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Hubble's constant $a(t)$ appears to be changing over time. The fine stucture constant $\alpha$, like many others in QFT, is a running constant that varies, proportional to energy being used to measure it. Therefore, it could be agued that all running constants have 'evolved' over time as the Universe has expanded and cooled. Both the local and global curvature of the Universe changes over time implying that so too does the numerical value of $\pi$. All these things are however constants (well, let's say parameters since they are not really 'constant'.)

In a discussion with astronomer Sir Fred Hoyle, Feynman said "what today, do we not consider to be part of physics, that may ultimately become part of physics?" He then goes on to say "..it's interesting that in many other sciences there's a historical question, like in geology - the question how did the Earth evolve into the present condition? In biology - how did the various species evolve to get to be the way they are? But the one field that hasn't admitted any evolutionary question - is physics."

So have the laws of physics remained form-invariant over the liftetime of the Universe? Does the recent understanding of the aforementioned not-so-constant constants somehow filter into the actual form of the equations being used? Has advances in astronomical observations, enabling us to peer back in time as far back as the CMB, given us any evidence to suggest that the laws of nature have evolved? If Feynman thinks that "It might turn out that they're not the same all the time and that there is a historical, evolutionary question." then this is surely a question worth asking.

NB/ To be clear: this is a question concerning purely physics, whether the equations therein change as the Universe ages, and whether there is any observational evidence for this. It is not intended as an oportunity for a philosophical discussion.

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"evolve over time" I think GR told us a lot about time, and in earth since 1916 that word shouldn't be used in an absolute way. –  HDE May 19 '11 at 12:08
    
@HDE: Yes I was a little unsure about the phrasing there. Whould it be more correct to ask if the laws 'remain form-invariant thoughout the lifetime of the Universe?' If I can further improve the wording please suggest how and I will edit accordingly. –  qftme May 19 '11 at 12:12
    
To the anonomous down-voter: would you care to explain your reasoning? –  qftme May 19 '11 at 14:49
    
    
@Dmckee: Regarding your first realated link - considering the fine structure constant in its capacity as the QED coupling, it scales logarithmically with energy; as a consequence of renomalization. Whilst its value at zero energy has been shown to be near-enough constant, for practical calculations at typical energies during the cosmic evolution it value has surely been diminishing as the Universe cools, no? –  qftme May 19 '11 at 15:59

3 Answers 3

up vote 11 down vote accepted

For many (most? all?) physicists, it's something like an axiom (or an article of faith, if you prefer) that the true laws don't change over time. If we find out that one of our laws does change, we start looking for a deeper law that subsumes the original and that can be taken to be universal in time and space.

A good example is Coulomb's Law, or more generally the laws of electromagnetism. In a sense, you could say that Coulomb's Law changed form over time: in the early Universe, when the energy density was high enough that electroweak symmetry was unbroken, Coulomb's Law wasn't true in any meaningful or measurable sense. If you thought that Coulomb's Law today was a fundamental law of nature, then you'd say that that law changed form over time: it didn't use to be true, but now it is. But of course that's not the way we usually think of it. Instead, we say that Coulomb's Law was never a truly correct fundamental law of nature; it was always just a special case of a more general law, valid in certain circumstances.

A more interesting example, along the same lines: Lots of theories of the early Universe involve the idea that the Universe in the past was in a "false vacuum" state, but then our patch of the Universe decayed to the "true vacuum" (or maybe just another false vacuum!). If you were around then, you'd definitely perceive that as a complete change in the laws of physics: the particles that existed, and the ways those particles interacted, were completely different before and after the decay. But we tend not to think of that as a change in the laws of physics, just as a change in the circumstances within which we apply the laws.

The point is just that when you try to ask a question about whether the fundamental laws change over time, you have to be careful to distinguish between actual physics questions and merely semantic questions. Whether the Universe went through one of these false vacuum decays is (to me, anyway) a very interesting physics question. I care much less whether we describe such a decay as a change in the laws of physics.

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B: Thanks for your answer. My intuition was that any change in the physical laws, whether we call that an evolution or not, would be a quasi-distrete change - perhaps corresponding to a change of state of the Universe as a whole (such as quark-gluon plasma => hadronized particle epoch.) I find it strange that the constants mentioned seem to change smoothly whereas the actual form of the equations seem to go from being applicable to non-applicable (or visa-versa) rather abruptly. Presumably a TOE should be able to reduce to the appropriate formalisms both before and after the change(?). –  qftme May 19 '11 at 15:06
    
i think there is an additional sense in which darwinian style selection can be applied in this context (and always asumming that in a given universe you define laws as "the patterns that do not change in any of the space dimensions, which time is only one"): the eternal laws of physics in our universe is (or not) a product of natural selection of universes which happens outside of time. the Anthropic principle is but one (and the most notorious) of such darwinian principles –  lurscher May 19 '11 at 17:35
    
@qftme no reason to think anything more strange than a phase-transition took place, which makes some terms in the generic hamiltonian be more important than others –  lurscher May 19 '11 at 17:36

It is not known. In most of mainstream physics, the laws of physics, which includes fundamental constants, are constant throughout spacetime (i.e.. throughout both space, and time). However, there are some theories in which fundamental constants vary throughout spacetime.

  1. Dirac's hypothesis of large numbers.

It really came out of some nice observations. $$\frac{r_H}{r_e} \approx 10^{42} \approx \frac {R_U}{r_e}$$ $$r_e = \frac {e^2}{4 \pi \epsilon_0 m_e c^2}$$ $$r_H = \frac {e^2}{4 \pi \epsilon_0 m_H c^2}$$ $$m_H c^2 = \frac {Gm_e^2}{r_e}$$

Copied from wikipedia... Kind of weird. $H$ is a hypothetical particle with the radius of our observable universe... \

Then, someone came up with this:, a varying Newton's Gravitational Constant:

$$G = \left(\frac{c^3}{M_U}\right)t$$

Kind of weird to have something varying over time but not space... And kind of weird to have something that varies at all, given it should have been a constant. They also proposed some variations in the classical electron radius etc.

  1. Brans-Dicke Theeory

Here, this is a modification to GR, where $1/G$ is replaced with a gravitational weakness scalar field $\phi$. So, wherever there is a $G$, they replace it with a $\frac1\phi$, and $\phi$ is chosen arbitrary depending on the particular Brans-Dicke theory (correct me if I'm wrong, though. I'm a bit unsure on this...).

Again, I want to emphasise that none of this is mainstream.

Edit: In Brans-Dicke theory, I just checked, $\phi$ is not arbitrary. It is determined by a field equation:

$$\Box\phi = \frac{8\pi}{3+2\omega}T$$

Where $T$ is the trace of the SEM tensor, $\omega$ is the Brans-Dicke second coupling constant and $\Box$ is some differential operator . . . . : $$\Box\phi=\frac{\partial ^ 2}{\partial a^2}\phi^a_a$$ ...

All Of, This is, however, note again, Not mainstream...

P.S. Just a note on the geology-biology example. I think it is quite irrelevant. *The* laws of Biology or Geology do not evolve, just like how the laws of physics don't evolve. Biological and Geological structures evolve, just like physical structures evolve and change with space. Everything is a physical structure. And just because there is a pile of rubbish somewhere doesn't mean that this pile of rubbish is everywhere, or that it has always existed, or that it will forever exist.

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You should know that the large-numbers coincidence is now called the "Hierarchy problem", together with the fact that there are three scales--- the neutrino/cosmological-constant scale at .1 eV, the Higgs scale at 1TeV, and the Planck scale at 10^19 GeV. These are equally spaced in log, hence the large-numbers, and the cc-scale is comparable to the age of the universe, probably as Weinberg suggested, because it's anthropic. –  Ron Maimon Aug 22 '13 at 22:10

Not exactly in line with your question, but you might wanna have a look at the theory of Cosmological Natural Selection, which says that a new universe is spawned within each black hole with parameters inherited from its parent universe, only slightly mutated. In this sesne the laws of physics would be evolving as parameters change. Also, I just asked a question about it here :)

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Thanks @John. I did take a look but I'm always a bit sceptical of anything Smolin says. He has been known to come up with quite a few crack-pot theories over the years. –  qftme May 19 '11 at 15:09
    
yeah, that's why I like his theories ;) –  JohnIdol May 19 '11 at 18:56
    
@Johnldol: Why would you like non-mainstream ideas?. –  Dimensio1n0 Jul 4 '13 at 8:14

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