# Learn How to Think Like Einstein

Albert Einstein's famous thought experiments led to groundbreaking ideas.

Albert Einstein is widely considered one of the smartest people who ever lived, significantly impacting our understanding of the world around us. His General Theory of Relativity has redefined what we know about space and time and is one of the pillars of modern physics. What’s also remarkable about Einstein’s achievements is that they relied largely on his mental powers and the intricacy of his imagination. He was able to discern and relate very complex scientific concepts to everyday situations. His thought experiments, that he called ** Gedankenexperiments **in German, used conceptual and not actual experiments to come up with groundbreaking theories.

**CHASING A BEAM OF LIGHT**

One of Einstein’s most famous thought experiments took place in 1895, when he was just 16. The idea came to him when he ran away from a school he hated in Germany and enrolled in an avant-garde Swiss school in the town of Aarau that was rooted in the educational philosophy of Johann Heinrich Pestalozzi, which encouraged **visualizing concepts.**

Einstein called this thought experiment the “germ of the special relativity theory.” What he imagined is this scenario - you are in a vacuum, pursuing a beam of light at the speed of light - basically going as fast as light. In that situation, Einstein thought, that light should appear stationary or frozen, since both you and the light would be going at the same speed. But this was not possible in direct observation or under **Maxwell’s equations,** the fundamental mathematics that described what was known at the time about the workings of electromagnetism and light. The equations said that nothing could stand still in the situation Einstein envisioned and would have to move at the speed of light - **186,000** miles per second.

*Artists pose in a laser projection entitled 'Speed of Light' at the Bargehouse on March 30, 2010 in London, England. (Photo by Peter Macdiarmid/Getty Images)*

Here’s how Einstein expanded on this in his Autobiographical Notes:

“If I pursue a beam of light with the velocity c (velocity of light in a vacuum), I should observe such a beam of light as an electromagnetic field at rest though spatially oscillating. There seems to be no such thing, however, neither on the basis of experience nor according to Maxwell's equations. From the very beginning it appeared to me intuitively clear that, judged from the standpoint of such an observer, everything would have to happen according to the same laws as for an observer who, relative to the earth, was at rest. For how should the first observer know or be able to determine, that he is in a state of fast uniform motion? One sees in this paradox the germ of the special relativity theory is already contained."

The tension between what he conceived of in his mind and the equations bothered Einstein for close to a decade and led to further advancements in his thinking.

**LIGHTNING STRIKING A MOVING TRAIN**

A 1905 thought experiment laid another cornerstone in Einstein’s special theory of relativity. What if you were standing on a train, he thought, and your friend was at the same time standing outside the train on an embankment, just watching it go by. If at that moment, lightning struck both ends of the train, it would look to your friend that it struck both of them at the same time.

But as you are standing on the train, the lighting that the train is moving towards would be closer to you. So you would see that one first. It is, in other words, possible for one observer to see two events happening at once and for another to see them happening at different times.

“Events that are simultaneous with reference to the embankment are not simultaneous with respect to the train,” wrote Einstein.

The contradiction between how time moves differently for people in relative motion, contributed to Einstein’s realization that time and space are relative.

*Lightning strikes during a thunderstorm on July 6, 2015 in Las Vegas, Nevada. (Photo by Ethan Miller/Getty Images)*

**MAN IN FALLING ELEVATOR**

Another thought experiment led to the development of Einstein’s General Theory of Relativity by showing that gravity can affect time and space. Here’s how he described it happened:

“I was sitting in a chair in the patent office at Bern when all of a sudden a thought occurred to me,” he remembered. “If a person falls freely, he will not feel his own weight.” He later called it “the happiest thought in my life.”

A 1907 thought experiment expanded on this idea. If a person was inside an elevator-like “chamber” with no windows, it would not be possible for that person to know whether he or she was falling or pulled upward at an accelerated rate. Gravity and acceleration would produce similar effects and must have the same cause, proposed Einstein.

“The effects we ascribe to gravity and the effects we ascribe to acceleration are both produced by one and the same structure,” wrote Einstein.

One consequence of this idea is that gravity should be able to bend a beam of light - a theory confirmed by a 1919 observation by the British astronomer Arthur Eddington. He measured how a star’s light was bend by the sun’s gravitational field.

**THE CLOCK PARADOX AND THE TWIN PARADOX**

In 1905, Einstein thought - what if you had two clocks that were brought together and synchronized. Then one of them was moved away and later brought back. The traveling clock would now lag behind the clock that went nowhere, exhibiting evidence of **time dilation**** **- a key concept of the theory of relativity.

“If at the points A and B of K there are clocks at rest which, considered from the system at rest, are running synchronously, and if the clock at A is moved with the velocity v along the line connecting B, then upon arrival of this clock at B the two clocks no longer synchronize but the clock that moved from A to B lags behind the other which has remained at B,“ wrote Einstein.

This idea was expanded upon to human observers in 1911 in a follow-up thought experiment by the French physicist **Paul Langevin.** He imagined two twin brothers - one traveling to space while his twin stays on Earth. Upon return, the spacefaring brother finds that the one who stayed behind actually aged quite a bit more than he did.

Einstein solved the clocks paradox by considering **acceleration and deceleration effects and the impact of gravity** as causes of the for the loss of synchronicity in the clocks. The same explanation stands for the differences in the aging of the twins.

Time dilation has been abundantly demonstrated in atomic clocks, when one of them was sent on a space trip or by comparing clocks on the space shuttle that ran slower than reference clocks on Earth.

How can you utilize Einstein’s approach to thinking in your own life? For one - allow yourself time for introspection and meditation. It's equally important to be open to insight wherever or whenever it might come. Many of Einstein's key ideas occurred to him while he was working in a boring job at the patent office. The elegance and the scientific impact of the scenarios he proposed also show the importance of imagination not just in creative pursuits but in endeavors requiring the utmost rationality. By precisely yet inventively formulating the questions within the situations he conjured up, the man who once said “imagination is more important than knowledge” laid the groundwork for the emergence of brilliant solutions, even if it would come as a result of confronting paradoxes.

## Why the number 137 is one of the greatest mysteries in physics

Famous physicists like Richard Feynman think 137 holds the answers to the Universe.

- The
**fine structure constant**has mystified scientists since the 1800s. - The number
**1/137**might hold the clues to the Grand Unified Theory. - Relativity, electromagnetism and quantum mechanics are unified by the number.

## Americans under 40 want major reforms, expanded Supreme Court

Younger Americans support expanding the Supreme Court and serious political reforms, says new poll.

- Americans under 40 largely favor major political reforms, finds a new survey.
- The poll revealed that most would want to expand the Supreme Court, impose terms limits, and make it easier to vote.
- Millennials are more liberal and reform-centered than Generation Z.

## Can you solve what an MIT professor once called 'the hardest logic puzzle ever'?

Logic puzzles can teach reasoning in a fun way that doesn't feel like work.

- Logician Raymond Smullyan devised tons of logic puzzles, but one was declared by another philosopher to be the hardest of all time.
- The problem, also known as the Three Gods Problem, is solvable, even if it doesn't seem to be.
- It depends on using complex questions to assure that any answer given is useful.

### The Three Gods Problem

<iframe width="730" height="430" src="https://www.youtube.com/embed/UyOGZk7WbIk" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe><p> One of the more popular wordings of the problem is:<br> <br> "Three gods A, B, and C are called, in no particular order, True, False, and Random. True always speaks truly, False always speaks falsely, but whether Random speaks truly or falsely is a completely random matter. Your task is to determine the identities of A, B, and C by asking three yes-no questions; each question must be put to exactly one god. The gods understand English, but will answer all questions in their own language, in which the words for <em>yes</em> and <em>no</em> are <em>da</em> and <em>ja</em>, in some order. You do not know which word means which."<br> <br> Boolos adds that you are allowed to ask a particular god more than one question and that Random switches between answering as if they are a truth-teller or a liar, not merely between answering "da" and "ja." <br> <br> Give yourself a minute to ponder this; we'll look at a few answers below. Ready? Okay. <strong><br> <br> </strong>George Boolos' <a href="https://www.pdcnet.org/8525737F00588A37/file/31B21D0580E8B125852577CA0060ABC9/$FILE/harvardreview_1996_0006_0001_0060_0063.pdf" target="_blank" rel="noopener noreferrer">solution</a> focuses on finding either True or False through complex questions. </p><p> In logic, there is a commonly used function often written as "iff," which means "if, and only if." It would be used to say something like "The sky is blue if and only if Des Moines is in Iowa." It is a powerful tool, as it gives a true statement only when both of its components are true or both are false. If one is true and the other is false, you have a false statement. </p><p> So, if you make a statement such as "the moon is made of Gorgonzola if, and only if, Rome is in Russia," then you have made a true statement, as both parts of it are false. The statement "The moon has no air if, and only if, Rome is in Italy," is also true, as both parts of it are true. However, "The moon is made of Gorgonzola if, and only if, Albany is the capitol of New York," is false, because one of the parts of that statement is true, and the other part is not (The fact that these items don't rely on each other is immaterial for now).</p><p> In this puzzle, iff can be used here to control for the unknown value of "da" and "ja." As the answers we get can be compared with what we know they would be if the parts of our question are all true, all false, or if they differ. </p><p> Boolos would have us begin by asking god A, "Does "da" mean yes if and only if you are True if and only if B is Random?" No matter what A says, the answer you get is extremely useful. As he explains: <br> </p><p> "If A is True or False and you get the answer da, then as we have seen, B is Random, and therefore C is either True or False; but if A is True or False and you get the answer ja, then B is not Random, therefore B is either True or False… if A is Random and you get the answer da, C is not Random (neither is B, but that's irrelevant), and therefore C is either True or False; and if A is Random...and you get the answer ja, B is not random (neither is C, irrelevantly), and therefore B is either True or False."<br> <br> No matter which god A is, an answer of "da" assures that C isn't Random, and a response of "ja" means the same for B. </p><p> From here, it is a simple matter of asking whichever one you know isn't Random questions to determine if they are telling the truth, and then one on who the last god is. Boolos suggests starting with "Does da mean yes if, and only if, Rome is in Italy?" Since one part of this is accurate, we know that True will say "da," and False will say "ja," if faced with this question. </p><p> After that, you can ask the same god something like, "Does da mean yes if, and only if, A is Random?" and know exactly who is who by how they answer and the process of elimination. </p><p> If you're confused about how this works, try going over it again slowly. Remember that the essential parts are knowing what the answer will be if two positives or two negatives always come out as a positive and that two of the gods can be relied on to act consistently. </p><p> Smullyan wrote several books with other logic puzzles in them. If you liked this one and would like to learn more about the philosophical issues they investigate, or perhaps if you'd like to try a few that are a little easier to solve, you should consider reading them. A few of his puzzles can be found with explanations in this <a href="https://www.nytimes.com/interactive/2017/02/11/obituaries/smullyan-logic-puzzles.html" target="_blank" rel="noopener noreferrer">interactive</a>. </p>## New tardigrade species withstands lethal UV radiation thanks to fluorescent 'shield'

Another amazing tardigrade survival skill is discovered.