Mach said [1], the principle of minimum xxxx, are they the natural purpose?
Born said in his "Physics in My Generation"[2], that while it is understandable that a particle chooses the straightest path to travel at a given moment, we cannot understand how it can quickly compare all possible motions to reach a point and pick the shortest path —— a question that makes one feels too metaphysical.
Speaking of the Hamiltonian principle and the minimum light path, Schrödinger recognizes the wonder of this problem [3]: Admittedly, the Hamilton principle does not say exactly that the mass point chooses the quickest way, but it does say something so similar - the analogy with the principle of the shortest travelling time of light is so close, that one was faced with a puzzle. It seemed as if Nature had realized one and the same law twice by entirely different means: first in the case of light, by means of a fairly obvious play of rays; and again in the case of the mass points, which was anything but obvious, unless somehow wave nature were to be attributed to them also. And this, it seemed impossible to do. Because the "mass points" on which the laws of mechanics had really been confirmed experimentally at that time were only the large, visible, sometimes very large bodies, the planets, for which a thing like "wave nature" appeared to be out of the question.
Feynman had a topic of minimum action in his "Lecture of Physics" [4]. It discusses how particle motion in optics, classical mechanics, and quantum mechanics can follow the shortest path. He argues that light "detects" the shortest path by phase superposition, but when a baffle with a slit is placed on the path, the light cannot check all the paths and therefore cannot calculate which path to take, and the phenomenon of diffraction of light occurs. Here, Feynman defined the path of light in two parts, before and after the diffraction occurs. If we take a single photon as an example, then before diffraction he considered that the photon travels along the normal geometric optical path, choosing the shortest path. After diffraction occurs, the photon loses its ability to "find" the shortest path and takes a different path to the diffraction screen, with different possibilities. This leads to the concept of probability amplitude in quantum mechanics.
To explain why light and particles can choose the "shortest path", the only logical point of view should be that light and particles do not look for the shortest path, but create it and define it, whether in flat or curved spacetime. Therefore, we should think about what light and particles must be based on, or what they must be, in order to be able to define the shortest paths directly through themselves in accordance with physics.
[1] Ernst Mach, Popular Scientific Lectures.
[2] Born, M. (1968). Physics in My Generation, Springer.
[3] Schrödinger, E. (1933). "The fundamental idea of wave mechanics. Nobel lecture " 12 (1933).
[4] Feynman, R. P. (2005). The Feynman Lectures on Physics(II), Chinese ed.
Keywords: light, Fermat principle of the shortest light time, Hamilton principle, Feynman path integral， Axiomatic
The Noble prize physics 2022 was awarded to researchers who proved that our universe is non-local. Non-locality means that everything in the universe influences everything at exactly the same moment.
Although it is difficult to understand the origin of instantaneous influences – there is no credible hypothesis – the consequences of non-locality in relation to observable/detectable physical reality is visible in the principle of least action and Feynman’s path integral. Because non-locality implies that the universe is transforming as a whole. This in opposite to existing ideas that the universe is the sum of its parts (the observable/detectable phenomena).
With kind regards, Sydney
A technically/physically plausible yet highly speculative model (and by most surely rejected due to immediate philosophical consequences - even touching religion by anyone’s individual rightly believe) is to assume universe is „just“ run by a large scale quantum computer (and hence effectively a simulation).
Think of it, please - before barking back:
If e.g. a mountain is just a simulation it will have all its proper physical aspects in such simulation, with all needed (by now measurement wise undetectable) aspects like it’s mass and structure down to the subatomic level.
But if such mountain would be a “just“ some fractal generated entity of “mountain type„ in some hypotized simulation, it could have some x/y/z/h/w coordinates and changing x would make such mountain instantly “jump“ on its virtual x axis (within the simulation).
That said - while it’s only an example and thought experiment, accepting experimentally verified EPR paradoxa or hypotized faster than light information propagation (which is the the same!) could indeed be fully explained in a very natural way by such information centric quantum supercomputer model … called „our universe“.
But as stated above - this is likely too much for most and especially more so for most scientific minded contenders here at RG. All I intended is to show up the theoretical possibility. For all practical purpose I personally prefer to stick to my iSpace model, able to drive constants of nature from very simple first order multiplicative first principles.
So while iSpace looks close to some simulation, it’s highly effective quantum physics:
Article New novel physical constants metric and fine structure const...
Preprint iSpace - Quantization of Time in iSpace-IQ Unit-System by 1/...
Conference Paper iSpace - Exact Symbolic Equations for Important Physical Con...
Dear Chian Fan,
let me indicate my point of view on how any particle chooses its shortest path.
In one of previuos comments I wrote you that the massless photon moves along the direction of its momentum step by step exciting the neighboring element of space. This space is electromagnetic in nature because all of its elements are the excited photons. Each neighboring element of moving photon has the "size" of action quantum h that is λ·P and τ·E with corresponding intervals of length λ and time τ. So, any path of photon will consist of integer number of h and it will be the least in the straight direction. Any space curvature (gravity or edge of the slit) will only change the direction of photon but not the least number of action quanta up to the final point. Photon has no choice: it is always forced to move along the shortest path.
A particle like an electron with a mass always takes in the surrounding EM space the place of corresponding photon. With the same λ=h/P as the particle has in the de Broglie's representation and with equal energy. I think that velocity of nonrelativistic electron is too less than the speed of light (photon) - the rate of excitation of the surrounding space by the electron. So, the electron can "know" far ahead what of its possible paths is the shortest. And you are right: light and particles do not look for the shortest path, but create it. With a good idea in your subsequent sentence.
Yours sincerely, Mikhail Dulin.
Dear Christian G. Wolf
A “large scale quantum computer” needs a 3D volume to transform its calculations into “tangible” existence. But that is not a realistic idea because every “point” inside the 3D volume must be accessible for the output lines of the quantum computer. And last but not least, it doesn’t solve the non-locality of our universe.
However, a 3D volume with an internal structure can be seen as a self generating fractal. But this is not a new idea because there are research teams that are trying to create corresponding models to “build up physical reality from scratch”. For example the Causal Dynamical Triangulations approach. [1]
Moreover, the first known description of such a realistic model originates from Parmenides of Elea (ancient Greek philosopher, about 500 B.C.). So I am sorry but the concept of a “calculated” universe is not an intriguing new idea. It is an unrealistic “persiflage” in relation to existing mathematical concepts (inclusive proposals for a “minimal length scale” by e.g. Werner Heisenberg[2]).
With kind regards, Sydney
References:
Dear Sydney Ernest Grimm ,
first of all thank you for your knowledge enhancing reply! However, all you stated is missing a crucial point:
Simulation of such a hypotized universe in a quantum computer will likely happen outside of our own universe, by some say higher entity. And that entity would imho have no practical problems to simulate all of perceived universe, as exactly like QM (and even todays simple typical ray tracing graphics cards show!) requires or implies - any events will happen only on observation - which practically means it’s a shell game of self consistency only: anything ever observed needs to be „stored„ and properly propagated by physical rules for any further (then consistent) observation.
To your other parts od your reply and given sources: I nowhere claimed this to be my genuine idea, or did I (maybe unintentionally)? So while good to learn from your references, there was and is no need to instruct me (or us) otherwise.
Dear friends of gravity, relativity, fundamental physics, quantum physics and elementary particle physics,
basically, quantum objects as well as vacuum and spacetime propagate according to the Schrödinger equation (Carmesin 2021a,b, Carmesin2022a,c, Carmesin_DPG, Carmesin_DPG_matter). In a semiclassical limit thereof, the principle of least action arises (Carmesin2021c, Carmesin2022b). In this manner, objects appear to find an optimal path.
Kind regards,
Hans-Otto Carmesin
Literature:
Carmesin 2021a: https://www.researchgate.net/publication/350373240_Quanta_of_Spacetime_Explain_Observations_Dark_Energy_Graviton_and_Nonlocality
Carmesin 2021b:
https://www.researchgate.net/publication/353851329_Cosmological_and_Elementary_Particles_Explained_by_Quantum_Gravity
Carmesin 2021c:
https://www.researchgate.net/publication/355889856_The_Elementary_Charge_Explained_by_Quantum_Gravity
Carmesin 2022a:
https://www.researchgate.net/publication/358581911_Quantum_Physics_Explained_by_Gravity_and_Relativity
Carmesin 2022b:
https://www.researchgate.net/publication/359426539_The_Electroweak_Interaction_Explained_by_and_Derived_from_Gravity_and_Relativity
Carmesin 2022c:
Carmesin, H.-O. (December 2022): Unification of Spacetime, Gravity and Quanta. Berlin: Verlag Dr. Köster.
Carmesin 2022_DPG:
https://www.researchgate.net/publication/366275369_Explanation_of_Quantum_Physics_by_Gravity_and_Relativity_-A_Possible_Course
Carmesin 2022_DPG_matter:
https://www.researchgate.net/publication/366275458_How_Excitations_of_the_Vacuum_form_Mass
“How do light and particles know that they are choosing the shortest path?”
To answer to this question it is evident necessary before to answer to the questions – what is “light”? what is “a particle?” what is something where “they are choosing the shortest path? – and what is “a path” at all?”, though, etc.
Really all these questions cannot be answered in mainstream physics, since in the mainstream philosophy and sciences, including physics, all really fundamental phenomena/notions, first of all in this case “Matter”, “Consciousness”, “Space”, “Time”, “Energy”, “Information”, – and so everything in Matter, i.e. “particles”, “fields”, ‘space”, “time,” etc. are fundamentally completely transcendent/uncertain/irrational,
– since from any transcendence quite logically inevitably only any transcendence can follow/be derived. Including, say, what is in the posts in the thread; an example is the rather popular, even “famous” in mainstream philosophy, “simulation hypothesis” of what is Matter and why it is as it is,
- which is evident nonsense; since, say, it evidently implies that besides Matter there exists also in a transcendent somewhere some much larger than Matter something – some unbelievable “a large scale quantum computer”, where some completely transcendent users for some quite transcendent reasons seems play in some computer game; etc.
The fundamental phenomena/notions above can be, and are scientifically defined only in framework of the 2007 Shevchenko-Tokarevsky’s “The Information as Absolute” conception, recent version of the basic paper see
https://www.researchgate.net/publication/363645560_The_Information_as_Absolute_-_2022_ed
- and the informational physical model that is based on the conception, to answer to this thread question it is enough to read the paper https://www.researchgate.net/publication/354418793_The_Informational_Conception_and_the_Base_of_Physics
First of all in this case in the model it is the really rigorously scientifically shown how the absolutely fundamental phenomena “Space” and “Time” are actualized in the concrete informational system “Matter” as the Matter’s fundamentally absolute, fundamentally flat, and fundamentally “Cartesian”, (at least) [4+4+1]4D spacetime with metrics (at least) (cτ,X,Y,Z, g,w,e,s,ct),
- in which the ultimate base of Matter – the primary elementary logical structures – (at least) [4+4+1]4D binary reversible fundamental logical elements [FLE], which compose the (at least) [4+4+1]4D dense lattice, is placed, while everything in Matter are only some specific disturbances in the lattice.
Including particles, including “light” that really is a flow of particles “photons”, are specific disturbances - “close-loop algorithms”, which run basing on the lattice’s FLEs hardware as sequential FLE-flipping,
- which appears at a particles creation, when some the lattice FLE is impacted by some 4D momentum, P, [“bold” means 4D vector] in the at least 4D space with metrics (at least) (cτ,X,Y,Z), and further such disturbances so propagate in the 4D space with 4D velocities that have identical absolute values be equal to the speed of light, i.e. with c., what is determined by FLE “size”, lP, and FLE binary flip time, tP, lP and tP are Planck length and Planck time, c=lP/tP.
At every FLE binary flip the FLE changes its state/angular momentum on the fundamental elementary action/angular momentum that is the Planck constant ћ, what relates to changing of a particle-information on 1 bit;
- and particles motion so happens at minimal number of bits/ changing of information, which is observed in mainstream physics as the “minimal physical action”, which mostly is observed as particles “shortest paths”.
I.e. particles by no means “choose” anything, including “paths”, they simply move in the lattice in the direction that is determined by impacting on particles momentums, and in complete accordance with the logical structures of the FLEs, which [FLEs] know physics absolutely completely.
A few SS posts on page 2 in https://www.researchgate.net/post/Are_there_any_other_theories_similar_to_Participatory_Universe_or_SuperDeterministic_Universe/2 are relevant to this thread question.
Cheers
Without external influences, there is just no reason for deviating from the straight-uniform motion.
Of course, this is the only path along which the action is minimal.
I have asked the same question. there is much exciting research in this area in the past 10 years concerning quantum time dilation.
Deleted research item The research item mentioned here has been deleted
Particles and light do not choose the path they travel, they don't have free will.
“…Particles and light do not choose the path they travel, they don't have free will.….”
- yeah, that is so. However at that it is evidently necessary to understand – why that is so?, i.e. why particles don't have free will? And what are “particles” and “light”, also though.
- the answer see in the last SS post in https://www.researchgate.net/post/What_is_time11#view=63c940bafa2ccd380d0b4943/6 , though to understand that what is written in this post is really true it is useful to read a few other SS posts on at least pages 4,5,6, and links in the posts.
Cheers
It's a no brainer, it does it locally. We are the one who chose the end point, and then devise a mathematical tool to determine the whole path. In Nature there are many particles with many different paths, some of which fulfill our desire.
In our time, science is for engineering, and our view of the world is subjected to that, but is is only one of many other aspects.
Just read Bernoulli and Euler to see that travel along the shortest path is equivalent to travel according to the principle of least reason, the equation of motion.
In engineering, the most important is the destination, so we have the Lagrangien formulation. But it is mathematically equivalent, through a simple Legendre transformation, to the Hamiltonian formulation, that basically describes the propagation of a wave locally. Waves have a built in rod to compare the distances, it is the phase. But it is more general. If there is a conservation law, it is always possible formulate the law of motion in a variational form. So the short answer could be, they don't know, we only use an ad hod quantity that is actually minimized.
Light and particles are not searching for shortest paths, they are creating and defining shortest paths.
Don't miss this sentence. This is the essential, necessary meaning. Only such an explanation can be logical and complete. There is no alternative. The Lagrangian and the Hamiltonian, is defined by the light and the particles themselves, not by Joseph-Louis Lagrange and William Hamilton. They're just discoverers.
Best Regards, Chian Fan
“…Light and particles are not searching for shortest paths, they are creating and defining shortest paths. Don't miss this sentence. This is the essential, necessary meaning. Only such an explanation can be logical and complete. There is no alternative. The Lagrangian and the Hamiltonian, is defined by the light and the particles themselves....”
- yeah, that is so - in the informational system “Matter” that is based on a simple binary reversible logics everything – particles, bodies, fields, etc., absolutely completely know all physical laws/links/constants, and everywhere and always behave in complete accordance with these laws/links/constants;
- including “shortest paths” means minimum number of binary operations that are necessary for particle/body/system to pass from a state one to a state two.
SS post on page 2 June 23 in
https://www.researchgate.net/post/H_denotes_the_constant_ratio_E_f_Ehf_is_it_possible_that_h_has_an_equation_both_without_E_and_f/2 is relevant in this case as well.
Cheers