A constant speed of light in all reference frames? Surely you can't be serious. [Physics]

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From: harald on 12 Mar 2010 06:51

On Mar 12, 12:17 pm, "Peter Webb"
<webbfam...(a)DIESPAMDIEoptusnet.com.au> wrote:
> > The geometry models what we find happens physically. Why you insist there
> > be some physical cause for why space and time is as modeled by Minkowski
> > geometry, but do not similarly require a physical cause for why it would
> > be
> > modeled by Euclidean geometry (especially when experimental evidence
> > points
> > to it NOT being so modeled) sounds rather hypocritical to me.
>
> There is obviously a physical cause for the way different types of
> maps can be used for describing the surface of the Earth, and
> similarly there is a physical cause for the different geometries that
> we can conveniently use for describing physical processes.
> Note that no experimental evidence points to my personal preference of
> geometry I use to describe it, just as you cannot know from the
> physics of the Earth what projection the captain of a ship prefers.
>
> _____________________________
> No. We are not talking about a map of the structure, we are talking about
> its underlying properties.

That means YES. ;-)

> Whilst we can model the earth in 2D, in reality it is a sphere. Your choice
> of projections doesn't change that.

Exactly.

> You don't need spherical geometry to navigate 10 kms by boat, Euclidean will
> do fine, but nobody denies the surface of the earth is spherical. And you
> don't need Minkowski geometry to model objects travelling at 100 kms/hr,
> Euclidean will do fine, but nobody (should) deny the Universe is
> "Minkowskian".

I would not trust a ship captain who claims that nobody (should) deny
the Earth is "Mercatorian"!
Euclidean geometry works perfectly well for describing accelerating
electrons upto any possible speed, as Lorentz and Einstein already
showed in 1904/1905.

Cheers,
Harald

From: PD on 12 Mar 2010 11:36

On Mar 11, 9:32 pm, Paul Stowe <theaether...(a)gmail.com> wrote:
> On Mar 10, 8:57 am, PD <thedraperfam...(a)gmail.com> wrote:
>
>
>
> > On Mar 9, 9:41 pm, PaulStowe<theaether...(a)gmail.com> wrote:
>
> > > On Mar 8, 8:05 pm, "Inertial" <relativ...(a)rest.com> wrote:
>
> > > > "PaulStowe" <theaether...(a)gmail.com> wrote in message
>
> > > >news:1132a230-92d9-484a-b0c1-d3a97532cad9(a)z10g2000prh.googlegroups.com...
>
> > > > >> >> SR explains it as having to be c due to the geometry of spacetime
>
> > > > >> > That's simply a silly idea...
>
> > > > >> That you think it is silly is your problem, not that of SR
>
> > > > > Something physical may be represented by a geometric description.
>
> > > > And our universe is represented by Minkowski geometry.
>
> > > Yes, you can descibe localized behavior with that format. BUT! to do
> > > so you must depend on finite light speed and its physical
> > > independence. Geometry neither predicts. explains, or has a basis for
> > > that.
>
> > That's incorrect, Paul. The geometric structure of spacetime imposes
> > both a finite speed of light AND makes it frame-independent.
>
> > The geometric structure of spacetime *necessarily* divides pairs of
> > events into three categories: spacelike-separated, timelike-separated,
> > and nullcone-separated. This structure also immediately leads to the
> > result that any wordline that could be traversed by something between
> > timelike-separated events will, in any other inertial reference frame,
> > still be between timelike-separated events. What this means explicitly
> > is that this object can never span two spacelike-separated events.
> > Thus, the universe of events is strictly divided into two completely
> > separated causal domains. The boundary of these domains is the null
> > cone. Since the null cone has a definite slope of space vs time, this
> > imposes a causal speed limit. (This limit does not exist in Euclidean
> > 3D+1D space -- it is a unique feature of the 4D space and its
> > geometry.)
>
> > Furthermore, while transformations between inertial frames will shift
> > the slopes between pairs of timelike events (that is, the speed of an
> > object traveling between the two events), the same transformation
> > between pairs of events on the null cone do not change slope. What
> > this means is that any object that can travel between two events on
> > null cone will have the same speed regardless of inertial reference
> > frame.
>
> > So you see, the geometric structure DOES imply both a causal speed
> > limit and the invariance of that causal speed limit with choice of
> > inertial reference frame. It just so happens that light appears to be
> > one of the candidate objects that can travel between nullcone-
> > separated events.
>
> > If you need to see how the structure does impose those limits
> > formally, I could point you to a reference book or two that derives
> > this unambiguously.
>
> > At the time that Einstein proposed special relativity, he did not
> > understand how such a geometric structure could produce those two
> > conclusions as necessary consequences. And so he just posited the
> > invariance of the speed of light as a postulate (or equivalently,
> > demanded that Maxwell's equations obey the principle of relativity).
> > It was only later that the geometric structure was uncovered and it
> > was understood how the light postulate follows directly from this
> > structure.
>
> > PD
>
> I wasn't going to bother with a reply since we have gone round & round
> on this very point. I find your argument without merit and I'm
> certain that you mind is made up. Why act like kid and continuously
> and say no it ain't, yes it is???

I'm not sure what you mean by "find your argument without merit". I'm
not attempting to make an argument. I'm explaining facts about the
theory and what implies what in that theory. If you do not understand
what implies what, and you were hoping that my response would make it
plainer to you, then perhaps this is what you mean by "without merit".
Perhaps something is "without merit" if you are not convinced.

>
> In minkowski math c can be any finite value.

Yes, and in Gauss' Law, the constant in the expression between the
field and the source charge can take any value. That value is
empirically determined. In that case, it is the constant epsilon-zero.
In this case, it is c. In the case of Gauss' Law applied to Newtonian
gravity, the constant is G.

> As Tom Roberts would
> argue the are nearly a infinite number of variations which fit this
> form. Thus it's dependent upon c being a 'physical' constant.

Yes, that is so. As is true for just about every physical law.

> And,
> as GR shows, it not even global.

I'm not sure what you mean by that. Even in GR, the slope of the local
lightcone is c always.

> Now why might that be??? The logic
> (actually lack thereof) and thought process is 'in my opinion' silly
> and no one, not in print nor herein has provided any argument that is
> convincing that the math and geometry is NOT! a resultant of physical
> processes rather some magical geometry...

It may well be the result of what you call "physical processes", which
I take to mean matter banging on matter in the fashion you're used to
from macroscopic physics. After all, Einstein's postulates were found
to be explainable in terms of something more fundamental, as I've
explained. It is entirely possible that there is another, more
fundamental principle or interaction that accounts for Minkowski
geometry, which in turn accounts for the 1905 postulates. The only
problem is, nothing of the sort has been successfully produced yet.
Since you feel very strongly that this is the only kind of fundamental
explanation that is worth anything, you are invited to produce one
that works.

You may be interested in investigating spin-foam models of quantum
gravity, which offer the attractive feature of being "backgroundless".
That is, they do not presume a pre-existing spacetime. Rather, space
and time *emerge* from the spin-foam. I have no idea whether you
consider such models (http://math.ucr.edu/home/baez/foam/ for some
introductory pointers) to be "physical processes" according to your
expectations, but they do have a feature I would guess would be
attractive to you -- that spacetime is a artifact of the explanation,
not the basis of the explanation. Note that, despite your
protestations that no one is working on a deeper explanation, loop
quantum gravity, spin-foams, and spin-networks are very much an active
and hot area of research.

PD

From: Bruce Richmond on 12 Mar 2010 12:56

On Mar 11, 10:54 pm, "Inertial" <relativ...(a)rest.com> wrote:
> "Paul Stowe" <theaether...(a)gmail.com> wrote in message
>
> news:722fe1d3-ba1d-4439-bffe-eda2ca668f82(a)p3g2000pra.googlegroups.com...
>
>
>
>
>
> > On Mar 10, 8:57 am, PD <thedraperfam...(a)gmail.com> wrote:
> >> On Mar 9, 9:41 pm, PaulStowe<theaether...(a)gmail.com> wrote:
>
> >> > On Mar 8, 8:05 pm, "Inertial" <relativ...(a)rest.com> wrote:
>
> >> > > "PaulStowe" <theaether...(a)gmail.com> wrote in message
>
> >> > >news:1132a230-92d9-484a-b0c1-d3a97532cad9(a)z10g2000prh.googlegroups.com...
>
> >> > > >> >> SR explains it as having to be c due to the geometry of
> >> > > >> >> spacetime
>
> >> > > >> > That's simply a silly idea...
>
> >> > > >> That you think it is silly is your problem, not that of SR
>
> >> > > > Something physical may be represented by a geometric description..
>
> >> > > And our universe is represented by Minkowski geometry.
>
> >> > Yes, you can descibe localized behavior with that format. BUT! to do
> >> > so you must depend on finite light speed and its physical
> >> > independence. Geometry neither predicts. explains, or has a basis for
> >> > that.
>
> >> That's incorrect, Paul. The geometric structure of spacetime imposes
> >> both a finite speed of light AND makes it frame-independent.
>
> >> The geometric structure of spacetime *necessarily* divides pairs of
> >> events into three categories: spacelike-separated, timelike-separated,
> >> and nullcone-separated. This structure also immediately leads to the
> >> result that any wordline that could be traversed by something between
> >> timelike-separated events will, in any other inertial reference frame,
> >> still be between timelike-separated events. What this means explicitly
> >> is that this object can never span two spacelike-separated events.
> >> Thus, the universe of events is strictly divided into two completely
> >> separated causal domains. The boundary of these domains is the null
> >> cone. Since the null cone has a definite slope of space vs time, this
> >> imposes a causal speed limit. (This limit does not exist in Euclidean
> >> 3D+1D space -- it is a unique feature of the 4D space and its
> >> geometry.)
>
> >> Furthermore, while transformations between inertial frames will shift
> >> the slopes between pairs of timelike events (that is, the speed of an
> >> object traveling between the two events), the same transformation
> >> between pairs of events on the null cone do not change slope. What
> >> this means is that any object that can travel between two events on
> >> null cone will have the same speed regardless of inertial reference
> >> frame.
>
> >> So you see, the geometric structure DOES imply both a causal speed
> >> limit and the invariance of that causal speed limit with choice of
> >> inertial reference frame. It just so happens that light appears to be
> >> one of the candidate objects that can travel between nullcone-
> >> separated events.
>
> >> If you need to see how the structure does impose those limits
> >> formally, I could point you to a reference book or two that derives
> >> this unambiguously.
>
> >> At the time that Einstein proposed special relativity, he did not
> >> understand how such a geometric structure could produce those two
> >> conclusions as necessary consequences. And so he just posited the
> >> invariance of the speed of light as a postulate (or equivalently,
> >> demanded that Maxwell's equations obey the principle of relativity).
> >> It was only later that the geometric structure was uncovered and it
> >> was understood how the light postulate follows directly from this
> >> structure.
>
> >> PD
>
> > I wasn't going to bother with a reply since we have gone round & round
> > on this very point. I find your argument without merit and I'm
> > certain that you mind is made up. Why act like kid and continuously
> > and say no it ain't, yes it is???
>
> > In minkowski math c can be any finite value.
>
> Indeed it can. But we observe it to have a particular value in our
> universe.

Would that be the value in meters per second, miles per second, miles
per hour.... I could go on.

> > As Tom Roberts would
> > argue the are nearly a infinite number of variations which fit this
> > form.
>
> All equivalent as long as c is finite
>
> > Thus it's dependent upon c being a 'physical' constant.
>
> Yes .. it just doesn't really matter that much what particular value it has.
> But it does have a particular value in our universe
>
> > And,
> > as GR shows, it not even global. Now why might that be??? The logic
> > (actually lack thereof) and thought process is 'in my opinion' silly
> > and no one, not in print nor herein has provided any argument that is
> > convincing that the math and geometry is NOT! a resultant of physical
> > processes rather some magical geometry...
>
> The geometry models what we find happens physically. Why you insist there
> be some physical cause for why space and time is as modeled by Minkowski
> geometry, but do not similarly require a physical cause for why it would be
> modeled by Euclidean geometry (especially when experimental evidence points
> to it NOT being so modeled) sounds rather hypocritical to me.- Hide quoted text -
>
> - Show quoted text -

From: Ste on 12 Mar 2010 13:00

On 11 Mar, 20:57, PD <thedraperfam...(a)gmail.com> wrote:
> On Mar 11, 2:15 pm, Ste <ste_ro...(a)hotmail.com> wrote:
>
>
>
>
>
> > On 11 Mar, 15:12, PD <thedraperfam...(a)gmail.com> wrote:
>
> > > On Mar 11, 6:43 am, Ste <ste_ro...(a)hotmail.com> wrote:
>
> > > > On 11 Mar, 01:51, "Peter Webb" <webbfam...(a)DIESPAMDIEoptusnet.com.au>
> > > > wrote:
>
> > > > > No, perhaps you didn't understand. As I say, this is *not* the twins
> > > > > paradox, because in the twins paradox only *one* twin leaves Earth.
>
> > > > > ________________________
> > > > > Its functionally the same. It is exactly the twins paradox, but with two
> > > > > twins apparently doing exactly the same thing.
>
> > > > > Even if you cannot see that, the explanation on the Wikipedia page of the
> > > > > Twins Paradox is trivially adapted for two twins.
>
> > > > > I assume that you do not understand the Wikipedia twins paradox page, or
> > > > > else you would know the answers to your questions already. Which parts don't
> > > > > you understand?
>
> > > > Let's just go through it step by step Peter, as we have been doing.
> > > > It's pointless spending 10 more postings arguing about how the
> > > > Wikipedia page does or does not answer the question, or how it is or
> > > > is not relevant. As I've just said in a post to Inertial, the only
> > > > analogy between my scenario and the twins paradox is that, in my
> > > > scenario, both twins leave Earth, and both return the same age as each
> > > > other - hence no paradox, and hence bearing no resemblance at all to
> > > > the twins paradox.
>
> > > First of all, let's establish what you think is paradoxical at all
> > > about the description of the twins in the twin puzzle. Then let's see
> > > whether this paradox is present in the case you mention.
>
> > As I understand it, the supposed "paradox" in the twins paradox was
> > that one returned younger than the other. It was, of course, not a
> > paradox at all, but that's besides the point.
>
> No, then you do not understand the paradox, because there is nothing
> contradictory in that statement at all. It may be surprising, but it's
> not contradictory, not paradoxical. Disagreement of clocks is not a
> paradox.
>
> The paradox, which is what is perceived (normally) by freshmen when
> first introduced to this statement, is embodied in their immediate
> classroom question: "But in the frame of the traveling twin, it is the
> earth twin that is moving away and returning. Since this is symmetric
> to the case of the traveling twin moving away and returning, then
> shouldn't the traveling twin expect the earth twin to be younger when
> they meet again?" Now perhaps the paradox is more apparent to you.
>
> However, the puzzle is specifically designed to emphasize the danger
> of oversimplifying. In fact, the two twins are NOT symmetric, because
> one unambiguously experiences acceleration and the other unambiguously
> experiences no acceleration. This then leads to a discussion of what
> produces the asymmetry in the time.

I know Paul. I know.

> Perhaps if you had started out by asking, "Since I don't see any
> obvious paradox here at all, perhaps someone could illuminate me as to
> why this is called the twin paradox?" Then at least you would have
> been on square one.

Really I just wanted to avoid going off on a long tangent about the
twins paradox. As I said, the scenario that were were addressing is
different from the twins paradox, in that we have three clocks, and
the two clocks with which we are now concerned (B and C) both return
to the origin point *synchronised* (albeit both lagging behind A),
whereas the twins' ages are not synchronised on the return of the
astronaut twin.

So let me say again. The twins paradox would be applicable if we were
talking about A and B, or A and C. In the event, we are talking about
what B and C observe of each other from their own reference frames.
There is, therefore, no correspondence with the twins paradox, because
unlike the twins, B and C return synchronised with each other.

From: PD on 12 Mar 2010 13:12

On Mar 12, 11:56 am, Bruce Richmond <bsr3...(a)my-deja.com> wrote:
> On Mar 11, 10:54 pm, "Inertial" <relativ...(a)rest.com> wrote:
>
>
>
> > "Paul Stowe" <theaether...(a)gmail.com> wrote in message
>
> >news:722fe1d3-ba1d-4439-bffe-eda2ca668f82(a)p3g2000pra.googlegroups.com...
>
> > > On Mar 10, 8:57 am, PD <thedraperfam...(a)gmail.com> wrote:
> > >> On Mar 9, 9:41 pm, PaulStowe<theaether...(a)gmail.com> wrote:
>
> > >> > On Mar 8, 8:05 pm, "Inertial" <relativ...(a)rest.com> wrote:
>
> > >> > > "PaulStowe" <theaether...(a)gmail.com> wrote in message
>
> > >> > >news:1132a230-92d9-484a-b0c1-d3a97532cad9(a)z10g2000prh.googlegroups.com...
>
> > >> > > >> >> SR explains it as having to be c due to the geometry of
> > >> > > >> >> spacetime
>
> > >> > > >> > That's simply a silly idea...
>
> > >> > > >> That you think it is silly is your problem, not that of SR
>
> > >> > > > Something physical may be represented by a geometric description.
>
> > >> > > And our universe is represented by Minkowski geometry.
>
> > >> > Yes, you can descibe localized behavior with that format. BUT! to do
> > >> > so you must depend on finite light speed and its physical
> > >> > independence. Geometry neither predicts. explains, or has a basis for
> > >> > that.
>
> > >> That's incorrect, Paul. The geometric structure of spacetime imposes
> > >> both a finite speed of light AND makes it frame-independent.
>
> > >> The geometric structure of spacetime *necessarily* divides pairs of
> > >> events into three categories: spacelike-separated, timelike-separated,
> > >> and nullcone-separated. This structure also immediately leads to the
> > >> result that any wordline that could be traversed by something between
> > >> timelike-separated events will, in any other inertial reference frame,
> > >> still be between timelike-separated events. What this means explicitly
> > >> is that this object can never span two spacelike-separated events.
> > >> Thus, the universe of events is strictly divided into two completely
> > >> separated causal domains. The boundary of these domains is the null
> > >> cone. Since the null cone has a definite slope of space vs time, this
> > >> imposes a causal speed limit. (This limit does not exist in Euclidean
> > >> 3D+1D space -- it is a unique feature of the 4D space and its
> > >> geometry.)
>
> > >> Furthermore, while transformations between inertial frames will shift
> > >> the slopes between pairs of timelike events (that is, the speed of an
> > >> object traveling between the two events), the same transformation
> > >> between pairs of events on the null cone do not change slope. What
> > >> this means is that any object that can travel between two events on
> > >> null cone will have the same speed regardless of inertial reference
> > >> frame.
>
> > >> So you see, the geometric structure DOES imply both a causal speed
> > >> limit and the invariance of that causal speed limit with choice of
> > >> inertial reference frame. It just so happens that light appears to be
> > >> one of the candidate objects that can travel between nullcone-
> > >> separated events.
>
> > >> If you need to see how the structure does impose those limits
> > >> formally, I could point you to a reference book or two that derives
> > >> this unambiguously.
>
> > >> At the time that Einstein proposed special relativity, he did not
> > >> understand how such a geometric structure could produce those two
> > >> conclusions as necessary consequences. And so he just posited the
> > >> invariance of the speed of light as a postulate (or equivalently,
> > >> demanded that Maxwell's equations obey the principle of relativity).
> > >> It was only later that the geometric structure was uncovered and it
> > >> was understood how the light postulate follows directly from this
> > >> structure.
>
> > >> PD
>
> > > I wasn't going to bother with a reply since we have gone round & round
> > > on this very point. I find your argument without merit and I'm
> > > certain that you mind is made up. Why act like kid and continuously
> > > and say no it ain't, yes it is???
>
> > > In minkowski math c can be any finite value.
>
> > Indeed it can. But we observe it to have a particular value in our
> > universe.
>
> Would that be the value in meters per second, miles per second, miles
> per hour.... I could go on.

A quantity can be thought of being something that is independent of
the units used to measure it. A basketful of wheat contains the same
quantity of wheat whether you choose to measure that quantity in
bushels, quarts, tablespoons, cubic decimeters, ziploc bags, or
kiloliters.

In a sensible system of units (one where the units of space are the
same as the units of time, rather than the artificially separate ones
imposed by historical convenience), the value of c is 1, which is
about the most obvious nonzero number you can imagine.

>
> > > As Tom Roberts would
> > > argue the are nearly a infinite number of variations which fit this
> > > form.
>
> > All equivalent as long as c is finite
>
> > > Thus it's dependent upon c being a 'physical' constant.
>
> > Yes .. it just doesn't really matter that much what particular value it has.
> > But it does have a particular value in our universe
>
> > > And,
> > > as GR shows, it not even global. Now why might that be??? The logic
> > > (actually lack thereof) and thought process is 'in my opinion' silly
> > > and no one, not in print nor herein has provided any argument that is
> > > convincing that the math and geometry is NOT! a resultant of physical
> > > processes rather some magical geometry...
>
> > The geometry models what we find happens physically. Why you insist there
> > be some physical cause for why space and time is as modeled by Minkowski
> > geometry, but do not similarly require a physical cause for why it would be
> > modeled by Euclidean geometry (especially when experimental evidence points
> > to it NOT being so modeled) sounds rather hypocritical to me.- Hide quoted text -
>
> > - Show quoted text -
>
>