Re: Problem with Einstein's Train Thought Experiment

On Apr 25, 6:06 am, mpc755 <mpc...@xxxxxxxxx> wrote:
The distance between B and M is 1 light year.

The distance between B and M' is 1 and 1/3rd light years.

The train is traveling in the direction of B and away from A at 1/3rd
the speed of light.

A'----------M'----------B'
-----A----------M----------B

A lightning strike occurs at B.

In 1 light year the light reaches M.

At this instance M' is co-located with M:

-----A'---------M'---------B'
-----A----------M----------B

How far does the light travel from B to M'?

It travels 1 light year in distance.

Since everything is relative, this also means that a lightning strike
at A' will travel 1 light year in distance to reach M.

This means that even though A' is 1 and 1/3rd light years away from M
at the time of the lighting strike, the light from the lightning
strike will travel 1 light year in distance to reach M.

If there was a single lightning strike at A/A' where A and A' where 1
and 1/3rd of a light year from M, then the light from A would travel 1
and 1/3rd of a light year in distance to M and the light from the
lightning strike at A' would only travel 1 light year in distance to
reach M.

At the time of the lightning strikes:

A'----------M'----------B'
A-----------M----------B
<-1 1/3 ly->

When light reaches M:

-----A'------------M'-----------B'
A--------------M----------B

Just as the light from B to M' will travel 1 light year in distance to
M', the light from A' travels 1 light year in distance to M. The light
from A travels 1 and 1/3rd light years in distances to M.

This is two different distances.

All of the light is traveling at 'c'.

The reason the light can travel two different distances is the light
emits out from A and 'c' and the light emits out at 'c' from A'.

The light emits out from A as if A is stationary.

The light emits out from A' as if A' is stationary.

http://www.youtube.com/watch?v=jyWTaXMElUk

You're right to think there are problems with the train experiment
(with the relativity of simultaneity, that is, because this train
experiment is the same as the clock experiment). However, you are not
getting to the central anomaly, because you don't understand the train
experiment as a piece of what Einstein called "practical geometry." I
discuss the influence of "practical geometry," that is, constructivist
mathematics, on twentieth century ideas in the article linked below.

However, if you what you are trying to do is to disprove the train
experiment, here is the disproof (from the paper). It's a pretty easy
logical error, but in order to see it, you had to understand the train
experiment as a piece of constructivist mathematics. By the way, this
is not news--this paper has been at SSRN for two years now. This
objection has not yet been overcome:


Are two events (e.g. the two strokes of lightning A and B) which are
simultaneous with reference to the railway embankment also
simultaneous relatively to the train? We shall show directly that the
answer must be in the negative. When we say that the lightning
strokes A and B are simultaneous with respect to be embankment, we
mean: the rays of light emitted at the places A and B, where the
lightning occurs, meet each other at the mid-point M of the length AB
of the embankment. But the events A and B also correspond to positions
A and B on the train. Let M1 be the mid-point of the distance AB on
the traveling train. Just when the flashes (as judged from the
embankment) of lightning occur, this point M1 naturally coincides with
the point M but it moves…with the velocity…of the train.

This passage is by now so familiar that we think there can be nothing
new to be seen in it. But there is: it is the term, “naturally
coincides.” This term (“fällt zwar…zusammen” in the German) leaps out
at us because we are looking at it with twenty-first century eyes, not
twentieth-century eyes; indeed, perhaps the most difficult cultural
task now before us is simply to realize that we are not living in the
twentieth century.

“Natural” coincidence is otherwise known as a spacetime point.
Einstein has already spent twenty-odd pages of this very brief book
(RELATIVITY) laying out the assumptions which underlie the train
experiment. He is very careful about being consistent with them, and
he is a devoted and very strict Euclidean. But Einstein was not, it
appears, quite careful enough. We know that he is assuming, along
with Euclid, that the definition of the coincidence of two points is a
point. However, we have never gotten (and never get, in any of
Einstein’s writings) a definition of a “natural” coincidence of two
points. This alone prevents us from going on and this argument, which
defined the twentieth century, abruptly ends. We also have a problem
if we try to resolve the issue ourselves. If we simply drop the term
“naturally” we run into a situation in which Einstein has told us to
assume two Cartesian coordinate systems, but now leaves us with one,
since, following from the definition of the coincidence of two points,
if two parallel coordinate systems coincide at one point, they
coincide at all points and are one coordinate system, not two. We
have been led to a contradiction.



Do you see? In order for the train experiment to hold, we can't do
with M "naturally" coinciding with M', and we can't do WITHOUT M
"naturally" coinciding with M'. This is actually the classic way
logical errors are found in arguments.

So there you go. What happens now, as I say in the paper, is that the
Pythagorean theorem is suddenly at issue, because it is no longer
invalid under GR, because logically we can't get to GR.

So my question is this:

where is the constructivist intervention in the Pythagorean theorem?

That is the scientific question of the moment. If you get the answer,
let me know asap.

Cheers,
John Ryskamp
philneo2001@xxxxxxxxx















.

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