portion "should" look like; but at any time, we might have new information come to us, as more of this region comes within our past light cone, that forces us to re-compute. And again, every time we re-compute, that yields a *new* 4-D spacetime that becomes our new best estimate of what block universe is the real one.

So each block universe, considered as a single 4-D model of a possible spacetime, is fixed; but we don't know exactly which possible 4-D model corresponds to reality; the best we can do is to estimate it based on the information we have and the decisions we make. A portion of each model we compute is fixed--the part that corresponds to our past light cone. But the rest of it can vary based on our decisions and on information coming in from regions that were spacelike separated from us until just now.

 

[bobc2]

As I asked earlier:

I wish. I would really like to see a 4-dimensional spatial universe dispelled. Then, we would be left with just deep mystery--something I could handle. It would be more comfortable to have just the mystery as compared to the spectre of implications that come along with the 4-dimensional space-space and still have mystery lingering.

No, I can't yet shake the 4-D space-space. But, PeterDonis did a credible job of flagging my blunder of identifying the Affine Space as a metric space.

Now, I just need PeterDonis to build the mathematical machinery properly, beginning with a R4 manifold and positive definite metric that allows me to freely choose coordinates (without resorting to Minkowski's imaginary ict). We then establish a 4-D orthonomal vector space consistent with defining Pythagorean Theorem distances in the coordinate system.

I would then try to visualize a simple example universe having two straight line 4-D objects that each begin at the orgin of the orthonormal coordinate system, tracing out world lines angled symmetrically about the 4th dimension of the orthonormal vector space. One object is rotated counter-clockwise 22.5 degrees, and the other object is rotated clockwise by 22.5degrees. PeterDonis would have to give us the field theory that allows a correct mathematical accounting of the 4-D objects.

At this point we are saying nothing about time and nothing about observers. There are no affine X1 coordinates established--and no charts--unless PeterDonis insists that we cannot have two 4-D objects in our universe without a chart. In that case we would have to let the two objects define the chart.

Now, I would want to choose another set of orthonormal coordinates, X1' and X4', rotated counter-clockwise by 22.5 degrees relative to the original orthonormal coordinates (X4' is rotated 22.5 degrees counter-clockwise to X4, and X1' is rotated 22.5 degrees counter-clockwise to X1).

We now pick a point on the clockwise rotated 4-D object and note that the distance from the orgin to the point is invariant--it can be determined equally well with either X1 and X4 or X1' and X4'.

If PeterDonis O.K.'s things so far, we can continue the pursuit of the affine space mapped onto the orthonormal cartesian space. (we still don't have any observers in our universe)

 

[PeterDonis]

Now, I just need PeterDonis to build the mathematical machinery properly, beginning with a R4 manifold and positive definite metric

Why do you keep insisting on a positive definite metric? The whole point of Minkowski spacetime is that the metric is *not* positive definite. That's what you need to describe a *spacetime* as opposed to a *space*.

 

[nitsuj]

With bob2c's last post I noticed another difference between block universe and the way I interpret spacetime diagrams. I think space is only 3 spatial dimensions which all share the quality of the same limited speed.

 

[stglyde]

With bob2c's last post I noticed another difference between block universe and the way I interpret spacetime diagrams. I think space is only 3 spatial dimensions which all share the quality of the same limited speed.

Don't ever forget that spacetime doesn't really exist like a particle or field do. When asked by reporters to summarize his theory, Einstein said: "People before me believed that if all the matter in the universe were removed, only space and time would exist. My theory proves that
space and time would disappear along with matter."

So it's just matter relationship with one another that we artifically called spacetime and model it as a 4th dimensional differential manifold which is not really there.

 

[bobc2]

Why do you keep insisting on a positive definite metric? The whole point of Minkowski spacetime is that the metric is *not* positive definite. That's what you need to describe a *spacetime* as opposed to a *space*.

It seems necessary for a 4-dimensional space-space (not space-time). Time should be nothing more than a parameter, playing exactly the same role as passage of time in the 3-D world. It seems elemental, given the different special relativity 3-D cross-sections that four spatial dimensions must be available for those views.

The Minkowski ict takes away the spatial equivalence of the 4th dimension in special relativity.

 

[nitsuj]

Don't ever forget that spacetime doesn't really exist like a particle or field do. When asked by reporters to summarize his theory, Einstein said: "People before me believed that if all the matter in the universe were removed, only space and time would exist. My theory proves that
space and time would disappear along with matter."

So it's just matter relationship with one another that we artifically called spacetime and model it as a 4th dimensional differential manifold which is not really there.

I never learned that spacetime doesn't exist?

It does exist, so I'm not sure in what sense you mean.

Who cares what Einstein told a reporter. (it seems like his point is regarding the role of calculating in defining, without objects to measure you can't determine spacetime's properties, from a physics perspective it's as if it doesn't exist. You need two to tango in other words ). I read that his theory implies spacetime is real and exists. It's properties effect everything.

 

[stglyde]

I never learned that spacetime doesn't exist?

It does exist, so I'm not sure in what sense you mean.

Who cares what Einstein told a reporter. I read that his theory implies spacetime is real and exists. It's properties effect everything.

Have you forgotten the thread "Spacetime doesn't really exist does it?"
https://www.physicsforums.com/showthread.php?t=487794&highlight=spacetime+doesn't+exist where you also participated? Someone there said:

"GR doesn't really describe gravity in terms of a field. GR deals with tensors, and the gravitational field is not a tensor. GR describes a gravitational wave as an oscillating curvature of spacetime."

Look spacetime is in same company as wavefunction, they are just mathematical abstraction.

Spacetime is just a 4 dimensional differential manifold.. curvature and other geometrical aspects are what producing "gravity". This means things like gravitational field as just PUN some love to say.

Now about Matter. Wave function is just a mathematical abstraction. It is all math. Large scale "things" are just results of decoherence of the mathematical wave functions.

Also Particles are just energy and momentum of the fields... or as Rovelli suggested.. "QFT should not be interpreted in terms of particle states, but rather in terms of eigenstates of local
operators."

Even virtual particles are just multi variate integrals, just purely mathematical artifacts as Neumaier emphasized.

btw... "don't exist" means no spacetime substrate.. for example... no "aether" substrate or "pilot wave" substrate... spacetime "aether" concept has problems with event horizons and pilot wave has problems with lorentz symmetry.. but if they can solve it.. then aether and pilot wave can be the substrate and make spacetime/matter "exist" in the sense there is a "material substrate".. but for now.. they are less likely...

In short, if you believe spacetime exist. Then you believe in spacetime aether? But it doesn't tally with the observations in event horizons in black holes.. so it's not likely.

 

[PeterDonis]

It seems necessary for a 4-dimensional space-space (not space-time).

I think you're missing the point. The 4-dimensional manifold we live in is a space-time, *not* a space-space. It has one timelike dimension and three spacelike dimensions. It has a metric that is not positive definite. These statements are invariant statements of physics; they do not depend on describing the timelike dimension using a "time" parameter. (For example, we can describe spacetime using null coordinates, which replace the timelike coordinate and one spacelike coordinate with a pair of null coordinates. But physically spacetime is still the same, just described differently.) So the 4-D manifold we live in is different, *physically*, than a 4-D space-space with a 4-D positive definite metric. You can't model the former with the latter.

Time should be nothing more than a parameter, playing exactly the same role as passage of time in the 3-D world.

I'm not sure I understand what you mean by this.

It seems elemental, given the different special relativity 3-D cross-sections that four spatial dimensions must be available for those views.

No, this is wrong. What the different SR cross-sections show us is that four *spacetime* dimensions must be available--three spacelike and one timelike (or, alternatively, as I said above, two spacelike and two null, which is physically the same thing). The different SR cross sections are *inconsistent* with there being four *spatial* dimensions, because the SR cross sections require a Minkowski metric, i.e., not positive definite. This is a genuine physical difference; you can't handwave it away.

 

[PeterDonis]

Have you forgotten the thread "Spacetime doesn't really exist does it?"
https://www.physicsforums.com/showthread.php?t=487794&highlight=spacetime+doesn't+exist where you also participated? Someone there said:

"GR doesn't really describe gravity in terms of a field. GR deals with tensors, and the gravitational field is not a tensor. GR describes a gravitational wave as an oscillating curvature of spacetime."

You should be careful interpreting this statement. If I'm wrong, bcrowell can jump in here and correct me, but I strongly suspect that by "gravitational field" in that statement he meant something like the "acceleration due to gravity", which is not a tensor. However, the "curvature of spacetime" *is* a tensor, the Riemann curvature tensor, and it's oscillations in that tensor that describe gravitational waves. I seriously doubt that bcrowell meant to imply that gravity, in the sense of spacetime curvature, and spacetime itself were not "real".

In short, if you believe spacetime exist. Then you believe in spacetime aether?

This is a non sequitur. Believing that spacetime "exists" does not require believing that there is some non-dynamical "background" portion of spacetime that does not interact with matter.

 

[stglyde]

You should be careful interpreting this statement. If I'm wrong, bcrowell can jump in here and correct me, but I strongly suspect that by "gravitational field" in that statement he meant something like the "acceleration due to gravity", which is not a tensor. However, the "curvature of spacetime" *is* a tensor, the Riemann curvature tensor, and it's oscillations in that tensor that describe gravitational waves. I seriously doubt that bcrowell meant to imply that gravity, in the sense of spacetime curvature, and spacetime itself were not "real".



This is a non sequitur. Believing that spacetime "exists" does not require believing that there is some non-dynamical "background" portion of spacetime that does not interact with matter.

but spacetime aether is dynamical.. see:
http://arxiv.org/PS_cache/arxiv/pdf/0801/0801.1547v2.pdf

My understanding is that if spacetime exist.. it should be a "thing".. but if it doesn't.. meaning it is just mathematical abstraction like wave function.. then it isn't a thing.. unless you meant spacetime is like a particle that has independent existence? but if spacetime points are real... then diffeomorphism invariance (general covariance) is wrong.. so how can spacetime be anything other than mathematical abstraction?

 

[PeterDonis]

but spacetime aether is dynamical.. see:
http://arxiv.org/PS_cache/arxiv/pdf/0801/0801.1547v2.pdf

Ah, ok, that clarifies what you meant by "ether" (the term has a lot of meanings). Then my response is, believing that spacetime exists does not require believing that there is a preferred "rest frame" at the quantum gravity level.

if spacetime points are real... then diffeomorphism invariance (general covariance) is wrong..

I don't see how this follows. General covariance just means that we can describe the spacetime manifold using any coordinate chart we like; in other words, that the physics of spacetime is independent of how we label the points in the spacetime with coordinates. It says nothing at all about whether the manifold itself, or the points in it, are "real". The latter question depends on what you mean by "real", but since we can measure the curvature of the spacetime manifold (as tidal gravity), it seems unproblematic to me to say that the manifold is real.

 

[bobc2]

...This is a non sequitur. Believing that spacetime "exists" does not require believing that there is some non-dynamical "background" portion of spacetime that does not interact with matter.

The post evoking this response was not mine. I'm not sure how it came out as my post.

 

[stglyde]

Ah, ok, that clarifies what you meant by "ether" (the term has a lot of meanings). Then my response is, believing that spacetime exists does not require believing that there is a preferred "rest frame" at the quantum gravity level.



I don't see how this follows. General covariance just means that we can describe the spacetime manifold using any coordinate chart we like; in other words, that the physics of spacetime is independent of how we label the points in the spacetime with coordinates. It says nothing at all about whether the manifold itself, or the points in it, are "real". The latter question depends on what you mean by "real", but since we can measure the curvature of the spacetime manifold (as tidal gravity), it seems unproblematic to me to say that the manifold is real.

Are you familiar with the Hole Argument?

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

"Einstein believed that the hole argument implies that the only meaningful definition of location and time is through matter. A point in spacetime is meaningless in itself, because the label which one gives to such a point is undetermined. Spacetime points only acquire their physical significance because matter is moving through them."

In other words. Spacetime points shouldn't be made of substance or General Invariance won't work. Now if Spacetime points are not substantive but just merely mathematical abstraction, then it may not have any independent existence. Without any matter/energy/stress.. do you think there would be spacetime?

 

[PeterDonis]

Are you familiar with the Hole Argument?

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

Did you read this in the introduction to that same Wikipedia article:

It [the hole argument] is incorrectly interpreted by some philosophers as an argument against manifold substantialism, a doctrine that the manifold of events in spacetime are a "substance" which exists independently of the matter within it. Physicists disagree with this interpretation, and view the argument as a confusion about gauge invariance and gauge fixing instead.

In other words, the hole argument does not show that general covariance is inconsistent with spacetime being a "real thing". All it shows is that GR is a gauge theory.

Without any matter/energy/stress.. do you think there would be spacetime?

Minkowski spacetime, with zero stress-energy tensor everywhere, is a solution of the Einstein Field Equation, so yes, there is at least one possible "spacetime" without any matter/energy/stress. Einstein, when he made that statement to reporters that you quoted, either didn't think of that or conveniently ignored it because he didn't want to try to go into subtleties in that context (for which I can't blame him).

In other writings, IIRC, Einstein argued that Minkowski spacetime was not a counterexample to claims of the sort he made in your quote, because it required asymptotic flatness as a boundary condition, which was an extra physical assumption over and above the EFE, since the EFE doesn't explain how the boundary condition "at infinity" comes into being. In essence, he argued that the only way to truly satisfy the conditions he described in what you quoted was for the universe as a whole to be closed, so the question of boundary conditions "at infinity" would not arise. Hawking seems to believe something similar with his "no boundary" proposal for quantum cosmology.

Bottom line, I think the question you posed in what I quoted above is a physical question on which the jury is still out. GR, as it stands, is compatible with either alternative, since it has both closed solutions and solutions with boundary conditions at infinity. (More precisely, whichever solution we end up adopting at the quantum gravity level, there will be a GR model that will work as the classical limit of that solution.)

 

[stglyde]

Did you read this in the introduction to that same Wikipedia article:



In other words, the hole argument does not show that general covariance is inconsistent with spacetime being a "real thing". All it shows is that GR is a gauge theory.



Minkowski spacetime, with zero stress-energy tensor everywhere, is a solution of the Einstein Field Equation, so yes, there is at least one possible "spacetime" without any matter/energy/stress. Einstein, when he made that statement to reporters that you quoted, either didn't think of that or conveniently ignored it because he didn't want to try to go into subtleties in that context (for which I can't blame him).

In other writings, IIRC, Einstein argued that Minkowski spacetime was not a counterexample to claims of the sort he made in your quote, because it required asymptotic flatness as a boundary condition, which was an extra physical assumption over and above the EFE, since the EFE doesn't explain how the boundary condition "at infinity" comes into being. In essence, he argued that the only way to truly satisfy the conditions he described in what you quoted was for the universe as a whole to be closed, so the question of boundary conditions "at infinity" would not arise. Hawking seems to believe something similar with his "no boundary" proposal for quantum cosmology.

Bottom line, I think the question you posed in what I quoted above is a physical question on which the jury is still out. GR, as it stands, is compatible with either alternative, since it has both closed solutions and solutions with boundary conditions at infinity. (More precisely, whichever solution we end up adopting at the quantum gravity level, there will be a GR model that will work as the classical limit of that solution.)

To clarify my point. Is the wave function real in the sense that there are really physical (or whatever) waves that interfere before say the double slit electron reach the detector? There isn't. So is Spacetime. Nothing is curving there in space or time. It is just a math model like wave function. Spacetime is not the territory but just a map.. and they say not to mistake map for territory.

We don't know how such complex mathematical abstraction like wave function and spacetime connect to our world and physicists don't care. Physics is just studying the math models with a a huge disconnect in correponding to our reality. Agree?

 

[PeterDonis]

To clarify my point. Is the wave function real in the sense that there are really physical (or whatever) waves that interfere before say the double slit electron reach the detector? There isn't.

That's another physical question on which the jury is still out. There is certainly a large school of thought in quantum physics that believes this, but it is not established the way, say, the Earth going around the Sun is.

So is Spacetime. Nothing is curving there in space or time. It is just a math model like wave function.

Tidal gravity is not "just a math model". It's a physical observable. It is true that one is not *forced* to model tidal gravity using a curved spacetime; one could use another model. But in the context of that model, "spacetime curvature" is simply another name for "tidal gravity", so if tidal gravity is real (which it is), then spacetime curvature is real.

Spacetime is not the territory but just a map.. and they say not to mistake map for territory.

Yes, but that does not mean that nothing named on the map is real. The United States of America is also part of a map; there is nothing in the territory that carries intrisic labels saying "this belongs to the USA". Does that mean the USA is not real?

This kind of discussion can degenerate very quickly into philosophy instead of physics. The map-territory distinction is supposed to forestall such degeneration, not cause it. The map is not the territory, but the reason for having a map is to guide you through the territory. You can't make use of the map that way if you don't think of the things the map is labeling as real.

We don't know how such complex mathematical abstraction like wave function and spacetime connect to our world...

Certainly we do. We use these complex mathematical abstractions to make predictions that are confirmed to many decimal places. That requires a deep knowledge of how they connect to our world.

...and physicists don't care. Physics is just studying the math models with a a huge disconnect in correponding to our reality. Agree?

No. This kind of statement needs a *huge* amount of support which you have not given, and which I don't see how you could give in view of the predictive accuracy of our models which I have just referred to.

 

[stglyde]

That's another physical question on which the jury is still out. There is certainly a large school of thought in quantum physics that believes this, but it is not established the way, say, the Earth going around the Sun is.



Tidal gravity is not "just a math model". It's a physical observable. It is true that one is not *forced* to model tidal gravity using a curved spacetime; one could use another model. But in the context of that model, "spacetime curvature" is simply another name for "tidal gravity", so if tidal gravity is real (which it is), then spacetime curvature is real.



Yes, but that does not mean that nothing named on the map is real. The United States of America is also part of a map; there is nothing in the territory that carries intrisic labels saying "this belongs to the USA". Does that mean the USA is not real?

This kind of discussion can degenerate very quickly into philosophy instead of physics. The map-territory distinction is supposed to forestall such degeneration, not cause it. The map is not the territory, but the reason for having a map is to guide you through the territory. You can't make use of the map that way if you don't think of the things the map is labeling as real.



Certainly we do. We use these complex mathematical abstractions to make predictions that are confirmed to many decimal places. That requires a deep knowledge of how they connect to our world.



No. This kind of statement needs a *huge* amount of support which you have not given, and which I don't see how you could give in view of the predictive accuracy of our models which I have just referred to.

Hmm...

Anyway back to Block Spacetime. Is it a consensus that the past no longer exist or is it only your belief? I just saw Michio Kaku in TV describing how to go back in time.. how come they keep saying this when the past no longer exist? Any idea of how many percentage of physicists share your view, etc.?

 

[PeterDonis]

Is it a consensus that the past no longer exist or is it only your belief? I just saw Michio Kaku in TV describing how to go back in time.. how come they keep saying this when the past no longer exist? Any idea of how many percentage of physicists share your view, etc.?

With regard to what physicists believe, as far as I know, all of this talk about going back in time is speculative (certainly the stuff I usually see Michio Kaku saying when he does TV specials is speculative); no physicist claims that we *can* time travel to our past, and no physicist claims to know for certain that it's impossible. It's just speculation.

 

[stglyde]

With regard to what physicists believe, as far as I know, all of this talk about going back in time is speculative (certainly the stuff I usually see Michio Kaku saying when he does TV specials is speculative); no physicist claims that we *can* time travel to our past, and no physicist claims to know for certain that it's impossible. It's just speculation.

About general invariance.. it is synonymous to diffeomorphism invariance isn't it.. although other physicists use diffeo morph to mean background independence (no prior geometry). Which do you use?

So far have we actually confirmed general invariance (diffeo morph) in experiments? What experiments actually do that?

I'm interested in local lorentz invariance in quantum gravity studies. General Relativity is not compatible with QM so GR may just be lower limit of a more primary theory. What is your favorite primary theory and Why?

 

[bobc2]

I think you're missing the point. The 4-dimensional manifold we live in is a space-time, *not* a space-space. It has one timelike dimension and three spacelike dimensions. It has a metric that is not positive definite.

No. The R4 manifold we live in is space-space and positive definite. I thought you would show us, based on this, the rigorous mathematical procedure for arriving at the coordinate transformations that apply to a special relativity approach to describing our physical experience in the manifold. The physical objects present on the manifold are independent of the manifold and its metric space.

I can lay out a big sheet of paper on the table with a cartesian chart having an X1 horzontal axis and a X2 axis. Then, I arbitrarily place pencils, rulers, sticks, etc. on the paper with random orientations. It would be difficult to find an easy mathematical representation of the object locations, orientations and their relatedness.

On the other hand, I can place objects on the grid in very special thought-out patterns that are ordered in a special way. It may be difficult to describe the positions and orientations of the objects using the cartesian coordinates. However, given the symmetries associated with the object placement, I can perhaps find a special system of coordinates,
X1' and X2', X1'' and X2'', etc., for mathematically expressing the positions and orientations of the objects--along with relatedness among the objects. If the objects are all long, and if they are all generally oriented with their long directions at less than 45 degrees with respect to the cartesian X2 direction, the new X2' and X2'', etc., coordinates would be special as compared to the X1, X1', X1'', etc.

The 4-dimensional positive definite manifold with 4-D objects populating the manifold, lying along 4-D world lines should be viewed the same way.

These statements are invariant statements of physics; they do not depend on describing the timelike dimension using a "time" parameter. (For example, we can describe spacetime using null coordinates, which replace the timelike coordinate and one spacelike coordinate with a pair of null coordinates. But physically spacetime is still the same, just described differently.)

But, they were arbitrarily chosen. And without time as a parameter, along world lines, you are left without a physically understood picture of reality. It's easy to talk about time as the 4th dimension (or some ill-defined mixture of space and time), but in reality no one has the foggiest idea what that means physically. However, a 4-dimensional space with time passing as a parameter as some aspect of the observer moves along the 4th spatial dimension at the speed of light--is a concept that can be envisioned. Without 4 spatial dimensions, you really don't know what you've got for reality--except as an abstract mathematical description.

So, the 4-D manifold we live in is different, *physically*, than a 4-D space-space with a 4-D positive definite metric.

No. I agree that you can model physics with the Minkowski metric. But, that seems arbitrary and contrived. And it gives us a physical picture that is really not comprehensible (on one really knows what it means to have time as a physical dimension). So, in that sense the Minkowski manifold is different from what we live in.

We don't need an R4 manifold other than positive definite with a Euclidean orthonormal basis chart. The coordinate space we live in can be obtained through coordinate transformations.

You can't model the former with the latter.

Why can't you do it with coordinate transformations? We do it with curves on a sheet of paper all of the time. We start with cartesian coordinates and then draw in hyperbolic curves and affine coordinates, etc.

I'm not sure I understand what you mean by this.

We use parametric equations all the time--for example, to describe motion of projectiles in 3-D space, i.e., Y(t) and X(t). Time is just a parameter along the world lines in exactly the same sense.

No, this is wrong. What the different SR cross-sections show us is that four *spacetime* dimensions must be available--three spacelike and one timelike (or, alternatively, as I said above, two spacelike and two null, which is physically the same thing). The different SR cross sections are *inconsistent* with there being four *spatial* dimensions, because the SR cross sections require a Minkowski metric, i.e., not positive definite. This is a genuine physical difference; you can't handwave it away.

Time is not needed at all to describe the 4-dimensional universe populated with 4-dimensional objects. Although, it is useful in computing distances along world lines, since obervers are "moving" along world lines at c. But, from the "birds eye view" you alluded to in an earlier post, you can remove consciousness from the observers (which are, from the "birds" view, after all, just 4-D objects) and the super hyperspace "bird" just sees a static 4-dimensional structure. It would never occur to the "bird" that he would need anything other than an R4 manifold with an orthonormal basis set along with appropriate transformations to describe what he is viewing.

 

[PatrickPowers]

We can describe spacetime using null coordinates, which replace the timelike coordinate and one spacelike coordinate with a pair of null coordinates.

I find this most intriguing. Might you offer a reference?

 

[PeterDonis]

About general invariance.. it is synonymous to diffeomorphism invariance isn't it.. although other physicists use diffeo morph to mean background independence (no prior geometry). Which do you use?

By "general covariance" I mean, as I said in a previous post, that you can describe spacetime using any coordinates you like. Since transformations between different coordinate systems are diffeomorphisms, this definition of general covariance is equivalent to diffeomorphism invariance of physical laws; i.e., valid physical laws must be expressible in a form that is diffeomorphism invariant. GR meets this requirement since it expresses all physical laws in terms of tensors and other geometric objects, which are diffeomorphism invariant.

I don't know for sure whether the above is equivalent to background independence or not. A physics that included "prior geometry" might still be expressible in diffeomorphism invariant terms. For example, suppose I have a theory that says that the "preferred frame" of the universe is the "comoving" frame in the standard FRW model, so that, for example, the motion of the Earth relative to this frame appears in physical laws. I could still write such laws in terms of tensors and other geometric objects; for example, I could express the motion of the Earth relative to the preferred frame as the contraction of the Earth's 4-momentum at a given event with a 4-vector normal to the spacelike hypersurface of constant comoving time t that contains that event. Such a law would be diffeomorphism invariant but would still express the presence of a preferred frame.

So far have we actually confirmed general invariance (diffeo morph) in experiments? What experiments actually do that?

How would you confirm diffeomorphism invariance in particular by doing experiments? The physical laws of GR are certainly confirmed very well, and those are expressible in diffeomorphism invariant terms. Does that count?

I'm interested in local lorentz invariance in quantum gravity studies. General Relativity is not compatible with QM so GR may just be lower limit of a more primary theory. What is your favorite primary theory and Why?

This is kind of getting off topic, but I agree that we are likely to find that GR is the classical, low energy limit of some quantum gravity theory that may look quite different. I don't have a "favorite" here because we have no experimental data in the regime where such a theory would be expected to show itself (particle energies approaching the Planck energy), so there are no constraints on such a theory other than the need to have GR as a low energy classical limit, which isn't a very tight constraint.

 

[PeterDonis]

I find this most intriguing. Might you offer a reference?

Try this page for a start:

http://www.mathpages.com/rr/s1-09/1-09.htm

 

[PeterDonis]

The post evoking this response was not mine. I'm not sure how it came out as my post.

That's weird, I'm not sure either. The editing window was still open on my post so I went back and fixed the quote. Sorry for the mixup.

 

[PeterDonis]

No. The R4 manifold we live in is space-space and positive definite.

What is your basis for this claim? It seems obviously false to me since spacetime is locally Lorentz invariant, not Euclidean invariant, which is what your statement would imply. (Btw, by "basis" I mean "physical basis"--what physical experiments show you that we live in an R4 manifold with a positive definite metric?)

We use parametric equations all the time--for example, to describe motion of projectiles in 3-D space, i.e., Y(t) and X(t). Time is just a parameter along the world lines in exactly the same sense.

*Proper* time, yes. *Coordinate* time, no. In your terms, all four coordinates, including the "time" coordinate, are functions of the "time parameter" along a timelike curve, which I'll refer to as proper time since that's the standard term. More precisely, a parametrization of a timelike worldline in spacetime is a one-to-one mapping of proper time values to 4-tuples of coordinate values.

I did not mean to say that such a mapping was not possible or that it was not useful for understanding coordinate charts. It certainly is. But proper time should not be confused with coordinate time; they are two different things.

But, they were arbitrarily chosen. And without time as a parameter, along world lines, you are left without a physically understood picture of reality.

I agree with this to an extent. Coordinates, in general, are not physical observables; in some cases you can choose coordinate charts that match up well with certain symmetries of a spacetime and therefore can be more or less equated to certain physical observables, but those are special cases. Proper time, however, is an obvious physical observable: it can be directly read off clocks that follow a given worldline.

But proper time is not left out of the coordinate models I was describing; in fact, it's precisely the physical requirement of making sure the correct proper time is assigned to any given segment of a curve that makes the metric so important. And it's precisely the physical fact that not all curves are timelike that requires a non-positive definite metric; along a non-timelike curve, there is no proper time, and parametrizing such a curve cannot be done using a "time" parameter. You have to use a parameter that corresponds to something else, physically, besides proper time.

Why can't you do it with coordinate transformations? We do it with curves on a sheet of paper all of the time. We start with cartesian coordinates and then draw in hyperbolic curves and affine coordinates, etc.

Yes, and we interpret the lengths along the curves, physically, as lengths--*proper* lengths. But lengths are not times; they are physically different things. You can measure time in the same *units* as length, by using the speed of light as a conversion factor, but that does not make proper times the same, physically, as proper lengths. So if we want to use an R4 manifold to model the actual physical spacetime we live in, we cannot put a metric on it that only allows for one type of measure along a curve; there have to be three (timelike, spacelike, and null), and the measures for nearby curves have to be related in a way that preserves Lorentz invariance. A Euclidean, positive definite metric simply cannot model that.

Note, please, that I am not talking now about "time" or "space" as coordinates; I am talking about them as physical measures along curves. The physical measure along a timelike curve is proper time; the curve can be expressed, as I noted above, as a one-to-one mapping between proper time values and 4-tuples of coordinates, and we can label points on the curve by their proper time values and talk about them without ever using coordinates. But the physical measure along a spacelike curve is proper length, *not* proper time; it is a physically different thing. That is why our model needs to treat time and space differently: because the physical measure along timelike curves is fundamentally different than the physical measure along spacelike curves.

We don't need an R4 manifold other than positive definite with a Euclidean orthonormal basis chart. The coordinate space we live in can be obtained through coordinate transformations.

No, it can't, for the reasons given above.

Time is not needed at all to describe the 4-dimensional universe populated with 4-dimensional objects.

As a coordinate, no. As a measure along timelike curves, which is fundamentally different than the measure along spacelike curves, absolutely yes, it is. Otherwise the correspondence between the model and the real world, which you are so concerned about, is not there.

But, from the "birds eye view" you alluded to in an earlier post, you can remove consciousness from the observers (which are, from the "birds" view, after all, just 4-D objects) and the super hyperspace "bird" just sees a static 4-dimensional structure. It would never occur to the "bird" that he would need anything other than an R4 manifold with an orthonormal basis set along with appropriate transformations to describe what he is viewing.

It sure would, as soon as he tries to capture the physical difference between timelike and spacelike curves. That difference does not require conscious observers following the timelike curves.

 

[stglyde]

By "general covariance" I mean, as I said in a previous post, that you can describe spacetime using any coordinates you like. Since transformations between different coordinate systems are diffeomorphisms, this definition of general covariance is equivalent to diffeomorphism invariance of physical laws; i.e., valid physical laws must be expressible in a form that is diffeomorphism invariant. GR meets this requirement since it expresses all physical laws in terms of tensors and other geometric objects, which are diffeomorphism invariant.

I don't know for sure whether the above is equivalent to background independence or not. A physics that included "prior geometry" might still be expressible in diffeomorphism invariant terms. For example, suppose I have a theory that says that the "preferred frame" of the universe is the "comoving" frame in the standard FRW model, so that, for example, the motion of the Earth relative to this frame appears in physical laws. I could still write such laws in terms of tensors and other geometric objects; for example, I could express the motion of the Earth relative to the preferred frame as the contraction of the Earth's 4-momentum at a given event with a 4-vector normal to the spacelike hypersurface of constant comoving time t that contains that event. Such a law would be diffeomorphism invariant but would still express the presence of a preferred frame.

Are you saying "prior geometry" is the same as "preferred frame"? This is getting confusing. Let us define the terms well so we can understand one another. In the Jan 2004 Sci Am cover story "Loop Quantum Gravity". It is defined thus (according to Smolin):

"In particular we kept two key principles of general relativity at the heart of our calculations.

The first is known as background independence. This principle says that the geometry of spacetime is not fixed. Instead the geometry is an evolving, dynamical quantity. To find the geometry, one has to solve certain equations that include all the effects of matter and energy. Incidentally, string theory, as currently formulated, is not background independent; the equations describing the strings are set up in a predetermined classical (that is, nonquantum) spacetime.

The second principle, known by the imposing name of diffeomorphism invariance, is closely related to background independence. This principle implies that, unlike theories prior to general relativity, one is free to choose any set of coordinates to map spacetime and express the equations. A point in spacetime is defined only by what physically happens at it, not by its location according to some special set of coordinates (no coordinates are special). Diffeomorphism Invariance is very powerful and is of fundamental importance in
General Relativity. "

You said diffeomorphism invariant can still be expressed in the presence of a preferred frame. Given Smolin input. You think diffeomorphism invariant can also be expressed in the presence of a background (background dependence or prior geometry)?

 

[PatrickPowers]

Try this page for a start:

http://www.mathpages.com/rr/s1-09/1-09.htm

I notice that this the ninth section of a full-sized book. I have read the first four sections and this seems to be exactly what I've been looking for. It will take a while to work through.

 

[atyy]

Let us define the terms well so we can understand one another. In the Jan 2004 Sci Am cover story "Loop Quantum Gravity". It is defined thus (according to Smolin):

...

The second principle, known by the imposing name of diffeomorphism invariance, is closely related to background independence. This principle implies that, unlike theories prior to general relativity, one is free to choose any set of coordinates to map spacetime and express the equations. A point in spacetime is defined only by what physically happens at it, not by its location according to some special set of coordinates (no coordinates are special). Diffeomorphism Invariance is very powerful and is of fundamental importance in
General Relativity. "

Smolin is wrong on a detail. Theories prior to general relativity can be expressed in diffeomorphism invariant form. As Andrade, Marolf and Deffayet say, "The point here is that any local theory (e.g., a single free scalar field) can be written in diffeomorphism-invariant form through a process known as parametrization."

 

[PeterDonis]

You said diffeomorphism invariant can still be expressed in the presence of a preferred frame.

Not quite. I said that a theory with a preferred frame *might* still be expressible in diffeomorphism invariant form, and I gave an example of how that *might* be possible. Basically, if it turns out that a theory with a preferred frame in it can still be expressed in any coordinates I choose, then it's still diffeomorphism invariant, even though it has a preferred frame.

Given Smolin input. You think diffeomorphism invariant can also be expressed in the presence of a background (background dependence or prior geometry)?

You'll note that Smolin does not say that background independence and diffeomorphism invariance are the same; he only says they're closely related. So it would appear that he would also admit the possibility that there could be a theory that was diffeomorphism invariant but not background independent. This is not to say that anyone actually has such a theory; just that the possibility means we should be careful about making dogmatic statements about what is "required" of a theory.

 

[atyy]

Not quite. I said that a theory with a preferred frame *might* still be expressible in diffeomorphism invariant form, and I gave an example of how that *might* be possible. Basically, if it turns out that a theory with a preferred frame in it can still be expressed in any coordinates I choose, then it's still diffeomorphism invariant, even though it has a preferred frame.
You'll note that Smolin does not say that background independence and diffeomorphism invariance are the same; he only says they're closely related. So it would appear that he would also admit the possibility that there could be a theory that was diffeomorphism invariant but not background independent. This is not to say that anyone actually has such a theory; just that the possibility means we should be careful about making dogmatic statements about what is "required" of a theory.

An explicit example of such a theory is given by Laddha and Varadarajan. Andrade et al refer to Torre who discusses such formulations at length.

Also, Newtonian and Nordstrom gravity both have formulations as geometric theories, even though they are more conventionally formulated non-geometrically.

 

[bobc2]

It sure would, as soon as he tries to capture the physical difference between timelike and spacelike curves. That difference does not require conscious observers following the timelike curves.

As usual you've done a comptetent job of representing the conensus view of special relativity. I understood your points quite well. I was never exposed to anything different throughout my graduate physics curriculum. Usually, whether it was a course in classical field theory, modern physics, special relativity, general relativity, cosmology, etc., we were given the Minkowski metric as a starting point, then went from there.

But I was never satisfied with that, because I don't believe it treats time correctly--and still have not resolved my concerns. My PhD advisor would not discuss the subject--he thought it was a waste of time. And at that stage as a student I knew he was right--that I needed to concentrate on learning physics before challenging established ideas.

At this point on the forum, I'm afraid I've pushed on this to the point of violating the agreed upon rules here. The forum advisors have given me more leeway than was probably justified. Hopefully, others have benefitted from the occasion to consider more carefully the fundamental mathematical machinery upon which special relativity is based (thanks primarily to PeterDonis's contributions).

 

[PeterDonis]

Usually, whether it was a course in classical field theory, modern physics, special relativity, general relativity, cosmology, etc., we were given the Minkowski metric as a starting point, then went from there.

But I was never satisfied with that, because I don't believe it treats time correctly--and still have not resolved my concerns.

This is where I get confused; the only "concerns" you have expressed that I can see are: (1) about time being a parameter, which I've agreed with and shown that relativity includes; and (b) that the metric of spacetime is not positive definite, which I've given a good physical reason for: timelike curves are physically different than spacelike curves (and null curves are different from both). So either I'm misunderstanding the point of these concerns, or there are other concerns that I'm not seeing. I don't think expressing them would violate forum rules.

 

[Passionflower]

I guess I need some clarification, how can you folks talk about a potential preferred frame in our spacetime which is obviously non-stationary.

 

[ghwellsjr]

I guess I need some clarification, how can you folks talk about a potential preferred frame in our spacetime which is obviously non-stationary.

Since Lorentz Ether Theory (LET) is indistinguishable from Special Relativity (SR) save for the claim that there exists a single preferred frame, Einstein designed his concept of spacetime in such a way that every inertial frame satisfies the requirements for a Lorentz ether frame and therefore can be considered a potential preferred frame.

 

[stglyde]

That's another physical question on which the jury is still out. There is certainly a large school of thought in quantum physics that believes this, but it is not established the way, say, the Earth going around the Sun is.



Tidal gravity is not "just a math model". It's a physical observable. It is true that one is not *forced* to model tidal gravity using a curved spacetime; one could use another model. But in the context of that model, "spacetime curvature" is simply another name for "tidal gravity", so if tidal gravity is real (which it is), then spacetime curvature is real.

PeterDonis. Can you please go to the thread below as I'd like to inquire more about this Tidal gravity and wave function thing which can become off topic in this thead. Thanks.

https://www.physicsforums.com/showthread.php?t=554273

 

[PeterDonis]

PeterDonis. Can you please go to the thread below as I'd like to inquire more about this Tidal gravity and wave function thing which can become off topic in this thead. Thanks.

https://www.physicsforums.com/showthread.php?t=554273

Sure, going there now.

 

[stglyde]

bobc2, what do you make of the following:

http://space.mit.edu/home/tegmark/dimensions.pdf

where Max Tegmark states only 3D space and 1D time is stable. Can you find any flaws in the paper? What is your comment on it?

 

[PeterDonis]

Sure, going there now.

Looks like the thread was locked; possibly because you started asking about spacetime again, which would belong back here, or possibly because it was perceived as pursuing your own speculative theory instead of asking about existing theories.

As far as the items you asked that were about modeling tidal gravity some other way than spacetime curvature, there is an alternate model that views gravity as a masless, spin-2 field on a flat background spacetime. I don't know of a good introductory online reference; I learned about it from The Feynman Lectures on Gravitation:

http://books.google.com/books/about/Feynman_lectures_on_gravitation.html?id=jL9reHGIcMgC

This "field on a flat spacetime" model turns out to be equivalent to the standard curved-spacetime model of GR, except for some concerns about whether the starting assumption of a flat background means the model can't deal with, for example, the FRW spacetimes in cosmology. So instead of viewing tidal gravity as a manifestation of spacetime curvature, you could view it as a manifestation of the massless, spin-2 field. But since the models give exactly the same predictions, one could just as well say that "spacetime curvature" and "massless spin-2 field" are different names for the same thing, the whatever-it-is-that-causes-tidal-gravity.

 

[stglyde]

Looks like the thread was locked; possibly because you started asking about spacetime again, which would belong back here, or possibly because it was perceived as pursuing your own speculative theory instead of asking about existing theories.

As far as the items you asked that were about modeling tidal gravity some other way than spacetime curvature, there is an alternate model that views gravity as a masless, spin-2 field on a flat background spacetime. I don't know of a good introductory online reference; I learned about it from The Feynman Lectures on Gravitation:

http://books.google.com/books/about/Feynman_lectures_on_gravitation.html?id=jL9reHGIcMgC

This "field on a flat spacetime" model turns out to be equivalent to the standard curved-spacetime model of GR, except for some concerns about whether the starting assumption of a flat background means the model can't deal with, for example, the FRW spacetimes in cosmology. So instead of viewing tidal gravity as a manifestation of spacetime curvature, you could view it as a manifestation of the massless, spin-2 field. But since the models give exactly the same predictions, one could just as well say that "spacetime curvature" and "massless spin-2 field" are different names for the same thing, the whatever-it-is-that-causes-tidal-gravity.

Ok.

Say. Can you think of an experimental setup that we average person can afford that can test for local lorentz invariance? Like some electronics apparatus that can be modified to become sensors for a rough test of orientation and boost lorentz symmetry or CPT symmetry? Think and brainstorm for an hour then please share. Thanks.

 

[stglyde]

Looks like the thread was locked; possibly because you started asking about spacetime again, which would belong back here, or possibly because it was perceived as pursuing your own speculative theory instead of asking about existing theories.

As far as the items you asked that were about modeling tidal gravity some other way than spacetime curvature, there is an alternate model that views gravity as a masless, spin-2 field on a flat background spacetime. I don't know of a good introductory online reference; I learned about it from The Feynman Lectures on Gravitation:

http://books.google.com/books/about/Feynman_lectures_on_gravitation.html?id=jL9reHGIcMgC

This "field on a flat spacetime" model turns out to be equivalent to the standard curved-spacetime model of GR, except for some concerns about whether the starting assumption of a flat background means the model can't deal with, for example, the FRW spacetimes in cosmology. So instead of viewing tidal gravity as a manifestation of spacetime curvature, you could view it as a manifestation of the massless, spin-2 field. But since the models give exactly the same predictions, one could just as well say that "spacetime curvature" and "massless spin-2 field" are different names for the same thing, the whatever-it-is-that-causes-tidal-gravity.

Googling "massless, spin-2 field on a flat background spacetime", there are indeed many researches about this.. interesting.. it's about going to flat minkowski space with spin 2 gravitons. Now how about going a step further backward.. like minkowski field on an Newtonian spacetime. I mean.. if we can remove the space curvature in GR by going to massless spin 2 field on a flat spacetime.. what is it not possible to move further back... like space+time field on Newtonian absolute space and time.. or something akin to it?

 

[nitsuj]

Ok.

Say. Can you think of an experimental setup that we average person can afford that can test for local lorentz invariance? Like some electronics apparatus that can be modified to become sensors for a rough test of orientation and boost lorentz symmetry or CPT symmetry? Think and brainstorm for an hour then please share. Thanks.

I think Tom Tom's have come down in price.

I hope it's okay I did someone else's homework

 

[stglyde]

Googling "massless, spin-2 field on a flat background spacetime", there are indeed many researches about this.. interesting.. it's about going to flat minkowski space with spin 2 gravitons. Now how about going a step further backward.. like minkowski field on an Newtonian spacetime. I mean.. if we can remove the space curvature in GR by going to massless spin 2 field on a flat spacetime.. what is it not possible to move further back... like space+time field on Newtonian absolute space and time.. or something akin to it?

After writing this. It slowly dawns on me there is indeed such thing. It's Lorentz Ether Theory which occurs in the backdrop of absolute space and time... just like how you can model massless spin-2 field on flat spacetime. You can actually take one step backward... LET field on absolute space and time! Now how do you connect gravity to Newtonian. There is one. It's called General Lorentz ether theory applied to Newtonian space and time! And all this appears not to be falsifiable! Is this 100% such that no experiment ever will distinguish them??