Re: Basic relativity question.

From: Bill Hobba (bhobba_at_rubbish.net.au)
Date: 12/25/04 

Date: Sat, 25 Dec 2004 00:00:38 GMT

"Dean" <deanw8@hotmail.com> wrote in message
news:5ecdd4e6.0412241331.4710178f@posting.google.com...
> Hi,
>
> I'm a physics student and have just started getting any kind of grip
> at all on the principles of relativity. I am, however finding some
> difficulty in coping with some of the ideas as they are very hard to
> grasp.

Yes relativity is counter intuitive - but very important. Special
Relativity (SR) along with Quantum Mechanics (QM) is part of Quantum Field
Theory (QFT) which forms the basis of the standard model (SM). The SM and
General Relativity (GR) together describe all currently known physics; so
relativity can be seen as central to modern physics. Combining GR and the
SM to form a single theory is a central problem of modern physics. But it
is best to understand just what the problem is - see
http://arxiv.org/abs/gr-qc/9512024. Do not be turned of by the math - skip
over what you do not understand and you will get the general idea. In fact
if you are studying physics it is a good idea to get into the habit of
reading papers early on and skipping over what you do not understand - as
time goes on you will find you will need to skip over less and less.

>
> What I am currently struggling with is the concept of time dilation
> and what the "proper" time is. I guess it boils down to a frame of
> reference thing.

Tom Roberts, a very knowledgeable person we are fortunate enough to have
post here, has written extensively on the correct way to view this.
Consider a rod placed on the x axis. Rotate it - the rods length remains the
same but the x component is different. Now is the x component any less real
than before? Of course not - it is just different. Exactly the same thing is
happening in SR. When you are moving relative to a stationary rod all you
are doing is rotating the rod through what is technically called a
'hyperbolic rotation'. Its length has not changed, simply its projection
onto our coordinate system. That projection is just as real as when it was
at rest. Similar comments apply to clocks as well. For more detail see the
following posts by Tom Roberts:
http://groups.google.com/groups?hl=en&lr=&c2coff=1&selm=3714210B.9081...
and
http://groups.google.com/groups?q=g:thl3384368904d&dq=&hl=en&lr=&c2co...
'Go back and look at my building analogy. GEOMETRY affects the RELATIONSHIP
between a measuring tool and the object being measured, but NEITHER object
nor measuring tool is "affected". The underlying process is geometrical
projection: In Euclidean space, lay a rod of length L along the X axis;
measure it using a ruler parallel to the X axis and you obtain L. But if you
measure it with a ruler inclined wrt the X axis, you must PROJECT the ends
of the rod onto the ruler; do that perpendicular to the ruler and you get a
value smaller than L. The distance between the ends of the rod is a spatial
interval, and measuring with a ruler ivolved PROJECTING that interval onto
the ruler; while the value obtained varies with the relationshiop between
ruler and rod, neither ruler nor rod are "affected" by the inclination of
rod wrt ruler. The EXACT same thing happens with clocks in SR -- there is a
geometrical PROJECTION involved. A given clock PROJECTS a spacetime interval
onto its own trajectory. A moving clock is INCLINED in the X-T plane wrt a
clock at rest on the X axis. But this is hyperbolic geometry, so a clock
with an inclined trajectory (i.e. is moving) registers a smaller value for
the interval between two points (e.g. the departure and arrival of the
traveling twin/clock) than does a clock with a trajectory that is not
inclined (i.e. is not moving).'

> A problem I have in a book might help me explain. If
> a clock is on a ship moving relative to me is moving then from my
> perspective the clock is moving. But for people on the ship the clock
> is stationary. The people on the ship have to be aware that they are
> on a ship and therefore "know" it is moving and if the ship is moving
> then the clock must be moving.

Ahhhhhh - but that is the crux of the matter - how do you know the ship is
moving? Movement is relative to some coordinate system - if you choose a
coordinate system fixed on the ship then that ship is not moving. For
exactness let us suppose the ship is a space ship in interstellar space
between galaxies and it is simply floating freely. Now according the
Einstein Equivalence principle (EEP) such a ship can, for virtually all
practical purposes, be considered what is called an inertial frame. A frame
of reference is defined as a conventional standard of rest on which
experiments can be done. An inertial frame is one in which Newton's first
law holds ie one in which free particles move at constant velocity (IMHO not
the best definition but it will do for a start). The real basis of
relativity is the following - called the Principle of Relativity (POR) - the
laws of physics are the same in all internal frames. Note according to our
definition of inertial frame if a frame is moving wrt to an inertial frame
at constant velocity then free particles will move at constant velocity so
it is also an inertial frame. However if we have a frame that is
accelerating wrt to an inertial frame then obviously free particles will
accelerate so the frame is not inertial. Hence inertial frames can be
considered to all be moving at constant velocity relative to each other.
The POR is the real basis of SR, the speed of light thing is simply fixing
the value of a constant that naturally occurs in the theory. See the
following:
http://arxiv.org/abs/physics/0110076,
and ancient, but I still think excellent post by Tom Roberts
http://groups.google.com/groups?hl=en&lr=&c2coff=1&selm=54jfst%24glp%40ssbunews.ih.lucent.com
and chapter 10 of
http://www.courses.fas.harvard.edu/~phys16/Textbook/
under the heading of Relativity without c.

> So therefore any observers on the ship
> are aware of their state relative to the rest of the world and know
> they are moving.

Certainly they are aware of their state relative to the rest of the
universe - but how do you know the rest of the unversed is moving an you are
not stationary? For non inertial frames the forces of acceleration will
give it away - but the POR guarantees for inertial frames there is no way to
tell (not quite true - but again it will do for a start - if you peek
outside the space ship and view the fixed stars - or galaxies in this case -
then you can tell but let us imagine you do not do that). It is well to
remember that inertial reference frames are conceptualizations - they do not
strictly speaking actually occur in practice. But that is nothing new -
remember Euclidian geometry speaks of points as having position but no
size - such do not exist is reality either - it is a conceptualization as
well - but a very useful one - same for inertial reference frames.

> So why doesn't the statement of the whole frame of
> reference thing collapse inwards on itself when you are dealing with
> time.

I do not understand what you are trying to say. I hope what I said above
helps ie an inertial frame of reference is like a point in Euclidian
geometry - a conceptualization.

Thanks
Bill

>
> It's much easier to deal with the problem of lengths and things as it
> can (at my level for the moment) be dealt with by differences in path
> lengths but I'm having real problems with the whole time thing.
>
> Sorry for the length of this post and I appreciate anyone who has got
> this far taking the time to read it. I would appreciate any help on
> the matter as I am struggling with the concepts.
>
> Cheers
>
> Dean

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