Thankyou all. Some interesting ideas to digest. "Breakdown" is a bit of a strong word, but what I was suggesting was the problem of infinity. It's like dividing by zero. You can't do it.

I should have explained what I meant by the law of gravity, and yes the Newtonian constraints are noted. I was told many years ago (and its possible this was false, or has since been disproven), by a reliable source (a professor), that tests had been conducted in a vacuum (or at least as close as it is possible to get) dropping a feather and a ball, and though the time difference was extremely small, the objects did not touch the ground at the same time, which contradicts our understanding of gravity and the laws of motion. Is this some sort of science myth? Like the perpetual motion machine? It might be? I have never heard anymore about it, but it has always stuck in my mind as an oddity.

Good point about energy becoming matter. That is one possible answer. And also the notion that "nothing" may not be true. That everywhere, at every point, there is always something, even if only a couple of atoms or something else.

I suppose these posts bring to my mind the difficult problem of: infinity, nothing, eternity. Can the universe exist forever - eternity? These are concepts our mind cannot comprehend. We live on a planet where everything has a beginning and an end. Nothing is eternal - or at least, if it is - we cannot concieve this. Its the edges of our science, zero, absolute numbers (to an infinite number of decimal places) which cause us problems. A universe which always "was" and has no limits or boundary, simply does not compute. But then again one that began at t=0, does not either. The Jews have a saying for this: "who can know such things?"

With regard to numbers, measurements in the real world, being to an infinite number of decimal places. That is nothing exists in nature which is exactly 100.000 mm wide with an infinite number of zeros behind it, it made me think that our engineering standards are not actually to make things more precise. It is the opposite. Our standards of manufacturing physical objects are to make things less precise. Nature is way too precise for us. We simply want to produce two objects to a lower degree of precision, say to four decimal places.

Yes I read about the Big Crunch in Astronomy Now magazine I think. You are right of course that a deceleration in expansion does no disprove the big bang theory.

I'm glad that we've given your cranial meat-machine something new to chew on. It should never be bored . That being said...

HKATER wrote:

Source of the post but what I was suggesting was the problem of infinity. It's like dividing by zero. You can't do it.

It is not necessarily logical to compare zero with infinity. The former is a place-holder within a numerological system and does not actually represent anything. Thus nothing in nature is 'zero'. The latter is an indeterminable value of something. Rather like the irrational value of Pi, infinity has no exact place on Ye Olde Number Line (whereas zero does, even if only as a placeholder) because in this case it has no absolute value. It is merely incalculable quantity - a non-natural number. Infinity certainly IS on the number line, but no-one is sure where in any situation it is applied, unlike zero.

Something else that is interesting to contemplate: Infinities are not actually 'infinite' in the sense of the word. There are different 'values' of infinities, which reflects as perfectly logical if we consider the prior idea that infinities merely represent an unknown, but unbounded high value on a Number Line. If you are interested in exploring this, then I'd suggest reading this article in the Scientific American that explains this peculiar notion: https://www.scientificamerican.com/article/strange-but-true-infinity-comes-in-different-sizes/.

HKATER wrote:

Source of the post I suppose these posts bring to my mind the difficult problem of: infinity, nothing, eternity. Can the universe exist forever - eternity?

Of course it can. There is nothing mathematically forbidding a universe (or SOMETHING) existing forever in some state or other. It's just not what we observe to be more or less true for our universe, such as we understand it. That is the clincher here: it's not that infinities don't exist, it's just that we can't really observe them. Take, for example, the Multiverse Theory. In it, physicist Brian Greene extrapolates that there are around nine possible types of "multiverses". Most involve infinities in some way, but the so-called "Quilted Multiverse" is interesting when one tries to think about observing infinities:  In Quilted Multiverse theory, the universe is an infinite planar grid. Every so often, a Big Bang is set off in this dimension-less space, and scatters light and energy 'outwards' in typical Big Bang fashion. The light from these Bangs is still traveling through space, to this very day, infinitely. The space between these dimensions (and the Bangs that caused them) is where the light from all the "big bangs" hasn't reached and hence contains no light, and therefore can't be seen until "our" section of light expands into it, creating our "cosmic particle horizon" (i.e. the biggest possible distance from which a particle could have traveled since the big bang). This should not be confused with the Cosmic Event Horizon, which is the limit beyond which no events can be observed or influence the observer due to the universe's expansion. Unfortuantely, due to relativity, if one would go beyond the particle horizon, you wouldn't see beyond the universe - just more of it because your perspective in space/time has shifted. You would be simply the new center of an observable universe.

So, put simply, we can only see as far as our light has reached (or had once it formed into something) and that is our own individual cosmic horizon. The reason I'm telling you about cosmic horizons is as follows: In such an infinite plane, there will be an innumerable number of universes, wherein everything and anything can conceivably occur. In typical Multiverse fashion, an unknown number of these universes would be sterile, lacking the required physical laws to do anything - or others would be totally alien, based on different configurations of natural law. But in an incalculable number of those, every possible outcome in this universe (or vice versa across the universes) will have occurred. The only problem is that we simply cannot obverse these alternate universes - they are forever locked beyond our respective event horizons, something that we could never see or fly past, even via FTL means.



As an aside, this theory relies on the universe being gravitationally flat (which although general relativity tells us is the case, we cannot demonstrate that in an infinite universe), but it's food for thought. I addition, if one applies the idea of certain infinities having differing values then others - then some interesting implications come up. Does it mean, for example, that there is some fixed number of possible outcomes defined by a unknown quantity of infinity? Or that at some point this process closes after some value of infinity is reached? These seem like non-sequiturs, but neat to think about.

Wat would dark matter be elementary particles, like leptons and quarks, or could it composite particles which became weakly interacting because its constituent particles bonded in such a way to make it so?  Also, why would it not interact via the other three fundamental forces but it interacts with gravity?  I remember reading that the sterile neutrino could be such a particle and because it only reacts with gravity, it would be able to travel either direction in time (because it wouldn't be bound to our brane- since, according to brane theory, gravity leaks in from outside our brane.)

Wow- looks like we all were thinking of composite particles haha.

Stellarator, I consider biological systems mechanical; if you look at individual cells, they are like powerhouse machines, and even inorganic matter like crystals can undergo evolution in a similar way. The whole is greater than the sum of the parts but that doesn't mean that the mechanical component isn't there- it definitely is.

Also, excellent post about other universes and zero/infinity!  We can divide by zero, but the answer we get wont be a specific number, but rather the concept of infinity.  Infinity can exist if we consider the number line to not actually be a line but a circle, and then we can analogize it to a sphere, which is another way to achieve infinity, on a sphere you can proceed infinitely in one direction- and eventually you will end back right where you started!  Our universe may be like this!  And it does not need to come from nothing- many theories of quantum gravity predict that the big bang was actually a big bounce of a previously contracting universe!  There are many values of infinity and I was looking for an article I read many years ago about different types of infinity and different kinds of weird numbers lol- maybe that article is the one you linked to?  The article I read mentioned Itzhak Bars who came up with double time theory- two dimensions of time, something that also fascinates me (and which Stephen Hawking injected into his idea of Imaginary Time, which does away with the big bang singularity. )  By the way, fascinating discussion about the possibility of life in other universes, Lee Smolin posits that universes evolve to quantumly select universes that prefer life, from previous generations of universes that had life in them!

You may be right about not being able to venture into other universes, but I think there is a possibility we could do it if we take a bubble of our space-time with us (and especially if Wat's Penrose Diagrams of Kerr Black Holes end up being correct.)  There is another way of doing it too, I expect light to be something that all universes have in common so if we could convert ourselves to pure energy we could journey through other universes even without bubbles!  This of course assumes that by the time we can do this, we'd be able to convert back to our regular matter selves when we return (and in that sense our journey through another universe may seem to us to be like a dream, or an out of body experience, or even a near death experience.)  I write about these possibilities in my Origin series.

A-L-E-X wrote:

Source of the post Wat would dark matter be elementary particles, like leptons and quarks, or could it composite particles which became weakly interacting because its constituent particles bonded in such a way to make it so?

Great question.  I don't know of theory leaning one way or other yet, and I can imagine either scenario being true.

A-L-E-X wrote:

Source of the post Also, why would it not interact via the other three fundamental forces but it interacts with gravity?

We might ask the same question for why neutrinos only experience gravity and the weak force.  

In general, which fundamental forces a particle will experience depends on what it is made of, and what types of "charge" (in a generalized sense) it possesses.  Mass is the property that gives rise to gravitation.  Electric charge gives rise to the electromagnetic force by interacting through photons (whether real or virtual).  Hadrons, being built from quarks, experience the strong nuclear force by exchanging gluons, and the manner in which gluons are exchanged depends on the "color charge".  Finally, the weak nuclear force is governed by a quantity called "weak isospin", and the force is exchanged by W and Z bosons.  W bosons are charged while Z's are neutral.

Neutrinos, lacking electric charge and not being made up of quarks, experience neither the electromagnetic force nor the strong force.  They interact only by the weak force (and gravity, because their masses are small but not zero, as evidenced by the neutrino oscillation).  But I feel this is less of an explanation for "why" (which is a tricky question and I like to refer to the latter part of my earlier post about the challenges of "why" questions), and more "how" they interact.

So what we can say about dark matter is that it must have some significant mass "per particle", it cannot be made up of quarks, and it cannot have electric charge.  Its properties are very similar to what a heavy, slow neutrino would be like.  Exactly like the "sterile neutrino" as you mention.

HKATER, thank you as well for your posting your questions!  This has been very good material for discussion.

HKATER wrote:

Source of the post what I was suggesting was the problem of infinity. It's like dividing by zero. You can't do it.

Yes, of course.  I think of infinity as a concept, not a number.  The simplest case is to imagine dividing something into smaller and smaller pieces.  The smaller the pieces, the more of them you get, and "in the limit" that the size of the pieces goes to zero, the number of them trends to infinity.  What infinity means here is that no matter how small you make your cuts, I can in principle choose a smaller cut and obtain a larger number of pieces.  But dividing something into pieces of zero size makes no physical sense.  "Infinity pieces" is not a number of pieces.

With the Big Bang theory, I can happily say that none of our understanding of the universe is contingent upon dividing by zero.  The Big Bang theory is about when the size of the universe was very small, but not zero.  The temperature and density and so forth are very large, but finite.  Presumably what really happens with the initial instant of expansion at t=0 is that these quantities are not truly infinite, and the size not truly zero, but just very, very close to them.  

With black holes, the classic prediction is that everything that falls into them goes to a point of zero size at the center.  We recognize this is absurd.  Whatever the "singularity" in the black hole really is is probably not an infinitesimal point, but something "close" to that.  However there is a very nice property of gravitational field which says the gravity outside of any spherically symmetric clump of matter is exactly the same as if that clump were compressed to a point.  In other words, it doesn't matter whether it's a true singularity or something small but of finite size inside the black hole.  The rest of the black hole's properties are exactly the same in either case.  So we can treat it as a true singularity and get all of the correct predictions for how black holes behave!

HKATER wrote:

Source of the post  I was told many years ago (and its possible this was false, or has since been disproven), by a reliable source (a professor), that tests had been conducted in a vacuum (or at least as close as it is possible to get) dropping a feather and a ball, and though the time difference was extremely small, the objects did not touch the ground at the same time, which contradicts our understanding of gravity and the laws of motion.  Is this some sort of science myth?

That would be a test of the "equivalence principle", which says that all objects, independently of their mass, fall with the exact same acceleration in a gravitational field (after excluding any other forces, like drag with the air).  It is an important principle for general relativity, and there are many ways to test it, such as with pendulums, dropping objects in vacuum, and observing satellites in orbit.

I don't doubt someone may have done a drop test and found a difference in their fall times, but I would strongly doubt that the difference was real and not caused by imperfections of their setup or failure to account for other effects.  At the very least, dropping two objects in a vacuum chamber is not a very high precision test.  

Here is a history of some experimental tests of the equivalence principle, and their precision:



In other words, the equivalence principle has been tested and shown to be correct to within 1 part in a billion billion!  So I believe you can be confident in using the equivalence principle in any situation you may encounter which might depend on it.

HKATER wrote:

Source of the post  A universe which always "was" and has no limits or boundary, simply does not compute. But then again one that began at t=0, does not either.

I don't think that either case would be nonsensical or forbidden by nature.  Ask instead, "what is consistent or inconsistent with observations?"

Let's propose for the moment that the universe is infinite in size and age and uniformly filled with the same stuff.  If this is true, then the night sky would be as bright as the surface of a star, because every line of sight would intersect a star.  Obviously, this contradicts observations.  So that set of propositions must be false.

What parts are false?  Maybe space is no longer filled with stars after some distance.  Can we test that?  Actually, we can!  If this was the case, then we would observe that edge as a sudden cutoff in the amount of light reaching us after a certain distance and redshift.  It would also contradict the principle of homogeneity, where we observe the universe is uniformly filled with the same stuff at all distances.

Maybe instead the universe is finite in size?  Again that can't be the case because if it was also infinitely old then we would see that edge.

The solution is that the age is finite.  The night sky is not as bright as a star because only light emitted from within a certain distance of us has had the time to reach us.  We know that this is the case, because we can observe how the universe has changed over time.  The farther back we look, the hotter and denser it was, ultimately going back to what was very nearly a singularity state of extraordinary high temperature and density.  We observe the Cosmic Microwave Background radiation, emitted from when the universe was 1100 times denser, and so hot that atoms could not exist.   Before that and even closer to that initial moment of expansion we call the Big Bang, conditions were so extreme that even protons and neutrons could not exist.  The universe was a violent sea of exotic subatomic particles.

What conditions were like "before the Big Bang", or if there is even a meaningful answer to it, is totally unknown.  But we may as well call this initial hot and dense state "the birth" of the universe as we know it.

A-L-E-X wrote:

Source of the post Stellarator, I consider biological systems mechanical; if you look at individual cells, they are like powerhouse machines, and even inorganic matter like crystals can undergo evolution in a similar way. The whole is greater than the sum of the parts but that doesn't mean that the mechanical component isn't there- it definitely is.

Yes, this is how I see it as well. Human beings like to imagine that organic life is special and unique (because they are it), whereas any other reflections of it  are inferior reflections. It's just another form of bigotry, a hang-over from those old primordial days when xenophobia could save your tribe from extinction and whatnot. Ultimately though, we're all just pieces of self-perceiving, interdependant matter!

A-L-E-X wrote:

Source of the post and then we can analogize it to a sphere,

Certain cosmological theories place it as a hypersphere, I.e. the 3 dimensional representation of a 4d sphere. It's a very cool concept.

A-L-E-X wrote:

Source of the post here are many values of infinity and I was looking for an article I read many years ago about different types of infinity and different kinds of weird numbers lol- maybe that article is the one you linked to?  The article I read mentioned Itzhak Bars who came up with double time theory- two dimensions of time, something that also fascinates me

Yes, there were a few published papers and articles exploring this sort of thing knocking around the web. I had bookmarked them, then lost the links  . But there are lots of discussions online dealing with that sort of thing and it's pretty fascinating stuff to read. The mere fact that there are different 'types' of infinite concepts is pretty mind-blowing.

A-L-E-X wrote:

Source of the post There is another way of doing it too, I expect light to be something that all universes have in common so if we could convert ourselves to pure energy we could journey through other universes even without bubbles!  This of course assumes that by the time we can do this, we'd be able to convert back to our regular matter selves when we return

I'm really not sure. Photons may not be ubiquitous to all universes. Think of it this way: if there are an infinite number of universes, then the chance of the one 'right next to us' having the physical laws similar enough to our universe to have photons as we know them is infinitely unlikely. As soon as you deal with infinities, everything is impossible to quantify.

It is wrong to say that anything is 'next to our universe'. This assumes that the 'space' of the multiverse spawns new universes right next to one another. More likely would be them inhabiting the same 'space' in some sort of superpositional manner, because if each universe is infinite, then there would be no boundary that it would 'share' with another universe. You couldn't reach other universes by finding an edge to them because you'd never find it. Some other means of transition is required. 

What do you think Watsisname? Is it even logical to draw conclusions like this?

Stellarator wrote:

Source of the post What do you think Watsisname? Is it even logical to draw conclusions like this?

I think this sort of speculation is extremely dubious.  It relies on all sorts of assumptions about how other universes would be, if they even exist, and how they would interact, if they even do.

As for infinity having different sizes, an easy way to see this is to imagine counting up all the positive integers.  Start at one, and off you go: "1, 2, 3, 4, ..." and on and on.  You would count forever -- there are infinitely many positive integers.  

But now imagine counting up all the numbers between 0 and 1.  Numbers like 0.65, 3/7, and 1/sqrt(2).  Where would you even begin?  0.1 is too big.  0.01 is too big.  0.00 and a quadrillion zeroes and a 1 is still too big.  Clearly, there are an infinite number of numbers between 0 and 1, but it's a different kind of infinity.  It is "uncountably many", as opposed to the integers which are at least "countable", in the sense that you can pick a starting point and proceed to count in some logical sequence.

Also weird is that the "size of infinity" for the set of numbers between 0 and 1 is exactly the same as for the set of numbers between 0 and 2.^‡  You might think there should be twice as many between 0 and 2, but there aren't.  Doubling every number in one set gives you the second set, so there is a 1:1 correspondence between them, and they are the same infinity.


‡ There is some problem with what we mean by "size" of infinity, and what I mean in this case is the "cardinality", or how many elements are in each set.  Since there is a 1:1 mapping between them, meaning every element in one set can be renamed to give the second set, the sets are of the same cardinality, and in that sense are equal infinities.

Watsisname wrote:

Source of the post It relies on all sorts of assumptions about how other universes would be, if they even exist, and how they would interact, if they even do.

Oh yes, this is more in the spirit of philosophical speculation then scientific existentialism. I don't think that universes can interact with one another, and if they did, it would either be very subtle or something we'd overlook due to it's unknown exotic nature.

Watsisname wrote:

Source of the post It is "uncountably many", as opposed to the integers which are at least "countable", in the sense that you can pick a starting point and proceed to count in some logical sequence.

How do other 'known' numbers that have infinite digits fit into this paradigm? Such 'irrational' numbers like Pi can, like the certain infinities you pointed out above, be placed somewhere in the number line - but it is impossible to say exactly where due to there unknown decimal representation. Could we ever quantify the exact digits of Pi? Do we actually have a better idea of Pi's placement then certain infinities?

Stellarator wrote:

Source of the post How do other 'known' numbers that have infinite digits fit into this paradigm? Such 'irrational' numbers like Pi can, like the certain infinities you pointed out above, be placed somewhere in the number line - but it is impossible to say exactly where due to there unknown decimal representation. Could we ever quantify the exact digits of Pi?

Yes, there is a proof that pi is irrational, meaning it has infinitely many digits and they never repeat (it cannot be written as a ratio of any two integers). So the number of digits of pi is the same as the number of integers on the number line.  They are countably infinite.  And this also means it cannot be exactly located on the number line -- only better and better approximated.

I've posted this before a while back, but I like to post it again because it's relevant: my favorite mathematical function, [math]y=\frac{sin(1/x)}{x}.  The classic example of a singularity where things become infinite is the function y=1/x, which blows up to +/- infinity as x approaches zero.  This function takes it a step further: it has infinitely many squiggles, on any finite interval that you choose around x=0.  You can zoom into it as much as you like, and you'll only find more squiggles, and they'll only get taller and steeper.

Also, the area under the curve (the integral from -infinity to +infinity) is finite, and exactly equal to pi, which is pretty cute.

Based on the above, would it be very wrong to say that pi represents a type of infinity that we can approximate in position?

Also, very cool that one can find pi in Singularities. I had come across this before, but it really drives home the essential nature of numbers in the universe .

Stellarator wrote:

Source of the post Based on the above, would it be very wrong to say that pi represents a type of infinity that we can approximate in position?

I think the way I would phrase it is that it takes infinite precision to specify what the value of pi (or what its position on the number line) is.  That is fairly interesting, since it clearly has a physical meaning, with its definition rooted in geometry.

Stellarator wrote:

Source of the post Also, very cool that one can find pi in Singularities.

One can find pi in all sorts of things.   The above example is perhaps not too astonishing since it involves the sine function, and where you have sines you have circles, but from visual inspection of the curve this result is probably not obvious at all.

My current favorite example of pi showing up in a surprising place is this one:

Watsisname wrote:

Source of the post One can find pi in all sorts of things.

YES! When I had learned about this phenomena I said to myself "WHAT IS THIS SORCERY?", and had a similar feeling that you get when watching a good magic show. But like a magic show, once you learn about all the different factors that result to this wonderful outcome, it's really quite special and new understanding dawns on you. 

It is truly amazing that you can see such things in action, as in the video above. One could say that the 'universe' that the computer program rendered in the video is a mathematically harmonious universe, since it can compute the pi infinity so elegantly. In our own universe, other physical laws and motions curtail this expression, and thus such an expression would be impossible to observe in this manner (though this pi repeat does show up elsewhere as we know).

Watsisname wrote:

Source of the post One can find pi in all sorts of things

And e.

(And since we're speaking of π, like, e^iπ = -1)

midtskogen wrote:

Watsisname wrote:

Source of the post One can find pi in all sorts of things

And e.

(And since we're speaking of π, like, e^iπ = -1)

And 137. This 33rd prime number seems to be deeply interwoven into the nature of reality, from quantum physics, to being the fine structure constant (roughly 1/137 - Arthur Eddington thought it was exactly equal) indicating how strong electromagnetism is, to the famed golden ration wherein dividing a circle with two radii yields sectors of 137^o - a so-called golden angle. Since the early twentieth century physicists believed it to be vital to cosmology - more famously Richard Feynman postulated that it was a centrally important number to scientists. I myself am quite aware that scientists can be wrong about things they are passionate about, and am a little amused at the media's exaggerated portrayal of these so-called 'magic-numbers', but I'm intrigued as to their communicative use in contacting totally alien civilizations. 

(I'm sure everyone here already knows about 137 - I'm just reflecting my fascination with this intriguing number .)

I think I have enough links in these posts to add to my favourite reading topics of "metaphysics" and "quantum mechanics" to keep me busy for a while. Reminds me of a book I have been meaning to read for years in my collection (have started reading it a few times) titled "The Goldilocks Enigma" by Paul Davies. It has some mind blowing concepts in it too.

On another topic, I have been wanting to write a space empire sci-fi book, a bit like star wars, for a while now, but the concept of time dilation and FLT has scared me off it. The idea that TIME is dependent on the speed of the traveller and that a returning traveller has aged at a different rate to those left on earth, makes space travel, communications and the whole concept of multi-solar space empires extremely problematic. Scifi writers ignore the problem completely - I don't blame them. The whole concept will give you a headache if you try to analyse it. The vast distances between stars and the necessary speeds required to get there is just crazy complicated. Add TIME effects (TIME DILATION) and it becomes impossible to imagine or recreate. i believe we will break the FTL barrier. Simply because if you can't travel faster than light, you won't be able to get there. But the topic is obviously controversial.

Alot of persons have commented on the absurdity of present scifi books and galactic empires, able to communicate almost instantaneously across hundreds and thousands of light years, but I think they are missing the point a bit. Yes it is absurd - but someday, somehow, mankind will have to tackle these problems. The alternative is we all live on a rock orbiting a star in an unexplored universe. Somehow the last scenario seems even more absurd. I believe our future is the stars. How we get there is like a giant puzzle for us to solve. We have always loved a challenge.