Re: A new theory with two postulates


SCW wrote:
PD wrote:

SCW wrote:
PD wrote:

SCW wrote:
PD wrote:

SCW wrote:
PD wrote:

SCW wrote:
Sam Wormley wrote:
SCW wrote:

No theory is infallible.


Fallibility is well known, and so far there has never been
a prediction of SR, GTR or QM that has been contradicted by an
observation.

Well SR has the Twins Paradox and Bohr & Einstein seemed to spend a lot
of time debating GR & QM.

The "twin paradox" is poorly named -- it isn't a paradox. It is a
puzzle that a good understanding of SR resolves quite nicely. It is
only a paradox with a shallow understanding of SR.

OK, enlighten us.

You mean "enlighten me"? I don't know where you're starting from. Ask a
specific question.

How is the Twins Paradox resolved in SR?

Well, since you asked a general question, I'll give you a general
answer.
There are (at least) two common mistakes that are made by beginners
that look at the twins puzzle.

Mistake 1: "The twins have symmetric situations. From the perspective
of the Earth twin, the traveling twin is moving, but from the
perspective of the traveling twin the Earth twin is moving."
The two are not symmetric at all. The traveling twin experiences
something that the Earth twin does not at all: the change in direction
(and an acceleration that accompanies that). It is this change in
direction that signals that one twin inhabits more than one inertial
reference frame, while the other does not.

So if they were symmetric? e.g. in similar space craft passing each
other and not turning around (no acceleration in play), what would the
effect be?

Well, for one thing, they'd never meet again to be able to compare
ages, would they?

Oh, come on! You're seriously saying that meeting again is important?
Where does this appear in the equations? They're quite capable of
comparing physical measurements whilst in motion.

.

Mistake 2: "It's the traveling twin's motion that makes him age less."
The motion is not the source of the difference in ages. There are two
spacetime events -- departure and reunion -- that mark the beginning
and end of this exercise. The Earth twin takes a (more or less)
straight-line path through spacetime between these two events. The
traveling twin takes a decidedly not straight-line path through
spacetime between these two events, as any spacetime diagram of this
puzzle will show. And in spacetime, the straightest path between any
two points in spacetime is the *longest* path. (The fact that it is not
the *shortest* path is due to the key differency between the metrics of
Minkowski flat space and Euclidean flat space.) A clock on a timelike
path through spacetime marks the length of that path, and so it is no
wonder that the Earth twin's clock reads more than the traveling twin's
clock at the second event -- the Earth twin's path through spacetime to
that event is longer.

OK, let's not consider departure or reunion, just passing each other.
The start and end of the exercise is some point just before they pass
and then is at some point just afterwards. Again there are no
accelerations in play.

Right, and at that moment they pass each other they would be the same
age and would wave at each other, and then they would never see each
other again. What kind of effect are you looking for?

Again that's not what the equations predict - at the point they pass
they should both witness dilations, this being a condition of their
relative velocity and the limit imposed by c_0. The eventual reunion is
a red herring.

What equations are you thinking about?
Most of the ones I know of regarding time dilation concern what two
observers will note about the time difference between two *events* they
both observe. What two events do these two observe as they pass each
other?

PD


.



Fixing the first mistake resolves the apparent paradox. Fixing the
second mistake shows the student what the clock is actually measuring
and why it comes out the way it does.

On a more general point, are any of the arguments that you have used in
your explanation mentioned in the 1905 paper? I'm sure that Space-Time
isn't.


No, it is not, nor is generalized 3D Lorentz transformation, nor is
mass-energy equivalence. Spacetime was something that Minkowski coined
*after* reading his student's (Einstein's) paper.

While there was a lot in the 1905 paper, it would be incorrect to say
that SR is completely contained there.

This sounds a lot like "additional theory" to me.


PD

SCW

.

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