## Student understanding of time in special relativity - by Rachel E. Scherr e.a. - Article review

This document contains article review "Student understanding of time in special relativity " by Rachel E. Scherr e.a.
To order to read the article select: https://arxiv.org/ftp/physics/papers/0207/0207109.pdf
• The text in italics is copied from the article.
• Immediate followed by some comments

### I. INTRODUCTION - page 1

Over the last five years, the Physics Education Group at the University of Washington has been investigating student understanding of key ideas in Galilean, special, and general relativistic kinematics.
One important issue is that all the teachers should teach the same. And if that is not the case the major discrepencies should be explained.
A major purpose is to identify and characterize the conceptual and reasoning difficulties that students at all levels encounter in their study of special relativity.
If this is the case than the reason is maybe the teaching material of the UoW. The question if the material is clear and if the writers have a clear understanding what it all means.
The emphasis is on the relativity of simultaneity and the role of reference frames.
As such the teaching material should clearly describe what both means i.e. the diference between simultaneity versus relativity_of_simultaneity and the role of reference frames (plural)
We found that, after instruction,many students are unable to determine the time at which an event occurs, recognize the equivalence of observers at rest relative to one another, and apply the definition of simultaneity.
Again the cause can be the teaching material itself

### II. PRIOR RESEARCH - page 1

There is currently only a small body of research on student understanding of relativity, mostly in Galilean contexts (in particular, relative motion).
This sentence is not clear. Within classical science relative motion is no issue. Relative motion is important in SR and GR. The outcome of any research which mixes both, is doomed to fail.

### Page 2

Galilean relativity
Many students tended to identify an object’s motion as intrinsic, not a quantity that is measured relative to a reference frame.
Both opinions can be true.
Motion of an object is a physical condition.
In order to measure motion of an object a reference frame is required.
Students tended to make a distinction between “real” motion, which has a dynamical cause, and “apparent” motion, which is “an optical illusion, devoid of any physical reality.”
In order to understand this sentence you need a broader context.
It is possible that there is "real" motion, in the case of apparent motion, but that observation is difficult. For example: it is difficult from within a moving train to measure that the train is moving. From the outside world, at rest, this is easy.
The student in the study classified certain relativistic effects (including length contraction) as distortions of perception.
To understand this sentence you first have to understand the difference between relativistic effects versus nonrelativistic effects.
Does this mean that this student means that length contraction is not real i.e. not something physical?
This is the only place in the document where length contraction is mentioned.
Unfortunate the document does not discuss other cases.
O’Brien-Pride has conducted interviews etc. in which university students appear to believe that the order of events depends on observer location.
There is a clear difference when events happen and when events are observed. Both require a combined description of the whole physical situation.

### III. FOCUS OF THE RESEARCH - page 2

Understanding the concept of a reference frame forms the foundation for understanding any topic in special relativity.
The concept of a reference frame i.e. one reference frame is not so difficult, because it is the starting point of defining positions of different objects.
It provides the basis for the determination of all kinematical (and other physical) quantities and serves as the framework for relating measurements made by different observers.
With kinematical quantities I assume they mean velocity and acceleration.
The use of the word framework requires clarification.
The concept of a reference frame presupposes an understanding of more basic measurement procedures.
That is the question. It is not so much the measurement procedure, but the measurement of what.
For clarity in the discussion that follows, we review the basic operational definitions associated with reference frames, i.e., the determination of the position and time of an event and the conditions under which two events are treated as simultaneous
Okay
An event in special relativity is associated with a single location in space and a single instant in time.
In Netonian mechanics this is the same
The position of an event is defined to be the coordinate label on a rigid ruler at the location of the event.
All observers in special relativity are assumed to be “intelligent observers” who use synchronized clocks.
What means synchronized clocks. Also the word observers is important.
When observers and clocks are involved a large reference frame is involved.

### Page 3

Two events at different locations that occur at the same time in a given frame are not simultaneous in any other frame.
That means an observer in that frame, at equal distance from these two events, will actual observe these two events simultaneous.
Consider a second observer which is at that same moment at the same position as the first observer. Also this observer will observe these two events simultaneous. However in his reference frame the two events are not simultaneous.
What is also important that the clock in the reference of the second observer that they run slower.
The relativity of simultaneity is among the key results of special relativity and one that is particularly difficult to grasp, as evidenced by the numerous “paradoxes” that arise from it.
I expect that "relativivity of simultaneity" is one of ther cornerstones of SR. See also Reflection part 4 - The relativistic world view i.e. SR and GR -

### Page 4

Students are told the time ordering of the events for one observer and asked about the time ordering of the events for the second observer.
Okay

### 1. Spacecraft question - page 4

All involve two volcanoes, Mt. Rainier and Mt. Hood, that erupt simultaneously according to an observer at rest on the ground, midway between the volcanoes.
Okay.
Students are asked questions that probe their beliefs about the order of the eruptions in the moving frame.
This requires a clear definition of the concept moving frame

### Figure 3 Explicit version of spacecraft question. - page 11

All observers are intelligent observers, i.e., they correct for signal travel time to determine the time of events in their reference frame.
A very important question is how does an observer takes care that he knows the exact time of all the events in his reference frame. That means he knows the sequence of events in his reference frame i.e. he knows which set events are simultaneous among each other.
Each observer has synchronized clocks with all other observers in his or her reference frame.
I think it is more practical to use the concept that each observer has a set of clocks available in a 3D grid. All these clocks are synchronized with his clock i.e. in his reference frame.

### Reflection part 1 - General

When you study this article the general conclusion is that SR is difficult to understand. Often the students have different and wrong idea's what certain concepts mean. When I use the word wrong, this implies there should als be something that is correct. The question is, if it is that simple.

When I look to my own life, the first thing that I learned is what is called Classical or Newtonian mechanics. Using that theory it was rather straight forward (later in life) to simulate the movement of the planets around the Sun. It was not simple, but IMO nothing extraordinary.
The next fase in my life I studied SR. Special relativity much more something mathematical. I learned the concepts length contraction, time dilation and relativistic mass.
All these concepts woried me because they start from the idea of a frame at rest which contains objects at rest which have dimensions at rest, and a mass at rest. A clock at rest, within that frame shows rest time. When these objects are in linear motions all these dimensions change as a function of the lorentz transformations.
Later in life I studied GR at my own initiative.
Comparing my own learning experience and comparing that with the results of this article I understand that when you have a certain understanding of Classical mechanics that the concepts of SR are difficult to grasp, specific because, particular with GR, they are diffult to demonstrate by means of experiment to back up the predictions. The main reason is the large speeds involved, close to the speed of light,

### Reflection part 2 - Science

If you want to understand the processes that take place in the Universe it is important to explain what it involves as clear as possible. Specific it is important to explain the differences in what I call the relative world view i.e. SR and GR (realtivity) versus the Classical world view.

If you want to explain something you should stick to certain rules.
One of the first rules is that you should explain something as clear as possible. Concepts which should be explained are: What are laws of nature, simultaneity, relativity of simultaneity.
A second rules is that all the concepts explained should be backup by means of examples or better by means of experiments.
A third rule is to minimize the use of words which almost mean the same. For example the use of the words: to see, to observe and to measure. Seeing implies also to measure.

One important tool to study science is mathematics, but its importance should not be overestimated. The laws of physics are descriptions of certain processes happening in the universe. Many of these processes are stable, small scale processes, and as such can be described in a mathematical notation. However it is not these laws that control these small scale processes. All these processes are physical processes and it is in the physical (mechanical, chemical) details that lie the explaination how something functions,works or operates.

### Reflection part 3 - Classical world view

The classical world view starts from the idea that there exists a universe, filled with objects. The universe is not static but dynamic. That means throughout the universe changes take place, related to the positions of the objects and the compositions of the objects. The fact that we exists and most important that we experience our existance, justifies the concept time. Observations as such justify the idea that the Universe also exists in time and as a consequence allows us to study the evolution of the universe in time.
One important concept is the state of the universe. The state of the universe is a description of the positions and compositions of all the objects in the universe at one particular moment.
The concept of state is important because it allows us to define new concepts. The first is the concept of an event. An event is a particular condition of the state of the universe at a particular moment at a specific location.
For example: The tracjectory of the earth is a sequence of events of the position of the earth. As such the tracjectory of the sun is a sequence of events of the position of the moon. The second concept is simultaneous. Two events are simultaneous if they belong to the same moment i.e. happened at the same time.
That means with every event along the trajectory of the earth there is also a simultaneous event along the trajectory of the moon.
Using that idea we can also define the following concepts: the past and the future.
Any event is always caused by one or more previous events in the past and any event inturn can be the cause of one or more events happening in the future.
This leads to the following rule: simultaneous events, happening at different places (A and B) can not influence each other. The reason is simple, because if A could influence B than A happened before B. If B could influence A than B happened before A or A happened after B.
This leads to a contradiction: A happend both before and after B. That is not possible. The only solution is they happened simultaneous.

An important tool to understand nature is to use clocks to measure the time of the events. In the classical the world view a clock is much more a virtual device. That means clock's are used in a form of a 3D grid which all indicate the same time for the state of the universe. That means when reading the clock nearest you can instantaneous know the location and the time of an event. You can also know the position of the earth at every event.
The observed time of the 6 grid points nearest a grid point is the time on your clock minus the basic distance between each grid point divided by the speed of light. That means when the speed of light is 300.000 km/sec and the basic distance is 300km then the offset is 1 msec.

One of most important areas of investigation is the movement of objects through space. This field of study is called celestial mechanics. The law that describes the movement of free floating objects is Newton's Law. The most important parameter is the mass of an object and the simplest example to study is a binary system i.e. a universe with (in principle) only two objects.
There are two ways to study a binary (star) system (considering objects as point masses):

1. From your own perspective. That means the other object moves around you.
2. From the view point of an external observer. That means the two objects revolve around each other (at a distance from the observer), around a common fixed point.
The second method is the most practical because both objects can be observed.
The fixed point defines an axis of rotation of the binary system, perpendicular to the plane of rotation of the two objects. Based on observation over a period of time, which gives the best results when the observer is somewhere on this axis of rotation, it is possible to calculate the masses of both stars. That is not correct; it is the proportion between the two.

This same method can also be used to calculate (in principle) the mass of a bullet fired from a gun, because after firing the bullet is also a free moving object which movement can be described by Newton's Law. As mentioned in Reflection part 2 - Science Newton's Law does not control the movement of the body. In fact every time when you use that law you have to test if the predictions of an experiment is in accordance with the results of the experiment. In the case of firing a gun extra temporary forces (outside gravity) can be at stake which can influence the outcome, and which should be taken into account in the calculations.

### Reflection part 4 - The relativistic world view i.e. SR and GR

The relativistic world view (relativity) also starts from the idea that there exists a universe, filled with objects. The universe is not static but dynamic. That means throughout the universe changes take place, related to the positions of the objects and the compositions of the objects. Relativity also assumes that we exist in time and also that the universe exists in time, however, and here I have to be carefull, these are relative concepts. However relativity also introduce the concept Space-time and that is an absolute concept. Space-time is a typical mathematical concept.

One important concept in relativity is an observer. Every thing that an observer sees is not absolute but relative. As such the length of a rod (at a distance) he observers is smaller than his real length.

An other important concept is a reference frame. In fact each observer has his own reference frame in which the observer is at rest. When there are more observers then within the reference frame of observer A, all the other observers are either at rest, which means that the distance which such an observer is fixed, or moving, which means that the distance which such an observer varies. Fixed distances are only possible for observers part of the same object. For example: two observers on the surface of the earth.

Relativity also uses the concept of simultaneity, but in relativity this is called relativity of simultaneity.
As mentioned in
Page 3 simultaneous events A and B in one frame X are not simultaneous in any other moving frame Y(inertial frame). That the events A and B are simyltaneous is established from the clock readings near the events A and B, based on clocks in frame X, which are all synchronized. That means that there should be a point P1 from which you should be able to observe both events A and B simultaneous and also (I assume) that the events A and B should not be able to physical influence each other.
However that same point P1 is also part of the moving reference Y. However in that reference frame the two events A and B are not simultaneous, based on clocks in frame Y, which are all synchronized. That means in frame Y either event A can influence event B or event B can influence event A. This depends which comes first.
This is strange because two events which are simultanous accordingly to observations made by two observers one at rest and one moving, is considered, firstly by the observer at rest, as that they can not influence each other and secondly, by the moving observer, as that they can influence each other This contraditionary opinion is based on a double set of synchronised clocks, resident in each reference frame with the physical constraint, that the moving set of clocks runs slower than the clocks at rest.

An other important issue is an inertial frame. The idea behind an inertial frame is that an object in empty space, on which no forces are enforced moves an a straight line with a constant speed. An observer, part of that object, can now define a frame, in which both the object and the observer are at rest and that frame is called an inertial frame. That is correct but this required an other frame from which that object is observed and from which the positions of that object are measured. At the same time it is important to consider that empty space does not exist and as such inertial motion. In practice all objects in the universe are constant subject of external forces and behave from our human earth based point of view in completely unpredictable ways at present.
SR leans very much on inertial frames and observers and may be that is a reason why people i.e. students have so much problems in understanding SR. If you want a broader view

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Created: 26 July 2019

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