RAGORDON2010

Lately, I’ve been using “Special Relativity and Classical Field Theory”, Leonard Susskind and Art Friedman, Basic Books, 2017, as a desk reference. They state on p.57 that “proper time” and “spacetime interval” are negatives of each other, each referencing spacetime distance. I have no citation I can give you regarding the Einstein-Minkowski story. It may be apocryphal.

Studiot, you are becoming one of my favorite responders because you seem to have a knack for leading me into areas I very much want to address. I am aware that Hermann Minkowski first dealt with the problems of the 4-space of t,x,y,z, i.e. "spacetime", circa 1908. His concern was how to specify a "distance" or separation between two spacetime events by building on Einstein's special relativity theory. This separation we now refer to as "proper time". I will have much more to say on Minkowski's contribution in later posts. It is worth noting here that, as the story goes, when Einstein first became of aware of Minkowski's paper, he mumbled something about mathematics muddling up good physics. (Hmm.) By "change of viewpoint" in the context of Special Relativity, I am working at a higher level of abstraction than simply relative velocities as seen by moving observers. This is what I am talking about - "We have, on one hand, the conventional scenario consisting of a single experiment and two inertial frames of reference in uniform relative motion and, on the other hand, an alternative scenario consisting of a single frame of reference and two separate but related experiments". (And, please, forget I ever mentioned the Earth and the Moon.)

I apologize for confusing you with my initial remarks. I hope you will see that I've tried to be more specific in my later posts. The Earth to Moon imagery was just a way of letting the readers know that I was going to present a change of viewpoint.

Thanks to all of you who have taken time to respond to my posts. The subject of Special Relativity deserves all the attention it gets. I think I’ve stumbled onto some sort of DNA test among followers of SR. We have, on one hand, the conventional scenario consisting of a single experiment and two inertial frames of reference in uniform relative motion and, on the other hand, an alternative scenario consisting of a single frame of reference and two separate but related experiments. I hold the view that both scenarios should be introduced and discussed in high school junior and senior science classes and also at the freshman university level. Let the students choose their preference according to their natural inclinations. Obviously I have my own preference but, particularly with the advent of General Relativity, the question of relationships across multiple reference frames becomes significant and must be introduced and discussed. Which brings me to the subject of scenario equivalence. Let me give an example. I pose the following question - Without invoking the mathematics of the the Lorentz transformations, is there a way to match an observation by observers in one reference frame with an observation by observers in the other reference frame? I believe Einstein wrestled with this question because he introduced the notion of the “mutually observed light flash” - a match is struck and the light flash is observed instantly by observers in both frames. Beginning with the conventional scenario, let’s not just talk about it - let’s do it, at least in thought. Let’s go back to the situation where I stand on the platform and you are on the speeding train along with the charged ball. This time, however, I want to insert a small firecracker inside the ball. Then, once the ball starts looping as I perceive it, and hopping as you perceive it, I zap the ball with a laser beam and set off the firecracker. Pow!!! The ball explodes at an object point (t,x,y,z) in my frame and at the corresponding image point (t’,x’,y’,z’) in your frame, where the object-image coordinates satisfy the Lorentz transformations. Obviously, I cannot reproduce this match-up in the related experiments scenario. I think what we have here might be what theoretical physicists refer to as a “broken symmetry”. It certainly looks like a broken symmetry to me. (Actually after re-reading the above text, I did indeed find a way to match up observations across related experiments, and I’ll describe it in a future post. In my next post, however, I want to discuss time dilation and “slow clocks”.)

Hi. Thanks for your post. You're right - all inertial reference frames are equivalent for illustrating physical laws. However for a long time, I have believed that the train stories cloud the importance of Special Relativity for our young high school juniors and seniors and college freshmen struggling to understand how physics challenges their intuitive understanding of how Nature works. That's why I have long advocated for the related experiments approach to teaching the subject - one fixed frame of reference and two separate but related experiments, as opposed to a single experiment and two frames of reference in uniform relative velocity (moving at speeds close to the speed of light, no less). Just a cursory review of questions students ask about slow clocks and shrinking meter sticks illustrate the depth of the confusion. In the related experiments approach, there are only one set of clocks, one set of meter sticks and, of course, one set of whatever additional laboratory apparatus is needed. My clocks do not run fast or slow or whatever, my meter sticks do not shrink or grow or whatever, etc. In my Monday/Tuesday imagery, I only flip a page on the calendar. Let me give you an example of how confusing things have gotten: Given a pair of spacetime coordinates (t,x,y,z) and (t’,x’,y’,z’) connected to each other by a Lorentz transformation - The conventional view: Two reference frames, Frame O and Frame O’, moving uniformly relative to each other, locate the SAME point in spacetime, where the first set of coordinates are specified by the clocks and meter sticks belonging to observers in Frame O and the second set of coordinates are specified by the clocks and meter sticks belonging to observers in Frame O’. The related experiments view: There is a SINGLE frame of reference in which a pair of related experiments are carried out - the first, say, on Monday, and the second on Tuesday - and where the two sets of coordinates identify SEPARATE points in spacetime. These points appear on the separate world lines produced by the experiments, or, in 3-space, on the separate paths of motion. Look, Einstein was fully aware of the fact that Maxwell's equations hold their form under a Lorentz transformation. Had he built on that observation and created a related experiments picture along the lines discussed here, we would stiil have Einstein's Theory of Special Relativity, but without the nonsense. As things stand today, the conventional view offers a weird, confused, unintuitive and abstract reach for reality. In contrast, the related experiments view is reality.

At the risk of wandering into the dreaded realm of Speculation, I wish to offer the following insight into Special Relativity. To help put you in a proper frame of mind for this offering, imagine standing on the earth and looking UP at the moon. Now imagine standing on the moon and looking DOWN at the earth. It's just a difference in viewpoint. To begin, we will go earth to moon: Imagine I am standing on a platform next to a train track, and you are on a train speeding past me at 0.8c. I apply a magnetic field across the track, and a charged object, say a ball, riding with you in your train gets caught up in this field. What happens? I will see the ball looping in a vertical plane. You will see the ball undergoing a serious of weird pogo stick hops and until it hops out the back door of your train. The Lorentz time and space transformations relate my measurements of the path of motion (t,x,y,z) for the looping ball to your measurements of the path of motion (t',x',y',z') for the hopping ball. Now let's go moon to earth: Imagine I set up the following experiment in my laboratory on a Monday - I accelerate the charged ball up to 0.8c, and expose it to the same magnetic field. I will see the ball undergo the same looping motion that I observed in the train situation. On Tuesday, I place the ball at rest on a table and apply the combination of electric and magnetic fields that your equipment measured in the train situation (i.e. the image fields produced by applying the Special Relativity field transformations to the magnetic field I applied across the track). In this case, I will see the ball undergo the same hopping motion you observed in the train. My observations (t,x,y,z) of the path of motion of the ball in Monday's experiment will map over to my observations (t'x'y'z') of the path of motion of the ball in Tuesday's experiment via the same set of Lorentz transformations, only here the initial velocity of the ball in the Monday experiment is playing the role of the relative velocity between train and platform. What we have shown here are pairs of object-image observations arising from a pair of object-image "related experiments". Nothing new here. Object-Image experiments are useful for illustrating symmetries in natural laws.