Quote:

---

We surely should have the ability to build faster than light space vehicles by utilising this well established physics.

---

Quote:

---

nice1 said:
How about a super/ferrofluid centrifuge?

---

Quote:

---

nice1 said:
Einsteins theory of relativity explains that gravity is a result of the curvature of space time itself...

http://www.guardian.co.uk/science/2007/apr/15/spaceexploration.universe

"Just as a bowling ball placed on a trampoline stretches the fabric and causes it to sag, so planets and stars warp space-time - a phenomenon known as the 'geodetic effect'. A marble moving along the trampoline will be drawn inexorably towards the ball.

Thus the planets orbiting the Sun are not being pulled by the Sun; they are following the curved space-time deformation caused by the Sun. The reason the planets never fall into the Sun is because of the speed at which they are travelling.

According to the theory, matter and energy distort space-time, curving it around themselves. 'Frame dragging' theoretically occurs when the rotation of a large body 'twists' nearby space and time. It is this second part of Einstein's theory that the Nasa mission has yet to corroborate."


If a rotating energy is twisting space time would this not be the ideal method for our vehicles to travel?

Is anyone working on using this for building flying and/or space craft? 

Also does this not by implication mean that the speed of light barrier is not a barrier for vehicles utilising the warping of space time itself to travel?


Why are we lagging behind with this so much?    We surely should have the ability to build faster than light space vehicles by utilising this well established physics.

---

Quote:

---

DieCommie said:
Its a 4-Dimensional space.

In math, a 'space' is a generalized idea.  http://en.wikipedia.org/wiki/Space_(mathematics)

That is dense description.


The normal way to try describing it without math is to first articulate what 1, 2 and 3 dimensions are.  Then use that pattern to get a figment of what 4 dimensions is like.  Then you describe how the time dimension in space time is different than that generic 4th dimension.  Does any of that sound familiar?

---

Quote:

---

So space-time is the fourth dimension?

---

Close, but I would word it a little different.  "Space-time" is a space spanned by four dimensions.  Spanned is the least amount of dimensions to describe the space.  Time is not the fourth dimension, it is a dimension.  One of the four in space-time.

Lets go over a few other kinds of space.  Some of this is probably familiar. 

A simple space to consider a flat 2-D space like a map.  It has two dimensions, horizontal and vertical.  To describe the space, we need to describe what happens when you move around in it.  What happens when you move up?  What happens when you move to the side?  We intuitively know that you when you move up a notch you go up one unit.  If you go to the right a notch, that is one unit.  These dont really effect each other, you can go up and that doesnt effect your right/left direction.  To describe this simple fact in mathematical notion, we use an object called a 'metric tensor'.  It contains the information on how moving around in the space works.  In our 2-D space the metric tensor is simple, 



The ones tell us how moving in the straight directions work, and the zeros tell us that each direction is independent of the other.  Also of note for our 2-D space is that the length of anything on it is described by the good ol' fashioned pythogrean theorem,
. 
That value of 'd' is known as the distance and its the same no matter how you orient the space.  Its known as being 'invariant'.


Now this simple 2-D space can easily be extended to higher dimensions by extending our 'metric tensor' and our 'invariant'.  For 3-D we get for our tensor,

,

and for our invariant,

.

The pattern just continues forever for higher and higher dimensions of this flat, simple space.  (Known as euclidean)




This first common example of a non-flat or non-eucledian space is to consider the surface of a sphere like a globe.  Here the space is still 2-D, because it is spanned by two dimensions.  But its not flat because its metric tensor is different,

.

This space has weird behavior, you can see that by the odd metric tensor.  This tensor contains all the information about the space, like tri-angles not adding up to 180, etc.  The invarient is also different,

.



So we have surveyed basic Euclidean space and an example of non-Euclidean space.  Note that you can make up just about any crazy metric you want!  That will describe a unique space, most of which are are not interesting.  A few others that are used in physics is 'phase space' and 'hilbert space'.

Phase space is used to describe large ensembles of particles or whatever.  Every particle you have will have a momentum and energy associated with it.  This collection of momentum and energy values that your particles have can be plotted or placed in a 2-D space where one dimension is energy and the other is momentum.  This is pretty abstract!  This is a space that our particles live in, but its not a physical space.  Its a space that describes energy and momentum.  You can then extend this space into higher dimensions by consider the momentum in each physical direction.  This gives you a 4-D energy/momentum space.  This idea is used a lot in both relativity and in the kinetic theory of gasses (stat. mech, ideal gas law, etc.).

Hilbert space is used to describe quantum states.  This is also pretty abstract (of course).  Hilbert space is an infinite dimensional space.  Here each dimension describes an observable quantum state.  Our quantum particle lives in this infinite dimensional space.  It may be spread out occupying many of these dimensions or only a few.  When observed it collapses to one and one alone.  In quantum physics you are often concerned in how your quantum particle evolves through its hilbert space and what dimensions/values it will display upon observation.



Now that we have looked at two exotic abstract spaces, lets finally get back to Special Relativity.


Space-Time is a a 4-D space.  3 of its dimensions describe different directions and 1 describes time.  But the metric for this space is not flat!  It is not Euclidean and doesn't follow the scheme we did up above.  The metric tensor for this space is,




and the invariant,




This space is weird!  It has that negative in front of the time component...  From that metric and invariant you can derive all the weird happenings of relativity.  The fact that time dilates, lengths contract, speeds cant surpass light.  And it can be combined with the energy/momentum space I described above to get E=mc² squared.  You can also derive much of electromagnetism from that metric alone.  (Historically it happened the other way, electromagnetism prompted the development of the metric.)

This is what 'space-time' is.  Its the 4D space with the metric above.  It describes our observations in areas where gravity is negligibly weak.  General Relativity uses much more complicated metric to describe space and time with the effects of gravity.





Lots of info there.  Basically a crash course in some conceptual linear algebra and its application to physics.  Hope some of it makes sense.

Quote:

---

marmarwoohoo said:
I've never understood what is actually meant by "space-time". Could you please try and explain this to me? What is it, and how can said substance (if it is a sustance) be bent? It boggles my mind. I can understand most scientific concepts if from a metaphorical perspective but this one eludes me. Can you help?

---

Space and time are the same thing or at least inextricably linked.  Gravity is a result of this space-time fabric being curved.

When you move, even walk down the road - you are time traveling   The old idea of linear time has been proven incorrect.  Time travel into the future is actually pretty simple, you just need to travel faster than the place you want to time travel relative too.

If you go fast in a rocket around Earth then you can travel into the future faster relative to the people who are time traveling slower on the planet.  You could even sit in a machine and vibrate yourself if you can find a way of vibrating yourself fast enough and live.


I'm a noobian too though I haven't done much on the physics theory.  I'm more interested in the implications of whats already discovered and how we can use that to travel space-time more efficiently.  Mostly just thought experiments (I'm sure many will look down on that) but its just a bit of side thinking for me when I have spare time.

Quote:

---

venetianblinds said:
nice post


what other areas of mathematics would one have to study to be able to understand what the equations of physics mean? this is something im just getting into, and after reading book after book on the conceptual ideas, i want to learn the math too. i got a few cheap textbooks from a used bookstore, linear algebra, precalculus, and differential equations. they are all pretty basic and introductory, but thats what i need. (any other subjects i should keep an eye out for when i check the math section next time im at the bookstore?)

---

Quote:

---

for instance, i read QED by feynman straight through yesterday, i just cant put those books down.

---