Nima Arkani-Hamed: "Almost all of us believe that spacetime doesn't really exist, spacetime is doomed and has to be replaced by some more primitive building blocks." https://youtu.be/U47kyV4TMnE?t=369

The only building block of spacetime is Einstein's 1905 constant-speed-of-light falsehood:

"Special relativity is based on the observation that the speed of light is always the same, independently of who measures it, or how fast the source of the light is moving with respect to the observer. Einstein demonstrated that as an immediate consequence, space and time can no longer be independent, but should rather be considered a new joint entity called "spacetime." https://www.bowdoin.edu/news/2015/04/physics-professor-baumgarte-describes-100-years-of-gravity.html

Pentcho Valev https://twitter.com/pentcho_valev

Cosmic (or Einsteinian?) conspiracy of the highest order:

"Einstein pulled all of these ideas together in his 1905 theory of special relativity, which postulated that the speed of light was a constant. For this to be true, space and time had to be combined into a single framework that conspired to keep light's speed the same for all observers." https://www..livescience.com/space-time.html

Neil deGrasse Tyson, Death by Black Hole: And Other Cosmic Quandaries, pp. 123-124: "If everyone, everywhere and at all times, is to measure the same speed for the beam from your imaginary spacecraft, a number of things have to happen. First of all, as the speed of your spacecraft increases, the length of everything - you, your measuring devices, your spacecraft - shortens in the direction of motion, as seen by everyone else. Furthermore, your own time slows down exactly enough so that when you haul out your newly shortened yardstick, you are guaranteed to be duped into measuring the same old constant value for the speed of light. What we have here is a COSMIC CONSPIRACY OF THE HIGHEST ORDER." https://www.amazon.com/Death-Black-Hole-Cosmic-Quandaries/dp/039335038X

Brian Greene: "If space and time did not behave this way, the speed of light would not be constant and would depend on the observer's state of motion. But it is constant; space and time do behave this way. Space and time adjust themselves in an exactly compensating manner so that observations of light's speed yield the same result, regardless of the observer's velocity." http://www.pbs.org/wgbh/nova/physics/special-relativity-nutshell.html

Pentcho Valev https://twitter.com/pentcho_valev

On Saturday, May 27, 2023 at 9:11:11 AM UTC-4, Pentcho Valev wrote:
> Nima Arkani-Hamed: "Almost all of us believe that spacetime doesn't really exist, spacetime is doomed and has to be replaced by some more primitive building blocks." https://youtu.be/U47kyV4TMnE?t=369
>
> The only building block of spacetime is Einstein's 1905 constant-speed-of-light falsehood:
>
> "Special relativity is based on the observation that the speed of light is always the same, independently of who measures it, or how fast the source of the light is moving with respect to the observer. Einstein demonstrated that as an immediate consequence, space and time can no longer be independent, but should rather be considered a new joint entity called "spacetime." https://www.bowdoin.edu/news/2015/04/physics-professor-baumgarte-describes-100-years-of-gravity.html
>
> Pentcho Valev https://twitter.com/pentcho_valev

Einstein does no better at deriving spacetime than any other theory which rests upon empirical evidence.
The evidence is strong for three dimensional space, and the sensibility of the tensor in that sensibility is likewise strong.
Time in a way breaks the symmetry that the tensor promised. The 4D claim offends the basic tensor operation of having an arbitrary reference frame. Time is unidirectional, and this hardly gets into the discussion. Always the lightcone projection has to be applied as a rendering to sensibility.
Rotate your reference frame; say x to t, and t to x or -x; whichever it is that doesn't go improper; the tensor sensibilities are gone. Your atoms have extruded into their lifespans in space. It is not the same thing. The original tensor sensibility is lost. Spacetime is structured.

A system that does not rest upon empirical data is known as a pure mathematics, or even a philosophy. To beget spacetime from such would indicate a candidate for a theory that has been only dreamed of, and this by very few. Even the string theorists happily go along extending into some higher dimensions without a care as to how the three or four we observe are so. Supposedly the quantum gravity people were going to get 'emergent spacetime' but even their energies seem to have disippated. Well I have bumped into a pure mathematics which challenges the human race in its status quo position. Why should it fall upon deaf ears? Oh, plenty of theories alight just there. Still, I should substantiate my claim so here goes once again into the supposedly uncensored free speech zone of USENET from google groups of course, where perhaps freedom isn't really free. Here we are on May 28, 2023; a Sunday one day before Memorial day... a troubling time for most...

The generalization of sign known as polysign numbers is simply a method which treats the real numbers as two-signed (-,+), which they already are, and goes on to consider three-signed numbers; four-signed numbers; and so forth; not to belittle the little sibling P1 either, whose time correspondence is excellent and beyond compare. So you see we are discussing a family of number systems in the full generality:
P1, P2, P3, P4, P5, P6, ...
and it happens that the reals are P2. We see that the reals obey:
- a + a = 0
and so to ponder P3 is simply a matter of extending this to:
- a + a * a = 0
and it should already be clear to the clear-headed ones that the signs of P3 are unique to the signs of P2 in behavior even while they get reused. As has already been stated this is a family of number systems of which P2 is but one sibling. To work in P2 is not to work in P3. Individual values have to specify their signature, such as P7, for instance in order for the value to be fully instantiated. Clearly to develop polysign and gain comfort we should start just at P3 and learn of its properties first, rather that claim to understand them all at once. Still, this is the beauty of polysign: they all operate on the same laws; it's just that those laws are n-ary; actually modulo-n. In P2 products are modulo two behaved by sign. Well then, clearly products in P3 will be modulo three behaved. A compact sign table for P3 reads: --=+,-+=*,-*=-,++=-,+*=+,**=*. They will commute so there is no problem there. Of course product values will rely upon the FOIL method, so P3 values like:
( + 2 * 3 )( -2 + 1 ) = (+2)(-2) * (+2)(+1) * (*3)(-2) * (*3)(+1)
= * 4 - 2 - 6 + 3 = * 4 - 8 + 3
= * 1 - 5 .
Some of this notation will look strange yet familiar, too. Sadly, we must give up the plus sign '+' as the sum operator, for its meaning as sign two with two strokes to draw it, which is mnemonically correct, cannot be the identity (neutral) sign in P3. The * symbo, with three strokes to draw it, takes its place as the identity sign. This can only be corrected by the introduction of a zero sign '@' whose modulo position will not vary in Pn. This exposes what could be called a mistake in notation which has denied the generalization of sign up to this point. I cannot claim the brilliance of so many great minds that have come before, and yet how they failed to perform this specific general mathematical option of generalization of sign must be put upon the table for consideration. Many greats have covered the ground of mathematics from their own fundamentals yet to my knowledge none have discovered polysign numbers. This detail should not be so. Anyway to dwell upon that problem too long will not be productive. The point is that what is being discussed here is something new and of a fundamental nature. P3 map to the plane. They do this just as P2 map to the line. In essence each Pn demands its geometry from the fact of the balance of the rays. For instance in P3:
- 1 + 1 * 1 = 0
and the geometry which corresponds with this statement is three rays, each labelled with its sign, 120 degrees apart on a flat piece of paper. Now, stepping one in each direction returns you to the same position. So you see the plane can be described with three directions of space rather than with four. Likewise what is known as '3D' space can be described with four directions (P4) rather than the six that enter the common language. Simply put: the ray is more fundamental than the line, which arguably is composed of two rays (P2). The very term 'dimension' is tied to the real line as fundamental, yet polysign is breaking with the line as fundamental. Though it is contaminated, I do freely use the old terminology, but I try to be careful just the same. P2 is 1D; P3 is 2D; P4 is 3D; P1 is 0D? Here we have entered remarkable territory.

A common P3 instance like:
- 1.2 + 2.3 * 3.4
will graph to a specific position. Still, this value can be reduced to:
+1.1 * 2.2
and in general this exposes what we could still call two dimensions in the reduced form. So in some regards the puzzling nature of polysign is hidden just there. Simply step back to P2, where a value such as:
- 5 + 2.3
can be instantiated. Clearly a reduced form does exist as -2.7. It happens that in P2 it is a singular value. In P4 generally there will be three values in the reduced form. It is tradition that we work in reduced values, and in terms of performing products quite a bit of manual labor is saved that way.
Still, computer algorithms will use the full form for obvious reason. Though this detail comes across as fishy for some there is no actual conflict here. What you are witnessing is more about convention and notation than anything. There is somehow an idea that a real value could contain both a negative and a positive component, but the fact that there is always the reduction possible to a single component is shadowed by the fact that that component then must carry a sign with it. Computer algorithms will keep the components in their sign positions and so operate very efficiently. Multiplying values s1 and s2 in Pn with x[n] indexing to the values goes very simply:
for( i = 0; i < n; i++ )
{
for( j = 0; j < n; j++ )
{
k = (i+j)%n;
x[ k ] += s1.x[i] * s2.x[j];
}
}

Pn are algebraically behaved, and in closing though I will leave it unproven here, P3 are equivalent to the complex numbers though they are in a new format. this means that he same laws which develop P2 as the reals develop P3 as the complex numbers. From my past interactions people shy away from this fact, and yet this alone can act as a powerful indicator of the goodness of polysign numbers. Above and beyond this detail the family of polysign numbers contains a natural breakpoint:
P1 P2 P3 | P4 P5 P6 ...
where the magnitude of the product no longer maintains as the product of the magnitudes. This is the familiar:
| z1 z2 | == | z1 | | z2 |
and so the possibility of support for emergent spacetime from pure mathematics is present in polysign numbers. Other than this, the product is algebraically behaved, and so the claim for finding 3D complex numbers and so forth can be laid here as well. Far more prescient is the tightness of their geometry to their algebra via the sign balance law.