Thread: The Definition of an Inertial Frame of Reference

I reject the claims made by backward thinking physicists that mathematicians must not define inertial frames of reference in a coordinate-free way.

Are you for or against the sacred oracles of the ancient opinions?

Shubee

I don't understand your opposition. Classical theoretical mechanics is based on generalised coordinate systems. They are not fixed to any cartesian, polar or spehrical coordinate system. Look up Langrange theory or Hamilton-Jacobi theory.

This makes no sense.

An inertial frame of reference is ine in which, classically Newtonian mechanics holds, or in more modern terms in which special relativity holds. One can show that, given any inertial reference frame, all other inertial frames are those in consyant motion with respect to it.

An inertial reference frame is an idealization. No physically-definable reference frame will be perfectly inertial, but the approximation is sufficient for many applications.

Your question merely demonstrates profound misunderstanding of the concept.

Originally Posted by Dishmaster

Classical theoretical mechanics is based on generalised coordinate systems.

That is good. However, the prevailing modern-day definition of an inertial frame of reference is not independent of a choice of coordinate system.

"In Newtonian physics and special relativity, an inertial frame of reference (or Galilean reference frame) is a frame of reference in which Newton's first law of motion applies: an object moves at a constant velocity unless acted on by an external force."

In relativity, velocity is understood to be a coordinate dependent quantity.

Originally Posted by DrRocket

This makes no sense.

The Quintessence of Axiomatized Special Relativity Theory features a generalized coordinate system such that ideal clocks move equal distances in equal proper time but motion in terms of coordinate time is nonlinear.

Originally Posted by Shubee

Originally Posted by DrRocket

This makes no sense.

The Quintessence of Axiomatized Special Relativity Theory features a generalized coordinate system such that ideal clocks move equal distances in equal proper time but motion in terms of coordinate time is nonlinear.

Complete rubbish. The author is clearly a crackpot.

This crap belongs in Pseudoscience, not in Physics.

Originally Posted by DrRocket

Originally Posted by Shubee

The Quintessence of Axiomatized Special Relativity Theory features a generalized coordinate system such that ideal clocks move equal distances in equal proper time but motion in terms of coordinate time is nonlinear.

Complete rubbish. The author is clearly a crackpot.

There are, of course, a few authors that understand the implications of nonlinear clock synchronization schemes. See this abstract:

The traditional proof of the linearity of Lorentz transformation makes use of a definition of simultaneity and a physical law for the propagation of light. For unravelling these two elements we use a reverse axiomatic approach to special relativity. In this case we are free, in principle, to introduce an arbitrary simultaneity. Linear coordinate transformations require a linear synchronisation. Lorentz transformation results from a special kind of linear synchronisation.

Is it your opinion that Wiley Online Library is not an authoritative source? How are the two papers different in their hypotheses, science and conclusions?

Originally Posted by Shubee

Originally Posted by DrRocket

This makes no sense.

The Quintessence of Axiomatized Special Relativity Theory features a generalized coordinate system such that ideal clocks move equal distances in equal proper time but motion in terms of coordinate time is nonlinear.

So.... what does "Axiomate" mean in this paper's usage? Normally the word "axiom" means the same thing as "postulate" or "assumption", and well...... I don't see how any one coordinate system would adequately claim to be more "axiomatic" than the next. They all have assumptions/postulates to them.

The closest I found in the paper to an explanation of what "axiomated" is supposed to mean was this:

Originally Posted by The Paper

1 What is Axiomatization?
For mathematicians like David Hilbert, the axiomatization of physics means modeling all
possible physical-theoretical frameworks in the same way that mathematicians typically
dene and investigate all fundamental mathematical structures. Consequently, it is to be
understood that this derivation of special relativity theory represents a mathematician's
perspective. It conforms to David Hilbert's philosophy of physics. [1].
Hilbert expressed the quintessence of his magnicent philosophy as follows:
\If geometry is to serve as a model for the treatment of physical axioms, we
shall try rst by a small number of axioms to include as large a class as possible
of physical phenomena, and then by adjoining new axioms to arrive gradually at
the more special theories. ...The mathematician will have also to take account
not only of those theories coming near to reality, but also, as in geometry, of
all logically possible theories. He must be always alert to obtain a complete
survey of all conclusions derivable from the system of axioms assumed." David
Hilbert, International Congress of Mathematicians, Paris France, 1900.

And....nope.... no clear definition here. Apparently "Axiomated" is just a new word for "minimizing assumptions". Most scientists call that "applying Occam's Razor." So....while it would be hard to disagree that we should do this when working with physics, I'm not sure Hilbert's theory quite counts a new innovation. All he is doing is coming up with new words to describe old ideas, and destroying those words' intended meaning in the process.

Originally Posted by kojax

So.... what does "Axiomate" mean in this paper's usage?

I believe that axiomatized special relativity simply refers to any derivation of special relativity that develops the topic with greater care and fewer assumptions.

The aim of The Quintessence of Axiomatized Special Relativity is to remove from Einstein's relativity theory everything that is confused, unnecessary and not amenable to experimental verification.

Originally Posted by Shubee

Originally Posted by kojax

So.... what does "Axiomate" mean in this paper's usage?

I believe that axiomatized special relativity simply refers to any derivation of special relativity that develops the topic with greater care and fewer assumptions.

The aim of The Quintessence of Axiomatized Special Relativity is to remove from Einstein's relativity theory everything that is confused, unnecessary and not amenable to experimental verification.

Greater care? Fewer Assumptions? That's just buzz word talk. Everything scientist tries to do things with the fewest possible assumptions and the greatest care they can.

What, do you think most of them just sleep in in the mornings, and play video games all day when they get to work?