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Thread: Theoretical manipulation of space-time organized list of approach?

  1. #1 Theoretical manipulation of space-time organized list of approach? 
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    Well, I'll start off by saying i'm only in grade ten (Canada) and in a first level entry physics class. I specifically took this course because of my sparked interest after reading some of Brains Greene's well written books on the presently 'hyped' physics studies. I'm Not the best with math (you guys probably here this annoying ' i'm not good at math but..' stuff all the time, so I apologize,) although I am extremely interested in the idea of a Warp drive, and as soon as I found the Alcubierre drive Wiki, I was hooked. Unfortunately I just passed my basic entry math course and know absolutely nothing in regards to the advance mathematics required to acquire a deep and sentimental respect for these studies and their applications. I would be fine, as I posses a motive that allows me to push almost any obstruction to reach my goal out of the way, if I were able to formulate a 'Plan of approach' to be utilized as my recommended academic path. This, is where the friendly and awesome folks on The Science forum come in. If any one reading this post has sufficient knowledge of 'the Alcubierre drive' and/or manipulation of the fabric of space-time, I ask of you to suggest a reasonable outline in a chronological list-like order of the academic tools required to learn in order to delve into this study.

    Thanks


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  3. #2  
    Moderator Moderator Markus Hanke's Avatar
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    If you are in grade 10 ( which I understand to be second-level, or high school ), then you have set your goal really high here. The "Alcubierre Warp Drive" is based on a particular solution of the Einstein field equations, which are the basic equations of a theory called "General Relativity", usually abbreviated as "GR". The fundamental idea of GR is that the gravitational field that accompanies all forms of energy ( mass, electromagnetic fields etc etc ) is not a force as in classical mechanics, but rather an intrinsic geometric property of space-time itself. In Einstein's GR this property is curvature - space-time in the presence of energy is not flat, but curved. In curved space-time many of our everyday "truth" in geometry no longer hold, e.g. the sum of the angles in a triangle is no longer 180 degrees, and "parallel" lines may indeed intersect. The mathematical description of this is based on an area of maths called differential geometry, or DG for short.
    Now, DG is an awfully complicated beast, even for seasoned mathematicians who have studied this field for decades. It is very difficult to suggest a path to understanding DG for someone who is in 10th grade. What I would say to you is however that it all starts with basic calculus; you need to be 100% proficient in your differentials and your integrals before you can even consider making a start on DG. I don't know how in-depth the treatment of calculus in the Canadian curriculum is, so you might consider doing some further study in that area to begin with.

    Leaving aside any maths for now, here is an important reminder - just because a particular geometry is mathematically a permissible solution to the Einstein field equations does not necessarily mean that it is physically possible. The Alcubierre metric is certainly very interesting, but in order to physically construct a "Warp drive" based on it, one would need what is called "exotic matter". Unfortunately there is no evidence whatsoever ( not even theoretically ) that such matter exists; without exotic matter the Alcubierre metric is merely a mathematical artifact without much physical meaning.

    EDIT : If you are interested in what is involved in finding solutions to the field equations, feel free to have a look at this thread which I had made a while back :

    Solving the Einstein Field Equations

    Bear in mind that this solution, the exterior Schwarzschild metric, is the simplest possible analytical solution. The Alcubierre metric would be much more complicated than this.


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    Quote Originally Posted by Markus Hanke View Post
    The Alcubierre metric would be much more complicated than this.
    And the more-than-annoying fact that it's now widely considered to be unworkable even if we could get the exotic matter.
    But don't let that put you off the subject xXplosionZz, there may be a thoroughly feasible solution to "FTL" travel somewhere.
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    Someone recently commented in a thread about some hot dog at NASA that is developing the drive, claims to require a fraction of the energies and won't answer any questions.
    Frankly, I think he's full of it, but that's just me...
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    Leaving aside any maths for now, here is an important reminder - just because a particular geometry is mathematically a permissible solution to the Einstein field equations does not necessarily mean that it is physically possible.
    i have had many discussion with people who don't seem to realise this point.
    Sometimes it is better not knowing than having an answer that may be wrong.
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    Moderator Moderator Markus Hanke's Avatar
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    Quote Originally Posted by Chrispen Evan View Post
    i have had many discussion with people who don't seem to realise this point.
    Yes, same here. It is a very important point to keep in mind. The Einstein field equations are by their very nature constraint equations only, and as such they permit mathematical solutions which are not physically realisable in our universe. On the other hand, metrics which are not a solution of the Einstein equations are never physically possible.
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    Hmm, I really wish I knew more about this 'field' equation stuff. Why would he create solutions for phenomena not physically realizable ?
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    Quote Originally Posted by xXplosionZz View Post
    Hmm, I really wish I knew more about this 'field' equation stuff. Why would he create solutions for phenomena not physically realizable ?
    why not? it's just maths.
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    Quote Originally Posted by xXplosionZz View Post
    Hmm, I really wish I knew more about this 'field' equation stuff. Why would he create solutions for phenomena not physically realizable ?
    Who is "he" ?
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    Quote Originally Posted by Markus Hanke View Post
    Quote Originally Posted by xXplosionZz View Post
    Hmm, I really wish I knew more about this 'field' equation stuff. Why would he create solutions for phenomena not physically realizable ?
    Who is "he" ?
    Miguel Alcubierre.
    "For the rest of my life I will reflect on what light is." - Albert E.
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    Quote Originally Posted by ostkef View Post
    Miguel Alcubierre.
    Because he wanted to find a way to construct a "warp drive", so he worked the equations backwards. He started with a metric that would describe the equivalent of a warp bubble, and asked himself what type of energy distribution was needed to create such a bubble. The field equations provided the answer. It became obvious immediately though that exotic matter was required to physically realize that.
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    Quote Originally Posted by xXplosionZz View Post
    Hmm, I really wish I knew more about this 'field' equation stuff. Why would he create solutions for phenomena not physically realizable ?
    So after working out his equations, Miguel realized that exotic matter was required.

    Now NASA's Sonny White is trying to create the matter required.
    "For the rest of my life I will reflect on what light is." - Albert E.
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    Moderator Moderator Markus Hanke's Avatar
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    So after working out his equations, Miguel realized that exotic matter was required.
    Yes, that's pretty much the upshot of it.

    Now NASA's Sonny White is trying to create the matter required.
    I am not sufficiently familiar with White's work to tell what exactly it is he is trying to do.
    We have no reason to assume or even suspect that such a thing as exotic matter exists, so I believe he is probably trying to circumvent this by taking advantage of a phenomenon called the Casimir effect. This is a quantum mechanical effect whereby one can produce a region with a net negative energy density between two capacitor plates. This effect is real, and such a region of space would have physical properties very much like the ones of exotic matter. However, it needs to be emphasised that this is an effect on microscopic levels only, it would not be easily possible to scale this up to our macroscopic domain. It would still be an interesting proof of concept, though.
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    Quote Originally Posted by Markus Hanke View Post
    So after working out his equations, Miguel realized that exotic matter was required.
    Yes, that's pretty much the upshot of it.

    Now NASA's Sonny White is trying to create the matter required.
    I am not sufficiently familiar with White's work to tell what exactly it is he is trying to do.
    We have no reason to assume or even suspect that such a thing as exotic matter exists, so I believe he is probably trying to circumvent this by taking advantage of a phenomenon called the Casimir effect. This is a quantum mechanical effect whereby one can produce a region with a net negative energy density between two capacitor plates. This effect is real, and such a region of space would have physical properties very much like the ones of exotic matter. However, it needs to be emphasised that this is an effect on microscopic levels only, it would not be easily possible to scale this up to our macroscopic domain. It would still be an interesting proof of concept, though.
    Unfortunately NASA hasn't announced any prelim tests.
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    Quote Originally Posted by ostkef View Post
    Unfortunately NASA hasn't announced any prelim tests.
    I don't think any tests have actually taken place yet...the White-Juday Warp Interferometer is still very much in the planning phase.
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    Wow, thanks guys! I'm going to look up the Casimir effect now. Any other ideas as too what I should look into to get a more broad sense of situations dealing with exotic matter?
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    Quote Originally Posted by xXplosionZz View Post
    Wow, thanks guys! I'm going to look up the Casimir effect now. Any other ideas as too what I should look into to get a more broad sense of situations dealing with exotic matter?
    Perhaps you should familiarize yourself with existing particles first - maybe look up the Standard Model of Particle Physics.
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    Quote Originally Posted by Markus Hanke View Post
    Quote Originally Posted by xXplosionZz View Post
    Wow, thanks guys! I'm going to look up the Casimir effect now. Any other ideas as too what I should look into to get a more broad sense of situations dealing with exotic matter?
    Perhaps you should familiarize yourself with existing particles first - maybe look up the Standard Model of Particle Physics.
    You could start here.

    http://www.particlezoo.net
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    Quote Originally Posted by ostkef View Post

    You could start here.

    http://www.particlezoo.net
    Handmade subatomic particle plushies ??
    Cheez, now I've seen it all !
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  21. #20  
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    Quote Originally Posted by Markus Hanke View Post
    Quote Originally Posted by ostkef View Post

    You could start here.

    http://www.particlezoo.net
    Handmade subatomic particle plushies ??
    Cheez, now I've seen it all !
    "for ages 13 and up"
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  22. #21  
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    Those are incredible, ahaha! Thanks for all the discussion, and are there any specific things you recommend I learn about 'The Standard Model', more extensively than others?
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  23. #22  
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    Quote Originally Posted by xXplosionZz View Post
    Those are incredible, ahaha! Thanks for all the discussion, and are there any specific things you recommend I learn about 'The Standard Model', more extensively than others?
    well, you'll need to "learn them all".

    you could start here

    The Particle Adventure
    "For the rest of my life I will reflect on what light is." - Albert E.
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    I'll do the whole adventure.. Thanks!
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