Dear Ni Ge,

  Why we cannot know the coordinates of the other referential? And what do you mean by "resolve the Heisenberg's undertainty principle"?

All the best,

Lucas

My question needs a lot of SRT/GR understanding.

Since, it should be clear that there is no time dilation (see my other question why), we can't determinate with exactitude what is happening between two moving referentials. So it seems that special relativity is the same problem as the problem to find the position and the speed of a particle (If we think about it, it is as we were the ground observer and our particle the moving observer).

In SRT/GR, we use Lorentz transformation to find each position. Why wouldn't we use them to find a position of a particle, it is why maybe Lorentz transformation could help us.

 Dear Ni Ge,

read my question below

https://www.researchgate.net/post/Why_Einstein_was_hating_Heisenberg_uncertainty_principle

We don't use Lorentz transformations to "find each position" any more than we used Galilean transforms in pre-relativistic physics. Such transformations aren't used for "finding" the position of anything. Lorentz transformations tell us e.g., that if I observe some event E from my position at time t at with coordinates (x,y,z) from my reference frame P, and you observe the event from reference frame P', I can account for the discrepancies in our observations. In other words, when we find effects like time dilation (which absolutely does occur), even though the disagreements between two reference frames involving this time dilation are equally "right" yet differ, we can use Lorentz transformations for either reference frame to derive the observations of the other.

What we can't do is use them to find the coordinates of something that we don't know the coordinates of except in so far as they seem not to have them (except when observed).

Dear Andrew,

I am sure that time dilation doesn't occur (see my other question why) and I would not like to discuss about it here, so you must assume here that it does not exist. If it doesn't exist, then you will see that in SRT you can't find anymore the right position by drawing what is happening (except with Lorentz transformation, but I am not sure).

Uncertainty principle is  consequence of non-commutative nature of position and momentum. There is no such thing in  relativity.  You can be sure  that there is no time dilation, but I think it is verified experimentally beyond any doubt. 

If you don't allow time dilation, you don't have the LT.  That means the laws of physics are not invariant. in different inertial frames.

Dear Debajyoti,

Did you read my question about two observers (0m and 5000m) comparing pictures taken in each referentials? Because of Shapiro effect, pictures should not be the same, they still are!

For a discussion about relativity, I propose you to read p.95/+99:

https://www.researchgate.net/post/When_it_comes_to_simultaneity_is_Einstein_correct_or_is_Dingle_correct

LT remain pertinent (since light is a constant), even for absence of dilation (see my picture).

Dear Ni Ge:

Ok. For the sake of argument, time dilation doesn't occur. Is length contraction out to? If both are, then what is the point of Lorentz transforms rather than classical (Galilean) transforms? Also, regardless of the point, as Debajyoti Sarkar stated, there is no uncertainty principle in special relativity. In fact, there is no uncertainty principle outside of quantum physics (I include particle physics as quantum physics here). Lorentz transforms are transforms. Given a frame of reference and a set of coordinates for e.g. a classical "particle" moving along some trajectory, you can transform the coordinates of the particle for any "slice" of spacetime such that you derive the coordinates for the particle from as "observed" from a different reference frame.

Perhaps there is an easier way to explain why your suggestion, creative though it is, can't work. Quantum systems do not have defined trajectories or locations except when measured. However, to measure anything you have to interact with it in some way, whether via light (as in e.g., vision or most microscopes), or bombarding it with something other than photons. The problem is that EVERY measurement of a quantum system fundamentally disturbs it. And it disturbs it in particular ways that depend mostly on what is measured most precisely. The classical example is position vs. momentum. The more I know where e.g., an electron is at time t, the less I can know about its trajectory because I've just knocked it in some direction by bombarding it sufficiently "hard" in order to get a good reading on its position.

Let's say I do this. I try to determine with great precision the location of a particle at time t. If all I'm concerned about is its position, then I have it. If I want to know where it will be, then how can Lorentz transforms possibly determine this? Similarly, if I measure it repeatedly but very gently, I will have a very low resolution in terms of position but I will have a much better idea about trajectory. Again, how can Lorentz transforms help?

Dear Andrew,

Galilean transformations doesn't work, because mesured with it light could be faster than c. Then you have to use LT. For the second part of your argument, I propose you to measure first the velocity, then use LT to find the position of it.

I know Galilean transformation doesn't work. It doesn't work because there is no absolute uniform motion. Alternatively, it doesn't work because classical "relativity" had assumed an absolute that everything could be seen as moving with respect to, and this assumption was wrong.

That wasn't my point. My point was that coordinate transformations of any type are irrelevant here. Heisenberg's uncertainty principle is based on the fact that there exist systems so small that any kind of measurement/observation disturbs them. In classical physics, the assumption was that we could measure any "observable" (any measurable property of the system) arbitrarily gently. If you are in a house during a power-outage, and you have a flashlight, turning it on will not cause windows to break, tables to fall over, or poke wholes in walls. Yet light can disturb systems (recall the photoelectric effect). By "disturb", I do not mean effects like shining a light in someone's eye or other obvious effects; I mean something like the photoelectric effect in which the constituent parts of a system are reconfigured or lost the way that under certain conditions we can detect the ways in which light waves "hit" metal, causing the emission of electrons. I am also talking about visible light, not e.g., infrared or UV light (or lasers, for that matter).

The point is that for a long time light was used as the primary way to measure properties of some system (whether via microscopes, vision, telescopes, etc.). Moreover, the disturbance caused by shining a light on something was so negligible the real source of measurement error was due to our experimental equipment. So there was good reason to believe that no matter how small or "delicate" a system was, we could always make our measurements "gentle" enough so as to not disturb the system any more than shining a flashlight at the moon disturbs the moon.

Quantum physics changed this. The uncertainty principle is commonly thought of as some kind total cut-off: electrons are so small that anything we want to know about them is limited by this "uncertainty" line we can't cross. In reality, the uncertainty principle is actually more like a way to determine HOW certain (and uncertain) a measurement can be and in particular the relationship between a more "certain" measurement of one property (spin along the x-axis, say) vs. another.

In fact, a lot of the "uncertainty" in quantum physics has nothing to do with the uncertainty principle. Some would argue almost all of the uncertainty is unrelated to the uncertainty principle. Whatever the case, Lorentz transforms can't suddenly make an electron stay in one place so that we can examine it's spin, measure it's velocity (by measuring its position, trajectory, and the distance traveled over some interval of time), or enable us to perform experiments in which quantum physics is temporarily suspended so that we can make classical measurements of quantum systems.

"Because of Shapiro effect, pictures should not be the same, they still are!"

Please show me a reference paper on it.  Make it clear about which experimental result you are talking about.

"I propose you to measure first the velocity, then use LT to find the position of it."

When you measure velocity, the  state collapses to a momentum eigenstate. Hence it is not possible to know the position of the particle as it is projected all over the position space.

Secondly, how can you find position just by measuring velocity? Two particle at different position can have same velocity.

Dear Andrew,

"Heisenberg's uncertainty principle is based on the fact that there exist systems so small that any kind of measurement/observation disturbs them."

I am not sure it was Heisenberg's thought, but Schrodinger's view.

Dear Debajyoti,

Actually, there is nowhere where you can find a discussion of it, because the reasoning is new and hadn't been treated by any paper (try it and you will see I am true).

To find the position with the velocity, I propose you to use the detectors (ground referential) position and add the LT speed (measured). But maybe I am wrong and you can't mesure it either on particles than with SRT. Then LT are incomplete.

I am not an expert on quantum physics, then you both might be right and I apologize for asking a such question.

Dear Ni Ge:

Schrödinger was the first to demonstrate that Bohr's attempt to divide the quantum realm not only from the classical but from reality (a netherworld of infinite-dimensional abstract Mathematica space) faced serious problems. His thought experiment didn’t just involve the idea that observation of quantum systems always results in non-trivial disturbances (what was the point? Heisenberg showed that a decade beforehand). His thought experiment demonstrated two things, each of which corresponds to one of the thought experiment’s two parts. The first part is linking the microscopic to the macroscopic in precisely the way Einstein, Bohr, Heisenberg, and just about everybody thought we shouldn't (although they disagreed as to the solution). A cat is in a box with a vial of poison that is sealed. However, it has a “timer” that will release the poison. Specifically, the vial of poison is triggered by atomic decay- a microscopic system so small it requires quantum mechanics. However, quantum mechanics demands that the atom be both decayed and not decayed (the superposition principle). Quantum experiments have shown this over and over and over again. The problem is that in this case the superposition state of the atom is what triggers the release of the poison, so one state triggers its release and the other doesn’t. Even worse, this means that one state results in the cat dying and another in the cat living. This was a dramatic illustration of the problems associated with thinking of quantum systems as isolated.

The second part of his experiment wasn’t about observation disturbing small systems, but the opposite. For many physicists, so long as all quantum “weirdness” took place in some other-worldly universe divorced from ours, the fact that these systems were so small that any observation/measurement would disturb them was nothing compared to the idea that, because quantum mechanics was a theory of the subatomic realm, and we are all made up of atoms, we might have to face the ways in which weird world of quantum physics carries over into our own.

The second part of Schrödinger’s thought experiment showed another unwanted link. Measurement in quantum mechanics (particularly after 1927) was supposed to be the only connection between quantum systems and reality. In other words, the “state” of a quantum system was a mathematical function, and the system a mathematical entity. Schrödinger showed that this entailed problems as well. The act of observation was said to “collapse” any superpositional state into a single, observed state. However, all experiments that confirmed this did so with tiny systems. By connecting the cat to the superposition state of the decayed or not decayed atom, Schrödinger set up a system that could be measured (in theory) the way all quantum measurements were made (and still are, in a certain sense). Opening the box didn’t just force an atom to be either decayed or not decayed, but a macroscopic system, a cat, to be alive or dead.

Schrödinger didn’t show that quantum systems are always disturbed by measurement. He showed that we can connect this disturbance to macroscopic systems. Heisenberg dealt with the ways in which systems will always be disturbed, but he was content to have these systems treated as isolated from our realm of experience. Schrödinger went in exactly the opposite direction: he showed that we can fundamentally “disturb” macroscopic systems.

We’ve done this now. There have been many, many experiments in which meso- and macroscopic systems are put in superposition states. The largest I know offhand was a molecule consisting of 430 atoms that was in two places at once (the paper was published in one of Nature’s journals in 2012).

Dear Andrew,

I completely agree with you. But in fact disturbed systems by measurement have never been proved. Schrödinger cat's box helps to understand that before opening the box, we can't say what is the state of the cat until the opening of the box provoking the state. (it is not the timer or the beam which provoke the cat's death/staying alive, but the opening of the box/measurement: why the cat is in a box?)

 This question was adressed by Salah Horchani in 1971, Sur un nouveau groupe de symétrie de la mécanique quantique relativiste, which appeared in Annales de l’Institut Henri Poincaré A, vol. 15, p. 321-349 http://archive.numdam.org/ARCHIVE/AIHPA/AIHPA_1971__15_4/AIHPA_1971__15_4_321_0/AIHPA_1971__15_4_321_0.pdf.  Yes, you do have to extend the Lorentz generators Mµn = xµd/dxn - xnd/dxµ to  their semidirect product with momenta d/dxµ and coordinates xµ, satisfying together the Heisenberg relations  [d/dxµ, xµ] = 1, to result in a 15-dimensional Lie algebra isomorphic to a contraction of the conformal one.

Dear Joël,

I don't understand a lot (as I said I am not an expert in quantum theory, maybe nor enough in mathematics), but this article seems to be REMARKABLE (I hope this article is well known by scientific community).

THANK YOU JOEL

Dear Ni Ge:

First, I would argue that any thorough analysis of the sciences reveals that proof is left to mathematics. We prove theorems, not theories. Second, there is no “disturbed system by measurement” theory, hypothesis, or similar notion that could even lend itself to a proof. To illustrate, imagine that we could prove things by experiments. The whole of quantum physics, particle physics, and the standard model do not just base this notion of disturbance on repeated experimental validation. It’s intrinsic to modern physics, and for good reason. Take away the principle and you essentially collapse a century or so of progress in physics.

As for Schrödinger cat's, it seems you are missing the core of the entire thought experiment (and actual experiments with quantum cats/kittens in the past decade or so). It’s not that before we open the box we do not know whether the cat is alive or dead. It’s that quantum physics requires the cat to be both alive AND dead until we open the box. To reiterate: opening the box doesn't tell us what the state of they system is (i.e., it doesn't tell us anythihng about whether the cat was alive or dead). Before the box was opened, both states (alive and dead) were true in that the cat was BOTH alive AND dead. Opening the box doesn't reveal whether the cat was alive or dead, it MAKES the cat either alive or dead.

Dear Andrew,

Quantum state, uncertainty principle and measure indetermination are three different things.

Dear Ni Ge:

We seem to be at a sort of impasse here, as both of us are describing quantum physics and stating that different things are true according to quantum physics. However, your last reply gave me an idea, because what you state are different things are very, very, very much connected. Better yet, you include "measure indetermination" as one of the elements of quantum physics that is different here. This gives us an opportunity to see where the breakdown in communication is. Heisenberg's uncertainty principle deals with observables, observables "act on" quantum states, and measure indeterminacy relates to the measurement problem and why observable properties aren't values but functions.

So all three concepts you bring up give us an ideal way to address the problem through a few simple questions:

1) Quantum physics has several basic postulates that underlie the entire theory. One of them is that the quantum state tells us everything about the system, or that it contains all the information about the system, or in various other phrasings that the state-vector we use tells us everything there is to know about the system. Another basic component of quantum physics is that there is not, even in theory, any possible way to know even a single property of a quantum system with such perfection, and the more we know about one property the less we know about others. To some this appears to be paradoxical, but it is actually quite  elementary and provides a good basis to establish common ground. To that end: why does quantum mechanics have as an axiom/postulate (something that is so intrinsic to the theory that without it the theory doesn't exist) state that we know everything there is to know via the state-vector or wavefunction, yet another basic, elementary, and crucial component of quantum physics (the uncertainty principle) tells us we cannot obtain sufficient information about a quantum system to determine even a single observable property exactly, let alone anything remotely close to to all possible observable properties Why is this?

2) You state that measure indetermination is distinct from the uncertainty principle. Can we measure the energy and momentum of an electron without disturbing it? If yes, how? If no, how is this not he uncertainty principle?

3) Imagine we have prepared a quantum system, and represented the values and so forth of this system the way we would in classical physics or basically all sciences (we represent notions like mass, speed, acceleration, etc. using values.). In order to prepare a quantum system. What about this process caused Einstein and later physicists to develop an ensemble interpretation of quantum mechanics?

4) Imagine I have some quantum system I have prepared and transcribed into a wave-function or similarly allowable representation in quantum physics. To what does this notation correspond to? That is, if I measure the velocity of a car, I can easily point to the car and say that the velocity is the sped at which it travels along a particular trajectory. Why doesn't the state of a quantum system correspond to anything in reality?

5) When we "measure" a quantum system, what role do observables play and why?

Dear Andrew,

When I read Joel article, it seems that relativistic quantum mechanics solves the observables problems by the concept of "localization" (not included in Galilean).

Did I well understand, Joel?

Quantum mechanics is a "complete" theory in a certain technical sense of the term. From a more common perspective, it isn't at all complete because quantum and particle physics build upon quantum mechanics and because other areas of physics are incompatible with all quantum physics (at the moment). That said, there is no accepted formulation of quantum physics, relativistic or not, which solves a number of fundamental problems in modern physics. As for "observables", they are Hermitian matrices that are constructed prior to any observation or measurement and they never yield values that correspond to any system in reality (i.e., any system that exists, any physical system, or any system that is known beyond statistical distributions and the like).

I just skimmed through Joel's link (why is it that French can't just have words like Lie Algebra but require "algèbres de lie"? It's almost as bad as classical Greek). but I can tell you the answer is definitely "no". Mostly because the issue isn't addressed. Also, there are many relativistic quantum mechanics. QED is probably the oldest and most studied, but neither it nor QCD nor indeed the standard model is without the problem of "localization" (as you put it).

Ni Ge,

I do not think that the classical Lorentz Transformation, LT, need to have anything to do with Heisenberg’s uncertainty principle.

However, if you consider the mathematical abstraction of LT to the Minkowski space you have the fundamental invariant: the Eigentime and its conjugate the Klein-Gordon relation, see more below.

If you now replace the classical entities with QM operators in the Klein-Gordon equation: -Eo2/c2=p2-E2/ c2, and in the conjugate Eigentime expression –c2d𝜏2=dr2–c2dt2, you will see that the whole (STR) structure is commensurate with the mathematical non-commutation relations of energy-time and momentum-space (Heisenberg) of fundamental importance in quantum mechanics.

Within this perspective LT is not incomplete, except that it does not contain gravitation.

Dear Erkki and Joel,

Then who is right? Salah Horchani (Lie) or Klein-Gordon (Euler-Lagrange)?

Thank you for your wise answers.

I think Horchani. Klein and Gordon maybe too, but they remain on the ground observation.

Ni Ge,

I think you said it.

Hi, 

In the usual approach, momenta are operators acting on the field of coordinates, which produces a dissymetry between them; Horchani's approach was to treat the coordinates themselves as operators on the same footing as momenta, and therefore fit to handle symmetrical questions such as Ni Ge asked. The problem becomes to provide a physical interpretation to the additional dimensions which appear then (as in the 6-dimensional representation of conformal Lie algebra). In string theory they label those as "very small". But nothing requires such a constraint in Ni Ge's question.

Dear Ni Ge,

Heisenberg uncertainty principle according to my transforms is related to time dilation and length contraction, by reinterpretation the Lorentz transformation according to Copenhagen School. Which leads the Lorentz factor is vacuum energy dependent by refusing the reciprocity principle. According to my transformation it is impossible the moving observer and the observer on the ground that agree the location of the moving train at the same point in space on the ground at the same time. That is because each observer has his own picture about the time and the passed distance of the moving train because of time dilation and length contraction. By refusing the reciprocity principle, it is resulted to commutation relations when we dealing with the four vectors according to my transforms. Remember according to my transformation it is leading to the wave-particle duality, and the concept of acceleration or deceleration is leading to vacuum fluctuations. See the attached file which represents a null vector. and read my paper.

I TOLD YOU NI GE I SUCCEEDED IN QUANTIZATION OF GRAVITY.

http://dx.doi.org/10.14299/ijser.2014.10.002

Have a look on my book "ESSAI (version V2) - L’univers pourrait-il être un réseau 3D et la matière ordinaire en être des singularités topologiques ?". You could find some interesting answers!

Book L’univers pourrait-il être un réseau 3D et la matière ordina...

Data Illustrated summary of the book "Universe and Matter conject...

Research Proposal Could the universe be a massive elastic 3D-lattice and ordin...

Dear Prof. Gremaud,

Thank you for the link. I think your theory is a wonderful explanation about how we can understand friction forces with Lorentz Transformations.

It seems that some researcher are on the way:

http://www.nature.com/news/how-gravity-kills-schr%C3%B6dinger-s-cat-1.17773

But it is not a matter of time dilation. Lorentz Transformations seems to be wrong.