Astrorelations - Impetus

What is a Wormhole?

Wormholes were first theorized in 1916, though that wasn’t what they were called at the time. While reviewing another physicist’s solution to the equations in Albert Einstein’s theory of general relativity, Austrian physicist Ludwig Flamm realized another solution was possible. He described a “white hole,” a theoretical time reversal of a black hole. Entrances to both black and white holes could be connected by a space-time conduit.

In 1935, Einstein and physicist Nathan Rosen used the theory of general relativity to elaborate on the idea, proposing the existence of “bridges” through space-time. These bridges connect two different points in space-time, theoretically creating a shortcut that could reduce travel time and distance. The shortcuts came to be called Einstein-Rosen bridges, or wormholes.

Certain solutions of general relativity allow for the existence of wormholes where the mouth of each is a black hole. However, a naturally occurring black hole, formed by the collapse of a dying star, does not by itself create a wormhole.

Wormholes are consistent with the general theory of relativity, but whether wormholes actually exist remains to be seen.

A wormhole could connect extremely long distances such as a billion light years or more, short distances such as a few meters, different universes, or different points in time

For a simplified notion of a wormhole, space can be visualized as a two-dimensional (2D) surface. In this case, a wormhole would appear as a hole in that surface, lead into a 3D tube (the inside surface of a cylinder), then re-emerge at another location on the 2D surface with a hole similar to the entrance. An actual wormhole would be analogous to this, but with the spatial dimensions raised by one. For example, instead of circular holes on a 2D plane, the entry and exit points could be visualized as spheres in 3D space.

Science fiction is filled with tales of traveling through wormholes. But the reality of such travel is more complicated, and not just because we’ve yet to spot one.

The first problem is size. Primordial wormholes are predicted to exist on microscopic levels, about 10–33 centimeters. However, as the universe expands, it is possible that some may have been stretched to larger sizes.

Another problem comes from stability. The predicted Einstein-Rosen wormholes would be useless for travel because they collapse quickly.

“You would need some very exotic type of matter in order to stabilize a wormhole,” said Hsu, “and it’s not clear whether such matter exists in the universe.”

But more recent research found that a wormhole containing “exotic” matter could stay open and unchanging for longer periods of time.

Exotic matter, which should not be confused with dark matter or antimatter, contains negative energy density and a large negative pressure. Such matter has only been seen in the behavior of certain vacuum states as part of quantum field theory.

If a wormhole contained sufficient exotic matter, whether naturally occurring or artificially added, it could theoretically be used as a method of sending information or travelers through space. Unfortunately, human journeys through the space tunnels may be challenging.

Wormholes may not only connect two separate regions within the universe, they could also connect two different universes. Similarly, some scientists have conjectured that if one mouth of a wormhole is moved in a specific manner, it could allow for time travel.

Although adding exotic matter to a wormhole might stabilize it to the point that human passengers could travel safely through it, there is still the possibility that the addition of “regular” matter would be sufficient to destabilize the portal.

Today’s technology is insufficient to enlarge or stabilize wormholes, even if they could be found. However, scientists continue to explore the concept as a method of space travel with the hope that technology will eventually be able to utilize them.

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Eh?

What she says: I'm fine

What she means: How come Rene Descartes is only remembered as a philosopher, and the guy who said "I think therefore I am"? The Cartesian plane is NAMED after him and still only hard mathematicians know that he invented it. Also, the whole Newton/Leibniz argument completely ignores the fact that Descartes allowed both of them to discover calculus, because of his theories/ideas and invaluable work with exponents - he literally laid the foundations of calculus but no one mentions him when discussing who invented it. He even invented the modern notation of writing powers as superscripts as well as the convention of using x,y,z for variables and a,b,c for constants. Most importantly he INVENTED ANALYTIC GEOMETRY and pulled everyone's collective heads out of their collective asses. He was one of the greatest mathematicians. But yeah, a cool philosopher too, let's let "Cogito Ergo Sum" be his only legacy.

Saint Veronica with the Veil (Original piece by Mattia Preti c.1655-1660) Touched by Clayshaper

Energy formulas for imaginary matter

An imaginary matter is the mirror image of the corresponding real matter.

Energy formulas for real matters are still useful for imaginary matters if an observer is in the imaginary space. Then how are energy formulas for imaginary matters expressed if an observer who is in the real space could observe imaginary matters?

Suppose that observer A is in the real space and observer B is the mirror image of observer A in the imaginary space.

The space velocity vector and spacetime velocity vector measured by observer A are the opposite of those measured by observer B in the same way that the left and right sides of the mirror image are swapped, i.e., the space speed measured by observer A is constant at the maximum speed c and the spacetime speed measured by observer A is variable.

The relationship of these velocity vectors are shown in the figure below.

Assuming an imaginary matter moves at speed vi measured by observer B, the space speed vsB, time speed vtB and spacetime speed vstB measured by observer B are as follows:

On the other hand, the space speed vsA, time speed vtA and spacetime speed vstA measured by observer A are as follows:

The following equation holds true for time speed.

Hence, the following formula is obtained for the spacetime speed measured by observer A.

The spacetime speed measured by observer A is smaller as the space speed measured by observer B is larger.

Real matters cannot move at the speed of light at the cost of having mass, while imaginary matters also have mass but move at the speed of light.

Mass energy vector is in the time axis of the space-time complex plain and the time axis is common between the real space and imaginary space. Hence, the magnitude of mass energy vector is invariant for the spatial inversion. The imaginary space axis is at right angles to the real space axis in the space-space complex plain.

Therefore, the mass energy of imaginary matter measured by observer A is expressed as follows:

where “−i” is the operator that transfers from the real space to the imaginary space and m is mass.

The energy formulas for real matters in the range of v>c express those for imaginary matters, but the energy formulas of total energy and momentum energy are exchanged for each other. Therefore, the momentum energy Es and total energy Est of imaginary matter measured by observer A are expressed as follows:

For an imaginary matter at rest (vi = 0),

The space speed of imaginary matters is always zero because they have no momentum energy. Hence, an imaginary matter is equivalent to the real matter with (square root of 2) times the mass of the imaginary matter, moving at the speed of light.

The space velocity and time velocity of real matter, light and vacuum energy and those of imaginary matter converted into the real space are arranged below.

  ・Real matter         : relative space speed and relative time speed   ・Light                    : absolute space speed and no time velocity   ・Vacuum energy   : neither space velocity nor time velocity   ・Imaginary matter : absolute space speed and absolute time speed

How did I watch 8 seasons of this

A delightfully concise animated proof of the sum of the arithmetic progression of the naturals.

Mathematics is beautiful. <3

Hi! Can you tell some uni or colleges math resources?

Can you be more specific? Like resources for studying for particular undergrad level classes?

A few “classic” online references:

Paul’s online math notes (https://tutorial.math.lamar.edu/): algebra, calc 1-3, diff eqs though I’ve mostly only used the calc ones. A common favorite

Khan Academy: haven’t actually used any of their math stuff for years but I remember their videos were good

3blue1brown: he has a series on calc, diff eqs, and linear alg. I haven’t actually watched many of these either but his videos are generally good and I know people who like the series in particular

If you mean higher level math, I tend to just use a search engine and end up referencing a mix of wikipedia, wolfram mathworld, random pdfs from various universities, and math stack exchange. And of course textbook pdfs

If you give me more details, I’ll see if I can think of anything else!