Independent Researcher

Question

Asked 13th Sep, 2023

# Is there a fundamental difference between coordination systems in classical, relativistic, and cosmological physics, what establishes a difference?

The choice of coordinate systems is a mathematical tool used to describe physical events. Local or universal spatial events occur in multiple coordinate systems of space and time or spacetime as we know it under classical, relativistic and cosmological physics.

Whether the fundamental laws of physics remains consistent across different coordinate systems.

## Most recent answer

Coordination system just imagination of any system. In that particular system, we just calculate any motion or any physical quantity in particular system. All systems do not contain infinite range, all theories are existing till particular coordinates. Dimensions could be change, but coordinate systems remain unchanged. So it doesn't matter.

## All Answers (6)

Tagore's Electronic Lab.

The specific question, in my post, questions the application of Cartesian coordinate system in classical, relativistic and cosmological physics, and how the coordinate system is affected, if any of the fundamental laws of physics are inconsistent among classical, relativistic and cosmological physics,or not?

University of Tours

No. The choice of coordinate systems doesn't and can't matter. The property that can and does matter is the choice of the group of transformations that leaves the equations of motion invariant, whatever the coordinate system is chosen to be. The only effect the choice of the coordinate system can have is in simplifying the calculations.

In applications to cosmology, the group of transformations that leaves the equations invariant is the group of diffeomorphisms; in flat spacetime it's the group of Lorentz boosts, rotations and translations-the Poincaré group. A special case thereof is the non-relativistic approximation, when the group is the Galilean group.

It's remarkable that this isn't taught more forcefully. This hasn't been cutting edge research for at least a century...

1 Recommendation

Tagore's Electronic Lab.

Dr. Stam Nicolis ,

I thank you for your enlightening description which emphasizes in physics that the choice of coordinate system is not as important as the choice of transition group which preserves the fundamental equations of motion. These transformation groups ensure that the laws of physics remain consistent, regardless of the coordinate system chosen. Specific examples of these groups include variations in cosmology, Poincaré groups in flat spacetime, and Galilean groups in non-relativistic contexts. The primary effect of the choice of coordinate system is to simplify calculations, and these principles have been well established in physics for over a century.

These will definitely help me to proceed with my research work with more confidence. I thank you again for your enlightenment.

1 Recommendation

University of Tours

Not only is the choice ``as important as the choice of the group of transformations'' but it doesn't make sense to discuss the two notions together.

1 Recommendation

Tagore's Electronic Lab.

Yes. I thank you Sir Stam Nicolis .

Independent Researcher

Coordination system just imagination of any system. In that particular system, we just calculate any motion or any physical quantity in particular system. All systems do not contain infinite range, all theories are existing till particular coordinates. Dimensions could be change, but coordinate systems remain unchanged. So it doesn't matter.

## Similar questions and discussions

NO.12 Should an Object at rest have Rest Momentum?

- Chian Fan

**A body at rest has rest Energy, so it should also have rest Momentum**.

Lao Tzu said, “Gravity is the root of lightness; stillness, the ruler of movement”(重为轻根，静为躁君)*. The meaning of this statement can be extended in physics to mean that "big-G determines how light or heavy an object is, and rest-m determines how easy or difficult it is to move".

According to the mass-energy equation** [1], E=mc^2, any object with mass m has "rest energy" [1], regardless of its inertial frame†. Note that E here is meant to be the energy lost when radiating the photon γ, which is absolute and unchangeable in any inertial frame. The mass-energy equation has been experimentally verified [2] as the correct relation.

According to special relativity [3], the mass of the same object is different in different inertial frames, m' = βm. Therefore, the energy of conversion of m of an object into photon γ is different in different inertial frames. This issue has been discussed in [4], but there is no consensus. Our view is that the "rest energy" is theoretically not Lorentz invariant, and the existence of a minimum value is a reasonable result. The most rational explanation for this is that the minimum corresponds to an absolutely static spacetime, i.e., absolute spacetime(Later we will show that absolute space-time and relative space-time are not in conflict). Analytically, this is one of the reasons why absolute spacetime should exist. The constant speed of light is another reason.

In all cases in physics, energy and momentum coexist and have a fixed relationship, not independent metrics. The energy-momentum ‡ of a photon, E=hν[5], P=h/λ[6]; the energy-momentum relation of Newtonian mechanics, E=P^2/2m; and the relativistic energy-momentum relation, E^2=c^2p^2+m^2c^4. Therefore, it is assumed that if there is a body of mass m that has "rest energy", then it should also have "rest momentum". There is a "rest momentum", and the rest momentum cannot be zero. The rest energy is not intuitive, and the rest momentum should not be intuitive too. The calculation of the rest momentum is the same as the calculation of the rest energy.

**The nature of mass looks more like momentum**; after all, energy is a sign of time, while momentum is a sign of movement. Therefore, instead of calling it the principle of equivalence of inertial mass and rest-energy[1], it should be called the principle of equivalence of inertial mass and rest-momentum. When positive and negative electrons meet and annihilate [7], -e+e→γ+γ, radiating two photons in opposite directions. Their energy is conserved and so is their momentum. Energy is a scalar sum, while momentum is a vector sum. It seems that the "rest momentum" inside the object should be zero. However, one could argue that it is actually the momentum of the two photons that is being carried away, but in opposite directions. The momentum of the two photons should not come out of nothing, but rather there should be momentum of the two photons, also in some balanced way, and probably playing a very important role, such as the binding force.

**Our questions are**:

1) Since energy and momentum cannot be separated, should an object with "rest energy" necessarily have "rest momentum".

2) Elementary particles can be equated to a " energy packet ", and energy is time dependent. If an elementary particle is also equivalent to a "momentum packet", the momentum in the packet must be related to space. Does this determine the spatio-temporal nature of the elementary particles? And since momentum is related to force, is it the force that keeps the "energy packet" from dissipating?

------------------------------------------------------------------------------

**Notes**：

* Lao Tzu，Tao-Te-Ching，~500 BCE. This quote is a translation of someone else's. There are some excesses that I don't entirely agree with. Translating classical Chinese into modern Chinese is just as difficult as translating classical Chinese into English.

** There is a historical debate about the process of discovery of the mass-energy equation, and digging into the history shows that there were discoverers and revisers both before and after Einstein, see literature [8][9]. Important contributions came from Poincaré, F. Hasenöhrl, Planck et al. Their derivations do not have the approximation of Einstein's mass-energy equation. And there is also a debate about the interpretation of the mass-energy equation. Notable debates can be found in the literature[10].

† There is a question here, i.e., is the rest mass Lorentz invariant? That is, is the rest mass the same in different inertial systems? Why?

‡ Einstein questioningly emphasized that energy and momentum seem to be inseparable, but did not explain it.

------------------------------------------------------------------------------

**References**：

[1] Einstein, A. (1905). "Does the inertia of a body depend upon its energy-content." Annalen der physik 18(13): 639-641.

Einstein, A. (1935). "Elementary derivation of the equivalence of mass and energy." Bulletin of the American mathematical society 41(4): 223-230.

[2] Rainville, S., J. K. Thompson, E. G. Myers, J. M. Brown, M. S. Dewey, E. G. Kessler, R. D. Deslattes, H. G. Börner, M. Jentschel, P. Mutti and D. E. Pritchard (2005). "A direct test of E=mc2." Nature 438(7071): 1096-1097.

[3] Einstein, A. (1905). "On the electrodynamics of moving bodies." Annalen der physik 17(10): 891-921.

[4] Is there a minimum value of m in the mass-energy equation E=mc^2? https://www.researchgate.net/post/NO7_Is_there_a_minimum_value_of_m_in_the_mass-energy_equation_Emc2；

[5] Planck, M. (1900). " " Verh. Deutsh. Phys. Ges 2: 237.

[6] Einstein, A. (1917). Physikalisehe Zeitschrift xviii: p.121

[7] Li, B. A. and C. N. Yang (1989). "CY Chao, Pair creation and Pair Annihilation." International Journal of Modern Physics A 4(17): 4325-4335.

[8] Ives, H. E. (1952). "Derivation of the mass-energy relation." JOSA 42(8): 540-543.

[9] Sharma, A. (0000). "The past present and future of the Mass Energy Equation DE =Dmc2." http://www.mrelativity.net/Papers/8/Sharma4.htm.

[10] Peierls, R., J. Warren and M. Nelkon (1987). "Mass and energy." Physics Bulletin 38(4): 127.

## Related Publications

The ``Cosmological Constant Problem" is generally regarded as one of the outstanding unsolved problems in physics. By looking at the actual physics behind the mathematics we show that a natural and simple resolution is provided by the fact that general relativity, the theory used to model cosmology, is a fundamentally classical theory of actual cla...

We have been told that nothing can travel faster than light, but in fact, most of the Universe has traveled away from us at superluminal speeds since time began, and in order to understand how that happens, we will need a brief introduction to cosmology and the relativistic Friedmann model for a radially expanding universe.