# Space is flat?

geordief
I was watching a Horizon program the other night on the BBC and was interested that they were able to repeat the "triangle on the surface of a sphere" experiment on the universe as a whole.

When this experiment is performed on the surface of the Earth on a large enough scale the angles of the triangle don't add up to 180 degrees and shows that the Earth is not flat to someone even though they may not be able to leave the surface.

So , to recap, they were somehow able to draw these lines in the universe (I have no idea how!) and came back with the discovery that the angles of the triangle actually added up to180 degrees.

They said that this showed that space was flat and not curved!

My question is this.
If space is flat why is space-time curved?

Cyghost
From what I understand there are 3 main theories on the form of space.

1. "Big Crunch Theory" A closed universe (such as a sphere) with sufficient matter of all kinds to allow gravity to eventually halt the expansion of the cosmos. Expansion become contraction and the universe would disappear from where it came.

2. "Flat Universe" where space has a curvature of zero and where total matter equals critical density, meaning that the universe would have no boundary and expands forever eventually slowing in infinite time but by definition "Infinity" has no limit.

3. "Open Saddle Shape" where total matter is less then critical density and would expands forever and its acceleration is driven by dark energy (an anti gravitational force) is currently quite a popular theory.

Q: If space is flat why is space-time curved?
A: Basically it is due to the contribution of matter that distorts the fabric of space-time.
Similar to the effect on light by Gravitational lensing.

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My question is this.
If space is flat why is space-time curved?
Because the space is expanding in time.

geordief
thanks!

Cyghost
@ d3mm
As I previously said they are all but theories..
The WMAP can show what ever it wants, but how one interprets the mathematics, it is still just another theory ready to dispute.
But the fact is space-time geometry is manipulated by matter.

d3mm
What is the evidence for the curvature of space?

How does it deal with the results from WMAP survey?

As I previously said they are all but theories..

So are gravity and quantum mechanics, you will have to do better than "it's just a theory".

@ d3mm
The WMAP can show what ever it wants, but how one interprets the mathematics, it is still just another theory ready to dispute.
But the fact is space-time geometry is manipulated by matter.
And what "data" do you think confirms this fact? You seem to misunderstand how science works, which is unfortunate. The WMAP data cannot show "whatever it wants" -- it shows the actual universe. Then we have a theory that predicts what the CMB should look like. Then we compare these predictions with the WMAP data. Science occurs. Wash, rinse, repeat.

What is the evidence for the curvature of space?

How does it deal with the results from WMAP survey?
d3mm -- are you seeking answers to these questions or were you posing them to Cyghost -- can't tell.

d3mm
bapowell, I was asking Cyghost to defend his position.

Cyghost
Yes I think we are probably going a little off topic of the original question "If space is flat why is space-time curved?"
but I will say I certainly do not claim to agree or disagree to the 3 models I fore-mentioned as I was only presenting a few of the popular examples of late I have not once in this post stated that I disagree that space is flat so I'm not certain what I am supposedly defending but here is a link to your request for a response to your question.

Q : What is the evidence for the curvature of space?

http://science.nasa.gov/science-news/science-at-nasa/2011/04may_epic/

Also what is your definition of flat?

From what I understand WMAP measured the "curvature" of space to within accuracy to 0.6% of "flat"

Is that truly flat?

http://en.wikipedia.org/wiki/Euclidean_space

Q2: How does it deal with the results from WMAP survey?

How does your question even relate to the posters question of "If space is flat why is space-time curved?"
which I answered 3 times now (Where there is significant gravitation due to matter space-time will become curved)

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Cyghost
And what "data" do you think confirms this fact? You seem to misunderstand how science works, which is unfortunate. The WMAP data cannot show "whatever it wants" -- it shows the actual universe. Then we have a theory that predicts what the CMB should look like. Then we compare these predictions with the WMAP data. Science occurs. Wash, rinse, repeat.

I think you may have misunderstood what I was trying to say regarding (how one interprets the mathematics from the data received) I think it would be naive to simply "Wash, rinse, repeat." and not consider any other possibilities. To me that is not what science is about either (which apparently I seem to misunderstand) and I appreciate the personal attack BTW.
It's like saying ok we have received this data from WMAP and as you stated "we have a theory that predicts what the CMB should look like then we compare these predictions with the WMAP data"
What if there is another theory that also produces the same data outcomes?
Is that not possible?
To simplify it for you :
1+1 = 2.
4-2 = 2.
Different equation but same result.
Again you have taken this way off topic from the original question.

Also:
Because the space is expanding in time.
I'm not sure I agree with your answer to the question he asked "If space is flat why is space-time curved?

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geordief
.

Q: If space is flat why is space-time curved?
A: Basically it is due to the contribution of matter that distorts the fabric of space-time.
Similar to the effect on light by Gravitational lensing.

Is it possible to know why matter should have this effect on SpaceTime or is it simply a mathematical consequence that when we model the situation that the outcome resembles the dimpled cushion effect?

Does antimatter have the same effect?

If space time is severely distorted (as in the spinning binary black holes scenario ,say) would that create the opportunity for a massless object to travel practically instantly from one side of the (SpaceTime) region to the other a bit like in an anciently active area of the Earth you might dig down and cross millions of geological years in a very short space because the strata have been stretched and thinned at that place (in other places the same amount of geological years might take longer to dig through)?

clamtrox
And what "data" do you think confirms this fact? You seem to misunderstand how science works, which is unfortunate. The WMAP data cannot show "whatever it wants" -- it shows the actual universe. Then we have a theory that predicts what the CMB should look like. Then we compare these predictions with the WMAP data. Science occurs. Wash, rinse, repeat.

I think the point he was trying to make is that you can only measure the angular diameter distance of the acoustic peaks from CMB, and then you infer the curvature by comparing your observation to the model. Interestingly enough, there are also direct ways of measuring curvature, but so far our observations are not good enough for constraining it enough to be useful. You can check out http://arxiv.org/abs/1102.4485 for more details.

clamtrox
Is it possible to know why matter should have this effect on SpaceTime or is it simply a mathematical consequence that when we model the situation that the outcome resembles the dimpled cushion effect?

What kind of explanation would satisfy you? At some point you're going to have to take something for granted. The laws of physics can't explain themselves. For general relativity, what is taken for granted is that matter curves spacetime according to the famous Einstein equation, and everything else follows from this assumption (well, and a few others)

Does antimatter have the same effect?
It does seem likely but very difficult to verify. Antimatter is so rare and gravitation is so weak, it seems unlikely that we'll be able to confirm this any time soon

geordief
What kind of explanation would satisfy you?
Any kind at all (I mean any theory). I can understand that it is acceptable to make a hypothesis and to then to test it to death but why should any phenomenon not have a physical( maybe not the right word? preceeding?) cause.
Maybe mathematics are the fundamental reality (as was believed by Pythagoras(?) I think).

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clamtrox
Any kind at all (I mean any theory). I can understand that it is acceptable to make a hypothesis and to then to test it to death but why should any phenomenon not have a physical( maybe not the right word? preceeding?) cause.

And if you knew the cause, what makes you think you wouldn't be asking for the cause of the cause? Let's say I explain gravity by saying that there are these tiny invisible butterflies that fly around, pour glue into your watch to make it run slow and stretch space by flapping their wings. Would you feel that is a satisfactory explanation, or would you then ask: "but why butterflies?"

There is one perhaps more physical explanation for gravity, but unfortunately it has turned out to be very difficult to make it work. It turns out that the usual GR description of gravity is completely equivalent with the force being carried by virtual spin-2 particles (like electromagnetism is carried by photons). Unfortunately to describe the theory like this, you'd need to dress it into the language of quantum field theory, and that is a project that's still not quite finished.

geordief
And if you knew the cause, what makes you think you wouldn't be asking for the cause of the cause? Let's say I explain gravity by saying that there are these tiny invisible butterflies that fly around, pour glue into your watch to make it run slow and stretch space by flapping their wings. Would you feel that is a satisfactory explanation, or would you then ask: "but why butterflies?"

There is one perhaps more physical explanation for gravity, but unfortunately it has turned out to be very difficult to make it work. It turns out that the usual GR description of gravity is completely equivalent with the force being carried by virtual spin-2 particles (like electromagnetism is carried by photons). Unfortunately to describe the theory like this, you'd need to dress it into the language of quantum field theory, and that is a project that's still not quite finished.
I am predisposed to believe that I would almost certainly be asking for the "cause of the cause" (otherwise I would be a believer in a God -which I am not)

And I don't mind outlandish causes if they fill the gap.

But I didn't ask for a theory of gravity -just ,in particular why an object with mass should distort spacetime (aside from a mathematical explanation).

Or is that the be all and end all of gravity-objects with mass distort SpaceTime and no further questions on the subject are relevant? (I don't mean to come across as indignant!)

Are you saying that my question "what in particular causes an object with mass to distort SpaceTime?" is a nonsensical question with the only possible answer "because it does" or "because that is what gravity is"

d3mm
Cyghost

My question is about the overall shape of observable universe, not what happens locally in the vicinity of a large mass. I am asking which of the three theories you mention, do you believe is the most appropriate after new evidence such as WMAP and the accelerating expansion of the universe.

Different equation but same result.
Again you have taken this way off topic from the original question.
Yes, I'm aware that multiple theories can offer competing explanations for a given data set. The reason that I misunderstood what you wrote is because you were not being clear. You state that "The WMAP can show what ever it wants, but how one interprets the mathematics, it is still just another theory ready to dispute." How one interprets the mathematics? I guess you mean -- how one uses mathematics to explain the data. OK, got it. But it's still not "just another theory to dispute." There is an entire program for comparing the merits of competing theories given data, and yes, this program needs to be exercised in the face of any scientific data. The argument you seem to be advancing is not specific to the CMB -- it can apparently be applied to anybody of data. It is simply impossible to use induction to obtain a uniquely correct theory. So, I am interested in knowing how your argument differs from that made by Hume et al. hundreds of years ago regarding the problem of induction.

If you want to debate the merits of competing explanations for the CMB, then fine. If you are just pointing out the obvious limitations of all experimental science, then I think you are taking this thread way off topic.

I'm not sure I agree with your answer to the question he asked "If space is flat why is space-time curved?
His question has to do with the fact that if space is flat (in the sense that R, the curvature scalar, is zero), how is it that space-time is curved? It has to do with the fact that the spatial metric components, $a(t)x^i$, while indeed giving flat hypersurfaces, are function of time. In this case, the curvature scalar is non-zero,
$$R \propto \frac{\ddot{a}}{a} + \left(\frac{\dot{a}}{a}\right)^2$$.

Do you still not agree?

Cyghost
Cyghost

I am asking which of the three theories you mention, do you believe is the most appropriate after new evidence such as WMAP and the accelerating expansion of the universe.

I'd probably trust the astrophysicists on this and would say model of the universe that is “flat and infinite" (although I use the term infinite loosely as the visible region of space) it seems to match the results pretty closely.

There is always the possibility of some form of galactic foreground contamination also the long delays in releasing the results was confusing, or if data was incorrectly inserted such as if the wrong spectral index is used to convert the difference between power spectra at different frequencies into a point-source contribution, then there will be a systematic error in the cosmological parameters.

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clamtrox
But I didn't ask for a theory of gravity -just ,in particular why an object with mass should distort spacetime (aside from a mathematical explanation).

Okay, let me rephrase my answer more clearly: This question is not answerable using general relativity. That theory has nothing to say about the mechanism. If you want to invent something, like the butterflies I mentioned in the previous post, then if that satisfies you, fine. It would be even better if you could come up with a mechanism which has some observable effect on physics, like small deviations in the gravitation field around massive bodies or in the path of photons, or whatever. If the mechanism has observable consequences, then you can make experiments and decide whether it's true or not. If it's something you've invented to keep you sleeping at night (like the many worlds interpretation of quantum mechanics), that's possible too.

Let me give you another example. In quantum electrodynamics, you describe the interaction between electrons and photons. The theory is extremely successful and accurate - it can predict basically everything you can see, and more. However, an inquisitive soul like yourself might ask: what's the mechanism through which the photons and electrons interact? And to that question the theory has no way to answer; they simply do.

Cyghost
Yes, The reason that I misunderstood what you wrote is because you were not being clear.

Ok I may have been a little ambiguous with my statement regarding the WMAP.

Do you still not agree?

No :)

No :)
OK. What exactly do you disagree with?

EDIT: Or, "No", you agree?

PhyPsy
Cyghost

My question is about the overall shape of observable universe, not what happens locally in the vicinity of a large mass. I am asking which of the three theories you mention, do you believe is the most appropriate after new evidence such as WMAP and the accelerating expansion of the universe.

The recent WMAP data has narrowed the range of possible curvatures of the universe, but unfortunately, it still leaves open the possibilities of a universe with positive or negative curvature. I suppose you could say it makes the possibility of a flat universe more likely, but if the universe truly is flat, will any measurements ever make us 100% sure of its flatness? It seems like we're just doomed to continue narrowing the range of possible curvatures further and further without really putting the nail on a curvature of 0.

Cyghost
"No" I agree this time.
Space is Flat (By flat I mean parallel and no intersecting lines) - Space-time is curved

Just a quick question : "Probably off topic again"
If space time is curved, then even the most minimal curvature would eventually produce a circle. Does that suggest space-time is circular?

Interesting relative quote:
"I hold that space cannot be curved, for the simple reason that it can have no properties. Of properties, we can only speak when dealing with matter filling the space. To say that in the presence of large bodies space becomes curved, is equivalent to stating that something can act upon nothing. I, for one, refuse to subscribe to such a view" -- Nikola Tesla

The recent WMAP data has narrowed the range of possible curvatures of the universe, but unfortunately, it still leaves open the possibilities of a universe with positive or negative curvature. I suppose you could say it makes the possibility of a flat universe more likely, but if the universe truly is flat, will any measurements ever make us 100% sure of its flatness? It seems like we're just doomed to continue narrowing the range of possible curvatures further and further without really putting the nail on a curvature of 0.
Yes, very true. Even with extremely precise future measurements, there will always be some margin of error about true flatness. There are people who make statistical arguments about the geometry of the universe using Bayesian model selection: http://arxiv.org/abs/arXiv:0901.3354. The idea is that the flat universe model is simpler and more predictive than one with curvature, in the sense that one with curvature requires an additional tunable parameter. If the data disfavors the added extravagance of extra parameters, the associated model is considered less likely.

Of course, this is a statistical argument that is best applied to statistical models. I like to think that our theories of the universe are more than mere statistical models, that they say something about physical reality. In this sense, I am personally not sure how to interpret studies that use Bayesian model comparison as a means of interpreting physics.

Cyghost
Cyghost

My question is about the overall shape of observable universe, not what happens locally in the vicinity of a large mass. I am asking which of the three theories you mention, do you believe is the most appropriate after new evidence such as WMAP and the accelerating expansion of the universe.

As I mentioned I do tend to sway to the current flat universe hypothesis from the WMAP survey but what I was trying to say previously is, and although it is again off topic I feel I should explain myself, that although the data matches a flat-infinite universe to an approximate but fairly accurate calculation, that doesn't mean I am 100% convinced that it is the only concrete hypothesis as suggested. We cannot see past the CMBR and can only speculate as to what is beyond.

As an example say the universe contained a extremely minute curvature from both negative to positive degrees such as in a ripple of a wave form and they were precisely equal so when you make your calculations regarding wave dynamics it also produces a close match for WMAP survey data and appears flat. If you measure curvature from one end to the opposite the resulting curvature equals zero as both equal negative and positive curvature cancel each other out.

Another Example:
If you imagine a pool of water and you drop a stone in the centre and observe the rippling wave forms that emanate from the centre you will see the ripples spread further and further apart and the resulting the area within each wave peak increases with time including the distance between each peak of the wave form with similar basic characteristics of expanding universe.
Even if you were located close to the peak of one of the ripples you could never see past or over the adjacent ripples as they are basically a similar height and as the opposite side of the peak must have a negative curvature and the areas beyond the peaks would not be visible within your entire viewing area so essentially from peak to peak is the only observable area, although beyond that observable area more ripple do exist. So speculating if our observable universe exists within the area between two wave peaks of a rippling universe it would be safe to say would could not view past the CMBR and the resulting curvature would appear zero as from one peak to the next it must contain equal positive and negative curvatures as the curvature reverses at the point of the trough of the waveform.
It is basically the same flat surface that was original present before the event (Dropping the stone) but now with a more fluid constitution but as the wavelength of the ripples gets longer and longer, the effects eventually disappear completely and the ripples would have no effect on the observable universe and would appear as a flat universe and that nothing had previously existed beyond CMBR, but it doesn't confirm that the universe was always flat and infinite.
So for me just saying ok well we have survey data so that is the final answer is not fulfilling all possibilities.
This is just a couple of examples of how the WMAP survey data may be misinterpreted and I don't claim to fully comprehend the advanced physics involved of the data conversion but just offering the thought that the universe and our understanding of it is an evolving process and we should be open to alternate possibilities.