What does it mean for something to be "logically possible"?

[Kharakov]

I suppose you don't understand that if spacetime is quantized in both direction and length, there would be virtually no interaction between particles.

You can't invoke imaginary things like non-discreet entities, entities made of infinitesimal things that occupy zero space and time, to solve real problems.

If spacetime is discrete:

Describe how a particle going N can intersect paths with a particle that went NE then NW after crossing the same originating point as the first particle. Keep in mind that for discrete length we'll use 1. A particle that went NE, then NW, would have traveled sqrt(2) units N, and can only travel north by 1.

So it will always be a multiple of 1, plus the square root of 2 distant from the originating point, while the particle that went directly north will always be a multiple of 1 distant from the originating point. The particle that is 1.414 off the "grid" would jump over the other particle because spacetime is quantized.

I have to go for a bit. ttyl

 

[ryan]

I suppose you don't understand that if spacetime is quantized in both direction and length, there would be virtually no interaction between particles.

You can't invoke imaginary things like non-discreet entities, entities made of infinitesimal things that occupy zero space and time, to solve real problems.

It isn't a real answer.

But on paper you can deal with imaginary points that occupy no space or time.

I am starting to wonder if it is even logically possible for a/the universe (where universe means all that exists) to be discontinuous anywhere.

Take a universe with only 5 particles in it. If there is no space between the particles, then the universe is continuous even though each particle is discontinuous. Then if there is space between the particles, then the space immediately follows from the particles, and a continuous universe prevails. And if the space itself is grainy, then something else immediately follows, and on and on this pattern goes.

And I am still waiting for your reply to my last post to you.

 

[untermensche]

You can't invoke imaginary things like non-discreet entities, entities made of infinitesimal things that occupy zero space and time, to solve real problems.

If spacetime is discrete:

Describe how a particle going N can intersect paths with a particle that went NE then NW after crossing the same originating point as the first particle. Keep in mind that for discrete length we'll use 1. A particle that went NE, then NW, would have traveled sqrt(2) units N, and can only travel north by 1.

What kind of particle?

What are you talking about?

Where did you see this happening?

 

[untermensche]

You can't invoke imaginary things like non-discreet entities, entities made of infinitesimal things that occupy zero space and time, to solve real problems.

It isn't a real answer.

But on paper you can deal with imaginary points that occupy no space or time.

I am starting to wonder if it is even logically possible for a/the universe (where universe means all that exists) to be discontinuous anywhere.

Take a universe with only 5 particles in it. If there is no space between the particles, then the universe is continuous even though each particle is discontinuous. Then if there is space between the particles, then the space immediately follows from the particles, and a continuous universe prevails. And if the space itself is grainy, then something else immediately follows, and on and on this pattern goes.

And I am still waiting for your reply to my last post to you.

Space itself is quantized.

All is quantized.

Nothing is discontinuous. The idea is irrational.

You can't turn ZERO into something real in the real world.

In the real world ZERO means it isn't there at all. So an infinitesimal slice of something in the real world isn't there. It doesn't exist.

It takes understanding the difference between the imaginary world of mathematics and the real world to understand.

 

[ryan]

I am starting to wonder if it is even logically possible for a/the universe (where universe means all that exists) to be discontinuous anywhere.

Take a universe with only 5 particles in it. If there is no space between the particles, then the universe is continuous even though each particle is discontinuous. Then if there is space between the particles, then the space immediately follows from the particles, and a continuous universe prevails. And if the space itself is grainy, then something else immediately follows, and on and on this pattern goes.

And I am still waiting for your reply to my last post to you.

Space itself is quantized.

All is quantized.

Nothing is discontinuous. The idea is irrational.

You can't turn ZERO into something real in the real world.

In the real world ZERO means it isn't there at all. So an infinitesimal slice of something in the real world isn't there. It doesn't exist.

It takes understanding the difference between the imaginary world of mathematics and the real world to understand.

The idea from what I was saying is that when we are talking about all that exists (universe) when one thing ends another begins (temporal); and where one thing ends another begins (spatial). The universe seems unavoidably continuous even though it is made up from discrete entities.

Somethings are theorized to exist in 0 space. Think of a singularities like point particles, the big bang or black holes. They occupy 0 space, but are still discrete in that they discontinue the properties of space that approach them.

 

[bilby]

FDI- feathers do fall more slowly than iron balls in the Earth's atmosphere, which the majority of us live within. And everyone knows that balls fall slower at the equator than at the poles.

Hitler didn't; but then, he only had one, and so lacked the means to attempt the experiment.

/Godwin

 

[bilby]

No. I am telling you.

Quantized means to actually exist.

Non-discreet existence of any kind is an imaginary delusion.

Non-discreet would mean something could be divided infinitely. An imaginary concept that only can take place in the imagination.

Because an infinite section of anything is equivalent to zero.

In other words, it doesn't exist except in the imagination.

There's your problem - you are telling, when you should instead be listening and thinking.

Yes, you are telling; but you are obviously and demonstrably wrong. The reasons why you must be wrong have been patiently explained in simple terms; and your only response is to move the goalposts, build and demolish straw men, and generally tie yourself in knots trying to avoid any admission that you might be wrong.

And so now when you are telling, your audience is laughing.

 

[fromderinside]

actually

 

[Kharakov]

If spacetime is discrete:

Describe how a particle going N can intersect paths with a particle that went NE then NW after crossing the same originating point as the first particle. Keep in mind that for discrete length we'll use 1. A particle that went NE, then NW, would have traveled sqrt(2) units N, and can only travel north by 1.

What kind of particle?

Doesn't matter. Force carrying particle. Photon. Whatever. A quantum field that extends continuously from a point in space. Whatever.

From the following diagram, if you have a rudimentary understanding of actual physical measurements and our recent conversation, you'll be able to tell that the object that went NE 1 quantized length unit then NW 1 quantized length unit will never transmit information to (and thus from) the same location in space as the particle, field source, or whatever that traveled directly north if length of space travel is quantized. Information transmission will jump over the locations of the other particle, information, field, or whatever.


1 unit of quantized length = 2 units of graph length

when the object (physically existing information, field source, particle, unterfeld, or whatever) that follows the green path starts going north again, it is either .414 or 1-.414 quantized length units from an object (information, field source, particle, unterfeld, or whatever) that went directly north the whole time (the object that followed the red path).

The top green line and red line indicate the next quantized length gap that the objects (information, field source, particle, unterfeld, or whatever) jump. The object that follows the green path will always be in a different area of quantized space, and only transmit information to places that the object that follows the red path cannot transmit information to, because it can only transmit information to quantized length portions of space away from it.




Is that a (poorly worded) proof that space cannot contain quantized lengths?

 

[ryan]

What kind of particle?

Doesn't matter. Force carrying particle. Photon. Whatever. A quantum field that extends continuously from a point in space. Whatever.

From the following diagram, if you have a rudimentary understanding of actual physical measurements and our recent conversation, you'll be able to tell that the object that went NE 1 quantized length unit then NW 1 quantized length unit will never transmit information to (and thus from) the same location in space as the particle, field source, or whatever that traveled directly north if length of space travel is quantized. Information transmission will jump over the locations of the other particle, information, field, or whatever.


1 unit of quantized length = 2 units of graph length

when the object (physically existing information, field source, particle, unterfeld, or whatever) that follows the green path starts going north again, it is either .414 or 1-.414 quantized length units from an object (information, field source, particle, unterfeld, or whatever) that went directly north the whole time (the object that followed the red path).

The top green line and red line indicate the next quantized length gap that the objects (information, field source, particle, unterfeld, or whatever) jump. The object that follows the green path will always be in a different area of quantized space, and only transmit information to places that the object that follows the red path cannot transmit information to, because it can only transmit information to quantized length portions of space away from it.

View attachment 12071


Is that a (poorly worded) proof that space cannot contain quantized lengths?

If I understand this, you are assuming we can measure any scale of graininess, but that might not be possible. So if your units were much less than a Planck length, we wouldn't be able to distinguish the difference between sqrt2 units and one unit.

 

[untermensche]

No. I am telling you.

Quantized means to actually exist.

Non-discreet existence of any kind is an imaginary delusion.

Non-discreet would mean something could be divided infinitely. An imaginary concept that only can take place in the imagination.

Because an infinite section of anything is equivalent to zero.

In other words, it doesn't exist except in the imagination.

There's your problem - you are telling, when you should instead be listening and thinking.

Yes, you are telling; but you are obviously and demonstrably wrong. The reasons why you must be wrong have been patiently explained in simple terms; and your only response is to move the goalposts, build and demolish straw men, and generally tie yourself in knots trying to avoid any admission that you might be wrong.

And so now when you are telling, your audience is laughing.

If only you had ONE argument you would not look like a total fool.

Your worthless opinion is noted.

- - - Updated - - -

What kind of particle?

Doesn't matter. Force carrying particle. Photon. Whatever. A quantum field that extends continuously from a point in space. Whatever.

From the following diagram, if you have a rudimentary understanding of actual physical measurements and our recent conversation, you'll be able to tell that the object that went NE 1 quantized length unit then NW 1 quantized length unit will never transmit information to (and thus from) the same location in space as the particle, field source, or whatever that traveled directly north if length of space travel is quantized. Information transmission will jump over the locations of the other particle, information, field, or whatever.


1 unit of quantized length = 2 units of graph length

when the object (physically existing information, field source, particle, unterfeld, or whatever) that follows the green path starts going north again, it is either .414 or 1-.414 quantized length units from an object (information, field source, particle, unterfeld, or whatever) that went directly north the whole time (the object that followed the red path).

The top green line and red line indicate the next quantized length gap that the objects (information, field source, particle, unterfeld, or whatever) jump. The object that follows the green path will always be in a different area of quantized space, and only transmit information to places that the object that follows the red path cannot transmit information to, because it can only transmit information to quantized length portions of space away from it.

View attachment 12071


Is that a (poorly worded) proof that space cannot contain quantized lengths?

Where did you see this?

 

[Kharakov]

Doesn't matter. Force carrying particle. Photon. Whatever. A quantum field that extends continuously from a point in space. Whatever.

From the following diagram, if you have a rudimentary understanding of actual physical measurements and our recent conversation, you'll be able to tell that the object that went NE 1 quantized length unit then NW 1 quantized length unit will never transmit information to (and thus from) the same location in space as the particle, field source, or whatever that traveled directly north if length of space travel is quantized. Information transmission will jump over the locations of the other particle, information, field, or whatever.


1 unit of quantized length = 2 units of graph length

when the object (physically existing information, field source, particle, unterfeld, or whatever) that follows the green path starts going north again, it is either .414 or 1-.414 quantized length units from an object (information, field source, particle, unterfeld, or whatever) that went directly north the whole time (the object that followed the red path).

The top green line and red line indicate the next quantized length gap that the objects (information, field source, particle, unterfeld, or whatever) jump. The object that follows the green path will always be in a different area of quantized space, and only transmit information to places that the object that follows the red path cannot transmit information to, because it can only transmit information to quantized length portions of space away from it.

View attachment 12071


Is that a (poorly worded) proof that space cannot contain quantized lengths?

If I understand this, you are assuming we can measure any scale of graininess, but that might not be possible. So if your units were much less than a Planck length, we wouldn't be able to distinguish the difference between sqrt2 units and one unit.

No. Scale does not matter if space is grainy (only allows specific quantized lengths to be traveled). If a particle is 1/2 a quantized length from another particle, and can only transmit information by full quantized length intervals, it will never transmit information to the particle that is 1/2 a quantized length away from it- it will skip over it if its......

 

[beero1000]

@beero1000- Can someone reach any point in Euclidean space if angles are continuous but length is quantized, or length is continuous but angles are quantized (with certain parameters of quantization so that one isn't simply rotating 2pi every time or something like that)?

Yes to both, with the caveat in the second case that the direction vectors span the space.

 

[beero1000]

What kind of particle?

Doesn't matter. Force carrying particle. Photon. Whatever. A quantum field that extends continuously from a point in space. Whatever.

From the following diagram, if you have a rudimentary understanding of actual physical measurements and our recent conversation, you'll be able to tell that the object that went NE 1 quantized length unit then NW 1 quantized length unit will never transmit information to (and thus from) the same location in space as the particle, field source, or whatever that traveled directly north if length of space travel is quantized. Information transmission will jump over the locations of the other particle, information, field, or whatever.


1 unit of quantized length = 2 units of graph length

when the object (physically existing information, field source, particle, unterfeld, or whatever) that follows the green path starts going north again, it is either .414 or 1-.414 quantized length units from an object (information, field source, particle, unterfeld, or whatever) that went directly north the whole time (the object that followed the red path).

The top green line and red line indicate the next quantized length gap that the objects (information, field source, particle, unterfeld, or whatever) jump. The object that follows the green path will always be in a different area of quantized space, and only transmit information to places that the object that follows the red path cannot transmit information to, because it can only transmit information to quantized length portions of space away from it.

View attachment 12071


Is that a (poorly worded) proof that space cannot contain quantized lengths?

You might want to look into the  Weyl tile argument.

 

[Kharakov]

What kind of particle?

Doesn't matter. Force carrying particle. Photon. Whatever. A quantum field that extends continuously from a point in space. Whatever.

From the following diagram, if you have a rudimentary understanding of actual physical measurements and our recent conversation, you'll be able to tell that the object that went NE 1 quantized length unit then NW 1 quantized length unit will never transmit information to (and thus from) the same location in space as the particle, field source, or whatever that traveled directly north if length of space travel is quantized. Information transmission will jump over the locations of the other particle, information, field, or whatever.


1 unit of quantized length = 2 units of graph length

when the object (physically existing information, field source, particle, unterfeld, or whatever) that follows the green path starts going north again, it is either .414 or 1-.414 quantized length units from an object (information, field source, particle, unterfeld, or whatever) that went directly north the whole time (the object that followed the red path).

The top green line and red line indicate the next quantized length gap that the objects (information, field source, particle, unterfeld, or whatever) jump. The object that follows the green path will always be in a different area of quantized space, and only transmit information to places that the object that follows the red path cannot transmit information to, because it can only transmit information to quantized length portions of space away from it.

View attachment 12071


Is that a (poorly worded) proof that space cannot contain quantized lengths?

Where did you see this?

It's logic.

If length (in space) is quantized, then fields are propagated over quantized length intervals, if a particle or field source point travels the path I described (ne then nw), it will be out of sync with a particle or field source point that traveled directly north.

By out of sync, I mean as described above. If length in space is quantized, the field source point traveling north will propagate its field out of sync with the field point source that is out of sync by .414 length units because it traveled diagonally.



Also. See Weyl's tile argument above.

 

[untermensche]

What kind of particle?

Doesn't matter. Force carrying particle. Photon. Whatever. A quantum field that extends continuously from a point in space. Whatever.

From the following diagram, if you have a rudimentary understanding of actual physical measurements and our recent conversation, you'll be able to tell that the object that went NE 1 quantized length unit then NW 1 quantized length unit will never transmit information to (and thus from) the same location in space as the particle, field source, or whatever that traveled directly north if length of space travel is quantized. Information transmission will jump over the locations of the other particle, information, field, or whatever.


1 unit of quantized length = 2 units of graph length

when the object (physically existing information, field source, particle, unterfeld, or whatever) that follows the green path starts going north again, it is either .414 or 1-.414 quantized length units from an object (information, field source, particle, unterfeld, or whatever) that went directly north the whole time (the object that followed the red path).

The top green line and red line indicate the next quantized length gap that the objects (information, field source, particle, unterfeld, or whatever) jump. The object that follows the green path will always be in a different area of quantized space, and only transmit information to places that the object that follows the red path cannot transmit information to, because it can only transmit information to quantized length portions of space away from it.

View attachment 12071


Is that a (poorly worded) proof that space cannot contain quantized lengths?

Where did you see this?

It's logic.

If length (in space) is quantized, then fields are propagated over quantized length intervals, if a particle or field source point travels the path I described (ne then nw), it will be out of sync with a particle or field source point that traveled directly north.

By out of sync, I mean as described above. If length in space is quantized, the field source point traveling north will propagate its field out of sync with the field point source that is out of sync by .414 length units because it traveled diagonally.

View attachment 12074

Also. See Weyl's tile argument above.

No. You misunderstood.

Where have you seen this happening?

Is this based on an observation of a particle moving in a perfectly straight line?

Or is this speculation on top of speculation?

 

[Speakpigeon]

More worryingly for these two brave conceptual scufflers, the result is broadly to impoverish the range of concepts one can use to think. Ryan just ends up here proving at least to himself that the notion of quantised space is useless because redundant with that of continuous space, ...
EB

I don't know what you are talking about.

Clearly I was talking about what you posted, which is quoted. How can you not know what I was talking about!?

I am on here testing ideas, and trying to learn more. There is so much to learn that I will probably never believe or trust my or anyone else's sense of certainty.

How is that relevant?

What I quoted clearly shows that you seem to find reasonable an argument to the effect that quantification couldn't possibly exist. If that was the case, such an argument would be a mindboggling tour de force.

Hmm... or, maybe, it just doesn't work at all after all.

Go figure.
EB

 

[Speakpigeon]

Quantized means to actually have existence.

Quantized, in the context of this conversation, means discontinuous or discrete.

Imagine that spacetime is 2 dimensional, direction is quantized in such a way that you can only go in 8 directions. Length is also quantized, so you can only go multiples of the fundamental length.

Take 2 particles. Move particle A north 1 fundamental unit from an origination point, move particle B northeast 1 unit from the origination point. There is no way that particle B would ever be able to run into particle A again, unless particle A somehow went northeast, or particle B went southwest 1 unit.

You know why? Moving 1 unit to the northeast means that particle B moved 1/sqrt(2) north, and 1/sqrt(2) east, while particle A went 1 unit north. There is no way that an integer multiple of 1/sqrt(2), other than 0, will ever fall on an integer value. The particles will never intersect.

Only if direction or length of spacetime are non-quantized, can you have particles or fields that intersect/interact equally with one another.



If either direction or length are non-quantized, there are inherent infinities built into the structure of spacetime (and the universe as a whole). Not only that, but the color blue exists as well.

Sorry to interject here but I disagree somewhat with your analysis here.

I agree with you that if both direction and length are fundamental things and quantified there's an impossibility. However, we can think of quantified space in a very different way.

Quantified space can be understood as a collection of discrete locations neighbouring or not neighbouring each other. Particles can only move directly from one location to any of the neighbour locations. And that's it. The two notions of length and direction can be thought of as only secondary, i.e. not fundamental.

So for example, a two-dimensional space could look like a chess board where two locations on the board are neighbours either only if they have a side in common or if they either have a side or a corner in common. In the first case, particles could be thought of as Towers only able to move from one square to another if the two squares have one side in common, which would result in each Tower having always four possible directions of movement, say, North, South, West and East (assuming the board itself would have no limiting sides). The shortest distance that a Tower could cover in this case would always be exactly 1, i.e. one location to one of the four neighbour locations).

If the second case, particles could be thought of as Queens, able to move between two squares if they have a side or a corner in common. Particles like this could always access eight possible directions, moving like Queens on a chessboard in straight lines from one location to the next.

In this case, however, the question of the distance covered is a bit more complicated because there are two basic models. One says that the distance covered from one location to the next is always 1 irrespective of whether it's done through a side or a corner. So, here, distances are quantified as multiples of 1. The other model would say that the distance covered is 1 in the case of a side move and square root of 2 in the case of a corner move. So, here, distances would be quantified as multiples of 1 or as multiples of square root of 2. No big deal since distances would be only secondary properties.

In either case, the space considered could be infinite, for example if its geometry is flat and without 'board sides', or finite, for example if the geometry is a closed one, like that of a cube for example, or if the space is limited by borders.

In other words, it is not necessary to import into your model of quantified space the particular topology of our ordinary continuous space, where distances are thought of as fundamental and broadly determined by a straightforward Pythagorean relation (square root of x square plus y square plus z square). You can conceive of distance relations in a wide variety of guises as long as they comply with the axiomatic definition of distance: Reflexivity: d(A,A) = 0; Symmetry: d(A, B) = d(B, A); Triangular inequality: d(A, B) + d(B, C) >= d(A, C).

This opens up possibilities a great deal, which only UM will inevitably complain about.

Lovely weather right now over Paris.

I'm getting emotional these days.
EB

 

[Speakpigeon]

I suppose you don't understand that if spacetime is quantized in both direction and length, there would be virtually no interaction between particles.

If it is continuous in either, then all points could be reached, and all directions of travel simulated.


@beero1000- Can someone reach any point in Euclidean space if angles are continuous but length is quantized, or length is continuous but angles are quantized (with certain parameters of quantization so that one isn't simply rotating 2pi every time or something like that)?

So, even if both direction and distance are quantised, particles would still be able to interact if the physics of interaction in your space is primarily determined by the quantified locations rather than by the distance covered or the direction of travel.

And space isn't therefore necessarily infinite to have any interactions.
EB

 

[Speakpigeon]

Doesn't matter. Force carrying particle. Photon. Whatever. A quantum field that extends continuously from a point in space. Whatever.

From the following diagram, if you have a rudimentary understanding of actual physical measurements and our recent conversation, you'll be able to tell that the object that went NE 1 quantized length unit then NW 1 quantized length unit will never transmit information to (and thus from) the same location in space as the particle, field source, or whatever that traveled directly north if length of space travel is quantized. Information transmission will jump over the locations of the other particle, information, field, or whatever.


1 unit of quantized length = 2 units of graph length

when the object (physically existing information, field source, particle, unterfeld, or whatever) that follows the green path starts going north again, it is either .414 or 1-.414 quantized length units from an object (information, field source, particle, unterfeld, or whatever) that went directly north the whole time (the object that followed the red path).

The top green line and red line indicate the next quantized length gap that the objects (information, field source, particle, unterfeld, or whatever) jump. The object that follows the green path will always be in a different area of quantized space, and only transmit information to places that the object that follows the red path cannot transmit information to, because it can only transmit information to quantized length portions of space away from it.

View attachment 12071


Is that a (poorly worded) proof that space cannot contain quantized lengths?

If I understand this, you are assuming we can measure any scale of graininess, but that might not be possible. So if your units were much less than a Planck length, we wouldn't be able to distinguish the difference between sqrt2 units and one unit.

If it is not possible in principle to measure something then it just does not make any sense to say that it exists at all. There would be quantification in any physical sense if quantification resulted in any difference that would be physically measurable at least in principle.
EB