What Do We See in a TE? James Robert Brown Understanding and the Aims of Science Leiden, June 2010

Not knowing is often central Galileo’s ship – relativity of motion Einstein’s elevator – gravity affects light Mary in black & white room – anti-physicalism Rawls – veil of ignorance

Idealizations? Aristotelian: ignore some features, eg, colour of a falling body, but we cannot ignore causal features that are truly at work (eg, the air) Galilean: falsify nature by simplification, eg, vacuum, frictionless plane. (McMullin)

Special Relativity Postulate 1: Laws of nature are the same in every inertial frame Postulate 2: The speed of light is the same in every frame. Definition: Distant events in frame F are simultaneous iff light from the two events meets at a mid-point.

Suppose we have two frames, the train and the track; the train is moving at velocity v in the track frame. Let e 1 and e 2 be two separated events (flashes) The observer in the track frame is midway between e 1 and e 2, and receives signals from each at the same time. Therefore, e 1 and e 2 are simultaneous in the track frame.

However, some time passes while the light signals come to the mid-points, so the train has moved forward. An observer midway on the train frame receives the signal from e 2 before e 1. So e 2 was earlier than e 1 in the train frame. Therefore: Simultaneity of events is relative to a frame. From this we can derive the length contraction and time dilation formulae

7 Relativistic Car & Garage Will the car, moving at velocity v, fit in the garage? They have the same rest length. ←

Let the rest length of the car and the garage each be L 0. Then the length in a frame when moving at velocity v is

9 Yes, it will fit in according to garage frame, since the car will be Lorentz contracted. No, it won’t fit in according to the car frame, since the garage will be Lorentz contracted. ← ←

10 Resolution: relativity of simultaneity The two frames disagree on the simultaneity of events. In the garage frame, the car’s front bumper was still in the garage after the rear bumper entered. In the car frame, the front bumper went through the garage back wall before the rear bumper entered.

11 What do we see in a TE ? Normally we try to visualize things realistically in a TE. But this would not work here. The visual appearance of a rapidly moving object in SR is not contracted It is rotated (degree of rotation depends on velocity). In the garage frame things would appear like this: Our intuition would be confused and we would not see the paradox. Somehow, we manage to see the right thing (ie, Lorentz contraction). ←

Rapidly moving objects appear to rotate

Roy Sorenson: TEs are experiments. Car-garage example seems to challenge this. – In a real experiment, the car would look rotated. – In the TE we suppress what it actually looks like. What’s going on? Perhaps we see phenomena ?

Phenomena Phenomena (right) are constructed or abstracted out of data (left). Bogen & Woodward McAllister on TEs

Idealizations -- again Aristotelian: ignore some features, eg, colour of a falling body, but will not ignore causal features that are truly at work (eg, the air) Galilean: falsify nature by simplification, eg, vacuum, frictionless plane. – McMullin: This is true for both real experiments & “subjunctive” reasoning (ie, TEs) – Galileo’s falling bodies TE fits this (vacuum) – But the car-garage example does not (appearance is falsified, not reality, ie, Lorentz contraction is real, rotation is not.)

Platonic idealization: – Rotation of car is not ignored; it is denied. – Not falsifying nature, falsifying appearance – Seeing things as they really are with the mind’s eye (phenomena?, the Platonic form?) – The is different than Galilean idealization, but Galileo would have accepted it. – Like Aristotle, everything causally relevant is included – Unlike Aristotle, appearance (to normal observer in normal conditions) rejected

Examples Aristotelian: Trolley car – ignore what clothes people are wearing, etc. Searle’s Chinese room – ignore gender, age of person in room, etc. Hard to find physics examples

Galilean: Galileo on falling bodies – ignore air Galileo’s ship & relative motion – ignore effects of moving at sea Stevin & static equilibrium – ignore friction of plane Newton’s bucket – ignore the material universe Einstein’s elevator – ignore huge acceleration or gravitational field Einstein chases a light beam – ignore impossibility of running that fast

Platonic: Car-garage – ignore appearance of rotation, but accept real Lorentz contraction Others ?

Upshot Phenomena, idealized in the Platonic sense This is an appearance-reality distinction in a TE One sees clearly what is happening. There is no residue that we fail to understand.

Understanding Via mechanisms? Via unification / covering theory? Via self-evident TE – understanding and self-evidence are linked. Given Lorentz contractions and equivalent frames, the car-garage paradox is immediately obvious – we can see it. Understanding the resolution requires understanding SR – here the standard question arises.

Bibliography Brown, J.R. (1991/2010) Laboratory of the Mind: Thought Experiments in the Natural Sciences McAllister, J. (2004) “Thought Experiments and the Belief in Phenomena” Phil. Sci. 71, McMullin, E. (1985) “Galilean Idealization”, Studies in the Hist and Phil of Sci, 16, no. 3, Weisskopf, V. (1960) “The Visual appearance of Rapidly Moving Objects” Physics Today, (Sept.) 24-27