Travelling through a wormhole in space
It means you can do it theoretically on paper. You take all the equations and stuff, and for some values the results give you cool answers. That doesn't mean that an example of it actually exists, though; it just means that you can find a solution to some equations which allow for it (or, often, simply don't prohibit it). Wormholes are classic examples - there are equations which describe them, but none have ever been observed (and we have no idea how to make one).
It means, the math does not forbid it. The math does not show it to be impossible. When you run through the math, the results may seem strange, but not entirely nonsensical or self-contradictory.
This is perhaps best compared to faster than light travel. The math of relativity blows up, or gives you self-contradictory results, if you try to have an object that travels faster than the speed of light. Things get divided by zero, and you get a big mess. FTL is forbidden by the laws of physics as we currently understand them.
Question - isn't that when you try to accelerate something to the speed of light? Doesn't the maths allow for objects moving permanently faster than light? Hypothetical particles like tachyons, for example? Or am I misremembering?
Bullgrit
Adventurer
I guess I'm getting hung up on the idea that looking at the math, (which I'm picturing as multitudes of equations, each filling up an entire whiteboard 
, can give someone the concept of something as extremely specific as a wormhole. It's not like a wormhole is like dark matter (another concept that the math allows [read: requires]) -- it seems that a wormhole is a very specific structure with a very specific function with very specific requirements, compared to dark matter that is basically, something has to be somewhere to make this calculate out.
I mean, I'm picturing someone looking at those whiteboards of equations, saying, "Hmm, what if this variable right here was a 2?" And the whole equation calculating out three feet away to "= tiny spacetime tubes connecting two points".
Bullgrit
, can give someone the concept of something as extremely specific as a wormhole. It's not like a wormhole is like dark matter (another concept that the math allows [read: requires]) -- it seems that a wormhole is a very specific structure with a very specific function with very specific requirements, compared to dark matter that is basically, something has to be somewhere to make this calculate out.I mean, I'm picturing someone looking at those whiteboards of equations, saying, "Hmm, what if this variable right here was a 2?" And the whole equation calculating out three feet away to "= tiny spacetime tubes connecting two points".
Bullgrit
In special relativity, if you have a particle moving faster than light, its mass must be imaginary. That's not a real, physical result, and thus cannot correspond to a real, physical particle.
There are quantum fields that can have imaginary mass (and are called "tachyonic" for it), but when the field does have that quality, it doesn't correspond to a real physical particle. It must first undergo what is called 'condensation', at which point it ends up with a real mass, and is going slower than light. Higgs bosons, which have been big in the news, are an example of a condensate from a tachyonic field.
I'm going to address a couple bits here out of order...
Actually.... not quite.
Dark matter (and dark energy) is not "required by the math". The math does not *predict* the existence of dark matter. Instead, the existence of dark matter is required to explain observation and empirical evidence. We have observed matter in galaxies and in the Universe moving in ways that it *shouldn't*, that cannot be explained by the matter we see and the math we have. From this, we *infer* the existence of matter we cannot see (and is thus "dark").
Hundreds of pages of squiggles can give you the concept of Middle Earth, and hobbits, magic rings, and wizards. All pretty darned specific.
Of course if you don't know the language, you can't *read* that book.
Just as English is a way to represent information and ideas, so is math - math is just a representation that is far more efficient at helping you manipulate certain kinds of ideas. It isn't easy to do, but once you've learned the language, yes, you can look at the equation, and say, "that represents a thing with these physical properties." It is kind of awesome.
Wormholes do not have a function, any more than hills have a function. A hill is ground that is shaped a given way by the forces put upon it. Yes, if I *build* a hill, then I say the hill has a function, but it only has such because I am *using* it for that function. When I go away, the hill remains, but it has no function. It is more appropriate to say that I can use the hill to perform a function, rather than the hill has the function innately. A wormhole is similar.
Actually.... not quite.
Dark matter (and dark energy) is not "required by the math". The math does not *predict* the existence of dark matter. Instead, the existence of dark matter is required to explain observation and empirical evidence. We have observed matter in galaxies and in the Universe moving in ways that it *shouldn't*, that cannot be explained by the matter we see and the math we have. From this, we *infer* the existence of matter we cannot see (and is thus "dark").
I guess I'm getting hung up on the idea that looking at the math, (which I'm picturing as multitudes of equations, each filling up an entire whiteboard
Hundreds of pages of squiggles can give you the concept of Middle Earth, and hobbits, magic rings, and wizards. All pretty darned specific.
Of course if you don't know the language, you can't *read* that book.
Just as English is a way to represent information and ideas, so is math - math is just a representation that is far more efficient at helping you manipulate certain kinds of ideas. It isn't easy to do, but once you've learned the language, yes, you can look at the equation, and say, "that represents a thing with these physical properties." It is kind of awesome.
Wormholes do not have a function, any more than hills have a function. A hill is ground that is shaped a given way by the forces put upon it. Yes, if I *build* a hill, then I say the hill has a function, but it only has such because I am *using* it for that function. When I go away, the hill remains, but it has no function. It is more appropriate to say that I can use the hill to perform a function, rather than the hill has the function innately. A wormhole is similar.
tomBitonti
Adventurer
Would you put the exotic matter required for wormholes in the same category as tachyonic matter? That is, a kind of matter which, if it existed, would behave in exceptional ways compared to ordinary matter, but for which there is no physical evidence?
I'm thinking this gets at the difference between the equations which are used, and the actual underlying physics (which is in the realm of what can be tested).
Although, if you look at neutron stars and black holes, those were predicted by looking at particular parts of the domains for equations (what happens when you put a lot of mass together). Not really a hard question, but it's curious that the implied objects (black holes) have been observed, while worm holes have not. I'm thinking that is not a hard question, since black holes do not require a new exotic kind of matter.
Thx!
TomB
I'm thinking this gets at the difference between the equations which are used, and the actual underlying physics (which is in the realm of what can be tested).
Although, if you look at neutron stars and black holes, those were predicted by looking at particular parts of the domains for equations (what happens when you put a lot of mass together). Not really a hard question, but it's curious that the implied objects (black holes) have been observed, while worm holes have not. I'm thinking that is not a hard question, since black holes do not require a new exotic kind of matter.
Thx!
TomB
Well, there are a few things often referred to as "exotic matter" for which we do have at least some physical evidence. Neutronium comes to mind - this is a material produced when matter gets so compressed that the protons and electrons get pressed together so much they combine into neutrons, but not so compressed it falls into itself to become a black hole.
We have neutron stars - objects so compact that there's nothing else (that we know of) that they could be made of! All our math says that it should exist. But its properties are... extreme, when compared to the matter of normal human experience.
With a couple such caveats, yes, for the most part, "exotic matter" is stuff that might exist, but would have some really weird properties that we have never directly seen in physical reality.
tomBitonti
Adventurer
I thought that neutronium was, more or less what is in the nucleus of an atom, with protons removed, and with a lot more of it (really, a lot more) than is in a typical atom.
Neutronium may have exotic properties, but, it doesn't seem to be quite the same as what worm holes are said to require, e.g., matter which is repelled by gravity. Neutronium is normal matter in an unusual configuration.
Thx!
TomB
Neutronium may have exotic properties, but, it doesn't seem to be quite the same as what worm holes are said to require, e.g., matter which is repelled by gravity. Neutronium is normal matter in an unusual configuration.
Thx!
TomB
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