Tag: relativity

Relativity Visualized by Lewis Carroll Epstein

The goal of this blog is to create a list of what I call super facts. Super facts are important and true facts that are nevertheless highly surprising to many or disputed or misunderstood by many. In a sense this is a myth busting blog regarding important information. However, I also make posts that are not super facts but feature other interesting information, such as this book review and book recommendation.

Relativity Visualized by Lewis Carroll Epstein

Lewis Carroll Epstein <<Link-1>> is a physicist, teacher and author who has written a number of physics books for layman. He is somewhat famous for coming up with ingenious ways of using diagrams, pictures and puzzles to explain complex matters without using mathematics. His approach is unorthodox but, in my opinion, quite successful. You still have to invest time in reading this 200-page long book and solving most of the puzzles to understand what is going on. The book features some math, notably regarding the derivation of the formula for energy-mass equivalency E = mc2. However, it is in a special section for “teachers only”.

It is an old book and the only version currently available on Amazon is the paperback version. The publisher of the paperback is Insight Press; First Edition (January 1, 1985), ASIN : 093521805X, ISBN-13 : 978-0935218053, 206 pages, item weight : 12.8 ounces, dimensions : 6.25 x 0.75 x 9 inches. It costs $48.99 on US Amazon. Click here to order it from Amazon.com.

The front cover features the title “Relativity Visualized” and the author’s name and in the background is the night sky with the milky way. At the bottom of the front cover is a train with a head lamp and a light beam | Relativity Visualized by Lewis Carroll Epstein
Front cover of the paperback version of Relativity Visualized by Lewis Carroll Epstein. Click on the image to go to the Amazon page for the paperback version of the book.

Amazon’s Description of the Relativity Visualized By Lewis Carroll Epstein

Perfect for those interested in physics but who are not physicists or mathematicians, this book makes relativity so simple that a child can understand it. By replacing equations with diagrams, the book allows non-specialist readers to fully understand the concepts in relativity without the slow, painful progress so often associated with a complicated scientific subject. It allows readers not only to know how relativity works, but also to intuitively understand it.

This is my five-star review for Relativity Visualized

Note, I wrote this review in 2016, so it is relatively old, pun intended. In my original Amazon review I used very large paragraphs. I have changed that by breaking up the paragraphs a bit but without changing the content in any way.

Relatively Intuitive

In my opinion the theories of relativity are among the most interesting intellectual achievements in human history. They revolutionized physics and changed the way we think about physics, space, time, mass, energy, electromagnetism and essentially everything in nature. Despite that fact, the theories of relativity are deterministic and possible to visualize, and unlike Quantum Physics they are not statistical in nature and they don’t have a big issue with interpretation.

I’ve been interested in this topic ever since I came across it as a high school student. Therefore, I did not learn a lot about relativity from this book. I was more interested in the approach to explaining it, and I think his approach is a very good one.

I’ve found that an explanation for relativity that lacks rigor and quantitative reasoning creates misconceptions. The reader may end up thinking he understands it when he doesn’t. I’ve also found that books that focus on deriving complex equations were not only unattainable to the layman but sometimes left the mathematically inclined student with a poor understanding of relativity as well.

Lewis Carroll Epstein’s book “Relativity Visualized” seems to succeed in making relativity accessible to both the layman and those who are mathematically inclined. He explains the special theory of relativity and the general theory of relativity using graphs, visual constructs, and logical puzzles that the reader solves for himself. In a sense he allows the reader to develop the theories of relativity on his own. He avoids equations and formulas, but the reader will still discover more exactly what is going on.

One thing that really impressed me with this book is its special focus on the difference between what you see/experience and what you measure. As an example, take two lights that flash at the same time (in your reference frame). They could appear to flash at different times if the distance between them is large. So, you will see them flash at different times. However, if you time the light flashes and take the distance into account you can measure that they flashed at the same time (non-relativistic situation).

In relativity the differences you measure between frames do not only arise from the distance the light travels or from Doppler Effects but also from the relativity of time and space as well, and Epstein explains the details without confusing the reader. He focuses a lot on simultaneity/non-simultaneity right from the very beginning, and in my opinion understanding relativistic non-simultaneity is crucial to understanding what is going on.

The book also discusses the General Theory of Relativity. The General Theory of Relativity is often seen as completely off limits to the layman. It is typically explained using complex tensor calculus, differential geometry, and topology, or alternatively in a non-technical vague way that leaves the reader clueless. General Relativity was born out of an enigma. Special relativity had shown that energy and mass are the same things, so light has mass. A light beam traveling through a gravitational field must thus bend.

However, that means that the side of the light closer to the mass will travel a shorter distance. From known properties of light (always a transverse/orthogonal wave) this means that the side of the light beam closer to the mass moves slower than the outer rim which would violate the constancy of the speed of light in vacuum.

To solve this enigma Einstein had to introduce a time warp in gravitational fields. Later he discovered that this time warp would cause objects to fall towards the masses that caused the time warp and the practical effect of this turned out to be essentially identical to Newton’s theory of gravity and thus the mysterious force of gravity could be removed. Einstein also discovered that there is a warp effect on space which is negligible unless the speed of the objects is large (like magnetism for electric forces). The book helps you visualize all of this without using complex math.

Lewis Carroll Epstein’s book contains unique pedagogic approaches, novel geometric representations of relativity, as well as engaging questions and answers. For this reason, the book is fiercely protected by copyright law. On the negative side, his writing style is somewhat rigid and old fashioned, the drawings and the graphics are sometimes of low quality, and the book might be quite a bit of work for the layman reader, so it requires that you are really interested. However, overall, this is a very rigorous, detailed, correct, and yet entertaining book that I highly recommend.

Good Myths

I also would like to mention another tool that Lewis Carroll Epstein use in his book, and that is the concept of a Good Myth. A Good Myth is a description that isn’t technical and maybe not exact but that isn’t wrong either. In a loose way it captures the truth of what is going on.

An example of one of these myths is that everything, including all of us, is always traveling through time and space at exactly the speed of light in vacuum. In other words, we are all traveling at the speed of c = 299,792,458 meters per second. If we are sitting still, then we are traveling through time at the speed of light. If we are traveling through space at the speed of light then we are not traveling through time at all, like photons, for which time does not exist.

If we are traveling through space at a high speed, then if we add, in a vector way (Pythagoras theorem), our speed in space to our speed in time, they together will add up to the speed of light in vacuum. But that means that we are traveling through time at a speed that is less than the speed of light. So, our clocks will run slower.

The back cover features the title of the book, praise for the book and very brief description | Relativity Visualized by Lewis Carroll Epstein
Back cover of the paperback version of Relativity Visualized by Lewis Carroll Epstein.

Other Posts on Relativity

Below is a list of other posts I made on Relativity

  • The Speed of Light In Vacuum Is a Universal Constant : to see post click here
  • Two events may be simultaneous for some but not for others : to see post click here
  • Time Dilation Goes Both Ways : to see post click here
  • The Pole-Barn Paradox and Solution : to see post click here
  • Book-Review : The Special Theory of Relativity by David Bohm : to see post click here

Do you feel that you are traveling through time at the speed of light?

To see the Super Facts click here

The Pole-Barn Paradox and Solution

Super fact 39 : Relativistic length contraction goes both ways. If two observers are moving compared to each other both will observe the length of the objects in the other’s system to be shorter in the direction of motion. The first observer will think that a yard stick in the second observer’s frame will be shorter whilst the second observer will think that the yard stick in the first observer’s frame is the shorter one.

Assume a pole and a barn are of equal length when both objects are stationary. If the pole is moving (at a high speed) compared to the barn, then the pole will be shorter than the barn from the barn’s perspective but longer than the barn from the pole’s perspective. Does the pole fit inside the barn or not? This is referred to as the pole-barn paradox, or the barn-door paradox, or the ladder paradox (if a ladder is used instead of a pole).

I call this conundrum a super fact because whilst most people have heard of relativistic time dilation and perhaps length contraction, the fact that it goes both ways comes as a surprising head scratcher. The situation is analogous to my super fact post “Time Dilation Goes Both Ways” where I state:

Super fact 38 : If two observers are moving compared to each other both will observe the other’s time as being slower. In other words, both observers will observe the other’s clocks as ticking slower. Time slowing down is referred to as Time Dilation. And this post is about how time dilation goes both ways.

Both the time dilation paradox and the pole-barn paradox are solved by the non-simultaneity in relativity. However, the pole-barn paradox is more concrete and perhaps more in your face. You can easily imagine the problematic paradox.

A picture of a girl, Amy who is speeding past a man, Alan and his barn. Amy has a pole. The pole is contracted along the direction of motion from Alan’s perspective and the barn is shorter along the direction of motion from Amy’s perspective | The Pole-Barn Paradox and Solution
Amy is speeding past Alan and his barn at a high speed. Amy has a pole. Because of the high-speed Amy’s pole appears shortened and will easily fit in Alan’s barn. However, to Amy it is Alan’s barn that is contracted, and her pole has the normal length and will therefore not fit in Alan’s barn.

Postulates of Special Relativity

The two postulates of special relativity are:

  • The laws of physics are the same in all inertial frames of reference. An inertial frame is a system that moves at a constant velocity.
  • The speed of light in a vacuum is constant for all observers, regardless of the motion of the light source.

The first postulate is called the principle of relativity and goes all the way back to Galileo Galilei. It means that no experiment can determine whether you are at rest or moving at a constant velocity. The reciprocity of length contraction follows from this postulate. If the length of the pole in the example above is half as long as the barn in both the barn frame and the pole frame then you could tell who was standing still and who was moving from that fact, and that violates the first postulate. The first postulate demands that if the pole is half as long in the barn frame and that the barn is half as long in the pole frame.

The second postulate is the more shocking one and is special to relativity. It was discovered experimentally at the end of the 19th century but was too difficult for scientists to accept at first so various ad hoc explanations were put forth to explain it away, until the theories of relativity were created. I designated this postulate as my super fact #4 and you can read about it here.

Length Contraction

Time dilation means that a time interval between two events in a certain frame is longer by a factor B in a frame moving relative to the first frame (see picture below). Let’s imagine Amy moving at the speed v compared to Alan and his barn. Amy passes the left side of the barn at a certain time and soon after the right side. The time difference from Alan’s perspective is T and the width of the barn is L, so L = vT. From Amy’s perspective the time difference is T’ and width of the barn L’ and L’ = vT’. We denote Amy’s measurements with a prime. Note the velocity must be the same in both systems. However, Amy’s clock ticks slower (from Alan’s perspective) so T’ = BT or T = T’/B (time dilation). So, L’ = vT’ = vT/B = L/B.

If the derivation of the formulas above is confusing to you, ignore the math, and just remember that Alan measures a shorter time for the passing of the pole (because Amy’s clock is slower) from his perspective and therefore the pole must be shorter as measured from his system. If Alan measures two seconds for the passing of the pole than Amy measures maybe four seconds. It is Amy’s pole, so her longer measurement corresponds to the proper length of the pole whilst Alan’s measurement is the contracted length. Note the length contraction can only happen along the direction of motion, not perpendicular to it. To read more about length contraction click here.

This picture shows the formula for time dilation, the expression for the beta factor, and the formula for length contraction | The Pole-Barn Paradox and Solution
The beta factor used in the formula for time dilation as well as length contraction.

Solution to the Pole-Barn Paradox

So, Amy’s pole cannot fit in Alan’s barn. The pole is moving fast so it must move in and out of the barn. Now let’s create the paradox. Imagine the barn having doors on each side that open for the moving pole and then close for a moment to entrap the pole and then they open as the pole leaves the barn. Here is the paradox, if they open and close at the same time, than the pole can be inside the barn (entrapped) from Alan’s perspective but not from Amy’s perspective. From Amy’s perspective the pole does not fit.

However, the solution to the paradox lies in “open and close at the same time”. If the doors open and close at the same time from Alan’s perspective, then they don’t open and close at the same time from Amy’s perspective.

From Amy’s perspective the door on the left side will open first and let the pole in and then after that the right door will open. After the pole has fully entered the barn and some of it is sticking out on the right-hand side then the left door will close but the door on the right will remain open  until the pole is entirely outside. Relativistic non-simultaneity solves the paradox.

A picture of a girl, Amy who is speeding past a man, Alan and his barn. Amy has a pole. The pole is contracted along the direction of motion from Alan’s perspective and the barn is shorter along the direction of motion from Amy’s perspective. There are two doors on each side of the barn. In Amy’s world the left door is open letting the pole into the barn, whilst the right door is closed. In Alan’s world both doors are close thus enclosing his shorter pole.
In Alan’s frame the doors can be closed at the same time and enclose Amy’s pole. In Amy’s frame the doors open and close to let the pole through but they don’t open and close at the same time.

Finally, below is a YouTube video that explains and solves the pole-barn / barn-door / ladder paradox simply and efficiently in a little over two minutes.

Book Recommendations on Relativity

To see the other Super Facts click here

The Special Theory of Relativity by David Bohm

The goal of this blog is to create a list of what I call super facts. Super facts are important and true facts that are nevertheless highly surprising to many, disputed among the public, or unnecessarily misunderstood. They are special facts that we all can learn something important from. However, I also make posts that are not super facts but feature other interesting information, such as this book review and book recommendation.

The Special Theory of Relativity by David Bohm

David Bohm a close colleague of Albert Einstein was one of the most interesting theoretical physicists of the 20th century. This book “The Special Theory of Relativity” is one of the most interesting and thorough introductory books on the Special Theory of Relativity that I have come across. It is a series of lectures on the topic. It features algebra, equations, and a little bit of differentials but not too much.

You may want to have some math, physics and some relativity under your belt before you tackle this book. In my estimate it is written for those who have taken high school AP physics and AP algebra, maybe calculus as well, or one or two college level physics classes and math classes (or more). It is probably too basic for professional physicists, but it is not written for laymen. I bought the paperback version.

  • Hardback –  Routledge; 1st edition (October 10, 1996), ISBN-10 : 0415148081, ISBN-13 : 978-0415148085, 256 pages, item weight : 13.6 ounces, dimensions : ‎ 5.75 x 0.75 x 9 inches. It is out of stock, and it costs $75.60 – $144.00 on US Amazon. Click here to order it from Amazon.com.
  • Paperback –  Publisher : Routledge; 1st edition (September 4, 2006), ASIN : 0415404258, ISBN-13 : 978-0415404259, 304 pages, item weight : 12 ounces, dimensions : 5.08 x 0.69 x 7.8 inches. It is out of stock, and it costs $12.36 – $17.21 on US Amazon. Click here to order it from Amazon.com.
  • Kindle –  Published : Routledge; 1st edition (September 29, 2015), ASIN : B009W3W6MG, 306 pages, it costs $10.10 – $13.77 on US Amazon. Click here to order it from Amazon.com.
The front cover of “The Special Theory of Relativity by David Bohm.”
Front cover of the paperback version of The Special Theory of Relativity by David Bohm. Click on the image to go to the Amazon page for the paperback version of the book.

Amazon’s Description of the Book

In these inspiring lectures David Bohm explores Albert Einstein’s celebrated Theory of Relativity that transformed forever the way we think about time and space. Yet for Bohm the implications of the theory were far more revolutionary both in scope and impact even than this. Stepping back from dense theoretical and scientific detail in this eye-opening work, Bohm describes how the notion of relativity strikes at the heart of our very conception of the universe, regardless of whether we are physicists or philosophers.

This is my five-star review for The Special Theory of Relativity

Note, I wrote this review in 2014, so it is relatively old, pun intended.

Lorentz Electrodynamics, Special Relativity, and our Perception of Reality

This book is a thorough and well written introduction to the “Special Theory of Relativity”. In addition to the basics of special relativity it covers the history of Special Relativity and it includes 60-pages of Lorentz Electrodynamics. The book also discusses Minkowski Diagrams, the Twin Paradox, relativistic Doppler effects, K-Calculus, and philosophy related to relativity. The book does not discuss General Relativity.

Bohm does not derive many formulas for electrodynamics, optics, quantum physics, thermodynamics, etc., and therefore this book does not resemble a textbook. Bohm’s focus is on a deeper understanding of the special theory of relativity itself, and on time and space.

He discusses perception of reality and includes discussions on child development, psychology and neurology related to perception, the meaning of the relational concepts in relativity, the structure of scientific revolutions (T.S. Kuhn), our perceptions of time and space, philosophy, and other related topics that cannot be classified as physics.

In K Calculus you draw the world lines of light pulses sent at constant intervals between different observers. Then you calculate what is essentially the Doppler factor K and uses it to explain what is going in relativity. In contrast the Lorentz transform is concerned with the space-time coordinates that you measure after taking into account that light have to travel a certain distance and that this takes time. Basically, the “actual time and space coordinates”.

K Calculus on the other hand is including both relativistic effects and the distance and time it takes for light to travel. K Calculus is thus not what you “measure” but what you “observe”. K Calculus makes it very easy to explain special relativity to an audience that is not strong in math and it also adds a new understanding to the special theory of relativity.

However, I see an inherent risk with K-Calculus in that it can end up fooling the student into believing that he understands relativity, for example, if a student incorrectly comes to believe that time dilation is some form of Doppler Effect.

Except for the fact that some of the mathematical derivations were unnecessarily complex I thought this book presented relativity lucidly, the philosophical discussions were insightful, and it added to my understanding of the topic. It should probably not be your first book on Special Relativity but it is a very good second book. I highly recommend it for those who want to think through the concepts of relativity a little deeper.

The back cover of "The Special Theory of Relativity by David Bohm"
Back cover of the paperback version of The Special Theory of Relativity by David Bohm. Click on the image to go to the Amazon page for the kindle version of the book.

To see the Super Facts click here

GPS uses relativity for accuracy

Superfact 23: GPS uses relativity for accuracy. Global Positioning Systems or GPS uses Special Relativity and General Relativity to guide you to your destination. In fact, GPS systems would be rendered useless without the Theories of Relativity.

Businessman finger pin for location points and search addresses on the world map application. Marking destination for travel or finding business places in GPS Satellite coordinates system online web | GPS uses relativity for accuracy
Stock Photo ID: 2502019165 by mayam_studio

Did you use Einstein’s Theories of Relativity to get to the grocery store today?

The theories of relativity may seem strange and impractical, something you only use for astrophysics, black holes, cosmology and extreme velocities. They feature strange concepts such as time dilation, the stretching and bending of space, events simultaneous to some are not to others, the universal constancy of the speed of light in vacuum, the energy and mass equivalency, etc. 

Therefore, it is a bit surprising that without the theories of relativity the GPS app on your phone would not be able to guide you to the grocery store. That’s why I call it a super fact that GPS uses relativity for accuracy.

Space satellite orbiting the Earth. 3D rendering
Stock Illustration ID: 1372134458 by Boris Rabtsevich

GPS and Time Dilation

GPS is a satellite-based  radio navigation system that provides location information and time anywhere on Earth. It is amazingly accurate. The basic GPS service provides users with approximately 7.0-meter accuracy, 95% of the time, anywhere on or near the surface of the earth.

The fact that the information is provided by satellites that orbit earth at high speeds and high above earth’s surface makes General Relativity and Special Relativity necessary. The GPS system needs to calculate precisely the time it takes for signals to travel from the satellites to a receiver on Earth for it to work. GPS satellites travel at high speeds causing a large enough time dilation that must be accounted for. In addition, they orbit earth high above earth’s surface where earth’s gravitational field is weaker than on earth’s surface. Clocks run faster in weaker gravitational fields due to gravitational time dilation, so you must correct that as well.

If you ignore relativity, you will accumulate a discrepancy of six miles in one day.  You are not going to find the grocery store that way, unless you use the old-fashioned method of reading a map. In a sense, if your GPS device finds the grocery store for you, you have proven Einstein right.

Below is a YouTube video animation visualizing the GPS system.

GPS Facts

  • The GPS project was started by the U.S. Department of Defense in 1973. It is also owned by the U.S. Department of Defense.
  • The GPS satellites were sent up by the United States Air Force (and not NASA).
  • The first NAVSTAR satellite, later called GPS, was launched in 1978.
  • There are 31 GPS satellites currently in orbit.
  • The system requires 24 GPS satellites.
  • The 24-satellite system became fully operational in 1993.
  • The Global Positioning System cost (the US government) $1.8 billion annually to operate and maintain.
  • The Global Positioning System is free to use for the public worldwide.
  • Making GPS free to civilians worldwide was a decision by President Ronald Reagan in 1983 after a Korean airliner was shot down for straying off course.
  • GPS satellites carry extremely accurate atomic clocks. As explained, GPS must account for relativity, special relativity as well as General Relativity.
  • Other satellite systems help improve GPS, including WAAS (in the U.S.), EGNOS (in Europe), and MSAS (in Japan).
  • GPS is not the only satellite navigation system. Other countries have their own satellite navigation systems. GLONASS (Russia), Galileo (EU), and BeiDou (China).
  • Ukraine is helped by both GPS and Galileo.
  • Russian forces have been actively jamming GPS signals in Ukraine.

Uses of GPS

  • Examples of consumer electronics that use GPS are smart phones, tablets, Smartwatches, Car navigation systems, Cameras (DSLR with GPS), some models of laptops, fitness trackers (Fitbit), and drones.
  • Examples of vehicles using GPS are cars, delivery vans, trucks, aircraft, trains, ships and boats.
  • Military uses of GPS include guided missiles, guided munitions, tactical radios, communication systems, soldier-worn devices for location tracking, military vehicles and military aircraft.
  • Additional examples of GPS use include construction equipment for site positioning and machine guidance,  tractors for precision farming and other agricultural machinery, surveying equipment, pipeline inspection drones, other inspection drones and rovers, emergency locator beacons, pet trackers, smart collars, livestock monitoring, personal trackers, and geocaching devices.

As you can see, GPS is extremely useful, and there are a lot of interesting facts about GPS.

To see the other Super Facts click here