Unification

01
Oct

# Are Space and Time Discrete or Continuous?

Split a mile in half, you get half a mile. Split the half mile, you get a quarter, and on and on, until you’ve carved out a length far smaller than the diameter of an atom. Can this slicing continue indefinitely, or will you eventually reach a limit: a smallest hatch mark on the universal ruler?

The success of some contemporary theories of quantum gravity may hinge on the answer to this question. But the puzzle goes back at least 2500 years, to the paradoxes thought up by the Greek philosopher Zeno of Elea, which remained mysterious from the 5th century BC until the early 1800s. Though the paradoxes have now been solved, the question they posed—is there a smallest unit of length, beyond which you can’t divide any further?—persists.

Credit: Flickr user Ian Muttoo, adapted under a Creative Commons license.

The most famous of Zeno’s paradoxes is that of Achilles and the Tortoise in a race. The tortoise gets a head start on the faster-running Achilles. Achilles should quickly catch up—at least that’s what would happen in a real-world footrace. But Zeno argued that Achilles will never pass over the tortoise, because in the time it takes for Achilles to reach the tortoise’s starting point, the tortoise too will have moved forward. While Achilles pursues the tortoise to cover this additional distance, the tortoise moves yet another bit. Try as he might, Achilles only ever reaches the tortoise’s position after the animal has already left it, and he never catches up.

Obviously, in real life, Achilles wins the race. So, Zeno argued, the assumptions underlying the scenario must be wrong. Specifically, Zeno believed that space is not indefinitely divisible but has a smallest possible unit of length. This allows Achilles to make a final step surpassing the distance to the tortoise, thereby resolving the paradox.

It took more than two thousand years to develop the necessary mathematics, but today we know that Zeno’s argument was plainly wrong. After mathematicians understood how to sum an infinite number of progressively smaller steps, they calculated the exact moment Achilles surpasses the tortoise, proving that it does not take forever, even if space is indefinitely divisible.

Zeno’s paradox is solved, but the question of whether there is a smallest unit of length hasn’t gone away. Today, some physicists think that the existence of an absolute minimum length could help avoid another kind of logical nonsense; the infinities that arise when physicists make attempts at a quantum version of Einstein’s General Relativity, that is, a theory of “quantum gravity.” When physicists attempted to calculate probabilities in the new theory, the integrals just returned infinity, a result that couldn’t be more useless. In this case, the infinities were not mistakes but demonstrably a consequence of applying the rules of quantum theory to gravity. But by positing a smallest unit of length, just like Zeno did, theorists can reduce the infinities to manageable finite numbers. And one way to get a finite length is to chop up space and time into chunks, thereby making it discrete: Zeno would be pleased.

He would also be confused. While almost all approaches to quantum gravity bring in a minimal length one way or the other, not all approaches do so by means of “discretization”—that is, by “chunking” space and time. In some theories of quantum gravity, the minimal length emerges from a “resolution limit,” without the need of discreteness. Think of studying samples with a microscope, for example. Magnify too much, and you encounter a resolution-limit beyond which images remain blurry. And if you zoom into a digital photo, you eventually see single pixels: further zooming will not reveal any more detail. In both cases there is a limit to resolution, but only in the latter case is it due to discretization.

In these examples the limits could be overcome with better imaging technology; they are not fundamental. But a resolution-limit due to quantum behavior of space-time would be fundamental. It could not be overcome with better technology.

So, a resolution-limit seems necessary to avoid the problem with infinities in the development of quantum gravity. But does space-time remain smooth and continuous even on the shortest distance scales, or does it become coarse and grainy? Researchers cannot agree.

In string theory, for example, resolution is limited by the extension of the strings (roughly speaking, the size of the ball that you could fit the string inside), not because there is anything discrete. In a competing theory called loop quantum gravity, on the other hand, space and time are broken into discrete blocks, which gives rise to a smallest possible length (expressed in units of the Planck length, about 10-35 meters), area and volume of space-time—the fundamental building blocks of our universe. Another approach to quantum gravity, “asymptotically safe gravity,” has a resolution-limit but no discretization. Yet another approach, “causal sets,” explicitly relies on discretization.

And that’s not all. Einstein taught us that space and time are joined in one entity: space-time. Most physicists honor Einstein’s insight, and so most approaches to quantum gravity take space and time to either both be continuous or both be discrete. But some dissidents argue that only space or only time should be discrete.

So how can physicists find out whether space-time is discrete or continuous? Directly measuring the discrete structure is impossible because it is too tiny. But according to some models, the discreteness should affect how particles move through space. It is a miniscule effect, but it adds up for particles that travel over very long distances. If true, this would distort images from far-away stellar objects, either by smearing out the image or by tearing apart the arrival times of particles that were emitted simultaneously and would otherwise arrive on Earth simultaneously. Astrophysicists have looked for both of these signals, but they haven’t found the slightest evidence for graininess.

Even if the direct effects on particle motion are unmeasurable, defects in the discrete structure could still be observable. Think of space-time like a diamond. Even rare imperfections in atomic lattices spoil a crystal’s ability to transport light in an orderly way, which will ruin a diamond’s clarity. And if the price tags at your jewelry store tell you one thing, it’s that perfection is exceedingly rare. It’s the same with space-time. If space-time is discrete, there should be imperfections. And even if rare, these imperfections will affect the passage of light through space. No one has looked for this yet, and I’m planning to start such a search in the coming months.

Next to guiding the development of a theory of quantum gravity, finding evidence for space-time discreteness—or ruling it out!—would also be a big step towards solving a modern-day paradox: the black hole information loss problem, posed by Stephen Hawking in 1974. We know that black holes can only store so much information, which is another indication for a resolution-limit. But we do not know exactly how black holes encode the information of what fell inside. A discrete structure would provide us with elementary storage units.

Black hole information loss is a vexing paradox that Zeno would have appreciated. Let us hope we will not have to wait 2000 years for a solution.

Go Deeper
Editor and author’s picks for further reading

arXiv: Minimal Length Scale Scenarios for Quantum Gravity
Sabine Hossenfelder’s detailed look at the past, present, and future of the question, is there a shortest length?

Fermilab Physics in a Nutshell: Planck length, minimal length?
Don Lincoln explains the Planck length and why it’s thought to be the smallest possible length.

The Nature of Reality: Do Black Holes Destroy Information?
A primer on the black hole information paradox.

Physics Today: Questions and answers with Amit Hagar
An interview with philosopher of science Amit Hagar, author of “Discrete or Continuous?: The Quest for Fundamental Length in Modern Physics.”

• mudmessiah1

That is similar in concept to the big bang as not an event in our past and is an event in our present. Quantum events have always existed and since in a black hole the time before it’s existence, the time of it’s existence, and the time when it doesn’t exist happen simultaneously, then singularity time exists as non existing in space. I imagine that by hopping over it’s space-time information entering S-time is not changed. It likely hops out of our time-space and into another.

• ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
SPACE-TIME IS A PARTICLE FIELD IN EMPTY SPACE

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

● Space-time is a lattice type string particle field in space.
● Empty space is completely empty / null / void. There is a big difference.

Space-time must be made out of something.
Space-time is NOT empty space.

You can easily fold up, distort and curve Space-time, but you are NOT going to do anything to the empty space it resides in.

To sum it up: What Einstein calls “Space-time” is a particle field in empty space.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~
WHY THE SPEED OF LIGHT IS “C”
~~~~~~~~~~~~~~~~~~~~~~~~~~~~

There is a high tension string particle field in space (not the string theory type). Everything is connected by the particle field and it moves along with largest mass in proximity (something like what gravitational fields would be doing).
A good 2-D model would be something like a spiders web (individual string lengths are approximately one Ångström).
Now imagine an infinite 3-D spiders web. If a vibration was set off in it, it would travel forever and the speed the vibrations travel (through the net) is the speed of light (that’s actually what light is, a vibration traveling through a string particle field)
The speed vibrations travel through the particle field is the speed of light “c”

The particle field strings have a certain amount of tension, length and mass. That makes ‘c’ the speed it is. If the tension, length or mass changed so would ‘c’

Here is a regular string tension formula…

Tension = velocity squared x mass / Length.

If we plug c in and rearrange we get…
TL = mc^2

Both sides of the equation are in joules or energy… equivalent to “E”.
It means the Tension of the strings in space times their length is equal to their energy.

This is why the speed of light is involved in Einsteins mass energy equivalence equation…

E = mc^2

…and actually why light travels at the speed of light…
I always wondered why… now I know.
It had to be something mechanical… tension and string lengths!

So, you can arrive at Einsteins famous formula from completely different directions.
You can think energy is contained in mass and released.

E = mc^2

Or you can think there is a particle field of strings and mass is inert, the energy is only potential… released (actually pulled) by tension on the strings.

TL = mc^2

They are equivalent. Which is correct? You do not know.

Tesla was correct…
“There is no energy in matter other than that received from the environment.” – Nikola Tesla

• ~~~~~~~~~~~~~~~~~~~~~~~~~~~
WHAT ARE STRINGS MADE FROM?

~~~~~~~~~~~~~~~~~~~~~~~~~~~

…that’s a mind bender.

Oxygen has 8 protons, 8 neutrons and 8 electrons making a total of 24 particles per atom.
Aluminum — number 13 — would have a total of 39 particles.
Gold — number 79 — would have 237 particles.
The properties of elements are known with great precision but they are in actuality just a different number of the same thing (that is true regardless of the theory).
Somethings might be soft, hard, liquid, gas, solid, different colors, magnetic, rubbery, stiff, etc. but they are all just a different number of the same particle. You don’t know the properties of it… you only know the properties of a large group of it.
In other words… even though you might know a string has a string-like shape, you can’t know what the string is made from because it is what is used to make things.

A different number (amount) of the exact same thing makes completely different things (elements.)

If you do a chemical test and you find out something is Aluminum… you have only found out there are 39 string particles in a group… not what the actual strings are.
So, it (a string) is not an element and cannot be like any element or molecule unless it is by pure coincidence.
The string (purely by happenstance) might be just like a bendable but non-stretchable fishing line or spiders web. But they also might be something that is completely inconceivable and unknowable to humans.

Also… when you look at Gold you can see it has a nice color, correct? No, gold is a group of atoms made from 237 particles each. And those particles are made from strings.
Color is only the frequency of vibrations that are traveling to your eye along the strings. No matter what you are looking at you are only seeing a different vibrational frequency from a different number of strings in a group.

Could a string actually have a color anyway? Or even be white, black or grey? I have absolutely no idea. I’m sure it cannot be invisible though, because…
for something to be invisible it would mean that light passes through it. And light is only a vibration coming from that same type of string. There isn’t anyway to see it but it is not invisible.

• vaccinia

The string IS a light ray….

• (not the string theory type)

• vaccinia

Perhaps, but it is the reality type! 🙂

• Dean

Classic example of an eternal question (as in all cases in life) that begs an answer: “Compared to WHAT?”

• Matheus

The concepts of discrete and continuous do not require relativization. Something can be deemed either discrete or relative without comparing it to another thing. The set of natural numbers, for instance, is discrete regardless of other sets of numbers.

• Anonymous

If we take something which appears continuous, like space- time, and look closely enough we may find discrete packets. On the other hand, if we take something that appears discrete, like an apple, and look closely enough we find a continuousness between its energy and the energy of the supposedly discrete objects around it, e.g the air, the table, us, etc. (As Einstein said, our separateness from the universe is an illusion).

I believe that the concepts of continuousness and discreteness, when applied to real objects, are potentially relative to the observer…we cannot step outside the universe and look in. We run into the same paradox when we search for a more meaningful definition of existence…a dictionary defines it as “to be”… and vice~versa. This is not to say that progress in understanding the discreteness or continuousness of real objects is not possible or even that progress in understanding these fundamental concepts is not possible, but vital for that progress is the recognition that we are, in fact, skirting the edge. Meaning that it is very easy for our disagreements over these issues to be more about how each party defines these concepts than about some fundamental aspect of reality.

• Aleksandar Blazhevski

Space and time MUST be discrete!!
And that’s even more basic idea, that doesn’t need explicitly modern theories such as quantum gravity or string theory.
I am graduated mathematician, so I’m very aware about the huge difference between the countable and UNcountable infinity. Continuous universe implies UNcountable number of “pixels” in between, radically complicating the mathematical calculations that are needed in the “computing background” of the Universe, so that it may follow the laws of physics.
In computer science there is fully developed theory of automata, not just finite, but with infinite memory (such as Turing machine). However, nobody even tries to consider an automaton with continuous distribution (such as Turing machine with continuous track, instead of a discrete one); because if we do so, many “simple” calculations would take infinite time to complete – which is a hellish situation in automata theory.

• paulfeakins

You’ve never heard of analog computers?

Analog computers are not really analog. “Analog” levels are are made up of a very large number of very small discrete quantum level events. The divisions are so small that it looks smooth at the macroscopic, day to day, “common sense” level.

• paulfeakins

Only if you assume that reality itself is made up of discrete elements. So your argument assumes your proposition.

• Aleksandar Blazhevski

I’ve heard of them just like an idea. I know theoretically that some difficult differential equations may be solved easily by an analog computer.
However, if you are about to create a new Universe (in the “God’s role”), you need much more supernatural power to make an Universe based on real numbers (so that real operations of the natural laws finish in finite time), than to make an Universe based on integers (integers operations themselves finish in finite time).

• D Webb

I don’t know whether it is or isn’t, but I don’t follow your logic here (perhaps because I’m not a mathematician).

You say, “Continuous universe implies UNcountable number of “pixels” in between, radically complicating the mathematical calculations that are needed in the “computing background” of the Universe, so that it may follow the laws of physics.”

Why would this necessarily “‘radically complicate the calculations’? After all, we don’t need to (for example) determine every Plank Length unit between here and Mars to land a probe there, even though our precision should theoretically be enhanced if we did so. Certainly, practicalities must count for something?

Similarly, infinite machine memory and ‘continuous distribution’ could theoretically utilize infinite calculations, but to what end in practical terms? Shouldn’t intelligent machines be able to determine when a solution is ‘good enough’ for a given application?

• vaccinia

So there you have it! The smallest discrete length in the universe is the Planck length.

When the singularity that formed the universe cracked, it fractured into a lattice that was defined by that original crack, the Planck length. The Planck constant defines the geometry of this universe and the attributes of spacetime as well, h is the indivisible hand that shapes the universe.

However, let’s go beyond this to first principles, Einstein did not get it quite right. Mass does not bend spacetime, mass IS bent spacetime. We can define Mass as spacetime curvature per square meter (square really representing an 11 dimensional space but you can still visualize this as curvature within a discrete volume, say a square).

A particle is equivalent to highly bent space (and vibrating space but I won’t get into that here), the more curvature per given volume the more mass. This particle can be thought of as the standing wave previously mentioned by seescaper.

To visualize this, take a piece of paper that is flat on a table and squeeze it into an omega shape by holding the ends, pushing them together. You can move the static bend (or wave form) that forms in the middle of the page with your thumbs from the middle of the paper where it originally is, towards the ends of the paper. Thus, one has a wave that is once has a discrete form like a particle but moves through the medium of the paper like a wave. This allows us to visualize De Broglies Wave-Particle duality since particles are really just bent space moving through the medium of spacetime.

Energy can be defined as the release or change of this spacetime curvature to, for lack of a better word, flatness over time. Thus, mass and energy are merely manifestions of the Geometrodynamic properties of the universe. All there is in the universe is spacetime and its geometric manifestations. Just sayin…..

• Aleksandar Blazhevski

First, you must agree that the Universe itself IS A COMPUTER, it follows its own computing laws, that we perceive as “laws of nature”. Many of these laws of nature/physics laws are just generalizations of the simpler laws of computing of the Universe.
No, we as engineers don’t need to “determine every Plank Length unit between Earth and Mars to send a rocket there”, but the Universe itself has to do all the calculations. If there is infinite continuous density of space, the calculations of moving a distance of an inch would take as much as time as traveling from Earth to Mars, because millions times * ∞ = ∞ again. There is a mathematical proof that there are as much as natural numbers (positive integers) as all integers (both positive, 0, and negative), even as much as all fractions of integer coefficients!!! So working with infinity is much harder, maybe even impossible for “God” to create continuous Universes, so we assert that our own Universe is very likely to be discrete, based on integers.

• billybob

“Split a mile in half, you get half a mile. ”
This works for mathematics, does not work in the physical world.
All measurements of real entities (excluding things you count) have an inherent inaccuracy, because they are real numbers.

• harpreet singh kalra

yes u r right ..take any number for instance and devide it by two..their is no chance of getting a 0(zero)..this is how Reality is,there will always remain something which u can set aside as non Real.

• ok, let’s see, ummm… I’m going to pick zero as my number.
Now I will divide it by 2…

0 / 2 = 0

Whoooops… I got a zero!

• Don Graham

Zero is not a number , it is a place holder.

• Even if that were correct it would mean he is trying to divide a number in half and he is expecting a place-holder as the answer.

• D Webb

Sabine, I must have missed something fundamental. In your 4th to last paragraph you discussed how images might be distorted due to particle interference resulting from descretization if those particles travel long distances, then say, “Astrophysicists have looked for … these signals, but they haven’t found the slightest evidence for graininess.”

Then in the next paragraph you hypothesize that light might be affected by imperfections associated with descretization, and say, ” no one has looked for this yet …”.

I’m confused since these two paragraphs sound like you’re talking about essentially the same phenomena. What did I miss, or misunderstand?

• Mike McClanahan

You’re looking like a real asshole, Mr. Wizard.

• Geoff Robbins

The astrophysical data was looking for changes in travel time for photons of different wavelengths – for example, blue light may be slowed fractionally more than red, or vice versa. I presume (although I may well be wrong about this) that the second option would smear out the arrival time of photons even if they all have the same wavelength (eg laser light).

• George N. Triantaphyllou

I think this discussion would be more complete if it included space-time discretization efforts published in EPJ Web Conf. 70 (2014) 00051 and in
E.J.Theor.Phys. 10 (2013) 28, 135-168. In such an approach, known particles, and possibly Dark Matter, are interpreted as “world crystal” defects which you are interested in, in a way unifying interactions, space-time and particles.

• You avatar is reminiscent of the basic fundamental universal particle.

The particle itself would be just the grey strings in the picture (no color and a lot thinner of course).
It would fit perfectly inside of a dodecahedron.
Actual string length is about one Ångström and it is fine enough
were 10 strings (20 radii) could curl-up into the size of a neutron.

Ok, I’ve got this figured out here. The “basic fundamental universal particle” is like a 3D asterisk. And we all know that at asterisk is used to represent something to note or a caveat. And in this case it probably means “I’m the ‘basic fundamental universal particle’ until science advances and finds out I’m not . . . I’m made up of even smaller particles.” Where’s my Nobel? 😉

• Thanks, I’ve actually been trying to figure out a simple way to describe that shape. 3D asterisk is quite good.

Stuff can only be chopped down to the string limit…
http://www.pbs.org/wgbh/nova/blogs/physics/2015/10/are-space-and-time-discrete-or-continuous/#comment-2285029983

Glad I could help. Remember to cite my contribution in YOUR Nobel speech. 😉

• If you ever go to a fair and see some clown making balloon animals sometimes he will also just attach 10 full length long and thin balloons together into a cluster and the shape will always be the 3d asterisk.
9 balloons would be too loose and 11 will not fit.
10 is the perfect number and it is also the axis of the dodecahedron
That is full length thin balloons.

If you use round balloons the shape also involves the dodecahedron
http://www.eventrent.co.nz/user/image/large/1522/BLC-1.jpg

There will always be 12 balloons if they pull the knotted ends into a common center.
That is exactly how many fit. It is the same as the faces of the dodecahedron.
Notice where the balloons always touch in groups of three? There are twenty spots like that. If you stuck drinking straws or pencils into all twenty spots all the way into the center… that is how the arrangement of strings form in the 3d asterisk. Just like the other thin balloon package.

Note: No one is shooting for those shapes when they tie balloons together.
Everyone comes up with the same shape because 12 round balloons or 10 thin balloons is how many fit together like that.
It’s automatic shapes.

Automatic shapes happen. It is the way everything happened.

• Anonymous

Reality is continuous until we look for discreteness.

• What if the answer is yes, but not the way we have thought that there is a single discrete space.

In other words, the discreteness would affect single matter and energy points and when two of them affect each other. Each matter would be interlaced in a fixed manner to space, but all of the matter would not be interlaced into the same discrete space.
So if I explain it simplified and with pixels: the object traveling is a size of a pixel and when you measure this single object, you can create a pixel map as its own universe and it travels it one pixel at a time and thus the time of this object is discrete as well.

In some cases the space-time of this object would be in sync with other matter so that their universes are the same: distance between two object is a multitude of the pixel size. Such as case would be when a photon travels through a hole in a wall: all of the photons traveling through the hole would be synchronized to the same pixel map with each other: to the pixel map of the matter where the hole is.

But for the most of the time, matter is not in sync with other matter: the distance between them is not a multitude of the pixel size. And such a case would be a star: matter and radiation in and from it would not be sync. And thus when the radiation arrives to here, they are still non-synced and thus we didn’t detect this effect with the measuring that has been made.

So the discrete effect is true for every photon, but it is not true for photons as a group unless there is a force that enforces them to it.

• OWilson

The classic theory of the split screen effect (wave or particle is) just a very rough experiment indeed.

The particle, wave, or energy vibration passing through these “slits” are moving through a veritable jungle (the particle field) not to mention the interactions with the very active atomic structure of the materials they are passing through, bouncing off, or otherwise being deflected.

The Young, Michelson-Morley, and Doppler (red shift), the Big Bang, even Relativity and QED are old explanations, and require the postulation of many “fudges” like constants, Inflation, dark energy and dark matter, to make it the unwieldy theories work.

It is at moments like this when the paradigm is about to shift.

Any lecture that starts off, “Well, we know that…….”, can never get us anywhere new.

• ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
ENERGY CANNOT BE OUT ON ITS OWN
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Everyone has the wrong idea of what energy, forces and fields are.
Energy is a particle vibration or movement.
You cannot have energy without a mass, energy is mass vibrating.
Energy cannot be out on its own. (a supposed mass-less particle is a particle nonetheless, but there are no mass-less particles, so that’s irrelevant)

Same thing goes for forces.
A force is a group of particles arranged in a field pulling each other… and all of the particles absolutely have to be physically connected.

A force (a group of connected particles) can only push very short distances and in rare circumstances like same pole magnets.

But the point is… a force has to have particles involved.
A force cannot be out on its own.

Most of mainstream physics is a misconception.

There is no such thing as pure energy.
Again… Energy is a vibration on a particle (or particle movement).

Can energy be converted into mass?
Ummm… no, energy already has mass involved, it is a particle vibration or movement. There is no pure energy and you are not going to convert energy into mass.

Think of a guitar string. If you pluck it… that is the energy. If you remove the guitar string from the scenario… can you still have the energy? No, of course not.

Can you convert the guitar string vibration into mass? No… that is ridiculous.

Look at what everything really is…

Dimensions and units…
mass = [M] = kilograms
length = [L] = meters
time = [T] = seconds
frequency = [T^-1] = seconds ^-1
speed = [L] / [T] …… = m/s
acceleration = [L] / [T^2] …. = m / s^2
momentum = [M] [L] / [T] … = kg_m / s
force = [M] [L] / [T^2] . = kg_m / s^2
energy = [M] [L^2] / [T^2] = kg_m^2 / s^2
power = [M] [L^2] / [T^3] = kg_m^2 / s^3

Notice mass [M] is not equal to energy [M] [L^2] / [T^2] …the vibration is missing

Here is what Einsteins famous equation really looks like…

[M] [L^2] / [T^2] = [M] [L^2] / [T^2]

Energy already is a mass times speed^2.

If you could just lop-off parts of an equation and claim whatever is left is equal… i.e. “energy equals mass” then you could also say that “power equals mass” and so does momentum and force. It is really stupid to think like that.
Speed is NOT equal to length. Speed is equal to length divided by time.
Energy is NOT equal to mass. Energy is equal to mass times speed squared.

• underwearbomber

Whether space-time is discrete or continuous is an interesting philosophical question. It is however not one that is likely to be answered at any time in the near or even medium term.

If we reflect on what we do know from the history of physics, there is a fascinating interplay between discrete and continuous approaches over 2 millennia.
There is no doubt for example that the hypothesis of Democritus that matter was made of indivisible indestructible discrete units ‘atomai’ was one of the most important and pivotal turning points in all of science. Yet we now know that atomic elements are fissile and fusible, and composed of even more fundamental building blocks such as quarks and leptons. But most of these are unstable and decay, hardly immutable or indestructible.

Light is another example. Newton had a corpuscular theory of light as discrete “particles” or “bullets.” This fell out of favor in the 19th century when wave properties of light, such as diffraction were studied more thoroughly. The last word on light and electromagnetism was supposed to be Maxwell’s eqs. which assume continuous electric and magnetic fields in a continuous space and time. Then the photoelectric effect was discovered, and in quantum theory we now talk about “photons,” i.e. discrete packets or particles of light. So Newton was at least partly right after all, but in a much more subtle way than he could have imagined. Again these light “particles” interfere like waves and are far from indestructible–being able to get created or destroyed. Since matter is also quantum, it also sometimes behaves as classical waves would, sometimes as classical particles would. This again hints at an underlying structure which is both–or neither.

So even today we cannot give an unambiguous answer to whether light is discrete or continuous. The answer likely depends on the nature of space-time itself, which is a long way from being resolved.

• If you were going to test if there is a medium for the conveyance of light, would you……

A) Test if the Earth is rushing through the medium.
B) Test if the Earth is NOT rushing through the medium.
C) Both of the above (same as: just test for medium, no constraints)

• If you were going to test if there is a medium for the conveyance of light, would you……

A) Test if the Earth is rushing through the medium.
B) Test if the Earth is NOT rushing through the medium.
C) Both of the above (same as: just test for medium, no constraints)

• ~~~~~~~~~~~~~~~~~~~~~~~~~~~~
WHY THE SPEED OF LIGHT IS “C”
~~~~~~~~~~~~~~~~~~~~~~~~~~~~

There is a high tension string particle field in space (not the string theory type). Everything is connected by the particle field and it moves along with largest mass in proximity (something like what gravitational fields would be doing).
A good 2-D model would be something like a spiders web (individual string lengths are approximately one Ångström).
Now imagine an infinite 3-D spiders web. If a vibration was set off in it, it would travel forever and the speed the vibrations travel (through the net) is the speed of light (that’s actually what light is, a vibration traveling through a string particle field)
The speed vibrations travel through the particle field is the speed of light “c”

The particle field strings have a certain amount of tension, length and mass. That makes ‘c’ the speed it is. If the tension, length or mass changed so would ‘c’

Here is a regular string tension formula…

Tension = velocity squared x mass / Length.

If we plug c in and rearrange we get…
TL = mc^2

Both sides of the equation are in joules or energy… equivalent to “E”.
It means the Tension of the strings in space times their length is equal to their energy.

This is why the speed of light is involved in Einsteins mass energy equivalence equation…

E = mc^2

…and actually why light travels at the speed of light…
I always wondered why… now I know.
It had to be something mechanical… tension and string lengths!

So, you can arrive at Einsteins famous formula from completely different directions.
You can think energy is contained in mass and released.

E = mc^2

Or you can think there is a particle field of strings and mass is inert, the energy is only potential… released (actually pulled) by tension on the strings.

TL = mc^2

They are equivalent. Which is correct? You do not know.

Tesla was correct…
“There is no energy in matter other than that received from the environment.” – Nikola Tesla

• ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
SPACE-TIME IS A PARTICLE FIELD IN EMPTY SPACE

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

● Space-time is a lattice type string particle field in space.
● Empty space is completely empty / null / void. There is a big difference.

Space-time must be made out of something.
Space-time is NOT empty space.

You can easily fold up, distort and curve Space-time, but you are NOT going to do anything to the empty space it resides in.

To sum it up: What Einstein calls “Space-time” is a particle field in empty space.
The particle field is made from individual yet connected particles completely filling space.
The field is NOT fixed in space, it moves-along-with / is-held-in-place-by the largest mass in proximity.
It’s something like the way gravity works (it’s actually responsible for gravity), relative strength due to size and proximity.
It’s all made from the same particles.

Part of the field is surrounding and moving with you.
You are completely immersed in the Earths field.
The Earth field moves with the Earth and is inside of the Suns field.
The Suns field encompasses the entire solar system (plus more) and moves with the Sun.
A Galaxy of course has a particle field and it moves with the Galaxy (as a whole and with the movement of individual stars and systems).

• janvones

“It took more than two thousand years to develop the necessary mathematics, but today we know that Zeno’s argument was plainly wrong…they calculated the exact moment Achilles surpasses the tortoise, proving that it does not take forever, even if space is indefinitely divisible.”

That is not quite right. When our tenth-grade calculus teacher proposed that infinitesimals were ~actually~ infinitely small, several classmates and I rebelled, to the point that the teacher, to his credit, told us to shut up and listen to the day’s lecture on the condition that he would stop teaching further until he had a proof we would accept.

The following day he gave us a proof that ~given whatever scale we would accept~ it would be mathematically possible to get a result an answer accurate enough to fit the desired level of precision.

In other words, we can always calculate another digit of pi if we have to, without implying that we have an infinitely accurate expression of pi.

• Mike S

I wouldn’t be surprised to see a resolution limit based on some sort of quantum uncertainty principle.

• abinico

The smallest unit of matter: Obama’s brain.

Oh, wow! Gosh! How ingenious you are! For a first-grader.

• KrisKrispy

Maybe for a toddler with a sippy cup wearing a pair of Pull-Ups.

• seescaper

First, there is no such thing as a “particle.” A particle would be an infinitely dense structure with an edge or boundary, describing a precise size.
What there is instead of a particle is a space-time standing wave resonance.
These centers of resonance can be called wave centers, and are the place where energy exchanges take place, in discrete quantized units, just as waves vibrate in distinct wavelengths.
Each wave center is formed from and is thus continuous with all other wave centers in the universe.
A wave center is a standing wave composed of two waves, an incoming wave derived from all the outgoing waves of other wave-centers in the universe, and an out-wave, which is formed from the flipping of the in-waves through 270 degrees in space at the wave-center. The flip can occur in one of two directions, and corresponds to what we call “spin.”
Space itself is this wave medium, and we cannot sense it any more than a fish senses water.
Further, the interconnectedness of all matter is the basis for the communication of information via quantum wave structures, and fully explains Mach’s principle.
The vibrational frequencies of these wave structures also provide a universal structure by which the passage of time may be measured.

The following is derived from and can be found at :

http://www.spaceandmotion.com/Wolff-Wave-Structure-Matter.htm

Principle I is: Quantum matter waves exist in space

and are solutions of a scalar wave equation:

Principle II is: At each point in space, waves from all wave center
‘particles’ in the universe combine their intensities to form the mass-energy density of space.

Mass-energy density of space ~ mc2 = hf = k [SUM(Fn)
2/rn2)]

In other words, at every point in space, the frequency f or the mass m
of a particle depends on the sum of squares of all wave amplitudes Fn
from the N particles inside the ‘Hubble universe’. Amplitude decreases inversely
with their range rn squared. The ‘Hubble Universe’ has a radius
R = c/H, where H is the Hubble constant.
This principle is a quantitative version of Mach’s Principle because the
space medium is the inertial frame of the law F=ma.

The above yields an equation of the cosmos:

Equation of the Cosmos. Can this mechanism be tested? Yes. If
a resonance’s In-waves can be dominant in its local space, then at some
local radius, ro from the center, self-mass-energy density must
equal the total density of waves from the other N particles in the
Universe. Evaluating this equality8 yields

ro 2 = R2/3N

The best astronomical measurements, R = 1026 meters,
N = 1080 particles, yield ro = 6 x 10-15
meters. To satisfy the test, ro should be near the classical
radius, e2/mc2 of an electron, which is 2.8 x 10-15
meters. It is. The test is satisfied verifying Mach’s Principle. This is
called the Equation of the Cosmos a relation between the ‘size’
ro of the electron and the size R of the Hubble
Universe. Astonishingly, it describes how all the N particles of
the Hubble Universe create the mass-energy density of space of the space medium and the
‘charge’ and ‘mass’ of each electron as a property of space.

Principle III – Minimum Amplitude Principle (MAP)

This third principle can be obtained from Principle II, but because
it is a very useful law of the universe, which determines how interactions
take place and how wave structures will move, I write it out separately:

The total amplitude of all ‘particle’ waves in space always
seeks a minimum.

This principle is the disciplinarian of the universe. That is, energy transfers
take place and wave-centers move in order to minimize total wave amplitude.
Amplitudes are additive, so if two opposite resonances move together,
the motion will minimize total amplitude. This explains empirical rules
such as, ‘Like charges repel and unlike charges attract’ because those rules
minimize total amplitude. The origins of some other rules are also now understood.
For example, MAP produces the Pauli Exclusion Principle, which prevents
two identical resonances (two fermions) from occupying the same state. Two
identical states are not allowed because total amplitude would be a maximum,
not a minimum. The operation of MAP is seen in ordinary situations like
the water of a lake, which levels itself, and in the flow of heat that always
moves from a hot source to a cold sink, which are example of the increase
of entropy principle.

• Waves can only happen in a medium.

“Space itself is this wave medium, and we cannot sense it any more than a fish senses water.”

Correct, but the medium is a string particle field.

“First, there is no such thing as a “particle.” A particle would be an infinitely dense structure with an edge or boundary, describing a precise size.”

Correct, and that is why everything must be made from strings.

Something / anything with any type of shape is impossible.

• seescaper

If you research the website information, as well as explore the website http://mwolff.tripod.com/8f.html you will find cogent explanations for spacetime that explains far more than so called “string theory.”

The only similarity is that strings may vibrate, however in the WSM, the medium of spacetime itself is created by the totality of resonance waves entering and emerging from resonant wave centers where energy exchanges occur. As you read through you will not find any references to “strings” as strings are not necessary and are irrelevant to this theory. Please do not get hung up on strings, and try to redefine everything you will find in terms of strings.
The WSM can derive Mach’s principle, force laws relativity, gravity, spin, antimatter, and the equations of quantum mechanics, all without invoking strings. It also provides the cosmic equation linking the largest to the smallest structures.

The big bang also is not necessary here. Each wave-center has it’s own observable universe defined by the set of other wave-centers in the infinite universe that it interacts with. The poor overlap with distant wave-centers accounts for the so-called red shift.
The MAP principle of least energy combined with the greater density of wave centers where there is more mass accounts for the force of gravity.
Unless or until there is a full string theory that explains all of this mathematically I will stick with the WSM.

• Thanks, that website looks interesting without being cranky.

~~~~~~~~~~~~~~~~~~~~~~~~

The theory I was referring to uses strings but not the string theory type. Check here for sample…
http://www.pbs.org/wgbh/nova/blogs/physics/2015/10/are-space-and-time-discrete-or-continuous/#comment-2288186688

• requiem_aeternam7

Hello seescaper, is there an email or social media page that you can be reached at. I would love to ask you some questions and discuss this with you. Thanks

• seescaper

Requiem, I am not a physicist, I am a doctor. I enjoy reading about physics and have never been happy about modern interpretations. I happened upon the work of MIT and NASA scientist Milo Wolff, and immediately was taken by the logic and elegance of his theories. If you read the information on the websites, as well as his books, I think you will find it makes more sense than other theories out there. There is more work to be done on this, for sure, but I believe he is either correct or close to the truth. Talking with me would not be that productive, as I cannot tell you anything more than you can read or research on your own.

• This article is seriously out-of-date and makes unwarranted assumptions. No treatment of some 30 reports on quantized space-time in J. Bin. Mech. E.g., “Directly measuring the discrete structure is impossible because it is too tiny.” Hello. This has already been done. And “defects in the discrete structure could still be observable” assumes presence of defects. And “If space-time is discrete, there should be imperfections.” Why? According to who? And the completely false statement: “no one has looked at this yet.”

Math describes the universe (though the math may be unclear in some areas), so . . . math works, right? If math describes the physical universe then 0.5 of something is always one-half of that something. You can always divide by 2 with numbers. So doesn’t that mean that infinity basically works in both directions? If space-time carries on forever, the “other direction” – looking inwards at smaller and smaller pieces of space – would seem to carry on forever, too. But what the hell do I know?!

• OWilson

Well, at least you know enough to recognize what we don’t know. For that you would get kudos from, say Penrose and Feynman.
Infinity is just a mathematical (and very human) paradox, that the universe does not need to box in and quantify, for human convenience.
In our universe, (but not in our minds) there are an infinite number of infinities, some greater, (add 1), some lesser (minus 1) infinities that can but cut up in pieces, each of which is still infinite.
Our mathematics can deal with these odd values, but our minds can not, as is the case with anything more than three dimensions.
There are still an infinite number of Nobel prizes out there to be won 🙂

Yes, infinity is infinitely hard to grasp, if not impossible. You say “Infinity is just a mathematical (and very human) paradox, that the universe does not need to box in and quantify, for human convenience” but could the universe “box in and quantify” infinity any more than a human could? (I’m not sure how the universe would communicate this to us, anyway.) And infinity can’t be quantified, wouldn’t you agree? It’s all very odd, to say the least. And then there is the concept of the multiverse. If not already, mind blown now! 🙂

• OWilson

I was a little premature in anticipating a Nobel winning paradigm shift in this area 🙂

We are like spiders in a dark cave, thriving on our immediate surroundings, but having no concept of an elephant, or Las Vegas.

Our knowledge of the big picture must forever be confined to the limits of the human mind.

It’s not so bad. Our children and future generations will not be deprived of the fun of staring at a clear night sky and wondering.

It will also always be a fertile ground for religious charlatans.

• James Doerfel

Realize what a positive result (confirming descretization) would entail in terms of history of science textbooks. I am excited for this experiment.

• Jack Daniel S

Planck Length
Is an increment so small that the energy required to observe something so small would invariably create a black whole.
https://youtu.be/EcnsuAr_JeE
https://youtu.be/hf2CxZPl7KI

• Robert Gallinat

What if these possible or hypothetical imperfections of space representing themselves exactly as this: gravity?

So gravity itself could be just an imperfection of space(time).

Then we would need to understand exactly the mechanism of physical space in order to understand the nature of its defects, say gravitation.

Maybe gravity is just a pseudo interaction and it is not bound to particles and their interactions but to curved spacetime as a physical entity in itself?

Because otherwise if the equivalence principle holds even in quantum physics we will not have only to develop a theory for quantum gravitation but for quantum inertia as well.

So spacetime would not be just only a stage for particle interaction but could have its own structure, influencing the particles and their bosonic force messengers.

Best regards from Berlin / Germany

• seescaper

http://www.spaceandmotion.com/Wolff-Wave-Structure-Matter.htm

from which the following is excerpted in order to understand what gravity is:

“16. The appearance and origin of Charge

Schrodinger predicted that charge was a shape in the structure of space.
In the WSM this happens because the In-waves of an electron resonance are very large at their wave center due to the 1/r2 dependence. Thus
space has a high mass-energy density of space near the resonance centers due to the large wave amplitude. The dense space at the central region propagates waves non-linearly (engineering jargon – in fact the wave-velocity changes!), which promotes energy transfer or coupling between two resonances. We observe this process and call it ‘charge.’ But as Schrodinger and Clifford wrote, there is no charge substance involved. It is a property of the wave structure at the center.

The high mass-energy density of space wave centers appear to us as the location of point charges because electric force interactions occur there. The center wave amplitude is finite, as shown in Fig. 3 and not infinite as
in the puzzling Coulomb law; otherwise the law is the same.

Origin of motion. The in-waves, on arrival at the wave-center, determine
this location which we observe as the particle location. Thus any matter
nearby, which changes the medium mass-energy density of space, also changes the in-wave velocity, thus changing the location of the wave-center which we observe as the motion of the ‘particle’. This motion is observed as the force of gravity. (See Fig: 4) The acceleration of matter also changes the wavelengths (Doppler effect) and moves their center producing energy exchange (inertia) to the wave medium similar to the W&F response of the universe.
This also produces Mach’s Principle because the mass-energy density of Space is a result of ALL the matter of the Universe.

• Robert Gallinat

Thanks for the link!

Yes I understand your idea but I think – no offense – we all have our theories about physics in general or about especially Gravitation.

This is not about the discussion of theoretical steps seeming to be logically correct.

We all see the apple falling to earth but earth is a big mass. How is it without the involvement of big masses? Is gravitation an “interaction” as em, weak, strong? Universally bound to particles and their bosons? Bosons/ gravitons bound to particles at least 1:1 if not 1:n?

I want a car or a plane or a space ship lifting off from earth without any noise, no heat emission, no air movement, just silent.

Newton modified: Non-local actio = local reactio.

For this I have to answer the question:

Can I create gravitation, space curvature, graviton emission technologically, without big masses involved? In my theory gravitation is no interaction, its not bound to single particles.

For this I have to understand this (gravity) in a way, that opens the path to technology, which is the ultimate proof of any theory.

My technology is the QAS / QES (Quantum Ambiguity Sensor / Quantum Entanglement Sensor). Look at my facebook page for “QAS”.

I just found that Sabine was approaching to the realm of my theory and I wanted to express this somehow.

Thanks a lot again!

Robert Gallinat
QAS Technology UG
Potsdam / Berlin // Germany

• Geoff Robbins

You’re vaguely in the same place as general relativity – yup, spacetime is viewed as an “object” in its own right, and gravity is a bending of this object. In the absence of other forces particles (including photons) travel in straight lines, but gravity, as a bending of spacetime, bends what we understand as a “straight line”. Ditto describing gravity as a “pseudoforce” to a certain extent, it doesn’t exist within quantum theory and, despite much effort, nobody has come up with a convincing way to integrate it.

• Robert Gallinat

No I’ am not in pseudo force league.

I’ am not thinking that gravity is a “force” in the same sense as GRT describes it, especially not if we go down to a level of single particles.

I do not think that single particles are gravitating to each other, so no gravitons. I think gravitation is an emergent phenomenon that emerges if an in itself discrete space produces transition defects (call it “entropy of space”) while hosting particles in a more dense packaging.

So you are not right. But instead I’ am following an algebraical approach.

And while in this approach space is described by a big group and QED / QCD is described by another group, there are transitions between both groups, described by subgroups and symmetries between these subgroups which are leading to events and time.

And these subgroups are transforming the dx and the dt in the space group (so finally spoken in an old fashioned style: the line element of the manifold) into delta_x and_delta_t in the QED / QCD group. Its a backward transformation from Planck scales (“pseudo infinitesimal” values) towards scales with a physical meaning.

If I’ am talking about “defects” or “imperfections”, I only used Sabines wording in that regard.

What I mean are some algebraical imperfections in the transition between both groups, and these imperfections are representing gravity. There are though no gravitons, no double copy gluons, no exchange bosons.

I’ am perfectly in the league of quantum gravity, but my model bounds gravity not directly to particles but to the influence that particles have in dense package onto space itself. It have not directly to do with GRT, it is just another formulation of it in some boundary cases.

I’ am convinced of a quantum behavior of space itself, that space is, as Sabine described it, is in itself not continuous but discrete.

• Ben Flanders von Eltz

• Middleman

This might be easier to resolve using “infinitesimal calculus.” Instead if the cauchy-style of calculus used today

space-time is one force represent itself in expansion configuration, we can split space and time into smaller quantitive , mathematized units but that it doesnt mean going to add meaningful explanations more than adding more interpretations of confessions or miscalculations to the meaning of nature of universe

• And that’s not all. Einstein taught us that space and time are joined in one entity: space-time.

• In string theory, for example, resolution is limited by the extension of
the strings (roughly speaking, the size of the ball that you could fit
the string inside),

• Even if the direct effects on particle motion are unmeasurable, defects in the discrete structure could still be observable.

• B Whitehouse

I’d like to propose what seems to me a simple way of understanding how discreteness and continuous flow coexist at the quantum level of photon particle-wave duality and the structure and flow of the expanding universe in what I’ll call an unfolding now.

This unity or Unification can be understood in a particular pattern, the umbilic or horn torus if you consider both its spacial “shape” and its particular temporal movement dynamics.

Besides the mathematics involved, this pattern can be easily understood by picturing it. I’ve chosen several images from the Internet to illustrate these points.

First, picture the torus with its two orthogonal circularities (around and vertical) as the discrete packet. (See the pink torus below from http://www.horntorus.com/illustration/standard_dynamic_horn-torus_still.html)

Second, see the side view of the double spiral motion shown in the “vortex” drawing by mathematician Arthur Young in Consciousness and Reality and the blue-yellow torus from the Institute for the Study of Consciousness. Picture the motion as emanating from the center and spiraling upward and outward and downward scribing an outer “spatial boundary” (though not finite) followed by an inward curvature that comes back through its spatial center to complete a cycle, a cycle of time.

If you follow the arrows you can see that this double spiral that has both L handed and R handed curves which are one continuous motion so in my mind could be called Spin 1, a complete toroidal cycle. This can describe any space and any time period.

This toroidal double spiral can also be seen from a top or bottom view as if looking down into the torus motion. From the top you see the L handed spiral that spirals out and down). From the bottom you see the R handed spiral (that spirals inward and upward). (The two halves of a complete cycle, like the expiration-inspiration halves of one breath’s cycle.)

When looking down from the top with the depth collapsed or where you see both spirals, you get the pattern shown in my crude wire model (basically the heart shape within the circle). (see also Cosmometry.net…..) Perhaps this could be seen as the probability wave form collapse into a discrete moment of experience.

If you can, picture the discrete form (whether from top or side) also in its shape as being a discrete event and the movement pattern as the movement from a beginning point through its time cycle to a completion of that event. So here we have both spatial and temporal connected. Furthermore at the completion of the time cycle of the event, lets call it a pulse, there is a jump to the start of another cycle, and we end up with nested flowing events, events that are discrete and embedded within a continuous flow. (The 5th-7th images below show how toroidal structures nest within each other though I don’t yet have an image of the nested toroidal spirals. #5 is from http://www.horntorus.com, and the 6th and 7th are from cosmometry.net.)

Remember that the toroidal movement is the means by which something moves within its own medium. So I’m even suggesting that the photon has toroidal properties and that it moves toroidally, within itself, showing both its particle discreteness and its wave flow. So Light’s medium is Light itself.

In addition, if we consider that the formula* for the shape of this torus is the same as for the volume of the hypersphere, regardless of scale, and for the discrete quantum of action which is the ultimate no-thingness (because for light, space and time are “not there”), then we can say we have an original starting from the no-thingness of the photon, actually the”smallest” photon (quanta) with its intrinsic (I’ll say toroidal) spinning out creating time and “particle movement” and space creating fields and eventually all matter and the expanding toroidal universe. I see all this expansion as nested pulses, each a discrete event but with ongoing ie continuous movement in an ever widening new toroidal pulse in all directions.

And here are my wildest speculations:

This Toroidal-Space-Time is the long sought unification of quantum and relativity theories.

Could the 2 spiral motions of toroidal space-time be the strings, the loops in string theory, especially since the torus is the only shape that can be twisted or morphed into any shape with two circularities, eg a cup or dimpled sphere like a cell? Also the torus motion pattern can be untwisted or unknotted or deformed from its 3d shape into a flat 2d circle.

Could gravity be the the toroidal space-time curvature that comes back inward, the attractive force? And could dark energy be that inward upward energy that also starts the next push outward, the radiating expansive force.

If our universe could be said to start from light (“smallest” photon having infinite energy i.e. the energy of the universe and power to create other particles) and be composed of and filled with light and its toroidal movement through other forms, maybe we could say in some new and different ways that the universe is holographic in the sense of “information” being projected from light as source into all form and structure and movement, ie toroidally holographic, not just a projection onto a surface. The information is carried in the frequency waves. Additionally, remembering that each discrete piece of a holographic film, ie image stored in frequency form, contains the information of the whole source albeit the smaller the piece the more foggy the image, then it is easy to see how the source is “hidden” within every individual part.

We can also see how one part and the whole are connected when we consider that a toroidal structure is mathematically described as the 7 color (see 8th image below), from Arthur Bloch’s Hypersphere) or 7 parts that are sequential but that curve around the donut shape of the torus with an outer and an inner curve connected in the middle or starting point such that all parts touch one another ie one is connected to all) and the flow pattern moves in a bootstrapping toroidal motion through itself, moving from within. It could be said to be from source through manifestations of source, both discrete and continuous creation. Also, the spirals involved relate to growth patterns and geometric relationships between structures. So now we have a pattern of the relationship of and evolution of one and all, from an infinitely small all powerful, ie infinite energy, beginning through an infinitely large toroidal universe.

For much of the above info on the torus, I am deeply indebted to mathematician Arthur M Young. The ideas on the discrete and continuous are my own.; also the spin 1, toroidal photon dynamic strings and light as its own medium, and the speculation of gravity as the natural toroidal space-time curvature i.e. rotational movement, etc. Obviously there is much more to be said than what I have written here, so this will be further explored in my forthcoming book.

*The Einstein-Eddington formula for the volume of the universe, the hypersphere, is 2⫪2R3 . This formula is “the same as the volume of the torus with the infinitely small hole!” (The Reflexive Universe p 262) and is also the formula for the quantum of action (as explained in Young’s essay “Is There confusion in Theoretical Science” p 8-12)

• ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
YOU ARE FOOLED INTO BELIEVING THE TRUTH
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Everything is made from strings (not the string theory type).

Strings (from any theory) are supposedly one dimensional 1-D.

Clusters of strings form protons, neutrons, electrons and when they group together they make atoms. Atoms of course form everything matter-wise — that includes you.
So you think you are 3-D but you are actually made from 1-D strings

A string of course has a length but it would also have to have and infinitesimally small thickness, that would give it a height and width, or three dimensions 3-D.

So you are fooled into thinking you are 3-D but it is actually the truth.

You are fooled into believing the truth.