Transformation Vs. Physical Law

[universal_101]

Do you now accept that the decay of muons can be explained by a law of physics that is not a coordinate transform? If not, then what possible logical reason can you have for not accepting it?

Do you mean, that Minkowski spacetime or metrics are the physical laws that govern the decay of Muons in motion ?

But then I'm wondering where does this concept of spacetime and the metrics comes from if not from the transformations. Since there must be a physical concept behind any physical law.

Why were these physical laws not discovered on their own !

And how come this physical law can be used to derive the transformations, which it could not if it were an actual physical law !

 

[Mentz114]

Do you mean, that Minkowski spacetime or metrics are the physical laws that govern the decay of Muons in motion ?

But then I'm wondering where does this concept of spacetime and the metrics comes from if not from the transformations. Since there must be a physical concept behind any physical law.

Why were these physical laws not discovered on their own !

And how come this physical law can be used to derive the transformations, which it could not if it were an actual physical law !

In order to do physics with equations we need coordinates and time derivatives of coordinates. This means we implicitly assume some space or spacetime where the coordinates make sense. The physical laws must be written in some such space, although coordinates are themselves not physical.

Relativity demands that we examine the laws in moving frames, and this where transformations of coordinates happen. We demand that physical laws do not change under a relabelling of spacetime points.

Your remarks show a deep lack of understanding of how physics is actually done and makes me wonder why you think you are qualified to make any meaningful remarks about any aspect of physics.

Your last two posts make no sense to me at all.

 

[Muphrid]

I admit, I've not read through the entire thread, but can I give this a shot?

A muon travels on an inertial path from point A to point B, separated by some proper time \tau, at which point it decays. This trajectory is characterized by four-velocity v.

An observer with four-velocity u will measure the elapsed time between events A and B as \tau v \cdot (-u). If it happens that the observer has the same four-velocity as the muon, then this reduces to \tau (in c=1 units), but any arbitrary observer will come up with a different result.

There is no transformation of coordinate systems going on here. There is only each observer taking the dot product of their own four-velocity vector and the four-velocity of the muon to find one component of the muon's four-velocity in a particular basis. That, in itself, makes a physical statement about the universe: that we are free to choose any basis we wish because any direction is equivalent to any other. We choose Minkowski spacetime to model the universe because it shares that property of isotropy with what we observe in the real world.

 

[harrylin]

Do you mean, that Minkowski spacetime or metrics are the physical laws that govern the decay of Muons in motion ? [..]

Such things are usually not called laws, as some of us explained much earlier in this thread.

Why were these physical laws not discovered on their own !

Not sure which laws you mean, but physical laws with gamma were largely discovered on their own - see post #236. Physicists solve puzzles of nature by contemplating different types of information.

And how come this physical law can be used to derive the transformations, which it could not if it were an actual physical law !

? The classical physical laws can be used to derive the "Galilean transformations" as I tried to explain many times incl. in post #236. Similarly the Lorentz transformations were first derived from physical laws, deduced from observations. And note that physical laws are always generalisations of ideas that emerged from observations.

 

[Dale]

I noticed that in your response you carefully avoided answering the questions:

Do you now accept that the decay of muons can be explained by a law of physics that is not a coordinate transform? If not, then what possible logical reason can you have for not accepting it?

Do you mean, that Minkowski spacetime or metrics are the physical laws that govern the decay of Muons in motion ?

The metric is the mathematical structure which defines geometry. I.e. it describes distances, durations, angles, and the causal structure. The metric will appear in any law where geometry is important (which is most).

The law that governs the decay of muons (in motion or at rest) is the one I provided >240 posts ago.

But then I'm wondering where does this concept of spacetime and the metrics comes from if not from the transformations. Since there must be a physical concept behind any physical law.

The various geometric concepts don't need coordinates nor coordinate transforms, no matter how much you wish they did. They are physical concepts in and of themselves. Or are you trying to claim that my table leg is perpendicular to my table top only if I perform a coordinate transform?

And how come this physical law can be used to derive the transformations, which it could not if it were an actual physical law !

Nonsense. What possible chain of reasoning could lead you to this absurd comment.

 

[GAsahi]

That isn't the only correct way to work the problem.

True, it is the most direct way of solving the problem. In fact, it is the standard way of solving this problem, there is no need to introduce any notion of "number of laps" (the variable a in your derivation).

 

[Dale]

True, it is the most direct way of solving the problem. In fact, it is the standard way of solving this problem, there is no need to introduce any notion of "number of laps" (the variable a in your derivation).

Agreed.

But again, there is no reason not to introduce a either. Reparameterizations are common and well accepted, no matter if they are needed or not.