Women usually love apples, although many holy books, including Genesis and the Quran, prohibited it. So it’s no surprise that my wife, as a woman, loves apples. In fact, she loves apples so much that she never forgets to give me an apple every morning before I leave home.
“What makes this so-called fruit of Eden so special?” I asked her once.
“An apple a day will keep you away from doctor,” she replied.
This is probably why I used to eat every atom of an apple as I drove to the college. Nowadays, I don’t eat apples, but I have kept this a secret from my wife.
I have not eaten any apples since I became a student of Dr. Michio Kaku in hopes of becoming a servant of physics. I remember when he explained to me string theory—famously known as the theory of everything— by using an apple as an example.
Suppose you cut an apple into billions of pieces, Kaku explained, “each piece is composed of many billions of smaller particles called atoms, the building blocks of matter. Everything you see, hear, touch, taste, feel, and smell in the world is made of atoms. But atoms are not the end of the story—they have little particles, called electrons, protons, and neutrons. And if you magnify each of these particles, you will see quarks. And if you continue magnify the atom, you will see filaments of energy that vibrate like strings of a violin that our ears sense as different musical notes. In the way different strings of a violin create different musical notes, little strings inside an apple vibrate in different patterns, producing different particles. Every particle in the universe arises from different vibrations in the way Beethoven used different violin strings to produce different symphonies, Kaku explained. Who, then, is the Beethoven of my apple? God? Of course not.
The God of my apple is the good doctor Kaku. My relationship with Kaku is similar to Michael Faraday’s relationship with Humphry Davy. The difference is that Faraday was an amazingly talented man who found his passion in electromagnetic induction, and I’m an amazingly ignorant man who found his passion in an apple.
Finally, I told my wife that I no longer looked at an apple from a consumer’s point of view.
“I recently realized that an apple is not a fruit.”
“What is it then?”
“An apple is like a musical note. So, urging me to eat an apple is the same as urging me to eat Beethoven’s Symphony Number 5.”
“What’s wrong with you?”
My wife looked annoyed.
“Thanks to Michio Kaku, I finally realized that an apple is more like a beautiful math equation,” I said.
“So, you are telling me that you won’t eat apples anymore?
“I actually won’t eat them because eating apples is not physics. Rather, holding one high is actually physics.”
She looked worried.
“Are you OK?”
This time, she sounded like Sigmund Freud.
I tried to apply Newton’s Third Law to defend myself.
“Honey, you need to know that there’s a lot of physics in holding up an apple, because not only is the apple pulled downward by Earth, but Earth is also pulled up by the apple, and with just as much force.”
A few days later, I overheard her conversation with a psychiatrist.
“Look Dr. Das,” my wife was saying. “Today, he sees an equation on an apple. Tomorrow, he’ll see an equation on oranges and grapes. And within a month, he’ll probably see an equation on every food. So you have to do something before he becomes a delusionally influenced thinker.”
I decided to ignore this conversation, since I strongly believed that I didn’t have any anorexia nervosa or schizophrenia. However, to my surprise, she gave me an apple again just before I got into my car.
“I made an appointment with Dr. Das,” she whispered in my ear.
Instead of getting angry, I left home immediately because I had to do an experiment with Newton’s law of motion and gravitation, and Albert Einstein’s theory of relativity. I was going to test why the laws of Newtonian mechanics are the same in all inertial reference frames and why light propagates at a definite speed c independent of the speed of the source or the observer.
I decided to do this experiment while driving to the college. It would be like killing two birds with one stone.
I looked at the speedometer: My car was going 60 MPH. My one hand was on the steering wheel, and the other was holding an apple. I dropped it in the moving car, and it did not fly into the back of the car. But I wanted to see the breaking point of Newton’s laws by increasing velocity of the car from 60 MPH to 100 MPH.
I carefully dropped the apple again. It fell straight down, again. I quickly made a comparison: The direction of Newton’s apple and that of my apple were the same: straight down, although our frames of reference were different. That is, in 1665, 23-year-old Newton was in garden when an apple fell straight down. I was in a car that was moving at 100 MPH. Why was the direction of the apple in the garden and apple in the moving car the same? Is it because my car was moving at uniform constant velocity?
Let’s do a thought experiment:
I realized that as soon as I dropped the apple, it wanted to keep moving in the direction of the car, which is in accord with Newton’s First Law and Einstein’s theory of relativity. This means that any observer inside the car will see the apple fall straight down, but any observer outside the car will see the apple follow a parabolic path, like a projectile, because the outside observer is in different inertial reference frame.
But if I conduct this experiment by using a car that is not moving, the observer inside the car and observer outside the car will see the same thing. Why? Because now, they both are in same frame of reference, because car is not moving.
Finally, I decided to take the roof off. Now my car looked like a wagon. I extended my hand and threw the apple up while the car continued to travel forward at 100 MPH. I had learned from Galileo how to neglect air friction and asked myself three questions: Will the apple land behind the car; or, will it land in the car; or, will it land in front of the car?
As the apple followed the arc, the car would be directly under the apple, right? In fact, the apple dropped right into my hand. What if I threw the apple and hit the break simultaneously, I asked myself? Now where would the apple fall?
But I was not able to complete this experiment. Why not? Two cops from the N.Y. Police Department pulled me over. Oh, drat, the NYPD.
“License and registration, please,” said one.
“Why, what did I do wrong, officer?” I asked.
“You drove 100 MPH. That’s way above the speed limit.”
“I was driving smoothly at constant velocity.”
“It doesn’t matter,” said the officer.
“Of course, it does. In fact, it is just as valid to say I was at rest and the Earth was moving.”
The cop was dumbfounded.
I very patiently began to explain the basics of Earth’s velocity.
“You don’t know that Earth moves 67,000 miles per hour, which is almost 1,000 times faster than my speed. By the way, you, too, are moving at about 30 kilometers per second relative to the sun.”
“We can arrest you for insulting the NYPD, do you know that?” said the younger cop.
“Look—guys—I don’t have even time to eat an apple, let alone insult the NYPD. I was actually testing Newton and Einstein’s theories by dropping an apple. By the way, I guess you saw the parabolic path of the apple, right?
“Boss, his roof is missing,” the younger cop whispered in the older cop’s ear.
“Where is the rooftop of your car?” said the older cop.
Instead of answering his question, I wanted to use this opportunity to teach them some beautiful mathematical laws of physics.
“The speed of the light is 300,000,000 miles per second everywhere, regardless its frame of reference or speed of the observer or the source. Thus, if you go toward or away from a source of light, it will measure the same speed for that light as someone at rest with respect to the source. Now tell me what would you see if you could ride a light beam?
“We have been riding on a light beam since we joined the NYPD. This is why we see criminals like you who shamelessly break laws,” said the older cop.
“We’ll give you four tickets: $500 for speeding, $600 for driving and dropping an apple simultaneously, $700 for taking the roof off, and $1,000 for insulting the NYPD.”
“You need to drop the $600, because simultaneity is not an absolute concept, but it’s relative—that’s the consequence of the theory of relativity,” I said.
“You can say it to the court,” said the older cop.
“Look officer, if I can tell you the secret of how to become 20 years younger—would you drop these charges?
“No,” said the younger cop.
“Wait a minute,” said the older cop. “You really can make me younger?”
“You want to take off some age, I guess?” I said.
“Correct—my wife who is 20 years younger than me thinks I’m too old for her. I have to give this bitch a good lesson. Now tell me how I can get younger?”
“Very simple—but you have to promise me first that you will drop these charges.”
“I’ll drop everything. I’ll even give you whatever you want—including free vodka.”
“It’s OK—I don’t need Vodka.”
“Now tell me how can I take off some years?
“The idea of taking years off your age actually comes from Einstein’s special relativity theory: The speed of light in empty space will always be 300,000,000 meters per second, regardless of the motion of the source or the motion of the observer,” I said. “The constancy of the speed of light is what unifies space and time. And for any observation of motion through space, there is a corresponding passage of time—so, if you can dilate time, you will be able to take off age. This process is known time dilation.”
“How would I dilate time?” said the cop.
“All you need to do take a high-speed, round-trip journey, while your wife stays home on Earth. When you return, you will be younger than your wife.”
“How much younger?”
“That’s depends on the relative speeds involved. If you maintain a speed of 50% of the speed of light for one year, the gap would still be there. However, if you can maintain a speed of 95% the speed of light, your wife would become one year older than you.”
“Why don’t you want me to maintain 100% of the speed of light—because I want to be much younger than that bitch.”
“That’s also possible.”
“Which airplane company you want me to make the trip on? I have a personal preference: I like Jet Blue Airways because it’s very cheap.” said the younger cop.
“I thought you would give me some kind of pill to take off age,” said the older cop.
“Well, I will give you something more beautiful than an ugly pill.”
“What is that?”
“A Beautiful Math Equation for Time Dilation—here it is:
“Boss, he’s trying to make fools of us,” the younger cop whispered.
“I knew it from the very beginning that you are under the influence of drugs. It’s illegal to take Vodka here in New York City while you drive. So I’m giving you a summons,” said the older cop as he gave me a yellow piece of paper.
“What’s this yellow paper for?” I said.
“I summoning you to court for carrying vodka,” he said.
I have had bad luck with police. I already got fined $500 months before for winking at the moon for Neil Armstrong. Dr. Serigne Gningue suggested that I fight that fine in court. However, I didn’t go because I knew that judges and police are all cut from the same cloth: They all are ignorant and corrupt.
But now I had no choice, because not only did they fine me $2,100 but they also summoned me to court. While on my way there, I was trying to come up with the list of four classical mechanics postulates challenged by quantum mechanics: The physical universe is deterministic; light consists of waves and rocks consist of particles; energy and angular momentum are continuous variables; and physical reality does not depend on an observer.
I could not finish the list because I was interrupted by a clerk and had to pay attention to the judge.
“Did you drink Vodka while drive?” judge asked.
“So why did you take the roof off your car? That’s the behavior of a crackhead.”
“I was actually doing a scientific experiment.”
“Your drivers’ license is revoked for 10 years.”
“Judge, I refuse to believe your brain contains atoms that were part of mine a few minutes ago,” I said.
“You know that we are breathing one another’s breaths. So one of the days when you may feel like you’ll never amount to anything significant, take comfort in the thought that you have been breathing the atoms that I exhaled in this courtroom. You’re a very fortunate guy.”
It turned out that the judge did not like my attitude. Eventually, the police escorted me from the courtroom before I could finish the sentence. I called my wife to drive me home. However, she drove me to Dr. Dey’s office instead.
While waiting to being called, I was trying to answer that question through the lens of quantum mechanics: The universe is not deterministic; both light and rocks exhibit behavior that seems characteristic of both particles and waves; light is quantized; and physical reality does depend on the observer.
Suddenly, my name was called, and we went into his office.
“How are you, young man?”
“Dr. Das, you know—I like to think that the moon is there, even if I am not looking at it.”
“You need to answer my question; otherwise, I won’t be able to treat you.”
“I heard that you no longer eat apples—why is that?”
I wanted to give this idiot a good lesson.
“Both you and the apple are made of stardust—in the sense that carbon, oxygen, nitrogen, and other atoms that make up your body originated in the deep interior of ancient stars that have long since exploded. So, like an apple, you, too, are a bag of atoms.”
I tried again.
“You don’t know that? Look, just as dots of light of only three colors combine to form almost every conceivable color on a television screen, only about 100 distinct kinds of atoms combine to form all the material in the universe, including you and me. That is, atoms are the building blocks of matter. In fact, molecules are nothing but combinations of two or more atoms. For example, two atoms of hydrogen (H) combine with a single atom of oxygen (O) to form a water molecule (H2O). Today—115 elements are known, but living things, such as you and an apple, are composed of five elements: oxygen, carbon, hydrogen, nitrogen, and calcium. So, eating an apple is like asking a how to serve Taco Bell”
“OK—very good. Now tell me whether you were born in winter or spring?”
“I was born in summer.”
“Do you take amphetamines or drugs?”
“None of that, no.”
“Do you have a family history of schizophrenia?”
The doctor turned to my wife.
“Your husband needs to take this following test, including DSM-IV-TR—a diagnosis for schizophrenia,” he said.
We left the office, and my wife drove me directly to New York Hospital Queens.
“Let’s get it done quickly,” she said as she parked the car inside the hospital garage.
“Get what done?”
I was mystified.
“You have to take this lab test,” she said.
“I won’t take it because I don’t have schizophrenia,” I said.
“Honey, many famous people have this disease, including John Nash. So it’s OK to have schizophrenia.”
“So you’re trying to say I’m sick?”
“I’ll go live with my mother if you don’t take it.”
“I don’t care, but I won’t take this test—period.”
After half hour of argument, she looked like she meant what she said. I looked into her eyes for the last time and said, “I thought you’re smarter than Mileva Maric.”
Two days later, I woke up to the sound of a phone ringing. It was 6:00 a.m. I reluctantly picked up the receiver.
“Open the door,” said my wife.
I wasn’t surprised. I knew she would come back. But I didn’t know she would come back within a day.
“I thought you had the key,” I said.
“I won’t come inside unless you open the door and apologize to me,” she said.
“I told you that you’re smarter than Mileva Maric,” I said as I held the door open for her.
“So you won’t apologize to me?”
“Of course I would. In fact, I’ll apologize to you thousands of times, but trust me, I don’t have schizophrenia.”
“I hope that’s true—I really hope so,” she said, trying to hide her tears.
I usually leave home at 7:00 a.m. However, today I decided to leave a few hours later because I wanted to heal our relationship. To my surprise, she gave me a five-minute-long hug just before I grabbed my car keys.
“Honey, they revoked your driver’s license.” Her voice choked with tears.
“OK—I’ll take the subway.”
“You want me to drop you off at the college?”
It was 11:30 when she dropped me off. I rushed toward my office, but I’d no idea that even more dramatic things were waiting for me. I was shocked to see Dr. Dey inside my office.
“Who sent you here, Doctor—my wife?” I said.
“Where did you get my office address?”
“I Googled your name.”
“What do you want?”
“I did not treat you well on Monday—I apologize.”
“I came here for a different reason—I actually wrote a letter to President Obama. I want you to read it before I mail it to him.
“What’s it about?”
“I explain why President Obama needs to prohibit the eating of apples in the United States. I’m also planning to write a similar letter to Ban Ki-moon to make sure nobody in the world dares to eat an apple.”
“I also decided to give up my clinical practice; instead, I’ll study physics to learn more and more beautiful math laws of nature.”
I took him to the admissions office and explained to him how many credits he needed to complete a master’s degree in mathematical physics.
But an even more dramatic thing happened when I returned to my office. I saw the two cops sitting in chairs, and the cops were dressed as civilians. They stood up as soon as I entered the room.
“Does it mean Isaac Newton is wrong?” I asked myself. “Does it mean that the world is not deterministic—and randomness is involved in the development of future events?”
In fact, I was shocked, just the way Newton was shocked when he saw an apple falling from above. After discovering gravity, Newton realized that there’s nothing unusual about an apple falling on the ground, and maybe there was nothing unusual about the cops being in my office either. But it seemed unusual to me because, unlike Newton, my mind was not capable of explaining natural events through the language of mathematics.
“I know you’re surprised to see us here. But we’re here to express our apology,” said the younger cop.
“We already sent a request to the authorities to drop the fine and other charges that we brought against you,” said the older cop.
And I expected them to say something even more dramatic: “We’re here to study mathematics and physics.”
I wasn’t wrong.
“I have realized that dedicating my life to math and physics is more important than working for the NYPD,” said the younger cop. “This is why I applied for early retirement.”
The older cop was even more dramatic.
“I’m already in school—it’s a not-for-profit online school with the goal of changing education for the better by providing a free world-class education for anyone anywhere,” he said. “The name of my school is Khan Academy. In fact, I spent almost 20 hours yesterday watching Khan Academy’s math and physics video tutorials. But one thing I still don’t understand is why the idea that nothing can go faster than the speed of light flies in the face of Newton’s picture of gravity.”
I started explaining this to him as I turned on the air-conditioning.
“To understand this paradox—let’s imagine that all of the sudden, the sun vaporizes and disappears from our solar system. What effect does the sun’s disappearance have on the Earth, according to Newton?”
“He thought gravity was a force that acts faster than light across any distance, and so we would immediately feel the effect of the sun’s disappearance,” older cop answered.
“However, Einstein disagreed with Newton because he knew that nothing travels faster than light—not even the wave of gravity,” I said, firmly. “In fact, it takes eight minutes for sun rays to travel about 100 million miles to Earth. Since nothing travels faster than light, how could Earth get affected by the sun’s disappearance before the darkness resulting from the sun’s disappearance reached Earth?”
“Is this why Einstein tried to fix Newtonian gravity by adding a new dimension—time?” the older cop asked.
“Yes, by using geometry—he explains how a single dimension of time bound together with a single fabric with three-dimensional space. This unified fabric is stretched by heavy objects, like our planets and stars. And this warping of space-time creates what we feel as gravity,” I said.
“So Earth is kept in orbit not because the force of the sun holds it, as Newton’s theory holds, but because it follows curves in the special fabric due to the presence of an even heavier object—the sun.”
“Yes—my new friend—you got it right: Einstein called this new picture of gravity general relativity.”
“So, the general theory of relativity is nothing but the updated version of Newtonian gravity?”
“That is correct. Now tell me what would happen if the sun disappears?” I asked them, after explaining how the speed of light flew in the face of Newton’s picture of gravity.
“The gravitational disturbance that results from the sun’s disappearance will form a wave that travels across the special fabric in much the same way a fable drop into a pond makes a ripple that travels to surface of the water. So we would not feel the change in our orbit around the sun until such waves reach Earth,” the older cop said.
“Wait a minute—I think I’m dreaming. I wish I were able to ride the synchronized to kick me back to reality,” I said to myself. “It cannot be. I cannot expect a cop—who does not even have a bachelor’s degree—to understand my explanation of the theory of general relativity. I actually expected him to say something like this: ‘Newton is genius—and Einstein is also genius.’ So I thought I was talking to myself in a dream.”
“Forgive me, gentleman—I’ve to leave right now. I’ll see you next time.”
I ran to Dr. Daniel Kabat’s office to see whether I was awake or dreaming. I explained everything to him everything and asked him to bite on my wrest finger to wake me up.
“Perhaps we can laugh together some other day because today is not one of my best days.”
“What happened, professor?”“I had to deal with three incidents since morning.” “T-H-R-E-E?” I was surprised. “I have experienced exactly three good events since morning.”
“The math of God has to add up in a very strange way.” “I am utterly convinced that God does not play dice with the universe,” I said, repeating Einstein’s famous line.
“Don’t tell God what to do.” He sounded like Niels Bohr.
“My God is not as same as the God of Abrahamic religions—I was being metaphorical. My God is actually the grand sum of the universe.”
Our conversation was interrupted by a phone call. Professor Kabat picked up the phone, and his face turned red immediately. He gave me a wink—I knew exactly what that meant. I left his office to give him some privacy and thought about how he would be able to cope with incident Number 4? Does it mean God will do something else to make sure his math adds up? I realized how badly we need the theory of everything to read the mind of God. I sank into deep thought while returning to my office.
Although the Industrial Revolution was the direct result of Newton’s equation f= ma, nevertheless, his laws break down when an object approaches the speed of light. Although nuclear power is the direct result of Einstein’s e=mc2, his theories break down at the Big Bang or at the center of black hole.
Their theories are not capable of reading the mind of God. String theory, a theory of everything, allows us to go before the Big Bang happened, when there might have been multiverses of the universes.
There is a problem. Godel’s theorem implies that pure mathematics is inexhaustible. Now I have to prove why Godel’s theorem is incorrect. I wrote Kaku’s famous equation of the string field theory on the blackboard as soon as I got into my room.
Math is a gateway to reality. So why did Godel claim that finding a complete and consistent set of axioms for all mathematics is impossible? I decided to put four more equations on the board: F=ma, e=mc2, ,
However, I couldn’t finish writing Maxwell’s equation on the board because I heard someone knocking on my door. I looked through the door’s peephole and was surprised to see the gray head of the judge who had revoked my driver’s license. He kept knocking on the door.
“What’s going on? It seemed like he also wanted to quit his job to study mathematics and physics,” I said to myself, but I decided not to open the door. I had more important things to do than helping a gray hair study something he wouldn’t understand anyway. I started writing the Maxwell equation on the board again...
Rashidul Bari teaches Mathematics at the College of Staten Island and Physics at Brooklyn Tech. His websites is: Bari Science Lab