Dear ‘connections’:
“Science is conveyed in the language of logic. Art is portrayed through connections not accessible to the conscious mind and recognized intuitively as meaningful. Common to both is the loving devotion to whatever transcends our personal concerns. I have just enough intelligence to see how inadequate my intelligence is when confronted with the transcendence of art and science and what exists.” “The eternal mystery of the world is its comprehensibility… The fact that it is comprehensible is a miracle.”

Dear ‘path’:
“The life of an individual has meaning only insofar as it aids in making the life of every living thing nobler and more beautiful. Life is sacred…it is the supreme value. Only a life lived for others is a life worthwhile.”

Dear “thinker”:
I find it hard to explain my thought patterns. They are often unconscious and spontaneous. “The words of the language, as they are written or spoken, do not seem to play any role in my mechanism of thought.”

“When I examine myself and my methods of thought, I come close to the conclusion that the gift of imagination has meant more to me than my talent for absorbing absolute knowledge.” Maybe sometimes I think in images.  Maybe sometimes I think in equations.  Sometimes in both.  I am not sure that my mechanism is transferrable. “All my life I have been a friend of well-chosen, sober words and of concise presentation. Pompous phrases and words give me goosebumps when they deal with the theory of relativity or with anything else.”

But what is transferrable and irreplaceable is persistence and determination. Nothing, not even genius or education or talent, will take the place of persistence and determination! Stay with the problem until you conquer it. “Only one who devotes himself to a cause with his whole strength and soul can be a true master.”

Dear Talullah:
This is a very hard, and yet at the same time easy question to answer. Hard, if you’re a pessimist. Easy if you’re an optimist. A short answer from an optimist: my purpose is “to create satisfaction of desires and needs of all… and to achieve harmony and beauty in human relationships.  Fulfillment comes to those who love and understand creatures, plants, and stars… so that every joy becomes your joy, and every pain becomes your pain. Out to friends of friends of friends.” Joy cubed.  Pain cubed.
My father gave me a small magnetic compass when I was a little boy. I played with it for hours. How could it “know” how to point North all the time?  Mysterious! It made an enormous impression on me and played a major role in my life ever after. Its mystery became a compelling reason to move ahead with my life. Yes, even one of many reasons for living. Music became another. And the pursuit of harmony [[in]] and beauty in mathematics, in physics, and in friendships. I always felt my own life was interesting and worth living. I guess that makes me an optimist. So I am convinced you can find meaning the same way i did…by following your interests, your curiosities, your passions. it works. try it!.

Dear Rufus:
In my professional life, I made two serious blunders. One is signing the letter to President Franklin Delano Roosevelt suggesting that the Nazis might be ahead of the U.S. in weaponizing nuclear fission. I believed at the time that if Hitler developed the atomic bomb before us, he might have ruled the world. As it turned out, we were mistaken. The Nazis were behind us. I regretted the loss of life at Hiroshima and Nagasaki, but the bomb shortened World War II. And changed history. “Had I known that the Germans would not succeed in producing an atomic bomb, I never would have lifted a finger.”

The second is the cosmological constant. I added this constant to my gravitational field equations to account for the observation at the time that the Universe appeared to be neither expanding nor contracting. It was thought to be in a “steady state” in 1915, which meant that ordinary gravity was attractive (objects fell to Earth; they didn’t fall up!)
I added a term in my equation to produce some kind of repulsive gravitational force to keep everything in a steady state. Ironically, once Hubble discovered that the Universe is expanding, we found that the constant added as a “blunder” at the time turned out to be prescient, in that it became needed to produce what is now called “dark energy” of repulsion which makes up about 85 percent of the observable mass-energy of the Universe! So what I thought was a blunder turns out to be profound. The joke is “I was wrong once; on that occasion, I said I was wrong and I was right”.I have made some other blunders of a personal nature, but I prefer to leave these in the dark.

Dear Serena:
It’s hard to escape the feeling that beautiful mathematical formulas have an independent existence and an intelligence of their own.  That they are wiser than we are. That we get more out of them than we originally put into them.
Eugene Wigner remarked on this phenomenon — the “unreasonable effectiveness of mathematics” in describing the natural and physical world. He said, “The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve”.

Dear Elliott:
“In Hitler we have a man with limited intellectual abilities, unfit for any useful work, bursting with envy and bitterness against all of those whom circumstance and nature had favored over him.  He picked up human flotsam on the street and in the taverns and organized them around himself”. Hitler thought “Aryan science” was superior to ”Jewish science” because “Aryan science” was rooted in experiment, whereas “Jewish science” was inferior according to Hitler because it was theoretical, argumentative, “Talmudic”. Hitler put a price on Einstein to have him assassinated, but Einstein was able to leave Germany unharmed. The Institute for Advanced Study in Princeton was created by the wealthy Bamberger family as a safe haven and permanent home for Einstein when he arrived in the U.S in 1933 and resided there until his death in 1955.

Recently, someone pointed out that maybe Hitler was on to something, in that there is a Talmudic quality to Special and General Relativity. In the study of the Jewish scriptures, students learn in study pairs, so that two viewpoints can always be brought to bear on the sacred texts. One student can always disagree with the other, and they can argue “on the one hand, on the other hand”. This has a parallel in Relativity, where two different “frames of reference” are invoked and imagined, in order to form profound conclusions. However, anti-Semitism, not this benign interpretation, was what Hitler had in mind.

Dear “starlight”:
I suggest you look at the diagram below, “Bending of Starlight”. In the upper left corner is an image of our Sun with the distant starlight appearing to bend as the starlight grazes the edge of the Sun. (Technically this had to be done during a total eclipse of the Sun so the bending could be seen without the blinding sunlight.) Notice how the image of the Sun rests on a two-dimensional grid, where the grid lines bend to suggest that the space around the Sun is “curved”. The cannonball resting on a mattress is another way of imagining how the light travels around the massive Sun. “Mass tells space-time how to curve, and space-time tells mass or light beams how to move”, according to John Wheeler.

In the lower-left part of this diagram, you see how slight an angle the light beam was deflected. By an amount equal to the size of a quarter (about an inch) as seen at a distance of four miles. On the right side of the diagram, you see how the bending of starlight can mimic a convex lens. This becomes the basis for “gravitational lensing” and a new field of observational astronomy. Astronomers can see behind or beyond distant objects like stars or galaxies using my equations, to see further than ever.

Dear Invention:

I wish I had said it. People attribute witty or wise sayings to me as a form of flattery, or as a way of exaggerating my fame and enhancing my already unearned reputation for doing what comes natural to me. People quote me as saying that the most powerful force in the Universe, the greatest invention of all time, is “compound interest”. I’m not sure I actually said this. But as the Italians say: “If it’s not true then it’s well-invented”.

Dear “1905”:
Yes, it’s true. I published four papers that year that were considered worthy of four Nobel prizes. One on the Photo-electric effect, for which I was awarded the Nobel in 1921. One on Brownian motion. One on Special Relativity. And my most famous discovery: the equivalence of mass and energy E=mc2.

Dear Certainly:
When light falls on certain metals, electrons are ejected. The intensity of the light determines how many electrons. The color of the light determines whether or not electrons are ejected at all. Red light does not eject photoelectrons (even if it is very bright). Greenlight does eject photoelectrons (even if it is very dim). If the light is considered a wave, the electron-ejection phenomenon cannot be explained. But I considered light to come in small energetic bundles, or particles, or “quanta”. The bluer the light, the more energetic the bundle is. Above certain energy of the light bundles (at a certain degree of blue-ness), electrons were ejected. And below this energy, none were emitted. I took this to mean that the light quanta had enough energy to un-bind or to pry- away from the electron from the atom it was bound to. For this was the first instance when a quantum theory was used, in order to correctly explain an experimental result. Much later on, I was not fond of “quantum mechanics” and Neils Bohr’s interpretation of it as sharp images of a blurry reality. I believed quantum mechanics provided a blurry image of a sharp reality.

Dear “Brownian”:
The Roman philosopher Lucretius (60BC) wrote “On The Nature of Things”: “Observe what happens when sunbeams are admitted into a building and shed light on its shadowy places. You will see a multitude of tiny particles mingling in a multitude of ways… their dancing is an actual indication of underlying movements of matter that are hidden from our sight… It originates with the atoms which move of themselves [i.e., spontaneously].” The idea that molecules of a liquid or gas are constantly in motion, colliding with each other and bouncing back and forth, is a prominent part of the kinetic theory of gases to explain heat phenomena. According to the theory, the temperature of a substance is proportional to the average kinetic energy with which the molecules of the substance are moving or vibrating. It was natural to guess that somehow this motion might be imparted to larger particles that could be observed under the microscope; if true, this would be the first directly observable effect that would corroborate the kinetic theory. And that’s what I did using statistical mathematics.

Dear ‘theoretical physicist’:
Is that what you want to be? “The scientific theorist is not to be envied. Because ‘Nature’, or more precisely ‘Experiment’, is not a very friendly judge of a theorist’s work. In fact, it often seems to be your Enemy. It never says “Yes” to a theory. In most favorable cases, it says “Maybe”, which often really means “No”. And in the great majority of cases, it says, simply, “No”. Think twice before you decide to become a theorist! How wretchedly inadequate a theoretical physicist as he stands before Nature—and before his students!” If I had to choose my career all over again, I would probably be a musician, since I get great pleasure from playing the violin.

Dear “Special”:
I will try my best. So here goes.

In this diagram, on the left side, imagine a woman is on a train and she sends a beam of light from the floor to the ceiling and back to the floor.

The amount of time the beam takes from her vantage point inside the train is the beam’s path (2L) divided by the speed of light (c).

The right-hand diagram visualizes what a man on the platform would see of her train moving past him from his vantage point. The light beam would appear to slant right and upwards and then slant right and downwards due to the motion of the train rightwards. The path is longer D from his point of view, so the time of flight the man observes is 2D divided by the speed of light(c).

Here’s the hard part. The speed of light(c) observed by the woman in her apparently stationary train is exactly the same speed of light(c) observed by the man on the platform watching her train move past him. This result is based on the famous surprising Michaelson-Morley experimental result that showed the speed of light is always the same no matter what is the speed of the source of light or the speed of the observer! So this means that the man will observe a longer time interval as viewed from the platform than the woman observes as viewed from inside the train. In other words, time will appear to slow down in moving systems observed from a stationary system. This result has been confirmed many times by observing the half-life of decaying particles at rest compared with their half-life when they are moving near the speed of light. This is one of the counter-intuitive results of Special Relativity.

Another counterintuitive result is that events that are simultaneous in a stationary frame of reference (see diagram above) are not simultaneous in a moving frame of reference (see lower diagram). The Michelson Morley experimental apparatus looks like this. It allows the speed of light to be compared in two directions perpendicular to each other by splitting the beam into two and then recombining them. If the apparatus is moving to the right, then the light wastes time chasing the apparatus transverse to the direction of motion. When the role of the two arms is exchanged by rotating the apparatus there should be a change in the train-and-platform experiment from the reference frame of an observer onboard the train Reference frame of an observer standing on the platform (length contraction not depicted)

travel times if the speed of light depends on the source or the observer. But no. The result was the speed of light was independent of the speed of the source or the speed of the observer. The length in the direction of motion must also contract in the direction of motion… another shocking result.

Dear “E=mc2”:
If a body emits energy E in the form of radiation, its mass decreases by an amount equal to E/c2. In other words, mass and energy are both different manifestations of the same thing. This is a somewhat unfamiliar conception for the average person to accept. I can derive this result but it would take several pages here. So instead I have decided to show you the first nuclear-powered aircraft carrier the ENTERPRISE with the result emblazoned on its deck. It must be true if someone thought to do this.

Dear “telegraph”:
Do you mean this? “The telegraph is very similar to a very long cat, where you pull its tail in New York, and it meows in Los Angeles. The wireless is exactly the same — only there is no cat.” Well, as I said before if it’s not true, it’s well-invented. That sounds like something I could have said. People attribute lots of wise sayings to me I never said or forgot I said.

For example, my so-called ‘rules of work’: “1. Out of clutter, find simplicity; 2. Out of discord, find harmony; 3. In the middle of difficulty lies opportunity.” Maybe I said this and forgot. There were 897 books about me and relativity in the U.S. Library of Congress, 19 of them by yours truly. Do you think I remember everything I said or wrote?

Dear, what good is:
Could you have tea for two without the two? Or three blind mice without the three? Or four corners of the Earth without the four?  Numbers are beautiful, and this is a good enough reason to have them.  But they are also useful in life, in science, in art. I guess you already know this, but can you think of your life without your phone numbers, your address, your age?

Global Positioning Satellites (GPS) came into use after I expired in 1955. But I’ve been following their progress. Originally put up into orbit around the Earth for military purposes at great cost, they have many civilian uses.

If your smartphone communicates with one satellite, you could be at many spots. Communicating with two satellites, you could be at two places. But with three, your exact location is determined, by “triangulation”. A fourth satellite synchronizes the clocks in the receiver and in the satellites. There are now 24 satellites in Earth orbit, which can pinpoint your location to within a few feet or even inches. But these will not work without correcting for the well-known but unusual effects of Special and General Relativity.
Each satellite has an atomic clock accurate to billionths of a second. According to Special Relativity, time in a moving object (the satellite) slows down if observed from a stationary observer (our smartphone on the ground). The GPS has to be corrected for this discrepancy.  According to General Relativity, time in an object in a weak gravitation field (the GPS) speeds up compared to a strong gravitational field (your smartphone on the ground). So your smartphone will not work unless these physics corrections are taken into account.

What good is physics?  I don’t know where to begin. The movement of the planets and stars is explainable with Newton’s Laws of Motion. The nuclear reactions in our Sun and the distant stars explain how they generate energy. Your beating heart is a living embodiment of the physics of fluid dynamics. All need physics principles to explain. Billiards! Tennis!  Golf! Football! Baseball! Physics is everywhere. Just look around you. “Science is a wonderful thing if one does not have to earn a living at it!”

Dear “visualize’:
A lot of people ask this question. Let me see if I can help you here. My colleague, Professor Banesh Hoffmann* (*the man Dr. Rosen learned Relativity from) said this: “Do not waste your time trying to visualize four dimensions; it is simply not possible.”

What he meant by this is that mathematicians do not need to “visualize” space curvature because they can do it by cleverly using the ideas of mathematics. One way is by analogy with two dimensions and three dimensions. Another way is by using the Pythagorean Theorem. In this analogy, imagine a cannonball resting on a mattress. The mattress is a two-dimensional surface. The cannonball represents the Sun, and the depression in the mattress represents, is analogous to, how the mass of the Sun distorts or “curves” or “bends” space around it. The curvature is “perpendicular” to the two-dimensional mattress surface, in a way that’s analogous to the way time is sort-of “perpendicular” to the three-dimensions of ordinary space. You can’t “visualize” this precisely, but you can sort-of “imagine” it in your mind’s eye or metaphorically.

The Pythagorean Theorem, remember from plane geometry, says that in a plane right triangle, the sum of the squares of the two sides of the triangle equals the square of the hypotenuse. Now, this is true only in a two-dimensional flat plane. On the surface of a sphere like the Earth, the curvature of the triangle (in a plane perpendicular to the plane of the triangle) distorts the Pythagorean Theorem relationships between the three sides of the triangle. The curvature in this third perpendicular direction can be measured by how far the Pythagorean Theorem no longer works. In other words, the degree of departure from “Pythagorean-icity” is an index of the curvature of space. This kind of thinking takes getting used to.

Dear “simplicity”:
“The laws of nature perceived by an observer are independent of his state of motion.”  In other words, if a car accident occurs at 42nd Street and Broadway at noon, the same laws of motion for the accident apply whether you the observer are standing nearby — or you the observer are on an airplane flying above the accident. The physics of the accident does not depend on the coordinates, location, or motion of whoever is watching the accident, the observer. “The laws of nature are to be formulated free of any specific coordinates because a coordinate system does not conform to anything real.” A yardstick is still a stick of the same length whether you measure it in inches, centimeters, or miles.  It does not matter where the observer is or what she is doing. There is no preferred or absolute frame of reference for an observer.   “All of science is nothing more than the refinement of everyday thinking.”

“I have to say that I never understood why the theory of relativity, with its concepts and problems so far removed from practical life, should have met with such a lively, indeed passionate, reception among a broad segment of the public.”