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Does Emmy Noether's First Theorem imply there is no free will?

  1. Jan 19, 2012 #1
    It's a question I've been lingering on to for some years now. If the laws of physics are invariant in time, then energy is conserved through time. Shouldn't that imply there is no free-will; there is no room in the laws of physics for energy to be shifted around inside each one of our brains as if we did have free-will? And furthermore, each moment of free-will would have to have a further change in the laws, for each and every one of us for each new free thought we have.

    *Edit* And I do realize that it is still an open-ended question what the exact laws of physics are and if they are actually invariant over time. But they appear to be exactly invariant in time at least in our local region of spacetime.

    Thoughts? I hope this is the right topic. It's heavy in physics, but maybe it should still be under philosophy?

    And has anyone heard of any similar arguments against free-will before?


  2. jcsd
  3. Jan 19, 2012 #2
    This is not the right place for this post... the 'philosophy' forum in 'general discussion' (https://www.physicsforums.com/forumdisplay.php?f=112) would probably be optimal. But anyway....

    The question of 'free-will' is, for the most part, out of the realm of hard 'science'---i.e. its just out of our grasp. None-the-less, there is a lot in your post that seems to me to be quite illogical.

    The total energy of the universe (isolated systems) must be conserved. Everyday we see a myriad of examples of energy being rearranged, redistributed, etc. A ball rolling down a hill, or a spring, are some classical examples. The same thing is happening millions of times a second while neurons are firing in your brain (and throughout your body).

    Further, why does 'free-will' have anything to do with rearranging energy?

    You seem to be supposing that free-will is forbidden by some physical law, why is this the case?

    I have not; generally the arguments against free will are based on a combination of macroscopic determinism* (that all large-scale phenomena are determined by initial conditions); and microscopic indeterminacy* (that all quantum interactions are determined stochastically and thus cannot be controlled).

    I just don't see how this follows

    * This is not standard (or even very-accurate) terminology; just something to get the idea across.
  4. Jan 20, 2012 #3
    Thanks for the reply. I took your suggestion and reposted it in the philosopher's forum... but it was locked for not citing references, heh. Here is my post there replicated:

    And to address you comments specifically:

    If the total energy of the universe is invariant, then the laws of physics cannot be changing in time (according to my understanding of Emmy Noether's theorem). So I am saying that this is the law of physics that is destroys any notion of free will, not supposing it (other than this is just a line of argument that might be incorrect). I believe you can think of Noether's theorem as the cause of/reason for macroscopic determinism.

    Does that clarify anything? Thanks for replying!
  5. Jan 20, 2012 #4
    You are being too vague. Most probably, there is a big misunderstanding that you have that is making what you say unintelligible cause you're using that misunderstanding as an implied argument, and we can't figure that that implied argument cause we don't share your misunderstanding. It would help if you would write down your chain of reasoning more explicitly: in what way do you jump from "physical laws being constant in time" or "conservation of energy" to "no free will". To us there is no direct correlation, but to you there apparently is. Please give more details, show us the train of thought.
  6. Jan 21, 2012 #5
    @mr.vodka has summed things up nicely. You also haven't addressed any of my initial points.
  7. Jan 21, 2012 #6
    Ok, this is my train of thought:

    1. We observe the universe to have constant energy and thus energy is conserved.

    2. Emmy Noether proved that if the Lagrangian admits some quantity as being constant, then there is a corresponding conservation law. The inverse holds true too, to my understanding.

    3. Conservation of energy (and more generally the four-momentum and stress-energy tensor), which we observe on the universe, means the laws of physics can't vary in time.

    4. For there to be non-determinism (free will or events that have no cause) in the brain, the laws of physics would have to be changing locally inside the brain over time. If there isn't that, then there is no free will.

    Which point am I being mistaken on? And I honestly thought I addressed your original comments zhermnes, but here I will go at it point by point.

    Yes, this is equivalent to my statement that our collective brain state is made of the entire energy state inside the brain. By Noether's first theorem this should imply the laws of physics are invariant inside our brains, and thus every neuron firing has a causal chain backwards to whenever the laws of physics were first invariant in time. Leaving no room for free will.

    It is my understanding that if free will existed, then determinism must be false. An indicator that determinism is false would be the laws of physics varying in time. In fact, Noether proved the two are equivalent. So, instead of speaking of determinism, we can just talk about the laws of physics being time invariant. If they are invariant then free will is an illusion and the rearrangement of energy inside our heads is just creating the illusion of free will.

    I am trying to not suppose it. I am arguing that it can be derived from our observations that the laws of physics are invariant over time. I understand that modern ideas in string theory involving the multiverse might have different laws of physics for different branes. We are also unsure if the laws of physics are even consistent in our universe at other locations that we can't observe. But thus far, locally, and for all observations, the laws of physics have been invariant in time.

    Thanks for taking the time to read my ideas and I hope this clarifies. If not, then maybe I'm just too out of it... I hope not! :)
    Last edited: Jan 21, 2012
  8. Jan 21, 2012 #7
    Here are a list of questions related to my arguments. Maybe this can help me figure out where I am going wrong:

    1) Is determinism synonymous with free will? Does free will mean there isn't a single cause for some event?

    2) Are the laws of physics invariant over time? There is of course the open question of locality and alternate branes, but ignoring those for the time being.

    3) I understand that current theorems involving quantum mechanics, Laplace's demon (see recent views section about David Wolpert's contributions to the problem), and the incomputability of the universe imply we can't actually know the exact state of the universe, but all that matters to the argument is the universe act deterministic. Is this incorrect?

    4) Does Noether's theorem not imply conservation of energy, four-momentum, etc, that the laws of physics must be invariant in time?

    5) Is there anything else besides energy inside our heads, sloshing around, collectively acting as brain states? If so, what is it? Is the jury still out?
  9. Jan 21, 2012 #8

    Ken G

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    To keep this from being idly philosophical, I'll stick to physics-based answers. Determinism is an aspect of a physical model. Free will is not-- there is not a physical model for free will. Thus, your question at present has no answer within physics. I will simply note that the answer depends quite sensitively on how you define "free will." For example, in court "free will" would mean "absence of coercion." That has nothing to do with whether or not the act was determined, it has to do with what determined it (i.e., the nature of the person doing the action, or the gun put to their head).
    No one knows. But currently, it is a law that the laws don't vary over time. Like any law, this one is provisional. However, it is not at all clear that variation of laws over time has anything to do with free will. Moreover, there is a physical error in your point #4 above: you asserted that to have non-determinism, the laws have to vary, but that assumes the laws are deterministic. There is no requirement for laws of physics to be deterministic, indeed quantum mechanics is a set of laws that do not allow an observation to be determined in advance by those laws.
    Things don't even act deterministically in quantum mechanics. It requires adding certain additional postulates to basic quantum mechanics to get a deterministic universe. And even if you do that, you just have a theory, not a complete description of everything. For example, Penrose believes that gravity acting on the scale of the Planck mass would have to be included to understand free will, but we have no theory yet that does that.

    The jury is still completely out on these issues.
  10. Jan 21, 2012 #9
    Thank you very much. So my argument fails in several categories. It fails by over stating the implications of Noether's theorem, the mistake in saying that everything can be described by energy conserving Lagrangians, and by the lack of determinism in quantum mechanics.

    And yes, there are different realms to discuss free will. I would say the purpose of the judge's use of free will is equivalent to us giving probability to dice. It's just a convenient heuristic that allows us to ignore the more difficult details (i.e. every event in the defendant's life).

    I still have trouble reconciling quantum mechanics with my notion of rolling dice. I've only really seen it in my solid state classes where we address passing through energy barriers.

    Anyways, thanks!
  11. Jan 21, 2012 #10

    Ken G

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    Yes, there are two very different types of non-determinism, the "I am not able to follow the details closely enough to predict the outcome", and the "the observable universe (i.e., what universe means in physics) itself simply does not contain enough details to make the outcome predictable." The former is a type of practical indeterminism, and the latter is more inherent indeterminism. Often, people imagine that dice fall in the former category, but we don't actually know that, it might very well depend on how the die is rolled. It might be possible to include enough details to predict a simple die roll, but a complicated enough roll might actually cross over into something inherently indeterministic. The answer to that depends on which interpretation of quantum mechanics is correct, in the sense of, which one will survive the next theory that is even better than quantum mechanics. If no such theory comes along, we'll just never know that answer, and even if one does, we still won't really know, because it might not be the "final theory" either.

    That's why I see determinism as just one particular way to model the universe, with all its advantages and disadvantages, but we just never get to know which model is "correct", and that's not really what physics is for anyway. The question for physics is never does determinism allow free will, it is, how does a deterministic model help us understand free will better? That will depend a great deal on what we mean by free will. I think you probably mean something along the lines of nonmaterialist agency, but we don't have any theory like that at present that we could even tell if it invoked determinism or not. But it would certainly be possible to have a theory of nonmaterialistic agency that was deterministic.
    Last edited: Jan 21, 2012
  12. Jan 22, 2012 #11


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    This thread has been reopened under the condition that it stick to discussing physics.
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