What does this mean?.

now there is no space in that corner — elucid

There isn't any corner either: the corner's moved with the space. Or: the space moving is the corner moving.

Hi,

Suppose there is some space and a small corner of it moves, now there is no space in that corner which means the space in that corner is non-existent. Correct me if I am wrong. — elucid

Suppose there is some space and a small corner of it moves, now there is no space in that corner which means the space in that corner is non-existent. Correct me if I am wrong. — elucid

Space doesn't bend, spacetime curves around a mass. This means that a clock located within the proximity of a mass will run slower than a clock located away from the mass. It also means that any matter or energy traveling in the proximity of that mass will be influenced by this curvature and its path will bend. We call that curvature gravity.

Ok, thanks for clearing that up. I must have misunderstood people talking about space curving. — elucid

Spacetime isn't an actual observable thing either, it's a mathematical tool — leo

For instance the phenomenon of gravitational lensing can be explained by saying that it is the trajectory of light that bends, rather than some undetectable space or spacetime — leo

So that thing that creates the separation between objects is only a mathematical tool. — staticphoton

And whatever it is that magically bends the light is more detectable than the curvature of "non existent" spacetime. — staticphoton

Yeah Einstein was an idiot — staticphoton

Not "bends the light", "bends the trajectory of light". When you launch a ball horizontally its trajectory gets bent right? Same idea. Even in Newton's theory of gravitation it is predicted that light gets deflected by gravity, its prediction is simply less accurate — leo

Otherwise you might as well say that a rock falls to the ground because the space between the rock and the ground shrinks. See the fallacy? — leo

Einstein agreed that spacetime is a tool of thought, not an actual thing, it's people like you who don't understand him — leo

So that thing that creates the separation between objects is only a mathematical tool. — staticphoton

There's not a "thing" that creates separation between objects. There's just the facts of their extensional relations — Terrapin Station

Have you ever heard of matter-antimatter pair production out of the vacuum of space? — staticphoton

Where is your explanation for the reason the "trajectory of light" bends? You accuse me of reification and yet you are treating a "trajectory" like it is a thing. It is not. — staticphoton

And the reason Newton predicted light bending is because he believed light to be strictly a particle. — staticphoton

The theory of general relativity offers a wonderful explanation of how matter and energy move around other matter, it is not "the truth", but a well crafted model that works extremely well within its limits. — staticphoton

The effects of time-space shrinking as you approach a massive object are well demonstrated. Time dilation is real. — staticphoton

May I ask how familiar are you with General Relativity? Are you mathematically trained to understand Einstein's application of differential calculus, tensors, and geodesics to develop the concept of space-time curvature? Because if not then you are just repeating somebody else's interpretation. — staticphoton

And I'm sure you understand Einstein really well, maybe as not to derail this thread you can start your own thread to school me about the real Einstein. — staticphoton

Sure, I have also read Einstein's historical papers on special and general relativity, have you? — leo

Einstein knew very well spacetime is a human creation, a tool of tought, that curved spacetime doesn't explain gravity, it's just one complicated but mathematically elegant way to describe it. — leo

It is inconceivable that inanimate Matter should, without the Mediation of something else, which is not material, operate upon, and affect other matter without mutual Contact…That Gravity should be innate, inherent and essential to Matter, so that one body may act upon another at a distance thro' a Vacuum, without the Mediation of any thing else, by and through which their Action and Force may be conveyed from one to another, is to me so great an Absurdity that I believe no Man who has in philosophical Matters a competent Faculty of thinking can ever fall into it. Gravity must be caused by an Agent acting constantly according to certain laws; but whether this Agent be material or immaterial, I have left to the Consideration of my readers.[5]
— Isaac Newton, Letters to Bentley, 1692/3

There's not a "thing" that creates separation between objects. There's just the facts of their extensional relations. — Terrapin Station

Methinks it works like how a 2D space (a flat sheet of paper) bends in 3D space and leaves behind 3D space. — TheMadFool

A--B
|  |
D--C

Another approach that aims to reconcile the apparent passage of time with the block universe goes by the name of causal set theory. First developed in the 1980s as an approach to quantum gravity by the physicist Rafael Sorkin — who was also at the conference — the theory is based on the idea that space-time is discrete rather than continuous. In this view, although the universe appears continuous at the macroscopic level, if we could peer down to the so-called Planck scale (distances of about 10–35 meters) we’d discover that the universe is made up of elementary units or “atoms” of space-time. The atoms form what mathematicians call a “partially ordered set” — an array in which each element is linked to an adjacent element in a particular sequence. The number of these atoms (estimated to be a whopping 10240 in the visible universe) gives rise to the volume of space-time, while their sequence gives rise to time. According to the theory, new space-time atoms are continuously coming into existence. Fay Dowker, a physicist at Imperial College London, referred to this at the conference as “accretive time.” She invited everyone to think of space-time as accreting new space-time atoms in way roughly analogous to a seabed depositing new layers of sediment over time. General relativity yields only a block, but causal sets seem to allow a “becoming,” she said. “The block universe is a static thing — a static picture of the world — whereas this process of becoming is dynamical.” In this view, the passage of time is a fundamental rather than an emergent feature of the cosmos. (Causal set theory has made at least one successful prediction about the universe, Dowker pointed out, having been used to estimate the value of the cosmological constant based only on the space-time volume of the universe.)

Space isn't a thing in itself that can bend. — Terrapin Station

The general theory of relativity brought with it a decisive change in this point of view. Space-time and matter were found to be interdependent, and there was no longer any question, which was the more fundamental of the two. Space-time was also found to have its own inherent degrees of freedom, associated with perturbations of the metric - gravitational waves. Thus, space can exist and change with time in the absence of electrons, protons, photons, etc.; in other words, in the absence of anything that had previously (i.e., prior to general relativity) been subsumed by the term matter.

A more recent trend, finally, has been toward a unified geometric theory of all fundamental interactions, including gravitation. Prior to the end of the 1970’s, such a program seemed unrealizable; rigorous theorems were proven on the impossibility of unifying spatial symmetries with the internal symmetries of elementary particle theory. Fortunately, these theorems were sidestepped after the discovery of supersymmetric theories. In these theories all particles can be interpreted in terms of the geometric properties of a multidimensional superspace. Space ceases to be simply a requisite mathematical adjunct for the description of the real world, and instead takes on greater and greater independent significance, gradually encompassing all the material particles under the guise of its own intrinsic degrees of freedom. In this picture, instead of using space for describing the only real thing, matter, we use the notion of matter in order to simplify description of superspace. This change of the picture of the world is perhaps one of the most profound (and least known) consequences of modern physics.

What would it mean for there to be a ripple in "the facts of their extensional relations"? — petrichor

Anyway the reason I said what I said about an N dimensional space bending in an (N+1) dimensional space is for a reason that appeals to my and hopefully other's intuitions. If a particular N dimensional space is to "bend" then it requires the next higher dimension to do it in. Now that I think of it might just be the right interpretation because take a flat sheet of paper (2 D space) and "bend" it. What do you notice? It acquires a 3 D form. — TheMadFool

I am no Einstein expert, and I don't pretend to deeply comprehend his theory, but what you are saying runs contrary to the impression I've gotten. Can you point me to a place where he expressed such thoughts? — petrichor

For one thing, Einstein's theory is often appreciated for restoring a local picture of gravity, of solving this problem that Newton expressed

But this influence can only be communicated if the trampoline surface (spacetime) is "something", if it has a fabric, if you will. One part in it pulls down on an adjacent part, which pulls down on the next adjacent part, and so on. It is like a chain, with each link pulling the next. If I pull on a chain you are attached to, this is not spooky action at a distance. It is entirely local. Every causal influence involves contact action. — petrichor

Also, notice that we recently measured gravitational waves, or ripples in spacetime. Can we make sense of this if space is as Terrapin Station describes? — petrichor

Speaking of degrees of freedom of space, what about standard big bang theory? Scientists speak of the space itself between galaxies expanding, even accelerating in its expansion. It apparently isn't simply a matter of them having been close together and then moving apart. The analogy often given is of drawing dots on balloon and then blowing it up. This is why galaxies far apart can be "moving" away from one another faster than the speed of light, and thus falling behind the cosmic event horizon. The objects can't move faster than light. But space can expand fast enough to make distances between objects grow at such a rate that light cannot cross it fast enough to bridge the gap. How would you understand any of this without thinking of space as "something" which changes its form? — petrichor

I tend to think space has to be something. And I strongly tend toward a belief that all forms of causality must be local and work by contact action. This, for me, makes the notion of spooky action-at-a-distance problematic. I strongly sympathize with Newton in the quote I gave earlier. — petrichor