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I would like this article to be accessible to students of all ages. Did I err on the side to too many words, and too little "equation boilerplate"? Would an example or two of its application help? Thermochap (talk) 14:15, 20 January 2008 (UTC)[reply]

It would benefit from an extra opening sentence or two that explains the concept in as simple a language as possible (e.g. avoiding jargon like "flat spacetime") before going on to the more technical definition. So even an absolute beginner in relativity could understand it. You could also mention some authors call proper velocity "celerity".

Somewhere in Wikipedia, whether on this page or somewhere else, could compare and contrast all the various ways of measuring motion: coordinate velocity, proper velocity, rapidity, doppler factor, Lorentz factor. And formulas to convert from any one to any other. --Dr Greg (talk) 12:01, 11 April 2008 (UTC)[reply]

A "low-cost" opening concept-wise is a good idea, as is mention of celerity as it gets more technical. The Lorentz factor/rapidity page might be a good place for the overview, given that the latter (albeit more abstract) is a grand meeting ground for all of these velocity parameters. Thermochap (talk) 13:30, 11 April 2008 (UTC)[reply]

Yes. I tried to make a table of "equations boilerplate", but I use 4 representations of one motion and do not know if somebody use the 4-th representation, which I named "quantum velocity". Here they are:

1) coordinate velocity: v;

2) proper velocity: v_τ;

3) rapidity: v_ψ measured in m/s or Ψ in radians;

4) quantum velocity: v_q in m/s and Q in radians;.

Two first of them are measurable and consequently represent two similar but different physical values.

Two last are computable, and can be used as parameters.

So we have 4 velocities and 8 accelerations.

Some main equations are on the right side of the attached picture.

The tremendous connections between accelerations are on the left side of it.

[1]

2. Couple of words about the "application help".

a) I want to see our whole Universe. I suspect that its space-time can be represented as 4-dimensional lattice, build in the 4-dimensional closed pseudo-Euclidean space. Geometry of Universe and geometry of space-time lattice must dock each other perfectly and tight. All four velocities can be used in order to look at the lattice and at the Universe from different angle and to correct the errors and to find the new correct solutions. So, the usage of proper velocity in the system with others gives us the cognitive benefit.

b) Our Universe is very huge but is not infinite. Consequently the space-time lattice and some pure math number series can be very big, but finite. As a result the PROPER ACCELERATION (this term is used widely, but it is not perfectly correct), felt by a person or device, could be

dv_q/dt = dv/dτ = γ dv/dt; instead of this:

dv_τ/dt = dv_ψ/dτ = γ³ dv/dt.

Both of these strings of equations are written on the quoted figure.

If so, then the "Around the world trip in the Universe" could be made much faster. So, the investigation of the future cosmic routs from all possible perspectives, including different types of velocities, is not just important, but vitally important.

Ivan Gorelik. Different representations of velocities, describing one and the same rate of motion. https://darkenergy.narod.ru/sr.html ~2026-10689-18 (talk) 08:24, 18 February 2026 (UTC)[reply]

Equation boilerplate in this case probably adds little to new understanding, so I think the article is a good start. Information on the utility of rapidity's Sinh (along with Cosh as the Lorentz factor and Tanh as coordinate velocity) is helpful for anyone (particularly beginners) wishing to solve high speed problems in context of a single spacetime slice. As in using the metric equation, the only post-Newtonian concept needed to start is that of proper time on the traveling object's clock.

Particle land speed records are more impressive when quoted in lightyears per traveler year (~10⁵c fixed, ~10¹⁰c collider) than in lightyears per map year (~1c). Log-Log plots of Lorentz factor minus one versus proper velocity are particularly interesting. Multiplying one of these by mass yields a family of kinetic energy versus momentum curves that make contact with many branches of everyday and modern physics. Proper velocity also helps put the integrals of constant proper acceleration (for use within a single spacetime slice) into simple form.

It looks like pedagogical examples (worked problems, for instance) are more commonly offered via external links. However added sections should gradually materialize that indirectly serve the purpose of providing more examples. Propervelocity (talk) 17:22, 22 January 2008 (UTC)[reply]

In this context I've added a figure, and an application section on comparing velocities. Thermochap (talk) 18:47, 27 January 2008 (UTC)[reply]

I've now also added sections on the disperson curve and proper acceleration apps mentioned above. Thermochap (talk) 15:12, 4 February 2008 (UTC)[reply]

If it wasn't for the reference to Taylor & Wheeler, I would have been bold and rewritten the first sentence of this section as

"Proper acceleration is the acceleration physically experienced by an object, that is, the acceleration measured by an accelerometer attached to the object. In flat spacetime it is the three-vector acceleration measured by an inertial observer who is instantaneously travelling at the same speed as the object."

However, whatever is written here ought to be compatible with the reference, and as I don't have a copy of Taylor & Wheeler I don't know if my rewording meets that condition.

If the less-clear phrase "instantaneously-varying frame" has to be used, the word "inertial" needs to be added. The technical phrase often used is "co-moving inertial observer". --Dr Greg (talk) 10:22, 7 June 2009 (UTC)[reply]

Thanks for the suggestions! The initial changes were indeed vague and confusing, even (perhaps especially) for some of the simplest examples of its application under discussion on internal joint-editing space at school. For now it uses "free-float" instead of "inertial" to specify the local reference frame, but basically following your insight.

Our internal page on proper acceleration itself now has much more clarity (and content) than the one here does. Since Wikipedia's proper acceleration page has started to evolve on its own, improvements there from my end will probably be added more gently in the days ahead.

Postscript on references: Edwin told me that the references to proper acceleration were removed in the second edition of Spacetime Physics because the publishers said that teachers didn't use them. He's also the fellow who first introduced me to the work of William A. Shurcliff on proper velocity. If I can locate Shurcliff's monograph around here somewhere, we may look into the possibility of making it available electronically. Thermochap (talk) 22:27, 7 June 2009 (UTC)[reply]

Hopefully this critique will be taken as constructive rather than just me tossing rocks. 1. Please check me here, I'm just a student of this stuff but I don't think proper velocity is a MEASURED quantity except when the observer is at rest with respect to the map, where it just is velocity. If I'm correct, this eliminates the core explanation found in the lede. My principle objection here is that there is no 'physical' quantity that is not measured by the observer (with respect to his/her coordinate frame). Confusing calculated quantities with measured quantities is confusing theory with 'physical reality'. 2. The first paragraph of the Introduction uses the term "super-relativistic". I'm not familiar with it. I understand "non-relativistic" and "relativistic", and assume that sub- and super- are synonyms for that. To me "super-relativistic" implies v > c, and so is non-sense. (Except when talking about possibly, group velocity?) 3. Half of first paragraph of the Introduction is "See Also" and NOT explanatory. It doesn't, imho, belong there ("see also" belongs at the end of any explanatory article, of course) 4. I simply don't understand how proper motion can "reside in a slice" of space-time. The meaning eludes me. How does this distinguish it from any other quantity...don't they all "reside" in a slice of 3-d space?? 5. Engineering applications vs coordinate free "insight". I'm lost understanding this. My GUESS is that the underlying claim is something like "its useful for quantitative models, rather than general principles"?? 6. Lose the junk on gyrovector rubbish. Its exotic and little used. (does NOT belong in the mainstream explanation) 7. You have a formula which uses |w|².....?? This implies that either you don't know that w² is IDENTICAL to |w|² or that w is complex (if not worse). 8. The same formula defines Beta_w as a function of w. I must be missing something. w=gamma*v, right? < dx/dτ = (dx/dt)(dt/dτ)> but you claim β_w = 1/(√(1-(w/c)²)) AND β=1/γ !!! At best this is massively confusing! beta for a given velocity is traditionally 1/γ, β for a given velocity is defined as √(1-(v/c)²), right? using the same symbol for a different quantity is just terribly confusing. That is: what does β_u mean??; is it beta for velocity u or is it β_w for some proper velocity u? Anyway, that's as far as I got in this before I became so confused I decided continuing was pointless.173.189.73.56 (talk) 18:48, 28 July 2014 (UTC)[reply]

If proper velocity eliminates the need for relativistic mass then why is transverse Mass different from longitudinal Mass?

Just granpa (talk) 07:19, 1 July 2016 (UTC)[reply]

Article talk pages are for discussions about the article, not about (aspects of) the subject—see wp:Talk page guidelines. You can ask at the wp:Reference desk/Science. Good luck. - DVdm (talk) 08:30, 1 July 2016 (UTC)[reply]