Re: A new theory with two postulates


SCW wrote:
PD wrote:

SCW wrote:
PD wrote:

[snip]

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?

Any one involving gamma - 1 / (1 - v^2 /c_0^2)^0.5

L' = L * gamma

t' = t * gamma

Yup, let's talk about that one. Both t and t' represent time intervals
between two events that are both measured by two observers. Which two
events are the ones you want to talk about in your (modified) twins
puzzle?

You didn't answer this.

"event" and time are not the same thing - an event certainly does not
have to marked against a clock. But in any case, please feel free to
choose one to illustrate your point.

Indeed, but you can't assume that an equation that says t or t' means
just plain "time" either. Equations are shorthand for a sentence. If
you don't know the sentence, it's easy to misconstrue the equation,
isn't it. In this case, the t and t' in this equation does indeed mean
the time between two *events* as observed between two observers.


If the first "event" for the first frame of reference (FoR1_event1)
could be just before the observers pass each other, and the second
"event" be just afterwards (FoR1_event2). Similarly, (FoR2_event1)
and (FoR2_event2) for the other observer. If you like you can create as
many "events" as you see fit - perhaps an "event" as the observers
pass?

An event is something that happens and is marked by 3 spatial
coordinates and 1 time coordinate by each observer. Try again.

I'm sorry, but are you saying that FoR_event1, or any other for that
matter, cannot be measured by 3 spatial coordinates and 1 time
coordinate?

I'm not entirely sure where this "[...] each observer." comes from
either. Two FoR's each making an observation would count as two events
- surely?

Certainly not. An event is something that *happens* that both observers
notice -- the explosion of a firecracker *there*, or a signal arriving
at a detector over *here*, or the meeting of two relatively moving
twins at a common coordinate.

Now, two observers may have different sets of *coordinates* for a given
event, but an event is an event.


.

In any of the "events" the observers in either FoR will witness a
dilation in length and mass.

How does one witness a dilation of a single event?

A single obersvation (i.e. a single event) would allow an observation
of L and m by FoR_1 of FoR_2.

Really? How do you measure a length L of an object with a single event?
By its very definition, you are looking at two different locations to
find the distance L between those two locations. An event is something
that happens at *one* place and *one* time.

.

That's like saying that a point in space expands.

I've really no idea where you got this from. Perhaps you can explain?
.

See the above. Try thinking first about what it means to measure a
distance L. What do you think is involved.


The question is, in a symmetrical system, what type of dilation does
each observer witness?

Once we get it clear what two events you're talking about, then we talk
about the type of dilation each observer witnesses.

FoR1_event1 & FoR1_event2 will do. Then we can compare the results to
FoR2_event1 & FoR2_event2.

You've only given specified (sorta) the times of two events, not where
they are. It will help if you manufacture something real that signifies
something that *happens* at a particular place and time.

.

You know, there's a really superb book by Taylor and Wheeler that could
clarify some of this for you. Have you considered reading?

Thanks for the reference.
.


m' = m * gamma

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

I'd be quite interested in seeing the equations that involve
"*events*"

Um... you listed them. What did *you* think those equations meant?

PD

I think that they mean that there is dilation due to velocity, which
has nothing to do with events.

That would be wrong.

The statement is a written English form of the dilation equation for
mass. In this equation:

m' = m* gamma

What's the operational definition of the m that you're reading into
this equation?

I wasn't, but ok, m = 1

No, I'm not looking for a value. What do you *mean* by mass m of an
object? What is mass to you?



or length

L' = L * gamma

There is no reference to an "event" in either of these equations.


L and L' is the distance measured between two *events*.

The distance between two events?

I've really no idea where you get this from.

Perhaps if you read a little relativity. Taylor and Wheeler will help.


If you're getting this from Taylor and Wheeler then I'd suggest you try
reading something else. Perhaps "College Physics" by E.Gillam & R.M.
King.

L and L' are the measurement of a length within each of the FoR's and
the ratio of L to L' is the dilation equal to gamma.

OK, how do you measure the length of something?


A measurement of L' and m' are can be made in a single observation by
FoR_1 of FoR_2 and vice versa

Are you sure? Be specific about what it is you actually do. This will
help you see the two events.


.


[...] Again, it would
be mistake to try to derive the sentence from the shorthand that the
algebra represents, if you don't know the sentence to begin with.

Really, that book by Taylor and Wheeler would save you much
wheel-spinning.

Thanks again for the reference.



You have a shallow understanding of SR, which is
why the twin's puzzle was created -- to educate people with a shallow
understanding of SR.

Why not explain which points that you do not agree with?

That's what I'm doing, by asking you some pointed questions.

You're asking me pointed questions? Forget the rest of the thread -
please restate your question.

I have in this message. Keep going, we're going to get someplace.



If one FoR observes the other then there
should be mass and length dilation (not to mention time).

This then begs the question, doesn't each FoR's witness an equal
dilation in the other?

Again, you haven't specified what "witnessing a time dilation in the
other" means, have you?

I haven't asked the question "[what] witnessing a time dilation in the
other [means]"


No, but you've asked if each see the same thing, and I'm asking you
what that "thing" means to you.

No I haven't asked what the "thing" is.

That's right. I'm asking YOU what the thing is. What do you witness
when you witness time dilation?


The point I made is that FoR_1 can make a single observation (or as you
say witness an "event") of FoR_2 and get a result for L' & m'.

You really seem to be hung up on the t & t' thing - very little of what
you consider seems to be related to L & m.

Actually, I've asked you something separate about each of these....

.


PD

SCW

.

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