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Javelin Argument for Infinity

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You write as if there's more than one 'gravitational model ("many such cosmological models"!!!)...hilarious.

 

So please, tell me about them because my poor college courses only taught one,the  Newtionian, which was proven false by GR.

 

....

You apparently have very little exposure to the Ricci tensor since you seem completely unaware of the Friedmann-Robertson-Walker big bang cosmologies. Yes, that's plural since there are three cases depending on whether spatial cross-sections of the universe have scalar curvature that is positive, zero or negative. What is more, these are not the only cosmologies possible via GR. You seem to be aware of only one case and ignorantly profess certitude that there is only one. Since you, by your own admission, were never schooled in GR, perhaps a little more humility on your part is in order. Have you heard of the post-Newtonian formalism? How about inflationary cosmological models? I didn't think so. Learn a little before laughing at those who know more than you do. Otherwise you just sound like a flat earther--hilarious.

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You apparently have very little exposure to the Ricci tensor since you seem completely unaware of the Friedmann-Robertson-Walker big bang cosmologies. Yes, that's plural since there are three cases depending on whether spatial cross-sections of the universe have scalar curvature that is positive, zero or negative. What is more, these are not the only cosmologies possible via GR. You seem to be aware of only one case and ignorantly profess certitude that there is only one. Since you, by your own admission, were never schooled in GR, perhaps a little more humility on your part is in order. Have you heard of the post-Newtonian formalism? How about inflationary cosmological models? I didn't think so. Learn a little before laughing at those who know more than you do. Otherwise you just sound like a flat earther--hilarious.

You apparently have misunderstood your Wiki. 

 

* 'FRW is correctly written to include Lemaitre, or 'FLRW'

 

** As such, FLRW is not a 'theory' of gravity;, but rather the accepted basis for Big Bang. 

 

  In other words, whatever you might be trying to say--and however you might be confused-- FLRW would be relevant to the conversation if and only if the arrow in question were somehow caught up in a Big Bang event. Otherwise, we're talking about fundamental GR which is, again, our only theory of gravity.

 

*** It's more correctly called a 'metric' because it gives all of the possibilities of expansion, with respect to the initial force and the counter-force of the gravity which The Bang created.

 

 

**** As a metric, it offers three general possibilities of outcome, which are the potential shapes of the universe: positive curvature, negative curvature, and none. This is what you confused as 'gravity'.

 

***** the 'theory' would be the arrival at the correct shape by means of measurement. Here, we refer to deSitter's elaboration of a flat model.

 

****** Ricci is used in the FLRW as a part of the Riemann tensor that's derived as a product of the Einsteinian and the metric tensor. This makes it a rather exotic fourth-order derivative.

 

As such, it expresses the potential curvatures of the created gravitational field against the expansion from Big Bang. To this extent, FLRW obviously includes extrapolated parts of GR.

 

******* Otherwise, the Ricci in the basic Einsteinian is a basic second order. Arrows flying into a gravitational field will  curve, just like anything else. What's important on a basic high-school level (yours) is that there is no place within the real universe in which arrows, or anything else, will exhibit the complete inertia that would not eventually curve back to its origin.

 

******** In terms of cosmology, what's interesting about the development of FLRW is that the equations now take us beyond the zero, to a time before the Big Bang. That's why it still serves as the basis for all Big Bang cosmology, as taught, for the last fifty years or so.

 

In other words, you seriously misunderstood some really basic stuff; so you get an F. 

 

As for myself, i like to paraphrase the film 'Quigley Down Under': "I said that I really didn't like Physics enough to have gone on to do a doctorate. But i never said that i wasn't good at it."

 

In this respect, you boorishly assumed that my admittedly 'few courses as an undergrad' were of the introductory sort that you might have taken yourself--ostensibly sufficient to have misunderstood Wiki, as it were.

 

Well, not. Because i could understand the math (high tester) and was 'pushed' into science by two academic parents, my 400 level stuff was complete by 11th grade. 'Did grad level QM in college as electives. 

 

'Rather boring, actually, because the theory is real easy. Either  you know how to plug in the numbers derived from an understanding of the math, or not. 'No more of a skill than. say, learning a musical instrument, or singing, neither of which i can do.

 

My love is the Linguistics of Spanish lit. Here i can use my math to derive refined models of lexiostatistics and glottochronology. How 800 AD Arabic poetry infused itself into modern Spanish poetry is, for me far more interesting than arrows flying through Hilbert Space with possible negative and positive curvatures, etc...

Edited by andie holland
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Andie, Perhaps you should stick to spanish lit. You made several false statements above, Yes, the Ricci tensor is the trace of the Riemann tensor, but it is not a product of the Einstein tensor and the metric. In fact, the Einstein tensor was discovered after the Ricci tensor and defined in terms of it. By the way, the Ricci tensor, being the trace of the Riemann tensor, involves second order derivatives of the metric. (Epic fail on your part and revealing that you have not the slightest idea what you are talking about.) In fact, if you assume spherical symmetry, the Einstein equations reduce to a system of first order pde's. I ought to know--my books, which are available on Amazon dot com, deal with this case.

This post, Andie, is not for you since you are not a worthy partner for discussion. Rather, the record must be set straight.

Also, I wish to add that only in the case of positive curvature do the arrows meet. If they do not traverse to the back side of the universe, then they will find themselves together when the universe undergoes the big crunch. Yes, should the universe collapse on itself then the arrows will indeed be at one location. However, time will cease to have meaning when that happens. In the other two cases of frw theory the arrows will forever float apart as the universe undergoes heat death.

I might add that any theory that determines a value for the Einstein tensor is a theory of gravity. Frw cosmology concerns gravity on a universal scale.

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Space could still be completely finite if it were wrapped up into a ball, so that a pair of javelins travelling in opposite directions would eventually collide head-on; a Pac-Man universe.

Again, this moves into, as aleph_1 pointed out, intrinsic geometry. By the career I've chosen, I'm predominantly Euclidean — geometrically. Two javelins traveling in opposite directions on a sphere do not constitute a planar straight line to me, which is how I interpret the ancient Greek javelin proposition. The conceptual finiteness of space emanates from the law of identity, not only as it applies to the metaphysical, but as it applies to conceptual realm as well.

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Space could still be completely finite if it were wrapped up into a ball, so that a pair of javelins travelling in opposite directions would eventually collide head-on; a Pac-Man universe.

Alternatively, the universe could have the topology of a torus so that on certain opposing trajectories the javelins would wind about the torus coming close multiple times and yet never colliding.

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Again, this moves into, as aleph_1 pointed out, intrinsic geometry. By the career I've chosen, I'm predominantly Euclidean — geometrically. Two javelins traveling in opposite directions on a sphere do not constitute a planar straight line to me, which is how I interpret the ancient Greek javelin proposition. The conceptual finiteness of space emanates from the law of identity, not only as it applies to the metaphysical, but as it applies to conceptual realm as well.

Locally, Euclidean geometry works quite well. However, for things like GPS and the motions of the planets Euclidean geometry is a poor approximation of what is observed. We can only deduce the intrinsic geometry of the space around us by what is observed, and these observations are at variance with Euclidean geometry.

We cannot be sure of the large-scale structure of the universe. The fate of the javelins is truly beyond what can be said with any certainty.

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Two javelins traveling in opposite directions on a sphere do not constitute a planar straight line to me, which is how I interpret the ancient Greek javelin proposition.

If this sphere were four-dimensional, with the three Euclidean sort of dimensions constituting its surface (like the 2d surface of a 3d sphere), then the only way to know it would be to travel all the way around until you arrived at your origin. If the universe were actually like that then we would be able to see Earth by looking at ANY arbitrary point in the sky, with a good enough telescope; that does seem somewhat implausible.

Still, it's intriguing.

Edit: I say it's implausible because someone actually looking out across the curvature of the universe, itself, would be able to see Earth simultaneously in EVERY point of the night sky. And this wouldn't be some weird trick; Earth itself would actually BE in every part of the night sky, simultaneously, some mind-boggling distance away. That smacks of a paradox to me. I don't have a telescope, though.

Edited by Harrison Danneskjold
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Alternatively, the universe could have the topology of a torus so that on certain opposing trajectories the javelins would wind about the torus coming close multiple times and yet never colliding.

True. And we just don't have enough evidence (at least I don't) to refute, nor really support a wide variety of such possibilities.

There is just so much that we have yet to discover.

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Locally, Euclidean geometry works quite well. However, for things like GPS and the motions of the planets Euclidean geometry is a poor approximation of what is observed. We can only deduce the intrinsic geometry of the space around us by what is observed, and these observations are at variance with Euclidean geometry.

We cannot be sure of the large-scale structure of the universe. The fate of the javelins is truly beyond what can be said with any certainty.

Inductive and deductive reasoning recognizes that deductions are derived from previously induced premises. Since Aristotle's time, deductive analysis has stood tried and true when adhered to properly, it has been the inductive side of the equation that remained problematic. I can agree that there are observations that appear to be at variance with Euclidean geometry, and that methods have been put in place that make GPS systems and sending probes into space, both which extend our abilities to locate beyond the accuracy of mariners tools  and observe beyond the range of the telescope.

 

Perhaps it is because I've not taken specific classes in this area. Maybe the similarities between Gauss and Reimann's work simply appear to be akin to the methods developed by Edgard De Smet. I have to work with what I know, and try to relate new information back to it, both mathematically and geometrically.

 

As to the fate of the javelins, infinity remains a mathematical construct per my understanding, and has no metaphysical counterpart. The question of how a straight line construct at such vast magnitudes can deviate from my understanding of what a straight line means remains a mystery at this point in my journey.

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Thanks Harrison, but again, developing this, first on the drafting board, and now with computer aided design software, all of this, up to elliptic space can be accomplished and expressed using descriptive geometry, or combinations of 2d sketches with other descriptive geometry techniques.

 

I'd need a better understanding of some of the more esoteric commands in the computer software to test it on the formulas given in the elliptic space section, the geometry described should be doable as well.

 

Straight lines can be struck through any described point, in any described direction which then can be analyzed with respect to any of these compound curvature surfaces in a variety of ways.

 

After the elliptic space, I would need to understand the math to understand how it relates to the geometry it is derived from.

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Inductive and deductive reasoning recognizes that deductions are derived from previously induced premises. Since Aristotle's time, deductive analysis has stood tried and true when adhered to properly, it has been the inductive side of the equation that remained problematic. I can agree that there are observations that appear to be at variance with Euclidean geometry, and that methods have been put in place that make GPS systems and sending probes into space, both which extend our abilities to locate beyond the accuracy of mariners tools  and observe beyond the range of the telescope.

 

Perhaps it is because I've not taken specific classes in this area. Maybe the similarities between Gauss and Reimann's work simply appear to be akin to the methods developed by Edgard De Smet. I have to work with what I know, and try to relate new information back to it, both mathematically and geometrically.

 

As to the fate of the javelins, infinity remains a mathematical construct per my understanding, and has no metaphysical counterpart. The question of how a straight line construct at such vast magnitudes can deviate from my understanding of what a straight line means remains a mystery at this point in my journey.

Deductive reasoning is ALWAYS axiomatic reasoning and remains as good as the axioms. Galileo demonstrated that Aristotle's deductive reasoning is defective in that it can lead to pure rationalism--good logic applied to concepts disconnected from reality. Galileo's marble experiments overthrew Aristotle's presumption of the sufficiency of rationalism and demonstrated the necessity of reduction to perception, I.e., induction.

What is the geometry of the universe? Einstein transformed geometry from a purely deductive science into an inductive one. (Riemann, some 60 years before Einstein, hypothesised that physical laws have a geometric basis but was unable to find the right formulation.) While we will never know the extrinsic geometry of the universe because we cannot remove ourselves from it in order to make the necessary measurements, we can determine some of the intrinsic geometry of the universe by reduction to perception.

Geometric theories of gravitation predict that time runs more rapidly away from the surface of the earth. Mass dilates time. This was observed by Gravity Probe A. Accounting for this time dilation is necessary for GPS systems for without doing so they will lose accuracy eventually amounting to errors measured in kilometers.

Geometric theories of gravity also predict that gyroscopes in orbit around the earth will drift in small but measurable amounts compared to purely Euclidean theories. This drift was measured by Gravity Probe B--one of the most important gravitational experiments in the last decade.

Curvature of space-time caused by masses is necessary to explain Mercury's perihelion advance. It is necessary for explaining the shift in spectral lines called gravitational red shift. It is necessary for explaining the bending of light on the limb of the sun. This theory is indispensable for explaining much of what we observe both terrestrially and astronomically.

Since geometry has been reduced to an inductive science, it does indeed require some humility on our part. We can only make assertions concerning those geometries that we know of and that are constrained by observation. In the class of possible geometries that we know of, Einstein's original theory remains viable. Euclid's does not.

Since we have not reduced the possible viable geometries to one, the fate of the arrows remains outside of our ability to deduce.

Concerning infinity, speaking of it as though it were an entity is pure rationalism as you point out. It would be arrogant to make any assertion about the size of the universe since we cannot reduce those assertions to observations. Is it bounded or not? Until informed by experiment, both possible geometries remain viable. Humility concerning the fate of the arrows is in order.

By the way, the mathematics involved in Riemannian geometry is hard. That of non-Riemannian geometries is harder. Good luck.

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