Definition talk:Translation Property

I chose the name "Translation Property" myself. I did not take the name from somewhere. --Ivar Sand (talk) 11:31, 13 November 2023 (UTC)

What's the point? Saying "$f$ has the translation property" is exactly the same thing as saying "$f$ is a translation".

Might as well say "A plane geometric figure has the circularity propery if every point on its circumference is the same distance from the center". Sorry, but it doesn't seem to add anything. --prime mover (talk) 12:17, 13 November 2023 (UTC)

Hence I propose deleting this and instead expand the page translation mapping, just as soon as you can find a source that you can cite, and please don't trawl the internet for obscure papers, get it from a text book. --prime mover (talk) 12:21, 13 November 2023 (UTC)

How does one find such a text book? I tried using the definition of translation property in a google search but that did not give anything. The field is the special theory of relativity. $f$ is the Lorentz transformation. $x1$ represents an event (a point on the x-axis) and $x2$ represents another event. The translation property expresses that there is no change in the difference between the positions of the two events in a different frame of reference if they are shifted along the x-axis by the same amount in the original frame of reference. Can someone help? --Ivar Sand (talk) 11:05, 16 November 2023 (UTC)

In its current context there is nothing about the definition which restricts it to special relativity. Nothing even that ties it down to anything less abstract than a general mapping on the reals.

I reiterate my suggestion (which is more of a command) that everything posted up, and especially definitions, comes sourced from a published text book.

Where to get such a text book? I use shops, myself. --prime mover (talk) 12:39, 16 November 2023 (UTC)

I'll try and look for the definition in some text book. It may not be too easy, though, because a function with the translation property is not necessarily a translation. Also, the definition may not exist anywhere else. But, no worries, I think we'll solve this. --Ivar Sand (talk) 11:25, 20 November 2023 (UTC)

Interesting. I would have thought that in the purest abstract sense, a translation is defined as a mapping which has the translation property. I would be interested to find a function which had the translation property but which was not in fact a translation. --prime mover (talk) 12:41, 20 November 2023 (UTC)

An example of a function with the translation property that is not a translation is the Lorentz transformation which has the form $f(x) = a (x - b)$ where a is normally unequal to $1$. --Ivar Sand (talk) 10:01, 30 November 2023 (UTC)

Thank you for this. That will need to be added to $\mathsf{Pr} \infty \mathsf{fWiki}$ in due course. --prime mover (talk) 11:05, 30 November 2023 (UTC)

I have contacted a librarian at the local library to help me find a text book with a definition equalling the translation property. She had no success, but she gave me a hint of what I could do to try and find it myself, but I had no success either.

I think that if such a definition should be found in a text book it would have a number but not a name as it does not signify something interesting mathematically. The translation property is more of a condition or requirement than a definition.

I feel obliged to inform of something concerning the starting point for producing the translation property and the four pages referencing it. The starting point was physics and the problem was a thought experiment and not a real situation. I wanted to produce the Lorentz transformation from the Galilean transformation with additional information from the theory of relativity but this was not how the Lorentz transformation was produced. --Ivar Sand (talk) 09:46, 1 December 2023 (UTC)

Here I take the perspective that the page names "Definition:Translation Property" and "Definition:Translation Mapping" are confusingly similar.

I have the following suggestions for solving the problem with the confusing translation property page name:

1. Moving the contents of the page containing the translation property to the 4 pages referencing this page. (Is there instead the possibility of creating a subpage for each of the 4 pages referencing the translation property page so that all these 4 subpages contain the same that the current translation property page contains?)

2. Removing the 4 pages referencing the translation property page as well.

3. Keeping the translation property page after all. In that case, its name should be changed so as to avoid confusing a reader with the concept of translation. My suggestions of new names:

- the relocation property

- the displacement property

- the translation expression

- the translation condition

The translation property is about a difference between function values (f(x1)−f(x2)) and translating this difference (f(x1+t)−f(x2+t)) without its value changing. Thus, a more descriptive name would be:

- difference between function values is invariant under translation

I hope these suggestions will help solving the problem with the confusing translation property page. --Ivar Sand (talk) 10:05, 5 December 2023 (UTC)

Again, we are back where we started.

As I pointed out, none of this material referring to "translation property" are sourced. I gather you're trying to put something together to underpin the theory of relativity, but adding pages ad hoc according to what seems to need to be defined, without reference to a source work presenting this material in rigorous detail is (in my opinion) the wrong way of going about this. --prime mover (talk) 11:47, 5 December 2023 (UTC)

Well, we are not really back were we started because I gave several suggestions on how to solve the problem above.

You insist that the definition page of the translation property should have a reference to a mathematical text book. I see your point. I am sorry that I am not able to provide such a reference. As I noted above there may not exist such a book. So, looking for it would maybe be a waste of time. --Ivar Sand (talk) 11:05, 7 December 2023 (UTC)