-4
$\begingroup$

Background:

As I was thinking about an alternative approach to the question: "why is there a finite speed of light, and why its magnitude corresponds to c?" –ultimately, I was trying to understand from which more fundamental theory could the electromagnetic permeability and permittivity of vacuum be derived from, as I share the view that only dimensionless constants are truly fundamental–, I felt on these papers (here and here) which seem to suggest that the speed of light is originated from the quantum properties of vacuum, more precisely, to the magnetization and polarization of fermion pairs in a quantum vacuum model. As far as I know, the existence of those short-lived (so-called) virtual particle pairs is made possible by the Heisenberg uncertainty principle (further reading).

I couldn't help but wonder if one could take the other way round, namely, if one could start from the special relativity principle which imposes c as the maximum speed of transmission of information/interaction and, by logical inference, find the necessity of an uncertainty principle which allows the existence of virtual particles pairs, that is, of quantum fluctuations in vacuum. As I am relatively new to these subjects (I am still at the undergraduate level), and I suspect my reasoning to be in some way inconsistent, I would appreciate the opinion of any more knowledgeable person. Also, please excuse any misunderstanding of the underlying physics.

My question is, then:

Could this link between the uncertainty principle and the finite speed of light be envisageable? If it were, could it act as a conceptual connection between the principles of special relativity and quantum mechanics? If not, which logical problems would it encounter?

P.S.: I also found this similar discussion on ResearchGate, which could be useful to anyone interested on answering this question.

$\endgroup$
6
  • 1
    $\begingroup$ I honestly have no idea what the papers you link are talking about. They don't seem to be self-consistent at all -- their model of the vacuum is inspired by an incorrect model of QFT (incorrect because virtual particles do not "pop in and out of existence"). If they actually used QFT, getting the speed of light out would be trivial since the theory is already relativistic. But then they proceed to describe the virtual particle pair as two masses connected by a spring (?!). They're guaranteed to get a sort-of right result by dimensional analysis, but it turns out wrong by a factor of 2... $\endgroup$
    – knzhou
    Mar 27, 2016 at 4:04
  • 1
    $\begingroup$ ...and then they add an arbitrary fudge factor. I mean, this is like those old papers that tried to get $\alpha \approx 1/137$ by numerology, except they don't even get $137$ at all! $\endgroup$
    – knzhou
    Mar 27, 2016 at 4:05
  • 1
    $\begingroup$ The other paper, again, is guaranteed to get a sort-of correct answer for the velocity of light by pure dimensional analysis. But its model for the propagation of light flies in the face of every theory known. It is not predicted by classical models of light, semiclassical ones, nonrelativistic quantum ones, or relativistic quantum ones. $\endgroup$
    – knzhou
    Mar 27, 2016 at 4:06
  • 1
    $\begingroup$ Basically, I don't think any of this has merit. Relativistic classical mechanics is consistent on its own, as is nonrelativistic quantum mechanics. Trying to sneak one of these theories out of the other doesn't really make sense. $\endgroup$
    – knzhou
    Mar 27, 2016 at 4:07
  • $\begingroup$ This makes little sense. See my answer below. $\endgroup$
    – Bob Bee
    Mar 27, 2016 at 5:22

4 Answers 4

3
$\begingroup$

In Research Gate it is a very bad discussion mainly based on a couple of articles in a Journal on physics by a the Center for Innovative Research. The main editor seems to be someone doing microelectronics in India. To me the whole Center and the articles seem totally unreputable. If you can find a reputable scientific organization publishing anything like that Please refer to it. If not the best thing in my mind is to totally remove this reference.

The question posed here could still be valid, but I think not. Virtual particles are a construct of QFT, which already includes c as part of it as needed to make QFT Lorentz invariant. QFT already assumes c, and also the uncertainty principle, which came from Quantum Mechanics. They cannot be derived from each other. So, before you have the concept of virtual particles in QFT you need both c and QM. Virtual particles can not be used to prove anything about c nor about the uncertainty principle. You are twisting physics around.

The other references cited about how c may come from those virtual particles talks about charged particles as the virtual particles. It is mostly speculative. Anyway, since that comes from electromagnetism it applies only to photons. But special relativity with c as the limit has been proven also for neutral particles. So those other references also makes no difference.

$\endgroup$
2
  • $\begingroup$ Thank you! I now can see that my question didn't make much sense. I'll try to delete it. $\endgroup$
    – dahemar
    Mar 27, 2016 at 10:16
  • 2
    $\begingroup$ @DavidHerreroMartí: You can't delete it, there is an accepted answer and several answers with score >1. $\endgroup$
    – Kyle Kanos
    Mar 27, 2016 at 11:10
3
$\begingroup$

Classical special relativity satisfies the speed-of-light-limit but not the uncertainty principle. So no.

$\endgroup$
-1
$\begingroup$

According to Heisenberg Uncertainty Principle, which is the basis of Quantum Mechanics and hence QFT, we can borrow some mass (out of nothingness) for a small period of time such that the their product follows that principle. To my understanding, universal speed limit of c and Heisenberg Uncertainty Principle are independent and complementary rather than having an inferior and/or superior relationship. We need both to understand Nature clearly.

$\endgroup$
-1
$\begingroup$

I will address the title question:

Could the Heisenberg uncertainty principle be derived from the speed of light limit?

The speed of light limit for electromagnetic interactions comes directly from the classical Maxwell equations. These equations have been validated by innumerable data .

Uncertainty relations appear mathematically in conjugate variables of Fourier transforms. It is worth reading the link to see the independent mathematics. The connection of the mathematical uncertainty depends on the choice of physics variables that are conjugate from the basic postulates of the theory.

Thus the Heisenberg uncertainty is a mathematical consequence of the wave nature of the equations and the postulates modeling the data quantum mechanically.

As far as special relativity goes, there is also an interesting relation derivable from the minkowski metric :

fourtransfspecrel

which can be, as the quote says, interpreted as an uncertainty relation with space and time variables.

Thus there exists a mathematical similarity: Both the HUP and the speed of light can be shown as mathematical uncertainties in variables. The two statements are independent and cannot be the consequence of each other because they are independent postulates of the respective theories.

$\endgroup$
8
  • $\begingroup$ I don't see how the lhs of the quoted equation $(\cdots)(\cdots)=1/c^2$ is the product of the standard deviations of conjugate Fourier variables. $\endgroup$
    – innisfree
    Mar 27, 2016 at 5:21
  • $\begingroup$ @innisfree he is making tau(proper tiem) zero for photons and doing some algebra. there exist space time fourier transforms : en.wikipedia.org/wiki/Space-time_Fourier_transform . $\endgroup$
    – anna v
    Mar 27, 2016 at 6:05
  • $\begingroup$ I don't understand this. Can you show explicitly that the speed of light can be shown as mathematical consequences of the Fourier transform properties of conjugate variables? $\endgroup$
    – innisfree
    Mar 27, 2016 at 6:23
  • 1
    $\begingroup$ @innisfree of course not. The speed of light constant is in the postulates of special relativity. I am trying to say that there is no logical connection between the HUP and special realtivity, except a serendipitous similarity that both can be considered as the effect on conjugate variables on a fourier transform, so no causal connection can be found, only mathematical similarity. $\endgroup$
    – anna v
    Mar 27, 2016 at 8:07
  • $\begingroup$ "both can be considered as the effect on conjugate variables on a fourier transform" - how so in the case of the limiting speed of light in SR? $\endgroup$
    – innisfree
    Mar 27, 2016 at 9:01

Not the answer you're looking for? Browse other questions tagged or ask your own question.