Super fact 36: Every continuous symmetry of the action of a physical system with conservative forces has a corresponding conservation law. This revolutionary insight was mathematically proven in 1915 by a relatively unknown woman, Emily Noether.
It is not easy to understand what this super fact means, and therefore it is easy to miss the fact it says something fundamental about the nature of reality. It says something profound about our Universe and all possible Universes. It is arguably one of the most profound discoveries in science. Since the discovery of Noether theorem, we do physics differently and we view our physical reality differently. In the book “The Theory of Almost Everything” the author, theoretical physicist Robert Oerter states that the standard model of elementary particles, or most of modern physics, rests on three pillars, special relativity, quantum physics, and Noether’s theorem. Which one of those three have you not heard of? I guess Noether’s theorem.
That question brings me to the second part of the super fact. Emily Noether did a lot for mathematics and physics in addition to her first theorem (stated above), and yet she is not well known. Albert Einstein said of Emily Noether : “Fräulein Noether was the most significant creative mathematical genius thus far produced since the higher education of women began”. Notice he didn’t say “woman genius”.
Why I consider Noether’s (first) theorem a super fact is because it tells us something fundamental about reality that is highly surprising and yet undisputable (mathematically proven) and not many of us know about it. The second part of the super fact, that despite being one of the greatest geniuses of the 20th century she is so unknown, is also surprising.
Noether’s Theorem What Does It Mean
Noether’s theorem, says that symmetries in the universe give rise to mathematical conservation laws. One way to understand this is by using an example. That the physical laws remain the same as you translate a system in time is an example of a continuous symmetry. If you do an experiment twice at two different times, let’s say at 8:00AM and at 9:00AM, and everything is set perfectly identical both times you are likely to get the same result. Well barring statistical/quantum uncertainty. The point is that the physical laws did not change. If the physical laws do not change between 8:00AM and 9:00AM, then you have a continuous symmetry.
Noether’s theorem says that if you have a continuous symmetry, you also have a conservation law, and the conservation law in this case is the conservation of energy/mass. If the physical laws do not change between 8:00AM and 9:00AM then mathematically the total energy / mass of the closed system must remain constant. It follows that energy is not destroyed or increased. At first it seems like the time symmetry and energy/mass conservation have nothing to do with each other, but the symmetry gives rise to the conservation law. So, if you ask the question, why is energy / mass conserved, the answer is because physical laws don’t change with time.
There are many symmetry-conservation law pairs in nature. Translational symmetry, the fact that the laws of physics stay the same if you move to the side or forward, results in the conservation of momentum. The symmetry of laws that does not change if moving around in a circle amount to the law of conservation of angular momentum. Other symmetries result in the conservation of charge. The converse is also true. If you find that a quantity is conserved you can find a symmetry, and if you find a symmetry that is broken you can find a quantity that is not conserved after all. There is not much in science that is more fundamental than that and in addition Noether’s theorem is very useful.
Emily Noether
Emily Noether was born into a Jewish family in Germany March 23 in 1882. She was the daughter of the mathematician Max Noether. She studied mathematics and completed her doctorate in 1907. At the time, women were largely excluded from academic positions, but she worked at the Mathematical Institute of Erlangen without pay for seven years. She eventually gained paid positions. She made huge contributions to abstract algebra, calculus of variations, topology and other mathematical fields. Her most important contributions are the Noether’s theorems, the first one described here. When Hitler came to power in 1933, she had to flee Germany. She got a position as a professor at Bryn Mawr in 1933. She died in 1935.
Concluding Summary
Noether’s Theorem changes how we view the Universe and the laws of physics. For example, the conservation of energy is not just something we empirically discovered. It follows mathematically from physical laws not changing by time. It represents a paradigm shift in science that arguably is as important as quantum mechanics or relativity and yet very few people have heard of it. I find that quite shocking.
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Newstrade
You would be quite right in saying that I had never heard of Emily Noether nor her theorem(s). Thank you for another enlightening post, Thomas! It’s always a pleasure to come here and learn something new! 😊
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Thank you so much for your kind words Kevin. It is quite amazing that such a huge discovery and paradigm shift, arguably as big as quantum physics or relativity is so completely unknown. Despite studying physics in college I had never heard about it until a few years ago. I just added this conclusion to my post.
Noether’s Theorem changes how we view the Universe and the laws of physics. For example, the conservation of energy is not just something we empirically discovered. It follows mathematically from physical laws not changing by time. It represents a paradigm shift in science that arguably is as important as quantum mechanics or relativity and yet very few people have heard of it. I find that quite shocking.
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I guess it truly just goes to show that despite all the knowledge we’ve collected over the ages there is still so much more out there
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Yes you are right. I view human knowledge as a sphere expanding into an infinite unknown and what we know as individuals a tiny bubble within that sphere.
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HI Thomas, I will ask Greg it he knows this theorem. Having a theorem named after you is a very high honour in mathematics or science. It is sad that women are always diminished.
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He might have. However, despite studying physics in college I had never heard about it until a few years ago. This is a huge discovery and paradigm shift arguably as important as quantum of relativity, and yet it is completely unknown. The fact that we can mathematically derive conservation laws (such as conservation of energy) from continuous symmetries like physical laws don’t change by time changes how we view physical laws, and it is very practical too.
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Hi Thomas, clever clogs Greg does know her. She contributed to Ring Theory which he has studied. 😀
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A remarkable woman, but if she did something equally brilliant today, she still may not receive recognition. Maggie
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Yes she revolutionized physics and all of science, and mathematics of course. I think that one reason her theorem has not received as much attention as let say quantum physics or relativity is because it is difficult to explain even in its simplest form. It does not advertise itself well. But maybe it also because she is a woman. It makes it harder get attention.
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I always enjoyed math and its set principles. My daughter took it for fun in college, so nice to see this. Thanks, Thomas.
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Thank you so much Denise. Yes it is a good example of mathematics revolutionizing science/physics. I just added this concluding summary.
Noether’s Theorem changes how we view the Universe and the laws of physics. For example, the conservation of energy is not just something we empirically discovered. It follows mathematically from physical laws not changing by time. It represents a paradigm shift in science that arguably is as important as quantum mechanics or relativity and yet very few people have heard of it. I find that quite shocking.
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Fascinating Thomas…. Energy I have learnt can not be destroyed it just transmutes or transforms .. I will leave it up to the mathematicians for equations etc … I Personally feel we still have so much more yet to discover about the Universe .. And I wouldn’t myself even try to fathom the depths of it….
Needless to say I am in Awe and wonder of the Cosmos, and I have no doubts soon we will find out much much more that will be mind boggling…
Like the recent discoveries under the Pyramids of Giza… Another mind blowing discovery that blows History to rethink its origins 🙂
I commend you Thomas on the detail fact finding missions you must go on in your Super Facts blog…. It must take time to put together for your posts.. Something I appreciate ..
Wishing you a great weekend.. 🙂
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Thank you so much for your very kind words Sue. Like I told Kevin, I view human knowledge as a sphere expanding into an infinite unknown and what we know as individuals a tiny bubble within that sphere. I wish you a great weekend too.
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Wow Thomas this is definitely another super fact I love this series…although it is difficult to explain and totally goes over my head it is great to see a woman recognised for her work albeit not in her lifetime it must have been so frustrating for her and other woman that there skills were stifled and not recognised by the males of the species. But well done to you for highlighting this wondeful intelligent woman and her achievements .
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Thank you so much Carol. Emily Noether was certainly a very important genius, someone who revolutionized everything we know, and yet she is not well known. People in the mathematics and physics community recognize her for her genius and importance, but elsewhere she is an unknown. It is strange how that happens. The fact that she was a woman certainly did not help, but I think that the fact that her discovery seems so abstract did not help. She will be remembered for her discovery as long as humanity exists, but most if us don’t know that.
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This is such an interesting post, Thomas! Physics and all that associated with it and all the mathematical theories blow my mind! Bravo on explaining it and breaking it down. I had never heard of Emily Noether before your post!
Also, I nominated you for the Sunshine Blogger Award- would love it if you have time to participate, but no obligation!
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Thank you so much for your kind words and the nomination Laura. It is quite amazing what Emily Noether accomplished. It is one of the greatest scientific discoveries in the 20th century and yet almost know one knows about it. I studied physics in college and didn’t hear about it until a few years ago, and when I saw it I just “wow!”.
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Lulu: “Our Dada reads a lot of science-y stuff and he says he never heard of her, either! It’s a shame she passed away at such a young age, but it sounds like she still contributed quite a bit while she was here!”
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Yes I studied physics in college and didn’t hear about it until a few years ago, and when I saw it I just said “wow!”. It is amazing how important stuff can just slip us all by.
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