1900: A physics genius wandering around Europe

Chapter 568 The limit of theory! Not the limit of space and time! General quantum mechanics merges again! The smallest scale!
The reversal just now made everyone suddenly realize.

"It turns out that what Professor Bruce was really asking was about the limits of the theory!"

"Instead of the limits of time and space!"

If so, this is a very interesting question.

Everyone present knew that every physical theory and even scientific theory had its own scope of application.

For example, Newton's laws of mechanics were considered applicable to any situation in the universe before the advent of relativity.

But now, everyone knows that Newtonian mechanics can only be applied at low speeds.

This is the limit of the theory.

This limitation applies not only to physics but also to other subjects.

For example, in chemistry, a certain reaction cannot exceed a certain temperature, otherwise the product will become another type.

Similar situations exist in biology, medicine, mechanics, etc.

Although relativity overturns Newtonian mechanics and includes Newtonian mechanics, it may have the same limitations.

From this perspective, everyone felt that Professor Bruce's concerns were not unreasonable.

Unless it is the ultimate cosmic truth, there is a high probability that human beings’ existing theories are flawed.

But here is the problem.

"This flaw is not necessarily a scale issue."

No matter how small an electron is, it must satisfy the probability waves and uncertainty of quantum mechanics.

No matter how big a star is, it must satisfy the curved space-time effect of general relativity.

Whether it is relativity or quantum mechanics, how can there be a limit boundary in scale?
And according to Professor Bruce, once a certain limit is exceeded, the theory will not be a problem of error size, but will simply fail!

What does that mean?

For example, Newtonian mechanics is not applicable to high-speed motion.

But if you insist on using it to calculate, you can also calculate the speed of the object, but the error will be larger.

But even so, as long as the error can be tolerated, the result can be used.

But it’s different when physical theories fail.

This is equivalent to you being unable to calculate the speed of an object using Newtonian mechanics.

"Inaccurate calculation" and "cannot be calculated" are two completely different concepts, and their meanings are also very different.

Therefore, everyone will be even more confused.

"Could it be that when an electron is small enough, its mass will not increase no matter how fast it moves? Does this not conform to the special theory of relativity?"

Obviously, this is impossible.

There was a heated discussion in the meeting hall.

after awhile.

Anderson stood up and said respectfully:

"Hello Professor Bruce, I am Anderson from California Institute of Technology."

“I want to try to answer that question.”

Li Qiwei smiled slightly when he heard this.

"Please say."

Anderson said:
"You once said that the material basis of relativity is astronomy, and the material basis of quantum mechanics is atomics."

"So, these two theories correspond to the upper and lower limits of the scale, respectively."

"I personally believe that there is no upper limit to the theoretical scale."

"Because the scale of star systems and even galaxies is already large enough for humans."

"But the current laws of gravity and general relativity predict this very well."

"So even if larger-scale cosmic structures are discovered in the future, they will still have to follow these physical theories."

"It's nothing more than a calculated greater mass, greater speed, and greater light intensity."

"The difference in size between stars and galaxies does not make any physical difference."

"But I personally think the lower limit of the theory is indeed worth discussing."

"The smallest structure known to mankind is the electron, and quantum mechanics was developed by studying the behavior of electrons."

"Although it is claimed to be applicable to all microscopic particles, perhaps in the future when we discover particles smaller than electrons, they may have new properties."

"Then quantum mechanics needs to be readjusted."

"So I think the lower limit is related to the size of existing particles."

Wow!
Anderson's answer caused a huge response among students.

Many people couldn't help but nod, obviously agreeing with this point of view.

However, bigwigs like Lang Zhiwan and de Broglie shook their heads slightly.

In their opinion, Anderson's answer was a bit too immature and missed the point.

At this time, Li Qiwei smiled and said:

"Mr. Anderson, there is a problem with your answer."

"That's when you assume that a physical theory can't accommodate undiscovered things."

“Although this cannot be proven mathematically, I personally disagree with your point of view.”

“A good physical theory should be able to predict or foretell unknown phenomena.”

"And what we're talking about now is what are the limits of what it can predict."

hum!
The students were confused and felt it was impressive.

They felt that Professor Bruce's realm was a bit high.

Li Qiwei stopped testing these geniuses and continued:

"Now, let me talk about my opinion."

"Some calculations will be used, so please pay attention or you may not understand."

Wow!
Everyone was excited instantly!

They wish they had a few more eyes, so how could they still be distracted?

With all the expectations, Li Qiwei said:
“For us humans, the world has its limits.”

"For example, according to the theory of cosmic expansion, the expansion speed of extremely distant places even exceeds the speed of light."

"Then anything that happens there will have nothing to do with us. This distance is a kind of limit."

"But this limit is not a theoretical limit."

"We are 99.99% sure that even in the region where the expansion of space exceeds the speed of light, quantum mechanics and relativity still hold true."

"The space-time there will be curved, and the position and momentum of the microscopic particles there are uncertain."

"This is the universality of the theory, and it is also the reason why I refuted Anderson just now."

After hearing this, everyone finally understood.

"However, in one special case, the theory may fail."

"We know that the most important step in understanding the microscopic world is measurement."

“Measure the position, charge, mass, etc. of an electron.”

“Without measurement, we cannot observe all the phenomena in the microscopic world, nor can we create corresponding theories to explain the phenomena.”

“Measurement is vital, but measurement itself has its limits!”

"In the macroscopic world, if a person wants to know how tall he is, he can just take a ruler and measure it."

"But if you want to know how big an electron is, a ruler won't work."

“For the microscopic world, the only way to measure it is to use another microscopic particle as a tool to measure the microscopic particle being measured.”

"But there is a huge difference between microscopic particles and macroscopic matter, which leads to the limit of measurement." "Now, everyone, follow me and do a thought experiment."

“Thought experiments are very important. I hope you will gradually learn and get used to this kind of thinking in the future.”

Everyone's eyes lit up as they listened. They felt that with Professor Bruce's explanation, they were already standing at the forefront of physics.

"Suppose now we want to measure a microscopic particle A."

"Then another microscopic particle B must be emitted to interact with it. Usually, B is a photon."

"If we want to measure the position of A accurately, we have to make the wavelength of the photon as short as possible."

“This is the only way to capture particle A exactly within the wavelength of the photon and achieve the [measurement] purpose.”

"The smaller the size of A, the shorter the wavelength of the photon."

“I think everyone can understand this.”

"But, according to E=hv, the shorter the wavelength of the photon, the greater the frequency, and therefore the higher the energy."

"When the size of A reaches a certain limit, the energy of the photon will also reach a limit."

"This energy limit is [mc]."

"Here m refers to the mass of particle A being measured."

"So mc is the total energy possessed by particle A according to special relativity."

"If the energy of the photon used for measurement exceeds mc, then when the photon hits particle A, particle A is likely to absorb this energy and produce a brand new particle A."

“Then the measurement process changes and we no longer know what we are measuring.”

"In other words, the measurement loses its meaning."

"At this point, the wavelength of the photon is the [measurement limit wavelength] of particle A."

"Once the wavelength of a photon is below this limit, then the photon hitting particle A is enough to create a new particle A."

"[The measurement limit wavelength] is obviously inversely proportional to the mass of particle A."

"The greater the mass of particle A, the greater its energy mc, and the greater the critical energy for measuring photons, so the shorter the wavelength, and accordingly, the shorter the [measurement limit wavelength]."

"In addition, the above method can be described more precisely according to the uncertainty principle."

"When the energy uncertainty of particle A is greater than mc, there is enough energy to create a new particle of the same type."

"At this point, measurement also loses its meaning."

Everyone was stunned and shocked.

Suddenly, Li Qiwei raised his voice and said:
"Notice!"

"The above is explained from the perspective of quantum mechanics and special relativity."

"Similar conclusions can be drawn from general relativity!"

"According to general relativity and stellar evolution theory, when an object with a mass of m is compressed to a certain radius, the object will directly form a black hole."

"This radius is the Schwarzschild radius."

"Obviously, the Schwarzschild radius is proportional to mass. The larger the mass of an object, the larger its Schwarzschild radius."

"For example, the Schwarzschild radius of the sun is 3 kilometers, and the Schwarzschild radius of the earth is 9 millimeters."

"That is, if the Earth could be compressed into a small ball with a radius of 9 mm, it would become a black hole."

"When I gave a speech at the University of Rome, I mentioned that a drop of water can be compressed into a black hole. This is the same principle."

"Mathematically, we cannot learn anything from inside a black hole."

"Inside a black hole, all physical theories are invalid."

"Therefore, if the energy of the photon is large enough, the new particle A produced may even directly become a black hole, and then the measurement really loses its meaning."

"The black hole will swallow up all the measurement photons."

"Although particle A is a microscopic particle, it also has a corresponding Schwarzschild radius."

"Now, we have linked the [measurement-limiting wavelength] of particle A to the [Schwarzschild radius]."

“As shown in the picture.”

Li Qiwei began to calculate and explain at the same time.

Everyone was shocked!

They have been completely immersed in this incredible thought experiment.

"Assuming that when the [measurement limiting wavelength] and [Schwarzschild radius] of particle A are equal, we can calculate the mass of particle A at this time."

"According to calculations, its value is 2.2×10^-8kg."

"I call this mass value the [limiting mass]."

"What does limiting mass mean?"

“It is the dividing line between the macroscopic world and the microscopic world!”

"For any particle whose mass is less than the limiting mass, the uncertainty range of the particle will exceed the Schwarzschild radius."

"That is, this particle will not collapse into a black hole, but will exist in the form of wave-particle duality."

"It can be understood that [wave properties] overwhelm [particle properties]."

"But if the mass of a particle is greater than the limit mass, the particle will directly form a black hole, and all physical laws will become invalid."

"Then any measurement at this point is meaningless."

"So, [the limiting mass] is the theoretical minimum mass of a black hole."

"Black holes below the limit mass will fall into the quantum world and transform into wave-particle duality instead of forming a macroscopic black hole."

"When the mass of particle A is the limiting mass, its [measurement limiting wavelength] is calculated to be 1.6×10^-35m."

"I call this length the [limit length]."

"It represents the smallest scale that can be described by existing general relativity and quantum mechanics."

"And the time required for light to travel the [limit length] is calculated to be 5.4×10^-44s."

"I call this time value [Limit Time]."

"It means that any phenomenon that occurs within a time interval shorter than this can not be described by existing physical theories."

"[Limit length] and [Limit time] are the limits of what physics can explore at present."

"That is: the smallest scale!"

boom!
The whole audience was shocked!

Then, there was deathly silence!

Everyone was stunned with shock.

Li Qiwei looked at everyone and smiled.

Obviously, the limit length, limit time, and limit mass are the Planck length, Planck time, and Planck mass in real history respectively.

Planck himself did not expect that the numbers he made up from a purely mathematical perspective would have such incredible physical meanings.

The key here lies in the speed of light c and Planck's constant h.

The former represents relativity, especially general relativity, while the latter represents quantum mechanics.

Through black holes and the uncertainty principle, both reach the same limit in different ways.

At this extreme scale, both relativity and quantum mechanics fail.

I have to say, this is a coincidence.

But this coincidence may contain some extremely profound truth.

Several constants in the universe are so amazing that the connections between them are far from being fully understood.

Perhaps these constants are the most fundamental structure of the universe.

If there was a formula that combined all the cosmological constants together.

So, can it calculate all the results of the universe?

(End of this chapter)