# Thread: The curvature of spacetime

1. ## The curvature of spacetime

Spacetime this, spacetime that....RIIIIIIIGHT

Is science actually suggestingg that space and time are one? And is science actually suggesting that this "spacetime" is curved? Does that mean that out there (even in our solar system, even US) there is a sort of "fabric" that is curved?

If this is only a model that helps us understand physics, and is purely mathematical, i have no problem with this whatsoever. Otherwise, please explain.

Thank you

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Everything is only a model that helps us understand physics, and this is one of those. The key point is, you can choose different coordinate systems, and the words you use to explain time and space will be different. This is related to the concept of a reference frame, where you can choose the same local ways of measuring time and space and get different answers from someone in a different reference frame (generally in motion with respect to you). So given all that, one is tempted to ask, what will be the same for all local observers? Answer: the curvature of spacetime (defined mathematically, there is no need for a "fabric", though one is free to imagine it if it helps), the speed of light, and the equations of physics. In general, all other measured quantities will be different, in predictable ways.

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Originally Posted by afterburner
Spacetime this, spacetime that....RIIIIIIIGHT

Is science actually suggestingg that space and time are one? And is science actually suggesting that this "spacetime" is curved? Does that mean that out there (even in our solar system, even US) there is a sort of "fabric" that is curved?

If you look at drawings and computer representations of “curved spacetime,” the so-called “fabric” of space, what they show are the gravitational fields of astronomical bodies. The field lines are curved and are placed close together, so that they look like a “fabric”, a curved cloth “fabric”. That’s all this so-called “fabric” is, curved field lines drawn on paper or on a computer screen.

4. sam 5 hit the head on the nail. The curvature of space time is just a way to describe the gravitational effects of large massive bodies. The space time corralation between space and distance. kinda like how we measure distance in how long (time) it takes light to travel 9,460,530,000,000 km

5. Originally Posted by afterburner
Is science actually suggestingg that space and time are one?
Three, but that's just me

6. I think you meant four. Length, breadth, width. Oh, and time. This curvature of the fabric of space time is a little confusing. We are not saying that the shortest distance between two points is not a straight line. It is. sort of,. generally. The forces of gravity are very strong. The cumulative gravity of the whole universe is less than that force that is expanding it. Your straight line may be distorted by strong gravity fields like groups of galaxies and black holes. Space is three dimensional and then there's time. Which to me seems to be the record of a moment. Thats in space and time. Remembering that its just the human race that measures the passage of time. Nothing else cares.

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Nothing else cares.
So maybe an important constituent of conciousness is the awareness that time can be quantified....and measured.

8. Originally Posted by astromark
I think you meant four.
No.

Details later.

9. Because of the relativistic distortions of both space and time that occur when objects travel near the speed of light (well, any speed, actually, but it only becomes noticeable at high speeds), it becomes very convenient conceptually and mathematically to consider time as just another dimension.

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A concept of time and space must clearly be a part of basic intelligence. That they appear different proves that there is some difference, and that they can be unified by relativity is probably a little like the reason that the different forces can be unified at high energy. The role of consciousness is a pretty big question in any of this, I'm not sure much is understood about the connection between intelligence, being aware of self, and being conscious, but that's a different thread!

11. Originally Posted by Ken G
That they appear different proves that there is some difference,
I'm not so sure. What about the two different views of the same cylinder, one end-on, one from the side. One view appears rounded, the other squared off. Though they appear different, they are still of the same cylinder.

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## neutrino flux density vs. curvature of spacetime

Originally Posted by Sam5
If you look at drawings and computer representations of “curved spacetime,” the so-called “fabric” of space, what they show are the gravitational fields of astronomical bodies. The field lines are curved and are placed close together, so that they look like a “fabric”, a curved cloth “fabric”. That’s all this so-called “fabric” is, curved field lines drawn on paper or on a computer screen.
Sam5. There's something else here, too. Any model of curved spacetime will be superimposed three dimensionally on an equivalent vector field of the ambient neutrino sea density. Any change in the mass of a central body that increases or decreases the local spacetime "curvature" will necessarily also distort the ambient neutrino spectra flowing through that region of spacetime. Such a distortion will propagate at c...neutrino sea velocity, coincident with spacetime distortion velocity....hence gravitational wave coincident with a change in the ambient neutrino sea flux density. Since there is no region of space known to be free of neutrinos, these two phenomena are inextricably linked.
Should neutrinos be shown definitively not to be massless, but instead, massive, and subluminal, then the two effects will propagate at two different speeds, like p-wave, s-wave seismology....and detectors located in three space...here(Earth), Mars, and an asteroid, could in principle triangulate the source of a neutrino burst, or gravitational wave. A larger baseline, here, Alpha Centauri planet?, Zeta Reticuli planet?...will give better resolution. Pete.

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Originally Posted by hhEb09'1
I'm not so sure. What about the two different views of the same cylinder, one end-on, one from the side. One view appears rounded, the other squared off. Though they appear different, they are still of the same cylinder.
The side of a cylinder is the same as its end?? That they are part of the same cylinder is another issue entirely. You and I are in the larger equivalence class of "humans", that does not make us the same.

14. Originally Posted by hhEb09'1
I'm not so sure. What about the two different views of the same cylinder, one end-on, one from the side. One view appears rounded, the other squared off. Though they appear different, they are still of the same cylinder.
I like the example of the fold-up paper coffee cup. Look down upon it, it's a circle. Look at it from one side, it's a square. Look at it from the perpendicular side, it's a triangle.

Incidentally, regarding spacetime curvature, probably the best explanation is Einstein's own words, in the book Relativity by Albert Einstein.

He uses a "hotplate" metaphor that is down-to-earth and understandable.

Space and time aren't exactly the same--in any frame of reference within a spacetime region small enough that spacetime can be regarded as nearly flat, the spacetime metric has negative coefficients for space coordinates and a positive coefficient for time coordinates. However, a different frame of reference will have different negative and positive coefficients--and some of the time from one frame of reference is mixed with the space of the other, and vice-versa. This results in, among other things, the "Twin Paradox". The (more difficult than the above) book "Exploring Black Holes: Introduction to General Relativity" by Wheeler and Taylor, explains this in detail, showing the mathematics.

Todd

15. Originally Posted by Ken G
The side of a cylinder is the same as its end??
I didn't say that at all.
That they are part of the same cylinder is another issue entirely.
It is the issue. You said "that they appear different proves that there is some difference" in talking about space and time. The example I gave was to illustrate that there can be two different appearances of the same thing. That there are different appearances does not prove that there is some difference, although there could still be a difference.

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Originally Posted by hhEb09'1
You said "that they appear different proves that there is some difference" in talking about space and time. The example I gave was to illustrate that there can be two different appearances of the same thing.
My point is simply that if two things are identical, they cannot be perceived as different. I hardly think that is a debatable issue. I'm aware that space and time can be transformed into each other when you change reference frames. You can also transform two 5 dollar bills into a ten dollar bill, and buy the same stuff, but that doesn't make them the same either. Choose your favorite analogy, there still has to be some difference or there can be no perception of difference. The entire universe is infused with this principle-- we have a principle that says spatial translations don't change things, but translations in age of the universe change things dramatically. I personally think it is a huge misnomer that people think relativity tells us time and space are the same.

17. Originally Posted by Ken G
My point is simply that if two things are identical, they cannot be perceived as different. I hardly think that is a debatable issue. I'm aware that space and time can be transformed into each other when you change reference frames. You can also transform two 5 dollar bills into a ten dollar bill, and buy the same stuff, but that doesn't make them the same either. Choose your favorite analogy, there still has to be some difference or there can be no perception of difference.
I dunno, my example/analogy sure seems to hold up. It's the same cylinder (i.e., identical, not just two similar cylinders) but the two perceptions are certainly different.
I personally think it is a huge misnomer that people think relativity tells us time and space are the same.
They may not be the same.

OTOH, You keep using that word. I do not think it means what you think it means.

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Originally Posted by hhEb09'1
I dunno, my example/analogy sure seems to hold up.
That's called "reasoning by analogy"-- you make an analogy and act as though it was evidence in support of your point. But the point that transcends all analogies is that a spacelike translation is different from a timelike one, in all reference frames. They are fundamentally different things.
Originally Posted by hhEb09'1
You keep using that word. I do not think it means what you think it means.
Literally, I know that a misnomer is a bad name for something, but I used it because in relativity it is essentially the name of space and time, i.e., as how they are labeled, that is fairly interchangeable (to within the minus sign that tdadvance mentioned). I really just mean misnomer in the sense of a confusing terminology, and that is the extent to which I called the overinterpretation of the similarity of space and time as a misnomer.

19. Originally Posted by Ken G
That's called "reasoning by analogy"-- you make an analogy and act as though it was evidence in support of your point.
No, it's a counterexample to your assertion. I wasn't really making an analogy. Just because two things look different doesn't mean that they are not actually the same.
But the point that transcends all analogies is that a spacelike translation is different from a timelike one, in all reference frames. They are fundamentally different things.
You're talking about abstract theory, then? Not reality? We don't yet know that for sure.

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Originally Posted by Ken G
(defined mathematically, there is no need for a "fabric", though one is free to imagine it if it helps),
Originally Posted by Sam5
The field lines are curved and are placed close together, so that they look like a “fabric”, a curved cloth “fabric”. That’s all this so-called “fabric” is, curved field lines drawn on paper or on a computer screen.
Both of these are correct, and I don't have a site saved to easily access a screen that shows this graph like picture, but it is certainly very useful to see, if you haven't.

However, now that we know that the vacuum of space is not empty, that is is made up of something, namely Dark Matter/Dark Energy, there is most certainly, a fabric of space/time.

Please, Ken, Sam, or anyone else, see if this statement about the fabric of space/time seems reasonable.

When you look at that graph paper view of the earth or sun causing a 'dent' in the graph, showing how things would 'fall' (spiral with velocity) into the 'dent', portaying how gravity would work. That is showing how 'mass' in a particlular location affects (curves) space/time, and the graph around the 'dent', the fabric is dark Matter/Dark energy...so the fabric of space/time is gravity.

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I think the words are somewhat arbitrary, what matters is that one has a picture that is useful for applying the necessary theory. Occam's razor suggests that the theory itself include no "fabric" in any literal sense, as it is not an essential component, but the equations are and if imagining a fabric helps apply them, then it has pedagogical value. I do think it is important to distinguish pedagogically useful terms from well established elements of "reality".

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Originally Posted by RussT
When you look at that graph paper view of the earth or sun causing a 'dent' in the graph, showing how things would 'fall' (spiral with velocity) into the 'dent', portaying how gravity would work. That is showing how 'mass' in a particlular location affects (curves) space/time, and the graph around the 'dent', the fabric is dark Matter/Dark energy...so the fabric of space/time is gravity.
Actually, that "graph" or "fabric" you are looking at called "events" in GR (think of it as the coordinates of spacetime, so we can measure the distance between two events). The graph is nothing more than a visualization of the "shape" of or the location of events in, spacetime.

As Grey so clearly pointed out(in another thread), Spacetime curvature is nothing more than GR using non-Euclidean geometry in describing the path lengths of test particles. Dark matter/Dark Energy would not be the "graph", but would change(as does stress-energy)the way the "graph" appears.

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Originally Posted by Tensor
Actually, that "graph" or "fabric" you are looking at called "events" in GR (think of it as the coordinates of spacetime, so we can measure the distance between two events). The graph is nothing more than a visualization of the "shape" of or the location of events in, spacetime.

As Grey so clearly pointed out(in another thread), Spacetime curvature is nothing more than GR using non-Euclidean geometry in describing the path lengths of test particles. Dark matter/Dark Energy would not be the "graph", but would change(as does stress-energy)the way the "graph" appears.
I think the term “fabric of space-time” is merely a metaphor.

3-D grid lines for Euclidean space would be like 3-D “checkerboard” grid lines, with no “warp” in them.

3-D grid lines for relativity would be warped around massive objects. But also, 3-D grid lines for gravitational potential points would also be warped around massive objects.

It is these imaginary grid lines that is what the “fabric” metaphor refers to, as in this drawing on the cover of an issue of Scientific American magazine:

http://i4.tinypic.com/103vez8.jpg

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Originally Posted by Sam5
I think the term “fabric of space-time” is merely a metaphor.

3-D grid lines for Euclidean space would be like 3-D “checkerboard” grid lines, with no “warp” in them.

3-D grid lines for relativity would be warped around massive objects. But also, 3-D grid lines for gravitational potential points would also be warped around massive objects.

It is these imaginary grid lines that is what the “fabric” metaphor refers to, as in this drawing on the cover of an issue of Scientific American magazine:

http://i4.tinypic.com/103vez8.jpg
Bingo, Sam5, good job.

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Originally Posted by Tensor
Actually, that "graph" or "fabric" you are looking at called "events" in GR (think of it as the coordinates of spacetime, so we can measure the distance between two events). The graph is nothing more than a visualization of the "shape" of or the location of events in, spacetime.
I agree 100%. The graph was designed to be able to depict these event points in a visually meaningful way, and it works extremely well, so well in fact, that everyone focuses on the curvature around the event point. And yes we measure the distance between these event points in a GR coordinate way, but the fabric of space is really all about the rest of the graph, between the event points, which is Gravity.

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Originally Posted by Tensor
Bingo, Sam5, good job.
Thanks. I should have said that years ago. Sometimes it take me years to figure out exactly how to say something in the simplest most basic way.

27. Title: Vacuum Energy: Myths and Reality
Authors: G.E. Volovik

We discuss the main myths related to the vacuum energy and cosmological constant, such as: ''unbearable lightness of space-time''; the dominating contribution of zero point energy of quantum fields to the vacuum energy; non-zero vacuum energy of the false vacuum; dependence of the vacuum energy on the overall shift of energy; the absolute value of energy only has significance for gravity; the vacuum energy depends on the vacuum content; cosmological constant changes after the phase transition; zero-point energy of the vacuum between the plates in Casimir effect must gravitate, that is why the zero-point energy in the vacuum outside the plates must also gravitate; etc. All these and some other conjectures appear to be wrong when one considers the thermodynamics of the ground state of the quantum many-body system, which mimics macroscopic thermodynamics of quantum vacuum. In particular, in spite of the ultraviolet divergence of the zero-point energy, the natural value of the vacuum energy is comparable with the observed dark energy. That is why the vacuum energy is the plausible candidate for the dark energy.

Read more (66kb, PDF)

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## Spacetime

Originally Posted by Tensor
Bingo, Sam5, good job.
So spacetime is really just a mathematical construction based on acceleration/gravity and spacetime is not a "real" entity?

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Define "real".

30. Originally Posted by Ken G
Define "real".
'blue on Tuesdays, red on Wednesdays, and of indeterminate colour on other days'

Spacetime has to be as real as space, or time, right?

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