What's the Big Idea?

What if Einstein never discovered the equation?

Sivanesan Subramaniam from Malaysia asks:

      What would have happened, if Einstein never discovered the equation?

My personal point of view is that  some other scientist would arrive to the same conclusions very soon. The special theory of relativity (and consequently the famous E=mc² equation) was 'in the air'. Lorentz transformations  and Poincare` group were used by Einstein in the formulation of his special theory of relativity. His big intuition consisted in giving a right interpretation of the effect, correcting some mistakes made by his predecessors and coming to the elegant formulation of the theory.

On the contrary, his general theory of relativity, with the new equations of gravitation, which was published ten years later, brought into the 1916 scientific community a really revolutionary and absolutely original new idea.

"c": scalar or vector?

Since David already answered, I add just a few words:

"c", the quantity which is considered a universal 'constant', is the "magnitude" of the velocity of light, not its direction, of course. Moreover, in the E = mc² formula the energy E is compared to the square of the speed of light: you can do the "square" of the magnitude of a vector, which is essentially a "number", not of the direction, so this should cancel any doubt.

Is "c" a scalar or vector?

Anupama from India writes:

I understand the equation of E=MC2 but really cant create a picture in my mind.

  E-stands for energy
  m-stands for mass

but

  c-stands for velocity of light or speed of ligt.

From my lessons on vectors and scalar quantities i've learnt that velocity
as -vector quantity(have magnitude and direction and speed-scalar
quantity(have only direction).well, my confusion comes here wheather to
consider'C'in einsteins equation as vector quantity or scalar quantity?

If it's considered a vector quantity the direction should also be included
in E=mc2 but this was not so. i would like to know wheather 'c'is vector
or scalar in his equation?

The speed of light "c" is a scalar (notice I called it "speed"). The energy is the same, regardless of the direction of the velocity. At the root of your confusion is probably word choice. Sometimes people are sloppy with their use of speed and velocity (I know I am guilty sometimes!).

Is a faster electron a heavier electron?

Here's a question that frequently gets asked about E=mc^2...

Somu Selvaraj asks:
According to quantum theory of light,it contains the packets of quanta called photons.When electromagnetic waves like X-rays,gama rays,incident on the surface of certain metals the electrons on them absorbs that energy and are ejected and that electrons are called photo electrons. My question is 'if the electrons get the energy from the light whether the mass of the will increase or not? here the according to Einstein,
     E=mc2
if it absorbs that energy would the mass of the electron differs or not.

The answer is "yes" the electron's mass really does increase.  Let's pretend you are sitting in a lab watching the metal. After the electron absorbs the packet of electromagetic energy ( = photon), its total energy increases. Normally, we tend to talk about the electron as having had its kinetic energy (roughly, the energy of motion) increased by this absorption. Since the kinetic energy and therefore the total energy of the electron has increased, according to E = mc^2, the mass must also have increased.

Because the kinetic energy has increased, the velocity has also increased. In general, whenever an object increases its velocity, its "relativistic" mass increases. If it were to stop (lose all its kinetic energy) its mass would return to its minimum, called its rest mass.   The rest mass is always the same, but the mass is only equal to the rest mass if the object is resting!

For everyday objects like cars or bicycles, the velocities are much too slow for the effects of Einstein's theory of relativity (E=mc^2) to be noticeable, but for subatomic particles, it's not too hard to make them move fast enough for relativity to be very important. Particle physicists deal with relativistic particles everyday!

The Motivation for Research in Physics

Here is a question that was submitted to us by one of our readers a few days ago.  It is a very important question that all scientists, from famous people like Einstein to graduate students like me, are asked throughout their careers.  Here is my attempt to tackle this very important question!

Abhimitra, from Sherwood High in India, writes:

The amount of money required to probe this universe or the aub-atomic particles is undoubtedly huge. Though we do talk about the applications of Elementary Particle Physics in the future, how right is it in this world,plagued with terrorism, evil and poverty, that such HUGE quantity of money is spent on something which may take DECADES or maybe even CENTURIES to really show some practical application. Instead, shouldn't we divert our resources to more immediate and necessary priorities, and try to eradicate ignorance from this world before we venture into these fields which we actually probe out of sheer curiosity? As a scientist, isn't it your moral responsibility to look into the consumption of resources and limit them according to properly set priorities? How do you really justify the money being spent on LHC?

Hi Abhimitra,

I really do not work on anything to do with the LHC in particular, but I will endeavor to answer your questions from the viewpoint of basic research in general.  Someone else can justify the LHC in particular.

To begin with, the amount of money spent on these projects, although quite sizable compared to my graduate student salary, is actually pretty small compared to the amounts that governments spend on a regular basis on other programs.  Also, the cost of these projects is also often shared between governments and organizations.  The bulk of my thesis experiment (The G0 Experiment), for example, was funded by the United States (the U.S. Department of Energy and the National Science Foundation), by CNRS in France, and by NSERC in Canada, along with manpower, hardware, and technical support from the collaborating universities, TRIUMF, and Jefferson Lab. 

It is true that many of the investments in basic research in such areas as nuclear and particle physics are long-term, and that applications of the research can take a long time to show up in everyday life.  However, that is not always true, especially for the technology designed for these experiments.  X-rays were almost immediately used for medical imaging after their discovery.  I just recently went to a seminar by General Electric on advances being made in medical imaging using the advances we are currently making in detector designs in nuclear and particle physics.  For that matter, advances have been steadily been being made in medical imaging as new developments have been being made through the past century!  (If you ever need an x-ray, CAT, PET, MRI or any medical scan, or radiotherapy to combat cancer, remember, physicists had to research all that before it could be applied to anything and the imagining techniques have been steadily getting better as our knowledge about these things grows.)

Even for the discoveries and developments that do take a long time to have a practical application, if those things had never been researched, there would never be any application at all.  If all the money had not been put into developing theories about electricity, magnetism and solid-state physics, into doing experiments to verify those ideas, into discovering new materials with specific properties, and into designing better technology to make use of all of these in the last century, you and I would not have computers and the internet to communicate with about this question!  How would you even be informed of the evils of the world that need to be dealt with if it was not for all of the research that went into the devices that allowed that information to be conveyed to you so rapidly (televisions, radios, telephones, etc.)?  And how will you work toward a better world without the tools that such research has provided?   Where do you think that all the amazing things in our present age came from?  They came from the investments of people, organizations, and governments into the work of scientists of the past and present!

I find it interesting that you say that we should eradicate ignorance before we allocate resources for research based on "sheer curiosity", since it is the curiosity and creativity of the human spirit that are the greatest tools we have in banishing ignorance. Without striving for knowledge, if we become complacent and believe ourselves to be already 'knowledgeable enough,' then how can we possibly fight ignorance?  Fighting ignorance is not simply an act you go out and do; it is a constant journey to better yourself and to make more information available so that others can better themselves as well.  The entire point of a career in any research field is to find out things we did not know and tell it to others so it can be used effectively for the betterment of mankind.  Research is about more than just "sheer curiosity".  It is about enriching the lives of everyone by understanding our universe better and by the advances we can make through that better understanding.  My job as a research scientist is in the very beginnings of a chain that connects to just about every aspect of life, and just because the windings of that chain are not immediately obvious all the time does not make my link unimportant. Without this vital link, there is no further chain to advance on, nothing for others to build on to help make a better world. 

Sadly, the evils you speak of are not unique to our world in this time.   Poverty, terrorism, and evil have been with us since the dawn of humanity, and persist despite the endeavors of many great people throughout the ages.  (That's a lot longer than the application of any physics discovery I know of.)  Everyone should do all that they can to combat such darkness.  But does that mean that all other advances of society should be halted to focus entirely on one or two issues?  That does not seem like a very balanced way to approach things.  Poverty is a much larger issue than just throwing money at it will solve, and diverting money from physics research will not help combat terrorism based on ideological disagreements.  If all research funding was diverted to other uses, who would be doing the research to collect the knowledge that will be needed to come up with better and lasting solutions to these problems?   

Everyone (not just physicists or scientists in general) has a moral responsibility about the consumption of resources according to "properly set priorities".  Why do you think that we set up governments where we elect people that we think will set those priorities along what we think is right and important? (I'm not saying that the system is perfect, though.)  And although the practical benefits are often long-term for physics, it is clear that there are tangible benefits that come from all the areas of physics.  What about areas of life that have no clearly practical benefits?  Does this mean that art, music, and movies should no longer be produced since they offer little practical benefit, but the production of these things consumes resources?  They are clearly beneficial in the enrichment, entertainment, and inspiration of lives, but they do not have much in the way of practical application.  Are you saying that there is a moral responsibility to cut out all things that consume resources but do not have immediate practical applications to life?

Like much of life, it is a balancing act, though.  It is wrong to neglect the present and the current issues that surround us.  As an illustration, if you ignore your responsibilities and never hand in homework in your history class in high school, you'll get in trouble, get detention and fail the class.  However, it is dangerous to do just enough to survive the present: to pass the class.  If you do not bother to learn more than you have to know to just squeak through with a passing grade in your classes, you will probably not pass the standardized college entrance exams, so you will not be able to go to college and progress in your education.  Though you addressed your immediate problems, you did not invest in your future wisely, so you are now limited in your options and will have to work much harder and longer to reach the same goal. Ideally, there should be work done both for the present and for the future so that we are prepared for what we do not even know is coming!

If you do not invest in the future, then there will not be as bright a future to look forward to, and when that future becomes the present, there will not be any tools or knowledge available to improve that present.

Best of luck to you in your future endeavors!

With Regards,

             Sarah K

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Many thanks to Vipuli Dharmawardane, for sharing her knowledge about the discovery of x-rays; to Jason Moscatello, for his careful proof-reading and astute editing comments; and to Kent Paschke, for his thoughtful proof-reading and the fun conversation that ensued.

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This question and my answer to it are also posted in the Career Week blog and my own blog, so if you would like to see more comments about this post, be sure to check the comments posted in the other blogs.  - SKP

Accepting and rewarding Einstein

These two questions were posted a couple of days ago by one of our readers. I will take a stab at them!

Eduardo Avaria of Chile asks:

Was a part of Einstein's geniusness his obstination in "guesing" that he had the right and everybody else, even newton, and the entire physic scene was wrong (in his photon theory as an example)?

And as a secondary question, i want to know why the physicist comunity take so long to give cientists the recognitions they deserve. Why Einstein had to wait till 1921 to get the nobel prize he deserved since 1904? Or the photelectric effect was only a "touchable screen" to award him for his marvelous job?

I'll address the first question first. I wouldn't say that Einstein was "guessing" at his equations for relativity, etc. Despite his reputation as being "not very good at math", he was still quite decent at it by most people's standards! He used conceptual and mathematical reasoning to arrive at many of his big discoveries - including E = mc^2. He could back up his claims with solid mathematics.

It is important to stand by your work to make it stick, but he wouldn't have stood by his work with much conviction if it wasn't supported by solid reasoning and math.

Now I'll tackle your second question: why did it take 17 years for Einstein to get the Nobel Prize in Physics?  Seventeen years is actually not that long to wait to receive a Nobel Prize! Many scientists have had to wait much longer. And some couldn't wait long enough - they died before they had been rightlfully honoured. Nobel Prizes are awarded only to the living, so it's often joked that you have to have a strong constitution to win a Nobel.

More importantly, new ideas take a little while to sink in with anyone - physicists included! Even Einstein's seeming simple and profound idea took some time to sink in. We physicists are notoriously sceptical when it comes to new ideas and love shooting them down. If, after lots of shooting, a new idea espaces unscathed, then it is deemed worthy. That's one of the best features of science - new ideas must stand up to scrutiny - most seemingly great new ideas have holes poked in them and die, but a few survive and sometimes go on to change our perception of concepts as profound as time and space.

Are the Einstein's dreams about a final theory only dreams or real science?

Luis Gustavo Lira of Peru asks:
Einstein had come back to the quantum theory after focusing on relativity. What are the most important contributions to the quantum theory? Was Einstein a genious or a lucky scientist how did the right questions? Are the Einstein's dreams about a final theory only dreams or real science? Dear Luis,
Your questions are very deep. I shall try to answer them the best I can.

1. What are the most important contributions to the quantum theory?
   Einstein got the Noble prize for the photoelectric effect in which he showed that light can behave like a particle, thus becoming one of the founders of the quantum theory, In his later years he also developed the Bose-Einstein statistics (in collaboration with S. N. Bose of India).
2. Was Einstein a genious or a lucky scientist how did the right questions?
   I believe that Einstein was a genius but he was lucky also. If coming up with Special Relativity and General Relativity in addition to "minor" stuff like the Photoelectric Effect (for which he won the Nobel Prize) is not genius then what is? That said, there is always an element of luck inn any such success story. What if Einstein had been born as goatherder in an impoverished family, say in India? He would probably have never learnt how to even read and write, forget about penning E = mc²! What I mean to say is that there is always an element of luck with the genes we are endowed at birth, the place we are born, the attitudes of the family/society towards curiousity/education. To use another analogy a seed thrown in an arid desert will die, but planted in fertile land will grow big.
3. Are the Einstein's dreams about a final theory only dreams or real science?
   Einstein's dreams about a final theory were dreams. He never succeeded in combining electromagnetism with general theory of relativity. But then isn't real science about dreams? Dreams of understanding the universe... The theory of everything has been a sort of a holy grail and physicists like Weinberg and Salam won the Nobel prize for making some progress towards it (more specifically for uniting electromagnetism and the weak interaction). Maybe just this year there will be a paper which combines the two or maybe we will have to wait until 2105 (if any of us reading this blog is still alive).

Making Einstein's Big Idea

    Like every NOVA, there’s a story behind the story and that’s true of Einstein’s Big Idea, our two-hour documentary drama that will be shown on PBS Tuesday, October 11th at 8 PM (check local listings). Back in 2001, Robert Krulwich, an ABC correspondent and now host of our magazine spin-off NOVA scienceNOW, was in my office. Robert was working with us on a NOVA special on the human genome project, and that night he was trying hard to convince me that a good way to explain genetics would be to use some little bride and groom figurines that he had picked up at his local bakery. Robert is an unbelievably smart and creative guy, but I wasn’t buying this particular idea. I took the little bride and groom and set them on a shelf in my bookcase, where they would live happily ever after. On that same shelf, there was a book that Robert pointed out to me, one he had read and loved. It was E=mc2: A Biography of the World’s Most Famous Equation by David Bodanis. Struck by Robert’s enthusiasm, I took the book home with me. From the minute I opened it, I was completely absorbed; David’s book explains each term in the equation by looking at the innovative men and women who, over the course of 400 years, came up with the ideas that set the stage for Einstein’s great breakthrough in 1905. I spent the whole weekend alternately exhilarated and a nervous wreck, worrying that some other more on-the-ball producer had beaten us to the punch and optioned the book. But when I tracked David down the next week, I learned to my relief that the rights were still available and we snapped them up. Thus, Einstein’s Big Idea was born.

    Or, sort of. In public television the distance between cup and lip is very large. It took us four years to raise the money for this show, and one action-packed year to make it. The most amazing experience for me took place at Chateau Cirey in the Charlemont region of France. We had gone there to shoot the stories of Emilie du Chatelet, the beautiful and brilliant French mathematician, and Antoine Lavoisier, the French tax collector whose passion for chemistry led to a new understanding of mass. Chateau Cirey was actually the home of du Chatelet, who lived there with her lover and mentor Voltaire. Together, the two established at Cirey a scientific and cultural academy. The chateau is now owned and occupied by an elderly French couple, whose delightful Parisian daughter had come to stay for the duration of the shoot. She told us that Cirey—except for her parents’ small apartment—remains essentially the same at it was in Voltaire’s time, right down to the volumes in the bookcases. The landscape we looked out upon, the trees and the fields, were the same, she said, as that seen everyday by du Chatelet and Voltaire. That simply blew my mind. But it also meant no heat and no electricity…big challenges for the large and complicated HD (high definition) shoot that we were mounting.

   Gary Johnstone, the talented writer-director of Einstein's Big Idea, asked my colleague Melanie Wallace (NOVA’s senior series producer) and me to be extras in a dinner scene in which Lavoisier meets his future wife and helpmate, another brilliant and beautiful woman, the 13 year-old Marianne Paulze. Decked out in our dinner gowns, bejeweled and made up to the hilt, we also wore four-foot tall wigs as dictated by the fashion of the day. Melanie had a bird’s nest built into hers and mine had a fruit basket with a little bunch of bananas. Those wigs, as you can imagine, were heavy. It was also freezing cold in the room, except right before shooting the scene, they would blast some heat in so our lips wouldn’t chatter. The heavy wig, warm air, and my jet lagged state all conspired against me, and every time the camera wasn’t on me – which was most of the time – my eyes would close and my head would slowly incline downward for a little nap on the table. That’s in the outs for our next joke reel, but Melanie and I did make it into the film. If you want to see us, look for the guests in the Lavoisier dinner  scene. But don’t blink. Our moment in the sun doesn’t last too long.

    Many people have asked me how we managed to keep the needs of the drama from infringing on either scientific or historical truth. My answer: That’s what advisors are there to help us do. And we had many, scientists and historians, who gave unstintingly of their time, kept us on the straight and narrow, and also let us know when a bit of latitude would be okay. One example of a question we came up against concerned the equation E=mc2 itself. In his 1905 publication, Einstein wrote the equation in another form, far less familiar to the untutored eye. While we were working on this project, I had visited the excellent Einstein exhibit at the Museum of Science in Boston. Concerned about how we could depict Einstein writing E=mc2, when it might be anachronistic, I scrutinized Einstein’s papers at the exhibit, and saw to my delight E=mc2 written in Einstein’s own hand – but in a document written after 1905. Our question to our advisors was: Can we show Einstein writing E=mc2 in a scene that takes place in 1905? We all felt the drama needed to visually connect our main character to his iconic equation. So we were mighty relieved (and a little surprised) when the advisors stamped it kosher without even much of a fuss.

    There are a number of reasons why I think Einstein’s Big Idea belongs on NOVA, though it is somewhat different from what we usually do. We want, of course, to give our viewers insight into an equation that changed the world. But the program is also a reflection on the scientific process, showing that great innovations do not spring fully formed from the head of even such a genius as Einstein, but are built one idea at a time over the centuries. And there’s another conclusion we hope our viewers, especially young people, will draw from this drama. It’s not always obvious who will be great in the scientific game. Michael Faraday was a blacksmith’s son at a time when mainly gentlemen became scientists. Emilie du Chatelet was a woman at a time when a woman, especially one who was young and beautiful, barely had a chance in science. And Lise Meitner, a Jewish physicist in Nazi Germany, was lucky to escape with her life, let alone her life’s work.

   Did we succeed in telling this rich and wonderful story of E-mc2?  Please watch and let us know what you think, here or at pbs.org/nova/einstein. In the end, you get to be the judge. 

        --Paula Apsell, Senior Executive Producer, NOVA

Who Makes Big Ideas?

"Einstein's Big Idea" (EBI, for short) was striking to me in ways I wouldn't have imagined before seeing it.  It doesn't dwell for long on the concepts, experimental techniques, or mathematics of a physical discovery.  Rather, it attempts the more ambitious goal of reconstructing the historical milieu of a set of previous discoveries, and then tries to show how the various pieces of the puzzle converged in a flash of insight to einstein.  In doing so, it certainly doesn't try and suggest that these insights were anything less than hard-won.  The underlying message seemed to me to be that important discoveries are actively discovered by a person (vs. being passively "arrived at" by a community consensus).  The show is also clearly trying to demonstrate that the talent for scientific discoveries has no preference for any particular type of person or background.  It doesn't matter whether one is man or woman, religious or heretic, insider or outsider, methodical or inspired.  The key features that seem to characterize the discoverer are a broad set of interests, a deep education, an open mind, and ultimately an overarching passion for the subject (and often for life -- and love -- itself).

In few cases were these discoveries their main goal; most of these people had interests in a broad variety of scientific, and often non-scientific problems.  Faraday was a former bookmaker, who ended up working in a chemist's laboratory, who was clearly obsessed with "trying things out" and assessing the consequences with open eyes, avoiding the assumptions which were shown to be blinding to those from more traditional backgrounds (a feature also attributed to Einstein later on).  Emilie du Chatelet was a polymath of the highest order, her contributions to physics and mathematics covering a wide range, and her particular involvement in the E=mc² story shown to be just one of her many obsessions.  Einstein was in many ways the most extreme case here, writing a series of papers in 1905 on essentially unrelated topics, each of them becoming classics in their fields.

Without a broad awareness of a variety of scientific phenomena and concepts, it is probably more difficult to have a mind open enough to accomodate the "happy accident" of a particular experimental result or a new (or sometimes old) mathematical technique.  Faraday was clearly able to visualize forces carried by invisible fields at a time when poeple only considered forces (like electricity) being somehow carried through wires.  He was able to take the growing set of results on electromagnetic forces and create heuristic pictures that let him organize the information and suggest new experiments.  Meitner was trying to build bigger nuclei, but was able to accomodate the possibility that nuclei could actually split apart, despite no previous evidence to suggest this before observations by her and her collaborators.  Einstein fought with the the contradictions between Galilean relativity (which makes velocities dependent on the motion of the observer) and Maxwell's electromagnetic theory (which predicted a constant speed of light in all frame) until he saw how to subjugate the former to the latter with special relativity.

And yet, in all cases deep scientific knowledge and rigor was a real prerequisite for progress.  Although a natural brilliance and some sort of "intuition" was involved in all of these jumps, all of these scientists were characterized by an intense training in their field.  Lavoisier was probably the most devoted to pure rigor, especially in his dealings with men like Jean-Paul Marat, whom he dismissed (leaidng Marat to plot Lavoisier's demise eventually...)  But even Faraday, while not traditionally educated, apprenticed with Sir Humphry Davy.  And thus, while he appeared to be the most natural talent, he probably had to suffer the most to develop his skills to prove himself to the establishment.  Einstein is famous for being a poor student - but it's more appropriate to say that he didn't apply himself in things that didn't interest him.  EBI shows him to be interested only in math, physics, philosophy, his viola (and the ladies) and essentially uninterested in everything else, but he applied himself intensely to those subjects he appreciated.

Finally, one also notices that these were people not simply intense about science, but about their lives in general.  Faraday was clearly the most religious of the bunch, belonging to a Quaker sect, but this was clearly tied in with his passion to elucidate patterns in the physical world.  Du Chatelet was a true bon vivant, living extravagantly outside of Paris with a succession of lovers.  Lavoisier had no need for a scientific career, finding his only true pleasure in life collaborating with his wife on his experiments.  And Einstein is portrayed in a way that emphasizes his passionate, bohemian, and evn artisitic temperament, as opposed to the thoughtful pacifist we often get to know from photographs, writings, quotes, and historical accounts.  The argument seems to be that intense personalities tend to have the drive (and maybe the need?) to challenge received truths and attempt to forge new ones.

So just a few (or more than a few) thoughts on the show and the issues it addresses.  Sorry for being long-winded, but there's a lot there!

Beauty & Simplicity

The first time I saw the famous E=mc² formula I'm sure it was not in a physics class: no other physics formula whatsoever became so popular and was so spread around (from t-shirts to comics) as this one. The main reason is its beauty and simplicity. Einstein's theories grew up on a fertile ground, prepared by several experiments performed in the previous years (I mention here for instance the famous 1887 Michelson-Morley experiment which provided a measurement of the speed of light). Einstein himself spent many years of study before arriving to present his special theory of relativity. Nevertheless, the final picture was apparently "clear" and confirmed what Einstein was saying: "most of the fundamental ideas of science are essentially
simple and may, as a rule, be expressed in a language comprehensible to everyone".

The experimental confirmation of E=mc² didn't arrive soon. In 1933 Irene and Frederic Joliot-Curie obtained the first photograph showing the conversion of energy (a quantum of light) into mass (two particles curving away from each other). Einstein said that "the whole of science is nothing more than a refinement of everyday life": since those days
his beautiful theory was brought into reality and became part of our life.