My Argument for a Completely Smooth Space-time and Why It Can't Be Quantized

[ryan]

If space-time is not perfectly smooth, then the length of any rigid structure would constantly change by at least a factor of 1.4 as it spins through 360 degrees in any space. Because the length that I claim would have to change this much as it spins in any granular space-time, obviously it would have been observed by now. For example, spokes in bicycle rims would not fit as the rim rotates, etc.

This is a tricky subject, so please bear with me. That said, this is simple and intuitive, so there is no need to bring up any advanced math or physics.

This will be an argument (possibly a proof) by contradiction. We will first try to construct a space-time structure that assumes space-time is not perfectly smooth (neither mathematically dense nor mathematically complete) 4 dimensional structure/fabric, and we will focus on the 3 spatial dimensions.

First of all, I will assume that there are only 2 possible categories of a granulated space-time. There would either be spaces between the space-time quanta, or it would have quantised shapes that touch each other everywhere, thus would completely fill any volume with no boundaries. Either one, I claim, would give the demonstratively false observation that I mentioned above.

I say there is no relevant difference between the two because we can imagine something like a carbon nanotube that stretches through a space-time that has gaps of nothing or gaps of another "subspace-time". If the gaps have absolutely nothing in them, then the nanotube might just carry on as if there is no gap there, hence there's nothing there, nothing to cause it to behave different than expected. Even if the gap of nothing is one kilometer long (assume that nothing can have extrinsic properties) then it is like there is no gap at all. And if there is some kind of subspace-time that space-time resides on, then we can just focus on this subspace-time and ask whether or not its coarse.

Now, if you're with me so far, then I want you to imagine the geometry of your space-time that would not allow a rotating body to change in length. You can use any shapes, you can even mix and match shapes. And remember; your shapes can be as small as you want them to be. The shape or shapes you have chosen cannot be smaller than some distance Ax,By and Cz. If you want, this can be the size of a Planck length or a million orders of magnitude smaller; it doesn't matter for my argument. Again, these shapes that you have chosen must be as large or larger than that of a volume having any fixed Ax, By and Cz distances.

So now let's go back to the carbon nanotube. Each particle that makes up the carbon nanotube can only be in a finite number of positions within your shapes, or else your shapes would consist of a perfectly smooth space-time. If you want your space-time quanta to be smaller than particles, if that is even possible, then that is fine too. If particles are points, then you might as well say that only one particle can fit in each quantized shape with excess space-time. And to make things easy, let's just say that each particle can only take up distances Ax, By and Cz within your shapes. For a shape small enough, this leaves only one place a particle can be in at a time in any given quantum of your space-time.

Okay, now here is the argument.

Picture the geometric makeup of your space-time. There will probably be an angle that a carbon nanotube can lie in where no space is wasted; this would be the case with a space-time of shapes where the borders touch each other perpendicularly to a straight carbon nanotube, such as cubes, spheres, etc. But with spheres, cubes or any other shape, there will only be three angles in R3 that will conserve space perfectly like this. As your tube changes its radial position, it will gain the distance it covers as it goes across the borders of your shapes at an angle instead of perpendicularly.

To summarize, what I find very interesting and convincing is that no matter what kind of shape or what kind of configuration of different shapes you use in constructing your space-time, the carbon nanotube will still have to eventually go from a perpendicular position with the borders of the shapes to an angle of 45 degrees with that same border. This will cause your tube to take a staircase position instead of following a straight line.

 

[Juma]

If space-time is not perfectly smooth, then the length of any rigid structure would constantly change by at least a factor of 1.4 as it spins through 360 degrees in any space. Because the length that I claim would have to change this much as it spins in any granular space-time, obviously it would have been observed by now. For example, spokes in bicycle rims would not fit as the rim rotates, etc.

This is a tricky subject, so please bear with me. That said, this is simple and intuitive, so there is no need to bring up any advanced math or physics.

This will be an argument (possibly a proof) by contradiction. We will first try to construct a space-time structure that assumes space-time is not perfectly smooth (neither mathematically dense nor mathematically complete) 4 dimensional structure/fabric, and we will focus on the 3 spatial dimensions.

First of all, I will assume that there are only 2 possible categories of a granulated space-time. There would either be spaces between the space-time quanta, or it would have quantised shapes that touch each other everywhere, thus would completely fill any volume with no boundaries. Either one, I claim, would give the demonstratively false observation that I mentioned above.

I say there is no relevant difference between the two because we can imagine something like a carbon nanotube that stretches through a space-time that has gaps of nothing or gaps of another "subspace-time". If the gaps have absolutely nothing in them, then the nanotube might just carry on as if there is no gap there, hence there's nothing there, nothing to cause it to behave different than expected. Even if the gap of nothing is one kilometer long (assume that nothing can have extrinsic properties) then it is like there is no gap at all. And if there is some kind of subspace-time that space-time resides on, then we can just focus on this subspace-time and ask whether or not its coarse.

Now, if you're with me so far, then I want you to imagine the geometry of your space-time that would not allow a rotating body to change in length. You can use any shapes, you can even mix and match shapes. And remember; your shapes can be as small as you want them to be. The shape or shapes you have chosen cannot be smaller than some distance Ax,By and Cz. If you want, this can be the size of a Planck length or a million orders of magnitude smaller; it doesn't matter for my argument. Again, these shapes that you have chosen must be as large or larger than that of a volume having any fixed Ax, By and Cz distances.

So now let's go back to the carbon nanotube. Each particle that makes up the carbon nanotube can only be in a finite number of positions within your shapes, or else your shapes would consist of a perfectly smooth space-time. If you want your space-time quanta to be smaller than particles, if that is even possible, then that is fine too. If particles are points, then you might as well say that only one particle can fit in each quantized shape with excess space-time. And to make things easy, let's just say that each particle can only take up distances Ax, By and Cz within your shapes. For a shape small enough, this leaves only one place a particle can be in at a time in any given quantum of your space-time.

Okay, now here is the argument.

Picture the geometric makeup of your space-time. There will probably be an angle that a carbon nanotube can lie in where no space is wasted; this would be the case with a space-time of shapes where the borders touch each other perpendicularly to a straight carbon nanotube, such as cubes, spheres, etc. But with spheres, cubes or any other shape, there will only be three angles in R3 that will conserve space perfectly like this. As your tube changes its radial position, it will gain the distance it covers as it goes across the borders of your shapes at an angle instead of perpendicularly.

To summarize, what I find very interesting and convincing is that no matter what kind of shape or what kind of configuration of different shapes you use in constructing your space-time, the carbon nanotube will still have to eventually go from a perpendicular position with the borders of the shapes to an angle of 45 degrees with that same border. This will cause your tube to take a staircase position instead of following a straight line.

As long as objects are much larger than the quanta then many quantas will be involved and this effect will be ignorable. Since particles rätravels as waves this is true at least for "normal" wavelengths.

 

[Bomb#20]

If space-time is not perfectly smooth, then the length of any rigid structure would constantly change by at least a factor of 1.4 as it spins through 360 degrees in any space. Because the length that I claim would have to change this much as it spins in any granular space-time, obviously it would have been observed by now. For example, spokes in bicycle rims would not fit as the rim rotates, etc.
...
To summarize, what I find very interesting and convincing is that no matter what kind of shape or what kind of configuration of different shapes you use in constructing your space-time, the carbon nanotube will still have to eventually go from a perpendicular position with the borders of the shapes to an angle of 45 degrees with that same border. This will cause your tube to take a staircase position instead of following a straight line.

Sorry in advance if I'm not following correctly; but you appear to be assuming a discrete space-time would have some sort of crystalline structure that a rotating macroscopic object would necessarily sometimes be aligned with and sometimes misaligned. If instead we postulate a noncrystalline glass-like structure to space-time, with the elementary grains of space-time positioned randomly with respect to their neighbors, then overall there would be no special directions and the geometric effects of the granularity you're describing would be confined to the Planck scale.

 

[ryan]

As long as objects are much larger than the quanta then many quantas will be involved and this effect will be ignorable.

No matter how small the quantum is, there will be a diagonal 2^(1/2) times longer than its sides 45 degrees from the diagonal. In other words, think of a frog that can only hop on pods that are put in a certain order in a pond. It will eventually have to hop extra far as it hops at different angles. But if the pond is covered with one huge pod, then it can go in a perfect line.

Since particles rätravels as waves this is true at least for "normal" wavelengths.

Let's keep it simple with objects that move through space like a particle.

 

[ryan]

If space-time is not perfectly smooth, then the length of any rigid structure would constantly change by at least a factor of 1.4 as it spins through 360 degrees in any space. Because the length that I claim would have to change this much as it spins in any granular space-time, obviously it would have been observed by now. For example, spokes in bicycle rims would not fit as the rim rotates, etc.
...
To summarize, what I find very interesting and convincing is that no matter what kind of shape or what kind of configuration of different shapes you use in constructing your space-time, the carbon nanotube will still have to eventually go from a perpendicular position with the borders of the shapes to an angle of 45 degrees with that same border. This will cause your tube to take a staircase position instead of following a straight line.

Sorry in advance if I'm not following correctly; but you appear to be assuming a discrete space-time would have some sort of crystalline structure that a rotating macroscopic object would necessarily sometimes be aligned with and sometimes misaligned.

That's exactly my point.

If instead we postulate a noncrystalline glass-like structure to space-time, with the elementary grains of space-time positioned randomly with respect to their neighbors, then overall there would be no special directions and the geometric effects of the granularity you're describing would be confined to the Planck scale.

There is probably a nice and neat mathematical way to explain this, but random shapes are actually worse than regular shapes. Think of any 3 dimensional shape. Now imagine the largest Ax, By and Cz length dimensions that can fit inside of it. This small space is a box (rectangular cuboid I think). At some angle, the atoms of a perfect carbon rod will have to take positions in these minimum spaces. There can't be two atoms in one of these boxes because then there would be a smaller distance in what is suppose to be a minimal distance.

With irregular shapes, there would be a lot of wasted measurable volume of space-time, and distances would be much longer than they could be.

 

[Juma]

No matter how small the quantum is, there will be a diagonal 2^(1/2) times longer than its sides 45 degrees from the diagonal. In other words, think of a frog that can only hop on pods that are put in a certain order in a pond. It will eventually have to hop extra far as it hops at different angles. But if the pond is covered with one huge pod, then it can go in a perfect line.

Since particles rätravels as waves this is true at least for "normal" wavelengths.

Let's keep it simple with objects that move through space like a particle.

But that is where your theory fails. Small things moves as waves, not particles.

 

[ryan]

No matter how small the quantum is, there will be a diagonal 2^(1/2) times longer than its sides 45 degrees from the diagonal. In other words, think of a frog that can only hop on pods that are put in a certain order in a pond. It will eventually have to hop extra far as it hops at different angles. But if the pond is covered with one huge pod, then it can go in a perfect line.



Let's keep it simple with objects that move through space like a particle.

But that is where your theory fails. Small things moves as waves, not particles.

Hmmm, I might not sure that it needs to be this complicated. I might have to come back to this in a few weeks because I am starting a chapter on particles in chemistry soon.

 

[Bomb#20]

There is probably a nice and neat mathematical way to explain this, but random shapes are actually worse than regular shapes. Think of any 3 dimensional shape. Now imagine the largest Ax, By and Cz length dimensions that can fit inside of it.

Individually, yes. The point is, the shapes are all jumbled together, so that over any substantial distance you'll have a roughly even mixture of Axs, Bys, Czs, and random diagonals of those. Rather than a trillion Axs all giving way to a trillion Bys in lockstep as the object rotates, which is what would happen with a regular crystal structure, instead some of the Axs will be stretched into Bys at the same time other Bys are shrunk into Axs, and it will all even out on average. Instead of growing by an inch as the spoke rotates 90 degrees, it will grow by a Planck length and then shrink by a Planck length a trillion times as the spoke rotates a trillionth of a degree.

This small space is a box (rectangular cuboid I think). At some angle, the atoms of a perfect carbon rod will have to take positions in these minimum spaces. There can't be two atoms in one of these boxes because then there would be a smaller distance in what is suppose to be a minimal distance.

Assuming the granularity is at the Planck length, there can't be any atoms in boxes; it's the other way around. There are a lot of boxes in each atom. The grains are about 10^-35 m across; the quarks in a proton are about 10^-15 m apart; and a carbon atom is a hundred thousand times larger even than that. Above, wherever it says "trillion", I should have said "trillion trillion". Forget nanotubes -- it's the atomic nuclei themselves that you need to think of as changing shape when they rotate with respect to the space-time grains. (Which they'd probably be doing anyway since an atom's nucleus is effectively liquid.)

With irregular shapes, there would be a lot of wasted measurable volume of space-time, and distances would be much longer than they could be.

No doubt; but there wouldn't be any direction with significantly less wasted distance than any other direction. So at a macroscopic level we'd never notice.

(None of this is to say that space-time actually is quantized, by the way. As far as I can see, we don't yet have the technology to distinguish smooth from quantized space-time, so we should remain agnostic about it.)

 

[ryan]

Individually, yes. The point is, the shapes are all jumbled together, so that over any substantial distance you'll have a roughly even mixture of Axs, Bys, Czs, and random diagonals of those. Rather than a trillion Axs all giving way to a trillion Bys in lockstep as the object rotates, which is what would happen with a regular crystal structure, instead some of the Axs will be stretched into Bys at the same time other Bys are shrunk into Axs, and it will all even out on average. Instead of growing by an inch as the spoke rotates 90 degrees, it will grow by a Planck length and then shrink by a Planck length a trillion times as the spoke rotates a trillionth of a degree.

This small space is a box (rectangular cuboid I think). At some angle, the atoms of a perfect carbon rod will have to take positions in these minimum spaces. There can't be two atoms in one of these boxes because then there would be a smaller distance in what is suppose to be a minimal distance.

Assuming the granularity is at the Planck length, there can't be any atoms in boxes; it's the other way around. There are a lot of boxes in each atom. The grains are about 10^-35 m across; the quarks in a proton are about 10^-15 m apart; and a carbon atom is a hundred thousand times larger even than that. Above, wherever it says "trillion", I should have said "trillion trillion". Forget nanotubes -- it's the atomic nuclei themselves that you need to think of as changing shape when they rotate with respect to the space-time grains. (Which they'd probably be doing anyway since an atom's nucleus is effectively liquid.)

With irregular shapes, there would be a lot of wasted measurable volume of space-time, and distances would be much longer than they could be.

No doubt; but there wouldn't be any direction with significantly less wasted distance than any other direction. So at a macroscopic level we'd never notice.

Yeah, you're right. Damn, the Nobel Prize shelf is going to have to wait.

One thing that I still find interesting though is that the geometry cannot be regular or even symmetrical in the area that the rod travels through. Though it's probably not a surprize to many.

(None of this is to say that space-time actually is quantized, by the way. As far as I can see, we don't yet have the technology to distinguish smooth from quantized space-time, so we should remain agnostic about it.)

I know that you are not arguing for a quantized space-time.

 

[Juma]

But that is where your theory fails. Small things moves as waves, not particles.

Hmmm, I might not sure that it needs to be this complicated. I might have to come back to this in a few weeks because I am starting a chapter on particles in chemistry soon.

Chemistry? That is at a much gtrearer scale. This is physics, quantum physics and smaller.

 

[beero1000]

Lol, proof.

 

[Underseer]

If space-time is not perfectly smooth, then the length of any rigid structure would constantly change by at least a factor of 1.4 as it spins through 360 degrees in any space. Because the length that I claim would have to change this much as it spins in any granular space-time, obviously it would have been observed by now. For example, spokes in bicycle rims would not fit as the rim rotates, etc.

This is a tricky subject, so please bear with me. That said, this is simple and intuitive, so there is no need to bring up any advanced math or physics.

This will be an argument (possibly a proof) by contradiction. We will first try to construct a space-time structure that assumes space-time is not perfectly smooth (neither mathematically dense nor mathematically complete) 4 dimensional structure/fabric, and we will focus on the 3 spatial dimensions.

First of all, I will assume that there are only 2 possible categories of a granulated space-time. There would either be spaces between the space-time quanta, or it would have quantised shapes that touch each other everywhere, thus would completely fill any volume with no boundaries. Either one, I claim, would give the demonstratively false observation that I mentioned above.

I say there is no relevant difference between the two because we can imagine something like a carbon nanotube that stretches through a space-time that has gaps of nothing or gaps of another "subspace-time". If the gaps have absolutely nothing in them, then the nanotube might just carry on as if there is no gap there, hence there's nothing there, nothing to cause it to behave different than expected. Even if the gap of nothing is one kilometer long (assume that nothing can have extrinsic properties) then it is like there is no gap at all. And if there is some kind of subspace-time that space-time resides on, then we can just focus on this subspace-time and ask whether or not its coarse.

Now, if you're with me so far, then I want you to imagine the geometry of your space-time that would not allow a rotating body to change in length. You can use any shapes, you can even mix and match shapes. And remember; your shapes can be as small as you want them to be. The shape or shapes you have chosen cannot be smaller than some distance Ax,By and Cz. If you want, this can be the size of a Planck length or a million orders of magnitude smaller; it doesn't matter for my argument. Again, these shapes that you have chosen must be as large or larger than that of a volume having any fixed Ax, By and Cz distances.

So now let's go back to the carbon nanotube. Each particle that makes up the carbon nanotube can only be in a finite number of positions within your shapes, or else your shapes would consist of a perfectly smooth space-time. If you want your space-time quanta to be smaller than particles, if that is even possible, then that is fine too. If particles are points, then you might as well say that only one particle can fit in each quantized shape with excess space-time. And to make things easy, let's just say that each particle can only take up distances Ax, By and Cz within your shapes. For a shape small enough, this leaves only one place a particle can be in at a time in any given quantum of your space-time.

Okay, now here is the argument.

Picture the geometric makeup of your space-time. There will probably be an angle that a carbon nanotube can lie in where no space is wasted; this would be the case with a space-time of shapes where the borders touch each other perpendicularly to a straight carbon nanotube, such as cubes, spheres, etc. But with spheres, cubes or any other shape, there will only be three angles in R3 that will conserve space perfectly like this. As your tube changes its radial position, it will gain the distance it covers as it goes across the borders of your shapes at an angle instead of perpendicularly.

To summarize, what I find very interesting and convincing is that no matter what kind of shape or what kind of configuration of different shapes you use in constructing your space-time, the carbon nanotube will still have to eventually go from a perpendicular position with the borders of the shapes to an angle of 45 degrees with that same border. This will cause your tube to take a staircase position instead of following a straight line.

• Perform an experiment to prove your hypothesis
• Publish your experimental results in a journalist

There. Was that so hard?

 

[ryan]

• Perform an experiment to prove your hypothesis
• Publish your experimental results in a journalist

There. Was that so hard?

Bomb#20 gave me a reason why I shouldn't pursue this any further.