The nature of our universe.

[batema (Mark)]

Hi

I am teaching my Yr 12 physics students about the future of our universe and am looking for, IF POSSIBLE, a simple way, HA HA, of explaining the difference between an OPEN, CLOSED AND FLAT UNIVERSE. I have read that these terms really relate to the expansion of the universe but still have problems getting my head around this.

Thanks.

Mark

[Robh (Rob)]

On a cosmological scale, considered from a geometric or mathematical point of view, for a ...
1. flat universe (zero curvature)
the angles of a triangle add to 180 degrees
parallel lines stay parallel with distance
for a right triangle, c^2 = a^2 + b^2

2. open universe (negative curvature)
the angles of a triangle add to less than 180 degrees (sides bow inwards)
"parallel lines" diverge with distance
for a right triangle, c^2 < a^2 + b^2

3. closed universe (positive curvature)
the angles of a triangle add to more than 180 degrees (sides bow outwards)
"parallel lines" converge with distance
for a right triangle, c^2 < a^2 + b^2

Regards, Rob

[batema (Mark)]

Thanks Rob. I remember reading about the triangles but another question I' sure I will get from students as well as from myself.

I can see frowards and backwards, right and left and up and down but what does a flat or open or closed universe look like. Does flat mean the universe is like all the galaxies etc on a 2 dimentional plane but that would seem to contradict my visual observations. A girl in my class the other day said this stuff just does my head in in a good way and me too.

Mark

[Robh (Rob)]

Our perception of the Universe is from observation at a local point.
Stars are both moving towards and away from us. Nearby galaxies are both moving towards and away from us.
On a large scale, distant galaxy clusters appear to be moving away from each other.
From special relativity, objects cannot travel faster than the speed of light but space itself can expand faster than the speed of light.
The Big Bang occurred 13.7 billion years ago but the edge of the observable Universe is now 46.5 billion light years.
In fact, the observable Universe can be smaller than the entire Universe as objects move beyond the cosmic event horizon.

Consider travel on the Earth. Coordinates determine our exact position on the globe and our local time. We can fly in a "straight" line and end up back where we started. We can even fly above the Earth and get a picture of our three-dimensional habitat. However, our every day experiences are in terms of a flat (two-dimensional) Earth e.g. local street directory. "Down" means to the centre of the Earth, a straight line, but north means to the North Pole, which is a actually a curved line. It's not too hard to extrapolate our local two-dimensional existence to a three-dimensional Earth.
However, a non-Euclidean model of the Universe is something way beyond our experience. The problem is that space-time is at least a four-dimensional concept and we can't get outside our Universe and get a picture of it. The analogy of ants living on the surface of an expanding sphere is usually used to grasp some concept of an expanding Universe. In reality, we have three dimensional space expanding with time. Up and down have some meaning locally but not on a Universe scale. In a closed Universe, space wraps back around on itself. A non-diverging laser beam could theoretically cross the whole Universe and return to its starting point. In practice, the Universe is not perfectly uniform and the laser would miss itself. In any case, the laser, traveling at light speed, will most likely lose its chase to get back as the Universe continues to expand.

The topology of the Universe is a theoretical description of the way matter influences space. The curvature of space is not something we can see other than in secondary phenomena such as the bending of starlight around the Sun or gravitational lensing. The higher the mass, the more the contraction of the space around it. In normal circumstances, we cannot tell whether the light from a star got to us in a straight line or a curved line. In fact, other than in a flat geometry, the very idea of a straight line is meaningless. Although the type of topology may be supported by scientific observations, there is nothing in our simple observations as space travelers that would lead us to distinguish between the models. This is because local experiences do not reveal the overall picture. To all intents and purposes we may seem to be traveling in a straight line while actually following a geodesic resulting from both local and Cosmic gravitational influences.
The topology of the Universe is important in terms of understanding its evolution and direction. The amount of matter (average matter density) determines the geometry of space and whether the Universe continues to expand or contract in the long term, whether expansion accelerates or decelerates. Dark energy is of course another added complication.

My viewpoint and interpretation.
Regards, Rob

[batema (Mark)]

Thankyou Rob for your detailed response. I'm having a meltdown just trying to fathom this but you have shed some light.

Mark

[pjwdesigngm (Paul)]

I'm a new member to Ice in Space, found this thread interesting.Wondered if others like yourselves see a similar structure between atoms and our solar system. The shells of atoms (electrons) and the orbits of the planets. I have read an article in Astronomy mag. July 2010 by Bob Berman, in this article, Bode's Law describes the link between our solar systems planetary orbits and revolutions within a mathematical sequence. Maybe, atomic structure follows a similar mathematical sequence, and likewise the Universe. I'm 63 years of age, and still trying to grasp within my feeble brain the smallest particle and the largest thing!
Thanks for letting me respond, Paul

[Robh (Rob)]

Originally Posted by pjwdesigngm

I'm a new member to Ice in Space, found this thread interesting.Wondered if others like yourselves see a similar structure between atoms and our solar system. The shells of atoms (electrons) and the orbits of the planets. I have read an article in Astronomy mag. July 2010 by Bob Berman, in this article, Bode's Law describes the link between our solar systems planetary orbits and revolutions within a mathematical sequence. Maybe, atomic structure follows a similar mathematical sequence, and likewise the Universe. I'm 63 years of age, and still trying to grasp within my feeble brain the smallest particle and the largest thing!
Thanks for letting me respond, Paul

There are some similarities and some very real differences between the physics of an orbiting electron as against an orbiting planet. The orbit of a planet is elliptical and essentially planar. Slower planets have much bigger orbits and take longer to get around the Sun. Individual orbits are not determined by the mass of the planet, even though they can vary considerably. However, the angular momentum of the planet is dependent on both its mass and angular velocity. Mass can also come into play as planets interfere with each other's orbits when they pass near each other. Here the governing force is gravity. The exact position of a planet at any time t can be predicted entirely by an equation.
Electrons have the same mass, have angular momentum and orbit in specific energy shells (quantum energy states) about the nucleus. An electron in a higher shell has more energy. Electrons, being quantum mechanical, exhibit both particle and wave properties e.g. they can collide with other particles and also be diffracted like light. An electron which drops to a lower energy orbit will release a photon, the difference between the energy levels. These are electromagnetic interactions. The exact position of an electron or photon at any time t cannot be predicted (Heisenberg's uncertainty principle).
A unified field theory is an attempt to explain the fundamental forces (e.g. the two mentioned above) in terms of a single field theory. Whether the similarities and differences of the above, gravity and electromagnetic forces, can be explained by a unified theory is yet to be seen.

Bode's law (hypothesis) was devised from an observation of comparative distances of the then six known planets, with a gap between Mars and Jupiter. The equation is not satisfied exactly but is close enough for many of the planets to give it some credence. It was really of not much consequence until Uranus and then Ceres (between Mars and Jupiter) were discovered to fit in with the hypothesis. Although Neptune broke the pattern, Pluto was roughly in the right place. For the outer planets, the distance from the Sun approximately doubles each time.
Over the years, there has been much debate about any scientific basis for the law and it has generally been discredited as pure coincidence. However, some simulations lend credence to the idea based on orbital resonance (when orbiting bodies exert a periodic gravitational influence on each other) or perhaps collapsing cloud models of planetary formation. As the hypothesis refuses to be shelved, extrasolar planetary systems with enough planets are being looked at to either credit or discredit the idea for good. 55 Cancri is a possible test case.

Regards, Rob.