David Bohm – Super Facts

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.

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

Superfact 5 : Two events may be simultaneous for some but not for others

Two events may be simultaneous for some but not for others. This means that two events that are simultaneous to an observer may happen at different times to other observers. If two lamps A and B turn on at the same time according to observer #1, lamp A may turn on first for observer #2, and lamp B may turn on first for observer #3. All three observers are correct because time is relative.

Previous Fact:

My previous blog post “The Speed of Light In Vacuum Is a Universal Constant” explained that the speed of light in vacuum compared to yourself is the same regardless of your motion or the origin of the light beam. A beam from a flashlight you are holding is traveling at a specific speed c = 299,792,458 meters per second as compared to you. If your friend is traveling at half the speed of light compared to you, he will still agree that the light beam from your flashlight is traveling at the specific speed c = 299,792,458 meters per second as compared to him, just like his own light beam by the way.

No matter how everyone is traveling everyone agrees that all light beams everywhere, emanating from everyone’s flashlights, all travel at exactly the same speed c = 299,792,458 meters per second. Like I said, the speed of light in vacuum is a universal constant. This is made possible by accepting that space and time are relative, but what does that mean? As mentioned in the other post this leads to the special theory of relativity.

I can add that since we are talking about relativity, or rather special relativity, relativistic effects have been very well tested by thousands of experiments and are not in doubt by the scientific community. Don’t be fooled by the word “theory” in special theory of relativity. “Theory” is not used the same way in science as in everyday language.

In this picture Amy is traveling past Alan in a rocket. Both have a laser. Both measure the speed of both laser beams to be c = 299,792,458 meters per second.

Relativity of simultaneity

Time is relative not only means that clocks are running slower in moving systems or that distances are contracted. It means that observers will disagree on how fast clocks are running and even disagree on whether events are simultaneous or not and in which order events occur.

If you are traveling through space at a very high speed and your wife/husband is back on earth, you can’t really ask yourself, “I wonder what my wife/husband is doing now?”, because what time it is back on earth depends on how it is calculated and by which observer. There is no universal now. Time is not absolute. Time is relative. The speed of light in vacuum is what is absolute.

I should add that if you combine space and time into spacetime you get an entity that is the same for all observers, the spacetime interval. You can say that in four dimensions the relativity disappears, but that is beyond the scope of this blog post.

Amy is traveling at a high speed to the left compared to two lamps A and B. Alan is standing still compared to the lamps. Adam is traveling at a high speed to the right compared to two lamps A and B. Alan turns on the lamps at the same time. After considering the travel time of the light she sees, Amy concludes that lamp B turned on first. After considering the travel time of the light he sees, Adam concludes that lamp A turned on first. I should add this non-simultaneity can only happen if the lamps are separated by a distance.

Below I am going to explain what is going on in more detail. If you don’t want to get into the details you can stop reading here. I am not going to explain the theory of special relativity, but I will explain some of the background and it gets a little bit complicated. Explaining scientific theories is not the goal of this blog. The goal of this blog is to list scientifically/expert accepted facts that are still disputed amongst the public or are highly surprising facts. Let’s look at time dilation first.

Time dilation

That clocks run at different speeds as a result of the constancy of speed of light in vacuum is pretty much well accepted. This is called time dilation. If Amy is passing Alan at a high speed, Alan will see Amy’s clocks running slower than his. This can be illustrated by the light clocks depicted below. The light clocks consist of light beams that are bouncing up and down between the floor and a mirror in the ceiling. Since light in vacuum is a universal constant, this is a very precise and reliable clock.

However, from Alan’s perspective the light beam in Amy’s system/spaceship must go farther than in Alan’s system (but note, from Amy’s perspective it is the opposite). Since the speed of all light beams in vacuum is a universal constant Amy’s clock is slower from Alan’s perspective.

Alan and Amy have identical light clocks. We call the time it takes for the light beam to go from the floor to the ceiling (one clock tick) Dt in Amy’s case and Dt’ (reference frame) for Alan. Amy is speeding past Alan towards the left. From Alan’s perspective Amy’s clock is running slower. Using Pythagoras theorem, it is possible to derive the formula for time dilation shown in the lower left corner.

When you realize that speeds and velocities are relative, a difficulty arises, perhaps even an apparent paradox. Let’s assume that you are flying in a rocket in space, and you meet another rocket, and your relative speed is 10 million miles per hour.

Is the other rocket standing still and you are moving at 10 million miles per hour? Is the other rocket moving towards you at 10 million miles per hour and you are one standing still? Or are both moving at the speed of 5 million per hour towards each other? Who gets to decide? Do we decide what is “standing-still” by tying it to a point on the surface of planet Earth, the center of planet Earth, the center of our solar system, or the center of our galaxy, or maybe another galaxy or an ether that no one can find?

The point is velocities are always compared to something and can be assigned arbitrary numbers. That means that if an observer, Amy, is speeding past another observer, Alan, at a high speed, then Alan thinks that Amy’s clock runs slower, but note, speed is relative, so we can reverse the situation. In fact, Amy thinks that it is Alan’s clock that runs slower.

It is equally correct to say that Amy is standing still and that it is Alan that is moving fast to the right. This time (pun not intended) the clock ticks Dt correspond to Alan’s clock ticks and Amy’s clock ticks are Dt’.

To understand how this works and why this is not a contradiction you need the Lorentz transform. The Lorentz transform is a so-called coordinate transform that incorporates time and space (as variable x), and it determines the specific time and space coordinate for one system based on the time and space coordinate for another and the relative velocity between the two. The Lorentz transform is a way of keeping account of time and space coordinates and using it correctly resolves any apparent paradoxes.

It is a bit more complicated to derive the Lorentz transform, and it is beyond the scope of this blog post. Suffice it to say that it is the vx/c² term in the equation that both explains how it is possible for both Amy and Alan to consider the other’s clock slower and introduces the non-simultaneity aspect of special relativity. You have to look at both space and time to get the full picture.

The Lorentz transform is a so-called coordinate transform that incorporates time and space (as variable x), and it determines the specific time and space coordinate for one system based on the time and space coordinate for another and the relative velocity between the two.

The Twin Paradox

There is one obvious paradox that I need to address. Let’s say that Amy and Alan are of the same age. Then Amy leaves earth and travels at high speeds toward the star Sirius. From Alan’s perspective Amy’s clocks are running slower and from Amy’s perspective Alan’s clocks are running slower.

What will happen if Amy turns around and returns to earth after visiting Sirius and they meet up again? Will Amy be younger than Alan or will Alan be younger than Amy. Will they both be younger than each other? Well, the latter is not possible. You have to keep count of the time and what happens is that during the decelerations/accelerations necessary for Amy to turn around as well as the speed-up/slow-down around earth, Amy will catch up on the time that she lost with Alan.

In other words, her acceleration will make it so Alan’s clocks will run faster. When she comes back and meets up with Alan back on earth, Alan will be much older than her.

Tag: David Bohm

The Special Theory of Relativity by David Bohm