## is space-time flat or curved over time?

If space-time is flat (on large scale), why then does this [above] picture show curves? Would I be right to say that space time at any one moment is flat but over time it is curved?
 Recognitions: Science Advisor In this picture, the space is curved because the universe is expanding. Think of it like this, if we put a coordinate axis on this, we can specify what each axis is: Up-down is a spatial component of the unvierse, call it x. Into-out of the screen is also a spacial component of the universe, call it y. Left-right is time in this picture, call it t. So what you see is as t(time) increases, the size of the universe (in x and y) increases. That's basically what this diagram is showing, it's not really making any claims about the curvature of space-time.

Recognitions:
 Quote by Gill tunnel If space-time is flat (on large scale), why then does this [above] picture show curves? Would I be right to say that space time at any one moment is flat but over time it is curved?
In flat FRW, space is flat, but space-time is curved. That is to say, the space-space components of the curvature tensor are zero, but the space-time and time-time components are non-zero.

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Homework Help

## is space-time flat or curved over time?

... I got here in connection with another one. Apologies for the resurrect.

The pic looks to me like an artists representation of a Hartle-Hawking (or similar) model. These models have finite, boundaryless space with the time boundaryless in the past. (There is probably a better way of describing this but I haven't had my coffee yet.)

Isn't that what the funnel-grid in the pic is representing.
The lines going left to right (ish) represent time, while the circles represent space but only one dimension of space is being shown. So, in this model, space is not infinite, but loops around on itself. If you travel far enough in one direction, it says, you will eventually end up back where you started.

The artist has added some misleading details to make it more dramatic - for eg. the funnel of the Universe has been enthusiastically filled with all manner of objects ... this is wrong: there is no "space" in there for those objects to sit inside of. The artist also shows the quantum-fluctuation stage as a bright light shining in all directions ... including into the blackness outside the Universe which is also nonsense: there is no outside to the Universe: that is what "Universe" means.

I think we are not supposed to pay much attention to the pretty pictures - they are supposed to accompany the picture not be literally part of it. It is like those QM energy-level diagrams that also put the wavefunction on the level - using it as a horizontal axis.

Viewed like that - OPs question is suddenly easier to answer:
 If space-time is flat (on large scale), why then does this [above] picture show curves?
...because, in this model, the very-large scale space-time is not flat.

Consider:
... on the short-scale, the surface of the Earth is curved because it has hills and stuff on it.
... on the large scale it is flat because all the hills go up and down about the same amount and large areas without any hills are very flat to look at;
... on the very-large scale, the surface of the Earth is a sphere.

So it is with space and time.
This model proposes a spherically closed space with a curvy time that becomes a semicircle right at that nipple in quantum-fluctuations. If you could move backwards in time and kept going in that direction long enough, you'd find yourself heading back forward in time but on the other side of the Universe - much like if you started out going south, and kept going in a straight line, you'd eventually find yourself travelling north on the other side of the Earth.

It is also possible to model the Universe as having infinite space ... but harder to draw.
 You can represent 2D space quite well with a Terry's chocolate Orange. It can even go as far 2.5D. Full 3D requires a lot of identical images rotated around on top of each other. Doesn't really help here with the time component. An updated image might be better as flat - a slice of the universe - which would avoid many visual amibguities, like the quantum fluctuations you note.
 Well to be honest I allways considered dismissing dark energy entirely. There is too much cloak and dagger around this subject and not enough evidence to support it. What if spacetime is not straight at all? We all know that einstein said space can curve - what if its already curved out like a slumped-together carpet? We know that if you remove gravity then the local area will "level out". The big bang could have left severe instabilities in the spacetime web that could be leveling themselves off and thus causing the expansion of the universe - a stretched out carped is bigger than a slumped-together one. Why don't we notice it then? Well simply because its so faint that is undetectable. Its a foregone conclusion that there isn't enough mass in the universe to collapse it back together, but there also is nothing outside the observable universe as far as we know to slow the process down. I know what you were gonna say, that i've lost my mind. I know that there has been some thermal variance found in the CMBR that could support the dark matter theory, but the same results could also support mine. And it would answer your question! Now... is there something I missed about my theory?
 Recognitions: Homework Help What if space-time is actually pretzel shaped? Or some sort of 4D Klein Bottle? Perhaps that ring of space in the diagram is actually more of a starfish shape? If "dark energy" has too little evidence for you, where does that leave the other speculations? The way to sort through speculations is to figure out what extra stuff each one requires ... dark energy requires some sort of mass we cannot (yet?) see: which is pretty bad, but the "slumped together carpet" suggests a hitherto unknown and unnoticed that makes the curve happen that way: magic? Leaves the field kinda open. There are a lot of possible geometries whose local effects are too small to notice. In fact, there is an infinite number - they just have to play out so that they are all the same in the bit of the Universe we can see. How do we decide which of these to adopt for further research? Say "Hello" to my little friend: Occam's Razor; which simply advises accepting the proposition with the least amount of extraneous male bovine faeces. This guides the research quite well and the Razor cuts slightly differently with new observations. Perhaps some future astronomers will detect a huge crystal sphere enclosing the whole Universe ... but until then, the crystal-sphere theory is way way down the list of Things To Investigate. All these descriptions are provisional to new observations. When you se epictures like above claiming to represent some truth about the Universe - remember that it is not supposed to be an Absolute Truth - just a conditional one. And the simplest one we feel we can get away with at the moment.
 Yes, well, I agree, but all we can do is speculate as to the answer of the threader opener's topic, since none of of the proposed have actually been validated by empirical science, even Einsteins theory of relativity has come into question recently. But that still leaves the question how... If space is expanding then its the same amound of space that is just being "stretched", which means that the proposed image is somewhat correct, however if there is more space being created somehow, the result would be the same, it is just the visualisation of the proposed image that is incorrect. All we know is that space between matter (where gravity is insuficient) is expanding somehow, and that it is accelerating, anything else, particularly the "why", has yielded only circumstantial evidence. Now if we accept this image as valid, Gill, the image, i believe, doesn't show space curving through time, but it is a visual representation of rate of acceleration at which the universe is expanding and nothing else. If we follow the image from left to right: First there was hyperinflation, which slowed through time and as time passed further, the expansion of the universe began accelerating again.

 Tags curve, flat, space, time