Tuesday, April 25, 2017

Quote Of The Day: How Length Contraction Entails Eternalism

Vesselin Petkov is a philosopher of physics who has written relentlessly on the reality of spacetime. He's one of the founders of the Minkowski Institute, an organization dedicated to (among other things) changing "the present situation in fundamental physics and lead[ing] the research on the major open questions," and is the current director. I emailed him a year ago to comment on my logical argument for eternalism and in response he said it "looks correct" and sent me a link to a short PDF that makes some additional arguments for the same conclusion.

The PDF, entitled The Ultimate Judge: Time does not Flow since it is the Fourth Dimension of the Real World, describes how the empirical evidence of time dilation and length contraction necessarily entail eternalism. Unless you want to deny your senses and empirical evidence as if they're an illusion forged on us by some unknown aspect of nature, the conclusion of eternalism necessarily follows. That is the only way to deny it. 

Below is an excerpt from one part of the PDF that makes an argument that the length contraction of a meter stick would be impossible if the meter stick existed only as a three-dimensional body, and not as a worldtube in 4 dimensional spacetime (which is what it is on eternalism).

It should be stressed that if the worldtube of the meter stick were an abstract geometric construction and what existed were a single three-dimensional meter stick (which constitutes a single class of simultaneous events), both observers would measure the same three-dimensional meter stick of the same length, i.e. the same class of simultaneous events, which means that simultaneity would be absolute and there would be no length contraction. So, if the meter stick were a three-dimensional object, neither relativity of simultaneity nor length contraction would exists, which means that all experiments mentioned above (that repeatedly confirmed these relativistic effects) would be impossible. This conclusion can be easily generalized - as a three-dimensional world is defined as everything that exists simultaneously at the present moment (as a single class of simultaneous events), if reality were a three-dimensional world evolving in time, then at every moment all observers would share this single three-dimensional world (since nothing else exists); therefore they would share the same single class of simultaneous events, which means that relativity of simultaneity would be impossible in contradiction with the experimental evidence.

This thought experiment clearly demonstrates that length contraction of a meter stick would be impossible if the meter stick existed as a three-dimensional body (not as a worldtube). An ordinary three-dimensional meter stick at rest with respect to an observer A is shown in fig. 1. What we see in the figure is what we perceive and take for granted that it is what really exists. According to Minkowski, however, the meter stick exists equally at all moments of its history and what is ultimately real is the worldtube of the meter stick as shown in fig. 2 (only part of the worldtube is displayed in the figure).

Assume that another meter stick at rest in another observer’s (observer B’s) reference frame moves relative to the first one at a distance 1 mm above it. Let us assume that at the event M the middle point of B’s meter stick (the mark “50 cm”) is instantaneously above the middle point of A’s meter stick. Lights are installed at every point inside A’s meter stick, which can change their color simultaneously at every instant in A’s frame. At the event of the meeting M all lights are red in A’s frame. At all previous moments all lights were green. At all moments after the meeting all lights will be blue. When A and B meet at event M this and only this event is present for both of them. At that moment all lights of A’s meter stick will be simultaneously red for A. In other words, at M the present meter stick for A is red (that is, all parts of A’s meter stick, which exist simultaneously for A at M, are red). All moments before M, when all lights of the meter were green, are past for A, whereas all moments when the meter stick will be blue are in A’s future. Imagine that B’s meter stick contains cameras, instead of lights, at every point along its length. At the event of the meeting M all cameras take snapshots of the parts of A’s meter stick which the cameras face. At event M all snapshots are taken simultaneously in B’s reference frame. Even without looking at the pictures taken by the cameras it is clear that not all pictures will show a red part of A’s meter stick, because what is simultaneous for A is not simultaneous for B.
When the picture of A’s meter stick is assembled from the pictures of all cameras it would show two things as shown in fig. 3 - (i) A’s meter stick photographed by B is shorter, and (ii) only the middle part of the picture of A’s meter stick (as measured, i.e., photographed by B) is red; half is green and the other half is blue. So what is past (green), present (red), and future (blue) for A, exists simultaneously as present for B. But this is only possible if the meter stick is the worldtube as shown in fig. 4.

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