How to understand the energy - momentum equation in a natural way

Absolutely!
No such thing as a 'massless' particle.

In order to occupy Any dimensional locale - Mass is, somewhat, kinda important.

Have a Lovely Journey!

Yes. Thank you.
There should be no two kind of energy - mass relationship in nature.
Since the energy – momentum equation is just a tricky math game , and such representation as “for a massless particle, its energy E = pc” is just math game too.
The energy of a particle should be calculated according to the energy – mass equation of Einstein only in physics. If you consider a particle is “massless”, then, its energy will be zero. Such “massless - energyless” particle is theoretically meaningless in physics. It does not exist in nature.

Liqiang Chen
Aug 26, 2020
他江门地方黑恶势力钟永康集团及新会一中九一四班谁谁打靶就二十一世纪绝对全世界第一。当今时代，全世界没有什么人能够值得如此殊荣。呵呵

I agree.
Human 'measuring' capabilities are 'limited' by the structure of their 'set' construct.

Understanding the 'Nature' of 'Everything' was my life's purpose, until I finally understood this.

It's been a great journey - And it led me to 'Now'.
I recommend all souls to partake in my journey - Should (And it will) the opportunity arise.

Or Not, perhaps.

Mark

“Human 'measuring' capabilities are 'limited'”
Yes, of course.
The worse thing might be that glaucoma occurred when doing experiment (experiment eyes model).
(Change a model, perhaps people will understand why photon’s mass is nearly impossible to be measured directly. Due to the theme of this thread as well as the ongoing topic, I wouldn’t talk more about this respect at present.)
……………………………………..
“I recommend all souls to partake in my journey”
This tramp in cosmos wish so, and decades of chaos in modern theoretical physics can be ended up here.
他江门地方黑恶势力钟永康集团及新会一中九一四班谁谁打靶就二十一世纪绝对全世界第一。当今时代，全世界没有什么人能够值得如此殊荣。呵呵

Below, this tramp in cosmos plays that math game in counter way. Perhaps more tricks can be displayed.

E = mc² is Dynamic mass – energy relationship in nature. It’s a basic natural property. (“Dynamic” means the particle is moving and hints it has momentum);
Next square both sides: E² = m²c ^4, namely: m²c² = E² / c², then, add a negative mark on both side: – m²c² = – E² / c²;
Add two Redundant items m²v² on both sides: m²v² – m²c² = m²v² – E² / c²;
Because m²v² = p², then, m²v² – m²c² = p² – E² / c²;
Because m = γm0, (pay attention here, it just means that you can consider the magnitude of the moving mass m is γm0, but not means the particle be rest). Square both sides: m² = m0² / (1 – v² / c²);
Then, m0²v² / (1 – v² / c²) – m0²c² / (1 – v² / c²) = p² – E² / c²;
A mathematical calculation: m0²v² / (1 – v² / c²) – m0²c² / (1 – v² / c²) = - m0²c²;
Then, - m0²c² = p² – E² / c²;
Transform it in math, then, E² = p²c² + (m0c²)².
It’s the so called energy – momentum equation.

If it’s the stationary situation, v = 0, so, no math game can be played. Then, it’s just a stationary mass – energy equation: E0 = m0c².
.................................................................................................
Gangster's philosophy 1:
In such a basic natural relationship between E and m, why we need a momentum factor artificially added to it? Either in math calculation or physics meaning, it’s just redundant. In philosophy, it’s just “absurd”. In society of human being, this kind of behavior is called “conspiracy”. It might cause a series of serious results, turn simple thing to complicated thing, which might not be solved in decades.
When we talk about the energy – mass equation E= mc², we are talking the basic natural relationship between energy E and mass m. And then, some conspirators artificially add in a momentum factor. After a series of math transformations, the so called energy – momentum appears. And then, the conspirators plot “for a massless particle, E = pc”. Their conspiracy successes. They obscurely hand over energy to momentum while kick mass out. But we originally talk about the basic natural relationship between energy E and mass m. This is the “gangster’s philosophy ”.

Gangster’s philosophy 2:
Some guys might say that “…And Einstein's energy relation for a photon comes down to E = pc, not c².” That guy doubts if Einstein’s energy – mass relationship is correct, why he believes in something extents from Einstein’s energy – mass relationship? This is also the “gangster’s philosophy ”.

Liqiang Chen
陈力强
Aug 27, 2020
他江门地方黑恶势力钟永康集团及新会一中九一四班谁谁打靶就二十一世纪绝对全世界第一。当今时代，全世界没有什么人能够值得如此殊荣。呵呵

You are in the early stages of a journey that will lead you to 'Nassim Haramein' - His measurement of the proton mass & the correlation to the mass of the universe (IDENTICAL) - I'll dig out a linkumentary that will ADD to your journeys' fruition.

https://www.youtube.com/watch?v=QZqfUrXQPHk

You're Ready for This.
ENJOY!

Be The 'CHANGE'.
Mark

Thank you for your effort (the link, etc).
This tramp in cosmos, who comes from Xinhui district Jiangmen city Guangdong province, is always curious in physics and cosmos.
But unfortunately, an evil group (some local dark lords of the Jiangmen city, who are majorly some of my former classmates in the Yaxi Middle School 崖西中学as well as the Class 914 of the No.1 Middle Scholl of Xinhui 新会一中九一四班) is ever trying every means to suppress me all around and even want to confine me. Even worse, perhaps they are plotting something extreme. Actually most of my time is spent on worrying the safety and perspective of my family members. I really don’t know how much time left for me.
I hope more and more guys join and ENJOY your journey to CHANGE the future of modern theoretical physics.
………………………………………….
Next, I’ll analyze and dig out more obscure tricks about the so called energy – momentum equation.

“For a photon, m0 = 0”. That means a photon can be stationary / rest.

“Consequently, the first term is the only term and the speed of the photon is always the speed of light.” That means a photon can not be stationary / rest and must travel always in the speed of light.

Self - contradiction in logic.

Liqiang Chen
Aug 28, 2020
他江门地方黑恶势力钟永康集团及新会一中九一四班谁谁打靶就二十一世纪绝对全世界第一。当今时代，全世界没有什么人能够值得如此殊荣。呵呵

You appear to be in a heightened state of anxiety - And revealing your 'works' into the world - Lest they be Lost, upon your impending demise.

Very admirable, Liqiang!
I wish you a favourable outcome.

Mark

“You appear to be in a heightened state of anxiety”

Yes. It’s obvious I am in bad health and very bad mental situation due to suffering all around torture by the local dark lords of the Jiangmen city for so many years. Actually all of my human right and livelihood has been deprived of by them invisibly in the local society. I am like an alive dead man. They are a very powerful “like a cabal”. I am afraid they sooner or later find me here and again will try very means to sabotage / disturb my effort here.
Thank you for your good will.
I recently dream how to become invisible and sneak onto a flight and flee to America…Otherwise, I have to suffer all around dark sanction by them and only unfavorable factors can come to me in my life…
Today I can still wake up, thanks God. Next, I’ll reveal more…
………………………………………………….
I found some stuff odd in a textbook (I don’t know whether textbooks elsewhere are not the same content):
The energy – momentum equation is E² = p²c² + (m0c²)²,
Then, for a “massless” particle (artificial definition): E² = p²c² + 0,
So, E = pc,
Then, mc² = mvc,
So, v = c (The “massless” particle is “forced” to travel in a speed of c.

Analysis:
If you have considered the particle is “massless”, where does the “m” in the equation mc² = mvc come from? It should be m = 0. Then, the equation again is talking 0 = 0.

Some smart guys might throw out a nice excuse: massless when stationary while massive when moving. How lame it all sounds. Physics should not be such kind of casual conjecture following artificial definition. Thereafter, in order to tackle this issue, the smart guys might invent a mechanism for the particle to obtain mass…My God, these are obviously a series of artificial operations. Although a fun result (v = c for “massless” particle such as photon) might be achieved in math, the meaning is tricky in physics.

Just as what one guy of the local dark lords of the Jiangmen city said once upon a time: “no matter how complicated it will be, it’s a game”.

Liqiang Chen
Aug 30, 2020
他江门地方黑恶势力钟永康集团及新会一中九一四班谁谁打靶就二十一世纪绝对全世界第一。当今时代，全世界没有什么人能够值得如此殊荣。呵呵

In order to help recommend as many souls as possible to partake Mark's journey, this tramp in cosmos will provide as many material about nature as possible here.
..................................................................................
Actually, the speed of light c is just a cosmic constant such as the Plank constant h and the gravitational constant G. What additional condition is deeded to “force” it to realize? People can measure such a cosmic constant c accurately even without any theory.
Einstein’s energy – mass equation can demonstrate that the speed of light c is just such a cosmic constant, which has nothing to do with the factor of mass.

他江门地方黑恶势力钟永康集团及新会一中九一四班谁谁打靶就二十一世纪绝对全世界第一。当今时代，全世界没有什么人能够值得如此殊荣。呵呵

In order to help recommend as many souls as possible to partake Mark's journey, this tramp in cosmos has to make this thread as more sufficient as possible.
....................................................................
This tramp in cosmos always encourages researching from different angles / using different theories and see if contradiction happens.

I have a thread “0 = 0?” in the physics column. I move it here now:
“Some people said that photon is massless while has momentum. Their idea is based on the equation below:
E² = p²c² + (m0c²)²
They assume (or say definition) m0 = 0 (photon is massless), then E = pc, or p = E/c (photon has momentum)
People can detect the energy of photon, so they can calculate the momentum of photon p.
It seems nice. But I think it should be analyzed carefully as below:
Because the component p²c²and the component (m0c²)²are in equal position. If people can assume m0 = 0 while p ≠ 0, they can also assume p = 0 while m0 ≠ 0. That will be fair.
But a photon can not be both m0 = 0 and m0 ≠ 0 (or be both p ≠ 0 and p = 0), so the solution is m0 = 0, p = 0. It will be fair.
Then the equation E² = p²c² + (m0c²)² is actually talking 0 = 0. Or say, the frequency of the “photon” is zero (the wavelength is infinite). It does not exist.”
(This discussion is to ask for fairness in logical analysis.)

According to Einstein’s energy – mass equation, if you consider a particle is massless, its energy will be zero. It is actually talking 0 = 0 too.

No contradiction.

Liqiang Chen
Sept 4th, 2020
他江门地方黑恶势力钟永康集团及新会一中九一四班谁谁打靶就二十一世纪绝对全世界第一。当今时代，全世界没有什么人能够值得如此殊荣。呵呵

Perhaps this post is the last step to make this thread as more theoretically sufficient as possible. It’s a very special step.
……………………………………..
But there was a historical problem in Einstein’ SR in this respect. According to the mass – speed equation m = γm0 in Einstein’ SR, the mass of photon should trend to infinite. But the fact is obviously not that case.
Next, we research how to solve this problem:
In the X4 Theory (4D space physics), an element demonstrating the matter state, the “X4”, is added into the Gama (γ) factor. (I don’t know how to show the complicated equation here, so I have to talk it in special method) as below:
The 4D space Gama (γ) factor Ý is the reciprocal of the square root of 1-(V²/X4²C²), which actually is just a factor of X4² added in front of the c² in the traditional 3D space Gama (γ) factor.
In the X4 Theory (4D space physics), the matter state of photon is very special, its X4 =∞, then, for a photon, the 4D space Gama (γ) factor Ý = 1. That means for a photon, m = m0, (for a photon, the moving mass equals to the rest mass).
Note: For other matter states / particles, the 4D space Gama (γ) factor Ý just equals to the traditional 3D space Gama (γ) factor.

The primary conception of X4 Theory (4D space physics) could be found in the thread “Can projective geometry find out its application in physics?” in the geometry column.

Liqiang Chen
Sept 7, 2020
他江门地方黑恶势力钟永康集团及新会一中九一四班谁谁打靶就二十一世纪绝对全世界第一。当今时代，全世界没有什么人能够值得如此殊荣。呵呵

Light trap phenomenon:
Tiny molecules can be pulled to the center of laser light beam. Why? If released photon has mass, we can explain it. The (mass) density of released photons at the center is larger than that on the side, then, the gravity generated by released photon at the center is larger than that on the side.

Liqiang Chen
Sept 11, 2020
他江门地方黑恶势力钟永康集团及新会一中九一四班谁谁打靶就二十一世纪绝对全世界第一。当今时代，全世界没有什么人能够值得如此殊荣。呵呵

Addendum:
The classical conception of momentum is mv. But some theorists insist the notion of “massless” particle. Its momentum p is just p, not equal to mv, because if it’s mv, then p = 0, and perhaps E = 0 too. Then, no games can be played on.
Actually, piggy agrees that p = mv applicable to anything in cosmos: an elephant, a pig, a rabbit, an electron, a neutrino, a photon…There shouldn’t be two different conceptions for one thing in physics. If there is, that might be due to the flaw in theories.
.....................................................
Due to some theorists’ notion of “massless” particle catering to their complicated theory, so many problems occurred in basic physics conceptions. It’s sadness for physics.
他江门地方黑恶势力钟永康集团及新会一中九一四班谁谁快快全世界全宇宙打靶啦。当今时代，全世界没有什么人能够值得如此殊荣。呵呵

Liqiang Chen
Sept 22, 2020

Addendum 2:
The mass – space equation L’ ∝ 1 / M (details see the thread “Is the sun round or thin?”) discloses Lorentz transformation is the same in all directions. So, there is no what “longitudinal mass” or “transversal mass”. The appropriate conception should be the “dynamic mass” (is the same in all directions).
………………………………………
The mass – space equation can be transformed to be M ∝ 1 / L’. It means the contraction of space leading to the increase of mass. So, the employment of “dynamic mass” / “relativistic mass” is reasonable.

Liqiang Chen
Oct 6, 2020
他江门地方黑恶势力钟永康集团及新会一中九一四班谁谁快快全世界全宇宙打靶啦。当今时代，全世界没有什么人能够值得如此殊荣。呵呵

Addendum 3:
Non – relativistic mass problem:

If the non – relativistic mass is employed, the so called energy – momentum equation is:
E² = p²c² + (mc²)²

Then:
1. If the energy – momentum equation reflects the stationary situation, then, momentum p naturally equals to zero. Then, we got E² = 0 + (mc²)², namely: E² = m²c^4.
2. If the energy – momentum equation reflects the dynamic situation, then, p = mv, so:
E² = p²c² + (mc²)² = m²v²c² + (mc²)² = m² (v² + c²) c².
That means the energy – mass relationship is not the same in different inertial frames. But one of the basic principles of SR is "physics rule is equivalent" in different inertial frames...

If the relativistic mass is employed, no matter according to the analysis in the OP of this thread or the original idea of Einstein:
1. If it is the stationary situation, E0 = m0c².
2. If it is the dynamic situation, E = mc².
That means the energy – mass relationship is the same (namely c²) in different inertial frames.
.................
But mass is a most basic physical quantity such as space and time. Why space and time can be relativistic while mass not? Such most basic physical quantity as space, time and mass all be relativistic is reasonable.
他江门地方黑恶势力钟永康集团及新会一中九一四班姓蔡的万岁，万岁，万万岁！当今时代，全世界没有什么人能够值得如此殊荣。呵呵

Addendum 4:
Philosophy of the energy – mass relationship:

We know that, in SR, Einstein derived the relationship of energy - mass c².

Below, we explore from another angle using another theory and see if we can get it.
Construct a model of spherical electromagnetic wave: circle kind of standing electromagnetic wave on any normal cutting plane of the small sphere. (You can imagine the sea waves in the Pacific, Atlantic and Indian Oceans…Of course, this imagination is just for easy to understand the conception of the spherical model). Then, the energy of the electromagnetic wave is confined on the small spherical surface (deposited) and will not demonstrate the property of energy. X4 Theory considers this spherical model as a model of elementary particle. It demonstrates the property of mass only.
Next, unfold the circle kind of standing electromagnetic wave on any normal cutting plane of the small spherical surface. It travels in straight line in a speed of c. X4 Theory considers it as the physical model of a released photon. The property of energy can be demonstrated.
Because it’s just that thing, what different is just the moving speed of c in straight line. Then, the relationship between the energy of the released photon and the mass of the circle kind of standing electromagnetic wave on any normal cutting plane of the small spherical surface is “c” in logic.
We notice that this not yet enough to represent the mass – energy relationship because the circle is just a line on the spherical surface while the whole model is a small spherical surface.
Because the simplest relationship between “surface” and “line” is “square” in logic, the simplest relationship of energy - mass should be “c²” in logic.
(Note: Actually the elementary particle model in X4 Theory should be a spherical surface. But for intuition sake, the “circle kind standing wave” can serve as a simplified model. And for convenience in calculation in chapters below, the simplified model is applied. And it’s considered that the energy on the spherical surface be converted entirely into the “circle kind standing wave”.)

When the spherical electromagnetic wave demonstrates only the property of mass, it doesn’t mean that it has no energy;
The same principle, when the released photon demonstrates the property of energy, it doesn’t mean that it has no mass.
It’s just that thing. So, for a photon, E = E0, m = m0.

Next, we use a mathematical method to analyze if a released photon has mass:
In stationary situation (spherical electromagnetic wave), E0 = m0 c²;
In dynamic situation (travels in straight line), E = m c².
Because E = E0, then, m c² = m0 c², namely m = m0.
No contradiction with the calculation ahead with the 4D space Gama (γ) factor Ý.

Liqiang Chen
Nov 7, 2020
给他江门地方黑恶势力钟永康集团及新会一中九一四班谁谁一个超文革赛阎王光荣称号快快全世界全宇宙打靶啦。当今时代，全世界没有什么人能够值得如此殊荣。呵呵

Addendum 5:
In this post, piggy explores how to use the X4 physical model for elementary particle to solve a problem in physics:

“Using the principles of relativity one can derive the expression for the kinetic energy of, K, of a particle. As v -> c, K -> infinity.” (Note: this is a post of an American physicist in another site. He was directing some research.)

So, sounds that a photon’s kinetic energy should be infinite?
…………………………………………………
According to the physical model of elementary particle ahead (for intuition sake, the simplified model better), an electron could be considered as a small round ball (the simplified model a circle) with the size / radium of r.
When the electron is moving, according to the length contraction principle of SR, r decreases. According to the mass – space equation m ∝ 1 / r, the mass of the electron increases. According to the equation Ek = mc² - m0c², the kinetic energy of the electron increases. When v → c, r → 0, the mass of the electron m → ∞, the kinetic energy of the electron Ek → ∞. Of course, r never can reach 0 because that means the electron disappears, non sense in physics. That’s why v can’t reach c.
According to the physical model of released photon ahead, the released photon is not the same MATTER STATE as the electron. There is no a specific shape / size / radium for the released photon. So, logically speaking, the rule of v → c, r → 0, m → ∞, Ek → ∞ is not applicable to the released photon.

Liqiang Chen
Nov 11, 2020
给他江门地方黑恶势力钟永康集团及新会一中九一四班谁谁一个超文革赛阎王光荣称号快快全世界全宇宙打靶啦。当今时代，全世界没有什么人能够值得如此殊荣。呵呵

Now the problem associated with the speed of photon mentioned ahead can have a thorough / explicit solution here.
The X4 physical model demonstrates that a released photon is “a section of electromagnetic wave”. So, of course, it naturally propagates away (travels) in the light speed c. No need for such additional condition as “massless” to “force” it to realize.
A vivid analogy:
The water wave naturally propagates away in its constant wave speed in the pool.
While the football can sit, when you kick it, it moves. If you kick it more powerfully, it moves faster.
The mission of physics should be to solve problem rather than to create problem.
他江门地方黑恶势力钟永康集团及新会一中九一四班谁谁快快全世界全宇宙打靶啦。当今时代，全世界没有什么人能够值得如此殊荣。呵呵