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Magnetism and electrostatics explained in terms of relativity, rather than
vice versa. And even I followed it when I skipped the actual math. :-)
http://physics.weber.edu/schroeder/mrr/MRRtalk.html
--
Darren New, San Diego CA, USA (PST)
Understanding the structure of the universe
via religion is like understanding the
structure of computers via Tron.
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Darren New wrote:
> Magnetism and electrostatics explained in terms of relativity, rather
> than vice versa. And even I followed it when I skipped the actual math. :-)
>
> http://physics.weber.edu/schroeder/mrr/MRRtalk.html
>
Indeed, wonderfully concise and clear. Should be required reading for
all physics freshers
John
--
"Eppur si muove" - Galileo Galilei
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On 24-8-2009 20:21, Darren New wrote:
> Magnetism and electrostatics explained in terms of relativity, rather
> than vice versa. And even I followed it when I skipped the actual math. :-)
>
> http://physics.weber.edu/schroeder/mrr/MRRtalk.html
>
It is 20 years ago but this is what I remember from one of the great
teachers of theoretical physics in Amsterdam that I had the pleasure of
attending the lectures of (Gerard Bauerle).
- let's assume we have a universe with 3 space-like coordinates and one
time coordinate
- what happens of we have a vector in this space that has to be
invariant to rotations?
- Surprise: what we have now on the blackboard are Maxwell's equations.
Ok, it took a number of hours to introduce the mathematics, but then we
had in 10 minutes shown that in such a universe fields move at a fixed
speed, aka lightspeed. General relativity was another 5 minutes work.
I'll read this page later. I have to do other things now :( but he
starts with relativity assumed and works from there. Gerard started with
a clean board.
Take home message for me (although I might not do his derivation
justice): light is simply a property of space, not something that is
added later.
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Darren New schrieb:
> http://physics.weber.edu/schroeder/mrr/MRRtalk.html
That's cool indeed! Somehow turns the picture of electromagnetism
upside-down (or rather, as it appears to me, puts it the right way round
onto its feet at last).
Makes the universe a tad simpler and easier to understand again.
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andrel schrieb:
> - let's assume we have a universe with 3 space-like coordinates and one
> time coordinate
> - what happens of we have a vector in this space that has to be
> invariant to rotations?
> - Surprise: what we have now on the blackboard are Maxwell's equations.
Sounds like an interesting approach, too.
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Or is space a property of light? I don't know the math but I doubt if we
can make space
fundamental -- thought I suppose we have to if we want to start with
geometry.;)
If I remember correctly, Einstein started with the behavior of light.
But I suppose that must
involve space (a coordinate system) so ... hmmm.... Interesting but
confusing topic.
David
andrel wrote:
> Take home message for me (although I might not do his derivation
> justice): light is simply a property of space, not something that is
> added later.
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David H. Burns wrote:
> thought I suppose we have to if we want to start with geometry.;)
Most things along those lines start with topology, not geometry, and then
find that geometry comes from topology if you restrict the topology to local
interactions.
> If I remember correctly, Einstein started with the behavior of light.
I recall that too. Basically, "c" showed up in a bunch of physics as a
constant without reference to the movement of the experimental setup.
--
Darren New, San Diego CA, USA (PST)
Understanding the structure of the universe
via religion is like understanding the
structure of computers via Tron.
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Yes and I used to think that it was Einstein who showed the velocity of
light to be constant
in all frames of reference. But it wasn't he started with that. I was
not able to find where
this idea actually came from. Any ideas?
David
Darren New wrote:
> I recall that too. Basically, "c" showed up in a bunch of physics as a
> constant without reference to the movement of the experimental setup.
>
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David H. Burns schrieb:
> Yes and I used to think that it was Einstein who showed the velocity of
> light to be constant
> in all frames of reference. But it wasn't he started with that. I was
> not able to find where
> this idea actually came from. Any ideas?
Been around a while. People looking for the "aether" though which light
waves were assumed to propagate, by measuring subtle changes in the
difference of c depending on direction (a) parallel to the earth's
movement on its orbit and (b) orthogonal to it, found that these subtle
changes were apparently... well, /very/ subtle indeed. Actually too
subtle to be measured, if there were any at all. At any rate, "aether"
theory would have predicted a lot more.
That's how this whole "no absolute frame of reference" thing started.
By the way, Einstein did /not/ show that light was travelling at
constant speed - that was Maxwell - nor did he show that this was the
case for every frame of reference - that was the experimenters (who
didn't really show it for /every/ frame of reference of course, but for
enough FoR to provide reason enough to seriously toy around with this idea).
All Einstein did was do just that: Take the "c appears to be constant in
all frames of reference" as a given for argument's sake, and see what
weird predictions he'd wind up with.
It was only the experimenters who showed that Einstein was right in his
predictions, and therefore it is prudent to assume that he was also
right in his initial presumptions.
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andrel <a_l### [at] hotmail com> wrote:
> - let's assume we have a universe with 3 space-like coordinates and one
> time coordinate
> - what happens of we have a vector in this space that has to be
> invariant to rotations?
> - Surprise: what we have now on the blackboard are Maxwell's equations.
That's a really fascinating approach. I should take the time to really learn
some of this, but it certainly helps to have an inspiring teacher. I just met
this guy a couple weeks back, and speaking of people who dabble in
relativity...
http://scholar.google.com/scholar?start=10&q=harry+ringermacher&hl=en
("Engineering warp drives" is my favorite, though I haven't looked at the actual
paper.)
But then I think he's a bit of an exception:
http://oldmerf.us.mensa.org/awards/copper_black/pastwinners/2003winner.php
He looks the part at least.
- Ricky
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clipka wrote:
> David H. Burns schrieb:
>> Yes and I used to think that it was Einstein who showed the velocity
>> of light to be constant
>> in all frames of reference. But it wasn't he started with that. I was
>> not able to find where
>> this idea actually came from. Any ideas?
>
> Been around a while. People looking for the "aether" though which light
> waves were assumed to propagate, by measuring subtle changes in the
> difference of c depending on direction (a) parallel to the earth's
> movement on its orbit and (b) orthogonal to it, found that these subtle
> changes were apparently... well, /very/ subtle indeed. Actually too
> subtle to be measured, if there were any at all. At any rate, "aether"
> theory would have predicted a lot more.
There were (are ?) several different interpretations of the results of these
experiments: (1)that the "light bearing aether" didn't exist, (2) it
moved with the earth,
(3) it exists but is theoretically undetectable, and perhaps more.
Didn't the "Lorentz-Fitxgerald"
contraction also come out of this as an attempt to preserve the aether?
But that shows up
in Einstein's relativity too.
>
> That's how this whole "no absolute frame of reference" thing started.
I think it started long before that even as far back as Newton (?)
>
> By the way, Einstein did /not/ show that light was travelling at
> constant speed - that was Maxwell -
So the idea that the speed of light is a constant comes from Maxwell. Does
simply "fall out" of his equations or is it an assumption or what?
Come to think of it, isn't the speed of any wave in an unchanging
unmoving medium
constant and dependent on the properties of the medium?
>nor did he show that this was the
> case for every frame of reference - that was the experimenters (who
> didn't really show it for /every/ frame of reference of course, but for
> enough FoR to provide reason enough to seriously toy around with this
> idea).
The idea that the velocity of light is a fundamental constant is
something dictated by
theory or maybe better a fundamental assumption of Einstein's theory.
>
> All Einstein did was do just that: Take the "c appears to be constant in
> all frames of reference" as a given for argument's sake, and see what
> weird predictions he'd wind up with.
I think two of his basic assumptions were (in my words):
1) The speed of light is constant in all frames of reference.
2) Other than that, the observations made from within any frame of
reference are valid
only within it.
>
> It was only the experimenters who showed that Einstein was right in his
> predictions, and therefore it is prudent to assume that he was also
> right in his initial presumptions.
Of course the "light bearing aether" survives in a way as the
"electrical and magnet fields of space".
David
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David H. Burns wrote:
> moved with the earth,
Fairly easy to disprove by observing things outside the solar system, IIRC.
> (3) it exists but is theoretically undetectable, and perhaps more.
> Didn't the "Lorentz-Fitxgerald"
> contraction also come out of this as an attempt to preserve the aether?
It was to explain why it was undetectable, IIRC.
> So the idea that the speed of light is a constant comes from Maxwell. Does
> simply "fall out" of his equations or is it an assumption or what?
It's based on the charge to mass ratio of the electron, IIRC. I used to be
able to calculate what the speed of light would be for different charge to
mass ratios, but that was back in high school.
The fact that it was based only on charge and mass and not the relative
speed of the observer is what made it a "constant".
> Come to think of it, isn't the speed of any wave in an unchanging
> unmoving medium
> constant and dependent on the properties of the medium?
Nope. Your wake never catches up with you when you're in a boat.
> The idea that the velocity of light is a fundamental constant is
> something dictated by
> theory or maybe better a fundamental assumption of Einstein's theory.
My understanding is that "the speed of light" showed up in a number of
physics equations unrelated to light as such. Thus, it had to be a constant,
or there would be an adjustment in those equations to account for the
observer's motion. Again, this is just my vague memory.
> I think two of his basic assumptions were (in my words):
>
> 1) The speed of light is constant in all frames of reference.
>
> 2) Other than that, the observations made from within any frame of
> reference are valid
> only within it.
The third being "the same thing happens regardless of the frame of reference
from which you look at it." I.e., what *actually* happened doesn't change
depending on how you look at it.
> Of course the "light bearing aether" survives in a way as the
> "electrical and magnet fields of space".
A field isn't aether. A field is a technical term that basically means "a
collection of vectors with certain properties." It's not a physical thing,
but a mathematical thing.
--
Darren New, San Diego CA, USA (PST)
Understanding the structure of the universe
via religion is like understanding the
structure of computers via Tron.
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David H. Burns wrote:
> clipka wrote:
>> That's how this whole "no absolute frame of reference" thing started.
> I think it started long before that even as far back as Newton (?)
>>
>> By the way, Einstein did /not/ show that light was travelling at
>> constant speed - that was Maxwell -
>
> So the idea that the speed of light is a constant comes from Maxwell. Does
> simply "fall out" of his equations or is it an assumption or what?
> Come to think of it, isn't the speed of any wave in an unchanging
> unmoving medium
> constant and dependent on the properties of the medium?
As far as I understand it it's a bit misleading (although technically
correct I suppose) to claim that Maxwell "showed" that the speed of
light is a constant. A constant speed of light does fall out of
Maxwell's equations, but I believe that the original interpretation was
that they were only correct when considered by an observer at rest with
respect to the aether (this is where clipka's next sentence about
different reference frames comes in).
Historically speaking I think that the reasoning actually happened the
other way around. From Maxwell's equations he determined that
electromagnetic waves propagate at a particular speed, which happened to
match the speed of light, and thereby inferred that light was actually a
form of electromagnetic radiation.
>> All Einstein did was do just that: Take the "c appears to be constant
>> in all frames of reference" as a given for argument's sake, and see
>> what weird predictions he'd wind up with.
>
> I think two of his basic assumptions were (in my words):
>
> 1) The speed of light is constant in all frames of reference.
>
> 2) Other than that, the observations made from within any frame of
> reference are valid
> only within it.
I think a better way of phrasing these might be as follows:
1) All the laws to physics are invariant to the velocity of the observer
2) This includes Maxwell's equations (and thus light must have a
constant speed independent of the velocity of the observer.)
Side note: I am not a physicist, so take everything with a grain of salt.
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David H. Burns schrieb:
> There were (are ?) several different interpretations of the results of
> these
> experiments: (1)that the "light bearing aether" didn't exist, (2) it
> moved with the earth,
> (3) it exists but is theoretically undetectable, and perhaps more.
> Didn't the "Lorentz-Fitxgerald"
> contraction also come out of this as an attempt to preserve the aether?
> But that shows up
> in Einstein's relativity too.
Indeed. Maybe starting with the concept of "frame dragging" first (the
"aether" moving along with the earth) might have resulted in the same
equations. That's just pure speculation though.
> So the idea that the speed of light is a constant comes from Maxwell. Does
> simply "fall out" of his equations or is it an assumption or what?
It indeed "falls out" of his equations that electromagnetic waves in a
vacuum must travel exactly with the same speed as had already been
measured for light (which actually was the first hint that light /is/ an
electromagnetic wave).
> Come to think of it, isn't the speed of any wave in an unchanging
> unmoving medium
> constant and dependent on the properties of the medium?
It is [*]. But every medium (other than space) also provides a
"standard" frame of reference: For instance, water waves on a stream
will move at the same speed in all directions relative to an observer
drifting on that very stream (the "standard" frame of reference), but
relative to an observer on the bank they will move faster downstream
than upstream.
This is not so for light: No matter whether you're a stationary (hah!)
outside observer or zipping along at near-lightspeed, you'll always see
the light go at some 300,000 km/s relative to you.
[* Well, it is not /strictly/ true, unless the direction and
polarization of the wave is also a given, as the speed of a wave may be
anisotropic regarding these parameters; for instance, there are
materials out there in which the speed of light depends on polarization,
causing what is known as "birefringence"; but taking these constraints
into account as well, you're right.]
> The idea that the velocity of light is a fundamental constant is
> something dictated by
> theory or maybe better a fundamental assumption of Einstein's theory.
The latter, exactly. Or, to be even more precise, it's the idea that the
assertions "the velocity of light in vacuum is a fundamental constant"
and "there is no preferred frame of reference with respect to the
propagation of light in vacuum" are not mutually exclusive.
> I think two of his basic assumptions were (in my words):
>
> 1) The speed of light is constant in all frames of reference.
That was /the/ basic assumption of his theory of special relativity, yes.
> 2) Other than that, the observations made from within any frame of
> reference are valid
> only within it.
I'm not sure what exactly you mean by that. Maybe the "you can't tell
whether your own frame of reference is being accelerated or at rest"
assumption of general relativity?
> Of course the "light bearing aether" survives in a way as the
> "electrical and magnet fields of space".
Yup.
Although the magnetic field, as we have just seen, appears to be only an
illusion caused by relativistic effects in the electric field.
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clipka wrote:
> Although the magnetic field, as we have just seen, appears to be only an
> illusion caused by relativistic effects in the electric field.
I haven't actually gone through the math on this one but my limited
understanding is that this isn't necessarily the case. In the case
where there exists a reference frame in which you can analyze the
situation with electrostatics then you can derive the electromagnetic
forces in another reference frame with special relativity, but that by
no means implies that there exists any frame which allows you do do away
with magnetic forces altogether.
I think that this paper gives this argument, although it's a bit lacking
in details for my taste:
http://www.iop.org/EJ/abstract/0143-0807/29/5/002
I'm instead inclined to have the take on it that it nicely illustrates
why electricity and magnetism are not separate forces, but rather two
difference aspects of the same underlying field.
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Darren New schrieb:
>> moved with the earth,
>
> Fairly easy to disprove by observing things outside the solar system, IIRC.
Not really. If light slows down or speeds up as it approaches the earth
(due to the "aether" exhibiting "local movement"), how could you
possibly tell the difference?
> It's based on the charge to mass ratio of the electron, IIRC. I used to
> be able to calculate what the speed of light would be for different
> charge to mass ratios, but that was back in high school.
Now that's a puzzler to me: Isn't the electron known to have two
"brothers" (muon and tauon) that differ from it only in mass?
So if that is so, then in a manner of speaking we /do/ have electrons
with different charge-to-mass ratios. Yet they all interact with the
same electromagnetic field, in which the propagation speed of
disturbances must obviously be independent of the particular particle
that caused them.
How can that possibly work out with the propagation speed of those
disturbances being dependent on the charge-to-mass ratio of the
electron? And how come that despite such a striking correlation
scientists have still not managed to find out how particles obtain a
mass at all, if the respective formula would be right before their eyes,
giving the electron a mass depending directly on its charge and the
speed of light?
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Kevin Wampler schrieb:
> I think that this paper gives this argument, although it's a bit lacking
> in details for my taste:
>
> http://www.iop.org/EJ/abstract/0143-0807/29/5/002
I'm not buying that, literally ;-)
(How I hate this practice of making scientific papers available only for
money...)
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clipka wrote:
> Kevin Wampler schrieb:
>> I think that this paper gives this argument, although it's a bit
>> lacking in details for my taste:
>>
>> http://www.iop.org/EJ/abstract/0143-0807/29/5/002
>
> I'm not buying that, literally ;-)
>
> (How I hate this practice of making scientific papers available only for
> money...)
Me too, I didn't realize that it was access-restricted. The title was
"Lorentz contraction and current-carrying wires" in case you can find it
elsewhere. It's not a research paper anyway, and they just give an
example where what appears an a purely magnetic force in one frame can't
be reduced to a purely electric force, but only to different mixes of
electric and magentic forces.
I'll just quote a bit from the introduction and the conclusion:
"This sets the scene for the following argument. Imagine a charged
particle q moving parallel to the current-carrying wire at the electron
drift velocity1 . In the ion frame, the interaction between the wire and
the charged particle is described in terms of magnetostatics. In the
electron frame, this interaction is described in terms of
electrostatics—see figure 1. Special relativity is then invoked to show
that the two expressions can be transformed into one another.
Unless warned explicitly, a student following this line of thought may
well be left with the impression that either electrostatics or
magnetostatics is redundant. In this paper, I will use the closely
related example of the force between two parallel wires carrying equal
currents in the same direction to illustrate that both electrostatics
and magnetostatics need to be retained."
...
"This derivation shows that the force between two parallel
current-carrying wires is purely magnetostatic in the rest frame of the
wires, but is a combination of electrostatic and magnetostatic forces in
the electron frame. This result should serve to dispel any notion of
redundancy of electrostatics or magnetostatics. While the derivation is
primarily aimed at the introductory undergraduate level, it could also
serve to limit the risk of seeing electromagnetic fields as something
that can only be done in the context of antisymmetric second-rank
tensors in higher level courses."
I don't have any idea how much to trust the author's conclusions though,
and I've had an irritatingly difficult time finding a definitive answer
on Google from a source I feel I can trust more.
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clipka wrote:
> Not really. If light slows down or speeds up as it approaches the earth
> (due to the "aether" exhibiting "local movement"), how could you
> possibly tell the difference?
They'd change apparent angles, methinks. I'm sure there's something clever
that could be figured out. :-)
> Now that's a puzzler to me: Isn't the electron known to have two
> "brothers" (muon and tauon) that differ from it only in mass?
Dunno. Probably.
> in which the propagation speed of
> disturbances must obviously be independent of the particular particle
> that caused them.
Don't ask me. I just know what the formula says. Or knew. IIRC.
I think the charge is based on probabilities of interactions between photons
and electrons. (I.e., the definition of "charge" is "how much the particle
interacts with the photon" or some such.)
--
Darren New, San Diego CA, USA (PST)
Understanding the structure of the universe
via religion is like understanding the
structure of computers via Tron.
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clipka wrote:
>> Come to think of it, isn't the speed of any wave in an unchanging
>> unmoving medium
>> constant and dependent on the properties of the medium?
>
> It is [*]. But every medium (other than space) also provides a
> "standard" frame of reference: For instance, water waves on a stream
> will move at the same speed in all directions relative to an observer
> drifting on that very stream (the "standard" frame of reference), but
> relative to an observer on the bank they will move faster downstream
> than upstream.
>
> This is not so for light: No matter whether you're a stationary (hah!)
> outside observer or zipping along at near-lightspeed, you'll always see
> the light go at some 300,000 km/s relative to you.
We can't get out of the medium to observe light waves as we can with
water waves.
> [* Well, it is not /strictly/ true, unless the direction and
> polarization of the wave is also a given, as the speed of a wave may be
> anisotropic regarding these parameters; for instance, there are
> materials out there in which the speed of light depends on polarization,
> causing what is known as "birefringence"; but taking these constraints
> into account as well, you're right.]
I have heard the apparent decrease in the velocity of light is explained
by the interference of light
re-emitted by the material so as to give the appearance of a decrease in
velocity. But the "true" velocity
of the light remains that in free space. (I did not altogether
understand this and may have it wrong.)
>> I think two of his basic assumptions were (in my words):
>>
>> 1) The speed of light is constant in all frames of reference.
>
> That was /the/ basic assumption of his theory of special relativity, yes.
>
>> 2) Other than that, the observations made from within any frame of
>> reference are valid
>> only within it.
>
> I'm not sure what exactly you mean by that. Maybe the "you can't tell
> whether your own frame of reference is being accelerated or at rest"
> assumption of general relativity?
That may be what I was getting at, but also the fact that the
"relativistic" effects
such as time dilation or increase in mass that I would observe in an object
(say a space ship) moving with 99.99% the speed pf light relative to me
are *not*
observed by its occupants and my observation is no more (or no less)
valid than theirs.
A lot of the paradoxes of relativity seem to arise from treating the
observations from two
or more frames of reference as if they were made from the same frame of
reference.
David
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David H. Burns schrieb:
>> This is not so for light: No matter whether you're a stationary (hah!)
>> outside observer or zipping along at near-lightspeed, you'll always
>> see the light go at some 300,000 km/s relative to you.
>
> We can't get out of the medium to observe light waves as we can with
> water waves.
Well, then compare it with the perspective of a person actively
swimming: Despite obviously being inside the medium, from his point of
view water waves going in the same direction as he is appear to be
slower than those going in the opposite direction.
You don't even have that with light, no matter how fast you "swim".
> I have heard the apparent decrease in the velocity of light is explained
> by the interference of light
> re-emitted by the material so as to give the appearance of a decrease in
> velocity. But the "true" velocity
> of the light remains that in free space. (I did not altogether
> understand this and may have it wrong.)
Given that refraction normally occurs due to different /phase/
velocities of light in two materials, but at the same time there have
been experiments reducing the /signal/ velocity of light almost to a
standstill... no, I guess that's oversimplified.
> That may be what I was getting at, but also the fact that the
> "relativistic" effects
> such as time dilation or increase in mass that I would observe in an object
> (say a space ship) moving with 99.99% the speed pf light relative to me
> are *not*
> observed by its occupants and my observation is no more (or no less)
> valid than theirs.
Which basically boils down again to saying that your /frame of
reference/ (which includes sort of a local definition of length) is no
more (or no less) valid than theirs.
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clipka wrote:
> You don't even have that with light, no matter how fast you "swim".
However, it must be pointed out that no human being has ever personally
managed a speed of any noticeable fraction of the speed of light to find
out.
I also have trouble with the notion that light emitted at the same time
from point x and point y, point x stationary to and point y moving
rapidly relative to point z, both beams of light will arrive at z at the
same moment, regardless of distance. (Which was one of the bits
mentioned in a simplified explanation of relativity I read once.)
--
Tim Cook
http://empyrean.freesitespace.net
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Tim Cook schrieb:
> I also have trouble with the notion that light emitted at the same time
> from point x and point y, point x stationary to and point y moving
> rapidly relative to point z, both beams of light will arrive at z at the
> same moment, regardless of distance. (Which was one of the bits
> mentioned in a simplified explanation of relativity I read once.)
The crucial thing here being "at the same time": Are you perfectly sure
what exactly constitutes simultaneity?
According to the theory of relativity, one can define simultaneity no
better than as "nearer in time than in space". For instance, an event
that happened a year ago (in /our/ frame of reference) two light-years
away is still happening "simultaneously enough" with whatever you're
doing right now.
If you were travelling at near speed of light, the spacetime region of
"simultaneity" does not change, even though you will percieve them as
happening at other spacetime coordinates - because you're using a
different spacetime coordinate system.
It's a bit like rotating objects in POV-Ray. Imagine POV's 3D space
representing a world of 2D space and 1D time. Pick any point and call it
"here and now". Let's say time is Y, and space is XZ. You can represent
"here" with a thin vertical cylinder, and "now" with a horizontal plane.
Now assume some object zipping through space at constant speed: It could
be represented by a slanted cylinder, right? So from that object's
perspective, "here" would be slanted.
But think about this: Your "now" is a plane perpendicular to your
"here". Why should that be different for the moving object?
Thus, accelerating an object does not mean to apply a /shearing/
transformation that would leave "now" untouched, but instead a
/rotation/ that redefines both "here" /and/ "now".
(With real spacetime, there is an additional quirk to it: For some
strange reason the "rotational" transformation associated with
accelerating an object appears to tilts its "now" plane in the
/opposite/ direction. Still, the above analogy may illustrate the
concept of a non-universal "now".)
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clipka wrote:
> Tim Cook schrieb:
>> I also have trouble with the notion that light emitted at the same
>> time from point x and point y, point x stationary to and point y
>> moving rapidly relative to point z, both beams of light will arrive at
>> z at the same moment, regardless of distance. (Which was one of the
>> bits mentioned in a simplified explanation of relativity I read once.)
>
> The crucial thing here being "at the same time": Are you perfectly sure
> what exactly constitutes simultaneity?
Just a quick pedantic note to the otherwise good explanation -- since
the light beams in his example are arriving at the same point, z, he can
of course be sure what "arrive at the same time" means.
As far as Tim's concern here goes, you can actually resolve it perfectly
well without need for relativity. Think of ripples in a pond. If I
throw a pebble into the pond, or drag a stick through it, the ripples
from these two sources will move at the same speed, even though the
stick is moving with respect to the surface of the water and the pebble
is not (assume of course that the stick is moving slower than the
ripples do). Viewing light in this way as waves propagating through a
medium (rather than particles as it seems you're thinking) is very close
to the pre-relativity view of light, and you can see how the speed of
light in this case would be independent of the speed of the source.
The surprising bit in relativity, of course, is that it's also
independent of the speed of the observer. And in fact, as clipka has
alludes to before, this has actually been verified by experiment:
http://en.wikipedia.org/wiki/Michelson%E2%80%93Morley_experiment among
others.
Intuitively, the concept might be made more palatable by an analogy to
classical mechanics. Let's say you're locked inside a train moving
straing at a constant speed with no windows on a perfectly smooth track.
What experiment could you do that would tell you how fast you were
moving? If you drop a ball you'll see that it always looks to you like
it falls straight down and gives no hit as yo your speed. You'll find
that any mechanical experiment you concoct behaves the same way --
exactly as it would if it were at rest. In some sense this isn't too
surprising since we hardly notice the the earth is racing through space
at thousands of miles per hour.
So on some level, it's intuitive that you can't do an experiment to tell
you what your "absolute" velocity is, you can only determine relative
velocities, for instance determining the velocity of the train relative
to the earth by looking out a window (if there were one).
The theory of relativity derives from assuming that this principle
*also* applies to experiments involving electromagnetic phenomena, such
as light, and that these too can't be used to determine your absolute
velocity. It turns out that this being the case leads to a view of
space and time which is different from the naive one in a manner such as
clipka described, but omitting this counter-intuitive result the
postulates leading to it are actually quite sensible.
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Kevin Wampler schrieb:
> Just a quick pedantic note to the otherwise good explanation -- since
> the light beams in his example are arriving at the same point, z, he can
> of course be sure what "arrive at the same time" means.
As for /arriving/ at the same time: Yes. As for being /sent/ at the same
time: No.
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clipka wrote:
> Kevin Wampler schrieb:
>> Just a quick pedantic note to the otherwise good explanation -- since
>> the light beams in his example are arriving at the same point, z, he
>> can of course be sure what "arrive at the same time" means.
>
> As for /arriving/ at the same time: Yes. As for being /sent/ at the same
> time: No.
Good point, I was implicitly taking x and y to be coincident at the time
of the light emission, but reading again this was an unjustified
assumption on my part.
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clipka wrote:
> You don't even have that with light, no matter how fast you "swim".
And, as I said, you can out-boat your wake. You can also fly supersonic,
which proves not only do the waves go different speeds relative to the
plane, the plane can actually outrun them.
--
Darren New, San Diego CA, USA (PST)
Understanding the structure of the universe
via religion is like understanding the
structure of computers via Tron.
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Tim Cook wrote:
> clipka wrote:
>> You don't even have that with light, no matter how fast you "swim".
>
> However, it must be pointed out that no human being has ever personally
> managed a speed of any noticeable fraction of the speed of light to find
> out.
Of course they have.
You can put an atomic clock on Southwest Airlines and measure the error you
caused at the other end by being out of the gravity well and traveling at
velocity.
You can just leave one in the basement and one at the top of a skyscraper
for a couple months and measure the difference.
> I also have trouble with the notion that light emitted at the same time
> from point x and point y, point x stationary to and point y moving
> rapidly relative to point z, both beams of light will arrive at z at the
> same moment, regardless of distance.
Assuming X and Y are both the same distance from Z when you start counting,
why wouldn't they? Even with regular waves, that'll happen.
--
Darren New, San Diego CA, USA (PST)
Understanding the structure of the universe
via religion is like understanding the
structure of computers via Tron.
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clipka wrote:
> As for /arriving/ at the same time: Yes. As for being /sent/ at the same
> time: No.
If X and Y are very close together in space when the beam is sent, sure. If
X is on the tracks and Y is on the train, and they each set off the
flashbulb as the arm on the side of the train strikes the pole stuck by the
side of the tracks, wouldn't that be a simultaneous event? I mean, the
contacts touch once, and there's only one contact, so how could it not be
the same time for both flashbulbs?
--
Darren New, San Diego CA, USA (PST)
Understanding the structure of the universe
via religion is like understanding the
structure of computers via Tron.
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clipka wrote:
>> We can't get out of the medium to observe light waves as we can with
>> water waves.
>
> Well, then compare it with the perspective of a person actively
> swimming: Despite obviously being inside the medium, from his point of
> view water waves going in the same direction as he is appear to be
> slower than those going in the opposite direction.
Does he? Or does he just observe a frequency change, i.e. see the crests and
troughs closer together or further apart, as with the doppler effect
in sound and light?
>
> You don't even have that with light, no matter how fast you "swim".
>
>> I have heard the apparent decrease in the velocity of light is
>> explained by the interference of light
>> re-emitted by the material so as to give the appearance of a decrease
>> in velocity. But the "true" velocity
>> of the light remains that in free space. (I did not altogether
>> understand this and may have it wrong.)
>
> Given that refraction normally occurs due to different /phase/
> velocities of light in two materials, but at the same time there have
> been experiments reducing the /signal/ velocity of light almost to a
> standstill... no, I guess that's oversimplified.
I wasn't convinced by the explanation and couldn't find a physicist to
comment
at the time.
>
>> That may be what I was getting at, but also the fact that the
>> "relativistic" effects
>> such as time dilation or increase in mass that I would observe in an
>> object
>> (say a space ship) moving with 99.99% the speed pf light relative to
>> me are *not*
>> observed by its occupants and my observation is no more (or no less)
>> valid than theirs.
>
> Which basically boils down again to saying that your /frame of
> reference/ (which includes sort of a local definition of length) is no
> more (or no less) valid than theirs.
Exactly, according to the relativity principle observations from within
any frame
of reference are valid for it alone.
A curious result of this is that any mass measurements contain two
components,
the inertial mass (the mass that would be measured if the object were at
rest with
respect to the measurer) and the relativistic mass due to the relative
velocity of the
object with respect to the observer.
David
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David H. Burns wrote:
>> view water waves going in the same direction as he is appear to be
>> slower than those going in the opposite direction.
> Does he?
Yes. As I've said, you can boat faster than your wake, and you can fly
supersonic. In both cases, all the waves look to be going backwards.
--
Darren New, San Diego CA, USA (PST)
Understanding the structure of the universe
via religion is like understanding the
structure of computers via Tron.
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Darren New wrote:
> You can put an atomic clock on Southwest Airlines and measure the error
> you caused at the other end by being out of the gravity well and
> traveling at velocity.
>
> You can just leave one in the basement and one at the top of a
> skyscraper for a couple months and measure the difference.
Nahhh, that just shows the clocks are inaccurate, with moving them,
uh...jostling the atoms so they vibrate differently.
...yeah!
> Assuming X and Y are both the same distance from Z when you start
> counting, why wouldn't they? Even with regular waves, that'll happen.
Well, sure, if you make *that* particular assumption...but the example I
was reading didn't specify, so I was confused.
Still am. Observation being one thing and actuality being another,
things do happen simultaneously. Saying that they don't because you
can't have an 'outside' frame of reference is hubris, imo. Like saying
nothing in the universe exists outside the radius of light being able to
travel since the big bang, with the observer (us) at the centre. It's
the whole earth-centric universe all over again.
--
Tim Cook
http://empyrean.freesitespace.net
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Tim Cook wrote:
> Well, sure, if you make *that* particular assumption...but the example I
> was reading didn't specify, so I was confused.
Well, if they're not the same distance from you when they flash, why would
you expect to see the flashes at the same time?
Or maybe I'm confused. You might be right. There's a "regardless of
distance" clause at the end that makes the thing nonsensical except for
c==infinity.
I read it more along the lines of "the bullet goes the same speed regardless
of how fast the gun is moving when you fire it" sort of thing.
> Still am. Observation being one thing and actuality being another,
> things do happen simultaneously.
Only if they're close to each other. There really is no "at the same time"
for objects widely separated.
> Saying that they don't because you
> can't have an 'outside' frame of reference is hubris, imo.
No. If you can have two events happen in one order for me and another order
for you, and there's *nobody* who can say what "at the same time" means,
then how do you have simultaneity?
Basically, you can't have "equal times" unless space has "equal places".
OK, so take a vector. What you're saying is "I can't believe the Z component
of a vector is sometimes zero and sometimes not zero, regardless of where
you put the origin and how you rotate the axes." The only way the Z
component stays zero regardless of where you put your axes is if the other
components are zero also.
> Like saying
> nothing in the universe exists outside the radius of light being able to
> travel since the big bang, with the observer (us) at the centre. It's
> the whole earth-centric universe all over again.
It's not earth centric because it's true of everyone. And "exists" means
"capable of having any sort of affect on the observer", in which case the
sentence is true. :-) It's as "non-existent" as the future is.
--
Darren New, San Diego CA, USA (PST)
Understanding the structure of the universe
via religion is like understanding the
structure of computers via Tron.
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Darren New schrieb:
>> As for /arriving/ at the same time: Yes. As for being /sent/ at the
>> same time: No.
>
> If X and Y are very close together in space when the beam is sent, sure.
Not even then. It would reduce the "simultaneity window" accordingly,
but never reduce it to zero. And note that the other effects you want to
observe diminish with the scale of your experiment, too.
> If X is on the tracks and Y is on the train, and they each set off the
> flashbulb as the arm on the side of the train strikes the pole stuck by
> the side of the tracks, wouldn't that be a simultaneous event? I mean,
> the contacts touch once, and there's only one contact, so how could it
> not be the same time for both flashbulbs?
Note that the flashbulbs won't go off simultaneously with the
establishment of the contact: Electric signals, too, only propagate at
the speed of light (if not slower).
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Tim Cook schrieb:
> Still am. Observation being one thing and actuality being another,
> things do happen simultaneously. Saying that they don't because you
> can't have an 'outside' frame of reference is hubris, imo. Like saying
> nothing in the universe exists outside the radius of light being able to
> travel since the big bang, with the observer (us) at the centre. It's
> the whole earth-centric universe all over again.
Yes, but this time we have a solid scientific reason: Because /we/ are
living on the earth, and it's where /our/ frame of reference happens to
be "centered" at.
So what's wrong with /us earthlings/ to be earth-centric? (After all,
that's the place where the vast majority of us is bound to be living in
for the next couple of millennia - so maybe a bit more earth-centricity
would do us some good, or we may not make it that long.)
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David H. Burns schrieb:
>> Well, then compare it with the perspective of a person actively
>> swimming: Despite obviously being inside the medium, from his point of
>> view water waves going in the same direction as he is appear to be
>> slower than those going in the opposite direction.
>
> Does he? Or does he just observe a frequency change, i.e. see the crests
> and
> troughs closer together or further apart, as with the doppler effect in
> sound and light?
Try it out, and you'll see that the crests and troughs will actually
apear to be moving at different speeds depending on direction - while
the distance between them will remain constant (which is /why/ they'll
appear to change their frequency).
> A curious result of this is that any mass measurements contain two
> components,
> the inertial mass (the mass that would be measured if the object were at
> rest with
> respect to the measurer) and the relativistic mass due to the relative
> velocity of the
> object with respect to the observer.
Yup. E = mc^2: From an outside observer's point of view, pumping energy
into some thing to speed it up to light speed also pumps up its mass.
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clipka wrote:
> Darren New schrieb:
>>> As for /arriving/ at the same time: Yes. As for being /sent/ at the
>>> same time: No.
>>
>> If X and Y are very close together in space when the beam is sent, sure.
>
> Not even then. It would reduce the "simultaneity window" accordingly,
Well, sure. Epsilon and all that.
> And note that the other effects you want to
> observe diminish with the scale of your experiment, too.
X and Y, not X and Z. :-)
> Note that the flashbulbs won't go off simultaneously with the
> establishment of the contact: Electric signals, too, only propagate at
> the speed of light (if not slower).
Certainly, modulo that stuff, yes. But if Z is light-days away, it's going
to be close to simultaneous. Unlike if, for example, X is light-days from
Y, where it makes no sense to talk about "one event."
It's a thought experiment, see.
--
Darren New, San Diego CA, USA (PST)
Understanding the structure of the universe
via religion is like understanding the
structure of computers via Tron.
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Darren New schrieb:
> Certainly, modulo that stuff, yes. But if Z is light-days away, it's
> going to be close to simultaneous. Unlike if, for example, X is
> light-days from Y, where it makes no sense to talk about "one event."
Still, those minor differences make... well, the difference.
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