Is Space-Time Dilation Just a Funny Concept or Does It Have Real Properties?

[Adrian2000]

Hi all,

I was wondering if anybody else here thinks the concept of space-time dilation/concentration (curvature) is a little bit funny, not in the sense of it having an effect on the neighbouring particles, but in the sense of actually stretching or contracting, as though it itself had certain properties and information, despite being nothing. Or am I missing something, and are the effects of general & special relativities only limited to the particles that experience them? The prime motive for this question, is, as I've said above, that it seems a wee bit difficult to prescribe empty space with information, its own internal set of rules, as, err, it doesn't have anything on which to 'stick' these rules to (it's nothing) - pardon the simplification.

Thank you for the help,
Adrian

 

[phinds]

Your confusion stems from your mistaken believe that time dilation, for example, is something that is "experienced". It is not. It is an observational phenomena.

You, for example, right now as you are reading this, are traveling at .999999c (relative to an accelerated particle at CERN) and from the frame of reference of that particle, you are MASSIVELY time dilated. Do you feel any different?

 

[Adrian2000]

Your confusion stems from your mistaken believe that time dilation, for example, is something that is "experienced". It is not. It is an observational phenomena.

You, for example, right now as you are reading this, are traveling at .999999c (relative to an accelerated particle at CERN) and from the frame of reference of that particle, you are MASSIVELY time dilated. Do you feel any different?

Sorry - I don't think you understood what I meant - I did not mean time dilation, I meant space-time dilation, and specifically the contortion of eucledian space to accommodate gravity. (I did not think of the 'time' aspect of space-time, as it's in a different category to the eucledian 'space')

I also don't have a problem with the effects of space-time dilation, but I am scratching my head at the implication that actual space, nothingness, contracts in proportion to gravitational pull.

 

[phinds]

Sorry, I don't think you understood what I meant - I did not mean time dilation, I meant space-time dilation, and specifically the contortion of eucledian space to accommodate gravity. (I did not think of the 'time' aspect of space-time, as it's in a different category to the eucledian 'space')

I also don't have a problem with the effects of space-time dilation, but I am scratching my head at the implication that actual space, nothingness, stretches in proportion to gravitational pull.

Ah ... gotcha.

I don't think it's helpful to think of space as a "thing" that gets "stretched/curved/whatever" but rather of spacetime as a framework in which things move according to the geometry caused by gravity.

If space is a "thing" that IS stretched/curved/whatever, then you have to answer what IS this thing that gets contorted.

 

[Adrian2000]

Ah ... gotcha.

I don't think it's helpful to think of space as a "thing" that gets "stretched/curved/whatever" but rather of spacetime as a framework in which things move according to the geometry caused by gravity.

If space is a "thing" that IS stretched/curved/whatever, then you have to answer what IS this thing that gets contorted.

Exactly! I was going crazy thinking that there's something wrong with me for not understanding Einstein's theoretical implications.

And yet, is this not what contemporary Physics is based on? In the sense that if you are right at the edge of the singularity [black hole] about to fall in, you occupy an infitesimally smaller amount of space than you would if you were at the event horizon [despite having the exact same molecular structure, if we assume that you haven't been ripped to shreds by that point]?? Sorry if it's a bad example, but I think you know what I mean.

 

[harrylin]

Sorry [..] I meant [..] specifically the contortion of eucledian space to accommodate gravity.[..]
[..] I am scratching my head at the implication that actual space, nothingness, stretches in proportion to gravitational pull.

Hi Adrian!

- GR says nothing about space being "nothingness" or not. Einstein interpreted his predictions as that space has physical qualities. Einstein thus discussed the "metrical qualities of [..] space-time".

- GR makes predictions about rods and clocks, not about invisible "space". And measuring rods are not predicted to stretch - nor is gravitational pull a factor!

Instead, according to a distant observer measuring rods are predicted to shrink when moved downwards in a gravitational field, if they are pointing downwards/upwards. You can read it here:
https://en.wikisource.org/wiki/The_Foundation_of_the_Generalised_Theory_of_Relativity
Scroll immediately down to § 22. Behaviour of measuring rods and clocks in a statical gravitation-field - if you are allergic for the equations you can simply skip them, and only read the plain English conclusions just under (71) and (71a).
Note: as you are there, you may also appreciate just under (72) ! :)

PS: that gravitational pull is not a factor, is currently being explained by means of example D here:
https://www.physicsforums.com/threads/time-dilations-on-confusing-situations.783613/

 

[Adrian2000]

Hi Harrylin!

Yes, and this is what I meant - IF said measuring rod appears shorter to an outside observer, does it have to do with the actual object (rod) being physically shortened, or does it have to do with space contracting around a gravitational field? And if it is the latter, then clearly this space, nothing IS actually something, and has internal properties, does it not? (according to GR, whether explicitly or implicitly?)

Adrian

 

[A.T.]

it seems a wee bit difficult to prescribe empty space with information, its own internal set of rules,

I meant space-time dilation, and specifically the contortion of eucledian space to accommodate gravity.

Non contorted Euclidean geometry itself is also a set of rules. Doesn't it seem difficult to you, to prescribe empty space with that information?

 

[Adrian2000]

Non contorted Euclidean geometry itself is also a set of rules. Doesn't it seem difficult to you, to prescribe empty space with that information?

Not to me, though I could be missing something (which is why I'm here :) ) - prescribing empty space with a system of coordinates doesn't give that space any 'information' as it were, but if we say that that space will warp under certain conditions, hey presto, you have space that has certain internal properties, conditions, etc, that means that whenever it's subject to gravity, it will shrink. Which means that it's not just nothing, which seems a bit off to me.

By the way, I hope I put this thread in the right section :/ (I didn't see a theoretical physics section)

 

[A.T.]

prescribing empty space with a system of coordinates doesn't give that space any 'information'

Euclidean geometry is more than that. It tells you for example that the sum of inner angles in a triangle is 180°. Doesn't it seem difficult to you, to prescribe empty space with that information?

 

[Adrian2000]

Euclidean geometry is more than that. It tells you for example that the sum of inner angles in a triangle is 180°. Doesn't it seem difficult to you, to prescribe empty space with that information?

Errr, I don't think so. The two examples aren't the same - the triangle doesn't grow to 181 degrees or 179 degrees based on its colour, or whatever external/internal factor you want to compare space-time concentration/dilation resulting from a gravitational field to. Can you elaborate?(To elaborate a bit myself, a triangle being 180 degrees isn't really native to eucledian space; it appears to me, at least off-the-cuff, to be nothing more than an geometric concept deduced through logic and maths - it doesn't actually amount to any information whatsoever in actual, physical eucledian space (not like you can turn eucledian space over and see a sticker saying 'FYI: here's a triangle, this is what it looks like, and its 180 degrees, no more no less!') - plus, we are the ones who decided what a triangle was, and how big a degree was, which means that we are the inventors and sole purveyors of the concept of a 'triangle' - I guess we can have a discussion whether the three dimensions is information in of itself, but it seems that space-time concentration/dilation according to gravity is a little bit different than identifying three axes in empty space. [P.S. And is XYZ also anthropogenic/centric? Hmm, need to read up on my maths.])

 

[A.T.]

Errr, I don't think so

So you have no problem with empty space containing the information that triangle angles sum to 180° (Euclidean geometry)? But you have a problem with empty space containing the information for any other value than 180° (non-Euclidean geometry)?

To clarify: Do you have difficulty with space containing...
a) ...any information?
b) ...just specific values?

 

[Adrian2000]

So you have no problem with empty space containing the information that triangle angles sum to 180° (Euclidean geometry)? But you have a problem with empty space containing the information for any other value than 180° (non-Euclidean geometry)?

To clarify: Do you have difficulty with space containing...
a) ...any information?
b) ...just specific values?

A.T. I'm not sure what your motivation is here, but all I'm asking is A. whether anybody else has a problem with space-time dilation/concentration (curvature) as it's commonly described in the literature, and/or B. can anybody confirm that I correctly understand said concept of space-time to affect not just the particles present within said 'plane' but also the space of said plane?

 

[A.T.]

I'm not sure what your motivation here is

I'm trying to pin down where your difficulty lies, in order to address it. Answering my request for clarification would be helpful here.

to affect not just the particles present within said 'plane' but also the space of said plane?

Is there any conceivable experiment that could tell the difference?

 

[Nugatory]

To elaborate a bit myself, a triangle being 180 degrees isn't really native to euclidian space; it appears to me, at least off-the-cuff, to be nothing more than an geometric concept deduced through logic and maths - it doesn't actually amount to any information whatsoever in actual, physical euclidian space

How would you decide whether there even is an "actual physical Euclidean" space? There's no doubt that we live in some space, but is it in fact Euclidean?

Select three points not all on the same line. Stretch strings tight between each pair of them to create a triangle. Then measure the three interior angles and add them up. This is not an abstract mathematical exercise, it's a direct measurement of something about the physical world that we live in.

The interior angles will not, in general, add to exactly 180 degrees, and the discrepancy will be greater in the presence of stronger greater gravitational fields. Thus we conclude that we do not in fact live in an actual physical Euclidean space (although it's a pretty good approximation for daily life).

 

[Adrian2000]

Ok, with respect to both AT and Nugatory, enough with the bloody triangles - is there or is there not a warping of space in the presence of gravity? And if so, is that native to the particles that undergo said effects? Or is it native to the space in which said particles exist and they are merely 'passengers'? And if the latter is considered true, then how would one reconcile it with the idea that space is made up of nothing, and thus has no internal conditions (because there's nothing in said space to enforce said conditions)?

 

[A.T.]

And if so, is that native to the particles that undergo said effects? Or is it native to the space in which said particles exist and they are merely 'passengers'?

Is there any conceivable experiment that could tell the difference?

And if the latter is considered true, then how would one reconcile it with the idea that space is nothing, and has no internal conditions (because there's nothing in said space to enforce said conditions)?

How is Euclidean geometry reconciled with this idea?

 

[Adrian2000]

Is there any conceivable experiment that could tell the difference?

How is Euclidean geometry reconciled with this idea?

Jesus AT you can really take the life out of a discussion. Eucledian Geometry is reconciled with the idea of space as nothing in the way that I explained above, in an edit of my 2nd response [to yourself]. The only information that empty space could perhaps have are the three dimensions, and frankly even that sounds dubious, but I don't know sufficient maths to know for sure. Whatever the case, I think the original counter-example remains apt - a triangle doesn't grow to 181 or 179 degrees because it changes colour, or size - but empty space does appear to change if it's subject to gravity.

 

[A.T.]

The only information that empty space could perhaps have are the three dimensions,

That alone doesn't imply Euclidean geometry. So how do you reconcile that specific geometry with your idea that space cannot have any information beyond the number of dimensions?

 

[Adrian2000]

That alone doesn't imply Euclidean geometry. So how do you reconcile that specific geometry with your idea that space cannot have any information beyond the number of dimensions?

AT, read what I wrote in my second response to you. Eucledian Geometry seems to be nothing more than a logical, mathematical, self-supporting construct existing outside of any actual 'eucledian', three-dimensional space. [read: it exists insofar that we know of it and understand it, like fiat currency (plus understanding)]

 

[Bandersnatch]

@Adrian2k, let me just say that what AT and Nugatory are doing is not being fixated on some irrelevant aspect of the conversation, but trying to make you examine what is meant by space and properties of space. Stopping and reconsidering your biases as to what you intuitively think of as "natural" is essential when dealing with the more exotic physical concepts.

 

[Adrian2000]

@Adrian2k, let me just say that what AT and Nugatory are doing is not being fixated on some irrelevant aspect of the conversation, but trying to make you examine what is meant by space and properties of space. Stopping and reconsidering your biases as to what you intuitively think of as "natural" is essential when dealing with the more exotic physical concepts.

You know this is why nobody talks to you people. I ask one simple question, I get a dozen questions about triangles in return. We can all revise our expectations of what's natural and what isn't in our free time - for now, let's focus - it's Monday and I don't want to waste my time anymore than I want to waste yours.

 

[A.T.]

Eucledian Geometry seems to be nothing more than a logical, mathematical, self-supporting construct existing outside of any actual 'eucledian', three-dimensional space.

Non-Euclidean geometries are also logical and mathematical constructs. Euclidean geometry is just one, among an infinite number of possible geometries. Why can empty physical space have that specific geometry, but not any of the others?

 

[Adrian2000]

Non-Euclidean geometries are also logical and mathematical constructs. Euclidean geometry is just one, among an infinite number of possible geometries. Why can empty physical space have that specific geometry, but not any of the others?

Now we're getting somewhere - that's fine, I think, but we are not talking about empty space having non-eucledian geomtries, we are talking about empty space actually contracting or dilating, as though it was physical, and objective.

 

[Ilja]

"Empty space" is not empty. It contains at least a gravitational field, which is nontrivial everywhere. It contains also a lot of other fields. Ok, for all these other fields one can at least say, that the values of the field in vacuum are trivial. For gravity, even this does not make much sense. At best, one can say that what looks like a Minkowski space is undistinguishable by observation from the most trivial state, which we name vacuum.

But, even if one accepts all this - all the fields are there, they have values. One can give them an interpretation, in terms of some ether, if one likes. The mainstream does not like this, and prefers to name them "fields", without any guess which properties such a field describes.

 

[A.T.]

I ask one simple question, I get a dozen irrelevant questions in return.

Is your question relevant to physics? I asked you twice to name a experiment that would distinguish the two alternatives, and you failed to name one.

 

[A.T.]

we are not talking about empty space having non-eucledian geomtries, we are talking about empty space actually contracting or dilating

Contracted/dilated as compared to what?

 

[Adrian2000]

"Empty space" is not empty. It contains at least a gravitational field, which is nontrivial everywhere. It contains also a lot of other fields. Ok, for all these other fields one can at least say, that the values of the field in vacuum are trivial. For gravity, even this does not make much sense. At best, one can say that what looks like a Minkowski space is undistinguishable by observation from the most trivial state, which we name vacuum.

But, even if one accepts all this - all the fields are there, they have values. One can give them an interpretation, in terms of some ether, if one likes. The mainstream does not like this, and prefers to name them "fields", without any guess which properties such a field describes.

Aha! But once again, is it the particles themselves that are affected by said field when they dilate/contract as outlined on the generally accepted model of space-time curvature? Or does it have to do with actual space-time curving? If so, that's fine if there are fields or no fields - space is objective, and is subject to change, with respect to things like gravity, meaning that space isn't nothing, which, as I've said before, seems funny somehow. Do you agree/disagree?

@AT - Dude, I am here because I don't know what I'm talking about and you're asking me to devise an experiment for a concept I do not have a clear understanding of? In which universe does that logic make sense? (and how am I obligated to present you with an experiment upon request?)
@AT 2 - In comparison to its past state, if nothing else. (Compared to space outside of the same gravitational field in the present if you like)

 

[Dale]

space isn't nothing

I agree, it isn't nothing. Of course, that does not imply that it is some matter either. Spacetime has a variety of geometrical properties (distance, duration, curvature, etc.). It does not have many properties that we typically associate with matter, such as a rest frame or charge and so forth, but it does have some, such as stress-energy.

Once you accept that it has the properties that it has and does not have the properties it does not have then you will be in a much better position to understand how it actually behaves.

 

[A.T.]

I don't know what I'm talking about

They how do you know that the questions posed to you are irrelevant?

how am I obligated to present you with an experiment upon request?

If there is no conceivable experiment that could answer your question, then it's not a physics question.

In comparison to its past state

The geometric model of gravity in GR applies to static gravitational fields as well.

Compared to space outside of the same gravitational field in the present if you like

That is a comparison to Euclidean space again. So we actually are talking about Euclidean vs. non-Euclidean geometry.

 

[Adrian2000]

I agree, it isn't nothing. Of course, that does not imply that it is some matter either. Spacetime has a variety of geometrical properties (distance, duration, curvature, etc.). It does not have many properties that we typically associate with matter, such as a rest frame or charge and so forth, but it does have some, such as stress-energy.

Once you accept that it has the properties that it has and does not have the properties it does not have then you will be in a much better position to understand how it actually behaves.

Ok, and this is where the rubber hits the road - how can it have properties, 'information' and still be space? Surely that means that it's not space at all, but some sort of 'zone' (if you like)? And then, if it does have said properties, in what 'space' does it exist in? A higher dimension of some sort? Multiverse?

 

[Adrian2000]

That is a comparison to Euclidean space again. So we actually are talking about Euclidean vs. non-Euclidean geometry.

How is curved space non-Eucledian?

 

[A.T.]

How is curved space non-Eucledian?

Euclidean geometry applies only in spaces without intrinsic curvature.

 

[Adrian2000]

Euclidean geometry applies only in spaces without intrinsic curvature.

Well, whatever three-dimensional space that allows for curvature then.

 

[Nugatory]

How is curved space non-Euclidian?

That follows directly from the definition of "Euclidean space" as one that has zero curvature (you might give this wikipedia article a try). It is a simple experimental fact that the space that we live in is not Euclidean, as straight lines and inertial trajectories do not behave as they would in a Euclidean space.

What may be throwing you here is that we all have a very strong bias that Euclidean space is somehow what's "natural", so that parallel lines not intersecting, the Pythagorean theorem holding, and the like require no explanation; whereas any observed deviations from these behaviors must be explained in terms of something acting to change the behavior away from its "natural" Euclidean behavior. You see evidence of this bias when you consider how long it took for people to accept that the two-dimensional surface of the Earth is not a Euclidean plane embedded in a three-dimensional Euclidean space - it's a non-Euclidian non-flat two-dimensional surface embedded in a three-dimensional Euclidean space.

 

[Dale]

Ok, and this is where the rubber hits the road - how can it have properties, 'information' and still be space?

All spaces have properties, so I don't know what would lead you to believe that having properties is antithetical to being a space.

Personally, I think that this is your key misconception. Spacetime is not nothing, it is a 4D pseudo Riemannian manifold. 4D pseudo Riemannian manifolds are topological spaces with a metric structure, and as such they have topological and geometrical properties. Any assumption that it should not have properties is simply a bad assumption which needs to be discarded.

And then, if it does have said properties, in what 'space' does it exist in? A higher dimension of some sort? Multiverse?

There are many embedding theorems about how a curved manifold may be isometrically embedded into a higher-dimensional flat manifold. However, none of those are necessary (nor even useful) for describing physics. All of the physics can be described from within the curved 4D manifold without reference to any higher dimensional manifolds.

 

[phinds]

AT, read what I wrote in my second response to you. Eucledian Geometry seems to be nothing more than a logical, mathematical, self-supporting construct existing outside of any actual 'eucledian', three-dimensional space. [read: it exists insofar that we know of it and understand it, like fiat currency (plus understanding)]

Yes it does. So does Riemann geometry (exist as a math model divorced from physicality). The fact that one (Riemann) describes space in GR and the other (Euclidean) seems to make some sort of profound difference to you, and the other folks here are just trying to ascertain WHY it makes such a difference.

 

[Dale]

Adrian2000, phinds makes a very good point above. Both Riemannian geometry and Euclidean geometry are "logical, mathematical, self-supporting constructs". They are both equally valid as mathematical frameworks and both self-consistent (logical).

There is no reason, a priori, why one should be a better model for reality than the other. That is a question that can only be determined by experiments. It turns out that Riemannian geometry predicts the experimental data better than Euclidean geometry.

So, we have to recognize that our preconceptions favoring Euclidean geometry over Riemannian geometry are simply that: preconceptions. Nature need not conform to our preconceptions, and in this case does not. When this happens, we always need to change our preconceptions because we cannot change Nature.

 

[Adrian2000]

What may be throwing you here is that we all have a very strong bias that Euclidean space is somehow what's "natural", so that parallel lines not intersecting, the Pythagorean theorem holding, and the like require no explanation; whereas any observed deviations from these behaviors must be explained in terms of something acting to change the behavior away from its "natural" Euclidean behavior. You see evidence of this bias when you consider how long it took for people to accept that the two-dimensional surface of the Earth is not a Euclidean plane embedded in a three-dimensional Euclidean space - it's a non-Euclidian non-flat two-dimensional surface embedded in a three-dimensional Euclidean space.

You are quite right with regards to Euclidean space, however..

It has nothing to do with 'natural' vs 'unnatural' - persons who advocate the wholesale discarding of what's 'natural' only replace one biased framework for another - it has to do with a logical, tangible understanding of what space actually means. Ok, great, we have space that has conditional properties like objects do. That makes it a zone of some sort, not a space. Which begs the follow-up question - how is this zone defined? By what? From where? Is there a higher plane of existence? And so on and so forth. It's wonderful that everybody here wants to re-assure me of the fact that human beings are human, but that's kind of beyond the point.

Yes it does. So does Riemann geometry (exist as a math model divorced from physicality). The fact that one (Riemann) describes space in GR and the other (Euclidean) doesn't seems to make some sort of profound difference to you, and the other folks here are just trying to ascertain WHY it makes such a difference.

Betrayal! (On a serious note, it makes absolutely zero difference to me - I have no idea where you got that from, and it actually makes me scared I made a blunder in my rhetoric earlier)

Adrian2000, phinds makes a very good point above. Both Riemannian geometry and Euclidean geometry are "logical, mathematical, self-supporting constructs". They are both equally valid as mathematical frameworks and both self-consistent (logical).

There is no reason, a priori, why one should be a better model for reality than the other. That is a question that can only be determined by experiments. It turns out that Riemannian geometry predicts the experimental data better than Euclidean geometry.

So, we have to recognize that our preconceptions favoring Euclidean geometry over Riemannian geometry are simply that: preconceptions. Nature need not conform to our preconceptions, and in this case does not. When this happens, we always need to change our preconceptions because we cannot change Nature.

Fellas, is this a joke? First triangles, now I'm the luddite hanging on to my Eucledian wheelbarrow while you're selling me Riemannian iPods? I couldn't care less about the nomenclature of the 'space' part of 'space-time'. I truly couldn't. Nevermind basic English comprehension, does anyone here have a lick of Physics knowledge and give me an elementary response to two basic questions??

Question 1: Is it true that space curves around gravity?
Question 2: If this is the case, does it not seem funny to anyone here that space itself, devoid of matter, radiation and anything else we understand to exist in this universe has the potential to warp under gravitational strain?? (Phinds seems to agree :/ )

 

[Dale]

Fellas, is this a joke? First triangles, now I'm the luddite hanging on to my Eucledian wheelbarrow while you're selling me Riemannian iPods?

Basically, yes (although without the unkind connotation of "Luddite", this is a normal learning process). It appears that you accept Euclidean space without question (and consider it to have no "properties"), but seem to consider for some reason that Riemannian spacetime has properties which are incompatible with it being a model of space.

Question 1: Is it true that space curves around gravity?

Yes. There is substantial experimental evidence for that.

Question 2: If this is the case, does it not seem funny to anyone here that space itself, devoid of matter, radiation and anything else we understand to exist in this universe has the potential to warp under gravitational strain?? (Phinds seems to agree :/ )

Sure it is funny. Everyone has to adapt their thinking when they are learning GR. However, once you do so, you see that it is completely logically self consistent and it is more consistent with the experimental data than any other model proposed to date.

 

[Adrian2000]

Sure it is funny. Everyone has to adapt their thinking when they are learning GR. However, once you do so, you see that it is completely logically self consistent and it is more consistent with the experimental data than any other model proposed to date.

It makes for a convinient explanation, and a good one too, but I'm wondering if it's more of a band-aid than a model of reality. Insofar that all the effects it describes indeed exist, and I don't dispute them, but the actual description of space-time has already been proven to break-down at the point of singularity, which can serve as a reductio-ad-absurdum counterargument to the theory, as well as a launchpad to a more comprehensive model of the universe. Other scientists have appeared to concede as much, with, if I recall correctly, Hawking stating that Einstein's model of space-time is functional for a macroscopic view of the universe, while quantum mechanics, the apparentely more sound model, being more appropriate for a microscopic view of the universe.

But that's not really what I want to argue;

I don't want to beat a dead horse, but I still have trouble understanding how empty, naked space that we can all experience, as we all exist in it, even if it's filled with matter and energy, is then conditional on something like gravity. It just doesn't add up to me. Not intuitively, not logically, not rationally or tangibly. I don't have the geometry to make heads or tails of Riemannian space, but I doubt it would convince me otherwise even if I did.

 

[Dale]

It makes for a convinient explanation, and a good one too, but I'm wondering if it's more of a band-aid than a model of reality. Insofar that all the effects it describes indeed exist, and I don't dispute them, but the actual description of space-time has already been proven to break-down at the point of singularity, which can serve as a reductio-ad-absurdum counterargument to the theory, as well as a launchpad to a more comprehensive model of the universe.

The same can be said of all physical theories. So while this is true, it is also not something that is new and unique to GR nor is it something that is likely to change any time soon for any physics theory.

I don't want to beat a dead horse, but I still have trouble understanding how empty, naked space that we can all experience, as we all exist in it, even if it's filled with matter and energy, is then conditional on something like gravity. It just doesn't add up to me. Not intuitively, not logically, not rationally or tangibly.

It doesn't add up to most beginning students intuitively either. As far as logically, rationally, and tangibly, you simply don't have the required background to judge. If you are interested in learning, then I would recommend starting here:
http://preposterousuniverse.com/grnotes/

It takes effort, but that effort is required before an informed claim regarding its logical consistency can be made.

 

[Adrian2000]

The same can be said of all physical theories. So while this is true, it is also not something that is new and unique to GR nor is it something that is likely to change any time soon for any physics theory.

Well hold on a minute there, that's not exactly true, is it? When has Quantum Mechanics been proven to have holes in its theory? And what of the Theory of Gravity, Big Bang/Higgs Boson stuff aside?

 

[PAllen]

AT, read what I wrote in my second response to you. Eucledian Geometry seems to be nothing more than a logical, mathematical, self-supporting construct existing outside of any actual 'eucledian', three-dimensional space. [read: it exists insofar that we know of it and understand it, like fiat currency (plus understanding)]

This is just wrong. You have to make other assumptions. Those assumptions prescribe geometry. Mathematically, there is nothing that favors Euclidean geometry as 'neutral' or 'natural'. It was physical experience that made it natural, for a long time, to e.g. assume the parallel postulate. As soon as the question was asked, mathematically, 'what if the parallel postulate was not true? ', it was found that there were no contradictions, and you simply got other geometries.

 

[Adrian2000]

This is just wrong. You have to make other assumptions. Those assumptions prescribe geometry. Mathematically, there is nothing that favors Euclidean geometry as 'neutral' or 'natural'. It was physical experience that made it natural, for a long time, to e.g. assume the parallel postulate. As soon as the question was asked, mathematically, 'what if the parallel postulate was not true? ', it was found that there were no contradictions, and you simply got other geometries.

Oh for god's sake, I already covered this, I said 'Eucledian' because I did not know of Riemannian space - the precise descriptor is the 'space' part of spacetime (as we observe it in reality).

 

[Adrian2000]

Right, unless anyone has anything else to add, I suppose the mature option would be to agree to disagree. (and for me to go back to the books, so I could make some independent conclusions with a measure of confidence rather than asking all of you to help me out, which you have, in your own way :) )

So thank you and adieu :)

 

[PAllen]

Oh for god's sake, I already covered this, I said 'Eucledian' because I did not know of Riemannian space - the precise descriptor is the 'space' part of spacetime.

No, you did not cover it. You claim trianges adding up to 180 degrees is natural. This is false. It is a consequence of other axioms. In particular, it is false if you assume the parallel postulate is false.

 

[Adrian2000]

No, you did not cover it. You claim trianges adding up to 180 degrees is natural. This is false. It is a consequence of other axioms. In particular, it is false if you assume the parallel postulate is false.

180 degrees is natural? What? It's logical and deductive, as you say, a result of a self-supporting framework of the definition of a 2-dimensional triangle.

I covered it at the bottom of the 2nd page, in my response to Dale.

 

[Dale]

Well hold on a minute there, that's not exactly true, is it? When has Quantum Mechanics been proven to have holes in its theory?

Sure, infinities crop up all the time in QM. The whole topic of renormalization was invented specifically to address those infinities.

 

[PAllen]

Where the hell are you getting your information from, pal? 180 degrees is natural? What? It's logical and deductive, as you say, a result of a self-supporting framework of the definition of a 2-dimensional triangle.

I covered it at the bottom of the 2nd page, in my response to Dale. So have a coke and relax. Bad enough with one AT, now we have a second one.

I saw no understanding of how properties you claim are natural and neutral are anything but that. Other choices are equally logical and deductive. It is nothing but our low precision physical experience that makes particular choices for geometric axioms seem natural.