Is acceleration a more absolute/fundamental quantity in the universe?

[cometraza]

TL;DR Summary

Acceleration can be defined in less arbitrary terms than velocity/distance. Does it suggest it is more fundamental out of these three quantities in the universe?

Was wondering if acceleration seems to be a more fundamental property/quantity in the universe as compared to velocity or distance because acceleration can be defined in more absolute terms in a frame depending on the forces acting inside that reference frame.
Considering a very simple example of a vehicle which accelerates from a standstill, we can define and measure acceleration (say via accelerometer) in more absolute terms while velocity can be arbitrary (i.e. velocity can be defined with reference to any other frame) or similarly distance also would require a reference point which can be arbitrarily chosen.

Does it suggest that acceleration is more absolute or more fundamental of these three?
(or am I missing something here?)

 

[anorlunda]

If something is fundamental, it would be hard to say that its derivatives and integrals were more our less fundamental.

 

[cometraza]

If something is fundamental, it would be hard to say that its derivatives and integrals were more our less fundamental.

Yes that seems to be more puzzling. Yet one can be measured without reference to another point or object (acceleration - by directly measuring the inertial force) while the others (velocity/distance) require a reference object or point (either within the same reference frame or outside).

 

[Vanadium 50]

Unless you can quantify it and say "resistance has a fundamentalness of six, but capacitance only five" this thread will circle around and around like ever other 'is A more fundamental than B' thread.

 

[PeterDonis]

Was wondering if acceleration seems to be a more fundamental property/quantity in the universe as compared to velocity or distance because acceleration can be defined in more absolute terms in a frame depending on the forces acting inside that reference frame.

The usual term for the property that acceleration (more precisely, proper acceleration) has that velocity and distance don't is "invariant". Most physicists take the view that physics is contained in invariant quantities, not coordinate-dependent quantities, so in that sense proper acceleration is "more fundamental", yes.

 

[PeroK]

Summary:: Acceleration can be defined in less arbitrary terms than velocity/distance. Does it suggest it is more fundamental out of these three quantities in the universe?

To begin at the beginning, we have Newton's second law, which involves acceleration rather than position or velocity:$$\vec F = m \vec a$$

 

[cometraza]

Just a quote on wiki which I found which might be relevant :
A. P. French writes, in Special Relativity:

"Note, though, that we are appealing to the reality of A's acceleration, and to the observability of the inertial forces associated with it. Would such effects as the twin paradox exist if the framework of fixed stars and distant galaxies were not there? Most physicists would say no. Our ultimate definition of an inertial frame may indeed be that it is a frame having zero acceleration with respect to the matter of the universe at large."

 

[PeterDonis]

Just a quote on wiki

Do you have a link?

Based on what the quote says, this does not look like a reliable source. You should be looking at textbooks or peer-reviewed papers.

 

[sysprog]

If there is only one velocity vector being considered, acceleration is immedately modellable as the second derivative of position with respect to time; however, if there is more than one first (velocity vector) derivative of position wrt time being considered, it's not as simple as that $-$ whether the acceleration in one direction is greater than in another, and also at least the third (jerk) and fourth (jounce) derivatives, on a per-vector basis, must be considered, as part of the overall tensor system, before you can rigorously state acceleration values.

 

[PAllen]

Just a quote on wiki which I found which might be relevant :
A. P. French writes, in Special Relativity:

"Note, though, that we are appealing to the reality of A's acceleration, and to the observability of the inertial forces associated with it. Would such effects as the twin paradox exist if the framework of fixed stars and distant galaxies were not there? Most physicists would say no. Our ultimate definition of an inertial frame may indeed be that it is a frame having zero acceleration with respect to the matter of the universe at large."

I will go further than @PeterDonis . The paragraph is expressing a strong form of Mach's principle. Contrary to the author, most physicists would disagree with this, including Einstein (reluctantly). More concretely:

1) Special Relativity says the opposite of this. It says proper acceleration versus inertial motion is a locally detectable difference even if there is only one device in an empty universe. Whether or not this is true is rather hard to test. Whether or not special relativity says this is not in doubt. Further, I think most physicists see the twin differential aging as the Minkowski analog of the Euclidean triangle inequality. A plane does not need any substance for the triangle inequality to be true. Neither does the universe in Special Relativity require matter for twin differential aging to be true.

2) The statement is trivially false in General Relativity (thus, I am sure, most physicists would disagree with the given statement). First, in General Relativity, an inertial frame is inherently a local construct rather than a global one. There are no global inertial frames at all. Further, a local inertial frame near a massive body has nonzero acceleration with respect to the matter of the universe at large (in any reasonable sense of the term).

[edit: I have verified that the quote does indeed come from a well respected book on Special Relativity by A. P. French - which I have not seen, thus have no opinion of. This in no way changes the validity of the statements above. (The book was apparently used as the basis of a course in SR at MIT in late 60s and 70s.)]

 

[PeroK]

Just a quote on wiki which I found which might be relevant :
A. P. French writes, in Special Relativity:

"Note, though, that we are appealing to the reality of A's acceleration, and to the observability of the inertial forces associated with it. Would such effects as the twin paradox exist if the framework of fixed stars and distant galaxies were not there? Most physicists would say no. Our ultimate definition of an inertial frame may indeed be that it is a frame having zero acceleration with respect to the matter of the universe at large."

It seems to me that the problem with that is:

1) If we take SR at its mathematical face value, then we have a flat Lorentzian manifold, where the twin paradox is simply the equivalent of the triangle inequality in Euclidean geometry. It needs no framework of fixed stars and galaxies to derive SR from first principles in an (empty) universe with isotropic and homogenous spacetime.

2) In a largely empty universe with at least the electromagnetic interaction, we could still build the LHC, presumably. If all we had in the universe was the Solar system, why would the experiments at CERN give fundamentally different results? Given that CERN is largely underground, no one down there is looking at the distant stars to see how fast the protons are being accelerated!

 

[cometraza]

Do you have a link?

Based on what the quote says, this does not look like a reliable source. You should be looking at textbooks or peer-reviewed papers.

Yes its a footnote in chapter 5, page number 156 of his book "Special Relativity".
You can check it here :
https://archive.org/details/special-relativity

 

[cometraza]

If all we had in the universe was the Solar system, why would the experiments at CERN give fundamentally different results?

Maybe because in that scenario the solar system itself as a whole might have been in a non inertial frame

 

[PAllen]

Maybe because in that scenario the solar system itself as a whole might have been in a non inertial frame

Say what??! There is no way in GR to represent the solar system as not consisting of all inertial paths (for the sun and the planets, and the solar system as a whole). French's comment simply requires that both SR and GR be substantially wrong in a near empty universe, with no known specific model of how this happens, or evidence in favor of it. Note, there are different senses of Machian behavior that Misner and Julian Barbour have discussed (that are part of GR, rather than contradict it), but basically nobody believes what French suggests.

 

[PeroK]

Maybe because in that scenario the solar system itself as a whole might have been in a non inertial frame

I think the onus would have been on AP French to describe and explain the CERN experimental results in a universe with only the solar system and explain how the presence of distant stars and galaxies would affect an essentially local experiment.

The Lorentz transformation and the basics of spacetime do not stand alone. The relativistic theory of energy-momentum and all of particle physics is built on top of that. If we didn't have Minkowski spacetime we'd know about it in lots of ways independent of space-travelling twins.

 

[geshel]

For me, the more interesting point is that the 3rd and higher derivatives never show up anywhere important.

 

[sysprog]

For me, the more interesting point is that the 3rd and higher derivatives never show up anywhere important.

Some of the guys call the 4th derivative of position wrt time 'snap' instead of 'jounce', just so that they can wryly call the 5th and 6th 'crackle' and 'pop', presumably in the supposition that in real life, no-one really cares about anything higher than at most the 4th . . .