# On the usual confusion among what it is and what is measure

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1. Dec 13, 2015

### MachPrincipe

I have found a book from my father epoch of undergraduate student in Physics. It was apperently Physics 101, and was written with a typewriter and the formulae with pen. I have gone straight to Special Relativity section and, to my dismay, and even if all formulae
were indeed correct, the interpretation was not. It said that the new approach by Einstein, based on measurements, relegated the really physical nature of lenght contraction by Fitzgerald and Lorentz to the oblivion, and thus the effect could not and never could be measured.
We are talking of 1950s as late. Since many years ago, I have seen similar confusions when explaining or trying to understand special relativity. It seems that the principle of constancy of the speed of light, which gives foot to the length contraction and time dilation in a very direct way also confuses some neophites when approaching for the first time the subject. Here I think there is a confussion among the coordinates of distant events as measured by different observers, and the time, finite which takes a signal to communicate these events to the observer placed in the origin of spatial coordinates coordinates. Things get event worst and feed even more this misunderstanding when leading with the electromagnetic Doppler effect. As it is composed of 2 main parts, namely one emminently classical and the other purely relativistic (transversal
Doppler effect being the maximum expression of the latter), the student can interpret that the effects of time dilation and length contraction are as physical (or rather unphysical) as the Doppler effect, and that all is a pure problem with the measurements in two relatively moving systems. Things even get worst, if possible, when pure relativists insist on interpreting spacetime intervals and thus not giving any credence to a time measured by a clock.... or someetimes giving too much credence and putting proper time in a priviledged status above coordinated times. What do you think of all of this mess? What is the best approach to teach relativity?
Personally I would insist on time dilation and lenght,contraction coming from the postulates and being completely real, physical. Later I would explain simoultaneity and derive Lorentz transf., and from there the relativity of these effects and why one observer is convincing of her measurements and why she believes the measurements of her boyfriend are those which are wrong. Later would introduce Doppler and finally examples of calculating time intervals of light emitted and received, so it can be seen tht the time used forr a ray to go from point A to point B is outside the different rates of clocks measuring these events.

man

2. Dec 14, 2015

### BvU

"What is the best approach to teach relativity?"

I'm sure the litterature on that has better and more recent material than a book from the fifties.

Any other, preferably more specific, questions ? All in good spirit, so no offence !

3. Dec 14, 2015

### MachPrincipe

I have not seen better book than Möller's. Modern does not mean better.

4. Dec 14, 2015

### Fredrik

Staff Emeritus
I haven't read the book you're talking about, but it sounds like you have misunderstood it. I'm not aware of any book that says that Lorentz contraction can't be measured. What they usually say is that the ether is undetectable.

Before Einstein, people thought of Lorentz contraction as a result of interactions with a mysterious substance known as the ether. They thought that objects moving relative to the ether were being compressed to a degree that can be computed from the object's speed relative to the ether. They thought that when an observer at rest relative to the ether, and an observer in motion relative to the ether, describe each other as compressed, only one of them is right, and the other is being tricked by the fact that his measuring devices are compressed. Einstein's work made it clear that there is zero justification for these beliefs. Minkowski's work provided an alternative explanation: When observers A and B both measure the size of an object at rest relative to B, they're measuring along two different "slices" of the congruence of world lines that describe the object's motion. So the source of the disagreement is that they're not measuring the same thing.

Proper time deserves a privileged status precisely because it's what clocks measure. To be more precise: The motion of a clock is described by a timelike curve in spacetime. The proper time of such a curve is by assumption the same as the amount by which the number displayed by the clock has changed from the event at one endpoint of the curve to the event at the other endpoint. This is the main assumption that's used to turn the mathematics of SR into a theory of physics.

Spacetime diagrams. I would also recommend units such that c=1, and to use matrices instead of systems of equations. Chapter 1 of Schutz ("A first course in general relativity") is pretty great. I would however use matrices more.

5. Dec 14, 2015

### Mister T

My understanding is that the contraction was thought to be due to forces within the object. That is what's meant by "physical nature". For example the arm of the MM interfereometer aligned parallel to the motion. What Einstein showed was that this viewpoint could not be supported through any experimental measurement. The point is not that length contraction isn't real, but rather that it's not due to forces acting within the object.

Does this mean you've decided to restrict your search for approaches?

Last edited: Dec 14, 2015
6. Dec 14, 2015

### BvU

Möller's looks OK, but I wouldn't use it nowadays. And it's not the book you described, I suppose ? I agree on the second item.

Don't know any more what you are after: You inquire in a didactical sense (as a teacher), as a student or otherwise ?

7. Dec 14, 2015

### MachPrincipe

[QUOTE="BvU, post: 5318380, member: 499340]

Don't know any more what you are after: You inquire in a didactical sense (as a teacher), as a student or otherwise ?[/QUOTE]

I own Schutz book and don't like it much. My approach is as a teacher point of view. A clarification: the book was authored by my father from the teaching of the professor, as a way of studying his course. The wrong point of view is something I found consistently among my student mates many years later. I think there is a basic misunerstanding of relativity if not properly explained from the beginning.

As for proper time, well, most of the time a light ray will be at x!=0. In the other hand, coordinate times are also measured by clocks. There is some apprehension to consider valid a time which is remote, but that is a prejudice rather than other thing. This is why I talked of a priviledged status, which is undeserved, IMHO, and contributes to the confussion.

8. Dec 14, 2015

### Fredrik

Staff Emeritus
Not sure what that has to do with anything. SR assigns a proper time to every piecewise smooth timelike curve in Minkowski spacetime.

Every clock measures the proper time along the curve that describes its motion. Sure, when we have chosen to use a coordinate system such that the time coordinate of every event on the time axis is equal to the proper time along the time axis from the origin to that event, then we can say that the clock measures coordinate time as well. But it's only because we chose the coordinate system to make that statement true.

The privileged status of proper time is well deserved. In my opinion, it should be emphasized more than it usually is.

9. Dec 14, 2015

### Fredrik

Staff Emeritus
Correct me if I'm wrong, but it seems to me that what you're saying is this: Your father misinterpreted his professor as saying that Lorentz contraction can't be measured, and you think that this is a common mistake, caused by bad books and bad teachers.

I'm not sure how to discuss that. If you could point out a passage in an actual textbook that you think teaches Lorentz contraction poorly, then there would be something to discuss.

10. Dec 20, 2015

### stevendaryl

Staff Emeritus
Just for clarification, there are really two different effects that are both referred to as "length contraction". One is physical, one is maybe not physical.

First, "length contraction" is a relationship between two different inertial coordinate systems. If $F$ and $F'$ are two inertial rest frames with relative velocity $\vec{v}$, then a rod oriented parallel to $\vec{v}$ that has length $L$ as measured in frame $F'$ will have length $L/\gamma$ as measured in frame $F$, where $\gamma = \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}}$. This notion of length contraction is not something that happens to an object, it's just a relationship between two different systems of measurement.

On the other hand, there is a related effect that is physical: Take a rod of length $L$ that is initially at rest in frame $F$, and is lined up parallel to $\vec{v}$. Now, gradually accelerate the rod until it reaches velocity $\vec{v}$. Then afterward, the rod will have length $L/\gamma$ as measured in frame $F$.

This second effect is not a relationship between two different frames, because all measurements are done in a single frame. It certainly is physical, and depends on the nature of the forces keeping the rod together. It's not going to be true for absolutely every object; for example, if the rod is made of putty, then the act of accelerating it might stretch or compress it, resulting in a length that is not the "ideal" value of $L/\gamma$.

Of course, the two effects are closely related, because the relativity principle says that if the forces in the rod are such that it tends to maintain a definite length (which is not the case for putty), then the length in frame $F$ when it is at rest in that frame, must be the same as the length in frame $F'$, when it is at rest in that frame. That, together with the Lorentz transformations, imply that a gently accelerated rod must physically contract.