Albert Einstein created his most famous theory amid personal struggle, political tension and scientific rivalry that almost cost him the glory of his discovery
The article is published with the permission of Scientific American Israel and Ort Israel
By Walter Isaacson
Albert Einstein created his most famous theory amid personal struggle, political tension, and scientific rivalry that nearly cost him the glory of his discovery * Einstein's understanding that gravity and acceleration are equal put him on an eight-year path toward the generalization of his special theory of relativity.
He strove to discover the correct mathematical formulas for his theory before his opponent, the mathematician David Hilbert, did. At the same time, Einstein also struggled on the home front, since he was then in divorce proceedings from his first wife and separated from his children, and at the same time he was courting his cousin, whom he would later marry.
Despite these challenges, Einstein prevailed and created one of the greatest scientific works of all time: his theory of general relativity.
General relativity was born out of a sudden thought. It was at the end of 1907, two years after the "Year of Wonders" when Albert Einstein created his special theory of relativity and his theory of quanta of light, but he was still working as an examiner at the Swiss Patent Office. The world of physics has not yet caught up with his genius. While he was sitting in his office in the city of Bern, he recalled, a thought "shook" him: "If a person falls in a free fall, he will not feel his own weight." Later, he would call this thought "the happiest thought of my life."
The story of the falling man became a legend, and in some of the descriptions it included paint that actually fell from the roof of an apartment building near the patent office. As in other great stories about gravitational discoveries, such as the story of Galileo dropping objects from the Leaning Tower of Pisa or the story of the apple falling on Isaac Newton's head, the popular description adds color to the facts. However, despite Einstein's tendency to focus on science and not on "purely personal matters," it is unlikely that he actually saw a real person falling from the roof and thought about a gravitational theory, and he certainly would not have called it the happiest thought of his life.
Soon, Einstein refined his thought experiment so that the falling person stays inside a closed chamber, such as an elevator, and falls in free fall. Inside that cell, he would be weightless. Any object he drops will float to his side. He would have no way of knowing, no experiment he could conduct, to determine whether the cell is falling in accelerated motion or floating in a gravity-free region of outer space.
Then Einstein imagined that this person is in that cell, far away in space, in a place where no gravity can be felt, and a constant force pulls the cell upwards in an accelerated motion. This person will feel their feet pressing into the floor. If he drops an object, it will fall to the cell floor in an accelerated motion, just as if he were standing on the surface of the Earth. There is no way to distinguish between the effects of gravity and the effects of accelerated motion.
Einstein coined the term "principle of equivalence." The local effects of gravity and acceleration are equal to each other. Therefore, they must be manifestations of the same phenomenon, some cosmic field that is responsible for both acceleration and gravity.
It would take Einstein another eight years to turn the thought experiment about the falling man into the most beautiful theory in the history of physics. He will leave his settled life, as a married man and father of children working in the Swiss patent office, and will move to live alone, as a professor in Berlin, estranged from his family and increasingly isolated from his colleagues in the Prussian Academy of Sciences due to the rise of anti-Semitism. The decision made in 2014 at the California Institute of Technology (Caltech) and Princeton University to upload a free online archive of Einstein's writings allows a glimpse into his attempts to maneuver between the cosmic and the personal during those days. We can enjoy his excitement at the end of 1907, when he scribbled down "an innovative consideration, based on the principle of relativity, on acceleration and gravity," as he put it. And then we can sense the sullen boredom that gripped him, a week later, when he rejected a patent proposal submitted by an electricity production company for an alternating current machine, saying that its claims were "improperly prepared, imprecise and unclear." The following years were to be full of human drama, as Einstein competed against an opponent in order to find a mathematical expression for relativity while at the same time struggling with his estranged wife over issues of money and the right to visit his two young sons. But in 1915, his work reached its climax: a complete theory that would change our understanding of the world forever.
light bending
For nearly four years after Einstein proposed that gravity and acceleration were equivalent, he didn't do much with that idea. Instead, he focused on quantum theory. But in 1911, when he finally managed to break through the walls of academia and become a professor at the German Karl-Ferdinand University in Prague, he turned his attention again to formulating a theory of gravity that would help him generalize the special theory of relativity: the relationship between space and time that he had defined in 1905.
While developing his equivalence principle, Einstein realized that this principle had some surprising implications. For example, his thought experiment with the cell showed that gravity would bend light. Imagine the cell is accelerating upwards. A beam of light enters through a pinhole in one of the walls. By the time the beam reaches the opposite wall, the light will be a little closer to the floor because the cell is shooting upwards. And if you can trace the path of the beam across the cell, the path will be bent due to the upward acceleration. The principle of equivalence means that this phenomenon should be the same, and one is whether the cell accelerates upwards or if it is at rest in a gravitational field. In other words, light has to bend as it passes through a gravitational field.
Einstein faced two ticking clocks: he could sense that Hilbert was getting closer to the correct equations, and he agreed to give a series of four formal lectures on his theory on Thursdays.
In 1912, Einstein asked a former classmate to help him with the complicated mathematics that might describe a warped and distorted four-dimensional space-time. Until then, his success was based on the talent to identify the principles of physics that lie in the infrastructure of nature. He left to others the task of finding the best mathematical expressions to describe these principles. But now Einstein realized that mathematics could be a tool for discovering, and not just describing, the laws of nature.
Einstein's goal when rowing toward general relativity was to find the mathematical equations that describe two interwoven processes: how a gravitational field acts on matter and tells it how to move, and how matter produces gravitational fields in space-time, and tells space-time how to curve.
For more than three years Einstein struggled with drafts and outlines that turned out to be flawed. Then, beginning in the summer of 1915, mathematics and physics began to merge.
personal disintegration
At this stage he had already moved to Berlin and became a professor there and a member of the Prussian Academy. But he found himself working almost without support. Anti-Semitism grew, and he did not create any circle of colleagues around him. He separated from his wife, Mileva Marich, a fellow physicist who served as a kind of barometer to test his ideas when he developed the special theory of relativity in 1905, and she returned to live in Zurich with their two sons, who were then ten and four. He had an affair with his cousin Elsa, the woman he would later marry, but lived alone in a sparsely furnished apartment in central Berlin, where he ate irregular meals, slept randomly, played his violin and persevered in his lonely struggle.
During 1915, his personal life began to crumble. Some of his friends pressured him to get a divorce and marry Elsa; Others disallowed him, that he should avoid being seen with her in public or allow her to get close to his two sons. Maric repeatedly sent letters asking for money, and at one point Einstein responded with a burst of bitterness. "In my opinion, such a claim is not up for discussion," he replied. "To me, your continuous attempts to lay your hands on anything in my possession are clearly disgraceful." He tried to keep in touch with his sons by letter, but they rarely wrote back, and he blamed Marić, claiming she was not forwarding his letters to them.
However, in the heart of this personal turmoil, Einstein was able to formulate, by the end of June 1915, many of the foundations of general relativity. That month he gave a series of lectures, one each week, on the subject of his developing ideas, at the University of Göttingen in Germany, the world's most important center for mathematics. First and foremost among the geniuses who worked there was David Hilbert, and Einstein was especially eager - perhaps too eager, as it would turn out - to explain the theory of relativity to him in detail.
rivalry
The visit to Göttingen was crowned with success. A few weeks later, Einstein reported to a fellow scientist that he had succeeded in "convincing Hilbert of general relativity." In a letter to another colleague he was even more enthusiastic: "I am really fascinated by Hilbert!"
Hilbert was equally fascinated by Einstein and his theory. Fascinated so much, that he soon sat down on his own to see if he could do what Einstein had not been able to do until then: find the mathematical equations that would complete the formulation of the general theory of relativity.
Einstein began to feel Hilbert breathing down his neck at the beginning of October 1915, right when it dawned on him that the current version of the theory in his hand, which he based on the "Antwerp", i.e. the outline, which he labored to polish for two years, suffered from serious deficiencies. His equations failed to adequately explain rotational motion. In addition, he realized that his equations did not have general covariance, meaning that they did not really make all accelerated and irregular motions relativistic, and they also failed to explain an anomaly observed by astronomers in the orbit of the planet Hema (Mercury). The perihelion of the planet Mercury, that is, the point where it is closest to the sun, moves gradually in a way that cannot be explained by Newtonian physics, nor by Einstein's version of his theory at the time.
Einstein faced two ticking clocks: he could sense that Hilbert was getting closer to the correct equations, and he agreed to give a series of four formal lectures on his theory on Thursdays in November to members of the Prussian Academy. The result was a stormy and exhausting month during which Einstein struggled with a series of equations, corrections and updates that he struggled to complete.
Even when Einstein arrived in the great hall of the Prussian State Library on November 4 to deliver the first of his lectures, he was still struggling with his theory. "For the last four years," he began: "I have been trying to establish a general theory of relativity." With great honesty, he detailed the problems he encountered and admitted that he had not yet been able to formulate equations that provide a complete solution.
Einstein was tortured by the tortures of frenzied scientific creativity, one of the most focused that history has known. At the same time, he faced personal crises in his family. Letters continued to arrive from his estranged wife demanding money from him and discussing guidelines regarding his relationship with their two sons. Through the mediation of a mutual friend, she demanded that he not ask their children to come visit him in Berlin, where they might discover his affair. Einstein assured his friend that in Berlin he lives in his own body and that his "isolated" apartment has an "atmosphere that almost resembles a church." The friend replied, referring to Einstein's work on general relativity, "and it should be so, since extraordinary divine forces are at work there."
In fact, on the day he presented his first article, he wrote a painful and heartbreaking letter to his eldest son, Hans Albert, who lived in Switzerland: "Yesterday I received your precious little letter and it gave me great pleasure. I was already worried that you don't want to write to me anymore... I will demand that we can be together for a month every year so that you can see that you have a father who is connected to you and loves you. You can also learn many beautiful and good things from me, which no one else can give you so easily... In the last few days I have completed one of the finest articles of my entire life; When you grow up, I'll tell you about him."
He signed off with a small apology for seeming so detached. "I am often so engrossed in my work that I forget to eat lunch," he wrote.
Einstein was also involved in a lawsuit and tense things with Hilbert. He learned that the mathematician from Göttingen had identified the flaws in the "Antwerp" equations. Einstein, who was afraid of losing the first mover's right, wrote Hilbert a letter and told him that he himself discovered the flaws, and attached to the letter a copy of his lecture from November 4.
In Einstein's second lecture, which he delivered on November 11, he imposed new correlation conditions by virtue of which his equations had generalized covariance. However, it turned out that the change did not greatly improve the state of affairs. He was close to the final answer but made little progress. This time, too, he sent his article to Hilbert and asked him how his journey was going. "My own curiosity is getting in the way of my work!" he wrote.
Hilbert sent him an answer that must have bothered Einstein. He said he had "a solution to your great problem," and invited Einstein to come to Göttingen on November 16 and have the dubious pleasure of hearing him. "Since you are so interested, I will be happy to lay out my theory in all its details for you next Thursday," Hilbert wrote. "My wife and I would be very happy if you stayed with us." Then, after signing his name, Hilbert felt compelled to add a jarring and disturbing footnote. "As I understand your new article, the solution you gave is quite different from mine."
come to a decision
Einstein wrote four letters on November 15, Monday, which provide us with a window into his interwoven professional and personal dramas. To Hans Albert he raised the possibility that he would like to go to Switzerland for Christmas to visit him. "Perhaps it would be better for us to be alone somewhere," such as an isolated inn, he told his son. "What do you think?"
He then wrote his estranged wife a letter of reconciliation in which he thanked her for her willingness to avoid "undermining my relationship with the children." And he also reported to a friend: "I introduced changes in the theory of gravity, after it became clear to me that there was a gap in my early proofs... I would love to come to Switzerland in New Year's Eve to see my dear son."
He also replied to Hilbert and declined his invitation to visit Göttingen the next day. His letter did not hide his anxiety: "The hints you gave in your messages arouse the highest expectations. However, I am forced to forego going to Göttingen… I am dead tired and suffering from a stomach ache… If you can, please send me a draft of your research to appease my impatience.”
During his hasty race to succeed in finding the exact formulation for his theory, Einstein reached a breakthrough that turned his anxiety into a feeling of transcendence. He tested a set of rewritten equations to see if they would yield the correct results for the unusual deviation in the orbit of the planet Hema. The answer received was correct: his equations predicted that the perihelion would deviate by about 43 seconds of arc per century. He was so excited that his heart fluttered and shocked. "I didn't know my soul from so much excitement and joy," he told one of his colleagues. In the ears of another physicist, he rejoiced: "The results of the perihelion movement of the planet Hema fill me with immense satisfaction. How much benefit we derive from the meticulous accuracy of astronomy, which I used to mock secretly!"
On the morning of his third lecture, on November 18, Einstein received Hilbert's new paper and was startled to see how similar it was to his own work. His reply to Hilbert was matter-of-fact and no doubt designed to emphatically declare the primacy of his own work: "The system you provide coincides, as far as I can see, exactly with what I have discovered in recent weeks and presented to the Academy," he wrote. Today I present to the Academy an article in which I quantitatively deduce from general relativity, without any guiding hypotheses, the perihelion movement of the planet Hema. No theory of gravity has achieved this feat so far.”
Hilbert responded kindly and generously the next day, and did not claim any precedence for himself. "Warm congratulations on conquering the Perihelion movement," he wrote. "If I could calculate as fast as you, in my equations the electron would have had to surrender and the hydrogen atom would have had to issue an official letter of apology explaining why it does not emit radiation." However, the next day Hilbert sent an article to the Göttingen scientific journal describing his own version of the equations of general relativity. The title he chose for the work did not excel in modesty. "The basics of physics", he called it.
It is not known whether Einstein carefully read Hilbert's article, or whether it influenced his thinking as he prepared his fourth lecture for the Prussian Academy, which was the pinnacle he was aiming for. In the end, he managed to produce in time for his final lecture on November 25, titled "The Field Equations of Gravitation," a set of covariant equations that outlined a general theory of relativity.
It was far from clear to the layman's eyes, unlike E=mc2, for example. And yet, with the succinct notation of tensors, where branching complexities can be squeezed into small tags on the margins of letters, the core of Einstein's field equations is compressed enough to adorn T-shirts worn by physics geeks. In one of its many versions, it can be written like this:
Rμν-½ gμνR = -8πGTμν
The left side of the equation - which is now known as the Einstein tensor and can be written simply using the expression Gμν - describes how the geometry of space-time is distorted and warped by objects with mass. The right wing describes the movement of matter in the gravitational field. The interplay between the two wings shows how objects curve space-time, and how this curvature, in turn, affects the movement of objects.
Already then, and to this day, there is a precedence debate on the question of which elements of the mathematical equations of general relativity were first discovered by Hilbert and not by Einstein. Whatever the facts, it was Einstein's theory that was given formal formulation by these equations, a theory that he explained to Hilbert during their time together in Göttingen that summer of 1915. Hilbert very kindly noted this in the final version of his paper: "The resulting differential gravitation equations agree , apparently, with Einstein's fundamentally spectacular theory of general relativity." And as he later summed it up: "Einstein did the work, not the mathematicians."
Einstein was tortured by the tortures of frenzied scientific creativity, one of the most focused that history has known. At the same time, he faced personal crises among his family.
Within a few weeks, Einstein and Hilbert restored their friendship. Hilbert proposed Einstein as a member of the Royal Society of Sciences of Göttingen, and Einstein responded with a heartfelt letter describing how two people who had glimpsed sublime theories should not succumb to mundane feelings. "A certain enmity has arisen between us in the past, and I do not wish to analyze its causes," Einstein wrote. "I fought the feeling of bitterness that accompanied it with complete success. I once again feel pure affection for you and ask you to try to reciprocate in kind. By all accounts, it would be a shame if two true friends, who have rescued themselves to some extent from our wretched world, did not enjoy each other's company."
"The wildest dreams"
Einstein's pride was understandable. At the age of 36, he produced a dramatic rewrite of our concepts about the universe. His general theory of relativity was not just an interpretation of any experimental data or the discovery of a more precise set of laws. It was a whole new way of relating to reality.
With the help of his special theory of relativity, Einstein showed that space and time do not have an independent existence, but together they form a fabric of space-time. Now, with the help of the general version of the theory, this fabric of space-time ceases to be just an arena containing objects and events. Instead, it received dynamics of its own, determined by the movement of the objects within it, and they in turn helped to determine that movement itself - just as the fabric of a trampoline curves as a bowling ball and a few billiard balls roll along it, and just as the same dynamic curvature of the trampoline fabric will in turn determine the The trajectory of the rolling balls will cause the billiard balls to move towards the bowling ball.
The curvature and fluttering of the fabric of space-time explained gravity, its equivalence to acceleration and the general relativity of all forms of movement. In the opinion of Paul Dirac, pioneer of quantum mechanics and Nobel laureate, this was "probably the greatest scientific discovery ever". And Max Born, one of the other great giants of 20th century physics, called it "the greatest enterprise that human thinking about nature has ever worked on, the most amazing combination of philosophical insight, physical intuition and mathematical skill."
The whole process exhausted Einstein. His marriage collapsed and war wreaked havoc in Europe, but Einstein was happier than ever. "My wildest dreams have come true," he exulted in the ears of his best friend, engineer Michel Beso. "General covariance. The perihelion movement of the planet Mercury is incredibly precise." He signed with the words: "Satisfied but kaput".
Years later, when his young son, Edward, asked him why he was so famous, Einstein answered with a simple image, describing his fundamental insight that gravity is a distortion of the fabric of space-time. "When a blind beetle crawls on the surface of a curved branch, it does not notice that the path it took is indeed curved," he said. "I got lucky and noticed what the beetle didn't."
About the writers
Walter Isaacson
He is the CEO of the Aspen Institute. He was the chairman of CNN and editor-in-chief of "Time" magazine. Isaacson authored several books, among them the book "Steve Jobs" (see Or in Hebrew translated by Ela Beshen and Naomi Carmel, Moden Publishing, 2011).
for further reading
The Field Equations of Gravitation. A. Einstein in Preussische Akademie der Wissenschaften, Sitzungsberichte, pages 844–847; December 2, 1915.
On the Generalized Theory of Gravitation. Albert Einstein; April 1950.
An Interview with Einstein. I. Bernard Cohen; July 1955
Einstein, his life and universe. Walter Isaacson, from English: David Medar, Attic Books Publishing, 2011.
More of the topic in Hayadan:
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I hope this is not classified information (I find it very hard to believe) if so don't answer or say it's impossible to say.
Did you also get to land and take off a phantom plane? Or did you only deal with navigation, electronics and armament?
rival
For no particular reason...just that they don't slander this plane 🙂
I also flew on other planes, but not for a long time.
Miracles,
Would you pilot a phantom plane?? Wow impressive! I wouldn't have thought for a second...
And why "absolutely not" regarding a pilot?
Israel
Indeed a great place - especially at the top of the cable car 🙂
I waited. Probably because I discovered military secrets.
Going to bed, coming back from Palm Springs tomorrow.
There are thousands of wind turbines here to generate electricity, a really heartwarming sight.
Good night.
rival
Definately not. I would navigate…
Miracles,
"Israel, sorry I made a noise to you...."
what exactly do you mean Don't tell me you were a fighter pilot...
Miracles
Not bad, the bottom line is they hit and that's what matters.
Not like the 101 greens that would hit anything but a target..
rival
Phantoms were the backbone of the Navy - the plane was specially built for aircraft carriers. It is also the only plane that was in the aerobatic team of the Navy - Blue Angels, and also in the team of the American Air Force - Thunderbirds.
The acceleration is horizontal, right? Think about what happens in a sharp takeoff - you feel the back of the chair being pressed against you, right? It is exactly equal to longitudinal acceleration!
In some flight trainers there is a movement system that tries to simulate accelerations. When taking off, the system raises the nose high, and when braking for landing lowers the nose low. You didn't think that Einstein's principle of equivalence would have a use for a HA flight trainer from the seventies, did you? 🙂 And you probably didn't think that this coach was initially established in Iran...
Israel
Sorry to disturb you….
Perhaps its massive appearance creates a feeling of heaviness. Was it common for a phantom plane to take off from an aircraft carrier? I don't remember seeing such planes taking off from an aircraft carrier, but maybe I'm not remembering correctly.
Not really. The same order of magnitude as the F-18 and smaller than the F-14.
Interesting, I remembered that I always saw F14 and F18 planes take off from it, I don't remember seeing Phantom planes take off from an aircraft carrier in the movies, it's a pretty heavy plane.
https://www.google.com/search?q=f4+carrier&rlz=1C1AVSW_enIL374IL375&espv=2&biw=1360&bih=677&source=lnms&tbm=isch&sa=X&ved=0ahUKEwiJ0OXchNbLAhUE92MKHZJ5AN0Q_AUIBygC
Miracles,
Are you sure phantom planes operated from an aircraft carrier?
In any case, the acceleration is horizontal, the pilot feels that he is being pushed back towards the back of the chair, I didn't understand why this would make him think he was soaring?
PS - Many pilots have suffered spinal injuries due to the use of an ejection seat, this is definitely extreme.
Miracles,
Are you sure phantom planes operated from an aircraft carrier?
In any case, the acceleration is horizontal, the pilot feels that he is being pushed back towards the back of the chair, I didn't understand why this would make him think he was soaring?
PS, many pilots have suffered spinal injuries from using an ejection seat, it is definitely extreme.
Miracles
Phantom is a barn door with two motors attached to it.. the most powerful thing in the world.
In El Arish during the Amna training at range 58 they would open burners on us from a height of 0.. the scariest thing in the world.
rival
Two anecdotes from the Phantom planes.
The first is that when taking off from an aircraft carrier, the acceleration is enormous, and at night there were pilots who thought the plane was taking off. As a natural reaction, they pushed and entered the sea.
The second - the evacuation chair comes out of the plane with a charge that explodes... So the idea is not so extreme 🙂
By the way, I suddenly realized that the example I gave before was not a good one, the whole point is that the elevator should be located on the ground (in the case of gravity) so that the person inside it feels the gravitational force of the planet, if the elevator is in space and the planet pulls it towards it then until it hits the ground The person in the elevator will feel zero gravity (he will float inside it) just like the weight in the accelerometer.
It's good to take it to an extreme case... I don't think this was the poet's intention, I think Einstein meant in this example a continuous acceleration over time that would be equivalent to gravity.
rival
And on the other hand - I found a situation where you are right. Gravity cannot appear suddenly, but acceleration can! Think of a spaceship with an explosive charge as an engine. All at once - enormous acceleration. Gravity cannot be created suddenly, and that's how you'll know for sure that it's acceleration 🙂
Miracles,
I understand what you're saying.
In the "accelerometer" entry on Wikipedia, there is a nice animation that simply shows the principle of operation of an accelerometer - a box with a spring attached to one of its inner sides with a weight at the end. When the box moves forward/backward (on the appropriate axis) the weight causes the spring to stretch or contract.
Strange, now that I understand how an accelerometer works, I see that the example I gave is a clear case of a situation where a body accelerates its speed (towards the planet) but the accelerometer fails to measure this acceleration because both the box, the spring and the weight move together at the same time Acceleration towards the planet.
What a piece, it's a bug in the device 🙂
rival
Let's think about how our accelerometer is built. The simple way to imagine it is as a bar with a parallel spring on it, the spring is fixed to the bar at one end and there is a weight at the other end.
This meter floats in space. At once - you accelerate all its parts in a certain direction. What will he show now?
Miracles,
I don't understand why you don't agree with statement 1, because as soon as the planet appears under the accelerometer, the accelerometer immediately (well, after less than a quarter of a second) begins to be attracted to it, why wouldn't it immediately show a reading? What does he care that he is surrounded by an open envelope called an "elevator", why should this affect his reading?
If the accelerometer is just floating in space, not inside an elevator, will your answer change?
Israel
Leonard Susskind describes what happens to a spaceship that falls into a black hole, both from the perspective of a passenger in the spaceship and from the outside.
As for the passenger, as long as the derivative of gravity along his body is negligible, he will not feel anything, even when crossing the ocean of events.
As for an outside observer - the spaceship crashes on the event horizon.
Miracles
Not necessarily, maybe an opponent is right.
Gravity increases - imagine that you are approaching a large mass, even a black hole, at enormous speed. The closer you are, the higher the pull and with it the acceleration observed from the outside.
Since the charge paradox you mentioned earlier established the absolute nonequivalence, i.e. that there is a difference between acceleration and gravity, it is possible that in the case I described the accelerometer would indeed show a reading.
Going to the palm springs.
rival
I disagree with 1. The accelerometer will constantly show 0. Don't think that at time 0 suddenly there is gravity. It must take time - it's physics...
Miracles,
Regarding the example you gave, I have nothing to say at the moment, it seems a bit strange to me, I don't know.
I thought of a simpler example that shows (in my opinion) that there is a difference between the two situations I mentioned earlier. Let's imagine an open elevator floating in outer space, with an accelerometer floating in the center. Tell me whether you agree with the following two claims:
1. If a large planet suddenly appears about one kilometer below the elevator, both the elevator and the accelerometer will immediately begin to be attracted to it, and the accelerometer will immediately show a reading greater than zero, as gravity pulls it towards the ground (the accelerometer will show a reading even before it hits the sides of the elevator!) .
2. If, instead of a planet, someone suddenly starts pulling the elevator "up" (toward the ceiling) in such a situation, contrary to section 1, the accelerometer will continue to show zero acceleration until the moment it hits the floor of the elevator!
Do you agree, and if not, explain. I remind you again that the elevator doors are open, there is no air in it and the accelerometer that hovers in the center is exposed to outer space.
rival
You didn't understand what I was saying. Let's place an accelerometer in the center of the spaceship, and there is space inside the spaceship. If the spaceship accelerates suddenly then the gauge will see the floor approaching and only then will it feel acceleration. If gravity is created at once, and assuming that the spaceship is fixed, or weightless, then in my opinion exactly the same thing will happen...
Sit in a chair - you don't feel gravity, you feel the counter pressure exerted by the seat.
Stretch your hand horizontally - even now you don't feel gravity, you feel the effort of the muscles that resist gravity. Do not believe? Release the muscles, and you won't feel any strength 🙂
Wow amazing, totally counter intuitive.
rival,
Assuming that the plane is full of "normal" air, the helium balloon will actually move forward...
https://www.youtube.com/watch?v=y8mzDvpKzfY
Miracles,
I am not insisting on anything and certainly I am not assuming that the theory of relativity is incorrect, it would be quite stupid to assume such a thing. I'm just trying to figure out how things work.
But it seems to me that I have largely understood where my mistake is, I need to think about it a bit more, but it seems to me that the answer to my question changes if it is a closed elevator filled with air, or an open elevator that is exposed to outer space.
In the case of a closed elevator, it seems to me that if they pull it up, the accelerometer will immediately show a reading because it will immediately move along with the air trapped in the elevator, just like a helium balloon in an airplane that accelerates and takes off, if when the airplane is still standing still the balloon is in the center of the airplane, then even when the balloon accelerates will stay there and not drift towards the rear of the plane behind.
On the other hand, if the elevator is open and you start pulling it up, in that case it seems to me that the accelerometer will show a reading only when it collides with the sides of the elevator and not before.
(Miracles if what I said before that the elevator stays in place bothered you with the theory of relativity, then let's say it is fixed on a solid pillar that is connected to the ground)
rival
Your question is spot on, even without the floor, but describing the suddenly doubled gravity is physically impossible.
But if the boss is the one who doubles it, the answer is yes.
and also negative.
The boss is omnipotent and has no problem doubling and if the meter is big enough he will rise instead of falling.
Israel
You're right... I tried to show that if you assume something illogical you reach illogical results.
rival
Why do you insist on ignoring what I said? If you assume that the theory of general relativity is wrong and you remove from it that the theory is wrong - you have not proven anything.
In the situation that the description of the principle of equivalence will be broken. So what?
The accelerometer hovers in the center of the station and shows zero acceleration/reading, the question is whether if the Earth's gravity suddenly increases by 2 times the accelerometer will show a different reading from zero even before it hits the floor or anything else.
Israel,
You've complicated matters, we're talking about a simple thought experiment, let's say that suddenly the mass of the earth doubles because that's how God wanted it, and when I said "it will immediately show a reading" I meant before it hits the floor.
(This is not a discussion about quantum theory at the moment and an immediate effect on particles, this is another discussion)
The earth's gravity will increase twice only if you put next to it a mass equal to its mass. If we suppose you brought to its center a compressed neutron star at almost the speed of light, then the effect of the double mass would reach the accelerometer at the speed of light.
I don't know what the calculations are for the third time derivative, but when the acceleration stabilizes the reading will be 0 in my understanding.
Good night.
What can I tell you, what you say just doesn't make sense to me. Are you saying that if an astronaut on the space station places an accelerometer so that it floats in the center of the room (and will of course show zero acceleration), then if the Earth's gravity suddenly doubles, the accelerometer will not immediately show a reading (acceleration)??
"If you accelerate a spacecraft at a constant acceleration over time, it will eventually reach the speed of light"
??
At any given instant of acceleration, you will be at exactly the same speed: 0. And at any given instant of acceleration, the light will be moving away from you at exactly the same speed: c
rival
To clarify: the principle of equivalence does not have to work in the case of gravity created in zero time. The principle says that it is not possible to distinguish between "normal" acceleration and gravity. If you accelerate a spaceship at a constant acceleration over time, you will eventually reach the speed of light, and then you might be able to tell.
storm
The dimension of time is found in the geriatric department. Everyone gets there.
1. The force of gravity suddenly starts to act (but the elevator stays at the same point relative to the ground! It does not move) What will happen is that the accelerometer which, as mentioned before, was hovering a meter above the floor of the elevator will immediately show a reading and drop down towards the floor of the elevator.
And what will happen after a second? Will the accelerometer continue to show a reading? After all, he is in free fall, so why would he see anything?
rival
Notice what you did. The assumption that general relativity is incorrect, and from that the conclusion that general relativity is incorrect.
And in any case, as I wrote earlier - the meter will see the floor of the spacecraft approaching it quickly. The meter, in both cases, will measure 0 acceleration, until it hits the floor.
life and miracles,
My assumption is that the elevator does not move and remains stationary, let's say it is hovering at a height of one kilometer above a planet that God has turned off its gravity, now we have two options:
1. The force of gravity suddenly starts to act (but the elevator stays at the same point relative to the ground! It does not move) What will happen is that the accelerometer which, as mentioned before, was hovering a meter above the floor of the elevator will immediately show a reading and drop down towards the floor of the elevator.
2. Gravity remains off but someone (God) starts pulling the elevator up away from the planet, in which case the accelerometer will show zero (unlike the previous example) until the moment the floor of the elevator hits it from below, and only then will it start showing acceleration.
I'd love to hear your opinion.
rival
An interesting example. Note that your meter is in free fall - then he will not feel that there is gravity, he will only notice that the elevator floor is touching him.
to the opponent
I do assume that the same planet did appear within 0 time. Let's say that God moved it from an "off" state to an "on" state.
You claim that the accelerometer will sense (section 1).
This. no Try to design such an accelerometer. Don't forget that the elevator and its contents are in free fall. You will find that it is impossible to plan it. The theory of relativity is built on this.
Is there proof of the existence of the time dimension?
I would love to hear a reference to the thought experiment I proposed with the accelerometer.
Consider the topic closed. 😀
Israel
I noticed this sentence 🙂 really puzzling.
What's more, there are several websites that talk about it, and they say what I said, and what Albenzo said - that the equivalence refers only to local systems.
Miracles
Many thanks for the article. Finally an exhaustive, though not complete, explanation of the problem.
On the other hand, the fact that the "cargo paradox" exists at all shows that the question is certainly correct, isn't it? The solution includes a curvature tensor and a Minkowski trap, which shows that your simple solution "toward the outside the electron is not accelerating and therefore does not radiate" is a bit.. simplistic.
The solution, by the way, does not appear in full in the article, only references to it.
Also note that the article ends with:
The radiation from the supported charge is something of a curiosity: where does it go? Boulware (1980) [2] finds that the radiation goes into a region of spacetime inaccessible to the co-accelerating, supported observer.
rival
1. Take an electron and place it on the table.
2. Raise an eyebrow and run around the armchair.
If in both situations you have a match, then you succeeded. And if not, then it's pretty clear that it's God. So
Miracles,
"A rival, there is no difference even though it is strange. Sit on a chair - where do you feel gravity? Put a block of jelly in an accelerating spaceship or on the floor next to you - the jelly will take the same shape.'
I'm really not sure you're right, I thought of a maybe better example than the whipped cream. Imagine an elevator in a space in which an accelerometer hovers at a height of one meter above the floor of the elevator:
1. If a large planet suddenly appears under the elevator and begins to exert its gravity on it, the accelerometer will immediately feel the gravity, even before it hits the floor.
2. If, on the other hand, we start pulling the elevator up, the accelerometer will not feel anything and will show zero acceleration until the moment it hits the floor.
Am I right, or am I right?
Israel
Read here … it will save us both: https://en.wikipedia.org/wiki/Paradox_of_a_charge_in_a_gravitational_field
rival
There is no difference, although it is strange. Sit on a chair - where do you feel gravity? Put a block of jelly in a speeding spaceship or on the floor next to you - the jelly will take the same shape.
rival
"The force will only be applied to the molecules in the lower part of the custard that are adjacent to the plate."
And won't a force act on the molecules above them? And for their part on those above them?
But I see the logic in your words, maybe there is a solution.
Double power is equal -
Working. going to work
The point is that it doesn't matter in terms of a body whether it accelerates or by gravity, see opponent's question. Also a charged body.
So why when he accelerates with an accelerated elevator in space he will radiate and when he is in a gravitational field not? Doesn't the elevator floor exert the same force on him in both cases? How does he know how to distinguish between them?
Israel,
"The shape, taste and aroma of the custard will be the same, because the floor of the elevator exerts the same force on each object, by acceleration or gravity"
You missed the point of my question even though I emphasized it:
1. In the case of gravity, the gravitational force will act equally on every molecule of the custard, both below, above and in the middle.
2. In the case of upward acceleration, only the floor will exert a force on the custard, the force will be exerted only on the molecules in the lower part of the custard that are adjacent to the plate.
So what, there is no difference between the two situations?
Israel
Both will arrive together...yet the proton will radiate and the neutron will not.
The positron of course!
relevance?
rival
"Say, and in our elevator there is a piece of jelly on a plate, or custard or whipped cream (that is, something soft and flexible), will its shape be the same in an elevator that is standing still and the Earth's gravity is acting on it, and in an elevator that is in space and is being accelerated upwards?"
In my understanding, your question nicely demonstrates the principle of equivalence. The shape, taste and aroma of the custard will be the same, because the floor of the elevator exerts the same force on every object, in acceleration or gravity, and this also includes the electrons of Nissim Arkman.
😀
Israel
I'll ask you - I go to the top of the Tower of Pisa and drop a proton and a neutron - who will reach the ground first?
Miracles
The equivalence principle only talks about what the electron feels. Did not you have enough ? 🙂
Can you explain what the difference is in terms of how an electron feels between acceleration and gravity? Doesn't he feel exactly the same?
Electron Galamod 🙁
Israel
To the outside the electron is not accelerating and therefore does not radiate. The equivalence principle only talks about what the electron feels. Did not you have enough ? 🙂 🙂
rival
There are many reasons for this. One is that the station will simply fall apart. A second reason is that the force of gravity depends on the radius, and because the person is larger relative to the radius, then the head will be in too low gravity, or the legs in too high gravity.
And another question,
Let's say that in our elevator there is a piece of jelly on a plate, or custard or whipped cream (that is, something soft and flexible), will its shape be the same in an elevator that is standing still and the Earth's gravity is acting on it, and in an elevator that is in space and is being accelerated upwards?
Because in the first case, the earth's gravity is applied simultaneously and uniformly on all the atoms and molecules of our whipped cream or piece of jelly. On the other hand, in the second case, only the floor of the elevator pushes and exerts pressure on the delicious whipped cream.
So what do you think, which of the whipped creams will be tastier?
The question is over,
Speaking of gravity, there is a lot of talk about the negative effects of not feeling gravity on the International Space Station, loss of calcium, the weakness of the bones... Why isn't artificial gravity actually produced there by spinning the station around an axis?
Grace
It has nothing to do with speed, relative or not.
According to the principle of equivalence, an electric charge placed on a table at rest relative to the ground is in acceleration.
My question is why it won't radiate as it would if we shake it sideways in space.
The elevator thing brings to mind a mathematical question that tortured me as a high school student.
This is a train car with the windows open and a locomotive pulling it at a speed of 85 km/h. A bee is flying inside the car.
A train arrives opposite with a carriage whose windows are open traveling at a speed of 100 km/h. The bee leaves the window of one train and enters the window of the other train just as soon as the two trains pass each other.
The question was: what is the speed of the bee?
Adversary/Confidential
You don't have to be smart - obviously if we enter information from an external source then you can know if you are in motion or not. In the elevator you see the floor number...
In my experience - if you make a loop in a plane in clouds then you have no way of knowing where it is up. Of course there are flight instruments that tell you your situation, but that's not the point here 🙂
And just something I remembered: in night take-offs of fighter jets from passenger planes, there have been several cases where pilots entered the sea immediately after leaving the ship. It turns out that the reason is the enormous acceleration of the take-off system - the strong pressure on your back gives you the feeling that you are taking off sharply and the immediate reaction is to try to lower the nose. In practice - the plane was almost horizontal and the pilots pushed themselves into the sea... (The phenomenon is called "Somatogravic Illusion")
Israel Shapira,
An electric charge in amber creates an electric field around it that can be measured by an observer outside the table, when the observer is not pulled by gravity (that is, an accelerator into space from the table's view) he will feel the radiation since an electric field appears as an electromagnetic field in the observer's system. There is no contradiction between the different systems, just a perceptual difficulty for us as slow people who are not used to relative speeds on a daily basis.
rival,
Of course you are right opponent. But that's exactly the point: all the other indicators - are you moving away from or closer to the sun, are relative indicators. From a physical point of view: there is no difference between the phenomenon of gravity and the phenomenon of acceleration.
But I don't understand enough in the field. Maybe it's just an Einstein metaphor. After all, in the end, Einstein reached his conclusions only because that's how Einstein thought. And then he found proofs for them, because... well, he's Einstein so he can find proofs.
I bought Einstein's biography and it says that he did get a "bachelor apartment" in Berlin, but the apartment had 7 rooms! On our scale this is really a singles apartment, a lot of singles.
"He determined that if you are inside a closed chamber ("elevator") you cannot, through any physical experiment, differentiate between gravity and upward acceleration"
Maybe it's a kind of cleverness, but I'm pretty sure that it's actually possible by measuring different elements that penetrate the walls of the elevator, such as radiation of various kinds, or the gravitational forces of nearby suns and planets (from which direction they come, at what angle, are they constant or changing over time and in what direction).
The meaning of the previous response is of course that small G is the determinant. A large G is Newton's constant.
Abraham,
"Ar Mio New", "G Mio New", "T Mio New" etc. (forgive me for the phonetic writing, I don't want to embed the plaster because I'm afraid that the automatic system will delay my response) are tensors. That is, it's not G times Mio times New, or even G times "Mio New". Miu and Niu are indices (for the sake of it, let's say they run between 0 and 3), meaning that this tensor - G Miu Niu - has 16 different components, all combinations of the indices between 0 and 3. You can think of it as a matrix with 4 rows and 4 columns. Not all components are independent, but that's not relevant right now. What is relevant is that the magnitude denoted G and the magnitude denoted G Mio New are completely different (if you know a little algebra, then say that G is the determinant of the tensor G Mio New). In fact, even though you only wrote one line - there are a lot of equations there (one equation for each choice of different mio and nio), hence the name "Einstein's field equations" and not "the field equation".
He also had to be a copywriter…
And later - a similar question
Why can't the "common factor" μν be "reduced" in the beacon Rμν-½ gμνR = -8πGTμν?
Thanks.
As someone who does not know tensors, I would like a brief explanation:
Why the left wing in the beacon Rμν-½ gμνR = -8πGTμν cannot be written short Rμν(1-½ g)
Einstein is sometimes mocked in various ways. They said that his wife, they said that Hilbert,...
However, Einstein's intellectual fingerprint is evident on every step. Similar ideas from special relativity, his famous thought experiments and also in the way he formulated physical "axioms" - and followed them to the end, without proof. For example, he stated that if you are inside a closed cell ("elevator") you cannot, through any physical experiment, differentiate between gravity and upward acceleration.
As for Didi, even if Einstein had failed in developing the equations, even if he had used Hilbert's mathematical abilities comprehensively and completely - even then he would not have deserved to be recognized as the discoverer of the theory of relativity. In this case, Hilbert was considered a talented and skilled student who helped his Rabbi with the mathematical aspect of the Torah. The fact that Einstein overtook a mathematician like Hilbert in a race is interesting in itself.
The theory of relativity is still the highest quality scientific project of one person. The closest major project was Newton's project. To Newton's credit, it can be said that he was a pioneer, and that he also developed the mathematics necessary for his physics. While Einstein developed his theory while standing on Newton's shoulders. However, Newton's theory is easy and intuitive. It is easy to explain to XNUMXth grade students and they internalize it easily. Not so regarding special and general relativity. These are difficult, non-intuitive, and even today there are very few people who understand them on Borin.
Or, without a doubt we said and we said and we repeated and we said and we both demanded..
The only question is whether we said it right..
Israel
There is no equivalence, as we have already said. The mosquito feels equivalence, as we have already said. Regarding an outside observer, there is no equivalence, as we have already said. Did we already say that?
And on the table isn't it in a hurry? So where is the equivalence?
Israel
If it's loaded it will beam with acceleration, but not on the table.
OK, but will the amber nugget radiate with acceleration? And on the table?
Israel
Albenzo explained correctly (as if, da!). The principle of equivalence does not mean that gravity and acceleration cannot be distinguished at all - this is an "Israeli" invention. That unfortunate fossilized mosquito in your block of amber cannot tell if it is in a rocket accelerating into space at 1G, or in your living room. As for an observer outside Amber, there is no problem knowing.
Miracles
It doesn't work out. If the principle of equivalence is sweeping, then a block of amber on a table should also radiate.
Albanzo explained it at the time:
"Einstein's equivalence principle is *local*. Meaning, an accelerated charge interacts locally with its environment which is exactly the same as the interaction of a particle in a gravitational field. But the principle of equivalence in no way means that the measurement of a non-local quantity cannot distinguish between acceleration and gravity.'
So if it is possible to distinguish in some measurement between acceleration and gravity, what is the difference between them?
Israel
If the block is at rest relative to you then there will be no radiation.
Miracles
If we wave a charged amber block to the sides quickly, then by definition it is an accelerated electric charge and I can measure the radiation with a radiation meter, right?
How about it lying on the table in the living room? Does it accelerate even then? Will my attorney be able to measure the radiation from a block of amber that is placed on the table in the living room? Where does the radiant energy come from?
Israel
The electron is at rest in the local axis system, but towards an external observer the electron accelerates and therefore radiates. If you (or your proxy) fall together with the electron then you will not feel radiation.
excellent managed to illustrate to me how fragile and difficult Einstein was.
Excellent article.
More interesting details - Einstein and Mileva had a daughter, Lieserl, who was born in 1902, even before their marriage, she was raised by Mileva's parents and it is not known where she went. She probably died at the age of 18 months.
Some claim, especially Serbs, that Milva Einstein is the real creator of relativity, while Albert the Fool only plagiarized it (see Gali Weinstein's article on the subject).
In the last years of Einstein's life at Princeton, he was among the few friends of the mathematician Kurt Gedel, who was one of the few people whom he admired without limit.
A question I have regarding the equivalence principle that I have not yet received a satisfactory answer to:
According to Newton, a body in free fall is accelerating. According to Einstein, no.
But what happens with an accelerating electric charge? It's supposed to emit electromagnetic radiation, isn't it?
So if it is in free fall, will it radiate or not?
And if the answer is no - will it radiate when it is at rest relative to the earth (at the Einstein acceleration)?