Yes, in three topics at least, as shown below, usually called modern physics: special relativity (SR), general relativity (GR), and quantum mechanics (QM).
The basis of both SR and GR, for more than 100 years, is the model of spacetime, a 4D universe, as first explained by Minkowsky [1]. To contrast, Newtonian mechanics was based on a 3D universe, where time is absolute and NOT influenceable by an experimenter.
From a basic theorem in topology, and even more basic type theory results, a continuous path in 4D may create a discontinuous path in a lower dimension, such as in 3D; any one-to-one mapping between spaces of different dimensionality must be discontinuous in that a continuous path in one space maps into a broken path in the other.
Therefore, there are discontinuities in the transition to 3D (Newtonian mechanics) from SR or GR, even at v 1, or h goes to zero.
The intuition gained in Newtonian physics is not efficient in modern physics, and will lead to contradictions in an arbitrary path taken in nature.
[1] Minkowsky, 120 years ago, that "Henceforth, space for itself, and time for itself shall completely reduce to a mere shadow, and only some sort of union of the two shall preserve independence."
The phrase "modern physics" usually implies both relativity and quantum mechanics. When v
Hello Goeller: Thank you. Modern physics is defined in the question itself, as including SR, GR, and QM. What you said on Newton is normal wisdom, but that the question points out is topologically wrong. Your other support is appreciated.
Btw, the question includes other conditions inside, not just v < < c, but the title would be too long for RG, maybe it will ve fixed by the time you read this note.
The mapping from 4D to 3D is not one to one, it is a projection, therefore the reasoning doesn't apply.
The limit of quantum mechanics when h tends to zero is classical mechanics, but not any classical mechanics. Contrary to what is widely believed, the limit is geometrical optics, not corpuscle mechanics. Thus neither is subsumed by the other, they are different theories. They can't be the same since they are different representations of a same Poisson structure.
It is straightforward to visualize what happens as v 0 is much more difficult, because it is NOT the world we live in. For example, if h = 0, there would be no atoms, and therefore no molecules, and no life. Or stars. This universe might be "explainable" in terms of Newtonian mechanics, but we wouldn't be here to do it.
I would add that, for v (infinity). Because c^2 = 1/(mu-naught * epsilon-naught), where mu and epsilon are coefficients that relate to the strength of the magnetic and electric forces respectively, if c --> infinity, then either mu or epsilon (or both) would go to zero, which would mean "no electric or magnetic forces," which again would mean we would not be here to discuss the situation.
Sorry, I'm doing this in my head. If c --> infinity, I think the strength of the electric field would go to infinity also (not zero). Either way, bad news for life.
Hello Claude Pierre Massé, Lawrence Goeller, and all: Thank you. A projection is the transformation of points and lines in one plane onto another plane by connecting corresponding points on the two planes with parallel lines, it is a mapping. If it involves spaces of different dimensionality, a projection also must show discontinuities, it is easier to prove -- try to project a helix (3D figure) perpendicular to its axis onto a paper, and you get a circle (2D figure), you also lose handedness.
We think we live in v < < c but an alien in Capella might disagree. Also, without special relativity working at a permanent magnet bar at rest with v = 0 in our hand, there would be no magnetic attraction. Light itself, in our room, at rest, would not exist. A medical MRI at rest in the clinic would not work. We live in a 4D world, even while not moving, time passes.
The topological arguments looks vague for me. (Especially for SR, with trivial R^4 space-time.)
3D Newtonian kinematics uses parametrized curves (parameter is time).
4D relativistic kinematics uses non-parametrized curves.
On could use 4D kinematics in Newtonian mechanics, see volume 1 of "Gravitation" by Misner, Thorne and Wheeler.
Hello Igael Azoulay
and all, As said in the discussion text, this is not a conceptual choice only, but must be also experimental, which one could then call natural, it is in nature. Reality, experimentally, must be at least 4D, it “does not fit” inside 3D in all cases. This is not 3+1, it is 4, integrated, you cannot separate. Now, this does not mean that reality cannot be >4, and exceed c in that context, of 8D or more...
Hello all: This thread arrived, in the past, at a conclusion, which is stated in the body of the initial text. There is no room to refuse to notice an obvious thing, or to re-explain here, the reasoning and references are available above, to anyone.
We are now ready to move to non-mathematical and non-physical aspects. We are talking about the historical and intersubjective aspects, which are important to us qua humans. Finding a humanly acceptable answer is difficult in physics or maths today, and, pretty soon, in all natural sciences. Therefore, this very thread is important.
We suggest, as in physics, that facts are what you were willing to believe. A bias, preventing a more complete vision. That is another motivation here, to abandon bias. It has no place going forward, and may prevent us from seeing what is plain to see.
Although almost all those points, and others not listed, are in my RG publications, I tend to see things through QM.
Reality is observer-dependent, in QM. Starting with the Heisenberg principle, observer and experiment cannot be dissociated. There is no objectivity in QM -- but there is a coherent abstract view one can pursue in QM.
Now, from that common, coherent, abstract view in QM, one can pursue instances of a subjective, intersubjective, and objective natures, and mixed, ordering them into a scale, even contradictory to themselves. It is a cornucopia of choices! All validated by the same common, coherent, abstract view that has the "seed thought" of the subject. It is like a manifold, connecting different domains to one another, although no connection is seen directly between them.
QM and SR are necessary for EM, so its easy to have RQM -- it is a "match made in heaven". Gravity is modeled by extrinsic curvature of spacetime in GR, when QM is utterly ignored, incompatibly, but more than that, it is of a different type, in HoTT and TCS terminology.
In this abstract view, one is concerned with testable relationships, one is focusing on the essence of a hypothesis in the Scientific Method. A hypothesis is not a guess, a hypothesis is a testable relationship, no more and no less.
Accordingly, SR is not a guess, but a testable relationship.
In that abstract sense, SR passed the QM test and the EM test, and yet it MUST be observer-dependent, which seems to contradict several old "principles", but actually extends them, it does NOT deny them. When I summarize, for example:
"Comoving observers NEVER measure time dilation or length contraction, whereas non-comoving ALWAYS do. It does not matter the acceleration, nor the velocity."
then goodbye to "relativistic speed" or "inertial observer", they are limited to a platonic model, a human-made domain, not Nature.
In Nature, an "inertial observer" can see different realities, whether comoving, or non-comoving; reality can be the same also, no matter the acceleration, nor the velocity.
What really distinguishes observers, is whether they are comoving or not. Here, as normal in Physics, comoving is a technical word, and means "same position and velocity", not necessarily identical objects; in cosmology comoving observers see the same wavefront, so it is coherent with other related fields.
Depending on the SR formulation as the stance that one uses, even no SR, more or less "paradoxes" will result. The less "paradoxes" the better. The same with EM, thus we want to eliminate what is not necessary. Can the Maxwell equations be excluded in EM? Other questions follow.
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