Cosmological Questions and Their Degenerate Answers

[cosmoboy]

There are many qusetions in science & cosmology which
have degerate answers some of them are as follows:

1. In the presence of matter space get curved so
massive particles as well as light photons do not move
along stright line. Now one could always assume that
photons also carry gravitational mass so they also get
attracted in gravity in place of assuming that space
get curved. Note that assuming that photons carry gravitational mass we are just postulating about photons but assuming that space get curved we are postulating about the behaviour of many unknown forms of matter.

2. Postulating that the space is expanding leads to the conclusion that remote galaxies are moving away from us.
But assuming that these are actually galaxies which are moving away from us in a non-expanding universe also leads same conclusion as well as observation. I know, that assuming that galaxis are moving in a fixed background leads to many difficult questions but does the
first option not ? i.e., what the space expanding into ?
(nobody like to talk about this issue and says that this is not expanding into anything, my objection is that if this is not expanding into anything then this is not the type of
expansion that we encounter in the daily life i.e., which
always expands into something. If the expansion of the universe is not the type of expansion which we face in daily life then why we call it expansion at all).

3. In special theory of relativity postulating that nothing can travel faster than the speed of light we
restrict the behaviour of that which have not been
yet discovered (fastets than light signal). Note that in
place of assuming that time interval get changed in moving frame we can always say there is a minium limit on the time interval which we need for communication.

 

[Dragongod]

I Agree with everything you say. Physics has many flaws with these areas and unifying the different branches of physics as well. To say spacetime expands using the definition that space is the absense of matter and energy automatically leads to a contradication. How can "nothing" bend or curve. It doesn't make sense. Einstein was obviously wrong on this matter unless he did define space as matter which in that case space would bend or curve.

And the whole thing about nothing going faster than light is bull. Gravitons go faster than light. if they didn't then we wouldn't be able to feel the force of gravitation by black holes but according to current science we can. Contradiction again.

Also like you say to assume that the "universe" is expanding is to be in agreement with the Big Bang theory which has way to many flaws to list.

 

[Dragongod]

If people would just accept my theory about "how it all happened" no one would have anymore questions. My theory is: if "nothing" can't exist than "something" always has to. That "something" would have to be matter and energy. That eliminates the possibility of people asking "well, where did that matter come from." You just respond it's not possible for something to come from nothing and therefore something(matter, energy) always had to be there. The problem is people keep thinking there was a begininng. It was always there, therefore its infinite. Then one day, due to the laws of attraction, particles came together and created an explosion. this fills in the gaps of the Big Bang theory. This theory explains the reasons for why matter is still expanding in the Universe and the problem with assuming that there was a begining. I can't find any flaws with it.

 

[cosmoboy]

I Agree with everything you say. Physics has many flaws with these areas and unifying the different branches of physics as well. To say spacetime expands using the definition that space is the absense of matter and energy automatically leads to a contradication. How can "nothing" bend or curve. It doesn't make sense. Einstein was obviously wrong on this matter unless he did define space as matter which in that case space would bend or curve.

These problems always come when we make a sentence without understanding it completely.

And the whole thing about nothing going faster than light is bull. Gravitons go faster than light. if they didn't then we wouldn't be able to feel the force of gravitation by black holes but according to current science we can. Contradiction again.

This is interesting that gravity travels faster than the
speed of light. Because we see that there sits a supermassive black holes that affect the surrounding material by gravity and this is possible if gravity tarvels faster than the speed of light. Since I have not
reach about this issue so I cannot say anything.

Also like you say to assume that the "universe" is expanding is to be in agreement with the Big Bang theory which has way to many flaws to list.

Let me put one more qusetion that has degerate answers.

4. Dark matter was mainly invoked for explaing the circular speeds of objects in outer parts of galaxies but
one can expalin it by using MOND also. There is nothing holy about the Newtonian mechanics. Even this is true for
GTR also one can always assume that gravity becomes repulsive at large distances in place of invoking the concept of dark energy about which we do not know anything.

 

[Dragongod]

very true. This too: Also its nearly accepted that gravity exist and gravity is defined as the force of attraction between everthing. Electrons and protons attract each other because of their opposing signs but according to current science gravity can attract eveything. If this is true, then WTF sign does gravity have¿¿¿ its not so much a contradiction as much as it is just unknown

 

[russ_watters]

2. Postulating that the space is expanding leads to the conclusion that remote galaxies are moving away from us.
But assuming that these are actually galaxies which are moving away from us in a non-expanding universe also leads same conclusion as well as observation. I know, that assuming that galaxis are moving in a fixed background leads to many difficult questions but does the
first option not ?

No, it contains significantly less problems.

i.e., what the space expanding into ?
(nobody like to talk about this issue and says that this is not expanding into anything, my objection is that if this is not expanding into anything then this is not the type of
expansion that we encounter in the daily life i.e., which
always expands into something. If the expansion of the universe is not the type of expansion which we face in daily life then why we call it expansion at all).

Ironically, you hit the nail on the head: no, it is not quite the same as the expansion we see in every day life. But why should it be? We can use examples in every day life but you need to avoid getting too attached to such analogies. They are imperfect.

One analogy that works reasonably well is the surface of a balloon: When you blow up a balloon, the 2d surface is expanding. What is the surface expanding into?

3. In special theory of relativity postulating that nothing can travel faster than the speed of light we
restrict the behaviour of that which have not been
yet discovered (fastets than light signal). Note that in
place of assuming that time interval get changed in moving frame we can always say there is a minium limit on the time interval which we need for communication.

That is not correct. The postulate exists because it must exist as a postulate for the sake of building a theory around it. Do not confuse that with meaning that the assumption has no experimental basis. It does have experimental basis and make no mistake: the fact that it is assumed doesn't preclude finding that the assumption is wrong.

 

[cosmoboy]

No, it contains significantly less problems. Ironically, you hit the nail on the head: no, it is not quite the same as the expansion we see in every day life. But why should it be? We can use examples in every day life but you need to avoid getting too attached to such analogies. They are imperfect.

If it is not like the expansion we are familer with then
why we should call it expansion at all ? since it create unnecesary confusions.

One analogy that works reasonably well is the surface of a balloon: When you blow up a balloon, the 2d surface is expanding. What is the surface expanding into?

It expands into a 3-dimensional space.I know it is not
always that a 'n' dimensional space requires 'n+1' dimensional space, sometime an 'n' dimensional space can expands in a 'n' dimensional space also, e.g., a flat sheet can expand in a '2' dimensional space. Actually problem of the expansion of the universe is as follows.

Our three dimensional space could be embedded into a
four dimensional space. For example, in FRW cosmology if we take 'k=+1' then this means that our universe is a
postively curved three surface like 'S3' which is embedded in a four dimensional 'R4' space. For 'k=-1' and
'k=0', we have three dimensional 'H3' and 'R3' surfaces
embedded in 'R4' space. This all looks easy mathematically, however, it is very very difficult to assume that how a 'R4' world will physically look like and why only 'R4', our three dimensional space which could be 'R3', 'S3', 'H3', 'T3' or whatever can always be embedded in a space of '3+n', dimensions where 'n' could vary from 0 to infinity. Nevethless, I still found it difficult to assume that an empty space can expand.

 

[russ_watters]

If it is not like the expansion we are familer with then
why we should call it expansion at all ? since it create unnecesary confusions.

"Expansion" is accurate, its just not the same as the expansion we are used to seeing. A circle on a piece of paper can be animated to expand in 2d, while the circumference is expanding in 1d. A sphere (my balloon analogy) can be made to expand in 3d while the surface expands in 2d. We live in a 3d space that is expanding in 4d. Its still expansion, its just not something easy (possible) to visualize. But it does seem you basically understand it...

This all looks easy mathematically, however, it is very very difficult to assume that how a 'R4' world will physically look...

And that's the rub - our preconceptions make it difficult to visualize, but why should that limit our understanding? To learn, you often have to let go of preconceptions.

Nevethless, I still found it difficult to assume that an empty space can expand.

Its not an assumption, its an observation. There is an enormous amount of observational evidence of this expansion.

 

[Dragongod]

i don't understand how a circle can be animated expand in 2d but its circumference can only expand in 1d. I always thought that anything that is on paper (2d) can only be 2d. how is it possible for something (the circle) in a purely 2d realm to exist in a 1d realm (the circumference).

 

[Nereid]

1. In the presence of matter space get curved so massive particles as well as light photons do not move along stright line. Now one could always assume that photons also carry gravitational mass so they also get attracted in gravity in place of assuming that space get curved. Note that assuming that photons carry gravitational mass we are just postulating about photons but assuming that space get curved we are postulating about the behaviour of many unknown forms of matter.

When you write it out in English, it gives me a headache

How about approaching it somewhat differently ... there are a bunch of good observational and experimental results, and there is a theory (General Relativity) which can 'account for' all those results, even to 4 (now 5?) decimal places. Further, you can 'do stuff' with GR, such as build a GPS system. Better yet, you can make predictions about what you will find (or see) if only you {did this experiment} or {observed these things in the universe}. In this sense, GR is a pretty good theory, and all ( ) you need to do is become 'fluent' in the relevant math ... the extent to which you tell yourself a satisfying story about the concepts is your privilege.

(You may consider this discomforting ... why can't astrophysicists write GR out in an intuitive, 'non-degenerate' fashion? Well, GR is a piece of cake compared with QM!)

2. Postulating that the space is expanding leads to the conclusion that remote galaxies are moving away from us.
But assuming that these are actually galaxies which are moving away from us in a non-expanding universe also leads same conclusion as well as observation. I know, that assuming that galaxis are moving in a fixed background leads to many difficult questions but does the first option not ? i.e., what the space expanding into ? (nobody like to talk about this issue and says that this is not expanding into anything, my objection is that if this is not expanding into anything then this is not the type of expansion that we encounter in the daily life i.e., which always expands into something. If the expansion of the universe is not the type of expansion which we face in daily life then why we call it expansion at all).

Russ has already addressed this well; just to add a few words on perspective/approach ... in one sense, science resembles nature - it abhors a vaccuum! Generally speaking, you need something to do your research on, and 'theory-free' research is a myth, so we always have some view (idea, hypothesis, theory, ...) that we're working within. You're free to postulate a 'fixed' universe in which galaxies 'expand away' from each other; your challenge is to build a model with your ideas such that it isn't strongly inconsistent with good observational and experimental results (and good theories, where the domains of applicability overlap, and ...). Indeed, if you do build a new theory that's 'better' in the sense that GR is 'better' than Newtonian physics, you will likely become famous, and have hundreds of books written about you!

3. In special theory of relativity postulating that nothing can travel faster than the speed of light we restrict the behaviour of that which have not been yet discovered (fastets than light signal). Note that in place of assuming that time interval get changed in moving frame we can always say there is a minium limit on the time interval which we need for communication.

Indeed. So if (when?) we discover an FTL signal, SR will be given the heave-ho!

4. Dark matter was mainly invoked for explaing the circular speeds of objects in outer parts of galaxies but one can expalin it by using MOND also. There is nothing holy about the Newtonian mechanics. Even this is true for GTR also one can always assume that gravity becomes repulsive at large distances in place of invoking the concept of dark energy about which we do not know anything.

This one is quite different from your other 3 ... most of the DM in the universe is in rich clusters of galaxies, not the halos of galaxies, and several independent lines of work give comparable values for the amount, distribution, non-collisional character, 'temperature', etc of DM. Of course, if MOND (or super-MOND) can get rid of the need for DM (i.e. 'account for' all the relevant good observational results), then Milgrom will become a hero.

In fact, there are some 'super-MOND' theories being published - check out the relevant threads here in PF's GA&C!

 

[Nereid]

If people would just accept my theory about "how it all happened" no one would have anymore questions. My theory is: if "nothing" can't exist than "something" always has to. That "something" would have to be matter and energy. That eliminates the possibility of people asking "well, where did that matter come from." You just respond it's not possible for something to come from nothing and therefore something(matter, energy) always had to be there. The problem is people keep thinking there was a begininng. It was always there, therefore its infinite. Then one day, due to the laws of attraction, particles came together and created an explosion. this fills in the gaps of the Big Bang theory. This theory explains the reasons for why matter is still expanding in the Universe and the problem with assuming that there was a begining. I can't find any flaws with it.

IIRC, you posted something similar elsewhere in PF ... have you written a paper on 'your theory' and submitted it to a peer-reviewed astrophysics/physics journal? If not, why not?

 

[Nereid]

Physics has many flaws with these areas and unifying the different branches of physics as well. To say spacetime expands using the definition that space is the absense of matter and energy automatically leads to a contradication. How can "nothing" bend or curve. It doesn't make sense. Einstein was obviously wrong on this matter unless he did define space as matter which in that case space would bend or curve.

Everything you write Dragongod may be good and true ... or it may be 'mental vomit' (or worse). Your challenge, if you choose to accept it, is to stop handwaving and pretend we're all from Missouri - show us that your ideas are consistent with all good experimental and observational results.

And the whole thing about nothing going faster than light is bull. Gravitons go faster than light. if they didn't then we wouldn't be able to feel the force of gravitation by black holes but according to current science we can. Contradiction again.

1) 'gravitons' don't exist, except in a consistent theory of quantum gravity (which itself doesn't exist).
2) GR gives a perfectly consistent description of how 'you' are 'able to feel the force of gravitation by black holes' - may I suggest you post a question* in the SR&GR section of PF? I'm confident you will get a well-constructed, patient reply.

Also like you say to assume that the "universe" is expanding is to be in agreement with the Big Bang theory which has way to many flaws to list.

Humour me please, list the three most egregious flaws (from your POV).


*e.g. "Within GR, how is it possible that we can feel the force of gravitation by black holes?"

 

[russ_watters]

i don't understand how a circle can be animated expand in 2d but its circumference can only expand in 1d. I always thought that anything that is on paper (2d) can only be 2d. how is it possible for something (the circle) in a purely 2d realm to exist in a 1d realm (the circumference).

The edge of a circle is a line. A line is 1d: it has length but no width. Similarly, the surface of a balloon is a surface: it has length and width, but no height.

 

[misskitty]

There are many qusetions in science & cosmology...

I will argree this part of your statement is very true. There are many questions everywhere in every scientific field which people are striving to answer.

2. Postulating that the space is expanding leads to the conclusion that remote galaxies are moving away from us.
But assuming that these are actually galaxies which are moving away from us in a non-expanding universe also leads same conclusion as well as observation. I know, that assuming that galaxis are moving in a fixed background leads to many difficult questions but does the
first option not ? i.e., what the space expanding into ?
(nobody like to talk about this issue and says that this is not expanding into anything, my objection is that if this is not expanding into anything then this is not the type of
expansion that we encounter in the daily life i.e., which
always expands into something. If the expansion of the universe is not the type of expansion which we face in daily life then why we call it expansion at all).

Russ has provided a very good explanation of your second query. If it's alright, I'd like to add to it. With space expanding, everything in it might be expanding as well. Meaning us too. So we may not even notice that the universe is expanding in our everyday lives; especially if we are expanding proportionally to the rest if the universe. However, I do believe Russ did mention something about evidence supporting the expansion of the universe, so I may be wrong. It is definitely something to think about when looking at the expansion query.

 

[cosmoboy]

Dear Friends,
As most of you are agreed that there are degenracies in
scientific explanations. These are mainly due to "observation selection bias". I think most us will agree
that scientific explanations are not the final truths, they are just models, they give one of the possible explanation for any observational feature in the universe. In this discussion one of the main issue which I raised was: in what the universe is expanding into ? let me put my answer which most of you might be familier with but nobody has posted.

It is well known that our universe is three dimensional so one can think that it is embedded into a '3+n' (where
n is an integer between 0 and infinity) dimensional space. In FRW cosmology we assume that it is
embedded into a 4-dimensional space. Actually a universe with non-zero curvature expands along the fourth dimension just like when we inflate a baloon it expands into a three dimensional space particularely one can think it expands radially. At this point there is no ! difference between the expansion of the universe and that of the baloon. Here main problem is that we can not visulaize the forth dimension (let us call it radial) along which the universe expands. It is like for a two dimensional creature it is difficult to visulaize the third dimensions. I will come back with more explanation.

 

[misskitty]

Now I feel rather stupid. Your last post made more sense. Now I feel really stupid. . We don't know what space is expanding into. We may not ever know.

 

[ohwilleke]

The fourth dimension is time. You visualize it every time you go to the movies.

 

[misskitty]

I knew that. It's the same when you watch tv.

 

[cosmoboy]

Now I feel rather stupid. Your last post made more sense. Now I feel really stupid. . We don't know what space is expanding into. We may not ever know.

Excatly ! in order to feel or to understand where our
three dimensional space in expanding into we have to
go away from it along the fourth dimension which seems
to be impossible.

 

[cosmoboy]

The fourth dimension is time. You visualize it every time you go to the movies.

This is totally wrong. The fourth dimension which I am talking about is not time. If you do not mind please look
at the derivation of FRW line element in any textbook (Peebles physical cosmology etc). There we start with the
discussion of embiddeing a three dimensional space in a four dimensional (all are spatial dimenions) flat or Eucledian space.

Note that time is considered a fourth dimenions only in special theory of relativity.

 

[Chronos]

This is totally wrong.

Agreed, with the caveat it is what follows, not preceeds this assertion that is wrong:

The fourth dimension which I am talking about is not time. If you do not mind please look at the derivation of FRW line element in any textbook (Peebles physical cosmology etc). There we start with the discussion of embiddeing a three dimensional space in a four dimensional (all are spatial dimenions) flat or Eucledian space.

Where did Peebles assert three dimensional space is embedded in a fourth spatial dimension?

Note that time is considered a fourth dimenions only in special theory of relativity.

And general relativity does not?

 

[cosmoboy]

Agreed, with the caveat it is what follows, not preceeds this assertion that is wrong:Where did Peebles assert three dimensional space is embedded in a fourth spatial dimension?

Principle of physical cosmology page 60

In case fou do not find it look at my notes

http://www.geocities.com/vichitravira/

 

[Nereid]

As this thread seems to have become 'about' GR (in the cosmological sense), I'm moving it to a place where it may get more technical expert attention.

 

[pervect]

I gather this is a "transplanted" thread from somewhere?

There are many qusetions in science & cosmology which
have degerate answers some of them are as follows:

1. In the presence of matter space get curved so
massive particles as well as light photons do not move
along stright line. Now one could always assume that
photons also carry gravitational mass so they also get
attracted in gravity in place of assuming that space
get curved. Note that assuming that photons carry gravitational mass we are just postulating about photons but assuming that space get curved we are postulating about the behaviour of many unknown forms of matter.

This is actually not an example of "degeneracy", because there are experimental differences between the two theories. GR, with space-time curvature, predicts twice the deviation of a photon than a Newton-like-theory which is couched in terms of forces. The difference is due to the space-space curvature terms in the space-time curvature tensor, i.e. it's due to the effects of pure spatial curvature.

2. Postulating that the space is expanding leads to the conclusion that remote galaxies are moving away from us.
But assuming that these are actually galaxies which are moving away from us in a non-expanding universe also leads same conclusion as well as observation. I know, that assuming that galaxis are moving in a fixed background leads to many difficult questions but does the
first option not ? i.e., what the space expanding into ?
(nobody like to talk about this issue and says that this is not expanding into anything, my objection is that if this is not expanding into anything then this is not the type of
expansion that we encounter in the daily life i.e., which
always expands into something. If the expansion of the universe is not the type of expansion which we face in daily life then why we call it expansion at all).

You are probably visualizing non-euclidean geometry as a curved surface embedded in a higher dimensional geometry. While this is not a bad visual aid, it's not the only way of dealing with non-euclidean geometry. The approach used in GR is to define a metric at every point in space-time, similar to the way that one defines a metric on the curved surface of the Earth. The purpose of the metric is to compute local distances from generalized coordinates. For instance, on the Earth, we can locate any point by two coordinates, such as lattitude and longitude. Ignoring the non-sphericity of the Earth for the time being, it is sufficint to point out that while a minute of lattitude always represents the same distance (one minute = 1 nautical mile), a minute of longintude does not represent the same distance - a degree of longitude is significantly smaller near the poles than it is near the equator. Thus the shape of the Earth can be studied purely in terms of its intrinsic geometry.

The "embedding" approach does not yield unique answers, there are many ways a specific geometry can be instantiated by different embeddings which all have the same intrinsic properties. Hence the metric approach is preferred, because it models what we can actually measure.

Your question regarding "what is the universe expanding into" is also a question that does not yield itself to experimental testing - that's why it is a philosophical question, and not a scientific one.
[/quote]

3. In special theory of relativity postulating that nothing can travel faster than the speed of light we
restrict the behaviour of that which have not been
yet discovered (fastets than light signal). Note that in
place of assuming that time interval get changed in moving frame we can always say there is a minium limit on the time interval which we need for communication.

It sounds like you are complaining about the fact that a theory makes a prediction. That's the job of theories - to make predictions that we can test.

That's not the only problem with your statements. For instance, tachyons are possible under special relativity, though they have stability problems, and may not yield FTL comm;unication even if they exist. Wormholes are another counter-example. Wormholes may not exist, but the fact that they are being seriously investigated theoretically shows that the topic of FTL and relativity is more complicated than you indicate. Note that it is still true that relativity predicts that one cannot exceed the speed of light by, for example, simply accelerating continuously in one direction.

 

[misskitty]

So if the fourth dimension isn't time in this case; what is it? I'm just breaking into GR so I haven't even hit special relativity yet.

Sidenote: someone please tell me what a tachyon is?

 

[cosmoboy]

So if the fourth dimension isn't time in this case; what is it? I'm just breaking into GR so I haven't even hit special relativity yet.

This is purely a spatial dimension, indistinguishable from other three spatial dimensions. Our world corresponds to a three surface on which the coordinates corresponding to this fourth dimension are constant. You can look about it in any cosmology textbook (Peebles, Physical cosmology, page 60) or at my notes http://www.geocities.com/vichitravira/

 

[Entropy]

If people would just accept my theory about "how it all happened" no one would have anymore questions. My theory is: if "nothing" can't exist than "something" always has to. That "something" would have to be matter and energy. That eliminates the possibility of people asking "well, where did that matter come from." You just respond it's not possible for something to come from nothing and therefore something(matter, energy) always had to be there. The problem is people keep thinking there was a begininng. It was always there, therefore its infinite. Then one day, due to the laws of attraction, particles came together and created an explosion. this fills in the gaps of the Big Bang theory. This theory explains the reasons for why matter is still expanding in the Universe and the problem with assuming that there was a begining. I can't find any flaws with it.

Dude, you're playing word games instead of discussing science. You forget that words are mearly relationships we assign things to communicate an abstact meaning. You seem to be seeking some concrete linguistics that we be universely interpreted the same. Well, you won't find it. Unfortunately, human language isn't concrete when you anyalsis descrete contexts, but only when you look at the overall message will you grasp anothers thoughts.

 

[pervect]

Space-time has 4 dimensions, three spatial dimensions and one time dimensions. To visualize curvature, one sometimes envisions additional dimensions, which do not have a name as they are just "visual aids". It's not possible to draw a picture of a 4-d space-time embedded in a higher dimensional space, but it is possible, for instance, to visualize a spherical surface "embedded" in a 3d space. To make some useful comparisons with relativity, it is convenient to imagine that the surface of the sphere is not a spatial surface, but has 1 spatial dimension and one time-dimension. One imagines this 2d sphere exists in some 3d space. The third dimension in this space cannot be experienced by the "linelanders", one spatial dimension beings living on the sphere, and it does not have a name, as it's just a visual aid.

LInelanders, being one dimensional, have a very simple concept of distance, which is "how far away is the next linelander". All linelanders are just points on a line.

If you draw geodesics on the sphere, which are "great circles", you can ask the question - how does the curvature affect the linelanders? The answer is simple - two linelanders following geodesic paths appear to be attracted to each other by some mysterious force. When there is no other force acting on them, the two linelanders (the two great circles) mysterioiusly start to approach each other, approaching each other faster and faster as time goes on. The velocity of approach reaches a maximum right when the two linelanders meet, then slows down as they separate.

Thus the line-landers interpret the curvature of space-time (1space+1time in their case) as a force, which is similar to gravitation, that attracts two adjacant linelanders to each other.

 

[selfAdjoint]

This is purely a spatial dimension, indistinguishable from other three spatial dimensions. Our world corresponds to a three surface on which the coordinates corresponding to this fourth dimension are constant. You can look about it in any cosmology textbook (Peebles, Physical cosmology, page 60) or at my notes http://www.geocities.com/vichitravira/

I went to your site, and followed on to your notes. And as I suspected from your comment about any cosmology textbook, the relevant passage includes developing the restricted metrics for various cosmological cases by regarding spacetime as a three dimensional manifold M cross the real line for time : $$M \times R^1$$, and then embedding M in four dimensional euclidean space $$M \subset R^4$$. This is PURELY NOTATIONAL. You are not intended to conclude that Peebles or any other author is asserting that space is separated from time and embedded in a higher dimensional euclian space like that. The form $$M \times R^1$$ is already an idealization of full spacetime for the limited purposes of cosmology, and the rest is just a device for exploring the shape of space within this idealization.

 

[cosmoboy]

Space-time has 4 dimensions, three spatial dimensions and one time dimensions. To visualize curvature, one sometimes envisions additional dimensions, which do not have a name as they are just "visual aids". It's not possible to draw a picture of a 4-d space-time embedded in a higher dimensional space, but it is possible, for instance, to visualize a spherical surface "embedded" in a 3d space. To make some useful comparisons with relativity,

This all is fine

it is convenient to imagine that the surface of the sphere is not a spatial surface, but has 1 spatial dimension and one time-dimension. One imagines this 2d sphere exists in some 3d space.

I do not know why you are involving time here. Curvature of space is a static property i.e., we are talking the curvature of "space" at some fixed time. Note that in
cosmolgy "k" reprsents this.

The third dimension in this space cannot be experienced by the "linelanders", one spatial dimension beings living on the sphere, and it does not have a name, as it's just a visual aid.

By the way all physical concepts are just aids to understand the universe. They do not have any independent existence.

LInelanders, being one dimensional, have a very simple concept of distance, which is "how far away is the next linelander". All linelanders are just points on a line.

This all is fine.

If you draw geodesics on the sphere, which are "great circles", you can ask the question - how does the curvature affect the linelanders? The answer is simple - two linelanders following geodesic paths appear to be attracted to each other by some mysterious force. When there is no other force acting on them, the two linelanders (the two great circles) mysterioiusly start to approach each other, approaching each other faster and faster as time goes on. The velocity of approach reaches a maximum right when the two linelanders meet, then slows down as they separate.

Thus the line-landers interpret the curvature of space-time (1space+1time in their case) as a force, which is similar to gravitation, that attracts two adjacant linelanders to each other.

This all is well understood.

 

[cosmoboy]

I went to your site, and followed on to your notes. And as I suspected from your comment about any cosmology textbook, the relevant passage includes developing the restricted metrics for various cosmological cases by regarding spacetime as a three dimensional manifold M cross the real line for time : $$M \times R^1$$, and then embedding M in four dimensional euclidean space $$M \subset R^4$$. This is PURELY NOTATIONAL. You are not intended to conclude that Peebles or any other author is asserting that space is separated from time and embedded in a higher dimensional euclian space like that. The form $$M \times R^1$$ is already an idealization of full spacetime for the limited purposes of cosmology, and the rest is just a device for exploring the shape of space within this idealization.

I do not understand what do you mean. I am just saying that at some fixed time one needs a fourth spatial dimension to have (visulaize) the curvature of "space".
Note that time comes in picture when we talk about the dynamics. One can always study the universe at some fixed time.

Most of the people think that curvature "k" which comes in cosmology is the curvature of "space-time". However, this is not trure, this is the curvature of spatial section.

 

[selfAdjoint]

I do not understand what do you mean. I am just saying that at some fixed time one needs a fourth spatial dimension to have (visulaize) the curvature of "space".

For some of us, "have" doesn't equal "visualize". The curvature of spacetime, (yes it curves in the general theory, as shown by, e.g. the Schwartzschild metric where t is nonlinear along with the space coordinates) is no less visualizable than is curvature in R⁴. The GR pseudo-Riemannian curvature is intrinsic and doesn't need an enveloping space.

Note that time comes in picture when we talk about the dynamics. One can always study the universe at some fixed time.

Different observers will orient differently toward spacelike and timelike. There is no one favored way to dissect the local neighborhood into space and time, much less the whole universe. I repeat that the M X R¹ model is an idealization, which is not in any way the full correct state of GR but a useful false model for discussion of limited kinds of things - cosmological things.

Most of the people think that curvature "k" which comes in cosmology is the curvature of "space-time". However, this is not trure, this is the curvature of spatial section.

In this cosmological model, but not in general.

 

[pervect]

So if the fourth dimension isn't time in this case; what is it? I'm just breaking into GR so I haven't even hit special relativity yet.

Sidenote: someone please tell me what a tachyon is?

It may be a bit advanced, but tachons are discussed in the sci.physics.faq in a couple of places. The first is probably more readable, and is about FTL and relativity in general, the second is a little more advanced

http://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/FTL.html
http://math.ucr.edu/home/baez/physics/ParticleAndNuclear/tachyons.html

Basically tachyons are hypothetical particles that always travel faster than light. Some interesting mathematical gymnasitics is required to achieve this - tachyons wind up with real energies and momenta, but an imaginary rest mass.