E8 — A secret of the universe?

Discussion in 'Physics & Math' started by Tiassa, Nov 16, 2007.

  1. Reiku Banned Banned

    Messages:
    11,238
    True, but there are actually three coordinates to this... do you know what they are///?
     
  2. Google AdSense Guest Advertisement



    to hide all adverts.
  3. Reiku Banned Banned

    Messages:
    11,238
    I'm starting to like you. I held you as a type of arguementer... This HAS NOW gone...


    Freinds?
     
  4. Google AdSense Guest Advertisement



    to hide all adverts.
  5. Reiku Banned Banned

    Messages:
    11,238
    And forgive my spelling please. I've gone all Amy Whinehouse on this site recently. Lol
     
  6. Google AdSense Guest Advertisement



    to hide all adverts.
  7. invert_nexus Ze do caixao Valued Senior Member

    Messages:
    9,686
    Three coordinates to what?
    And what's the deal with the '///'?

    I simply say things as they are. I maintain everything I've ever said about you and your writing. You simply erred in believing that I was attacking you rather than making observations. I was actually trying to help you. I do that. Sometimes.

    No.

    Stop that. You've apologized for spelling and grammar far too many times. You'd do better to put more effort into your writing than apologies.

    Besides, poor grammar and spelling are the least of your concerns although they are certainly an impediment.
     
  8. Reiku Banned Banned

    Messages:
    11,238

    I'm not answering this anymore. Guess why?
     
  9. invert_nexus Ze do caixao Valued Senior Member

    Messages:
    9,686
    Oversensitive again?
     
  10. Reiku Banned Banned

    Messages:
    11,238
    No.. but.. I tried, and yet i missed: I want to be nice to everyone here, but you basically said you WOULDN'T BE A FREIND...


    What choices do you leave one?
     
  11. Reiku Banned Banned

    Messages:
    11,238
    In conclusion... how can I conform with someone who won't?
     
  12. invert_nexus Ze do caixao Valued Senior Member

    Messages:
    9,686
    What the hell does being a friend have to do with anything? I'm not here to make friends. I'm here to discuss, debate, etc.

    Besides, you're way to sensitive to be my friend. I like people who are a bit more thick-skinned. Also, who are more intellectually honest.

    Anyway. This is going off-topic and my feelings won't be hurt when it gets deleted.
     
  13. TruthSeeker Fancy Virtual Reality Monkey Valued Senior Member

    Messages:
    15,162
    What is the 248 thing, then?

    But that would be only 4 dimensions out of 8. What about the other 4?

    So what is a "symmetry"? And how many people knew before those ones?
     
  14. BenTheMan Dr. of Physics, Prof. of Love Valued Senior Member

    Messages:
    8,967
    Ok, there are some technical words here. Just use them as labels.

    This is where it gets tricky. ``Dimension'' has a lot of different meanings. When I say ``E8 is 8 dimensional'', this means that the symmetry exists in an abstract, eight dimensional space. The 248 thing is a set of points, which describe an eight dimensional lattice---I would say that the ``adjoint'' representation of E8 is 248.

    Because I can think in two dimensions pretty easily, let me give you an example. Another symmetry is SU(3). SU(3) describes a two dimensional space. The ``adjoint'' representation of SU(3) is eight dimensional---this means there is an eight point lattice in two dimensions. It looks like this:

    SU(3) lattice.

    Don't worry about the pi's and K's and stuff... The two points in the middle should be on top of each other---this is no coincidence that there are two points on top of each other AND that the SU(3) symmetry is two dimensional.

    If we were able to think in eight dimensions, the 248 of E8 would exist as a lattice. This is (I think), what the picture Tiassa posted was---a two dimensional projection of a lattice in 8 dimensions. I think.

    So now symmetry has a good intuitive meaning: you can consider the symmetry as describing the ways you can rotate the lattice without changing what it looks like.

    Well, the other four dimensions are ``internal'' dimensions. Now we are using the word ``dimensions'' in two different ways---the math way and the physics way. Before we even talk about space-time dimensions, let's think of it this way. I think what Lisi showed is that the symmetry E8 contains smaller subgroups, so that E8 => SO(3,1) + SU(3) + SU(2) + U(1). What does this mean? Well, we know very well that SU(3) describes the strong nuclear force, SU(2) describes the weak nuclear force, and U(1) describes the electromagnetic force. And, SO(3,1) describes gravity. So E8 contains all of the physics that we know of---this is Lisi's big conclusion.

    Now, SO(3,1) describes space-time, so technically ``dimension'' turns into ``dimension''. I really apologize about this, and I don't know if I can make it any clearer.

    I don't know what the main conclusions of Lisi's paper are---it seems to me confusing that he can get space-time out of E8, but also particle physics, in a manner that he hopes to be consistent with loop quantum gravity. In some sense, LQG takes space-time as something fundamental, but Lisi's conclusions don't seem to imply that. In short, I think we are confused about the same thing---the confusion is between what a mathematician means by ``dimension'' and a physicist means by ``dimension''.

    I don't know if any of this has been helpful, so apologies if you are more confused.
     
  15. 2inquisitive The Devil is in the details Registered Senior Member

    Messages:
    3,181
    Thanks Ben, that helps a lot. I still have a long way to go understanding everything however. For instance, when you state SU(3) describes a two dimensional space and the SU(3) lattice describes 8 points in a two dimensional space, I kind of get that. Where I get confused is how SU(3) also describes the strong nuclear force. ?? Is there any way to expand on that a little for us uneducated laymen?

    Please Register or Log in to view the hidden image!

     
  16. TruthSeeker Fancy Virtual Reality Monkey Valued Senior Member

    Messages:
    15,162
    Sort of how like a cube dimension can be represented by 3 dimensional points? When you take to the next level, the 3 dimensions become, collectively, a "dimension"?


    That's what the caption in the picture said, actually, and I had previously stated the same. I know what you mean by all that. I don't know how he didn't get lost. That would be something really difficult to map.

    Oh, ok. That explains that...

    You can make it clear by using the word "forces" as opposed to "dimensions". It's confusing because we think of space-time as our "dimension", or a receptacle that contain us. We don't think of it as the force related to the dimension. That was obvious to me when I read relativity, but maybe it is not so obvious. Relativity simply explains gravity by adding the time dimension to the equation. Another thing that causes the confusion is that SO(3,1) is the only part that we can experience directly, day-to-day. We don't see it as only 1 dimension of the whole picture- it IS the whole picture to us (well, it appears to be).

    Now, 1 thing that is confusing me now. Why SO(3,1) + SU(3) + SU(2) + U(1) adds up to 8 dimensions? SO(3,1) represents 4. So somehow, SU(3) + SU(2) + U(1) represents other 4 dimensions. How does that work?

    That's because space-time is NOT fundamental. If E8 is truly the fabric of the universe, space-time is certainly not fundamental at all.

    To clear up the confusion, it might help see the difference as "geometrical dimension" vs "physical dimension".... does that help?

    Well, I hope I helped clear up some of the confusion.... LOL!

    Please Register or Log in to view the hidden image!

     
  17. TruthSeeker Fancy Virtual Reality Monkey Valued Senior Member

    Messages:
    15,162
    Maybe the 8 points are the 8 particles that create the strong nuclear force.... or at least that's what it appears to be, from Lisi's paper...
     
  18. invert_nexus Ze do caixao Valued Senior Member

    Messages:
    9,686
    Ben,

    So, what about the properties of a time dimension that make it special? I suggested that one has no freedom of movement along this dimension. Is this the case? Is there more?
     
  19. Reiku Banned Banned

    Messages:
    11,238
    Invert

    We actually spend more time in the 4th dimension than what we do in space. This is because time is rushing against all matter against the speed of light, the same speed of time. If one studies the math correctly, one will realize that time is inseprable, therefore i do not understand how string theory SHOULD successfully remove a time dimension (just because it is a problem), as ben put it.

    This is why i don't like string theory to current. Simply because it contradicts a contradiction.
     
  20. BenTheMan Dr. of Physics, Prof. of Love Valued Senior Member

    Messages:
    8,967
    Well, the technical difference is that SO(3,1) is a ``non-compact'' lie algebra. This basically means that the idea of ``rotations'' has to be generalized. SU(3) is compact---you can draw a picture of it in a plane. In SO(3,1), the time direction cannot be represented on a plane, and so you cannot ``rotate'' in time. You have to use a generalized transformation---these are called boosts. These are exactly the Lorentz boosts of special relativity.
     
  21. BenTheMan Dr. of Physics, Prof. of Love Valued Senior Member

    Messages:
    8,967
    This is exactly right.
     
  22. Reiku Banned Banned

    Messages:
    11,238
    Ben

    ''These are exactly the Lorentz boosts of special relativity.''


    I thought this. But isn't it usually called 0(3_1), OR AM I MISSING SOMETHING?
     
  23. BenTheMan Dr. of Physics, Prof. of Love Valued Senior Member

    Messages:
    8,967
    Yeah kind of.

    Well, I'm not sure what htis means.

    SU(3) is two dimensional, and both SU(2) and U(1) are one dimensional.

    I certainly agree with this---this is why I think Loop Quantum Gravity is wrong. Space-time is an effective description, and (to me) cannot be fundamental.

    Maybe. I'm actually curious to read this paper now, even though I probably won't. For example, Lisi doesn't address the fact that one just can't quantize gravity. But this is essentially what he's doing.
     

Share This Page