A “common center” is relative to a particular gravitational field. The moon, for instance, orbits around the common center which is “in” the earth.
Please provide your source for the claim that Einstein said there is a “common center to the universe towards all objects will eventually fall.”
That does not sound like something Einstein would have said because if there is a common center in the universe then the universe would rotate. And if the universe rotates, then it violates Mach’s Principle. Is the Universe Rotating?
It would have been quite a news item and cast doubt on General Relativity, IMHO. Moreover, if there exists a common center outside the universe, then the universe would be orbiting it.
For Lurkers interested in an introduction to Relativity with graphics:
Do Parallel Lines Meet At Infinity?
Asked by a student at St-Joseph Secondary School on October 5, 1997:
I am curious. Could this ever happen?
If you are talking about ordinary lines and ordinary geometry, then parallel lines do not meet. For example, the line x=1 and the line x=2 do not meet at any point, since the x coordinate of a point cannot be both 1 and 2 at the same time.
In this context, there is no such thing as "infinity" and parallel lines do not meet.
However, you can construct other forms of geometry, so-called non-Euclidean geometries. For example, you can take the usual points of the plane and attach to them an additional point called "infinity" and consider all lines to also include this additional point. In this context, there is a single "infinity" location where all lines meet. In a geometry like this, all lines intersect at infinity, in addition to any finite point where they might happen to meet.
Or, you could attach not just one additional point, but a whole collection of additional points, one for each direction. Then you can consider two parallel lines to meet at the extra point corresponding to their common direction, whereas two non-parellel lines do not intersect at infinity but intersect only at the usual finite intersection point. This is called projective geometry, and is described in more detail in the answer to another question.
In summary, then: in usual geometry, parallel lines do not meet. There is no such thing as infinity, and it is wrong to say that parallel lines meet at infinity.
However, you can construct other geometric systems, whose "points" include not only the points of familiar geometry (describable as coordinate pairs (x,y)), but also other objects. These other objects can be constructed in various ways, as described in the discussion of projective geometry. In these other geometric systems, parallel lines may meet at a "point at infinity". Whether this is one single point or different points for different classes of parallel lines, depends on the particular geometric system you are considering.
You may also be interested in our answers and explanations page, which contains a discussion of the question does infinity exist?
As an example:
In my opinion, his understanding of mathematics as a deeper revelation of the divine is far, far more important than his math theories.
From Plato through the likes of Gödel, Wigner, Barrow, Penrose, Tegmark and Vafa - mathematicians and physicists have noticed the mysteriousness of math and stood in awe of it though oftentimes unable to convince others who could not see what they were seeing. But Nicholas of Cusa’s understanding was much deeper than theirs because his was spiritual.
Nicholas of Cusa also saw what so many of us on this thread see and have commented on using different terms but the point is the same – that man cannot perceive God through sensory perception (“learned ignorance”.) He probably wouldn’t have used the metaphor I used earlier but the point is the same, i.e. that a maggot has a better chance of describing a human in terms sensible to a maggot than man has in describing God in terms sensible to a man.
And much like Einstein, Nicholas of Cusa perceived the universe is relative – laying the groundwork for Kepler’s laws of planetary motion and suggesting that perfect circles do not exist in a physical sense. Noting again here that Einstein's Relativity leads to the conclusion that straight lines do not exist in a physical sense.
But Nicholas of Cusa – like most everyone else until the 1960’s (Einstein included) – understood the universe to be steady state, physically infinite.
Nicholas of Cusa of course was long departed this world by then – but Einstein wasn’t. His reaction to the possibility (which was confirmed after his death) was to propose a cosmological constant. He later called that his worst mistake, it was kluged.
If Nicholas of Cusa were alive at the time, I imagine his reaction to the news that the universe is finite and expanding – that there was a beginning of real space and real time – would be much like that of Jastrow’s – i.e. that it is the most theological statement ever to come out of science. There was a beginning of space/time, an uncaused cause of causation itself – while the theologians were still reeling from the implications of Darwin’s theory here comes the most remarkable observation that God cannot be denied.
me: Infinity is an unbounded quantity greater than every real number
Jo kus: I disagree. Infinity has no "quantity" because there is no distinction. Minimum and maximum are IDENTICAL! There is absolutely NO distinction in infinity. You have already admitted as such when you say "all points on an infinite line are the same". Infinity is not "one plus the last number"!
Also, I have not destroyed “the” definition of eternity, but rather challenged your definition of it. You are the one rejecting the definition of eternity as “time without end.”
Jo kus: I have already addressed this error. "time without end" is only projected in one direction. Eternity is without end in EITHER direction. Thus, there is no future or past in eternity. In "time without end", we realize that time has a starting point, but without end. That is TWO DIFFERENT things, A-G
Me: If it were “no time” or “timelessness” then it would be the ex nihilo - void, null, empty – which preceded God’s Creation of “all that there is” – both spiritual and physical
Jo kus: That is revelation. "Before" God created time, there was nothing. We believe God created from nothing.
And geometric physics (Vafa, Wesson, et al) has posited several theories of multiple temporal dimensions. If even one additional dimension of time exists, then time in our four dimensional perception (3 of space, 1 of time) is not a line but a plane. Past, present and future are all points on the plane. A change at a point, affects all points on the plane.
Sci-fi writers love these theories, of course.
Another Freeper extended the plane theory of time to volume. But since he, MHGinTN, is writing a book and this is one of its features, I will say no more.
As for me, I testify once again that eternity is relative to time – that God created both space and time, both spiritual and physical – whether time is a line, a plane, a volume or a moment only God knows. And what the character of time in the new heaven and new earth is (Revelation) also only God knows. To say that God exists in eternity – or that eternity is a property of God - is to anthropomorphize Him into a small ‘god’ our minds can comprehend.
God’s Name I AM has no time boundary or limitation at all. That is why “everlasting to everlasting” is sensible in speaking of God the Creator – there is no time in which He is not. And He is, i.e. He is not time-bound.
God’s Names Alpha and Omega are time relative only in the sense of First Cause and Final Cause. “All that there is” whether spiritual or physical was created by and for Jesus Christ, Who is the Only begotten Son of God.
That God speaks to us space/time bound creatures at all is a blessing. God the Father has revealed Himself to us through Jesus Christ, through the Holy Spirit, through Scriptures and through Creation, both spiritual and physical.
Nicholas of Cusa evidently saw a revelation of God in Creation, in the mathematics.
So do I. That is why I call the "unreasonable effectiveness of math" God's copyright notice on the Cosmos.
Jo kus: "the Spirit PROCEEDS from the Father THROUGH the Son". The Father is the principle of the Spirit. Kosta, anything to add? Otherwise, you have expressed the catholic/orthodox trinitarian belief.
Kosta50: Insofar as A-G's statement "The Spirit is from the Father by the Son" makes the Son a necessary co-element in Spirit's procession, which is not the Trinitarian belief.
But when the Comforter is come, whom I will send unto you from the Father, [even] the Spirit of truth, which proceedeth from the Father, he shall testify of me: - John 15:26
Nevertheless I tell you the truth; It is expedient for you that I go away: for if I go not away, the Comforter will not come unto you; but if I depart, I will send him unto you. – John 16:7
That is a far cry form saying that parallel lines intersect at infinity. There is no reason why two equidistant lines maintaining equidistant separation can not remain perfectly parallel on a curved (warped) surface.
A definition of parallel is that something remains equividstant from another object over extended distance. Parallel lines cannot, by definition, intersect. It doesn't matter that no such entity exists in the real universe (which is only a conjecture!), only convergent lines will intersect.
Please provide your source for the claim that Einstein said there is a “common center to the universe towards all objects will eventually fall.”
That is the only way that he can make a claim that parallel lines intersect at infinity. They must have an infinitissimal angle of convergence in order to meet at infinity. If he didn't make that claim then he is wrong.
As you said: However, you can construct other forms of geometry, so-called non-Euclidean geometries
All man-made models. There is nothing absolute or "ordained" about modern cosmology. Simply new observer definitions and "angles." No matter what geometry you use, two parallel lines cannot have a common point in infinity and remain parallel.
In math, one can add variable to get the desired answer. If the model works, it is not necessarily "true" but working. Like the Ptolemaic navigation system. Ptolemy added epicycles to account for observed behavior. It describes the observed phenomenon, but it does not reflect what we know of plenary motion today empirically.
From Plato through the likes of Gödel, Wigner, Barrow, Penrose, Tegmark and Vafa - mathematicians and physicists have noticed the mysteriousness of math and stood in awe of it though oftentimes unable to convince others who could not see what they were seeing. But Nicholas of Cusa’s understanding was much deeper than theirs because his was spiritual.
Nicholas of Cusa also saw what so many of us on this thread see and have commented on using different terms but the point is the same – that man cannot perceive God through sensory perception (“learned ignorance”.) He probably wouldn’t have used the metaphor I used earlier but the point is the same, i.e. that a maggot has a better chance of describing a human in terms sensible to a maggot than man has in describing God in terms sensible to a man.
Well, on this we agree, and that was my initial point to Dr. Eckleburg. I also enjoyed the way he discussed minimum and maximum within eternity, as it helped to understand the concept a bit. I do agree that mathematics help us to understand ever so slightly the concept that is beyond the physical.
I do not see the point in continuing to argue about "eternity" and "time without end". It is more than theological, since we KNOW that time must have had a beginning. It is logically impossible to consider an infinite regression of time and ever reach today. Thus, time began at some point. Eternity does not have a beginning because there must be an uncaused cause to begin the process. Nor can there be a "starting point" when all points are indistinct. There is no maximum or minimum, no beginning or end point.
Naturally, then, since time is a creation, then God is not subject to it AND God is transcendent and beyond time, unless He chooses to enter into time. As such, as I have tried to explain, eternity is thus timelessness, without BEGINNING or end. It is one moment of changeless NOW. ALL points in time are like geometric points in infinity. They are indistinct and unity. Thus, if we consider this and apply it to time, we can say that all points in time are the same, changeless and immediately accessible to One who is transcendent.
Thanks for your discussions on the subject. No doubt, neither of us has really touched even the tip of the iceberg on the subject. My point was that the human wisdom has reached its pinnacle when we realize that we are ignorant about God.
Regards
***And there are several others who believe that time does not exist at all.... ***
I suppose that all depends upon how you define time. ;^)
What a strange thread.