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In Physics, the principle of relativity is the requirement that the equations describing the laws of physics have the same form in all admissible frames of reference.

However, according to this and this paper, it seems Bernoulli's Equation is a frame-dependent example in both Newtonian and relativistic mechanics.

Which kinds of laws are frame-independent and which are not?

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What do you mean by 'kind of law'? Bernoulli's Equation isn't a law -- it's a simplification of the Euler equations under isentropic conditions. –  tpg2114 Dec 23 '12 at 2:59
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So your question is more "What makes a law frame independent?" I am really unclear on your question as it is written. –  tpg2114 Dec 23 '12 at 3:26
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Again -- do you mean to ask "What makes a law frame-independent?" By asking "What kinds of laws" implies you are looking for either a list of frame-dependent laws or something more vague like "Conservation" which also doesn't make sense. If you are interested in what constraints make something frame-dependent, you really need to re-write your question to clarify that. –  tpg2114 Dec 23 '12 at 3:34
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I think that the misunderstanding comes from the use of "law" in your question. A law in my vocabulary is "conservation of energy",etc. In this day and age in physics laws are called, by definition, those that ARE CONSISTENT with special relativity. All previous formulations, in Newtonian for example, that might have been called laws in the nineteenth century are out of date in physics as we know it presently. –  anna v Dec 23 '12 at 4:44
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@JohnRennie: Oops. I read this as "which law of physics" (narq) and not "which kind of law" (perfectly OK, and a good question imho). Reopened, thanks for noticing :) –  Manishearth Dec 23 '12 at 14:20
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All basic laws of physics are frame-independent. They either exhibit Galilean (non-relativistic) or Lorentzian (relativistic) invariance. Examples are Newton's laws (Galilean), Maxwell's equations (Lorentzian), Navier-Stokes equations (Galilean), etc. A notable exception is formed by Schrödinger's equation which, upon closer inspection, can be fixed into being Lorentz invariant under transformations up to first order in $v/c$.

Phenomenological laws and laws derived from the basic laws if physics often fail to be frame-independent. Such instances of frame-dependence occur when specific assumptions are made that single out a specific frame of reference. The Bernouilli equation being an example as it is derived under the assumption that a reference frame is chosen in which the fluid flow is stationary. Another example is given by the diffusion equation, the derivation of which assumes a reference frame can be found in which convection is absent.

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it's not true that they either exhibit Galilean or Lorentzian invariance, they all obey the latter. Galilean invariance is an approximation for v<<c –  Physiks lover Dec 23 '12 at 20:02
    
these are two distinct symmetries which become indistinguishable in the limit $v/c -> 0$. –  Johannes Dec 24 '12 at 12:05
    
Yes, I can see that you're right now. –  Physiks lover Dec 26 '12 at 0:47
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