Need Help Understanding Expanding Universe

[courtney1111]

Hello,

I am hoping someone can help me to understand that the universe is expanding and other questions that brings up. If it is expanding, does that mean that there is an edge or a place that the universe has not reached yet but will reach at some point? What would be in the space that it has not reached yet? Are we able to see the entirety of the universe in all directions? Meaning that we can know everything that is out there or are there places that we will never be able to see?
I realize that my questions are probably a little childlike. I already feel like a kindergartner amongst Ph.D's so please try not to be to hard on me. I am just trying to understand.

Thanks,
Courtney

 

[marcus]

The usual model universe that cosmologists work with is the simplest possible that makes a good fit with the data.

For simplicity, it has no outside. Space is all of space. So it is a mistake to try to picture it from the outside. You can't get outside and see it expand because there is no outside. There is no edge or boundary--that would add a lot of needless unwanted complication to the model.

So think about how the creatures inside something that is expanding experience the expansion process from the inside. For them a uniform pattern of expansion is not like ordinary motion, because nobody gets anywhere by it. Everybody just gets farther apart from everybody, without moving (in the ordinary sense.)
That's how they experience expansion.

It helps some people to watch this simple computer simulation:
http://www.astro.ucla.edu/~wright/Balloon2.html
It is expansion of a reduced dimension world. All existence, all creatures are in the infinitely thin surface of the balloon. Imagine that there is only this surface, no inside of the balloon, no outside of the balloon. their experience is all within the infinitely thin surface.
Watch carefully. You will see galaxies sitting still and wiggles of light moving among the galaxies. each galaxy sees the other galaxies getting farther and farther away, but nobody moves, no galaxy gets anywhere. Each galaxy stays at the same latitude longitude position in their world.

That's just an analogy, a toy model. Real space is 3D, not an infinitely thin curved 2D surface.
Real space may be infinite volume, or (if it somehow curves around and rejoins itself) finite volume. That's hard to imagine but it is mathematically possible.

 

[courtney1111]

THANK YOU! I really do understand exactly what you mean. One more question, if you don't mind. Are we able to see the entire universe? I guess I am asking if all of space has been mapped out. Are there still things to be discovered?

 

[marcus]

Courtney we *definitely* do not see the whole thing!
According to the best most recent estimates I've seen, we don't even come close.
I'm not an cosmology expert, just a retired mathematician who loves cosmology. I try to follow other people's research.
If you (or anybody) wants some numbers about how much farther it extends (at least) beyond the most distant matter we can see, then just ask.

 

[Chronos]

I agree with marcus, with one caveat - we can 'see' the entire observable universe. The cosmic microwave background, currently at z ~ 1100, will forever be the limit of the observable universe in EM wavelengths.

 

[Mark M]

Also, you may want to read this article.

 

[mrspeedybob]

One modification to the balloon analogy that I like is to picture the radial dimension of the sphere as time. The BB happens at T=0, the center of the balloon. inside the balloon is the past, outside the balloon is the future. We see the 3D surface at T=now as space. This helps explain why the universe expands, it is simply the nature of spheres that the surface area gets larger if the radius gets larger. Similarly it is simply the nature of hyperspheres that the surface volume is larger now, with a radius of 13.7 billion years then it was with a radius of 5 billion years.

Please note that while this may be a convenient way to construct a mental image it cannot be an accurate model of the cosmos. Once you start crunching the numbers with it you find that it predicts a universe that is either much smaller or much older then we know the universe to be.

 

[Farahday]

Hello,

I am hoping someone can help me to understand that the universe is expanding and other questions that brings up. If it is expanding, does that mean that there is an edge or a place that the universe has not reached yet but will reach at some point? What would be in the space that it has not reached yet? Are we able to see the entirety of the universe in all directions? Meaning that we can know everything that is out there or are there places that we will never be able to see?
I realize that my questions are probably a little childlike. I already feel like a kindergartner amongst Ph.D's so please try not to be to hard on me. I am just trying to understand.

Thanks,
Courtney

If the cosmos is finite then it must contain a finite amount of space, mass and energy. Each unit has a defined location, physical domain and configuration. Even if the cosmos is expanding, for any time=T simple summation should be able to determine where some mythical cosmic wall exists.

Theorists have come up with an interesting hypothetical twist in which space curves in upon itself in such a way that for every given point 'A' there is a point 'B' within a finite distance at which motion in any direction will not increase the distance between the two; in fact, if a traveler who could instantaneously traverse a sufficient distance encountered such a point, he would begin to return to his point of origin. The concept describes a "finite but unbounded" Universe and implies a cosmos enveloped in a spherical spacecage. There is no evidence, no principle of logic, science or mathematics and no law of nature that implies the existence of any point, however distant, at which progress becomes regress.

There are two ways things in nature increase in size: inflation (adding more material) and expansion (increasing volume and decreasing density). The first implies the cosmos is somehow conjuring up new materials and/or new locations to occupy (magical thinking). There is no evidence for the second.

If there ever was a Big Bang (and the jury is certainly still out), the only logical version would be that within our local neighborhood (45 billion light years or so with its theoretical expansion factor) of that infinitely populated expanse we call the cosmos, an immensely large volume of mass somehow collapsed into a hyper-critical black hole which then regurgitated. I could almost (but not quite) lend credence to that scenario, but it certainly didn't create the Universe. At most it was a colossal rearrangement of elements which already existed.

 

[Naty1]

Here is a balloon model discussion from these forums:

http://www.phinds.com/balloonanalogy/


A 'next step' analogy: Wikipedia has a visually enhanced model:

http://en.wikipedia.org/wiki/Metric_expansion#Understanding_the_expansion_of_Universe

 

[Farahday]

Here is a balloon model discussion from these forums:

http://www.phinds.com/balloonanalogy/


A 'next step' analogy: Wikipedia has a visually enhanced model:

http://en.wikipedia.org/wiki/Metric_expansion#Understanding_the_expansion_of_Universe

Unless Big Bang is a local event, Universal expansion would imply a finite cosmos. Expansion - in whatever form you wish to cast it - means increase and only that which is measurable or limited can be increased. If the cosmos is, indeed, infinite, then there is no farthest and there is no 'all'...there is always more.

 

[mrspeedybob]

There are two ways things in nature increase in size: inflation (adding more material) and expansion (increasing volume and decreasing density). The first implies the cosmos is somehow conjuring up new materials and/or new locations to occupy (magical thinking). There is no evidence for the second.

There is actually a great deal of evidence for the second. I suggest you google cosmological redshift and supernova surveys.

If there ever was a Big Bang (and the jury is certainly still out), the only logical version would be that within our local neighborhood (45 billion light years or so with its theoretical expansion factor) of that infinitely populated expanse we call the cosmos, an immensely large volume of mass somehow collapsed into a hyper-critical black hole which then regurgitated. I could almost (but not quite) lend credence to that scenario, but it certainly didn't create the Universe. At most it was a colossal rearrangement of elements which already existed.

This theory was postulated some years ago, but does not seem to fit the data we now have. Particularly the observation that cosmological expansion is accelerating. If this theory were correct the expansion would be slowing down due to gravity.

 

[mrspeedybob]

Unless Big Bang is a local event, Universal expansion would imply a finite cosmos. Expansion - in whatever form you wish to cast it - means increase and only that which is measurable or limited can be increased. If the cosmos is, indeed, infinite, then there is no farthest and there is no 'all'...there is always more.

This is incorrect. Expansion does not imply finiteness. Expansion is a verifiable fact. The jury is still out on finiteness, though in my opinion infinite is more likely because only an infinite and expanding universe can have zero total energy. I find the zero energy universe idea appealing because it can spontaneously exist without violating conservation of energy.

 

[Whovian]

Unless Big Bang is a local event, Universal expansion would imply a finite cosmos. Expansion - in whatever form you wish to cast it - means increase and only that which is measurable or limited can be increased. If the cosmos is, indeed, infinite, then there is no farthest and there is no 'all'...there is always more.

\begin{rant}
Let's break this down.

Unless Big Bang is a local event, Universal expansion would imply a finite cosmos.

Exactly what I plan to disprove.

Expansion - in whatever form you wish to cast it - means increase

Correct,

and only that which is measurable or limited can be increased.

And that's where we're going wrong. There's no reason to think this. Why should something being not limited mean it can't increase? At no two points in an infinite Universe is the distance between them infinite, and we can easily increase a real number. Similarly, the distance between any two points is measurable, as it is not infinite.

Anyway, even something being infinite doesn't mean it isn't measurable or it can't be increased. For instance, there's a fairly basic proof that the number of real numbers is "more" than the number of real integers.
\end{rant}

 

[Farahday]

There is actually a great deal of evidence for the second. I suggest you google cosmological redshift and supernova surveys.

Google is not as good as SLAC, CERN, FERMI and other more credible sources. Been there, done that.

This theory was postulated some years ago, but does not seem to fit the data we now have. Particularly the observation that cosmological expansion is accelerating. If this theory were correct the expansion would be slowing down due to gravity.

Not if the density of mass to space were higher OUTSIDE our sphere of observation.

 

[Farahday]

\begin{rant}
And that's where we're going wrong. There's no reason to think this. Why should something being not limited mean it can't increase?

In order to detect in increase one must have a measurement. If condition A is larger than B then there is an increase. Any value you assign to A or B is a defined (finite/limited) quantity.

At no two points in an infinite Universe is the distance between them infinite, and we can easily increase a real number. Similarly, the distance between any two points is measurable, as it is not infinite.

Anyway, even something being infinite doesn't mean it isn't measurable or it can't be increased.

Yes it does. Infinity is the LACK of a quantifiable definition.

For instance, there's a fairly basic proof that the number of real numbers is "more" than the number of real integers.
\end{rant}

Duhhhh... The set of integers is a subset of the set of real numbers.

 

[Naty1]

There are two ways things in nature increase in size: inflation (adding more material) and expansion (increasing volume and decreasing density). The first implies the cosmos is somehow conjuring up new materials and/or new locations to occupy (magical thinking). There is no evidence for the second.

Neither of these is the standard cosmology modeled by the FLRW universe. For example, inflationary expansion retained a constant energy density. Nature is more complex than either of those statements implies.

Unless Big Bang is a local event, Universal expansion would imply a finite cosmos. Expansion - in whatever form you wish to cast it - means increase and only that which is measurable or limited can be increased. ...

Again, this conflicts with standard cosmology. We observe universal expansion, the FLRW model depicts it, and no one knows if the universeis finite or infinite. That statement is
pure speculation without supporting theoretical or observational evidence.

 

[Whovian]

In order to detect in increase one must have a measurement. If condition A is larger than B then there is an increase. Any value you assign to A or B is a defined (finite/limited) quantity.

"Infinite" quantities can also be defined. And, again, assuming the Universe is infinite, even though there is no limit to the distance between two points, it is always going to be finite.

Yes it does. Infinity is the LACK of a quantifiable definition.

Quite incorrect. http://en.wikipedia.org/wiki/Infinity#Set_theory

Duhhhh... The set of integers is a subset of the set of real numbers.

Oh. I had a completely different proof in mind.

 

[Farahday]

Neither of these is the standard cosmology modeled by the FLRW universe. For example, inflationary expansion retained a constant energy density. Nature is more complex than either of those statements implies.

Yes, IF the standard model was correct. A flat Earth used to be the standard model, also.

Again, this conflicts with standard cosmology. We observe universal expansion, the FLRW model depicts it, and no one knows if the universeis finite or infinite. That statement is
pure speculation without supporting theoretical or observational evidence.

You observe red shift...and that observation only pertains to extremely distant objects. We do not detect any expansion of the space between atoms/molecules locally that would lead us to believe the phenomenon is universal.

And a finite universe is simply illogical on its face. It would contain a finite number of units of mass/energy/space and each would occupy a defined volume and have a defined configuration. Simple summation would predict where some mythical cosmic wall might exist.

You can torturously contort all the equations you wish to cast the shape of the cosmos into a 'finite but unbounded' spherical spacecage, a hyperbolic, flat or pretzel shaped doodad, but no matter how vast the number of items you wish to consider, their size and shape could be summarized and a boundary would be determined.

I know of no such boundary. Is it made of green cheese?

 

[Whovian]

You can torturously contort all the equations you wish to cast the shape of the cosmos into a 'finite but unbounded' spherical spacecage, a hyperbolic, flat or pretzel shaped doodad, but no matter how vast the number of items you wish to consider, their size and shape could be summarized and a boundary would be determined.

Also incorrect. The common "torus" model (more of a 3-torus) would introduce no such boundary. The surface, not the interior of the 3-torus and the 4-dimensional "space" surrounding it, is considered to be the Universe, so there is no boundary whatsoever.

 

[Number Nine]

Duhhhh... The set of integers is a subset of the set of real numbers.

This is such a profoundly ridiculous view of basic set theory that I refuse to believe that you possesses even the slightest education in mathematics; it then follows that you lack any appreciable knowledge of physics. Everyone, stop feeding the crank.

 

[Chronos]

Why be so insulting, number nine? Why not objectively define your objections?

 

[Number Nine]

Why be so insulting, number nine? Why not objectively define your objections?

I admit that I may have been overly sensitive, given that I've recently been spending time with a group of Cantor cranks, but I get the distinct impression that he isn't entirely serious. He strongly downplays the evidence for the big bang (ignores the CMB!), misrepresents expansion as involving the Universe expanding into something, and really seems to have trouble with the concept of infinity in set theory.

 

[Farahday]

Why be so insulting, number nine? Why not objectively define your objections?

Chronos, #9 has obviously embarrassed himself enough...leave the poor guy alone. He obviously doesn't know integers are real numbers.

http://en.wikipedia.org/wiki/Real_number "In mathematics, a real number is a value that represents a quantity along a continuous line. The real numbers include all the rational numbers, such as the integer −5 and the fraction 4/3, and all the irrational numbers such as √2 and ∏"

 

[Farahday]

Originally Posted by Farahday
You can torturously contort all the equations you wish to cast the shape of the cosmos into a 'finite but unbounded' spherical spacecage, a hyperbolic, flat or pretzel shaped doodad, but no matter how vast the number of items you wish to consider, their size and shape could be summarized and a boundary would be determined.

Also incorrect. The common "torus" model (more of a 3-torus) would introduce no such boundary. The surface, not the interior of the 3-torus and the 4-dimensional "space" surrounding it, is considered to be the Universe, so there is no boundary whatsoever.

? I was not referring to a torus...although I am fond of my trusty 2006 model SE. I was referring to the torture of mathematical principles as it applies to the notion of a finite but unbounded cosmos. In a finite cosmos there are a finite number of "things". Each has its own domain (size and configuration). No matter how large the number of "things" may be, by summation of their volumes and relative positions, a boundary could ultimately be calculated.

 

[Number Nine]

Chronos, #9 has obviously embarrassed himself enough...leave the poor guy alone. He obviously doesn't know integers are real numbers.

The fact that the cardinality of the integers is less than that of the reals has precisely nothing to do with the fact that they are a subset of the reals (I suppose you believe that the interval (0,1) is countable). Please take care to read posts carefully before responding.

Each has its own domain (size and configuration). No matter how large the number of "things" may be, by summation of their volumes and relative positions, a boundary could ultimately be calculated.

You seem to have trouble with the notion of a "boundary". The word has a very specific mathematical definition (which wikipedia will describe), which is what is being used in the this thread. Finite does not imply boundedness; the 3-torus described earlier is an excellent example (finite, but I can move as far as I want in any direction).

 

[Chronos]

An infinite universe also has warts. As Olber pointed out some centuries ago, it is illogical to assuem the universe is both spatially and temporaly infinite. You can duck this logic bomb be assuming there are regions of the universe that are causally disconnected from us - which may even have different physical laws and constants. The problem here is in proving the existence of any causally disconnected regions. It may well be impossible by definition. The best we can say for now is the observable universe is finite. We can observe the EM boundary of the universe which is called the surface of last scattering. It is believed to have originated when this universe was only a few hundred thousand years old. Prior to that time the universe was a hot dense plasma that even light could not escape.

 

[Farahday]

The fact that the cardinality of the integers is less than that of the reals has precisely nothing to do with the fact that they are a subset of the reals --snip--

Thankyou for that concession.

You seem to have trouble with the notion of a "boundary". The word has a very specific mathematical definition (which wikipedia will describe), which is what is being used in the this thread. Finite does not imply boundedness; the 3-torus described earlier is an excellent example (finite, but I can move as far as I want in any direction).

http://en.wikipedia.org/wiki/Finite_set
Finite set
In mathematics, a finite set is a set that has a finite number of elements. The number of elements of a finite set is a natural number (non-negative integer), and is called the cardinality of the set. A set that is not finite is called infinite.

If there are a finite number of elements in the cosmos and each has a boundary then the finite set has a boundary defined by those elements. Assuming it is pretzel shaped or spherical is inconsequential.

 

[Farahday]

An infinite universe also has warts. As Olber pointed out some centuries ago, it is illogical to assume the universe is both spatially and temporaly infinite. You can duck this logic bomb be assuming there are regions of the universe that are causally disconnected from us - which may even have different physical laws and constants. The problem here is in proving the existence of any causally disconnected regions. It may well be impossible by definition. The best we can say for now is the observable universe is finite. We can observe the EM boundary of the universe which is called the surface of last scattering. It is believed to have originated when this universe was only a few hundred thousand years old. Prior to that time the universe was a hot dense plasma that even light could not escape.

If the phenomenon of existence were the result of cause and effect, the cosmos would have to be finite - or have expanded at an infinite rate of for an infinite time. However, that is not the case. The phenomenon if existence is the SOURCE of cause and effect, not the result of it.

Something must exist in order to change or be changed. If existence is required in order for change to occur then cause and effect is a function of being rather than the opposite. Existence CAN be reconciled with the principles of logic (won't burden you with the details), but not by employing cause and effect.

Once one gets over the commonly biased assumption that the universe was "created", an infinite cosmos becomes much more acceptable.

 

[Number Nine]

Thankyou for that concession.

There was no concession. You claimed that there were "fewer" integers than reals because the integers are a subset of the reals. That is plainly false. My emphasis on this claim of yours seems off topic, but there is a reason I keep bringing it up (see below).

f there are a finite number of elements in the cosmos and each has a boundary then the finite set has a boundary defined by those elements. Assuming it is pretzel shaped or spherical is inconsequential.

The topology of the Universe is not inconsequential. You've made several statements (e.g. regarding the cardinality of infinite sets) that suggest that you really don't have a very good understanding basic mathematics. This is fine, of course, because most people have no need to understand things like set theory. The problem is that you insist on developing and defending very strong opinions about physics and mathematics despite your lack of education. The notion of "boundedness" has already been explained to you, and you keep repeating the nonsense that I quoted above despite the corrections of several people in this thread. It is a fairly elementary result, for instance, that a 3-sphere has no boundary, nor does a 3-torus (as has been pointed out already).

 

[detective]

new here and just a closet theorist .. i have always liked einsteins thought experiments and this can help navigate a way through the deeper mysteries ...if applied locally and used as a tool we can try to understand a bigger picture...

...an expanding universe can be likened to a five year old child embarking on a ''circumnavigation'' of the earth...on foot

if that child has not strayed from a set, straight course theoretically he/she should find themselves back to the exact spot they started...but as we all know...this is a total impossibility...in amongst a whole range of reasons...the surface of the Earth is not even..or homogenous..

that particular child is not worried about what is under his/her feet..nor the sky above...just the job in hand on the surface, and so what happens when that child is asked to do a second ''circumnavigation''...four or five years older, with longer strides and different eyes...then happens to miss the mark also and as well, because of the non homogenous nature of the journey

ask that young person to keep attempting this project ad infinitum and the result can only ever be...always different

no one ever informed that young child that they were in fact circumnavigating anything...we knew... but he/she didn't ..so how would that ''child'' ever ''see'' a boundary ?

we are mostly thinking like ''flat landers'' in which there is never an edge to expand from and even if we ''witnessed'' expansion...the outcome is...we wouldn't really know what we are looking at...

happy to be torn to shreds and just loving the bigger picture...cheers

 

[Farahday]

There was no concession. You claimed that there were "fewer" integers than reals because the integers are a subset of the reals. That is plainly false. My emphasis on this claim of yours seems off topic, but there is a reason I keep bringing it up (see below).

The original post by Whovian:
--snip--
For instance, there's a fairly basic proof that the number of real numbers is "more" than the number of real integers.

My response :
Duhhhh... The set of integers is a subset of the set of real numbers.

The number of integers in infinite. The number of reals is infinite. Neither set is quantifiable, but the set of integers is included in the set of real numbers and in any relative context, if the set of real numbers contains ANY number other than those found in the set of integers, that set IS relatively larger. This is simple common sense. Don't know what kind of escoteric reasoning you might have been taught, but I was probably BSing in math (3.7/4.0 GPA) when you were in diapers...never try to BS a BS'er (by your posts I assume you are an undergraduate student, my apologies if this is incorrect).

The topology of the Universe is not inconsequential. You've made several statements (e.g. regarding the cardinality of infinite sets) that suggest that you really don't have a very good understanding basic mathematics. This is fine, of course, because most people have no need to understand things like set theory. The problem is that you insist on developing and defending very strong opinions about physics and mathematics despite your lack of education. The notion of "boundedness" has already been explained to you, and you keep repeating the nonsense that I quoted above despite the corrections of several people in this thread. It is a fairly elementary result, for instance, that a 3-sphere has no boundary, nor does a 3-torus (as has been pointed out already).

I'm familiar with the Minkowski continuum and Einstein's spacetime. I am also familiar with the works of Charles Lutwidge Dodgson. They have much in common. The hypotheses that time can be considered a dimension and the theory that the observed cosmological red shift is expansion related have lured the discipline of cosmology into an academic rabbit hole.

I don't, for a moment, suspect this will change within my lifetime - it does so stimulate scholars' abilities to publish curiouser and curiouser theses - but eventually common sense will prevail and eventually cosmology will awaken back to reality.

Until then I'll just 'Keep My Head'.

 

[Number Nine]

They have much in common. The hypotheses that time can be considered a dimension and the theory that the observed cosmological red shift is expansion related have lured the discipline of cosmology into an academic rabbit hole.

Do you have any credible evidence that the redshift is related to anything other than expansion? This is beginning to sound remarkably like crankery.

Neither set is quantifiable, but the set of integers is included in the set of real numbers and in any relative context, if the set of real numbers contains ANY number other than those found in the set of integers, that set IS relatively larger.

Plainly false. The reals outnumber the integers because there exists no surjective function from the integers to the reals. The even integers, on the other hand, have exactly the same cardinality as the set of all integers, because there exists a bijection between them. The same is true of the set of natural numbers and the set of rational numbers; both sets have exactly the same size, as do the set of all real numbers and the unit interval (0,1). The problem you're having here (which is the same problem you're having in physics), is that you are incapable of grasping anything that violates "common sense".

 

[Farahday]

new here and just a closet theorist .. i have always liked einsteins thought experiments and this can help navigate a way through the deeper mysteries ...if applied locally and used as a tool we can try to understand a bigger picture...

...an expanding universe can be likened to a five year old child embarking on a ''circumnavigation'' of the earth...on foot

if that child has not strayed from a set, straight course theoretically he/she should find themselves back to the exact spot they started...but as we all know...this is a total impossibility...in amongst a whole range of reasons...the surface of the Earth is not even..or homogenous..

that particular child is not worried about what is under his/her feet..nor the sky above...just the job in hand on the surface, and so what happens when that child is asked to do a second ''circumnavigation''...four or five years older, with longer strides and different eyes...then happens to miss the mark also and as well, because of the non homogenous nature of the journey

ask that young person to keep attempting this project ad infinitum and the result can only ever be...always different

no one ever informed that young child that they were in fact circumnavigating anything...we knew... but he/she didn't ..so how would that ''child'' ever ''see'' a boundary ?

we are mostly thinking like ''flat landers'' in which there is never an edge to expand from and even if we ''witnessed'' expansion...the outcome is...we wouldn't really know what we are looking at...

happy to be torn to shreds and just loving the bigger picture...cheers

Time dilation, the speed limit of 'C' and many other anomalies of contemporary science are explainable within a three spatially dimensional perspective. Pundits use the esoterically mystical 'time dimension' rather than the incantation "hocus pocus' because that archaic term is no longer acceptable to the orthodox scientific community. They use it to claim the cosmos is finite (limited) but unbounded (unlimited). Time is only a measurement - a comparison of the relative rate of change of some process against another standard such as the rotation of the Earth or the vibration of a cesium atom.

Theorists have come up with an interesting hypothetical twist in which space curves in upon itself in such a way that for every given point 'A' there is a point 'B' within a finite distance at which motion in any direction will not increase the distance between the two; in fact, if a traveler who could instantaneously traverse a sufficient distance encountered such a point, he would begin to return to his point of origin. The concept describes a "finite but unbounded" Universe and implies a cosmos enveloped in a spherical spacecage. But there is no evidence, no principle of logic, science or mathematics and no law of nature that implies the existence of any point, however distant, at which progress becomes regress.

 

[Number Nine]

Can someone close this thread? It has clearly descended into abject pseudoscience and crankery. The OP is now dismissing LCDM and general relativity entirely.

 

[Farahday]

Plainly false. The reals outnumber the integers because there exists no surjective function from the integers to the reals. The even integers, on the other hand, have exactly the same cardinality as the set of all integers, because there exists a bijection between them. The same is true of the set of natural numbers and the set of rational numbers; both sets have exactly the same size, as do the set of all real numbers and the unit interval (0,1).

LOL - That is what I said. But in English...for those who don't speak Esoterica.

The domain of all integers does not completely fill the domain of all integers PLUS any additional element.

Happy now - or do you want to continue to talk over the heads of the unannointed in hopes of bolstering your argument?

The problem you're having here (which is the same problem you're having in physics), is that you are incapable of grasping anything that violates "common sense".

Like a magician, nature is a master illusionist. Much of it seems to defy common sense until you learn THAT IT DOESN'T!