This shows you still do not understand my 24-lines proof that shows E in E=mc² is just a real number which cannot be associated with the unit of energy joule(J).

My proof still applies even if mass varies with speed as in relativistic mass m=γm₀. The SI definition for force is F=ma= mass x acceleration giving unit in newton(N); it doesn't care if mass has been changing with velocity.

Your proof is not based on experimentation. It's based on

*a priori *reasoning, and very fallacious reasoning at that. Basically, you're doing nothing more than typical human thinking, which is more irrational than rational. Now, this "irrationality" has a certain cadence based on emotions, mental schema, psychology, hormones etc, but it's not what is called logical.

Historically, there have been a variety of units of force and conversion factors.

www.npl.co.uk

Consider the excerpt from above. The writer takes great care in specifying that "for unchanging mass", implying the the acceptance of relativity and that mass is not actually unchanging.

For a changing mass, then mass also becomes a function and thus a derivative of it can be taken. Hence, the "adjustment". The "change" is a logical extension of the concept. It still represents mass, but more accurately than previously assumed. Just that with sig figs, that degree of accuracy usually doesn't apply in real life...but for something like GPS, it's a very important and influential application. For the matter of convenience of calcuation, it's better to teach a bit of the classical version. It takes a lot of brain power to fully comprehend the relativistic paradigm.

**Force is defined as the rate of change of momentum.** For an unchanging mass, this is equivalent to mass x acceleration.

So, 1 N = 1 kg m s-2, or 1 kg m/s2.

chan said:

This shows you do not yet understand fully the meaning of Newton's three laws of motion. Your situation is not surprising as very few physicists (even the Ph.D) understand the deeper subtlety of Newton's laws and his mechanics in the "Principia".

Indeed, using modern concepts of mechanics and calculus notation, Newton's 2nd law is: F=d/dt(p); p being momentum. **BUT, the Principia of Newton is developed where p=mv and m is invariant. **This leads to the SI usage of F=ma; but here, we care only for m and a at the relevant instant.

Newtonian mechanics does not allow any alternative definition of momentum p to be inserted into F=d/dt(p), only p=invariant mass x velocity allowed. Unfortunately, mainstream physics academia does not understand this most fundamental aspect of Newton's "Mathematical Principle of Natural Philosophy" - they created and prefers to promote "Un-Natural Philosophy".

Bolded are false premises.

Then you make the fallacy of "appeal to nature".

In addition, you try to use equivocation again by using "invariant". Your sense is the colloquial sense of invariant but perhaps a physicist would read it as the proper physics sense. Then that spawns a giant windbag of text as two different senses are used.

You really think that's sound reasoning? It's a deliberate attempt to cause confusion.

Excerpt:

When Newton formulated has second law, it was in a slightly different form than F = ma, the actual statement was that F = d(mv)/dt = dp/dt where p = mv is the momentum. In words, the net force acting on an object causes its momentum to change. If the net force is zero, the momentum does not change, it is conserved.

Chan said:

If we could define momentum at will, we may have infinite number of alternative mechanics by defining p=(γ^n)m₀v where n=1,2,3...infinity - current relativistic mechanics is just one of this infinite choices possible.

We know Newtonian mechanics works with the strict adherence to p=invariant mass x velocity only and NOT any alternative. This is because all our space programs launching of satellites and spacecrafts rely 100% on Newtonian mechanics - nothing from special relativity needed. We also know the orbits of planets obeys Newtonian mechanics.

The Michelson Morley experiments have been debated for over a hundred years; it's boring to rehash. About GPS, have you consulted with the Chinese physicists who built the Beidou system.

You still do not understand why I differentiate: F= ma -- (I) and F=d/dt(γm₀v) -- (II).

E=mc² is derived using the work-energy theorem W= ∫ Fds. The calculus of integration works only on real numbers. Though F has unit of newton and ds has unit of meter, we strip F and ds off their associated units in calculus. The result of W= ∫ Fds is just a real number - WITHOUT UNITS.

If we put F=ma -- (I) in W= ∫ Fds, we can associate W with a real unit of energy, the joule(J or newton-meter).

If we put F=d/dt(γm₀v) -- (II) in W= ∫ Fds, we CANNOT associate W with any real unit of energy. This is because F=d/dt(γm₀v) has no real unit in force. So here, W= ∫ Fds gives a real number that cannot be associated with any real unit of energy. This means relativistic kinetic energy=W=(γ-1)m₀c² is only a real number with no real unit in energy.

Complex numbers can be integrated, not sure where you got the statement "integration works only on real numbers". There is the question of whether your use of the term "real numbers" refers to the mathematical sense or the colloquial sense of "real" because you have a very frequent habit of using ambiguous sense of a word in a sentence, which is equivocation.

The Second Law is the rate of change of momentum. It's been discovered mass is not constant.

In addition, your use of "law" another example of using different senses of the same term in an argument. "Law" has many definitions and context matters. Here, you switch between the scientific sense and the "legal sense", akin to a violation of law. Indeed, you try argue relativity is false because it doesn't correspond with F=ma. But F=ma is not the actual definition, as explained above. It's the result of taking the derivative of momentum

*assuming* mass is constant, which has been disproven by experimental observation, independent of human meddling.

The very broad conceptualization of Newton's 2nd Law is not contradicted or discarded by relativity, merely an adjustment to mass is introduced to make calculations that correspond to the actual behavior of mass. As already stated, all of your windbag sentences boils down to not accepting mass as changing.

Scientific laws are a more "practical" manifestation to obtain correct calculations, where as "legal laws" can be violated and punishment or relief obtained. It's clear; the calculations are more accurate in more situations with relativity than without. Similar to the "approximate of circles" vs heliocentric-based calculations; the reality corresponds with the better measurements.

In addition, under relatively, mass still is recognized as part of the equation, just that the equation has to reflect the nature of mass as changing depending on velocity.

General relativity is the basic theoretical framework for the data processing in BDS.

The BeiDou Navigation Satellite System (BDS) is essentially a precise time measurement and time synchronization system for a large-scale space near the Earth. General relativity is the basic theoretical framework for the information processing in the master control station of BDS. Having...

satellite-navigation.springeropen.com

While most of this discussion uses special relativity, this paper states that BDS uses general relativity. So, you just popped out a sentence with no explanation, leading a reader to infer someone cooked up a no-relativity system...yeah nice try but it's not pure Newtonian mechanics and nothing new like you want it to be.