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This is likely to be a rather strange question.

I have been working in physics in an attempt to obtain a PHD. My initial plan was entirely experimental, however I have not obtained enough data by itself. This is due to a combination of difficult experiments, and temperamental equipment and its repeated failures; I was and am simply not capable of repairing the systems without any replacement components by myself.

This is ok I had thought, I can attempt to slightly extend a pre-existing theoretical framework to explain the few results that I do have. However this is not my supervisor, or even departments expertise, so I have for the last year and half attempted this myself. After much effort I have been able to replicate the prior theoretical calculations of the model.

However despite having the best grasp of the model out of anyone I have spoken to in my department, there are significant parts where I just do not have a clue.

I have reached a point where I have 2 months left to submit, and I do not yet have a sufficient understanding of the theory to be able to tell if it is actually valid for what I am trying to use it for.

Is it acceptable to just shut up and apply it anyway, and be deliberately vague and sparse in describing it and the necessary mathematics so that I do not include things I do not understand?

Or do I just throw in the towel and save myself another 2 months of absolute torment?

Many thanks.

Edit in response to comments: it's rather that I do not understand some of the mathematics necessary.

There is a set of 6 eigenfunction equations, where they all have the same eigenvalues. All the authors in the literature only care about the eigenvalues, where I need the eigenfunctions. I had assumed that they were all the same, like the eigenvalues, but upon attempting to write a thesis chapter on them I now realise that they are not. This is a problem as my calculations are based upon the eigenfunctions.

There is only one of the eigenfunction equations in the literature. I am able to, with initial difficulty, solve it and obtain the same eigenvalues as the literature. I then do some stuff with the eigenfunction that was not done, and obtain another different eigenvalue equation based upon an operator corresponding to the measuremrnt data I do have. But I cannot derive the original equation in the literature, and I cannot derive the other, not stated in the literature, 5 equations.

Noone has worked on it for decades, and the original authors, and those who initially extended their work, are all dead.

Hence why I state that I do not understand it. I can state what I have done, that I cannot derive the equations, and that I know it is wrong without the other 5 solutions. I am 90% certain I can solve the other 5 equations if only I could understand how they are obtained.

Unfortunately I just get bogged down in attempting to follow the derivation, 1.5 years of attempting to follow it and I still just do not follow it.

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    Isn't there anyone else you can ask? 2 months is tight, you really should had done that earlier, but the world is bigger than you department – Fábio Dias Jul 27 '17 at 19:29
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    Answering the title question: No, you are very unlikely to obtain a PhD if you don't understand your own thesis. (The only chance would be if your dissertation committee failed in their duty to properly examine you.) You should try to find someone outside your department who can help. Surely people in your department can connect you with someone appropriate. – Thomas Jul 27 '17 at 19:31
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    In your educational system, who actually decides whether you pass? In many systems, it's effectively your supervisor, in which case you need to have a frank conversation with him or her. – Nate Eldredge Jul 27 '17 at 19:31
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    There's "understanding", and then there's "understanding". I think it is typical that even very good PhD students have a relatively superficial understanding of the significance/context of their own work, simply and inevitably due to lack of experience. But if the question is about "ok-ness", that's more serious than "understanding" (depending on what we make these words mean, of course...) – paul garrett Jul 27 '17 at 19:35
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    For many complex experiments, no one, and I mean no one, has a full understanding of all the details. – Massimo Ortolano Jul 27 '17 at 21:55
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Of course, it would be good if someone around you can help you see what needs to be done to legitimize your use of "the other 5 equations". If you post to MathStackExchange, someone might be able to help, for example, if no one physically nearby can.

In any case, honesty and at least a nominal "dispassion" about things is the best approach, I think. Say what you assume, say what you can verify, say what previous sources say, etc. It's ok, I think, if your results are "relative" (=relative to assuming that certain sources are ok, plus assuming that certain extensions, which you've tried but failed (so far) to validate yourself first-hand, are ok...), as long as you are very clear on what your results are relative to.

Don't bluff... :)

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    Ok , so I shall be absolutely clear on what exactly the problem I think is, and not attempt any obfuscation. This can then be good enough or not. – user50746 Jul 28 '17 at 9:12
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Or do I just throw in the towel and save myself another 2 months of absolute torment?

Nobody except you would be able to decide. But, given what you write, failing could be an option. Academia is a hard sport, and your health might be more important than some theory. I see bad examples around me.

In case you decide to proceed, here are some thoughts:

  • Ask an online service (such as Google scholar) for which papers cite the original framework. Some of the authors referencing the framework might be living. Write them e-mails.

  • Apply Feynman's problem-solving algorithm. (It's not a joke, I'm very serious.) In less extravagant terms, improve your working style.

  • Apply for an extension.

  • ...

Bear in mind that, after all, the problem might be unsolvable with the methods at your disposal.

E.g., the mature Ostrogradsky once asked Paris mathematicians for help for solving a particular problem. They took quite some time, and finally responded "This task can be solved only by one person: the Russian professor Ostrogradsky. He lives in Petersburg. You should contact him.".

But one proper piece of advice: no torment; go home at 6pm whatever you do.

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  • Do you mean the famous, look at the problem and write down the solution, Feynman method? – user50746 Jul 28 '17 at 9:11
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    @PlokavianNerveGas Do not skip step 2. – JeffE Jul 28 '17 at 12:25
  • @JeffE I shall think as hard as is possible without shattering my fragile psyche. – user50746 Jul 28 '17 at 17:10
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For a PhD you should demonstrate two things: that you have become an expert in your (very very small) chosen topic, and that you have learned how to do credible research in that topic. From your description you don't seem to have demonstrated either at this point, so I would find it concerning if you did get a PhD.

Kicking in the towel isn't the only option though.

  • You say no-one in your department understands the material. But it is extremely unlikely that no-one in the world does. There are many theoretical physicists, and many mathematicians. Even if they are not familiar with the exact problem, there will be someone you can talk to who knows far more about eigenfunctions than you seem to.
  • Get an extension. If you've been allowed to go substantially beyond the expertise of those supervising you where you don't understand and no-one else is supporting you, then someone has not really been taking their responsibilities seriously enough.
  • Try and find a summer school on the mathematics you need.
  • Explore the options for graduating with a lower degree.
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    -1 For all we know the OP is an expert in the experimental side of the matter. It seems like a series of factors + lack of anticipation from themselves and their supervisor led to this situation. – user347489 Jul 28 '17 at 6:44
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    @PlokavianNerveGas, I think one's advisor is meant to help!!! Otherwise, what's the point? Contrary to myths, a PhD student does not become a world expert in a few months or years, but, rather, needs some advice from experts, that is, their advisor and others. – paul garrett Jul 28 '17 at 12:27
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    @PlokavianNerveGas A PhD is an apprenticeship as a researcher. Your supervisor should be training you to be a researcher. – Jessica B Jul 28 '17 at 13:46
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    @PlokavianNerveGas findaphd.com/advice/doing/phd-supervisor-expectations.aspx – Jessica B Jul 29 '17 at 9:03
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    @PlokavianNerveGas No, higher education is not just providing the time and library resources. Otherwise what would the teacher be there for? There is also guiding the use of time to relevant resources, and helping with the interpretation of those resources where you get stuck. And providing a 'big picture'. – Jessica B Jul 29 '17 at 9:07

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