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Comment by stareatgoats | Hacker News Reader

Quite OT, but these phenomena always reminds me of how wrong (popular understanding of) Einstein actually is. Whereas gravity according to that understanding warps the fabric of space itself, these pictures prove that gravity actually only appears to warp space.

I.e. our intuitive, euclidean concept of space is actually the most correct, albeit an abstract, inferred phenomenon.

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We certainly need the concept of Euclidean space in order to make sense of the phrase "warped space". Fortunately, our "everyday" space is almost Euclidean, so this condition is met. If we lived in a different place in Universe, not sure what our concepts could have been. But I think same applies to just any concept we derive from our observations. E.g., we would never be able to form a notion of ice if we lived near some star. But I can't see how your statement about "real" vs "apparent" follows from here.

"Real" vs "apparent" simply follows from what we can infer from the picture, i.e. the galaxies appear to be several because of the light-warping effect of gravity, in reality they are not.

Further, I don't think space (or time for that matter) are comparable to the notion of ice, but let's keep it simple for now :-)

How about this: we live in a rare oasis in the Universe where the things are more or less 'stable', and due to this, we can form more or less consistent concepts (not 100% consistent, but enough for most practical purposes). Beyond this oasis - who knows, maybe the notions of space and time themselves become fuzzy (not unlike ice, by the way - though you objected to comparison). And this view is not that far-fetched - look no further than quantum mechanics, which is an example of what happens when we cross the boundaries of the 'oasis'. We still can write formulas, but we don't understand the meaning. I personally believe that just everything we "know" - applies only in the vicinity of our habitat. Won't be surprised if all our observations about the Universe turn out to be illusions resulting from infinite warping of just everything :)

yes, I actually subscribe to this view too. We are observing things at the borders of the capacity of our instruments that is so far removed from our natural habitat as humans that we may never understand much more. I don't think we should give up however, and the distinction between appearances and reality is fundamental to proceeding further IMO.

To clarify, it seems to me probable that real space itself (and time for that matter) is/are exempt from such localized notions. They probably 'permeate' or 'contain' everything, have always done and will always do, regardless of location and scale. It is obviously possible that they may lose relevance at a certain scale, but that scale is nowhere near our current horizon AFAICT.

I'm not so sure about this exemption. It's just very difficult for us to reason about it. And even formulating a counter-argument in a meaningful way requires some notions we don't have. Tangentially related: http://www.paradise.caltech.edu/cook/Workshop/Physics/QMQues...

No, this phenomenon actually proves that space really is warped, otherwise you wouldn't see the light from behind a galaxy cluster because light follows a straight line.

Even the concept of 'warped' space itself indicates that the intuitive, euclidean concept is correct, the light does in fact not travel in a straight line, it follows a 'warped' line.

The difference between the two is that the 'warped' space is what we observe (because observing is an electromagnetic process, subject to gravity), 'real' space is something we can only infer (or observe in photos like in the linked article)

I don't think that's quite right. You can theoretically detect the local curvature of space by measuring the angles made by a sufficiently exact triangle. If space is flat, such a triangle will have interior angles that sum to a half turn. If it's curved, it will deviate from that. And that's something you can do more or less entirely locally and is a property of the space you're inhabiting.

We can know the Earth is round without any reference to Euclidean space or Euclidean coordinates- just trace out a big triangle and you could observe that the interior angles will sum to more than 180 degrees.

Right on! Gods bless the humble triangle, bane of charlatans. (it's been a long night of polishing the thesis and now... scotch... I'll see myself out.)

With all due respect, you don't seem to understand what I am saying: I completely agree that such measurements will show that space is curved, it's not like we disagree there. These measurements are however appearances, with the twist that such measurements provide the only viable map of locations.

The real space is useless for most intents and purposes (since our interactions are bounded by the properties of light and gravity, and thus appearances is what guides us).

It seems important to make the conceptual distinction however, and not confuse reality with appearances, in this case as well as every other.

No, it proves that the path of the visible photons we're detecting have been altered by forces of attraction.

I'd be interested to hear how you came to that conclusion, as these pictures show the complete opposite to me. In a vacuum, light takes the shortest distance between two points. That light is bent by gravity shows that gravity is changing what it means to be the "shortest distance". That is, space itself is being warped by the presence of mass.

Sure, maybe this explains better: The picture shows how light from a galaxy or galaxies from behind the galaxy cluster SDSS J0146-0929 are bent around it. It makes it "seem as though the galaxy is in several places at once".

The key word is "seem", which means that the light-bending characteristic of gravity make space seem like something it is not. Hope this helps.

"Seem" refers to the lens like nature or the warped space.

So, here's an example. Suppose you're in a toroidal space. It's an Asteroids world: you're in a cube, and if you pass through one wall you find yourself passing back into the cube from the opposite one.

If you look in the right place, you will see the back of your head- several times! So there's an illusion of seeing yourself in several places at one time. But toroidal space really is different from normal space (even if it's basically flat and Euclidean, the geodesics are different).

So it seems to me that you can have warped spacetime that produces illusions like duplicate galaxies.

Yea thanks, that is exactly my point; warped space produces illusory concepts of reality.

So, an apparent illusion of disagreement seems to have occurred ;-)

Right, but you seemed to be arguing that illusory images meant that the curvature itself was illusory, whereas in my toy universe space really is toroidal, and anyone using the existence of multiple images to suggest otherwise would be wrong (because I set up the universe that way). In fact, such images would be convenient evidence that space was actually toroidal. I don't see how Einstein rings are any different- they can't be evidence against actual curvature of actual spacetime. You'd expect double and triple images if spacetime was curved.

One prediction of GR is that if there were enough mass in the universe, the global curvature would be positive everywhere and the universe would close in on itself and be connected more like a sphere than a plane. If you moved in a straight line you would eventually return to your starting point. That doesn't seem to be the universe we live in (as far as anyone can tell, it's flat) but that certainly seems like a prediction about the actual curvature of actual spacetime.

I don't seem to be able to get my point across, but thanks for playing anyway. I really believe this point is of some philosophical and ultimately scientific value, however still largely misunderstood, but didn't really expect a forum comment (albeit on HN) to make a significant dent. Have a good day!

What made you come to this conclusion?

Tough one to answer since I believe I already explained the reasoning in the comment. I'll be happy to play if you think something is unclear there. The only rule is; you need to say what you think of this yourself.

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