1900: A physics genius wandering around Europe

Chapter 125 Explanation : The mass-energy equation came out of nowhere and shocked everyone!

After proving that the law of conservation of momentum still holds true in the theory of relativity, Li Qiwei did not stop. He continued, "The same is true for energy."

"What Professor Planck meant by energy is kinetic energy, the energy that an object has after it moves."

"According to the definition of Newtonian mechanics, kinetic energy is expressed as [E=1/2mv]."

"A small slider with a mass of m is at rest on the ground, so its kinetic energy is 0."

"When we push the slider with a constant force F, the slider moves a distance S and then accelerates uniformly to a speed v."

"If we calculate the work done by the force F over the distance S, we find that it is exactly equal to the kinetic energy of the slider, 1/2 mv."

"This is also the content of the kinetic energy theorem, that is, the work done by external forces on an object is equal to the change in the object's kinetic energy."

"If you want to still satisfy conservation after the LQW transformation, the kinetic energy needs to undergo the following changes."

"First, we calculate the work done by the external force by multiplying force by displacement, or E = FS."

"Although the force F can be expressed as [F=ma], I have just derived a new definition of momentum in relativity."

“So, I use the rate of change of momentum [△p/△t] to represent F.”

“This saves a lot of computation and is logical.”

"We assumed earlier that the force F is constant and the slider is moving with uniform acceleration, but this is only a special case."

"In order to ensure universality, we assume that F and S are changing, so calculus is needed here."

"As shown in the picture, I will start calculating."

“Click, click, click, click.”

"After some calculations, I got the definition of new kinetic energy in the theory of relativity."

Everyone was indifferent at first, then gradually frowned, and finally widened their eyes in shock.

The formula that Li Qiwei finally derived was: [E=γmc-mc].

He went on to explain: "This is the basic principle of adhering to the theory of relativity, which holds that the laws of physics should satisfy the new definition of kinetic energy obtained after the LQW transformation."

"In this formula, γ is called the relativistic factor, which is related to the object's velocity v. γ = 1/√(1-v/c)."

"I know that you may not be used to this way of expressing kinetic energy."

"But Newtonian mechanics is an approximation of relativity. If you don't believe me, just try it."

"I just need to Taylor expand γ, first order, second order."

"OK. Now it becomes the kinetic energy form defined by Newtonian mechanics that we are familiar with: E=1/2mv."

"This proves that Newtonian kinetic energy is only a second-order approximation of relativistic kinetic energy."

"m is still the mass we know, a physical quantity that does not change with speed and reference frame."

"And E is the kinetic energy that the object possesses because of its motion."

"Look carefully at this formula. If the object's velocity v is equal to 0, then γ is equal to 1."

"The kinetic energy becomes E=mc-mc=0. That is, the kinetic energy of a stationary object is 0, which is consistent with our cognition."

"But as the speed of an object increases, the relativistic factor γ begins to be greater than 1."

"The difference between γmc and mc is getting bigger and bigger, and as a result, the kinetic energy of the object is increasing."

"mc can be understood as the energy that an object with a mass of m has when it is at rest. I will simply call it [static energy]."

"And E is the kinetic energy of the object. Kinetic energy plus static energy is naturally the total energy of the object."

"That is, [E+mc=γmc], where γmc is the total energy that an object has due to its motion."

"Of course, if we change the equation to another form, we can also understand that the mass of an object increases as its speed increases."

"But I think that understanding is missing some important physics."

"So, after the above derivation, we can get a simple formula."

“A stationary object still has energy, collectively known as static energy.”

"And the rest energy of an object has a corresponding relationship with its mass, that is, [E=mc], where c is the speed of light."

"I call this equation the mass-energy equation."

When this famous equation was gradually deduced by Ridgway through the theory of relativity.

"hiss!"

Countless people took a breath.

"boom!"

Then the venue was in an uproar.

Everyone looked at the formula that seemed to be written by God himself.

I couldn't stop screaming madly in my heart:
what's the situation?
Aren't energy and mass supposed to be independent concepts?
How can there be an equation?

This is totally inconsistent with Newtonian mechanics.

In Newtonian mechanics, when an object is at rest, its energy is zero.

"No way, absolutely impossible."

"Doesn't this mean that mass can be converted into energy?"

According to this formula, an object still has energy even when it is at rest, and the amount of energy is related to its mass.

The most important thing is that we have to multiply it by the speed of light squared. What does this mean?
Doesn't that mean that the energy contained in a tiny apple is an astronomical figure?

Mr. Nobel once invented an explosive called TNT. (Note: It was not actually invented by Nobel, but people at that time believed that he invented it.)
The energy produced by the explosion of one kilogram of TNT is four million joules.

According to the mass-energy equation, the energy contained in an apple is roughly equivalent to the energy of the explosion of 500 million tons of TNT.

"hiss!"

The physicists who calculated the results were immediately numbed by shock and stared in disbelief.

This is simply a fantasy!

For a time, even senior physicists such as Thomson were confused.

What kind of physics freak has Bruce deduced?
When we were calculating the momentum just now, it was still within everyone's acceptable range, and everyone thought there was nothing wrong with the idea.

But when it comes to kinetic energy, how come such a result is obtained?

Those physicists who were deeply influenced by traditional physics were all muttering to themselves at this moment.

Lord Kelvin, Lord Rayleigh, Professor Keyes.

They objected unanimously: "How is that possible? Mass and energy are two completely different concepts."

At this moment, even those who had supported Li Qiwei before were shocked and speechless.

The subconscious mind thinks that something must have gone wrong.

E=mc?

Doesn't this mean that energy can be obtained through mass loss? And it is an enormous amount of energy, because it needs to be multiplied by the astronomical figure of the speed of light squared.

Li Qiwei took in everyone's expressions and everything.

He even had a premonition of what associations everyone would have.

including but not limited to:

【Mass can be converted into energy. 】

【Mass is a form of energy.】

【Mass loss can be converted into energy. 】

Unfortunately, all of the above perceptions are wrong.

At this time, Lord Kelvin could not help but stand up and said, "Bruce, your previous derivation is very brilliant, but I have some questions about the mass-energy equation." "First, where does the energy of a stationary object come from?"

"Second, according to the mass-energy equation, doesn't it mean that we can gain energy by losing mass?"

Li Qiwei smiled faintly. As expected, older generation physicists like Lord Kelvin could not accept the mass-energy equation.

Because it is so incredible, it can be said to have completely subverted the imagination of the Newtonian system.

This is the charm of relativity.

While others were as confused as Lord Kelvin, Li Qiwei smiled and said, "Thank you for your question, Lord. I think many people have the same doubt."

"First, when an object is at rest, its energy is diverse, including internal energy, chemical energy, various potential energies, etc." At this time, he did not dare to mention nuclear energy.

"But I don't care what kind they are. When I add them all up and divide by c, I get the mass m of the object."

"[Mass is a measure of energy]. This sentence is very important. You can ponder it carefully."

Lord Kelvin's face was still full of doubt, and it was difficult for him to understand the profound meaning of this sentence for a while.

Rutherford nodded thoughtfully, as if he understood something.

"As for the second question, the so-called [mass loss] and [mass can be converted into energy] are actually misunderstandings."

“I want to ask everyone a question, what is quality?”

Everyone was whispering to each other, feeling that Li Qiwei was a little puzzled. Quality is quality, what else could it be.

However, the senior physicists were all pondering and appreciating Li Qiwei's profound meaning.

There is no way. Li Qiwei now feels like he is in a different dimension from them.

Every sentence contains earth-shattering and subversive information.

Li Qiwei did not wait for an answer and continued: "In Newton's time, everything in the universe was made up of physical particles."

"Various physical phenomena are nothing more than the arrangement, combination and movement of these particles."

"And the laws of motion of particles are governed by Newtonian mechanics."

"In this case, the particles that make up matter are believed to be indestructible."

"Later, chemists discovered that the total mass of a substance remains unchanged before and after a chemical reaction. This is the famous law of conservation of mass."

"Chemical reactions are just the arrangement and combination of atoms. As long as the type and number of atoms do not change, the total mass will naturally not change."

"This law further proves the view that matter is indestructible."

"As long as we think that [the mass of an object is equal to the sum of the masses of all the particles that make up the object], then mass is synonymous with matter."

"Because people subconsciously believe that as long as it is matter, it must be composed of particles."

"But!" Li Qiwei suddenly raised his voice.

“What is energy in this context?”

"Let's take a chemical reaction, the burning of coal, as an example."

"From a chemist's perspective, combustion is when carbon atoms in coal combine with oxygen atoms in the air to form carbon dioxide molecules, and this process releases energy."

"But the types and numbers of atoms remain the same before and after burning, so the mass remains the same."

"In this classical system, mass and energy are two distinct things."

“Mass is the sum of the masses of all the atoms, and energy is just a byproduct of the reactions.”

"So, Lord Kelvin's understanding of the mass-energy equation is that the atoms that make up matter are destroyed, and the mass of the destroyed atoms is converted into energy."

"That idea is, of course, wrong."

"Because in the system of relativity, matter can no longer be regarded as just a bunch of atoms, and mass is no longer the sum of the masses of its constituent atoms."

“A stationary object contains not only the energy of its constituent atoms, but also the energy of the atoms themselves as a result of their interactions.”

"And the mass of an object is a measure of all this energy."

At this point, Li Qiwei actually didn't dare to go deeper. He didn't mention the existence of electromagnetic fields, which cannot be seen as real particles.

How to unify physical particles and electromagnetic fields?
Newtonian mechanics doesn't work, nor does relativity, and even quantum mechanics.

Only the combination of relativity, quantum mechanics and field theory to form the "quantum field theory" can explain this problem.

The Standard Model of Particle Physics, which is well known to later generations, is based on quantum field theory.

However, this explanation of the mass-energy equation of relativity is sufficient and does not require any more details.

So he continued:

"Take the burning of coal as an example. In this chemical reaction, the quality actually changes as well."

"The carbon and oxygen atoms combine to form carbon dioxide molecules, releasing energy, so the mass that measures energy naturally decreases."

"It's just that because the energy released by the chemical reaction is very small, after dividing by c, the decrease in mass is very, very small, so we can't notice it."

"But in charcoal combustion, E=mc still needs to be satisfied."

"Of course, all the above derivations refer to the static energy of an object, not its kinetic energy."

"As the speed increases, the kinetic energy of the object increases. As the energy increases, the mass naturally increases as well. This is what is called kinetic mass."

"However, I hope that everyone will not pay too much attention to the term kinetic mass. Mass has nothing to do with the state of motion of an object."

When Li Qiwei finished his explanation, the venue fell into deathly silence.

Everyone's expression was frozen, as if time had been paused.

Lord Kelvin had completely lost the ability to think. It would have been better if he hadn't asked. He became even more confused after asking.

In the entire venue, perhaps Einstein was the only one who could understand Li Qiwei without any obstacles at this moment.

As for others, it will take some time to digest.

Thus, a strange picture appeared.

Li Qiwei stood upright on the stage, saying nothing, and looked quietly at the people below.

Everyone in the audience, including the host Lorenz, kept their mouths open as if thinking, with all their eyes focused on Li Qiwei.

One minute two minutes.
A full three minutes later.

Finally, there were bursts of thunderous discussions in the conference hall.

"Oh my God, even the concept of mass is problematic. I feel like physics doesn't exist."

"I thought the mass-energy equation was outrageous enough, but I didn't expect Bruce Lee's explanation to be even more outrageous. You told me that mass is not the sum of the masses of the particles?"

"Hey, I thought I could create powerful weapons out of thin air. I thought as long as I could find a way to make the apple lose quality, I could gain energy."

"Now it seems that this is not the case at all."

At this moment, the only word that came to everyone's mind was stunning.

Otherwise, it would be impossible to explain how Li Qiwei's brain came up with these things.

By this time, the senior physicists had come to their senses.

As long as we keep thinking in the theory of relativity and abandon Newton's classical mechanics, Ridgway's analysis is completely correct.

Although the results are magical and bizarre, they are the physical laws under the theory of relativity, which are fundamentally different from the laws of the Newtonian system.

Planck and Thomson looked at Li Qiwei with wry smiles.

The former lamented that Li Qiwei has completely surpassed his teacher and will reach a higher level.

The latter sighed and wondered how he could supervise this doctoral student. He might as well go back and let him graduate.

In the third round of academic competition on relativity, Li Qiwei won!

However, the controversy is not over yet
(End of this chapter)