Large Hardon Collider

[Woozie]

0 would be nothing there. Infinitely small would be as close to 0 as you can get without getting there, wouldn't it? So maybe a cubic planck or something.

Or whatever would be as close to the concept of 0.000...(infinite 0s)...1, with so many 0s in between that you can't possibly add another one.

(Yeah, I know, that's not how it works, but whatever the closest non-flawed real thing is to that would be infinitely small)

Or perhaps envision the asymptote of 1/x as x approaches infinity, the result gets closer and closer to 0 but never quite reaches there.

There's no such thing as being as close to 0 as you can get without getting there. For any real number greater than zero, there are an infinite amount of numbers in between. Actually, what you said works when you look at the limiting case. This is the only way to get a number infinitely small (i.e. infinitely close to zero), but in this case, your number can be shown to be equal to zero. There's no way to get infinitely close to a number without being equal to the number. If you find any two (real) numbers, either the two numbers are equal, or there are numbers in between the two numbers (meaning it's still possible for one number to get even closer to the other). So any time you hear someone use the term "infinitely close to zero", then technically the number they're referring to is equal to zero, but they're using it as a limiting case.

0.000....(to infinity) with a 1 and the end is zero. I could show this mathematically if you want, but you can understand this intuitively by noting that the 1 at the end never actually shows up. The closest non-flawed real thing to zero would be the situation I described above.

For any x, you can choose a value such that 0 < x < 1/n, even as n goes to infinity.

This is true for any (non-zero) real number, n, regardless of size. But saying this is true for any natural number is way different than saying it's true for the limit. By it's very definition, the limit of 1/n has to be able to made smaller than ANY natural number k > 0. You can't say "Well if you stop at any given n in R there's always a smaller number" if we're referring to the limiting case. In the limiting case, there exists no number greater than zero that's smaller than 1/n. So the number is infinitely close to zero, and has a property that no number except zero can have, and thus, is zero (if we're talking about the limiting case, as Neo and Khamsim are). Adding an infinitesimal amount to something doesn't make it non-zero. The only reason we can manipulate expressions of this form is because we assume the values are finite but very small at first, and then when we finish whatever math needs to be done, we then take the values to become infinitesimal (zero). If your physical answer is still infinitesimal in a situation where zero can't be an answer, then you have a problem.

So yes, from a purely mathematical perspective infinitely close to zero IS zero. A number infinitely close to any other number is that same number (in R). Infinitely small and zero are identical. This isn't something that's debatable. It's provable. Ironically, we actually just went over this in analysis a few days ago (they wont let me test out for some reason so I have to sit through the whole course D: I have to take Mechanics I/Quantum I/E&MI too. I think it's BS that if a person already knows a subject, they have to pay hundreds to take the course anyways instead of just testing out and saving time and money).

[Eliseos]

BEC's do not involve zero volume, and infinitely small is not 0.

Like others have said, that's exactly what you do as you take the limit as the denominator approaches 0. Every time you derive or integrate something, this happens. Woozie pretty much hit every point on it.

[Eliseos]

In other news, I was excited to see the newly upgraded hubble featured on major news sites with pictures like this APOD: 2009 September 10 - The Butterfly Nebula from Upgraded Hubble

[Max™]

Like others have said, that's exactly what you do as you take the limit as the denominator approaches 0. Every time you derive or integrate something, this happens. Woozie pretty much hit every point on it.

In purely mathematical terms, this is true, and I was wrong on that point.

In purely physical terms, this is no longer reasonable to argue as a true statement. There is nothing but proof that you can not arbitrarily take a limit as close to any number as you wish, and so in reality you can not say infinitely small is zero.

In reality you can not say something is infinitely small either.


I think Neo is confusing mathematical objects with real objects and blaming me for doing that.

[Neosutra]

Actually no Max, Ive given several explanations for the physical singularities and described the difference between a mathematical one and a physical one. This little tangent started when you attempted to explain a quantum singularity as a "break in the mathematics" or an incorrect model, when that is completely inaccurate and ignores the many plausible solutions and actual physics of the situation.

[Khamsin]

(sorry Max, but, as I've said before, your argument style seems incoherent to me. I'm not saying you're wrong, I'm just saying that even if you tried to tell me that 2+2=4 or that the world is round, I still wouldn't know what the hell you were talking about)

But the world is round. Let me explain it in a colorful fashion for you.

Imagine a jump rope tied end to end so that it forms a closed loop. Now place a mirror next to it and imagine if you could take the reflected jump rope out of the mirror to create two jump ropes. Repeat until you have infinite jump ropes.

Now, take each jump rope loop and configure it so that it's circumference is related to it's diameter by a ratio of pi. Stand one loop up on end, and place the next loop in the same place, only rotated slightly around it's Z axis. Do the same for half of the loops. Now take a loop and wrap it around the other jump ropes sideways at the middle. Take another and place it in the same spot, rotated slightly around it's X or Y axis. Do the same for the remaining jump ropes.

Now, shake the jump ropes around a bit until they all knot up. What you'll have is an infinitely dense mesh grid of knots that form roughly the shape of the world, which is round.

Spoiler: show

Sorry, just bored!

[Boyiee]

But the world is round. Let me explain it in a colorful fashion for you.

Imagine a jump rope tied end to end so that it forms a closed loop. Now place a mirror next to it and imagine if you could take the reflected jump rope out of the mirror to create two jump ropes. Repeat until you have infinite jump ropes.

Now, take each jump rope loop and configure it so that it's circumference is related to it's diameter by a ratio of pi. Stand one loop up on end, and place the next loop in the same place, only rotated slightly around it's Z axis. Do the same for half of the loops. Now take a loop and wrap it around the other jump ropes sideways at the middle. Take another and place it in the same spot, rotated slightly around it's X or Y axis. Do the same for the remaining jump ropes.

Now, shake the jump ropes around a bit until they all knot up. What you'll have is an infinitely dense mesh grid of knots that form roughly the shape of the world, which is round.

Spoiler: show

Sorry, just bored!

Spoiler: show

infinitely bored?

[Khamsin]

Spoiler: show

infinitely bored?

Spoiler: show

No, just infinitesimally entertained.

[Max™]

Actually no Max, Ive given several explanations for the physical singularities and described the difference between a mathematical one and a physical one. This little tangent started when you attempted to explain a quantum singularity as a "break in the mathematics" or an incorrect model, when that is completely inaccurate and ignores the many plausible solutions and actual physics of the situation.

No, in GR, a singularity is a break in the mathematics, and is what results from modeling black holes.

More specifically, it is a point where you can no longer model interactions accurately.

Spacetime can be described wonderfully in terms of worldlines, an event horizon is a location where worldlines can go in, but not out. You can still describe worldlines beyond a horizon though, in some sense.

A singularity is a terminus to all worldlines which cross it, and in traditional black hole solutions a singularity is the point where all worldlines inside of an event horizon converge.

Time is oriented differently, as are physical degrees of freedom, on the other side of a horizon.


I've never heard of a plausible solution of a singularity done in a purely quantum mechanical fashion, but I've never heard of a purely quantum mechanical manner to describe spacetime with which didn't leave me with the urge to scream "BACKGROUND DEPENDENCE" afterwards.

[Max™]

Spoiler: show

But the world is round. Let me explain it in a colorful fashion for you.

Imagine a jump rope tied end to end so that it forms a closed loop. Now place a mirror next to it and imagine if you could take the reflected jump rope out of the mirror to create two jump ropes. Repeat until you have infinite jump ropes.

Now, take each jump rope loop and configure it so that it's circumference is related to it's diameter by a ratio of pi. Stand one loop up on end, and place the next loop in the same place, only rotated slightly around it's Z axis. Do the same for half of the loops. Now take a loop and wrap it around the other jump ropes sideways at the middle. Take another and place it in the same spot, rotated slightly around it's X or Y axis. Do the same for the remaining jump ropes.

Now, shake the jump ropes around a bit until they all knot up. What you'll have is an infinitely dense mesh grid of knots that form roughly the shape of the world, which is round.

Spoiler: show

Sorry, just bored!

<Obi Wan> I have failed you, I see that now.

(hint: it helps if you understand the concepts of modern physics enough to be able to ask questions if you aren't sure where I'm trying to connect these "colorful" explanations to current theories, but before you write me off as nothing but these visuals and metaphors, you should know they are extremely simplified and distilled so that any layman can grasp the concepts in a more intuitive manner... so I believe you zinged yourself , didn't you?)

[Khamsin]

So if the observable universe is all a single knotted up mesh of propertyless material only observable at intersecting, tangled strands... what are the physics behind the interaction of this strand and itself? What are the dimensions and space occupied by this mesh? There has to be more than one dimension of it, in order to tangle with itself.

Why does it become observable only when tangling with itself? If this mesh is propertyless, how does a knot in it suddenly gain value? Wouldn't that violate some law or another on conserving information, matter, or energy? Can a knot untie itself and the energy it represents disappear from the universe? Or a new tangle form, and new energy is created?

[Max™]

So if the observable universe is all a single knotted up mesh of propertyless material only observable at intersecting, tangled strands... what are the physics behind the interaction of this strand and itself? What are the dimensions and space occupied by this mesh? There has to be more than one dimension of it, in order to tangle with itself.

Schiller proposed it was a single strand, I work from the idea that there are at least three sets of strands, and they are most likely large loops.

The interactions between crossings/knots and the flat sections show up as a topological description of the four forces we observe.

The dimensions and space are the same thing, btw, and there are three different orientations possible of threads against other threads, thus three spatial dimensions.

The three directions/dimensions we observe as space/time/spacetime are not something which these objects exist IN, they are something which emerges as a large scale structure composed OF these objects.

Why does it become observable only when tangling with itself? If this mesh is propertyless, how does a knot in it suddenly gain value? Wouldn't that violate some law or another on conserving information, matter, or energy? Can a knot untie itself and the energy it represents disappear from the universe? Or a new tangle form, and new energy is created?

He insists on the unobservable aspect, I do not. He is trying to preserve a different form of quantum interaction than I am though.

A knot can untie itself, but it would induce a change in the crossing states/topological structure of the fabric around it. When particles decay you observe various decay products, same idea.


The only reason that the strands are required to be unobservable is to preserve a non-local form of interaction allowing traditional quantum mechanics to function unedited.

They can be observable in a sense/possess properties if you discard non-local behavior entirely and move to a different description of causal interaction.

[Khamsin]

But what are the physics of the strands interacting with each other? What describes the reaction of one strand meeting another, how can we model and predict that effect, and what is the science that says "This propertyless strand, when intersecting that one, will do ______ because ______"? What part of science says that our observations of weak and strong interactions, electromagnetism, and gravity should arise naturally and expectedly from this tangling of strands? The strands must have some property to them besides dimension to cause such an effect, wouldn't they?

[Max™]

Topological interactions as described by simple knot theory provide the effects you are looking for.

Treating them as if they have no property but dimension, and thus a minimal dimension (the planck length) produces the forces in a rather surprisingly simple manner.

[Max™]

Going back to the singularity discussion.


In General Relativity, mass is not treated as something with properties, it is merely the source of the stress-energy tensor, which helps determine the overall metric of the spacetime being considered.

Basically you take the value you want to calculate a spacetime for, that being the stress-energy tensor, along with affecting a few others which I won't go into as they just confuse the point more, solve the equations, and you produce a set of solutions describing the curvature and behavior of the mass in question.

When you increase the mass beyond a certain point, as noted by Schwarzschild, you are no longer able to calculate paths which enter and then leave a certain region around the object in question.

You've produced an event horizon.

The curvature could be thought of as being too steep beyond a certain point, paths can be plotted going in, but not out, not even for a beam of light.

Now, if you take this extremely curved spacetime and calculate what effect it has on the mass which produced it, you inevitably produce (as Penrose and Hawking showed) a singularity.

A point beyond which you can not calculate the future trajectories of any path which crosses it.

So now you have a hole, and inside that hole you have an end point.

You can drop something into the hole and it can swirl around, and you can calculate this.

Yet if it crosses that end point, that's it, it's gone. You can not produce any reasonable calculations about that path.


It does NOT state what it is, which is not surprising, as you never stated what the object which created this structure in spacetime was in the first place.


There is no well defined lower bound in General Relativity beyond which you should obviously stop increasing the curvature, and stop tightening the noose which is about to cut off any paths crossing the future singularity.

This is because there is no physical treatment of what matter is, only the fields which affect matter, and the fields which accompany it.


Do you see a problem there?

[Eliseos]

This thread needs some love, so here's some Water Present Across The Moon's Surface, New Research Shows

[Mizango]

This thread needs some love, so here's some Water Present Across The Moon's Surface, New Research Shows

I was going to post this when I got home! A remarkable find, further proof that things we thought were exclusive and special to us is more common then previously thought.

[Eliseos]

Definitely. It makes a lot more sense since we found water in Mars' soil also (technically we already knew it was on Mars, due to the lakes, but not in the soil itself). Hopefully this helps moon missions become more viable, and the public doesn't see it as a waste. I saw some TED talk of how a driller wanted to mine lunar ice to be used for a fuel on the return trip from a moon mission. This would help ease the cost, since they would only need enough fuel to get to the moon, then mine the rest of their fuel for the return voyage.

[Mizango]

This will hopefully expedite out plans to place a settlement on the moon by 2025. I mean I know its only a quart per ton of lunar soil but still, that is a major find.

Combine this with what we found on Mars, Ice and geysers on Saturn's moon Enceladus and on Titan.

Again, its not magic. This is what you call awesome.

[Blarg]

After the devil buried the dinosaur bones he planted that water on the moon.