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Got asked, "Why does there 'need' to be a UFT"

  1. Mar 19, 2015 #1
    I was working today with a mathematics grad student, and in the lull of the work he asked me about why physicists insist on there being a unified field theory that unites all four forces of the universe into a single equation. I sort of paused for a moment and thought before I answered, and I ended up hand waving a bit and said that the logic of the physicist is that since nature does seem to operate logically and predictably, and that we've defined how nature works mathematically pretty well so far, that it stands to reason that there should be some unification of all the forces that control the universe. He pointed out that didn't really answer the question as to why we think there 'needs' to be a UFT. I bowed to that and just said, no, I suppose there doesn't need to be one ultimately. The universe could just have completely separate mechanisms for gravity and the other forces. I wasn't really happy with that, but I wanted to leave and he started ranting about how he thinks physicists just made up the idea of tensors, so I just peaced out. But it got me thinking more about it and I was wondering what you guys who obviously have lived and breathed this idea of a unified field theory for years think about why there needs to be, or maybe a more reasonable way to say it would be why does it 'look' like there is a UFT. What do you think?
     
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  3. Mar 19, 2015 #2
    Many physicists don't believe a Theory of Everything is necessarily out there (or even possible). Stephen Hawking, for example. But why wouldn't we try to come up with one? I mean, why did we need to make calculus rigorous by creating mathematical analysis if calculus worked already? Because we're always striving for greater and greater accuracy in our works.
     
  4. Mar 19, 2015 #3

    ShayanJ

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    Really strange for a math grad student. He should have been an applied math student! Otherwise he was simply not a good student.
    Because mathematics itself works exactly the same way, some one just comes up with something and discusses some properties of it and later mathematicians continue the discussion. It should be more strange for him in mathematics itself because at least in physics, nature motivates the introduction of concepts but what motivates them in math? Only the imagination of the mathematican. Don't take me wrong! I'm not saying physics is better than math in this respect, I love both math and physics and one of the reasons I love math is exactly the above thing. So I think that the mentioned student neither knew enough about pure math nor enough about theoretical physics.
    Also, mathematicians first came up with tensors, not physicists!
     
    Last edited: Mar 19, 2015
  5. Mar 20, 2015 #4

    sophiecentaur

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    The fact that many of the relationships between everyday variables can be expressed in very simple linear terms seems to lead people to believe that there is no limit to this very simple modelling - i.e. we can use square laws, exponential laws, convolution, transforms and will eventually get complicated enough to describe 'everything'. That is an extremely naive suggestion and based on faith rather than experience. In a way Maths is to blame for this assumption about 'Laws' being there to be discovered but Maths is not the real World. It is far more accurate to say that we can get better and better approximations in our models of the World - and that's all.
    It is a very human trait (a flaw, even) to expect a TOE to exist because it gives a much more cosy feeling about things than to acknowledge that we will never get there.
     
  6. Mar 20, 2015 #5
    So would you say there's no hole in our description of the universe that a UFT would fill? Because that's what pop-science has led a lot of people to believe.
     
  7. Mar 20, 2015 #6

    ShayanJ

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    The hole we need to fill, is finding a quantum theory for gravitation. There are several candidate theories which only one of them is a candidate for being a TOE, string theory.(And its the only candidate) But a TOE is not needed nor there are strong indications for the existence of one. its just that by the introduction of string theory, people realized its possible to have a single theory that includes all interactions. So its wrong to say that a goal of modern physics is unification of fundamental interactions. Its not a goal, its only a possible future of theoretical physics which may turn out to be only a speculation.
     
  8. Mar 20, 2015 #7
    If all the pop-sci I've read is to be believed, a quantum theory of gravitation is important for understanding the real nature of black holes. I'm unable to comment on the validity of this, though.
     
  9. Mar 20, 2015 #8

    HallsofIvy

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    Actually, "tensors" were invented by Levi-Civita and Ricci-Curbastro, working in differential geometry before physicists started thinking of modelling space time in terms of differential geometry. In fact, Einstein had to learn both differential geometry and tensors before he wrote his "General Theory of Relativity".

     
  10. Mar 20, 2015 #9
    I think as an undergrad he avoided topology and dif. geometry like the plague for some reason. Idk, that certainly wasn't MY view of it by any means. He was just kind of a prick.

    Thanks though. If I have to work with him again I'll let him know he's got some reading on diff. geometry to do :D

    That's a great explanation. I think that's more or less what I was trying to get across, I just wanted to avoid invoking string theory if I could because I didn't want him to start ranting about that too. The tangents he took in this conversation were numerous as it was. But thanks. What you said, said a lot.
     
  11. Mar 20, 2015 #10
    Actually Gδdel's proofs apply here. (That should be an umlaut over the o.) Physics is a (consistent) mathematical system of more than sufficient complexity. So there must be theorems in Physics which cannot be proven true. If a (provably) true theory of everything exists, it would only apply locally, or over some limited domain. Do the problems most mathematical physics have with singularities match this model? Or does the possibility of causality violations make and complete physics inconsistent? Very good questions, and I can only provide guesses not answers.

    in other words, any theory of everything must be incomplete or inconsistent. Any theory which admits time travel, even for one nanosecond by one particle is likely to be inconsistent. In other words, any experiment can have the result of a shoe falling from nowhere to generate unexpected data. However, it is possible to ignore those possible materializing shoes and get useful results. But it is difficult to design time machines with a restricted theory, even if the theory says they can be built. Is it possible to create a physics that admits of some time travel and is still consistent? Possibly, but I wouldn't know where to begin.
     
  12. Mar 20, 2015 #11

    ShayanJ

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    This isn't an established fact, among the reasons of which, I can mention the fact that the current physics we have in hand, is not a well defined mathematical structure. Whether future physics will be different, is something we should wait and see.
    I also should say that my incomplete knowledge about Godel's theorems tells me that they are not general enough to give us such conclusions. But I'm not sure about this.
     
  13. Mar 20, 2015 #12

    sophiecentaur

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    I meant the converse. The 'everything' cannot be covered by any 'theory'. How can people imagine it can? There is no evidence to suggest that.
     
  14. Mar 20, 2015 #13

    mathman

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    I am not sure it has been covered, but one major reason for a unified theory is to handle the problem that quantum theory and general relativity are incompatible where they are both need. The most revealing problem is trying to describe what happens inside a black hole.
     
  15. Mar 20, 2015 #14
    Certainly. Just making sure I wasn't missing something :)
     
  16. Mar 20, 2015 #15

    ShayanJ

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    A theory of Quantum Gravity will solve the problem. It doesn't have to unify gravity with other interactions.
     
  17. Mar 21, 2015 #16
    Um, you have to understand how Godel's Proof works. It shows that if you can embed a very simple arithmetic (Peano arithmetic, which doesn't even require integers) then the system as a whole is either incomplete (some true things are not provably true) or inconsistent (there are false things that can be proven true in that formalism). It would probably take a book--and a not very readable one--to define the standard model well enough to decide that it was incomplete. Inconsistent can be done pretty quickly. For example, almost every attempt to define physics inside a black hole ends up inconsistent, Whether that inconsistency applies outside the event horizon is model dependent.
     
  18. Mar 23, 2015 #17

    ShayanJ

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    That's what I mean...why should a TOE contain arithmetic axioms?
    A TOE is a physical theory. It can be inconsistent and imprecise from a mathematical point of view but be a good physical theory! I don't think Godel's theorems apply to such a thing.
     
  19. Mar 23, 2015 #18

    sophiecentaur

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    As an Atheist I have no problem with a theory of 'not everything'. People of 'faith' (admitted or not) may want to think that an ultimate truth is out there somewhere. It may be connected with the life after death thing and the notion that, when we die, everything will be revealed. Personally, again, it is no disappointment that there ain't an answer to everything. That fits with my experience so far and I have 'got over it' fine.
    Just imagine that a theory of everything comes up that includes an element of chaos in it. That could spoil a lot of days for a lot of people.
     
  20. Mar 24, 2015 #19
    I can't imagine a TOE that does not use arithmetic. Even if you could come up with a TOE based on string theory that used only topology, embedding Peano arithmetic in topology is possible.. http://en.wikipedia.org/wiki/Peano_axioms will tell you much more than you want to know about Peano arithmetic and related systems. Basically what you need is the natural numbers (for example the number of holes in a topological object,), equality, a successor function (how to add a hole to an object) and induction. There are games you can play with the axiom set that result in equivalent systems.

    You could argue that a finite theory of everything could avoid infinities, but that is sophistry. The integers may be unbounded, but any well formed theorem in PA does not involve infinities. For example the fairly well known diagonalization proof that the rational numbers are the same order of infinity as the integers basically shows that a map can be constructed such that for any rational number R there is a unique integer and vice-versa.

    What you end up with is that if there is a consistent TOE, it can not be proved consistent inside this universe. That does not mean that the new theory is useless, just that the universe will have properties that cannot be derived from the new theory. That means the best we can get is to run experiments and not finding any contradictions. However, that shoe, or more realistically an extremely high energy cosmic ray can come along and mess up any particular experiment. In other words there will always be room to look for new physics, even if you don't find any.
     
  21. Mar 24, 2015 #20

    dx

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    There is no "need" in a logical sense. It is just based on a faith in the intelligibility of the world, and past historical experience. As we discover more about fundamental physics, the whole structure seems to become more "unified", in the sense that the number of independent conceptual elements becomes smaller. Things that were previously considered separate become related or unified. Overwhelming evidence points to the existence of a kind of "final stage" or an "eschaton" in this process of unification, that is generally called "quantum gravity"
     
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