Introduction
Background
Learning Difficulties in SR Education
Simulation Tools in SR Education
Design Objectives
Design
User Interface
Design Decisions
Usability Test and Improvements
Evaluation
Method
Participants
Data Collection and Analysis
Task Design
Thought Experiment 1 (Tennis Balls)
The correct answer is that the tennis balls will hit the tree simultaneously in every inertial frame, because it is a single event. A screenshot of a simulation of TE 1 in Relativity Lab is shown in Fig. 5.Two tennis balls are being thrown toward a tree, one coming from the left and one coming from the right. The tennis balls hit the tree simultaneously in the inertial frame of the tree. There is also an airplane flying over the tree.Question: do the tennis balls hit the tree simultaneously in the inertial frame of the airplane?
Thought Experiment 2 (Einstein’s Train)
The correct answer is that the events of light detection are not simultaneous in any inertial frame that is not the carrier’s rest frame. Due to the invariant speed of light, the light flashes require less time to reach one end of the carrier and more time to reach the other end of the carrier in an inertial frame that is moving with respect to the carrier. A screenshot of a simulation of this TE in Relativity Lab is shown in Fig. 6. Note that the simulation does not strictly require a train carrier.A laser is placed in the middle of a train carrier that is travelling at a velocity near the speed of light. The laser emits flashes of light toward the left and the right ends of the carrier, where observers are located. In the inertial frame of the carrier, the observers detect the light beams simultaneously.Question: is the light detected simultaneously in an inertial frame that is moving with respect to the carrier?
Results
TE 1 (tennis balls) | Pair 1 | Pair 2 | Pair 3 | Pair 4 | Pair 5 | Pair 6 | Pair 7 | Pair 8 |
---|---|---|---|---|---|---|---|---|
Agreed on a prediction | x | x | x | x | x | x | x | x |
Formulated a correct prediction | x | x | x | x | x | x | x | |
Constructed a correct simulation | x | x | x | x | x | x | x | x |
Switched inertial frames | x | x | x | |||||
Confirmed correct prediction | x | x | x | x | x | x | x | |
Rejected incorrect prediction | x |
TE 2 (Einstein’s train) | Pair 1 | Pair 2 | Pair 3 | Pair 4 | Pair 5 | Pair 6 | Pair 7 | Pair 8 |
---|---|---|---|---|---|---|---|---|
Agreed on a prediction | x | x | x | x | x | |||
Formulated a correct prediction | x | (x) | (x) | (x) | ||||
Constructed a correct simulation | x | x | x | x | x | x | ||
Switched inertial frames | x | x | x | |||||
Confirmed correct prediction | x | (x) | x | (x) | ||||
Rejected incorrect prediction | x | (x) | x | x | (x) |
Thought Experiment 1 (Tennis Balls)
Student 1 (pair 2): [The tennis balls] are coming from different directions but they’re going at the same speed, so I think that they arrive simultaneously (...) The velocities of the tennis balls do not suddenly change. It is just that they are now different compared to the airplane.
Student 1 (pair 4): From the perspective of the airplane, one [tennis] ball goes faster than the other, because they are going in opposite directions.
As she was unsure of her interpretation of an inertial frame, she struggled to make a clear prediction.Student 2 (pair 6): If [the TE] is about actually hitting the tree, then the inertial frame of the airplane does not influence it. Then it is just about one moment. But suppose that it seems from the airplane that the tennis ball has hit the tree already, while it may not yet be so, then it is [dependent on] the inertial frame of the airplane.
Student 1 (pair 1): This is what we thought would happen, so that is nice.
Student 1 (pair 4): [The tennis balls] do arrive simultaneously (...) Ah yes, the tree also moves along.Student 2 (pair 4): Ah yes, that’s it. The tree also moves in that direction.Student 1 (pair 4): I forgot that the tree also moves.
Finally, it is noteworthy that five student pairs observed the simulation only from the inertial frame of the airplane. They did not verify that they had constructed the TE correctly by confirming that the tennis balls hit the tree simultaneously in the inertial frame of the tree.Student 2 (pair 4): Ah yes, these two [velocities] compensate for each other.
Thought Experiment 2 (Einstein’s Train)
Student 1 (pair 1): Not simultaneous (...) I think light always goes at the speed of light, no matter how you look at it (...) The light particles do not go faster in one direction than in other direction (...) Then [the light] should travel the same distance at the same time in both directions.
Student 1 (pair 7): Now everything is moving, because we are not in the inertial frame of the train.Student 2 (pair 7): [The scientists] also move along, so it should be so that they [detect the light] at the same moment. Because everything is just going toward the right.Student 1 (pair 7): The laser does not move, right? It is just that the whole thing is moving.
Student 1 (pair 6): Not [simultaneous], because the light is moving along with the speed of the train, so the one who is standing behind will get [the light] earlier than the one who is standing at the front.Student 2 (pair 6): In principle the wagon is just something by itself, and the scientists are standing inside of it, so the fact that it moves should not matter, right? The scientists and the light source are moving at the same speed so then it does not matter that it moves, right?Student 1 (pair 6): Yes it does because [the train] is moving toward the right and one [scientist] is standing right and the other is standing left, so the light has to go further to reach [the right scientist] than [the left scientist].
Student 2 (pair 1): But we don’t have a carrier.Student 1 (pair 1): No man, I don’t think that matters.
Student 1 (pair 4): There isn’t really a train carrier.Student 2 (pair 4): Ah, then we will use a bus.
Student 1 (pair 6): It is correct that the light has to traverse a shorter distance toward [the left scientist] than toward [the right scientist], so it arrives earlier at [the left scientist].
Student 1 (pair 7): This is not what we expected at all.Student 2 (pair 7): The [light flashes] are both equally far from where they had started, but this [light flash] goes to the left so it hits the [left] scientist much earlier (...) When we thought about [the TE], we viewed it from the laser, where everything is standing still, but now we see that everything moves to the right.
Student 2 (pair 4): Yes, this is what I had in mind.
The other five student pairs selected a different inertial frame after a suggestion by the researcher.Student 1 (pair 2): Why do [the light flashes] reach the two persons simultaneously in this inertial frame and not in the other? (...) Here [the observer] is moving toward the light burst. I expected that it would look the same from the wagon as in the [stationary inertial frame].
General Evaluation
Student 1 (pair 8): I found that it was sometimes unclear because I could not really give a good explanation of the events.
Student 1 (pair 1): First, you work out [the TE] on paper. Then you run the [simulation] experiment and from that you check whether your hypothesis was correct. Then you draw your conclusion from that.
Student 1 (pair 5): On a test, for example, I’ve got this picture in my head, and then perhaps I could understand it better (...) Actually I am going to project this into my mind now to see what happens.