The terms absolute and relative

[Dale]

The terms "absolute" and "relative"

In discussions about relativity I use the term "absolute" as a synonym for "frame invariant" and "relative" as a synonym for "frame variant". I went to look for an authoritative definition and could not find one, so I am a little concerned.

Is my usage correct, and does anyone have an authoritative definition that confirms or contradicts my usage?

 

[ghwellsjr]

If you put another word after "absolute", like time, space, rest, simultaneity, etc, then you can find individual "definitions". But since these terms have fallen out of favor, they are not considered to be "frame invariant". Prior to Einstein, they would be considered independent of any concept of a frame, I would say. For example, Einstein uses the phrase "absolute rest" to deny its relevance.

But in terms of those things that are relevant, such as the speed of light, then your definition of "absolute" would apply. However, due to the historical contexts of the word, I think it can be confusing to limit it to your definition. Otherwise, what would we mean by the statement, "There is no absolute rest"? We mean that there is no single preferred frame that can be called absolute rest, not that rest is an invariant feature of all frames (whether or not it is).

 

[Dale]

OK, so you would use the word "absolute" to refer to a priveliged frame, and simply use the word "invariant" to refer to things which different frames agree on. That sounds reasonable to me.

Do you by any chance have a good reference for that usage?

 

[ghwellsjr]

OK, so you would use the word "absolute" to refer to a priveliged frame, and simply use the work "invariant" to refer to things which different frames agree on. That sounds reasonable to me.

Do you by any chance have a good reference for that usage?

Not really, just those compound searches.

 

[Naty1]

Dalespam, you know a lot more about relativity than I, but in several threads lately..I don't think you happened to participate... aspects which relate to your question, I think, have been thrashed about which may be of interest in formulating the terminology you choose.

"Invariant" turns out to have aspects that I have not yet fully deciphered:

I picked up 'Lorentz invariant' from language in posts here in Physics forums and never thought about it precisely...but a few days ago I saw 'Lorentz covariance' in a post and went to Wikipedia to look up the difference...they seem to ONLY discuss "Lorentz covariance' when I searched 'Lorentz invariance'...yet there is a link within the article to "Lorentz invariance in loop quantum gravity"...which has another link in it back to the original 'Lorentz covariance' article. So I am not positive how such terminology applies even here. [see below] Also, in Wikipedia, when one looks up 'frame of reference" one finds this opening which says:

http://en.wikipedia.org/wiki/Frame_of_reference

A frame of reference in physics, may refer to a coordinate system or set of axes within which to measure the position, orientation, and other properties of objects in it, or it may refer to an observational reference frame tied to the state of motion of an observer. It may also refer to both an observational reference frame and an attached coordinate system as a unit.

so here we seem to have one phrase and three possible meanings! I suspect it's the transforms, invarient or covariant, between coordinates that we are interested in not the axes...??

I concluded this with help from Mentz in another thread [unsure yet if it is precisely accurate]:

...The difference between ‘invariant’ and ‘covariant’: 'Invariant' means an identical value [a scalar which is a rank zero tensor] while 'covariant' means tensor components may change among observers but a contraction [to a scalar which is a rank zero tensor] remain the same.

in which Mentz posted:

We can describe a mathematical expression as covariant, which means it's written in tensors. Doing physics covariantly means that we are not plagued with artifacts induced by coordinate basis changes. An easy way to remember this is to think of the 4-velocity. The components are physically meaningful but frame dependent, while the contraction with itself is an invariant.

so if that's accurate math, then the physical is this:


Unsure where I got the following...as an apparent example...

...Only scalars that remain invariant between coordinate systems, like temperature can be called “tensors of rank 0”…. although frequency is a scalar, it is not a tensor of rank 0...observers in relative motion will measure different values...

Separately, in yet another discussion BenCrowell made this observation:

Only gauge-invariant quantities are observable. The Riemann tensor is gauge-covariant, but in order to give us a measurable quantity, we need something gauge-invariant; hence, we need to make a scalar somehow. [This coincides with Mentz and PAllen, that all observables are scalars.]

Lorentz scalars are invariant. I use the word scalar to indicate a single numerical value, which may be a component of a vector or tensor. Individual measurements are single numbers.

 

[harrylin]

[..] "Invariant" turns out to have aspects that I have not yet fully deciphered:

I picked up 'Lorentz invariant' from language in posts here in Physics forums and never thought about it precisely...but a few days ago I saw 'Lorentz covariance' in a post and went to Wikipedia to look up the difference...they seem to ONLY discuss "Lorentz covariance' when I searched 'Lorentz invariance'...yet there is a link within the article to "Lorentz invariance in loop quantum gravity"...which has another link in it back to the original 'Lorentz covariance' article. So I am not positive how such terminology applies even here. [..]

Oops, that reminds me of the fact that I also tend to mix them up.

Usually mathpages is quite good on such things - and it does discuss them, here:

http://www.mathpages.com/home/kmath398.htm

 

[Dale]

Thanks for the link. It doesn't help with "absolute" vs "invariant", but it really is clear on the distinction between "invariant" and "covariant".

 

[Austin0]

In discussions about relativity I use the term "absolute" as a synonym for "frame invariant" and "relative" as a synonym for "frame variant". I went to look for an authoritative definition and could not find one, so I am a little concerned.

Is my usage correct, and does anyone have an authoritative definition that confirms or contradicts my usage?

HI I would agree with ghwellsjr , even without looking for authoritative sources , it is almost certain there is no "frame invariant" definition of absolute . Only a plethora of contextual meanings.

Though your definition is certainly concise and logical, the word itself definitely has a lot of attached associations in science and philosophy. Like the word simultaneous this might lead to ambiguity with some people.
Generally in the context of SR it seems to be used specifically in reference to an absolute reference frame. Newtonian or Lorentzian

If this is any more authoritativly correct than yours I have no idea.

But if you aren't having a problem with being understood maybe there is no cause for concern ;-)

 

[Austin0]

If you put another word after "absolute", like time, space, rest, simultaneity, etc, then you can find individual "definitions". But since these terms have fallen out of favor, they are not considered to be "frame invariant". Prior to Einstein, they would be considered independent of any concept of a frame, I would say. For example, Einstein uses the phrase "absolute rest" to deny its relevance.

But in terms of those things that are relevant, such as the speed of light, then your definition of "absolute" would apply. However, due to the historical contexts of the word, I think it can be confusing to limit it to your definition. Otherwise, what would we mean by the statement, "There is no absolute rest"? We mean that there is no single preferred frame that can be called absolute rest, not that rest is an invariant feature of all frames (whether or not it is).

In th case of light it seems to me there are two definitions.
Absolute constancy as meaning all photons are traveling at this speed wrt vacuum outside of gravitational influence and does have a connotation of actuallity, and frame invariance which refers to measured speed as per 2nd Postulate. Have you ever seen a version where the term absolute is used in 2nd postulate referring to measurement in frames?.

 

[bahamagreen]

"...all photons are traveling at this speed wrt vacuum..."

In the context of SR, how can vacuum be something with respect to which anything can have any definite speed, relative or absolute? Isn't c always relative to and absolute within only inertial FOR?

Maybe when you say c wrt vacuum you mean c wrt an inertial frame of vacuum? That does not sound quite right either...

I guess what I mean is, if c is a constant, and this is wrt vacuum, then vacuum would seem to take on a constant, too , just as absolute as c - the vacuum would always be at 0m/s relative to c.

This vacuum at 0m/s wrt c makes me wonder how the definitions and clarifications of relative and absolute apply here...?

 

[Austin0]

"...all photons are traveling at this speed wrt vacuum..."

In the context of SR, how can vacuum be something with respect to which anything can have any definite speed, relative or absolute? Isn't c always relative to and absolute within only inertial FOR?

Maybe when you say c wrt vacuum you mean c wrt an inertial frame of vacuum? That does not sound quite right either...

I guess what I mean is, if c is a constant, and this is wrt vacuum, then vacuum would seem to take on a constant, too , just as absolute as c - the vacuum would always be at 0m/s relative to c.

This vacuum at 0m/s wrt c makes me wonder how the definitions and clarifications of relative and absolute apply here...?

I think I may have phrased it imprecisely. As I understand it, the speed of light is related to the permitivity and permeability of the vacuum of free space. The speed itself can apparently be directly derived from Maxwells equations regarding these qualities of the vacuum. And I think those values are in fact considered constants of free vacuum but variable in the presence of matter.
. When I said that, the intended meaning was; without a specific reference frame, but as a consequence of the nature or geometry of spacetime itself.
Not as using the vacuum as a reference frame which of course makes no sense.

That this speed is also considered to be absolute in the sense of being the fastest speed possible within that geometry.

 

[harrylin]

Thanks for the link. It doesn't help with "absolute" vs "invariant", but it really is clear on the distinction between "invariant" and "covariant".

Sorry, I didn't comment as I simpy agree with ghwellsjr; that topic already came up in a thread by mangaroosh. There I similarly only gave examples of how that word has acquired different meanings, apparently due to its use in the context of classical mechanics where it didn't matter - but it does matter in modern relativity. I see no objection to use the word "absolute", as long as the context makes the intended meaning clear or if the intended meaning is clarified ("in the sense of").

 

[Ich]

I have no authorative answer, but here's what I think:

For defining "absolute" vs "relative", one should concentrate on the meaning of "relative", "absolute" is just the opposite in this context.
"relative" means a property of an object in relation to something else. So relative quantities are those for which you need at least two objects to define them. ("object may be something abstract like a "frame", too.) "Absolute" quantities are in reverse those intrinsic to only one object.
That means: while all four dimensional geometric objects are covariant or invariant, this property does not distinguish between absolute and relative.

For example, the scalar product of an object's four momentum is absolute, its restmass squared.
Its scalar product with another object's four velocity instead is relative: Its relativistic mass in the second object's rest frame.
But both are scalars, thus frame invariant. The only difference is the number of objects needed for the definition.

 

[Naty1]

Dalespam:

In discussions about relativity I use the term "absolute" as a synonym for "frame invariant" and "relative" as a synonym for "frame variant".

I originally thought 'absolute' was probably ok...not so much after thinking about it more...and seeing the above viewpoints...it seems, as I illustrated in some quotes above, that 'invariant' and 'covariant' [and 'contravariant'] are more precise distinctions. And as others have posted, 'absolute' has some historical implications and baggage.

Is there some advantage in using your language...?

I have found your prior posts in these forums concise and technically correct once I understood them... So if there is was any imprecision, I have not noticed it. Using precise, perhaps technical language, may make getting started more difficult, but helps avoid misunderstandings.

I would think if you use 'absolute' to refer to only 'frame invariance' and in the same writing refer to, say, 'invariant mass', that language raise questions in the readers mind as to the difference between 'invariant' and 'absolute'.