Hi Guys,

I'm a relativity hobbyist. I am getting intrigued by the postulate of
the special relativity which says that the speed of light is constant
in vacuum.

Further on, the theory of relativity also says that the speed of light
is independent of the reference frames. Now, as per this theory,
someone moving at at the same speed as the speed of light would still
find that the speed of the light beam moving parallel to him as 'c'
(which is a universal constant) !!

I feel that he should find that speed to be zero, as he himself is
moving at the same speed as the light beam.

I know this confusion should be due to my lack of proper understanding
and hence could anyone please shed more "light" on this ?

Thanks.
Astro.

"Astroguru" wrote in message oups.com...
Hi Guys,

I'm a relativity hobbyist. I am getting intrigued by the postulate of
the special relativity which says that the speed of light is constant
in vacuum.

Further on, the theory of relativity also says that the speed of light
is independent of the reference frames. Now, as per this theory,
someone moving at at the same speed as the speed of light would still
find that the speed of the light beam moving parallel to him as 'c'
(which is a universal constant) !!

I feel that he should find that speed to be zero, as he himself is
moving at the same speed as the light beam.

I know this confusion should be due to my lack of proper understanding
and hence could anyone please shed more "light" on this ?

Thanks.
Astro.

According to the theory physical objects cannot reach the
speed of light as seen in another inertial frame, so asking
what you would see if you "would have the speed of light"
is meaningless. Still according to the theory, flying in parallel
with the same speed as a light beam is just not possible.
Whatever you do, you cannot move with it. You always
locally measure the light signal to have the same speed c.
The equations that are used in the theory reflect this nicely.

Dirk Vdm

Astroguru wrote:
Hi Guys,

I'm a relativity hobbyist. I am getting intrigued by the postulate of
the special relativity which says that the speed of light is constant
in vacuum.

Further on, the theory of relativity also says that the speed of light
is independent of the reference frames. Now, as per this theory,
someone moving at at the same speed as the speed of light would still
find that the speed of the light beam moving parallel to him as 'c'
(which is a universal constant) !!

I feel that he should find that speed to be zero, as he himself is
moving at the same speed as the light beam.

I know this confusion should be due to my lack of proper understanding
and hence could anyone please shed more "light" on this ?

Thanks.
Astro.

Well, you must be just beginning as a relativity hobbyist, because this
is the conundrum that Einstein said got him started thinking about all
this relativity hoo-ha from the start.

In a nutshell, the answer is that no massive object can move at the
speed of light, so the hypothetical situation is unphysical. Any
massive object will move at a speed less than c, and for that observer,
light will travel at measured velocity c.

This is true even for a massive object that is moving (according to
another observer) at 0.9999999999 * c. Reconciling what those two
observers measure for the speed of light and the speed of the observers
is precisely what produces the rest of special relativity.

You've just begun your understanding, just scratched the surface.

PD

Well, I agree if we go by the theory and use lorentz equations than
probably we can not reach the speed of light. But is this restriction
not just imposed because of those equations ?

I mean if I replace 'c' by 'x' (my own arbitrary constant equivalent to
three times 'c' for example) then the equations would still hold true
and then I definitely cannot reach 'x' but can achive 'c' for sure !!
Is it not possible that we just are unable to measure anything beyond
'c' as of now and hence we are restricting ourselves to the 'c' ?

"Astroguru" wrote in message oups.com...
Well, I agree if we go by the theory and use lorentz equations than
probably we can not reach the speed of light. But is this restriction
not just imposed because of those equations ?

Of course not.
Equations can't impose anything on nature.
The equations merely *reflect* the theory.


I mean if I replace 'c' by 'x' (my own arbitrary constant equivalent to
three times 'c' for example) then the equations would still hold true
and then I definitely cannot reach 'x' but can achive 'c' for sure !!
Is it not possible that we just are unable to measure anything beyond
'c' as of now and hence we are restricting ourselves to the 'c' ?

Either there is a limit or there isn't.
Everything we do suggests that the limit is c.
If you have reasons to postulate that there is no limit, or
that the limit is something other than c, you are entirely
free to do that, but you have some work ahead of you.

If you are interested and if you have the mathematical
background, take a close look at section 10.8 of
http://www.courses.fas.harvard.edu/~...tbook/ch10.pdf
and perhaps first, at section 14.9 in
http://www.courses.fas.harvard.edu/~...appendices.pdf
Enjoy...

Dirk Vdm

On Wed, 01 Jun 2005 07:49:36 -0700, Astroguru wrote:

Well, I agree if we go by the theory and use lorentz equations than
probably we can not reach the speed of light. But is this restriction not
just imposed because of those equations ?

Sure it is! Absolutely! :-)

The equations define the "model" of the universe provided by the theory of
special relativity. According to those equations, there is a
_contradiction_ if there is an observer traveling at C. So, within the
"model" of the universe, there can be no such observer. End of that
part of the story.

Now, out in the real world, we ask if the model agrees with reality; and
that question is answered by experiment rather than by quoting equations.
In real experiments in the real world, things behave very much as the
model objects in the model provided by SR behave. So we conclude that, so
far as we know, reality behaves like the model of the world provided by
relativity. Since nothing which has mass can reach C in the model, we
conclude that, most likely, nothing which has mass can reach C in reality,
either.



I mean if I replace 'c' by 'x' (my own arbitrary constant equivalent to
three times 'c' for example) then the equations would still hold true
and then I definitely cannot reach 'x' but can achive 'c' for sure !! Is
it not possible that we just are unable to measure anything beyond 'c'
as of now and hence we are restricting ourselves to the 'c' ?

You are confusing the speed of light with the "c" in special relativity.
They happen to be the same value (as far as anyone can tell) but they
wouldn't have to be -- there's nothing about the basic model provided by
special relativity that makes electromagnetic radiation "special".
Relativity provides a model in which there is _some_ special speed which
can't be exceeded; that speed is called "c". It appears that
electromagnetic radiation travels at "c". If it turned out that EM
radiation travels at 0.999999*c, for instance, it might cause problems for
Maxwell's equations, but the Lorentz transforms would not be affected.

As to the "real" speed limit being 3 times the speed of light -- no way.
They've both been measured very precisely, and photons either travel at c
or travel only very slightly slower than c. Certainly they travel
far faster than (1/3)c.

--
Nospam becomes physicsinsights to fix the email

"sal" wrote in message news
On Wed, 01 Jun 2005 07:49:36 -0700, Astroguru wrote:

Well, I agree if we go by the theory and use lorentz equations than
probably we can not reach the speed of light. But is this restriction not
just imposed because of those equations ?

Sure it is! Absolutely! :-)

hehe... we seem to take a rather different point of view here.
Did you see my reply "Of course not" before you answered?


The equations define the "model" of the universe provided by the theory of
special relativity. According to those equations, there is a
_contradiction_ if there is an observer traveling at C. So, within the
"model" of the universe, there can be no such observer. End of that
part of the story.

Now, out in the real world, we ask if the model agrees with reality; and
that question is answered by experiment rather than by quoting equations.
In real experiments in the real world, things behave very much as the
model objects in the model provided by SR behave. So we conclude that, so
far as we know, reality behaves like the model of the world provided by
relativity. Since nothing which has mass can reach C in the model, we
conclude that, most likely, nothing which has mass can reach C in reality,
either.

So we do agree.
The only difference is that in my view the "theory" is put one
step higher than the equations. Reasons for doing so are because
the postulates aren't cast in equation form - they are rather
meta-equations - , and of course ultimately the theory can be
expressed without the equations. I mean, *very* ultimately.
Let's hope the OP doesn't get too confused by that.




I mean if I replace 'c' by 'x' (my own arbitrary constant equivalent to
three times 'c' for example) then the equations would still hold true
and then I definitely cannot reach 'x' but can achive 'c' for sure !! Is
it not possible that we just are unable to measure anything beyond 'c'
as of now and hence we are restricting ourselves to the 'c' ?

You are confusing the speed of light with the "c" in special relativity.
They happen to be the same value (as far as anyone can tell) but they
wouldn't have to be -- there's nothing about the basic model provided by
special relativity that makes electromagnetic radiation "special".
Relativity provides a model in which there is _some_ special speed which
can't be exceeded; that speed is called "c". It appears that
electromagnetic radiation travels at "c". If it turned out that EM
radiation travels at 0.999999*c, for instance, it might cause problems for
Maxwell's equations, but the Lorentz transforms would not be affected.

As to the "real" speed limit being 3 times the speed of light -- no way.
They've both been measured very precisely, and photons either travel at c
or travel only very slightly slower than c. Certainly they travel
far faster than (1/3)c.

Here we completely converge again :-)

Cheers,
Dirk Vdm

On Wed, 01 Jun 2005 16:16:29 +0000, Dirk Van de moortel wrote:


"sal" wrote in message
news
On Wed, 01 Jun 2005 07:49:36 -0700, Astroguru wrote:

Well, I agree if we go by the theory and use lorentz equations than
probably we can not reach the speed of light. But is this restriction
not just imposed because of those equations ?

Sure it is! Absolutely! :-)

hehe... we seem to take a rather different point of view here. Did you see
my reply "Of course not" before you answered?

No, I wouldn't have posted the response had I seen it. I didn't have much
to add to it, really.


The equations define the "model" of the universe provided by the theory
of special relativity. According to those equations, there is a
_contradiction_ if there is an observer traveling at C. So, within the
"model" of the universe, there can be no such observer. End of that
part of the story.

Now, out in the real world, we ask if the model agrees with reality;
and that question is answered by experiment rather than by quoting
equations. In real experiments in the real world, things behave very
much as the model objects in the model provided by SR behave. So we
conclude that, so far as we know, reality behaves like the model of the
world provided by relativity. Since nothing which has mass can reach C
in the model, we conclude that, most likely, nothing which has mass can
reach C in reality, either.

So we do agree.

Well, we're both working from the same texts, more or less, so I would
hope so!


The only difference is that in my view the "theory" is put one step
higher than the equations. Reasons for doing so are because the
postulates aren't cast in equation form - they are rather meta-equations
- , and of course ultimately the theory can be expressed without the
equations. I mean, *very* ultimately. Let's hope the OP doesn't get too
confused by that.


...

As to the "real" speed limit being 3 times the speed of light -- no
way. They've both been measured very precisely, and photons either
travel at c or travel only very slightly slower than c. Certainly they
travel far faster than (1/3)c.

Here we completely converge again :-)

Right, and for the first time this week I think I kept my foot well away
from my mouth while posting.

I still wish I could remember where I read that Einstein objected
to a universe of infinite volume and finite mass on aesthetic grounds.
Does that ring a bell, by any chance?


--
Nospam becomes physicsinsights to fix the email

"sal" wrote in message news
On Wed, 01 Jun 2005 16:16:29 +0000, Dirk Van de moortel wrote:


"sal" wrote in message
news

[snip]

As to the "real" speed limit being 3 times the speed of light -- no
way. They've both been measured very precisely, and photons either
travel at c or travel only very slightly slower than c. Certainly they
travel far faster than (1/3)c.

Here we completely converge again :-)

Right, and for the first time this week I think I kept my foot well away
from my mouth while posting.

You got tired of the taste? ;-)


I still wish I could remember where I read that Einstein objected
to a universe of infinite volume and finite mass on aesthetic grounds.
Does that ring a bell, by any chance?

I think it has become common knowledge.
In Pais perhaps?
Or in Fred Hoyle's autobiography? [Must-read, by the way]

Dirk Vdm

Thanks Dirk and Sal.

You were right, I was confused by 'c' in lorentz equations with the
speed of light (though the original theory revolves around the same).
Those PDF files were very useful for clearing up the things.

Section 10.8 derives the equations independently without 'c' and it
uses 'V' instead, and possible values of 'V' are 0 V = infinity.
This, however, still implies a possibility that 'c' 'V' (means I can
still travel at the speed of 'c' .. may not be at the speed of 'V' !!!
)

Please let me know if still I can't do this, I mean is there any other
fact that would prevent me in thinking so.... I'm not casting any
doubts on the validity of the theory or lorentz equations, I just want
ot know what kind of implications would be there if 'c' is being less
than 'V' ?

Also, as sal says:

As to the "real" speed limit being 3 times the speed of light -- no way.
They've both been measured very precisely, and photons either travel at
c or travel only very slightly slower than c. Certainly they travel
far faster than (1/3)c.

How do we measure this __Speed limit__ ? Is it not the case that
currently we are not aware of anything that travels faster than light,
and hence we are imposing the limit as being 'c' ?

I know, I may be ridiculous or funny but I feel this is the right place
to get answers to my stupid questions

Cheers,
Astro.