Derivation of E=mc2 from Four-Vector Definitions in Special Relativity

[Nugatory]

Is there any way to derive the relation based on Newtonian mechanics clearly and convincedly?

No, because that relation does not hold in Newtonian mechanics.

 

[Mister T]

Is there any way to derive the relation based on Newtonian mechanics clearly and convincedly?

No. Starting with the Newtonian expressions for the relationships between force, momentum, and energy you can derive some approximate relations. Using the postulates of special relativity you can derive more general expressions that match very closely, when the speed is low, those approximate relations.

In other words, you can derive the Newtonian expressions from the relativistic expressions, but you can't derive the relativistic expressions from the Newtonian expressions.

 

[Ziang]

No, because that relation does not hold in Newtonian mechanics.

Is there any way to modify Newtonian mechanics so that the mass-energy equivalence can be derived from absolute space and time?

 

[SiennaTheGr8]

No.

 

[Sorcerer]

Is there any way to modify Newtonian mechanics so that the mass-energy equivalence can be derived from absolute space and time?

Yes. By changing the transformation rule from the Galileo to the Lorentz. That is, by turning it into special relativity ;) (but no, not from absolute space and time lol)

 

[Ziang]

I heard of a modified Newtonian mechanics which could yield mechanical expressions and the mass-energy equivalence as well from absolute space and time. The theory also gives better results than Newtonian mechanics does. May I write down some of its expressions here?

 

[Sorcerer]

I heard of a modified Newtonian mechanics which could yield mechanical expressions and the mass-energy equivalence as well from absolute space and time. The theory also gives better results than Newtonian mechanics does. May I write down some of its expressions here?

This forum only deals with established and accepted theories. If it's experimental and cutting edge, there is a sub-forum, and if it isn't peer reviewed stuff, it probably isn't welcomed here.

In any event, the only reason you get E = mc² is because of the very assumption that time doesn't tick the same for all clocks. That is built into the Lorentz transformation itself. I suppose there are/were different interpretations of the math, but since E = mc² was discovered, and even before it, no one really doubted the math (Lorentz himself accepted his own transformations, despite his slowness in warming to Einstein's interpretation, including his equation that leads to length contraction, but Lorentz attributed it to the moving matter being deformed).

 

[PeterDonis]

I heard of

Can you give a valid reference (textbook or peer-reviewed paper)?

 

[Ziang]

Can you give a valid reference (textbook or peer-reviewed paper)?

I found it on Amazon. A thin book titled "Beyond the world of relativity". Mathematics in the book is simple. I think scientists will get interested in the way it leads to the equivalence from absolute space and time.

 

[PeterDonis]

I found it on Amazon. A thin book titled "Beyond the world of relativity".

Can you give a link?

 

[Ibix]

Can you give a link?

Partial (I think) copy at Google Books edit: removed the link because I'm pretty sure it doesn't meet our standards - you can find it easily enough by googling for the title.

I haven't had a proper look - Google Books doesn't seem to get along with my phone's browser.

 

[Ibix]

I haven't had a proper look

Now I have (don't know why I can scroll around now - I couldn't before - such are the mysteries of computers). If that is the book that Ziang is talking about then I very much doubt it meets our acceptable reference standards. It apparently simply assumes that Newtonian gravity is correct without any supporting argument, then concludes that event horizons don't exist (around equation 9).

 

[Sorcerer]

Now I have (don't know why I can scroll around now - I couldn't before - such are the mysteries of computers). If that is the book that Ziang is talking about then I very much doubt it meets our acceptable reference standards. It apparently simply assumes that Newtonian gravity is correct without any supporting argument, then concludes that event horizons don't exist (around equation 9).

Seems the author’s motivation is religious:

“In 1987, Nguyen resettled in the United States. Once his new life became stable, he tried to find the answers to his questions in Buddhism, and he recognized and accepted the Buddhist beliefs of space and time are absolute.”Poor fellow. If only he would have realized that relativity says SPACETIME intervals are absolute.

 

[Ziang]

It apparently simply assumes that Newtonian gravity is correct without any supporting argument,

All theories have some assumptions or postulates. So I thought this assumption could be accepted. And because of this assumption, I called it a modified Newtonian mechanics.
Compare to SR, it gives more expressions as potential energy and gravitational red/blue shift.
Compare to Newtonian mechanics, it also gives more expressions as Doppler effect and mass-energy equivalence.
Anyway, it shows a way to derive the equivalence from fundamental definitions of natural concepts in Newtonian mechanics, in absolute space and time.

 

[Sorcerer]

All theories have some assumptions or postulates. So I thought this assumption could be accepted. And because of this assumption, I called it a modified Newtonian mechanics.
Compare to SR, it gives more expressions as potential energy and gravitational red/blue shift.
Compare to Newtonian mechanics, it also gives more expressions as Doppler effect and mass-energy equivalence.
Anyway, it shows a way to derive the equivalence from fundamental definitions of natural concepts in Newtonian mechanics, in absolute space and time.

What about relativistic kinetic energy? How does he derive that, which has the Lorentz factor?

 

[PeterDonis]

All theories have some assumptions or postulates. So I thought this assumption could be accepted. And because of this assumption, I called it a modified Newtonian mechanics.
Compare to SR, it gives more expressions as potential energy and gravitational red/blue shift.
Compare to Newtonian mechanics, it also gives more expressions as Doppler effect and mass-energy equivalence.
Anyway, it shows a way to derive the equivalence from fundamental definitions of natural concepts in Newtonian mechanics, in absolute space and time.

It appears that the reference @Ibix found is indeed the one you were referring to. That reference is not a valid source for PF discussion; it is not a textbook or peer-reviewed paper and appears to be the author's personal speculation.

Thread closed.