What Do We See in a TE?

James Robert BrownUnderstanding 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 e1 and e2 be two separated events (flashes)

The observer in the track frame is midway between e1 and e2, and receives signals from each at the same time. Therefore, e1 and e2 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 e2 before e1. So e2 was earlier than e1 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 L0.

Then the length in a frame when moving at velocity v is

L L v cv 02 21 /

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, 1164-1175

McMullin, E. (1985) “Galilean Idealization”, Studies in the Hist and Phil of Sci, 16, no. 3, 247-273

Weisskopf, V. (1960) “The Visual appearance of Rapidly Moving Objects” Physics Today, (Sept.) 24-27