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I thought when a theory carries paradoxes, and they go unresolved, eventually they get called inconsistencies and the theory is assumed wrong somewhere.

GR doesn't work at distances, say between adjacent galaxies. The answer I got about that was that at such distances what does it mean to talk about the velocity of Andromeda.

The reason that's unconvincing is while it's obviously true in objective reality, A set of abstract theory and equation don't have to worry about practical realities...they work with simplified scenarios, and if they fall down, then normally we say the theory is wrong. Not absolutely wrong...no one ever means that. But wrong...or Right let's say, within limiting bounds.

I didn't say that at the time, but what was said to me was that GR is a LOCAL theory only. I don't think that true in the sense of a formal position. And this matters because if GR is wrong outside a certain bounds, then by informally saying it's always been a local theory, what we're really doing is avoiding the issue.

But let's say it is a local theory, and this is the context of my question.

If GR is a local theory, why is being used in other contexts as a primary source for large scale observables and knock-on cosmology theory out to the very edge AND BEYOND the visible universe?

And that's not the only 'edge' GR gets extended. The implied properties of Spacetime, now results in serious scientists apparently, arguing for BlockTime as a candidate for inclusion in our most precious and hard won incumbent knowledge. l

And actually the space time relatedness between points is very similar to what is being asked in that Andromeda paradox. This seems so wrong.

Sorry had to take back the total surrender :)

I think it's a reasonable question (not the one above) why paradoxes in GR are treated differently. The Andromeda Paradox, no matter what purpose its invention was to serve, demonstrates a result of the tools, that wouldn't happen.

Why is it preferable to entertain something like blocktime that totally dehumanizes us, but not see fit to entertain that a paradox has a traditional context in science of signalling a problems in theory

Lucy Meadow
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  • That GR is a local theory simply means that there is no "spooky action at a distance". – AV23 May 07 '15 at 14:22
  • Do you maybe have a wrong definition for "local" in physics theories?. http://en.wikipedia.org/wiki/Principle_of_locality – anna v May 07 '15 at 14:25
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    Can you explain what you mean by GR doesn't work at distances, say between adjacent galaxies? From the context I'd guess you think the Andromeda paradox means GR doesn't work at these distances. If so, you are wrong. – John Rennie May 07 '15 at 14:27
  • All theories we have are wrong on some level. That's normal and part of the scientific method. A successful scientist simply knows where a theory is wrong in such a way that he or she can have a realistic hope of fixing it a little. As for your particular concern about GR, I think that is more the result of a lack of understanding how GR works than of an actual problem with the theory. – CuriousOne May 07 '15 at 15:00
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    Your title claims that SR has problems, but you don't mention them in the body at all. – Ross Millikan May 07 '15 at 15:03
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    "Both Special and General Relativity carry long term unresolved paradoxes." [citation needed] – dmckee --- ex-moderator kitten May 07 '15 at 15:03
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    Woah now! What's with all the downvotes? Sure this question displays a certain misunderstanding with the concept of a local theory and it mistakes this to mean GR isn't valid over long distances, but it's still a clear question. It shows some research has clearly been done, and it presents everything needed for someone to effectively answer the question. +1. This may say stuff that's wrong, but it's a good question. – Jim May 07 '15 at 15:13
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    @ACuriousJim: I haven't downvoted at the moment because I'm waiting for clarification. There may some significance to the question that isn't obvious, as there was to Lucy's previous question. However it does appear to that the whole question is founded on a fallacy, and therefore is not a good question. And this is precisely what downvotes are meant to indicate. If clarification is not forthcoming I will be joining the downvoters. – John Rennie May 07 '15 at 16:20
  • @JohnRennie Well, I can't argue with you if you give a clear reasoning and a timeframe of leeway. But I can thank you for taking the time to explicitly lay out your motivations – Jim May 07 '15 at 17:03
  • Down voting is fair...I've got a point but I sort went a bit mad while whiting. Mark me down! – Lucy Meadow May 07 '15 at 20:10
  • I know what 'local' means in the normal context. But that wasn't the context. It happened on this site. The Andromeda paradox was being explained. And I must have asked whether that was a limitation of the theory. He said, no because GR only works locally. He was talking about not working at a distance in context of the Andromeda paradox. but it's my fault because it sounds like he was wrong and I just took his word for it that he was speaking from a position that wasn't just his – Lucy Meadow May 07 '15 at 20:15
  • Both Special and General Relativity carry long term unresolved paradoxes --> why do I need to cite for this? Isn't it true that there are paradoxes with both theories and they are not resolved in that there isn't agreement that are among the very best people (in Relativeity) – Lucy Meadow May 07 '15 at 20:21
  • Hi JohnRennie, thanks for holding back till the midnight twang :o0 JohnRennie, I don't understand how it can be true that GR works for the problem that became and remains a paradox. You might be saying it words for something else. And that's probably right because my question was assuming the man on the page it happened on, was speaking for widely shared view that GR only worked locally (i.e. that was why the paradox) – Lucy Meadow May 07 '15 at 20:29
  • hi hi hi - OH dear I got this wrong. I didn't understand the Andromeda paradox, it looks like, the first tirme round. I just went back and looked and it was clear.

    Sorry to mess up your site with trash!!

     – Lucy Meadow May 07 '15 at 20:37
  • OK now I understand it much better and I'm back to asking why this paradox, rather than be accepted as device for illustrating the weird and wonderful of GR instead be entertained as a clue to what is wrong with GR? Simultaneity could be something that transpires from the way the objects in the theory are set up. It may be wrong. A paradox can be a good signal that something is wrong or needs adjusting – Lucy Meadow May 07 '15 at 20:58
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    @LucyMeadow: the proper meaning of paradox is an inconsistency, and there are no inconsistencies in relativity. The popular meaning of paradox is something that is unintuitive, and there are lots of things in relativity that are unintuitive. However this is a failure of human intuition not of relativity. Experiment is the ultimate arbiter, and relativity (both flavours) has passed every experimental test that has been thrown at it. So let me emphasise that there are no paradoxes in relativity. – John Rennie May 08 '15 at 05:18
  • Sorry for the really long pause...it was the above comment on meaning of "Paradox" in his belief - and no-one stepping in to correct him....just really made everything seem really futile. – Lucy Meadow Jul 10 '15 at 08:50
  • sorry for the long pause. JohnRennie...this is not the meaning of 'paradox' and not close to be a reasonable proxy. A paradox by definition is apparent but ultimately resolved sometime in the future. It's proper to invoke the concept in preliminary tense of calling something 'paradoxical'. Which is not the same as saying it's a 'Paradox'. Which it isn't until the suspected resolution is confirmed. Which if after reasonable time and effort it remains not, then isn't a paradox it's an inconsistency, or contradiction, or whatever. It isn't and wasn't to begin with, a paradox. – Lucy Meadow Jul 10 '15 at 10:08
  • So now you know. And along with it, that my use was proper. And the limitation I defined General Relativity with, was also correct. Paradox you could have opened a dictionary for; the limitation as said, you could've sourced from any directly relevant scholarly work. – Lucy Meadow Jul 10 '15 at 10:16
  • e.g. right here top of the google result "Given this situation, in the presence of more complicated frames and/or gravity, relativity generally relinquishes the whole concept of a distant object...." – Lucy Meadow Jul 10 '15 at 10:22
  • having a well-defined speed. As a result, it's often said in relativity that light always has speed c, because only when light is right next to an observer can he measure its speed— which will then be c." - http://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/speed_of_light.html So there it hasn't been resolved as you claimed, other than weakly as the scholar invokes for himself, by saying it's a sensible assertion to be making, say, the speed of light is constant at a distant location such as an adjacent galaxy...because - he says - there is no way to set up a measurement. – Lucy Meadow Jul 10 '15 at 10:27
  • But the real reason is that, for example, at distances like between galaxies, applying the theory of general relativity results in the nonsense of, for instance, the tiniest shift in your posture, twitch of the nose, on distances like that will accumulate large relativistic shifts, including that something that a moment ago happened last week, now won't be happening till next week *(and yet we seem to know it will be happening, despite the decision to happen-it hasn't happened yet. – Lucy Meadow Jul 10 '15 at 10:32
  • And meat of my question was, at minimum, why with this a known paradox that continues to be unresolved - at the very minimum, has not translated into a consistent view of GR as a theory that should not be used to attempt inferences across large scales and distances. The example I cited was the obviously daft 'blocktime'. Why is that inference, which takes place so distantly distance is transcended to History. – Lucy Meadow Jul 10 '15 at 10:38

2 Answers2

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You are misunderstanding the word local in this context. GR deals with long distance gravitation just fine, even between here and Andromeda. Local means that at a given time the gravitational response of an object (like the Milky Way) just depends on the fields that are around it, and that the fields only depend on the fields nearby a little earlier and the nearby masses. In other words, the theory expresses everything in space and time differential equations. GR gives us the way to calculate those fields and how they evolve in time. The only known problem with GR is at very short distances and very high energy densities where quantum effects come into play.

The Maxwell equations are local by the same definition. They also work fine for predicting the light we see from Andromeda. Newton's gravity is not local. It would say that the Milky Way would react gravitationally to where Andromeda is now, not 2.5Myr ago.

Ross Millikan
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  • OK sorry about that. Save that I definitely know about locality. This was said to me in context of the Andromeda paradox. – Lucy Meadow May 07 '15 at 20:18
  • I mean, can I adjust my question (well not for real but here) to ask this: When theories carry paradoxes that go unresolved, don't we call it an inconsistency and assuming something is wrong? – Lucy Meadow May 07 '15 at 20:19
  • Neither of these theories have paradoxes. Both have limits to their applicability. SR only works in inertial frames, but is approximately right if accelerations are small, which they often are. GR works in accelerated frames, and as far as we know it is perfect outside the quantum limit. What paradoxes are you referring to? – Ross Millikan May 07 '15 at 21:38
  • Are you aware you're taking at me not to me. What am I supposedto gain from a bucket of assertions with a twist poured over my head like this? Also you're to back anything anym= ore than you have mastered it.It didn't help that you don't know what a paradox is. – Lucy Meadow May 08 '15 at 17:54
  • There are two senses of paradox. One is a true inconsistency. If that were found, we would invalidate the theory it was found in. The other is a perceived paradox, like the twin paradox in SR. When you analyze it properly, there is no inconsistency, but it can be stated in a way that seems to be a paradox. As far as I know, there are no true inconsistencies in SR or GR. If you believe there is one, you should be specific about stating it and ask how or if it has been resolved. – Ross Millikan May 09 '15 at 03:19
  • Thanks for this Ross. I don't think there's anything wrong with GR in a serious way. I'm learning physics right now and believe its important to build up a resistance to a beautiful theory before getting too deeply into it. Otherwise you can ending up loving it too much which can lead to stagnation. – Lucy Meadow May 10 '15 at 20:34
  • Answering what you say...IMHO the meaning of 'paradox' is not quite what you say. All paradoxes are 'perceived paradoxes'. If a paradox is a true inconsistency then it's not a paradox but an inconsistency. This is one of the possible resolutions of the [perceived] paradox. – Lucy Meadow May 10 '15 at 20:38
  • answering your point....you could be right and thanks for that. If the thought experiments of SR/GR described as paradoxes are educational devices as you suggest (i.e. can be stated as paradoxes but actually there's a known resolution with sufficient knowledge) then I should be able to run the calculations in say, Andromeda Paradox and get the right answer. The reason I wrote the question is because I think the resolution is actually not that, but a principle of GR relating to simultaneity. If that's true, then I was just wondering ..... – Lucy Meadow May 10 '15 at 20:45
  • ....what that means for the field equations, or the current ways we set up problems. How does this matter resolve in terms of the original problem? Does it mean the way we set up equations only work up to a certain distance between objects? If true, then does this trace back to fundamentals in the Field Equations? Or is it something else....in which what else is in the way we set up problems? – Lucy Meadow May 10 '15 at 20:48
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Let me give a simple example from computer graphics:

Suppose I am given the task to fit a three dimensional shape, lets say a mountain, so that I can then plot it any way I want in three dimensions. I would take a set of mathematical complete functions, as an example take the Fourier series because the mountain has many ups and downs, and will fit with the expansion up to as many terms as necessary to give me a good three dimensional resolution form of the mountain.

There will be many components of sines and cosines adding up to my final fit.

Does this mean that the mountain is composed by different bits of sines and cosines added up?

General Relativity gives us a complete set of functions to describe our observable universe and has been validated where ever it has been tested, i.e. it predicts and it fits known observations. It is a very successful physics theory , locality and all : no action at a distance, all interactions happen at (x,y,z,t) four dimensional points.

It is a successful theory and can be used to evaluate unobservable situations in the same way that there will be coefficients for all the fourier transform terms in the model above, but it makes little sense to tie up oneself in a knot about unphysical "predictions" in GR, i.e, that no experiment can be made and no observations of it. Physicists tend to trust the predictions because the parts that can be tested work. The rest is mathematics.

anna v
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  • Hi anna thank you for answering....I see your point, but nothing is taken away from GR by entertaining objects like paradoxes - even if they are invented to illustrate a positive feature - nevertheless have a historical meaning that should be kept in mind. – Lucy Meadow May 07 '15 at 21:10
  • Can I also add, that I don't think it's correct to keep 4D spacetime on the 'Robust' list, for now. This is because Julian Barbour pioneering work on Shape Dynamics demonstrates that time can be taken right out of the picture in a theory that is dynamically indistinguishable from GR. Bambours theory is currently being shifted in the direction of centre stage. If he's right, spacetime is feasible wrong as a physical reality – Lucy Meadow May 07 '15 at 21:13
  • I had not heard of the man so I googled. It is not correct that his "world view" is making a dent in the direction of current theoretical research. – anna v May 08 '15 at 03:26
  • ddyou don't sound like your very open to this, but FWIW the result of your googling is wrong.You probably used a simple query strong whih you can't do for a complex object.. I'll drop it because I think you've signalled your are closed to it true or not. – Lucy Meadow May 08 '15 at 17:45