Undercurrent

If it makes you feel better, there are quite a few General Relativists who believe that the infinities that arise in GR, spec. the singularity at the centre of a black hole, are real, and that the Ricci scalar at that point actually is "infinity."

m.

eh

An infinite universe is compatible with the big bang. In fact, it is one possible model of the universe predicted by GR.

Shadowy Man

And it appears that the universe is compatible with that model. The data support the model that the universe is spatially infinite.

crocodile deathroll

If you had a stop watch and no matter how far you advanced into the future, the instant you stopped it, the concept of eternity will always disappear into a finite number doesn't if it is 100 years 10^100 years or 10^10^10^10^10^100 years. That property would be a constant. Eternity as a concept will always self annihilate itself.

So forever is dead.

[ December 15, 2002: Message edited by: crocodile deathroll ]</p>

eh

Yeah, it does seem that the universe is flat in the euclidean sense. But someone on this board pointed out that even a flat universe can be finite, if it has the right topology. Some kind of torus shape would apparently allow the universe to be flat, and expand forever yet be finite. I'm not sure if this true or not.

Answerer

Sorry to ask, but which data are you talking about?

Shadowy Man

Studies of fluctuations in the CMB are an example of the projects showing evidence of a flat universe. MAXIMA and BOOMERANG being two of the more recent ones.

The data agree pretty strongly with the theories that predict a flat, spatially infinite universe.

Oxymoron

How about the charge density of an electron in QED? (thus the requirement for virtual particles to mitigate the singularity.)

Bob K

Can we find infinities in realities?

The following is a description of the infinities, and finities, of reality, of the universe.

It can be posted as a separate Topic, but it functions as a Reply, albeit lengthy, for this present Topic.

Basic Philosophy

A thing is an object, a unity, an identity which has a longer duration in time than a related event.

Examples: A woman named Jane, a ball, and a man named Dick.

An event is a relationship between or among things, and occurs in a limited and therefore specific period of time, a specific length of duration between two timepoints, usually of shorter duration than related things.

Example: Jane throws the ball to Dick.

A concept is a mental representation, idea, of a thing.

A principle is a mental representation/idea of an event.

Causality is the principle, the mental representation/idea, describing events in which people/things/events who/which are causes causing/creating/arranging/organizing people/things/events who/which are effects, and who/which can become causes of effects.

Example: Jane causes, is the cause of, the effect of the ball traveling through space towards Dick.

An explanation is the description of a causality, the relationship between/among things in an event, things/events as causes causing/creating/arranging/ordering things/events as effects.

The Universe

The universe consists of the combination of three realities: 1. The spatial reality, space; 2. the temporal reality, time; and 3. the physical reality, physics, matter/energy.

Each independent reality has its own infinity.

1. Space, the spatial reality, is the unbounded, infinite vastness, area, arena, place, location, stage, theatre, etc., which would be a pure vacuum if not for the presence of matter/energy, physics, has no substance, no limiting distances, and thus gives us an understanding of spatial infinity, and, though having no substance, having yet the infinity of duration in time.

Space, being infinite in dimension, conceptualizable as a latticework of rigid rods, 100% non-deformable for dimensions or straightness, either parallel to each other or crossed at right angles to each other, would be extended without end, without limit, by additional rigid rods, there being no limit to the number of rigid rods which could be attached to the latticework of space.

Space, therefore, by being unbounded, unlimited geometry, a pure vacuum except for the presence of the matter/energy which is the physical reality, is 100% open, with no possibility of ever being closed.

The presence of matter/energy, the physical reality, in space cannot and does not ever deform space. A pure vacuum cannot be deformed because it is totally substanceless, totally without matter/energy, with nothing to deform. Space, the pure vacuum, is pure nothing, absolute nothing, absolute nothingness, infinite emptiness. Matter/energy, the physical reality, produces electromagnetic and gravitational fields, and potentially other fields, within space, and each field, being comprised of matter/energy of some kind, including matter/energy of a kind, or kinds, not currently observed, is a cause of relevant/related effects upon things/events comprised of matter/energy, including whatever are the observed deformations of things/events comprised of matter/energy.

Thus, the infinity of space consists of its unbounded, unlimited spatial dimensions, no end to its length, width, height, etc.; and space, as a pure vacuum, except for the presence of matter/energy, the physical reality, is infinite in duration.

2. The temporal reality, time, is the use of time-intervals (TIs) for the measurement of the occurrences of events in sequences of events.

TIs are arbitrary, chosen by men, for subjective as well as objective reasons. TIs can be, and most often initially are, periodic motions. Once the duration of the periodic motion is established as a TI, the TI becomes independent of the original periodic motion. Thus, a TI is a standard of measurement of time.

There are two types of time-intervals: variable time-intervals (VTIs) and invariable time-intervals (ITIs).

When VTIs are used, in common clocks, atomic clocks, etc., in variable time-interval clocks (VITCs) which are not designed to be motion-sensing and self-adjusting for changes of velocity/gravity, or otherwise intended to by synchronized by radio signals, then time, the measurement of time-intervals for the measurement of occurrences of events in sequences of events, history, will appear to vary when such clocks are subjected to changes of velocity/gravity.

A. Einstein, on page 99 of his book, Relativity, defined time thus: “Mechanical clocks serve for the definition of time.”

AE thus used VTIs, variable time-intervals, for the development of relativity, and, thus, in his theories, time was variable, and, being variable, was not independent of space, thus permitting the concept of spacetime.

When ITIs are used, in clocks which are designed to be motion-sensing and self-adjusting, or otherwise synchronized by radio signals, so everywhere such ITI clocks (ITICs) are to be found, the measurement of time is identical, then we have universal time, absolute time, which can be used for measuring time from an arbitrary Timepoint, T0, forwards into the future and/or backwards into the past:

Infinity &lt;- Backwards &lt;- T-2 &lt;- T-1 &lt;- TO -&gt; T+1 -&gt; T+2 -&gt; Forwards -&gt; Infinity

We find, therefore, no end to the measurement of ITIs into the past or the future, therefore we see what is temporal infinity, the infinity of time, with time never having a beginning nor an ending.

ITIs give us the independence of time from space. Regardless of where they are in space, how fast they are traveling in space, regardless of their acceleration, deceleration, or constant velocity, regardless of their reference frame, ITIs in ITICs give us the independence of time from space, and thus eliminate spacetime as a necessary physical concept.

The present moment, the Now, is the unique configuration, or pattern, or arrangement, in space, in the spatial reality, of all things/events comprised of matter/energy, in a arbitrary and therefore finite duration of time, conceptualizable as one timepoint, preferably as one timepoint, or as a duration between timepoints.

With the succession of timepoints the configuration of matter/energy changes and thus motion is observed. Things here at the timepoint of T0 are there at timepoint T+1; things that were yonder at timepoint T-1 are hither at timepoint T0. Thus for a time period of the succession, sequence, of timepoints T-2 -&gt; T-1 -&gt; T0 -&gt; T+1 -&gt; T+2, at each timepoint there is a unique configuration of matter/energy that comprises, is, the Now for that timepoint.

Past Nows are previous unique configurations of matter/energy which can never be replicated, because a replication would occur at a new timepoint in the sequence of time and would require considerable energy, additional energy which would have to come from without the known universe, which is impossible, because there is only one universe. Thus, time travel into the past is impossible. Future Nows have yet to occur and therefore have not yet occurred, therefore time travel into the future is impossible.

Because past Nows cannot be replicated, and the present Now evolves into the next Now, there is a forward direction for the arrow of time. Where time can be counted backwards, into the past, the Now cannot evolve into the past, instead, it can only evolve into the future, hence the forever forward direction of the arrow of time.

History is the recorded occurrences of people/things/events in the sequence of the event we call time. Because we can measure time using invariable time-intervals for consistency we can assign occurrences of people/things/events to specific timepoints according to our measurement of the ITIs which define each unique timepoint, each Now.

The understanding of time gives us an understanding of the temporal reality, which is time itself and its infinity, its infinite, never-ending measurement of time-intervals, therefore its infinite duration.

The temporal reality thus gives us a measurement of the infinite duration of the spatial reality, space, the physical reality, matter/energy, and time itself.

3. The physical reality, physics, matter/energy, the matter/energy of which all things and events are comprised, has been observed to be indestructible, only convertible, matter convertible into energy, and vice versa, and experimentally confirmed, E = mc2 and m = E/c2; matter/energy has infinite duration in time, and, therefore had no beginning and will have no ending.

The indestructibility and thus infinite duration in time of the physical reality, matter/energy, including the electric charge, gives us the infinity of the physical reality.

Though infinite in duration, matter/energy, physics, the physical reality, is limited in quantity, and therefore is finite, and, therefore, has a finity (the opposite of an infinity).

Within matter/energy is the electric charge, which has been observed and confirmed to be indestructible yet convertible, infinite in duration in time, with the sum total quantity being the same, never changing, and a finite quantity, another finity.

The spatial reality, space, the temporal reality, time, and the physical reality, matter/energy, combine to produce the universe.

Because of the infinity of the unbounded space which is the spatial reality, the infinity of the measurement of time into the future, or backwards into the past, using invariable time-intervals, and the infinity of the duration of the physical reality, physics, matter/energy, we have an understanding of the infinite nature of the universe, no beginning, no ending.

Causality is people/things/events who/which are comprised of matter/energy and who/which are causes causing/creating people/things/events who/which are likewise comprised of matter/energy and who/which are effects, cause-and-effect, graphically, cause -&gt; effect.

The source of causality is the physical reality, matter/energy, which, having infinite duration, no beginning and no ending, proves the necessary reality of infinite succession of causality. All regressions seeking a cause will come back to matter/energy as the source of causality.

Thus, there never was a first cause, nor will there ever be a final effect which shall not become a cause of another effect.

Nothing will ever come from nothing; something will always come from something, and always has.

The universe, comprised of the spatial reality, space, the temporal reality, time, and the physical reality, physics, matter/energy, could not have begun in a Big Bang, nor can it be ended in a Big Crunch. Space was thus not created in a Bang, nor time, nor matter/energy, and space will not be eliminated/destroyed in a Crunch, nor time, nor matter/energy.

Thus, from an understanding of time, we can understand the infinite vastness and duration of space, the infinite duration of matter/energy, and the infinite duration of time itself.

eh

Bob K wrote,

Space, the spatial reality, is the unbounded, infinite vastness, area, arena, place, location, stage, theatre, etc., which would be a pure vacuum if not for the presence of matter/energy, physics, has no substance, no limiting distances, and thus gives us an understanding of spatial infinity, and, though having no substance, having yet the infinity of duration in time.

This is wrong. Space is merely the relationship of matter/energy. Much like how a sentence is merely the relationship of words, and cannot exist without these same words - space cannot exist without energy. Though it may be infinite in extent, it is also possible that space is finite.

If you want to claim space can exist without matter, then you're into the concept of an aether. Since this space clearly exists, it is a thing, and your claim about it having no substance is made logically impossible.

ITIs give us the independence of time from space. Regardless of where they are in space, how fast they are traveling in space, regardless of their acceleration, deceleration, or constant velocity, regardless of their reference frame, ITIs in ITICs give us the independence of time from space, and thus eliminate spacetime as a necessary physical concept.

I don't see how this is true. Those clocks ticking are merely the movement of atoms, and very much depend on the space they are in. There is no universal time, and like space, you can't have time without energy.

Your failure to grasp the fact the space and time are simply relationships of matter/energy leads you to the false conclusion that the big bang could not have occured. Space is not the 'nothingess' you think, and is as logically sound as a circle square. Once you realize that, you'll see that modern cosmology makes some sense after all.