Tag Archives: Emmy Noether

It’s A Noether Day!

Last week we celebrated Albert Einstein’s birthday (he turned 140). Now we need another cake so we can celebrate the other March major mathematician’s birthday — Emmy Noether turns 137 today.

To my regret, despite that I frequently invoke her name (she co-starred with Albert in the Special Relativity series), her work in mathematics is pretty far above my head, and I’m simply not qualified to write about it. I can say that her work connects mathematical symmetry with physical conservation laws. She also made significant contributions to abstract algebra.

Just recently, I’ve begun to nibble at the edges of the latter in the form of group theory as a part of studying rotation.

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SR #X2: Sorry, No FTL Radio

Earlier, in the March Mathness post, I mentioned Albert Einstein was born on March 14th. That’s also Pi Day, which deserved its own pi post (about pizza pi), so old Al had to wait for me to address a topic I’ve needed to address for several months.

To wit: Some guy was wrong on the internet.

That guy was me.

Back in 2015 (also celebrating Einstein’s birthday), I wrote a series of posts exploring Special Relativity. Near the end of the series, writing about FTL radio, I said (assuming an “ansible” existed) I wasn’t convinced it violated causality if the frames of reference were matched.

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March Mathness

Time for math!

I have a special fondness for the month of March. For one thing, it contains the Vernal Equinox — one of my favorite days, because it heralds six months of light. (As a Minnesotan, Spring has much more impact than it did when I lived in Los Angeles.)

March is when the weather elves begin preparing for the April Showers that create May Flowers. It’s when baseball Spring Training is in full swing with the regular season looming (lately, even at the end of the month; this year on the 28th).

It also contains some important birthdays: Albert Einstein (3/14) and Emmy Noether (3/23), to name two, and in their honor I have myriad math posts planned!

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Ball Game Symmetry

Many of the fundamental laws of modern physics are based on laws of symmetry. (Which makes Emmy Noether a founder of modern physics.) Just as the Yin-Yang metaphor offers a way to view and deconstruct existence, symmetry is also a way to understand the world around us.

In the past (here and here, for instance) I’ve looked at various sports in abstract ways designed to bring out commonalities among groups of game types. (For instance, tennis, ping-pong, volley ball, badminton, squash, and racquetball, are all “volley” games with similar operation and constraints.)

Today I’m going to look at symmetry in various sports. As always, of course, focusing on baseball, because it’s so unique.

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SR #22: Relative Time

sr22-0Last time we saw that Em non-paradoxically time-travels over three years into Al’s future by flying 12 light years at half the speed of light for just over two decades. Her journey completed, Em has aged only 20.8 years while Al has aged 24.

That may not seem like much of a gain, but Em was only moving really fast — not really, really fast. If she travels at 99% of light-speed, her round trip shortens to 1.7 years while Al doesn’t wait much longer than it takes light to make the six light-year round trip: 12.12 years! And at 99.9% c, Em’s whole trip takes her only half a year!

Today we break down dime tilation. I mean, time dilation!

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SR #21: Paradox Resolved

sr21-0So far this week we have Em taking a round-trip to planet Noether at half the speed of light. Upon  her return she discovers that, while she’s aged 23.8 years, Al (who stayed home on Earth babysitting Theories) has aged 27. It took her well over twenty years to do it, but Em effectively traveled 3.2 years into the future.

Last time we saw that — so long as Em is in constant motion — there is symmetry between Al and Em with regard to who is moving and who isn’t. Both can claim the other is (or they are). Both views are valid. Until Em stops. Or starts, for that matter.

Today we look at Em’s “time shadow” — it’s a key to the puzzle!

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SR #X1: Starting and Stopping in the Twins Paradox

passing spaceshipThis is an eXtra post in the Special Relativity series. It explores a sub-topic in detail that may not be of interest to most readers — either the detail or the sub-topic itself. The purpose of the post is to pre-answer, or serve as a reference for, obvious questions that the technically astute might ask (often questions I once asked).

This article is about the acceleration and deceleration that seems required in the Twins Paradox illustration. Some even refuse to accept the illustration as valid under the belief that changing speed significantly alters the picture.

Here I try to show how we can completely ignore it.

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SR #20: One-way Symmetry

sr20-0aLast time we watched friend Em make a six light-year trip to planet Noether while friend Al stays home on Earth working on Theories. It turns out that Al ages 27 years while Em ages only 23 (point 8). This is not due to special diet, but to Special Relativity slowing Em’s clock on account of her fast motion through space.

We also saw that once Em stops at Noether, this breaks the symmetry of the two valid points of view regarding their motion (Em and ship are moving vs Al, Earth, and space, are moving).

Today we examine the trip before that point, while it is symmetrical.

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SR #19: “It’s Twins!”

sr19-0We’ve covered a great deal of ground in the last four weeks. (Writing a series of posts this long is a new experience for me! I hope you’re getting something out of it, too.) We’ve learned that motion, velocity, simultaneity, and length, are all relative to your frame of reference — motion changes your perception of these things. This week we’ll see that time is also relative — motion changes that, too!

So far we only needed a (very imaginary) train to demonstrate the effects of Special Relativity. An Earthly frame of reference was enough to illustrate how motion affects velocity, simultaneity, and length.

But when it comes to time, we’re gonna need spaceships!

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SR #13: Coordinate Systems

sr13-0The main topic this week was how simultaneity is relative to your frame of reference. How there are (virtual) lines of simultaneity where all points on some line — at all distances from you — share the same moment in time. For any instant you pick, that instant — that snapshot — includes all points in your space.

A line of simultaneity freezes the relative positions of objects at a given moment — which enables distance measurements. Simple example: When their watches both read 12 noon, Al and Em were 30 miles apart. A more mathematical example uses x, y, & z (& t), but it amounts to the same thing: a coordinate system.

The gotcha is that simultaneity and coordinate systems are relative when motion is involved!

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