INRE:"... most physicists and mathematicians struggle to find a practical definition". Perhaps you can cite some source that there is any sort of 'struggle' - there is a well established definition of time, the inverse of 'universal' which is the 'relative' in the theory of relatively. And it is very 'practical', evidenced by billions of dollars of terrestrial ( fiber optic networks ) and space based infrastructure ( GPS and Starlink ) - see "Inside the box: GPS and relativity" ( https://www.gpsworld.com/inside-the-box-gps-and-relativity/ ).

The accounting of relative frames of reference is what makes these possible: "There is more to relativity than the special theory and general theory. There is the Sagnac effect associated with our rotating reference frames attached to Earth, in which we’d like to determine a position. The principle of constancy of the speed of light cannot be applied in a rotating reference frame, where the paths of the radio rays are not straight lines, but spirals. (Receivers at rest on Earth are moving quite rapidly: 465 meters per second at the equator.) There is also the Shapiro delay associated with the slowing of electromagnetic waves as they near Earth, which amounts to a fraction of a nanosecond.

And utility of 'non-universal', ie. 'relative time is demonstrated at scales from the subatomic in colliders to the cosmic with data from the James Webb Space Telescope - because any observer by definition will be in their own frame of reference.

And incidentally, it would have to be 6D+, not 4D because rotation would have to be accounted for.

This is only a

preliminary answer first to shed light to the question (what are the different temps of the university?) and its answer and second to thank our fiend from INRE for his helpful answer.

In fact, it is the most direct response and the most clear on the subject.

(Is there any  link to citation from a source on a type of struggle into physical science, mathematics, etc. on the definition of the time.

In the next phrase INRE affirms that it is clear that the milliards of dollars are spent each year in the search for the true terrestrial and non-terrestrial temps (universal)!?

Here It is necessary to explain what is  the  definition of physics which is composed of two parts, experimental and theoretical physics:

1- The experimental physique concerns the measuring  of phenomena  depending on time.

We all know that the Earth real time t defined as 1 second =1/86 164.09053 of the time of revolution of the Earth around the sun (one year) is not universal but only local to our Earth and is not eligible to universal physical calculations.

The universal experimental time can be achieved or measured via the atomic clock.

2- The only universal theoretical time in a 4D x-t unit space is that presented by Einstein in his special relativity.

This is a very successful development, but one with inherent flaws.

A. Einstein did not specify or rigorously define the time interval dt that can be applied to general time-dependent situations.

This means that Einstein's specificity to time in what is called event space remains limited to the case of two inertial frames of reference.

To be continued

1- A rigorous reform of mathematics and physics, ResearchGate, IJISRT journal,

January 2025.

> This is only a preliminary answer first to shed light to the question (what are the different temps of the university?) and its answer and second to thank our fiend from INRE for his helpful answer.

[Clarification, "INRE:" is an email convention, and abbreviation derived from “In re” a Latin phrase that means “in the matter of”]

INRE: "university", did you mean 'universe'?

>Is there any link to citation from a source on a type of struggle into physical science, mathematics, etc. on the definition of the time.

INRE:"definition of the time". I would submit that the term "time'( and thus any entailing "definition of time" ) is so generic the word is useless, without some declaration of even rough ontological frame of the domain(s) involved ( https://en.wikipedia.org/wiki/Ontology_(information_science)#Domain_ontology ). For instance, that might be along some chosen abstract axes, from pure symbolic math(s) applied mathematics theoretical physics experimental physics applied physics technology engineering operations to ordinary human senses and cognition: all of these domains have their own lexicon(s). On naive observation it might appear looking at the entire chain that there is some sort of 'struggle' with a common definition, but the terms representing the concepts ( lexicon ) are well established and have internal consistency within each domain, and the interfaces between the domains. Any perceived lack of 'commonality' across domains might also be induced by historical legacies as each domain has been evolved and refined over time.

INRE: "In the next phrase INRE affirms that it is clear that the milliards of dollars are spent each year in the search for the true terrestrial and non-terrestrial temps (universal)!?

The figure I mentioned was not in reference to 'search' ( R&D? ), it was for already practical established operational products and services, and it wasn't expressed as millions ('milliards'?) of dollars I said 'billions' - the annual global market size for Positioning, Navigation, and Timing (PNT), which are fundamentally based on the existing robust definitions of time is valued at USD 103 billion in 2023 ( Source: https://www.fortunebusinessinsights.com/gps-market-110523 ). That is just the PNT equipment - globally there is trillions of dollars of infrastructure that relies on that equipment across all sectors of the world economy. All of that relies on reliable excruciatingly detailed domain "practical" definitions of "time".

At the other end of the spectrum, the R&D 'search' aspect, the $4.75 billion Large Hadron Collider (LHC) which is basically a large relativistic 'clock' and just the narrow quantum computing market size alone is worth 1.6 billion USD ( https://www.marketsandmarkets.com/Market-Reports/quantum-computing-market-144888301.html ). That points to what the universal common definition of 'time' currently is. The notions of sideral and solar time represented as "1 second = 1/86164.09053 of the time of revolution of the Earth around the sun (one year)" hasn't been the case for nearly a century, when Sidor Rabi proposed clocks based on atomic beam magnetic resonance (1930's).

Which leads to the current definition fundamentally based on the Theory of Relativity, that it is a property of space itself, the relationships between mass, energy, and velocity - "time" is somewhat buried in the 'E' and 'c' variables which are based on time in conventional equation E=Mc2.( Sabine Hossenfelder briefly addresses this emerging 'edge' of knowledge in "Is Time Real?" at https://youtu.be/PdL8CudJTcs?t=259 )

But there has been no contrary evidence in any of the domains that suggest is 'struggling' ( https://www.nist.gov/programs-projects/optical-clock-atomic-structure-and-theory ), although there is some minor controversy about M ( the gravitational constant https://physics.nist.gov/cgi-bin/cuu/Value?bg ) at cosmological scales ( https://link.springer.com/article/10.1007/s10569-023-10138-3 ) - but escape velocity near a black hole probably need not be included in a "practical definition.

> Here It is necessary to explain what is the definition of physics which is composed of two parts, experimental and theoretical physics:

INRE: "... composed of two parts, experimental and theoretical physics". Two categories are insufficient to support an approach to 'time definition'( See the 'domain chain' mentioned above: "pure symbolic maths applied mathematics theoretical physics experimental physics applied physics technology engineering ...". All of these domains inform each other up and down the chain. Consideration of only those two ( experimental and theoretical ) fails because it doesn't include the 'math(s)' categories which provides the fundamental conceptual tools that support descriptive and predictive efforts ( an example of this is found in the progress of quantum mechanics, new math(s) created an explosion of new insights: https://en.wikipedia.org/wiki/History_of_quantum_mechanics ). Information also comes from the opposite direction, from inconsistencies revealed by implementing engineered systems in the real world ( like satellite communication revealing the 'beginning of time", The Big Bang https://en.wikipedia.org/wiki/Cosmic_microwave_background#Discovery).

INRE:" ... presented by Einstein in his special relativity. ... This is a very successful development, but one with inherent flaws.

A. Einstein did not specify or rigorously define the time interval dt that can be applied to general time-dependent situations."

This means that Einstein's specificity to time in what is called event space remains limited to the case of two inertial frames of reference."

Of course he didn't define some sort of 'interval' 'dt', as with 'time' defined withing a reference frame - it wasn't the domain he was addressing, and a 'theory should be conceptually simple but that doesn't prohibit extension for situations involving greater complexities. Those concepts appear much further along the chain, in those other domains. It isn't limited to "the case of two inertial frames of reference", the StarLink system will have 12,000 satellites ( possibly 42,000 ) each with it's own inertial frame of reference, communicating with each other via lasers ( https://www.lightnowblog.com/2024/02/ir-lasers-link-9000-starlink-satellites-and-move-42-million-gb-per-day/ ) experiencing relativistic effects. From ( https://www.eejournal.com/article/darpa-funds-space-lasers-to-bring-non-sectarian-internet-communications-to-outer-space/ ): "... After all, the orbiting satellites are moving fast enough for relativistic effects to become apparent. These DSP capabilities are likely to be based on FPGA implementations for the foreseeable future, at least until there’s enough experience to codify the algorithms into standards." - so it is evident that derivations of Einstein's theory already support "time interval dt that can be applied to general time-dependent situations" like satellite networks.

So hardly 'limited' to only two reference frames.

No doubt just as Newtonian physics was subsumed into Relativity, that will will be followed by a more encompassing theory, however progress doesn't invalidate the current basis, merely extends it.

A. Einstein did not deeply understand the theory of relativity.

1-He used 5 assumptions which can actually be reduced to just 2 [1].

2-Additionally, he assumed two inertial frames of reference, the light speed constancy C and the Lorentz transformation x-t to arrive at his relativistic x-t transformation (note that the Lorentz transformation and the light speed constancy are equivalent and that both are universal laws of physics which have no proof[1]) that are fundamentally unnecessary.

3-As a simple example, We can prove that the theory of special relativity arises from the 4D control of the volume entanglement of a cooling curve of any metal cube with a side of 10 cm [2].

The statistical theory of Cairo techniques shows that speed of the entanglement signal = T1/2 *log 2 * L^2/ α.

If you substitute the thermal diffusivity value α in the thermal tables and measure the cooling curve half-time T1/2, you get the exact value of C=2.9 E8 m/s.

1-A rigorous reformulation of Einstein's derivation of the special theory of relativity, ResearchGate, IJISRT journal, February 2022.

2-Theory and practice of control volumes - Detailed Analysis, ResearchGate, IJISRT journal, Jan 2025.

A. Einstein did not deeply understand the theory of relativity.

Even if we just consider the point in time when he first came up with the idea, he ( or anyone else ) couldn't have 'understood deeply' his own theory - for instance: "In the early years after Einstein's theory was published, Sir Arthur Eddington .. Because the theory was so complex and abstruse (even today it is popularly considered the pinnacle of scientific thinking; in the early years it was even more so) ... Ludwik Silberstein, during one of Eddington's lectures he asked "Professor Eddington, you must be one of three persons in the world who understands general relativity." Eddington paused, unable to answer. Silberstein continued "Don't be modest, Eddington!" Finally, Eddington replied "On the contrary, I'm trying to think who the third person is."

But even if that is the case, since then, after nearly a hundred years not only of his subsequent work ( including experimental predictions ) but also the cumulative work of thousands of other physicists, astronomers, etc. about special and general relativity, the consensual reality is now 'deeply understood' across many domain disciplines along that chain of domain abstractions from pure math(s) down to the cell phone in your pocket that gives you driving directions.

> 1-He used 5 assumptions which can actually be reduced to just 2 [1].

Even if there are "5 independent and irreducible hypotheses from his own point of view", since the original work over a hundred years ago, those assumptions and hypotheses have been refined addressed in detail by their own experiments - in fact those lines of inquiry have generated their own evidence all along the chain from pure symbolic math(s) applied mathematics theoretical physics experimental physics applied physics technology engineering operations. If you are addressing General Relativity and Special Relativity, it is not sufficient to critique Einstein and Lorenze's work a hundred years ago, one would also have to address the cumulative work of every physicist that occurred afterwards ( https://en.wikipedia.org/wiki/Timeline_of_gravitational_physics_and_relativity#1900s ) and demonstrate how your assertion is supported by the accumulated observational evidence since then ( i.e. can one build a GPS constellation, functioning laser communications satellite network, or a gravitational wave observatory based on your 'fork' from the main line of relativity at 1904 ).

> 2-Additionally, he assumed two inertial frames of reference, the light speed constancy C and the Lorentz transformation x-t to arrive at his relativistic x-t transformation (note that the Lorentz transformation and the light speed constancy are equivalent and that both are universal laws of physics which have no proof that are fundamentally unnecessary.

Contemporary technological civilization is built on the conceptual basis of "Lorentz transformation and the light speed constancy", so they are fundamentally necessary.

> 3-As a simple example, We can prove that the theory of special relativity arises from the 4D control of the volume entanglement of a cooling curve of any metal cube with a side of 10 cm.

There is a reason why almost every physics experimental apparatus involving magnetism, radiation, electricity, etc. uses spheres or toroids - cubes are only uniform on three planes, so any effects observed will be, crudely put, 'lumpy'. But the entire reasoning based a small lump of metal is extremely local ( I assume that why the mention of 'control volume', a boundary which is conceptually the anti-thesis 'universal'). "any metal"? Even the metal itself will cause a dependency, that's why NIST uses ytterbium ( https://physics.aps.org/articles/v15/s126 ) and even that needs be cooled to nano-Kelvins.

We finally arrive at the phenomena of entanglement.

The entanglement between space and time is a universal law of physics.

Before the Big Bang, there was only a unitary 4D x-t vacuum containing space, time, energy density and entanglement.

The four physical quantities above led spontaneously and inevitably to what is called the Big Bang.

Schrödinger's error is to formulate his QM wave equation and deduce entanglement when the opposite is more true.

Entanglement had deceived A. Einstein and E. Schrodinger as well.