The Muon Lifetime Experiment and Neo-Lorentzian Interpretations of Special Relativity

[structureoftruth (Matthew Dickau)]

@T_aquaticus

Newton’s First Law applies to a spaceship with a constant velocity and can be defined as an inertial frame in Newtonian physics. Do you agree?

Yes, that is literally what I said an inertial frame is.

@T_aquaticus

@structureoftruth

But from the rest of your paragraph it seems what you actually want to ask is how we can define a privileged reference frame. And the answer to that (in the neo-Lorentzian interpretation) is easy: the privileged frame is the one that describes what actually exists in the changing 3D universe at a moment in time. The privileged frame is a theoretical postulate of the neo-Lorentzian interpretation, and it turns out to be empirically undetectable, but this doesn’t invalidate the concept.

Objects moving at a constant velocity with respect to each other actually exist in the universe.

This is a complete non-sequitur. I think we’re on different pages here.

@T_aquaticus

So the speed of light should be the same for every observer no matter what their relative velocity is?

The measured speed of light is, yes.

@T_aquaticus

In other words, relativity.

Yes… the neo-Lorentzian interpretation is an interpretation of special relativity. It’s not like its some non-relativistic theory. Time dilation (e.g. slowing of all physical processes) and length contraction occur for objects in motion relative to the privileged frame, as a causal consequence of the laws of physics. In any other inertial frame, you have apparent time dilation and length contraction for objects in motion relative to that frame, as can be shown from the effects of time dilation and length contraction on the moving observer’s instruments.

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I’m sensing something of a disconnect between us in this conversation, so allow me to try and clarify my position. Your original comment in Jim’s thread was this:

@T_aquaticus

how do you think velocity would change the physical constants that govern muon decay? What is the mechanism?

My main intent was to point out that, in fact, the muon decay rate does depend on velocity, that this is exactly what we see in the muon lifetime measurements, and that the mechanism for the change in decay rate is nothing other than the usual laws of physics operating on a moving system rather than a stationary system.

In retrospect I didn’t even need to mention the neo-Lorentzian interpretation to make this point - it can be validly made from any reference frame. (It is just that I’m used to invoking it in relation to the privileged reference frame of the neo-Lorentzian theory.) Time dilation and length contraction are not just transformations that result from changing your reference frame. They are also, in the perspective of any one reference frame, physical effects that happen to moving objects, explicable by reference to the laws of physics described in that frame. See John Bell’s paper, “How to Teach Special Relativity”.

Time dilation, in particular, is (again, from the perspective of a single reference frame) the slowing down of physical processes for systems in motion, compared to systems at rest. And (in principle, because QFT is complicated and they generally do not compute the quantum state directly) it can be seen for the muon in how the quantum state for a moving muon evolves differently than the quantum state for a stationary muon.