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Posts Tagged ‘relativity’

19 December was the 141th anniversary of the birth of Mileva Marić Einstein. But who remembers this brilliant scientist? While her husband, Albert Einstein is celebrated as perhaps the best physicist of the century, one question about his career remains: How much did his first wife contribute to his groundbreaking science? While nobody has been able to credit her with any specific part of his work, their letters and numerous testimonies presented in the books dedicated to her(1-5) provide substantial evidence on how they collaborated from the time they met in 1896 up to their separation in 1914. They depict a couple united by a shared passion for physics, music and for each other. So here is their story.

Mileva Marić was born in Titel in Serbia in 1875. Her parents, Marija Ruzić and Miloš Marić, a wealthy and respected member of his community, had two other children: Zorka and Miloš Jr. Mileva attended high school the last year girls were admitted in Serbia. In 1892, her father obtained the authorization of the Minister of Education to allow her to attend physics lectures reserved to boys. She completed her high school in Zurich in 1894 and her family then moved to Novi Sad. Mileva’s classmates described her as brilliant but not talkative. She liked to get to the bottom of things, was perseverant and worked towards her goals.

Albert Einstein was born in Ulm in Germany in 1879 and had one sister Maja. His father, Hermann, was an industrial. His mother, Pauline Koch came from a rich family. Albert was inquisitive, bohemian and rebel. Being undisciplined, he hated the rigor of German schools so he too finished his high school in Switzerland and his family relocated to Milan.


Mileva Marić in 1896 when she entered the Polytechnic Institute in Zurich

Albert and Mileva were admitted to the physics-mathematics section of the Polytechnic Institute in Zurich (now ETH) in 1896 with three other students: Marcel Grossmann, Louis Kollros and Jakob Ehrat. Albert and Mileva became inseparable, spending countless hours studying together. He attended only a few lectures, preferring to study at home. Mileva was methodical and organized. She helped him channel his energy and guided his studies as we learn from Albert’s letters, exchanged between 1899-1903 during school holidays: 43 letters from Albert to Mileva have been preserved but only 10 of hers remain(5). These letters provide a first-hand account on how they interacted at the time.

In August 1899, Albert wrote to Mileva: « When I read Helmholtz for the first time, it seemed so odd that you were not at my side and today, this is not getting better. I find the work we do together very good, healing and also easier.” Then on 2 October 1899, he wrote from Milan: “… the climate here does not suit me at all, and while I miss work, I find myself filled with dark thoughts – in other words, I miss having you nearby to kindly keep me in check and prevent me from meandering”.

Mileva boarded in a pension for women where she met her life-long friends Helene Kaufler-Savić and Milana Bota. Both spoke of Albert’s continuous presence at Mileva’s place, where he would come freely to borrow books in Mileva’s absence. Milan Popović, Helene’s grandson, published the letters Mileva exchanged with her throughout her life(4).

 By the end of their classes in 1900, Mileva and Albert had similar grades (4.7 and 4.6, respectively) except in applied physics where she got the top mark of 5 but he, only 1. She excelled at experimental work while he did not. But at the oral exam, Professor Minkowski gave 11 out of 12 to the four male students but only 5 to Mileva. Only Albert got his degree.

Meanwhile, Albert’s family strongly opposed their relationship. His mother was adamant. “By the time you’re 30, she’ll already be an old hag!” as Albert reported to Mileva in a letter dated 27 July 1900, as well as « She cannot enter a respectable family ”. Mileva was neither Jewish, nor German. She had a limp and was too intellectual in his mother’s opinion, not to mention prejudices against foreign people. Moreover, Albert’s father insisted his son found work before getting married.

In September 1900, Albert wrote to Mileva: “I look forward to resume our new common work. You must now continue with your research – how proud I will be to have a doctor for my spouse when I’ll only be an ordinary man.“ They both came back to Zurich in October 1900 to start their thesis work. The other three students all received assistant positions at the Institute, but Albert did not. He suspected that professor Weber was blocking him. Without a job, he refused to marry her. They made ends meet by giving private lessons and “continue[d] to live and work as before.“ as Mileva wrote to her friend Helene Savić.

On 13 December 1900, they submitted a first article on capillarity signed only under Albert’s name. Nevertheless, both referred to this article in letters as their common article. Mileva wrote to Helene Savić on 20 December 1900. We will send a private copy to Boltzmann to see what he thinks and I hope he will answer us.” Likewise, Albert wrote to Mileva on 4 April 1901, saying that his friend Michele Besso “visited his uncle on my behalf, Prof. Jung, one of the most influential physicists in Italy and gave him a copy of our article.”

The decision to publish only under his name seems to have been taken jointly. Why? Radmila Milentijević, a former history professor at City College in New York, published in 2015 Mileva’s most comprehensive biography(1). She suggests that Mileva probably wanted to help Albert make a name for himself, such that he could find a job and marry her. Dord Krstić, a former physics professor at Ljubljana University, spent 50 years researching Mileva’s life. In his well-documented book(2), he suggests that given the prevalent bias against women at the time, a publication co-signed with a woman might have carried less weight.

We will never know. But nobody made it clearer than Albert Einstein himself that they collaborated on special relativity when he wrote to Mileva on 27 March 1901: “How happy and proud I will be when the two of us together will have brought our work on relative motion to a victorious conclusion.”

 Then Mileva’s destiny changed abruptly. She became pregnant after a lovers’ escapade in Lake Como. Unemployed, Albert would still not marry her. With this uncertain future, Mileva took her second and last attempt at the oral exam in July 1901. This time, Prof. Weber, whom Albert suspected of blocking his career, failed her. Forced to abandon her studies, she went back to Serbia, but came back briefly to Zurich to try to persuade Albert to marry her. She gave birth to a girl named Liserl in January 1902. No one knows what happened to her. She was probably given to adoption. No birth or death certificates were ever found.

Earlier in December 1901, their classmate Marcel Grossman’s father intervened to get Albert a post at the Patent Office in Bern. He started work in June 1902. In October, before dying, his father granted him his permission to marry. Albert and Mileva married on 6 January 1903. Albert worked 8 hours a day, 6 days a week at the Patent Office while Mileva assumed the domestic tasks. In the evenings, they worked together, sometimes late in the night. Both mentioned this to friends, he to Hans Wohlwend, she to Helene Savić on 20 March 1903 where she expressed how sorry she was to see Albert working so hard at the office. On 14 May 1904, their son Hans-Albert was born.


Mileva and Albert’s wedding picture in 1903

Despite this, 1905 is now known as Albert’s “miracle year”: he published five articles: one on the photoelectric effect (which led to the 1921 Nobel Prize), two on Brownian motion, one on special relativity and the famous E = mc2. He also commented on 21 scientific papers for a fee and submitted his thesis on the dimensions of molecules. Much later, Albert told R. S. Shankland(6) that relativity had been his life for seven years and the photoelectric effect, for five years. Peter Michelmore, one of his biographers(7), wrote that after having spent five weeks to complete the article containing the basis of special relativity, Albert “went to bed for two weeks. Mileva checked the article again and again, and then mailed it”. Exhausted, the couple made the first of three visits to Serbia where they met numerous relatives and friends, whose testimonies provide a wealth of information on how Albert and Mileva collaborated.

Mileva’s brother, Miloš Jr, a person known for his integrity, stayed on several occasions with the Einstein family while studying medicine in Paris. Krstić(2) wrote: “[Miloš] described how during the evenings and at night, when silence fell upon the town, the young married couple would sit together at the table and at the light of a kerosene lantern, they would work together on physics problems. Miloš Jr. spoke of how they calculated, wrote, read and debated.” Krstić heard this directly from relatives of Mileva, Sidonija Gajin and Sofija Galić Golubović.

Zarko Marić, a cousin of Mileva’s father, lived in the countryside property where the Einsteins stayed during their visit. He told Krstić how Mileva calculated, wrote and worked with Albert. The couple often sat in the garden to discuss physics. Harmony and mutual respect prevailed. Gajin and Zarko Marić also reported hearing from Mileva’s father that during the Einstein’s visit to Novi Sad in 1905, Mileva confided to him: “Before our departure, we finished an important scientific work which will make my husband known around the world.” Krstić got this same information in 1961 from Mileva’s cousin, Sofija Galić Golubović, who was present when Mileva said it to her father.


Mileva, Albert and their son Hans-Albert in 1905

Desanka Trbuhović-Gjurić published Mileva’s first biography in Serbian in 1969(3). It later appeared in German and French. She described how Mileva’s brother often hosted gatherings of young intellectuals at his place. During one of these evenings, Albert would have declared: “I need my wife. She solves for me all my mathematical problems”, something Mileva is said to have confirmed.

In 1908, the couple constructed with Conrad Habicht an ultra-sensitive voltmeter. Trbuhović-Gjurić attributes this experimental work to Mileva and Conrad, and wrote: “When they were both satisfied, they left to Albert the task of describing the apparatus, since he was a patent expert.” It was registered under the Einstein-Habicht patent. When Habicht questioned Mileva’s choice not to include her name, she replied making a pun in German: “Warum? Wir beide sind nur ein Stein.“ (“Why? The two of us are but one stone”, meaning, we are one entity).

The first recognition came in 1908. Albert gave unpaid lectures in Bern, then was offered his first academic position in Zurich in 1909. Mileva was still assisting him. Eight pages of Albert’s first lecture notes are in her handwriting. So is a letter drafted in 1910 in reply to Max Planck who had sought Albert’s opinion. Both documents are kept in the Albert Einstein Archives (AEA) in Jerusalem. On 3 September 1909, Mileva confided to Helene Savić: “He is now regarded as the best of the German-speaking physicists, and they give him a lot of honours. I am very happy for his success, because he fully deserves it; I only hope and wish that fame does not have a harmful effect on his humanity.” Later, she added: “With all this fame, he has little time for his wife. […] What is there to say, with notoriety, one gets the pearl, the other the shell.”


Mileva and Albert in 1910.

Their second son, Eduard, was born on 28 July 1910. Up to 1911, Albert still sent affectionate postcards to Mileva. But in 1912, he started an affair with his cousin, Elsa Löwenthal while visiting his family who had moved to Berlin. They maintained a secret correspondence over two years. Elsa kept 21 of his letters, now in the Collected Papers of Albert Einstein. During this period, Albert held various faculty positions first in Prague, back in Zurich and finally in Berlin in 1914 to be closer to Elsa.

This caused their marriage’s collapse. Mileva moved back to Zurich with her two sons on 29 July 1914. In 1919, she agreed to divorce, with a clause stating that if Albert ever received the Nobel Prize, she would get the money. When she did, she bought two small apartment buildings and lived poorly from their income. Her son, Eduard stayed frequently in a sanatorium. He later developed schizophrenia and was eventually internalised. Due to these medical expenses, Mileva struggled financially all her life and eventually lost both buildings. She survived by giving private lessons and on the alimony Albert sent, albeit irregularly.

In 1925, Albert wrote in his will that the Nobel Prize money was his sons’ inheritance. Mileva strongly objected, stating the money was hers and considered revealing her contributions to his work. Radmila Milentijević quote from a letter Albert sent her on 24 October 1925 (AEA 75-364). ”You made me laugh when you started threatening me with your recollections. Have you ever considered, even just for a second, that nobody would ever pay attention to your says if the man you talked about had not accomplished something important. When someone is completely insignificant, there is nothing else to say to this person but to remain modest and silent. This is what I advise you to do.

Mileva remained silent but her friend Milana Bota told a Serbian newspaper in 1929 that they should talk to Mileva to find out about the genesis of special relativity, since she was directly involved. On 13 June 1929, Mileva wrote to Helene Savić: ”Such publications in newspapers do not suit my nature at all, but I believe that all that was for Milana’s joy, and that she probably thought that this would also be a joy for me, as I can only suppose that she wanted to help me receive some public rights with regard to Einstein. She has written to me in that way, and I let it be accepted that way, for otherwise the whole thing would be nonsense.”


Mileva later on (unknown date)

According to Krstić(2), Mileva spoke of her contributions to her mother and sister. She also wrote to her godparents explaining how she had always collaborated with Albert and how he had ruined her life, but asked them to destroy the letter. Her son, Hans-Albert, told Krstić(2) how his parents’ “scientific collaboration continued into their marriage, and that he remembered seeing [them] work together in the evenings at the same table.” Hans-Albert’s first wife, Frieda, tried to publish the letters Mileva and Albert had sent to their sons but was blocked in court by the Einstein’s Estate Executors, Helen Dukas and Otto Nathan in an attempt to preserve the “Einstein’s myth”. They prevented other publications, including one from Krstić(2) on his early findings in 1974. Krstić mentions that Nathan even “visited” Mileva’s apartment after her death in 1948. On July 1947, Albert wrote to Dr Karl Zürcher, his divorce lawyer: “When Mileva will no longer be there, I’ll be able to die in peace.”

 Their letters and the numerous testimonies show that Mileva Marić and Albert Einstein collaborated closely from their school days up to 1914. Albert referred to it repeatedly in his letters, like when he wrote: « our work on relative motion”. Their union was based on love and mutual respect, which allowed them together to produce such uncommon work. She was the first person to recognize his talent. Without her, he would never have succeeded. She abandoned her own aspirations, happy to work with him and contribute to his success, feeling they were one unique entity. Once started, the process of signing their work under his unique name became impossible to reverse. She probably agreed to it since her own happiness depended on his success. Why did Mileva remain silent? Being reserved and self-effaced, she did not seek honors or public attention. And as is always the case in close collaborations, the individual contributions are nearly impossible to disentangle.

Pauline Gagnon

This article first appeared in Scientific American as an Opinion piece

To find out more about particle physics and dark matter, check out my book « Who Cares about Particle Physics: making sense of the Higgs boson, the Large Hadron Collider and CERN ».

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(1) Radmila Milentijević: Mileva Marić Einstein: Life with Albert Einstein, United World Press, 2015.

(2) Dord Krstić: Mileva & Albert Einstein: Their Love and Scientific Collaboration, Didakta, 2004.

(3) Desanka Trbuhović-Gjurić: Mileva Marić Einstein: In Albert Einstein’s shadow: in Serbian, 1969, German, 1982, and French, 1991.

(4) Milan Popović: In Albert’s Shadow, the Life and Letters of Mileva Marić, Einstein’s First Wife, The John Hopkins University Press, 2003.

(5) Renn and Schulmann, Albert Einstein / Mileva Marić, The Love Letters, Princeton University Press, 1992.

(6) Peter Michelmore, Einstein, Profile of the Man, Dodd, Mead & Company, 1962.

(7) R.S. Shankland, Conversation with Albert Einstein, Am. J. of Physics, 1962.


This article appeared in symmetry on March 12, 2015.

You’ve heard of Einstein’s E=mc2, but what does it mean?

You’ve heard of Einstein’s E=mc2, but what does it mean?

With Einstein’s birthday just around the corner on March 14 (which also happens to be Pi Day), it seems appropriate to take a fresh look at one of his biggest accomplishments with a short video.

In 1905, Einstein published four papers that radically changed how we look at the world around us. Dubbed Einstein’s “Annus Mirabilis,” or “Year of Wonders,” it gave us revolutionary new ideas about light, atoms and how your frame of reference makes a big difference in your perception.

It was Einstein’s final paper that year that really took the (birthday) cake. In it, he gave us a deceptively simple idea—that mass and energy were equivalent. He even summed it up for us with the tiny equation E=mc2*.

However, while appearing simple, the implications of E=mc2 are huge and far-reaching. To find out why, sit back, enjoy some birthday cake (or pie, depending on how you’re celebrating), and watch the video!

*Although we are most familiar with E=mc2, Einstein didn’t quite say it that way in the original paper. It was actually in the form of a sentence in German: “If a body gives off the energy L in the form of radiation, its mass diminishes by L/V2.”

Chris Smith


This week the OPERA experiment released a statement about their famous “faster than light” neutrino measurement. In September scientists announced that they had measured the speed of neutrinos traveling from CERN to Gran Sasso and they found that they arrived slightly sooner than they should do according to special relativity. There was a plethora of scientific papers, all kinds of rumors and speculation, and most physicists simply refused to believe that anything had traveled faster than light. After months of diligent study, OPERA announced that they may have tracked down two sources of experimental error, and they are doing their best to investigate the situation.

But until we get the results of OPERA’s proposed studies we can’t say for sure that their measurement is right or wrong. Suppose that they reduce the lead time of the neutrinos from 60ns to 40ns. That would still be a problem for special relativity! So let’s investigate how we can get faster than light neutrinos in special relativity, before we no longer have the luxury of an exciting result to play with.

The OPERA detector (OPERA Collaboration)

The OPERA detector (OPERA Collaboration)

Special relativity was developed over a hundred years ago to describe how electromagnetic objects act. The electromagnetic interaction is transferred with electromagnetic waves and these waves were known to travel extremely quickly, and they seemed to travel at the same speed with respect to all objects, no matter how those objects were moving. What Einstein did was to say that the constancy of the speed of light was a fundamental law of nature. Taking this to its logical conclusion meant that the fastest speed possible was the speed of light. We can call the fastest possible speed \(s\) and the speed of light \(c\). Einstein then says \(c=s\). And that’s how things stood for over a century. But since 1905 we’ve discovered a whole range of new particles that could cast doubt on this conclusion.

When we introduce quantum mechanics to our model of the universe we have to take interference of different states into account. This means that if more than one interaction can explain a phenomenon then we need to sum the probabilities for all these interactions, and this means we can expect some strange effects. A famous example of this is the neutral kaon system. There two lightest neutral kaons are called \(K^0\) and \(\bar{K}^0\) and the quark contents of these mesons are \(d\bar{s}\) and \(s\bar{d}\) respectively. Now from the “outside” these mesons look the same as each other. They’ve got the same mass, they decay to the same particles and they’re made in equal numbers in high energy processes. Since they look identical they interfere with each other, and this gives us clues about why we have more matter than antimatter in the universe.

Since we see interference all over the place in the Standard Model it makes sense to ask if we see interference with a photon. It turns out that that we do! The shape of the Z mass peak is slightly asymmetric because of interference between virtual Z bosons and virtual photons. There are plenty of other particles that the photon can interfere with, including the \(J/\psi\) meson, and the \(\rho\) meson. In fact, any neutral vector meson with no net flavor will do. Einstein didn’t know about any of these particles, and even if he did he never really accepted the conclusions of quantum mechanics, so it’s no surprise that his theory would require that the speed of light is the fastest speed (that is, \(c=s\).) But if the photon interferes with other particles then it’s possible that the speed of light is slightly lower than the fastest possible speed (\(c<s\)). Admittedly, the difference in speed would have to be very small!

In terms of quantum mechanics we would have something like this:
|light>_{Einstein} = |\gamma>
|light>_{reality} = a_\gamma |\gamma> + a_{J/\psi} |J/\psi> + a_Z |Z> + \ldots

As you can see there are a lot of terms in this second equation! The contributions would be tiny because of the large difference in mass between the massive particles and the photon. Even so, it could be enough to make sure that the speed of light is ever so slightly slower than the fastest possible speed.

At this point we need to make a few remarks about what this small change in speed would mean for experiments. It would not change our measurements of the speed of light, since the speed of light is still extremely fast and no experiment has ever showed a deviation from this extremely fast speed. Unless somebody comes up with an ingenious experiment to show that the difference between the speed of light and the fastest possible speed is non-zero we would probably never notice any variation in the speed of light. It’s a bit unfortunate that since 1983 it’s been technically impossible to measure the speed of light, since it is used in the definition of our unit of length.

Now we know that photons can interfere with other particles it makes sense to ask the same question about neutrinos. Do they interfere with anything? Yes, they can interfere, so of course they do! They mix with neutrinos of other flavors, but beyond that there are not many options. They can interfere with a W boson and a lepton, but there is a huge penalty to pay in the mass difference. The wavefunction looks something like this:
|\nu_e>(t) = a(t)_{\nu_e}|\nu_e> + a(t)_{\nu_{\mu}}|\nu_\mu> + a(t)_{\nu_{\tau}}|\nu_\tau> + a(t)_{We}|We>
(I’ve had to add a time dependence due to neutrino mixing, but it’s essentially no more complicated than what we had for the photon.)

That means that the photon could get slowed down slightly by the interference with other particles (including particles in the vacuum) and that neutrinos could get slowed down more slightly by their interference terms with other particles. And that way we could get neutrinos traveling faster than the speed of light and special relativity could remain intact. (In this description of the universe we can do what used to seem impossible, we can boost into the rest frame of a photon. What would it mean to do that? Well I suppose it would mean that in this frame the photon would have to be an off-shell massive particle at rest.)

The SN 1987 supernova, a rich source of slower than light electron neutrinos (Hubble, ESA/NASA)

Now I’ll sit back and see people smarter than I am pick holes in the argument. That’s okay, this isn’t intended to be a serious post, just a bit of fun! There are probably predictions of all kinds of weird effects such as shock waves and time travel that have never been observed. And there are plenty of bits I’ve missed out such as the muon neutrinos traveling faster than electron neutrinos. It’s not often we get an excuse to exercise our analytic muscles on ideas like this though, so I think we should make the most of it and enjoy playing about with relativity.