[JohnDuffield (OP)]

This came up on a thread about infinity started by jeffreyH, and I thought it deserved a thread of its own.

If you ask around about the size of the universe, some people will tell you about the size of the observable universe. The radius of this is thought to be 46 billion light years. I don't think there's much of an issue with that.

If you then ask about the size of the whole universe, some people will say we don't know. I think that's fair enough myself. However some people will say it's infinite. And on seemingly good authority too. See for example this NASA article where you can read this:

"Recent measurements (c. 2001) by a number of ground-based and balloon-based experiments, including MAT/TOCO, Boomerang, Maxima, and DASI, have shown that the brightest spots are about 1 degree across. Thus the universe was known to be flat to within about 15% accuracy prior to the WMAP results. WMAP has confirmed this result with very high accuracy and precision. We now know (as of 2013) that the universe is flat with only a 0.4% margin of error. This suggests that the Universe is infinite in extent; however, since the Universe has a finite age, we can only observe a finite volume of the Universe. All we can truly conclude is that the Universe is much larger than the volume we can directly observe."

I have no issue with the universe being flat. But I take exception to the inference that a flat universe is an infinite universe. It's a non-sequitur. It just doesn't follow. This thinking is a bit like measuring the curvature of the Earth, and when you can't detect it, declaring that the Earth is infinite. You just can't make this claim, especially since it's at odds with Big Bang cosmology. The universe can't have grown from a small size to an infinite size in a finite time, and I do not accept that the early universe was already infinite. Particularly since I don't see how an infinite universe can expand - the "pressure" of space would be counterbalanced at all locations. I also think that we can't "truly conclude that the universe is much larger than the volume we can directly observe".

What do you think?

[Ethos_]

 The universe can't have grown from a small size to an infinite size in a finite time,

What do you think?

I think you're confusing the term "universe", referencing the material locality we presently reside within with the so-called "Bulk Universe" that our currently observable one is only a part of. What scientists refer to as the "Bulk" can be, and in my opinion is truly infinite. Our present existence within our observable and material locality is, of a truth, only a finite portion of the infinite "Bulk".

[jeffreyH]

Well this is ignoring the curvature of spacetime in the whole universe. Where gravitation and mass density become infinitesimally low does the curvature then flatten out? Can it ever completely flatten without being at an infinite distance from any source? A system that curves can be likened to a hyperbolic space. What about negative curvature? Does such a thing exist? Can something that appears to be expanding in actual fact be contracting? Is this a consequence of the curvature and what bearing does this have on a universe with infinite extent?

[alancalverd]

"Flat within 15%" sounds to me like rolling hills, or maybe Scotland. But then I live in East Anglia, and round 'ere we knows what flat looks like, boy. 

[yor_on]

How would you define gravity Jeffrey? Can there exist a vacuum of where gravity is not a property? I don't know but my view is that even when 'flat', the property of it should be there? and the definition of a universe as infinite, homogeneous and isotropic, with conservation laws and physics being the same wherever I go, demands its 'bulk' to present itself the same, a equivalent 'universe', no matter from where you stand looking out. That tells me that if I could go to the limit of what we can see today, what we from here might define as the Big Bang  looking at light reaching us from there. It should be the same view as I have from here, although there is a weak anisotropy measured, as I remember. The universe may not be perfectly 'even' but it seems very close to it. And if it doesn't I would expect physics to be in trouble.

[jeffreyH]

How would you define gravity Jeffrey? Can there exist a vacuum of where gravity is not a property? I don't know but my view is that even when 'flat', the property of it should be there? and the definition of a universe as infinite, homogeneous and isotropic, with conservation laws and physics being the same wherever I go, demands its 'bulk' to present itself the same, a equivalent 'universe', no matter from where you stand looking out. That tells me that if I could go to the limit of what we can see today, what we from here might define as the Big Bang  looking at light reaching us from there. It should be the same view as I have from here, although there is a weak anisotropy measured, as I remember. The universe may not be perfectly 'even' but it seems very close to it. And if it doesn't I would expect physics to be in trouble.

Think of this. An observer watches his companion from a safe distance approach an event horizon. He decides to calculate his friends speed using the gravitational constant. He determines he is traveling at near light speed and yet he sees his companion slowing down. The companion determines his own speed and does in fact get the right answer. Whose gravitational constant is wrong? It is like one person wading through water while a distant person wades through treacle. The observer in water would see the other person slowing down because of the density of the medium. So what is getting denser to slow down the astronaut at the event horizon? If he is in vacuum then it has to be spacetime. If the gravitational constant varies in a varying gravitational field then the Planck dimensions must too. This is the easy part. The hard part is the mechanism that alters the path of a particle and why it only attracts. This does not sit well with electromagnetism.

[JohnDuffield (OP)]

I think you're confusing the term "universe", referencing the material locality we presently reside within with the so-called "Bulk Universe" that our currently observable one is only a part of. What scientists refer to as the "Bulk" can be, and in my opinion is truly infinite. Our present existence within our observable and material locality is, of a truth, only a finite portion of the infinite "Bulk".

That's what they say, but I don't buy it.

Well this is ignoring the curvature of spacetime in the whole universe. Where gravitation and mass density become infinitesimally low does the curvature then flatten out?

Let's just simplify things by setting aside the expansion of the universe. If you have an energy density that's homogeneous, you will find that your light beam goes straight.

Can it ever completely flatten without being at an infinite distance from any source?

If you shine a light beam between two massive stars, it will go straight.

A system that curves can be likened to a hyperbolic space. What about negative curvature? Does such a thing exist? Can something that appears to be expanding in actual fact be contracting? Is this a consequence of the curvature and what bearing does this have on a universe with infinite extent?

I don't think the universe has a negative curvature.

How would you define gravity Jeffrey? Can there exist a vacuum of where gravity is not a property?

Yes. If the energy density is uniform light goes straight.   

I don't know but my view is that even when 'flat', the property of it should be there?

If it's flat there's no overall gravity. Note that the early universe didn't contract when it was small and dense. 

and the definition of a universe as infinite, homogeneous and isotropic, with conservation laws and physics being the same wherever I go, demands its 'bulk' to present itself the same, a equivalent 'universe', no matter from where you stand looking out.

The isotropy is an assumption. For all you know, there may be some people somewhere who look up to the night sky, and half of it is black. 

That tells me that if I could go to the limit of what we can see today, what we from here might define as the Big Bang  looking at light reaching us from there. It should be the same view as I have from here, although there is a weak anisotropy measured, as I remember. The universe may not be perfectly 'even' but it seems very close to it. And if it doesn't I would expect physics to be in trouble.

It's just an assumption. If I could snap my magic fingers such that you were instantly relocated to a planet 46 billion light years away, you might see something very different to what we see.

[JohnDuffield (OP)]

Think of this. An observer watches his companion from a safe distance approach an event horizon. He decides to calculate his friends speed using the gravitational constant. He determines he is traveling at near light speed and yet he sees his companion slowing down. The companion determines his own speed and does in fact get the right answer. Whose gravitational constant is wrong? It is like one person wading through water while a distant person wades through treacle. The observer in water would see the other person slowing down because of the density of the medium. So what is getting denser to slow down the astronaut at the event horizon? If he is in vacuum then it has to be spacetime. If the gravitational constant varies in a varying gravitational field then the Planck dimensions must too. This is the easy part. The hard part is the mechanism that alters the path of a particle and why it only attracts. This does not sit well with electromagnetism.

It does actually. And it goes all the way back to Newton's Opticks: "Doth not this aethereal medium in passing out of water, glass, crystal, and other compact and dense bodies in empty spaces, grow denser and denser by degrees, and by that means refract the rays of light not in a point, but by bending them gradually in curve lines?" Newton was really interested in light. And light is all to do with electromagnetism. Why don't you start a new thread on this, and I'll tell you what I can. 

[yor_on]

That's not a easy part Jeffrey, that's questioning constants. If you do you also need to redefine everything that rest on constants. Both you and John seem to be wondering in those terms. The point is that I don't think it should simplify anything, it should just complicate the definitions we use.
==

For example, we have this definition of a isotropic and homogeneous universe. That one will no longer be true. We have another stating that physics should be the same wherever you go to measure, that one will no longer be true. Then you have the definitions of a light quanta, and further definitions going out from that, no longer true. I suspect one would need to rewrite physics to make it work. (and symmetries will be very difficult to define)

[JohnDuffield (OP)]

That's not a easy part Jeffrey, that's questioning constants. If you do you also need to redefine everything that rest on constants. Both you and John seem to be wondering in those terms. The point is that I don't think it should simplify anything, it should just complicate the definitions we use.

It doesn't complicate anything, it clears up some "fine tuned" multiverse myths. See for example this and this about the fine structure constant. It's a "running" constant. Which means it isn't constant. And see this Baez article:

"Einstein talked about the speed of light changing in his new theory.  In his 1920 book "Relativity: the special and general theory" he wrote: "... according to the general theory of relativity, the law of the constancy of the velocity of light in vacuo, which constitutes one of the two fundamental assumptions in the special theory of relativity [...] cannot claim any unlimited validity.  A curvature of rays of light can only take place when the velocity [Einstein means speed here] of propagation of light varies with position."  This difference in speeds is precisely that referred to above by ceiling and floor observers."

People think the speed of light is constant, but that's the locally-measured speed of light. The "coordinate" speed of light varies with gravitational potential, hence this Shapiro quote:

"The proposed experiment was designed to verify the prediction that the speed of propagation of a light ray decreases as it passes through a region of decreasing gravitational potential".

For example, we have this definition of a isotropic and homogeneous universe.

IMHO it is homogeneous on the largest scale, but the isotropy is just an assumption. It isn't based on anything scientific.   

That one will no longer be true. We have another stating that physics should be the same wherever you go to measure, that one will no longer be true.

It's no big deal. People are always looking into tests of Lorentz invariance.

Then you have the definitions of a light quanta, and further definitions going out from that, no longer true. I suspect one would need to rewrite physics to make it work. (and symmetries will be very difficult to define).

IMHO it's just a tweak here and there for physics. The popscience is what gets the rewrite.

[yor_on]

"It doesn't complicate anything, it clears up some "fine tuned" multiverse myths."

That would then be your interpretation John. Don't think you will find many scientists agreeing with it.

[JohnDuffield (OP)]

"It doesn't complicate anything, it clears up some "fine tuned" multiverse myths."

That would then be your interpretation John. Don't think you will find many scientists agreeing with it.

Honestly, you will. A lot of scientists really dislike the multiverse. Here's George Ellis writing in Scientific American about it. Google on multiverse pseudoscience.

[yor_on]

It's not about multiverses to me. That one, to my mind, belongs more to the subsequent interpretations you might do from a 'Copenhagen model', or any of the others existing. What I wrote about was constants, and what I expect physics needing to do, redefining them. I also mentioned the isotropic and homogeneous universe we see, as a example of what we need to redefine if so. The problem isn't as simple as you think, a lot of logic assumptions build on each other, so reducing constants to variables you would find it extremely hard to 'correct' it all. I actually looked into that at one time, and even though I didn't collect all data I proved to my own satisfaction that it would create a really messed up situation. The ones we have work, and are, all considered, remarkably simple.
==

It doesn't really matter whether the universe prefer a complicated or a simple solution. It works any way. But if I have two theories, where one gives me a really hard time comprehending it, whereas the other is simple and so easier for me to understand, I will go for that one. Presuming that both theories cover the experiments and universe we observe/measure.

[yor_on]

and yes, a multiverse do change our ideas about what physics is about. But so did relativity, and Newton, and Maxwell. And your weak experiments can be seen as a try to get back to a universe as it once was thought to be. Some sort of container in where we find causality, action and reaction, and limits, but as a linear proposition. The universe though seems trickier than that, it seems as if it uses both, non linear as well as linear physics, 'simultaneously' depending on experiment made, what you search for. This duality we see is not only limited to light it seems.
=

I'll add this one, it's from here but older, relatively speaking

There is a non-linearity to all of the universe we know, macroscopically as well as at the quantum level. But there is also a strange linearity surrounding and infusing it, as the Feigenbaum constant shows us, both macroscopically and on a quantum level as I understand it.

Now for what’s called ‘scars’ in chaos theory.

“According to Michael Berry, a leading theorist in the study of quantum chaos at the University of Bristol, this issue of linearity is a red herring. "This is one of the biggest misconceptions in the business," he says. His critique rests on the fact that it is possible to recast nonlinear classical equations in a linear form and linear quantum equations in nonlinear form.

 Berry's preferred explanation for the difference between what happens in classical and quantum systems as they edge towards chaos is that quantum uncertainty imposes a fundamental limit on the sharpness of the dynamics. The amount of uncertainty in a quantum system is quantified in Heisenberg's uncertainty principle by a fixed value known as Planck's constant. In classical mechanics, objects can move along infinitely many trajectories," says Berry. This makes it easy to set up complicated dynamics in which an object will never retrace its path-the sort of behaviour that leads to chaos. But in quantum mechanics, Planck's constant blurs out the fine detail, smoothing away the chaos."

This raises some interesting questions. What happens if you scale down a classically chaotic system to atomic size? Do you still get chaos or does quantum regularity suddenly prevail? Or does something entirely new happen? And why is it that macroscopic systems can be chaotic given that everything is ultimately built out of atoms and therefore quantum in nature? These questions have been the subject of intense debate for more than a decade. But now a number of experimental approaches have begun to offer answers. …

Quantum billiards

More recently, signs of quantum suppression of chaos have come from another experimental approach to quantum chaos: quantum billiards. On a conventional rectangular table, it is quite common for a player to pot a ball by bouncing the cue ball off the cushion first- In the hands of a skilled player, such shots are often quite repeatable. But if you were to try the same shot on a rounded, stadium-shaped table, the results are far less predictable : the slightest change in starting position alters the ball's trajectory drastically. So what you get if you play stadium billiards is chaos. In 1992, at Boston's Northeastern University, Srinivas Sridhar and colleagues substituted microwaves for billiard balls and a shallow stadium-shaped copper cavity for the table. Sridhar's team then observed how the microwaves settled down inside the cavity. Although their apparatus is not of atomic proportions (a cavity typically measures several millimetres across) , the experiment exploits a precise mathematical similarity between the wave equations of quantum mechanics and the equations of the electromagnetic waves in this two- dimensional situation. If microwaves behaved like billiard balls , you would not expect to see any regular patterns. The experiments, however, reveal structures known as "scars" that suggest the waves concentrate along particular paths.

But where do these paths come from? One answer is provided by theoretical work carried out back in the 1970s by Martin Gutzwiller of the IBM Thomas J. Watson Research Center in Yorktown Heights near New York. He produced a key formula that showed how classical chaos might relate to quantum chaos. Basically, this indicates that the quantum regularities are related to a very limited range of classical orbits. These orbits are ones that are periodic in the classical system. If for example , you placed a ball on the stadium table and hit it along exactly the right path, you could get it to retrace its path ,after only a few bounces off the cushions.However, because the system is chaotic, these paths are unstable. You only need a minuscule error and the ball will move off course within a few bounces. So classically you would not expect to see these orbits stand out. But thanks to the uncertainty in quantum mechanics, which "fuzzes" the trajectories of the balls, tiny errors become less significant and the periodic orbits are reinforced in some strange way so that they predominate.

Sridhar's millimetre-sized stadium was a good analogy for quantum behaviour, but would the same effects occur in a truly quantum-sized system? This question was answered recently by Laurence Eaves from the University of Nottingham, and his colleagues at Nottingham and at Tokyo University. Eaves conducted his game of quantum billiards inside an elaborate semiconductor "sandwich" . He used electrons for balls, and for cushions, he used a combination of quantum barriers and magnetic fields. The quantum barriers are formed by the outer layers of the sandwich, which gives the electrons a couple of straight edges to bounce back and forth between. The other edges of the table are created by the restraining effect of the magnetic field, which curves the electron motion in a complicated way. As in Sridhar's stadium cavity, the resulting dynamics ought to be chaotic.

Number Crunching

To do the experiments, Eaves needed ultraintense magnetic fields, so he took his device to the High Magnetic Field Laboratory at University of Tokyo; which is equipped with some of the most powerful sources of pulsed magnetic fields in the world. Meanwhile his colleagues in Nottingham, Paul Wilkinson, Mark Fromhold, Fred Sheard, squared up to a heroic series of calculations, deducing from purely quantum mechanical principles what the results should look like.In a spectacular paper that made the cover of Nature last month, the team produced the first definitive evidence for quantum scarring, and precisely confirmed the quantum mechanical predictions. Sure enough, the current flowing through the device was predominantly carried by electrons moving along certain "scarred" paths. Quantum regularity was lingering in the chaos rather like the fading smile of the Cheshire Cat in Alice's Adventures in Wonderland. “

So, now we have a little more evidence for it’s not being non-linearity alone ruling, but rather like a intricate mosaic of both ‘linearity’ and ‘non-linearity’ constituting the ‘laws’ creating ‘SpaceTime’. And with it we’re starting to get an idea of what ‘free will’ might be seen as, something actually able to vary in itself, but still falling prey to statistics and probability theory. And with it our universe becoming weirder than ever .

Now what would that have to do with my thoughts on light not moving? Well, if the universe is becoming a mosaic, as I see it, then ‘moving parts’ just complicates it. But, we see the universe moving, don’t we? Well, maybe we do? But, if it moves, how do ‘shadows’ correspond to a barrier?

Institut d'Optique reported on the direct observation of Anderson localization of matter-waves in a controlled disorder. “From the quantum theory of conduction, in which electrons are described as matter waves, we can draw a naďve picture based on the idea that electrons with certain momenta can travel freely through the crystal, while others cannot as they diffract from the periodic structure played by the lattice. “

Fifty years ago, Philip Anderson, 1977 Physics Nobel Prize winner, worked out that tiny modifications of the lattice, such as the introduction of impurities or defects, can dramatically modify this behavior : the electron that would move freely inside the solid does not simply diffuse on the defects as expected for classical particles but they can be completely stopped.

On a macroscopic scale, that would be like saying that a few blades of grass scattered haphazardly over a golf course could completely stop a full-speed golf ball in its tracks : this would be a surprising situation, since we all know that small perturbations can only slow the movement of material objects, but can never stop them. In the light of fundamental discoveries made in the 1930s about semi-conductors that led to the invention of the transistor and then to integrated circuits, this phenomenon called 'Anderson Localization' created and is still creating strong interests among physicists.”

Did you notice “electrons are described as matter waves” I must admit that I like that, it’s kind of ‘hard’ imagining a golf ball being superimposed in two places simultaneously, on the other hand, it’s almost as hard imagining a wave being it, so?

“In our experiment, ultra-cold atoms play the role of electrons. They are chilled to a temperature close to absolute zero (-459.67 degrees Fahrenheit) to generate a Bose-Einstein condensate (BEC), in which all the atoms can be described as a single wave function. We allowed these BECs to expand from a small starting spot along a single direction imposed by a laser-induced atomic waveguide. To “simulate” the disordered environment, we created a perfectly controlled disorder by shining laser light through finely ground glass onto the expanding atoms — creating then a random distribution of light and dark regions. Without disorder, the atoms propagate freely, but when disorder is present, all atomic movement stop within a fraction of a second. We then observed the atomic density profile. Its exponential form, characteristic of Anderson Localization is the awaited direct proof that random diffusion of matter can hinder the diffusion process.”

[Bill S]

But then I live in East Anglia, and round 'ere we knows what flat looks like, boy.

Should that have been "bor", or are you too far from Norfolk for that?   []

[chiralSPO]

Particularly since I don't see how an infinite universe can expand - the "pressure" of space would be counterbalanced at all locations. I also think that we can't "truly conclude that the universe is much larger than the volume we can directly observe".

What do you think?

First, I agree that we have to be very careful about drawing conclusions about that which cannot be observed directly or indirectly.

Second,an infinite plane (or space) can expand. The questions regarding "Hilbert's Hotel" (http://en.wikipedia.org/wiki/Hilbert%27s_paradox_of_the_Grand_Hotel) show this.

I don't think pressure, as you have defined it, is the best way of thinking about this. Perhaps instead think of an infinite (and stretchy) plane that has a perpendicular pressure applied. The plane would stretch and distort, ultimately having a greater (but still infinite) area. This isn't a perfect analogy, because it requires changing the curvature of the plane, but it is more easily pictured than just dilating the whole thing (without changing the curvature, or anything other than distances).

[jccc]

my answer is the universe is infinity.

based on charged particle has infinity force range.

it is easy to think the universe is infinity.

if it has boundary, what's out side?

[PhysBang]

I have no issue with the universe being flat. But I take exception to the inference that a flat universe is an infinite universe. It's a non-sequitur. It just doesn't follow.

If someone, like JohnDuffield, rejects contemporary cosmology (and especially rejects learning the relevant mathematics), then that person can't follow the reasoning. This does not mean that there isn't reasoning.

This thinking is a bit like measuring the curvature of the Earth, and when you can't detect it, declaring that the Earth is infinite.

It is, actually, quite similar. If one has good theoretical reasoning to suppose that the Earth was either an infinite flat plain or a sphere, but the best attempts to measure the curvature of the Earth came up to 0, then the proper inference would be that the Earth was an infinite flat plain.

There are good theoretical reasons to suppose things about the geometry of the universe. Einstein laid this reasoning out. If someone wants to read all of Einstein instead of cherry-pick very specific sentences from him, one will find that Einstein is part of laying out this reasoning.

You just can't make this claim, especially since it's at odds with Big Bang cosmology. The universe can't have grown from a small size to an infinite size in a finite time, and I do not accept that the early universe was already infinite.

OK, so here we see that JohnDuffield would rather stick to his own dogma instead of learn about the contents of "Big Bang cosmology". What we learn from this is not something about physics, but about JohnDuffield's abilities and character. This is relevant when deciding how to evaluate claims that JohnDuffield makes about physics.

[yor_on]

Don't know about you guys but this sentence tickle my imagination. "So classically you would not expect to see these orbits stand out. But thanks to the uncertainty in quantum mechanics, which "fuzzes" the trajectories of the balls, tiny errors become less significant and the periodic orbits are reinforced in some strange way so that they predominate." As if there was some sort of Mach principle hiding microscopically perhaps? If it now can be broken down to relations? there are so many presumptions we do measuring, using local definitions, as everything taking a 'time' for example, forgetting that this is a observer dependency hinging on our use of a ideal local clock and ruler. That makes any observation a relation.
=

Defining a local clock to 'c' doesn't change this situation. It still is a 'observer dependency' by which we measure something else. Our 'tools of the trade' as they say. If we now presumed that at some scale 'time' (strictly locally) disappear, dissolve, whatever. We still wouldn't be able to prove it other than indirectly, as our local 'clock and ruler' never cease to work for us. It's easy to see thinking of a clock, and, to me, has nothing to do with time dilations unless you want to call the local macroscopic interpretation of your wrist watch a time dilation too. It's much harder to imagine what happens to the ruler at that scale. Defining it as a 'stopped clock' locally at/under that scale though it shouldn't matter. The local ruler should cease too as I think.

But if you assume there to be a limit for a discreteness then you also need a reason for particles, and a macroscopic universe, coming into existence. And that? Mach principle should have to do with it, in some way, as well as the Pauli exclusion principle does. Maybe not its old form? (Mach) but in some variation of it.

[guest39538]

This came up on a thread about infinity started by jeffreyH, and I thought it deserved a thread of its own.

If you ask around about the size of the universe, some people will tell you about the size of the observable universe. The radius of this is thought to be 46 billion light years. I don't think there's much of an issue with that.

If you then ask about the size of the whole universe, some people will say we don't know. I think that's fair enough myself. However some people will say it's infinite. And on seemingly good authority too. See for example this NASA article where you can read this:

"Recent measurements (c. 2001) by a number of ground-based and balloon-based experiments, including MAT/TOCO, Boomerang, Maxima, and DASI, have shown that the brightest spots are about 1 degree across. Thus the universe was known to be flat to within about 15% accuracy prior to the WMAP results. WMAP has confirmed this result with very high accuracy and precision. We now know (as of 2013) that the universe is flat with only a 0.4% margin of error. This suggests that the Universe is infinite in extent; however, since the Universe has a finite age, we can only observe a finite volume of the Universe. All we can truly conclude is that the Universe is much larger than the volume we can directly observe."

I have no issue with the universe being flat. But I take exception to the inference that a flat universe is an infinite universe. It's a non-sequitur. It just doesn't follow. This thinking is a bit like measuring the curvature of the Earth, and when you can't detect it, declaring that the Earth is infinite. You just can't make this claim, especially since it's at odds with Big Bang cosmology. The universe can't have grown from a small size to an infinite size in a finite time, and I do not accept that the early universe was already infinite. Particularly since I don't see how an infinite universe can expand - the "pressure" of space would be counterbalanced at all locations. I also think that we can't "truly conclude that the universe is much larger than the volume we can directly observe".

What do you think?

The answer is an axiom of yes, because placing a smaller box into a larger box.

Ask  yourself how many times you can do this?

The only answer is an infinite amount of times.

There is only two logical choices that lead to one conclusion.

Analogy - I and you are standing in a cave, we are within a space within a box within an outer space.


You are either in a space within a space or a space within a box, if you were in a box like the cave you know outside of that box is a space.

Only infinite can it be, a space within a solid or a space within a space.


There is no third option,