space-time:fabric, foam, or what?

[tomc]

Hi,

 

I am not a scientist so my understanding of space-time is based on books, magazine articles, and internet searches that are light on math.

 

If space-time is a fabric or foam that can be warped, what makes up the fabric or foam? From what I understand, so far, string and M theories may fit in somewhere.

 

Do strings make up the "membrane" in M theory? Is this "membrane" the fabric or foam of space-time? I am probably way off track and thought I might find some answers here before I become terminally confused.

 

Thanks,

 

Tom C

[Severian]

In my opinion, we should simply regard space and time as a "rule" for determining a "distance" between two events. So all events have a particular property with respect to any other event called "distance" and how these distances are related is give by the "rule" of space-time (e.g. a Minkowski metric). The bending of space-time is then simply an alteration of this rule.

[Martin]

Tom C,

what Severian says here is precisely the idea of space and time we have from classic vintage-1915 General Relativity. GR is still the best theory of spacetime geometry and gravity that we have. I don't see how what Sev says could be improved, as a concise statement.

 

In my opinion, we should simply regard space and time as a "rule" for determining a "distance" between two events. So all events have a particular property with respect to any other event called "distance" and how these distances are related is give by the "rule" of space-time (e.g. a Minkowski metric). The bending of space-time is then simply an alteration of this rule.

 

Ideas like superstring and M may well be irrelevant, and so far don't provide a mathematical model of the continuum that can serve as a satisfactory replacement. Ideas like "fabric" and "spacetime foam" are as yet merely verbal---unfortunately they have not been translated into usable unambiguous mathematical models.

 

It's anybody's guess what new math model of spacetime will eventually replace the one implemented in GR. If you want some suggestion of what it might look like, I would recommend Ambjorn and Loll's article in Scientific American---I have a link in my sig.

 

What they describe is more recent than anything you can read about in a Brian Greene or Stephen Hawking book. And looks to me considerably closer to the goal of a new continuum, a quantum spacetime geometry. Actually Ambjorn and Loll's model derives from a Stephen Hawking idea going back to 1980s which hit a snag. Ambjorn and Loll removed a key roadblock around 1998 and gave it a new start, after which the approach made a lot of progress.

 

For now, until some new quantum continuum model emerges as a clear favorite and is tested with real data, we have to adhere to GR. In terms of tested proven theories we don't have any real alternative. It's the best theory of gravity, and the best model of what spacetime geometry is, that we have.

 

In GR, geometry is represented by a metric a mathematical tool for specifying distances which was defined around 1850 by a young fellow named Riemann. The message of GR is that all there is is the metric---geometric relationships among events. Apart from geometry there is neither space nor time. Indeed the gravitational field is realized as the metric itself---gravity equals geometry.

 

The thing to notice is that a metric (as invented by Riemann and improved by Einstein and the fellow Sev mentioned, named Minkowski) might not be the only way to represent geometry. What people like Loll are trying to do, and people like Laurent Freidel, is to come up with a definte math object which will be as useful as the metric-on-a-manifold developed during the period 1850-1915 by Riemann, Minkowski, Einstein and others. Satisfactory progress will depend on developing a new way to present the universe's dynamically changing geometry as a usable math object that people can calculate with and check against data.

 

The neat thing about Ambjorn and Loll's approach is that they can simulate little quantum universes in the computer. Have them come into existence, evolve, stop them and study them, evolve some more, go out of existence.

They have simulated millions of universes. They can accumulate statistics on them, correlations. Each universe has an amplitude (a kind of probability weighting) and they are able to average up their universes, to derive a kind of path integral or average geometry. Under the simplest assumptions this turns out to be a classic spacetime geometry solving the GR equation---that is, it turns out to be the right thing. This happened this year.

 

It was a first. Classic 4D universe emerging from a messy quantum chaos. Taking shape by itself as a weighted average of many random universes (individually wacky irregular uncertain unsmooth without even a fixed dimensionality at small scale.)

 

I hope you have a look at the Loll SciAm link. What they did this year does not prove that their approach is the final answer. All it shows is what the other people will have to duplicate with their other approaches. It raises the bar and indicates what to expect from a new model quantum continuum. (And of course it could be right too, but until testing nobody can tell right, the main thing now is to move ahead.)

Edited December 5, 2008 by Martin

[iNow]

Great post, Martin.

[tomc]

Thank you, Martin and Severian, for your informative replies.

 

I believe that I now have a more reasonable approach to further research the concept of space-time.

 

Tom C

[granpa]

the answer is:

 

there is one flock of sheep in Scotland and they are black on one side.

Edited December 7, 2008 by granpa

[tomc]

Granpa,

 

I am not sure how to interpret your answer.

 

Tom C

[iNow]

TomC,

 

I'm pretty sure granpa was not trying to assist with your question, and was instead citing the final line of a well-known math joke. Why he did this, I have no clue, but you really shouldn't worry much about it since it's not relevant to your inquiry.

 

 

A mathematician, a physicist, and an engineer were traveling through Scotland when they saw a black sheep through the window of the train.

"Aha," says the engineer, "I see that Scottish sheep are black."

"Hmm," says the physicist, "You mean that some Scottish sheep are black."

"No," says the mathematician, "All we know is that there is at least one sheep in Scotland, and that at least one side of that one sheep is black!"

 

 

He may have been trying to use allegory or illusion to suggest that just because we interpret the information we have about the universe in a specific way does not mean that our interepretation is correct, nor that we have all of the information we need to make any such assumptions. Where this approach fails, of course, is that we can apply this "lack of complete information" assertion to just about anything we study. I see no reason to give up in the face of incomplete data, myself... no reason to just throw our hands in the air as a result. That would be silly. Quite the opposite, it should motivate us to learn more, by asking questions and looking for answers like you have here.

[snp.gupta]

the answer is:

 

there is one flock of sheep in Scotland and they are black on one side.

 

TomC,

 

.....final line of a well-known math joke. Why he did this, I have no clue, but you really shouldn't worry much about it since it's not relevant to your inquiry.

 

 

A mathematician, a physicist, and an engineer were traveling through Scotland when they saw a black sheep through the window of the train.

"Aha," says the engineer, "I see that Scottish sheep are black."

"Hmm," says the physicist, "You mean that some Scottish sheep are black."

"No," says the mathematician, "

All we know is that there is at least one sheep in Scotland, and that at least one side of that one sheep is black!"

 

 

Sir,

 

Does this “single sheep with one side black” really exist???

 

I will ask more directly, Is space-time continuum really required????

[iNow]

I presume it would depend entirely on which math (which set of assumptions... which system, etc.) you are using. The word "manifold" and the name "Minkowski" come to mind.

[north]

Hi,

 

I am not a scientist so my understanding of space-time is based on books, magazine articles, and internet searches that are light on math.

 

If space-time is a fabric or foam that can be warped, what makes up the fabric or foam?

 

THIS is the ultimate question and of which there is NO answer by anybody

 

I have asked this question for years

 

space is a consequense of matter

 

time is a mathematical concept , based on the fundamental movement(s) of energy and matter

 

time is NOT in any way a substance

[snp.gupta]

THIS is the ultimate question and of which there is NO answer by anybody

 

I have asked this question for years

 

space is a consequense of matter

 

time is a mathematical concept , based on the fundamental movement(s) of energy and matter

 

time is NOT in any way a substance

 

:-)'Space-time continuum' is that required really any where????, even as a concept???

[Martin]

In my opinion, we should simply regard space and time as a "rule" for determining a "distance" between two events. So all events have a particular property with respect to any other event called "distance" and how these distances are related is give by the "rule" of space-time (e.g. a Minkowski metric). The bending of space-time is then simply an alteration of this rule.

 

:-)'Space-time continuum' is that required really any where????, even as a concept???

 

Gupta sir, you have asked this question twice now, with many interrogation marks and emoticons ????

 

How about instead of asking again you read and think about what Sev said in post #2.

 

Personally I would of course be pleased if you would also read what I said in post #3 supporting what he said. And also if you would read the short SciAm article by Loll and Ambjorn that I referred to, but that would just be icing on the cake.

 

You are not asking an especially original question, and in any case it is one which has already been effectively answered by Severian. He is a working experimental particle physicist and he says that spacetimecontinuum is NOT required.

 

Forget the continuum, he says, focus on the geometrical relationships. Einstein said essentially the same thing in 1916. Sev's statement in #2 is sophisticated, but as always with him (in my experience) it is consistent with conventional mainstream thinking. The guy supervises grad students doing their PhDs, so listen and ask followup questions to what he says.

 

We have to be on the lookout here for egomaniacs with delusions of grandeur----people who don't listen, ask merely rhetorical questions, think their own ideas are especially brilliant, and generally act like jerks.

 

If on the other hand you want to engage me on the topic, read the SciAm article I cited in post #3 for starters and ask about that. It is the Loll link in my sig.

[north]

Tom C,

what Severian says here is precisely the idea of space and time we have from classic vintage-1915 General Relativity. GR is still the best theory of spacetime geometry and gravity that we have. I don't see how what Sev says could be improved, as a concise statement.

 

 

 

Ideas like superstring and M may well be irrelevant, and so far don't provide a mathematical model of the continuum that can serve as a satisfactory replacement. Ideas like "fabric" and "spacetime foam" are as yet merely verbal---unfortunately they have not been translated into usable unambiguous mathematical models.

 

It's anybody's guess what new math model of spacetime will eventually replace the one implemented in GR. If you want some suggestion of what it might look like, I would recommend Ambjorn and Loll's article in Scientific American---I have a link in my sig.

 

What they describe is more recent than anything you can read about in a Brian Greene or Stephen Hawking book. And looks to me considerably closer to the goal of a new continuum, a quantum spacetime geometry. Actually Ambjorn and Loll's model derives from a Stephen Hawking idea going back to 1980s which hit a snag. Ambjorn and Loll removed a key roadblock around 1998 and gave it a new start, after which the approach made a lot of progress.

 

For now, until some new quantum continuum model emerges as a clear favorite and is tested with real data, we have to adhere to GR. In terms of tested proven theories we don't have any real alternative. It's the best theory of gravity, and the best model of what spacetime geometry is, that we have.

 

In GR, geometry is represented by a metric a mathematical tool for specifying distances which was defined around 1850 by a young fellow named Riemann. The message of GR is that all there is is the metric---geometric relationships among events. Apart from geometry there is neither space nor time. Indeed the gravitational field is realized as the metric itself---gravity equals geometry.

 

The thing to notice is that a metric (as invented by Riemann and improved by Einstein and the fellow Sev mentioned, named Minkowski) might not be the only way to represent geometry. What people like Loll are trying to do, and people like Laurent Freidel, is to come up with a definte math object which will be as useful as the metric-on-a-manifold developed during the period 1850-1915 by Riemann, Minkowski, Einstein and others. Satisfactory progress will depend on developing a new way to present the universe's dynamically changing geometry as a usable math object that people can calculate with and check against data.

 

The neat thing about Ambjorn and Loll's approach is that they can simulate little quantum universes in the computer. Have them come into existence, evolve, stop them and study them, evolve some more, go out of existence.

They have simulated millions of universes. They can accumulate statistics on them, correlations. Each universe has an amplitude (a kind of probability weighting) and they are able to average up their universes, to derive a kind of path integral or average geometry. Under the simplest assumptions this turns out to be a classic spacetime geometry solving the GR equation---that is, it turns out to be the right thing. This happened this year.

 

It was a first. Classic 4D universe emerging from a messy quantum chaos. Taking shape by itself as a weighted average of many random universes (individually wacky irregular uncertain unsmooth without even a fixed dimensionality at small scale.)

 

I hope you have a look at the Loll SciAm link. What they did this year does not prove that their approach is the final answer. All it shows is what the other people will have to duplicate with their other approaches. It raises the bar and indicates what to expect from a new model quantum continuum. (And of course it could be right too, but until testing nobody can tell right, the main thing now is to move ahead.)

 

Martin

 

through all this how does continum geometry either by GR or Quantum gets us any closer to the actual physical dynamics which involves cause,effect and affect and in NO particular order , of any dynamics out there( the Universe )

 

this space-time geometry concept has failed to provide the real explaination of the goings on ( physical dynamics of the interaction(s) of energy and matter ) other than to say it is " geometric " )

 

well ... not that the geometry is not important , it is , its just that the geometry is the result of the consequence of the physical dynamics of objects and their inherent natures

 

hence we theories based on space-time which in the physical-dynamics of the Universe means nothing really

[snp.gupta]

....... He is a working experimental particle physicist and he says that spacetimecontinuum is NOT required.

 

Forget the continuum, he says, focus on the geometrical relationships. Einstein said essentially the same thing in 1916. Sev's statement in #2 is sophisticated, but as always with him (in my experience) it is consistent with conventional mainstream thinking. The guy supervises grad students doing their PhDs, so listen and ask followup questions to what he says.

 

We have to be on the lookout here for egomaniacs with delusions of grandeur----people who don't listen, ask merely rhetorical questions, think their own ideas are especially brilliant, and generally act like jerks......

 

.

 

Resp Martin sir,

That’s what I also want to derive from you sir, I want to provoke a bit, hence I asked repeatedly same question.

 

That is a correct answer…

Warm regards

=snp

[Baby Astronaut]

Martin, on the last page of that article by Ambjorn and Loll, what does the following mean?

 

A fractal is a bizarre kind of space where the concept

of size simply does not exist. It is self-similar,

which means that it looks the same on all scales.

I understand that it repeats itself, but don't get how size doesn't exist. Wouldn't the subsets of a fractal be smaller as you go deeper? If so, then size does exist when you compare a larger piece with its subdivisions.

 

For example, the cantor set image on page 7 has a line subdivided into smaller and smaller sets. And measuring them, the size differences are obvious.

[Martin]

I understand that it repeats itself, but don't get how size doesn't exist.

 

I think you understand it correctly. I think they should have said simply

"A fractal is a kind of space that is self-similar,

which means that it looks the same on all scales."

 

Popularized accounts sometimes have useless overthetop extra verbiage. Not necessarily always the authors' fault though.

 

Loll's professional journal writings are excellent---clear, careful, accurate---what you see in the SciAm is generally a blend of the named author and the editorial staff.

The editorial people will jazz up the style to whatever extent they think needed to keep general readership awake and interested.

I think I know what they meant though. they didn't have to say "bizarre"----that is hype. But if you were an intelligent point dropped into a fractal you would have no visual clue about what scale things were. You have to have something, like your own body, that is not the fractal, in order to tell size.

Edited December 24, 2008 by Martin

[NowThatWeKnow]

Tom C,

what Severian says here is precisely the idea of space and time we have from classic vintage-1915 General Relativity. GR is still the best theory of spacetime geometry and gravity that we have. I don't see how what Sev says could be improved, as a concise statement.

 

Is a particular piece of matter at rest in space or is it moving through space is the real question. If there is a difference, or space is expanding, then there must be a fabric of space but we have not been able to define it yet. Space must be more then just a yardstick.

 

A couple of things tell me there is a so called fabric of space. If we look at the balloon with dots explanation of the expanding universe, it would be hard to imagine that matter set in motion could explain what we observe. It seems space is expanding and most matter is at rest in space.

 

E=MC^2 tells me that it takes a lot of energy to move matter at Relativistic speed through space. This shows there is a difference between between resting in space and moving through it. I do not think Relativistic speed can be maintained relative to a current location with out energy. Therefore there must be a fabric of space. The teaser is what is the speed relative to. Since space is expanding, speed is only relative to its current location in space.

 

Looking in opposite directions we can see galaxies moving away from us at close to the speed of light. Their separation speed relative to each other well exceeds the speed of light. Special relativity says matter can not break the speed of light so space must be expanding. If space is expanding then there must be a fabric of space to expand.

 

Where am I going wrong?

[Martin]

If space is expanding then there must be a fabric of space to expand.

 

Where am I going wrong?

 

It's an interesting conundrum. General Relativity is merely the best theory we have so far (of where geometry comes from and how it is affected by matter, essentially the dynamics of the distance function).

 

GR has an answer to your question, but it would be unfair to present that as the final answer. We know GR has its limits. We'd like deeper explanations revealing what underlies GR, why it works.

 

GR's answer is that you shouldn't think of space expanding. You should concentrate on the distance function, the metric. You are encouraged to think of distances expanding. Without attributing any material existence to space. Severian said this rather clearly at the outset.

 

I'm told that Aristotle had a similar notion---he said space has no physical existence, there is only the sum total of geometric relationships between things. In the case of space-time it would be the relations between events. But in any case no fabric. Einstein had some mathematical argument for why space could have no objective reality---why there could be no fabric. There is only the metric itself, the geometry. And the metric is the gravitational field.

 

But I think you are saying you are dissatisfied with that. You would probably like some more meaty less abstract idea of the continuum. Not just disembodied geometry (although GR as a dynamics of changing geometry does work rather well.)

 

I mentioned the article by Renate Loll in the SciAm.

I also recently read Frank Wilczek's new book The Lightness of Being.

He thinks there is an underlying physical existence to the vacuum and this can be made to include GR----to have a particle physics vacuum but with dynamically changing geometry. I'm not sure just what he has in mind. But he is a Nobel laureate and creative and a rather good writer. It is provocative.

I think finding some physical reality underlying GR (where matter and dynamic geometry are joined at the root) is a work in progress, and at the present moment I just can't come up with a satisfactory response to your question. Maybe I will just reply in terms of the classic GR view and leave it at that---even though we both know that GR is not the final answer.

Edited January 5, 2009 by Martin

[NowThatWeKnow]

GR's answer is that you shouldn't think of space expanding. You should concentrate on the distance function, the metric. You are encouraged to think of distances expanding. Without attributing any material existence to space. Severian said this rather clearly at the outset....

 

I understand what you are saying but I pointed out a few of the many things that seem to contradict it. The first paragraph explaining GR has in it

"the observed gravitational attraction between masses results from the warping of space and time by those masses." So when we witness gravitational lensing we are warping a metric of nothing (space and time) but still get results. Does that make sense to you?

 

We can consistently prove mathematically that space can be bent by gravity. That should be good for a theory showing space has some unknown fabric. There are plenty of photons, gravity and maybe some kind of web or dark matter/energy.

 

Beside that, you told me in another thread that "I would urge you to stick to sources that are no more than 4 or 5 years old." GR is a little out dated.

 

I also recently read Frank Wilczek's new book The Lightness of Being.

He thinks there is an underlying physical existence to the vacuum and this can be made to include GR...

 

I knew it.

[gre]

Why can't space and time just be considered properties of matter (just like mass, gravity, etc.)

 

If matter can't exist without time and 3D space, I'd bet time can't exist without matter or 3D space either.... If true, this seems to spell out that matter is the source for all time and visible space as well.

 

Maybe time is a collective property (like gravity) that spreads out from the extreme density of black holes, and maybe time is just a "density" of space.

 

For example, when an object accelerates towards the speed of light, doesn't the objects density increase from an observers prospective (+ time slows down)? But the "space" of the object contracts .. Isn't that how it works?

[NowThatWeKnow]

For example, when an object accelerates towards the speed of light, doesn't the objects density increase from an observers prospective (+ time slows down)? But the "space" of the object contracts .. Isn't that how it works?

The density does increase from an observers prospective because you have to combine rest mass and the energy required for relativistic speed to get relativistic mass. Now I am wondering if from the objects point of view the observer is equal to rest mass + energy required for relativistic speed. It would seem that the one under power would be the only one with the increased relativistic mass. Help me Martin.

 

Not sure about the rest of the stuff you said.

[gre]

The density does increase from an observers prospective because you have to combine rest mass and the energy required for relativistic speed to get relativistic mass. Now I am wondering if from the objects point of view the observer is equal to rest mass + energy required for relativistic speed. It would seem that the one under power would be the only one with the increased relativistic mass. Help me Martin.

 

Not sure about the rest of the stuff you said.

 

 

I would think the mass density (+ space density) of the moving object increases in its reference frame, and the observer's mass density (+ space density) decreases from the moving objects perspective. The observer would just see a small dense object flying by, I think.

[NowThatWeKnow]

I would think the mass density (+ space density) of the moving object increases in its reference frame, and the observer's mass density (+ space density) decreases from the moving objects perspective. The observer would just see a small dense object flying by, I think.

 

My interpretation of Wikipedia. you can look it up.

 

You have "rest mass" and you have "relativistic mass". If you set an apple on a scale you get the rest mass. If the apple flies by you at near the speed of light you combine the rest mass and the energy needed for relativistic speed and get relativistic mass. If you take your scale and hop on the moving frame with apple and weigh it you will have your original rest mass weight. I do not think the apple would actually gain density. You just have to add the energy needed for the motion relative to the observer.