I think one may find tidal forces would start demolition of the stick well before it could approach the event horizon, unless it was an imaginary stick.
And so we could observe the ends of a stick as it's ends are eaten away...it would be dust that would pass the event horizon.
It depends on the mass of the black hole.
The event horizon radius is proportional to the black hole mass.
The larger the mass, the greater the radius, the lesser the tidal forces.
For a supermassive black hole, tidal forces at the event horizon are insignificant.
In the sticks frame of reference nothing significant happens as it crosses the event horizon of a supermassive black hole.
An imaginary stick with no ends would of course pass right thrue unaffected by physics and out the other side leaving that black hole sitting on our never ending stick like meat on a skewer and it travels onward collecting galaxies etc into eternity.
On the positive I remember after being reminded.
The stick with out ends is like an exercise to imagine the difficulty of grasping the unimaginable enormity of the universe.
Last night I sat outside under a perfect sky thinking about what was before me.
Thinking of the Hubble Deep field knowing everywhere there are so many galaxies.
Makes the problems of the day trivial.
On the positive I remember after being reminded.
The stick with out ends is like an exercise to imagine the difficulty of grasping the unimaginable enormity of the universe.
Last night I sat outside under a perfect sky thinking about what was before me.
Thinking of the Hubble Deep field knowing everywhere there are so many galaxies.
Makes the problems of the day trivial.
yes indeed xelasnave,
.....a humble reminder of how "universally trivial" life is on this planet.
It's astonishing to see the huge numbers of people who place the Earth at the center of "everything" in terms of importance. In fact this arrogance and ignorance extends to spiritual and moral importance. Is it any wonder that the behaviour of humans collectively and individually is sometimes so self destructive and cruel?
A stick without any ends may well be an imaginary artifact of the mind, but it appears that this does not apply to human arrogance and ignorance. If you divide the actual knowledge that humans claim to possess by the "absolute truth" and total knowledge out there, you would get something approaching zero. Not a bad approximation of zero. That Socrates chap was one clever bugger
Mirko,
Our frame of reference is the same as the Earth's.
That's exactly what I mean by rising above the surface. As soon as you do that, you see the curve. You have adopted an outside frame of reference. The point is to stay within the surface, a 2-dimensional universe. It's an analogy after all. Perhaps the problem of infinity can always be overcome by adding another dimension and looking at it from the "outside". You would need to step outside the universe though, as you've said to Alex below.
Quote:
Originally Posted by sjastro
The pathway is defined by the circle inscribed on the sphere. There are no limits. It doesn't matter how many times we travel around this circle, the radius of the circle remains the same.
The radius does not need to change for an infinitely long journey to be possible.
Quote:
Originally Posted by sjastro
By calculating the radius through the circumferential distance travelled, we can find the surface area of the sphere which is finite.
Granted, this does not necessarily form part of the agument, but are we actually able to calculate the radius based on distance travelled, as opposed to obtaining an approximate value?
Quote:
Originally Posted by sjastro
When I mean resolved, I'm referring to the angular resolution of the anisotropic detail in the cosmic radiation background.
There has been a progressive increase in detail from COBE to WMAP to the Planck probe.
Since the detail is now well resolved, cosmologists are able to measure the angular size of individual structures with greater precision.
The measurements are consistent with a flat univese.
Steven
That's the status as at today. I know of something else that was observed as being flat but later found to be (nearly) spherical
xela, you would made a good disciple of the great Socrates
although Socrates was condemned to self administer hemlock after being found guilty of corrupting the youth of Athens. An interesting offense, seeing as the Socratic method of gaining wisdom by "posing questions" and continually probing and questioning the infinite ether of knowledge is a teaching philosophy used today in almost every school. (some argue that education systems today avoid the Socratic method, especially with young children, and prefer the early schooling years to a military training type experience where the natural creativity and curiosity of children is "drummed" and hammered out of them. Out the other end are nice obedient corporate citizens who rarely question anything they are told and are driven by individualism and materialism.)
Science, as a grand pursuit of uncovering knowledge has been contaminated by corporate greed and market forces. Our political system has also suffered the same contamination, yielding to short term profits and thrills. I was particularly touched by a recent Nobel Prize in Physics handed out to inventors of the blue LED. Whilst this is a great invention which finally enables a white LED to be manufactured, how does this compare to say Paul Dirac's PhD thesis completed in his early 20's? or one of the 3 great papers published by Einstein in 1905?
Dreamless pathetic politicians and leaders controlled by greedy sociopathic and narcissistic bankers and corporate dead beats. A compliant corporatised media does the rest....
You are right it is indeed a wonderful world.
I suggest expanding your observations perhaps in a new thread.
Out of respect to Steven I think we should engage the question he has founded this thread upon.
I
That's exactly what I mean by rising above the surface. As soon as you do that, you see the curve. You have adopted an outside frame of reference. The point is to stay within the surface, a 2-dimensional universe. It's an analogy after all. Perhaps the problem of infinity can always be overcome by adding another dimension and looking at it from the "outside". You would need to step outside the universe though, as you've said to Alex below.
Given that I am walking on the surface, not jumping or flying off it, nor drilling a hole through the Earth and travelling through it, my motion is purely confined to the surface.
There is no outside frame of reference in this example. I don't have to be outside the sphere to know its a sphere. I can measure its intrinsic curvature.
Quote:
The radius does not need to change for an infinitely long journey to be possible.
That doesn't define whether a surface is finite or infinite.
A spherical surface is finite and unbounded. The surface of the Earth is finite irrespective how many times we travel around the circumference.
Quote:
Granted, this does not necessarily form part of the agument, but are we actually able to calculate the radius based on distance travelled, as opposed to obtaining an approximate value?
Assuming the Earth is a true sphere we can measure the circumferential distance C travelled. Since the pathway takes on a great circle, the radius r is simply C/2*pi.
This also the radius of the Earth which has surface area of 4*pi*r^2 which is finite.
Quote:
That's the status as at today. I know of something else that was observed as being flat but later found to be (nearly) spherical
The difference here is the evidence itself rules out the Universe as a 3-sphere. Cosmology doesn't suggest the entire Universe has to be of a particular geometry to start with.
The options are flat, closed (spherical) or open (hyperbolic).
Assuming the Earth is a true sphere we can measure the circumferential distance C travelled. Since the pathway takes on a great circle, the radius r is simply C/2*pi.
This also the radius of the Earth which has surface area of 4*pi*r^2 which is finite.
I'm aware of the formula. Do we know what exactly pi is?
Quote:
Originally Posted by sjastro
The difference here is the evidence itself rules out the Universe as a 3-sphere.
Sounds like it's all done and dusted then & any researchers still working on this particular problem would be wasting their time.
I'm aware of the formula. Do we know what exactly pi is?
PI is irrational but it is a finite number.
The surface area of the sphere is still finite.
Quote:
Sounds like it's all done and dusted then & any researchers still working on this particular problem would be wasting their time.
A misconceptions about science.
Scientific theory is only as good as the technology performing the observation or experiment. With improvements in technologies, scientific theories undergo retesting and are never done and dusted.
The Newtonian model of the moon's orbit as being in freefall around the Earth is a good example. For 250 years theory agreed with observation until Apollo astronauts put mirrors on the lunar surface which allowed a far more precise measurement of the Earth Moon distance.
It was found that the moon is not in freefall but is moving away from the Earth.
The successive improvements in measuring the anisotropic detail in the cosmic radiation background has only reinforced that the universe is flat.
The GUT (10^-43 to 10^-38 sec) and Electroweak (10^-38 to 10^-12 sec) eras followed the Planck era (0 to 10^-43).
The recent discovery of the Higgs Boson supports a cosmological model which includes the GUT era followed by the Electroweak era.
When the GUT era ended the strong force separated from the other forces. This decoupling event resulted in a huge release of energy which cause the of "inflation" period. Just to put "inflation" in perspective, the Universe actually expanded by a factor of 1035 in only 10-32 seconds.The Universe exploded from the size of a single electron to the size of a table tennis ball in only 10^-32 seconds. (that's the theory anyway)
There are many unanswered questions about the early Post Planck eras let alone what happened prior to 10^-43 seconds - where there is absence of any Physical theory or observation.
Even though Inflation theory does help explain both the Horizon Problem and the Flatness problem, its by no means settled. (Physicists dont even understand what the bulk of the Universe is made up of with modest understanding of the Baryonic matter that makes up our reality - whatever that it. I would prefer to give Physicists and philosophers another 20 or 30 thousand years of hard work and serious thought - maybe more. Imagine how long Chemists will need to sort things out, a discipline which is more complex than Physics. Biology more complex than Chemistry and then we have psychology)
Last edited by Eratosthenes; 19-05-2015 at 12:23 AM.
