martillo

... Fine if your intention is just to represent all rational numbers. A different story is to represent the physical Space of the Universe.

In a) which would be the finite size of the steps? In b) it would depend if the space is infinite or finite.

Seems it all depends in how you define the steps or the resolution of the grid.

I think it would depend on how the grid is defined. For instance could be a grid in steps of 1/3 or whatever 1/n with integer n. Some rational numbers could apply in a grid while others don't. But of course an entirely integer grid could in principle be possible too. As @joigus said may be is something undecidable for us.

I agree. +1 Except if the space be actually discretized in a grid with some imperceptible resolution. In this case places represented by irrational numbers would not really apply.

Yes, in the case of a discrete grid the number of the steps in any finite time would be finite, countable. If there's no grid, the movement is continuous and can be thought as in uncountable infinitely small steps.

Could a difference be in if there exist a grid on the space or not? I mean, a difference would be if the movement of the particles would be in discrete steps or continuous.

I apologize, it wasn't you that said that the "proper time" is the same for any observer. Actually seems it isn't the case. May be it applied for a special case only. Searching about the concept now...

Why have you presented that thought experiment where there's no time dilation then? I don't get it. Some time dilation must have happened and the twins would not present the same age at the end in your example:

Someone said otherwhere the "proper time" is the same for any observer. Can it be said that "proper space" is also the same for any observer? Then would follow that "proper space-time" is always just an Euclidian flat space and an absolute time the same as in Classical Physics. The "space-time curvature" would be just apparent to the observers. The problem with this is that Relativity Theory becomes just an "apparent theory" describing things that actually does not take place anywhere. This is not what is sustained by the mainstream. It is said for instance that time dilation is real with the example of the muons' decay as an experimental proof for RT. Something does not match to me here...

This only enforce my thinking in that a complete new theory is needed.

Thank you, martillo. We agree in some things while disagreeing in the end: I don't believe any possible ether solves the things, I think in a complete new theory or model on an empty space. I think the current theories are true only in part and wrong in other parts. The big challenge is to build the puzzle with all the right parts only. The try on "welding" them is a dead end row for me.

Said to Genady: The exceptions make the rules. 😄 (all math...)

The exceptions make the rules. 😄 (all math...)

A necessary but not sufficient condition, I agree...

I saw it, "Enough of crackpots...". May be I'm considered as crackpot so I must mention two geniuses: "Without speculation there is no good and original observation." Charles Darwin. "No great discovery was ever made without a bold conjecture." Isaac Newton.

No, mathematics is not the machinery that runs the universe. Is the "tool" to describe the laws but does not explain how they are implemented.

Right, but this does not prevent us to think in how the laws are applied over the particles to make the universe run. As you said in that post: Still sailing I think.

"The Feynman Lectures on Physics": https://www.feynmanlectures.caltech.edu/I_07.html (just with a google search) Thanks for the readings. Very helpful. +1 I stay with: "No one has since given any machinery." I think all those geniuses didn't have the opportunity to know about computers and virtual games...

For me the fundamental entity is force F and the emergent property is Energy E defined as: E = ∫Fdx. Yes they do. IMHO the "Wave Mechanics" part of QM is not real. The concept of the photon and its dynamics (E = hν, photoelectric effect, Compton effect, etc.) is real. The equation E = mc2 is real for the photons but considering photons with mass m such that λ = h/mc. It is that those formulas do work but the theories developed behind are wrong for me. They are valid but for different physical phenomena than the described by those theories or models. Unfortunately I can't explain it more, entering in the category of personal theories I know...

I knew the conversation could lead us to the subject of wave-particle duality and here my participation reaches the end I think. I'm currently working on a model of particles that explains their wave-like behavior so solving the wave-particle problem for the particles' approach but I know this enter in the category of personal theories and I perfectly know I cannot go on with this here (@swansont remarked it to me several times). The wave-like behavior is explained with the concept of trains of particles which leads to a structure for the particles, a new model of the elementary particles surge and so on. Impossible to describe all this shortly. Too many areas of Physics affected. I appreciate very much all the time given to me by all of you in the forum. It is very important in my work to be able to discuss some things here but for my pain I'm not able to continue the conversation. Thanks a lot anyway.

Right at the beginning in your link it is said: "The Ehrenfest theorem, named after Paul Ehrenfest, an Austrian theoretical physicist at Leiden University, relates the time derivative of the expectation values of the position and momentum operators x and p to the expectation value of the force �=−�′(�) on a massive particle moving in a scalar potential �(�),[1]" Then it deals with particles. It deals with waves' functions but associated to the position and momentum of the particles. The associated Schrodinger's wave equation for instance, is related to the probability for a particle to be at some position at some time, it does not represent a particle made by waves but a wave mathematically associated to a particle. It's all about particles at the end.

I'm trying to get to your point but it is being rather difficult for me. I think what you are really asking is which of them, forces or energy, actually determines the kind of the reality of the universe. I mean, Newtonian Physics seems to be force based -- everything made by the forces -- while Relativity Physics seems to be energy based -- everything made by energy. If this is not what you are asking please let me know to be able to answer you properly. If that is actually the case then I would stay with forces because is what let me choose between a particles-based universe against a waves-based universe. Waves cannot explain forces. Only interference with addition or subtraction of their intensities is possible between waves, a wave cannot exert a force to another wave. For instance how to explain attraction or repulsion between things made of waves, how to explain collisions and bounces between them? All of them well verified as present in the reality we are. The universe becomes then particles-based then and not waves-based. Forces is then the determinant thing of the reality of our universe.

Both, forces and energy are two things of the same reality. Why only one would be real and the other not? You are right. Actually that experiment hasn't been tested for considerable different velocities in the labs so I cannot reach a valid conclusion. Only if different results would be obtained the existence of a preferred frame would be deduced. As for now you are right there's nothing that can demonstrate the existence of that frame. @swansont is right in that what matters in that experiment is the velocity relative to the crystal target.

But the 'rest' wavelength of a particle at rest is always infinite. λ =h/mv.