Say a meteor spontaneously appears 10 light years away, moving directly
toward the earth at a speed of .95c. The distance and speed are based
upon the earth's typical frame of reference.

At this rate it will reach earth in about 10.5 years. (T/F)?

10 years pass...

Suddenly a very powerful telescope spots a meteor moving directly
toward the earth. It appears to be 10 light years away. (T/F)?

1st month passes... The meteor now appears to be 1.75 light years
closer.
2nd month passes... The meteor is now 3.5 light years closer
A little more than 6 months pass... The meteor appears to have traveled
the full 10 light years.

Although the meteor never moved faster then the speed of light, the
relativistic Doppler effect would make it seem to have covered 10 light
years in a mere 6 months. The velocity is almost 20c from the
perspective of the earth.

Is that possible? Am I overlooking something?

Steven wrote:
Say a meteor spontaneously appears 10 light years away, moving directly
toward the earth at a speed of .95c. The distance and speed are based
upon the earth's typical frame of reference.

At this rate it will reach earth in about 10.5 years. (T/F)?

10 years pass...

Suddenly a very powerful telescope spots a meteor moving directly
toward the earth. It appears to be 10 light years away. (T/F)?

1st month passes... The meteor now appears to be 1.75 light years
closer.
2nd month passes... The meteor is now 3.5 light years closer
A little more than 6 months pass... The meteor appears to have traveled
the full 10 light years.

Although the meteor never moved faster then the speed of light, the
relativistic Doppler effect would make it seem to have covered 10 light
years in a mere 6 months.

And note, you didn't even use relativity to reach that
conclusion. All you needed was the known speed of light.
Yes, your conclusion is correct.

But note also, you use the word "seem", which you have
not defined with any precision.

The velocity is almost 20c from the
perspective of the earth.

No, a physicist would correct her observations for Doppler
and conclude that the velocity is .95c. That is what the
velocity *is*.


Is that possible? Am I overlooking something?

Of course it's possible to *seem* to be traveling at 20c,
depending on what you mean by "seem". But not to actually
*be* traveling that fast.

Dear Steven:

"Steven" wrote in message
oups.com...
Say a meteor spontaneously appears 10 light years
away, moving directly toward the earth at a speed of
.95c. The distance and speed are based upon the
earth's typical frame of reference.

At this rate it will reach earth in about 10.5 years. (T/F)?

10 years pass...

Suddenly a very powerful telescope spots a meteor
moving directly toward the earth. It appears to be
10 light years away. (T/F)?

1st month passes... The meteor now appears to be
1.75 light years closer.
2nd month passes... The meteor is now 3.5 light
years closer
A little more than 6 months pass... The meteor
appears to have traveled the full 10 light years.

Although the meteor never moved faster then the
speed of light, the relativistic Doppler effect would
make it seem to have covered 10 light years in a
mere 6 months. The velocity is almost 20c from the
perspective of the earth.

Is that possible? Am I overlooking something?

Just to add a little to russell's response...
If it were in fact moving faster than the speed of light, how
could you see it at all those different times? The object would
outrun any light that left it in the forward direction.

So the fact that you can see it at all those different times
means something.

You may want to review the FAQ on this topic:
URL:http://hermes.physics.adelaide.edu.a...erluminal.html

David A. Smith

N:dlzc D:aol T:com (dlzc) wrote:
Dear Steven:

[snip]

Just to add a little to russell's response...
If it were in fact moving faster than the speed of light, how
could you see it at all those different times? The object would
outrun any light that left it in the forward direction.

Thanks, that's a nice addition.

I was wondering also if the o.p. is suffering a bit from
a common misconception, namely, that special relativity
is merely about the optical illusions that occur because
the speed of light is finite. That's wrong. Rather, and
it's a bit amazing when you first understand this, the
point of special relativity is to explain the real stuff
that remains *after* you correct for the illusions. In
the o.p.'s post there was in fact nothing that required
SR to explain. OTOH, if the o.p. had asked about, say,
the frequency of the Sodium D lines in light emitted by
the meteor, then relativity would have been required.

Just out of curiosity, what would happen if you got rid of the "optical
illusion?" Imagine a theoretical universe that is identical to ours
except that the speed of light is increased to infinity. All
information is instantly transferred across the entire universe. Would
Einstein's relativity theories still apply? Or would Newton's theories
of motion be more appropriate?

Dear Steven:

"Steven" wrote in message
ps.com...
Just out of curiosity, what would happen if you got rid
of the "optical illusion?" Imagine a theoretical universe
that is identical to ours except that the speed of light
is increased to infinity. All information is instantly
transferred across the entire universe. Would
Einstein's relativity theories still apply? Or would
Newton's theories of motion be more appropriate?

Considering that all we are, and all we know, is based on a
finite c, I would suggest that in such a Universe, neither an
Einstein nor a Newton (or even Ogg the first caveman scientist)
would exist. The size of things is established by c. So the
Sun's size is established by c. An infinite c, and the Earth is
orbiting within the core of the Sun (and every other Sun, for
that matter).

Now consider that some (perhaps kooky) cosmologists propose an
infinite c in the Universe, at the time of the Big Bang. Before
matter (or even the four forces) "congealed". I don't think you
can have discernable long range structure in an infinitely-small
(by any reasonable definition of length) Universe.

So the answer to your question is "neither".

David A. Smith

Steven wrote:
Just out of curiosity, what would happen if you got rid of the "optical
illusion?"

I probably should have phrased things more carefully. The
part that I was calling "optical illusion" was, or at least
I intended it to be, the pure Doppler part. In other words,
it's the part you correct for in order to understand the
underlying physics. A bit like shooting your arrow "below"
the fish you see in the water, because you know that's
where the fish *really* is. You correct for appearances.

The interesting thing is, even *after* you do these corrections,
you get real effects like twins having different ages when
they reunite after one has taken a long journey moving very
fast. That's no illusion. It's real. And it's been
observed, many many times. (Although, the twins are usually
particles, not humans. In some famous experiments, the twins
were atomic clocks.)

Imagine a theoretical universe that is identical to ours
except that the speed of light is increased to infinity. All
information is instantly transferred across the entire universe. Would
Einstein's relativity theories still apply? Or would Newton's theories
of motion be more appropriate?

The Lorentz transformation (which is the essential mathematical
expression of SR) reduces to the Galilean transformation in
the limit as c - infinity. So in a sense, the answer is yes
to both your questions.

Steven wrote:


Although the meteor never moved faster then the speed of light, the
relativistic Doppler effect would make it seem to have covered 10 light
years in a mere 6 months. The velocity is almost 20c from the
perspective of the earth.

Is that possible? Am I overlooking something?

Epstein gives a similar example in his book Relativity Visualized,
showing that you can sometimes "see" things move faster than the speed
of light. As has been pointed out, relativity is concerned with what is
left after you account for the transmission time of light. Thus, if we
use a powerful telescope and "see" something happen on a star that is 3
light years away, we know that what we are seeing actually happened 3
years ago.