Re: Doppler effect

On Feb 5, 7:02 pm, Randy Poe <poespam-t...@xxxxxxxxx> wrote:
On Feb 5, 5:23 pm, Peter <Poakfi...@xxxxxxx> wrote:





On Feb 4, 10:46 pm, Randy Poe <poespam-t...@xxxxxxxxx> wrote:

On Feb 4, 8:30 pm, Peter <Poakfi...@xxxxxxx> wrote:

Hi! Please, can someone tell me, is the Doppler effect a relativistic
effect?

There is a classic Doppler effect.

For instance, if I am speeding toward a stationary source of
light, I find the frequency, and energy, of the light increases.

Yes it does.

But
it does not really, because the source is stationary.

If you are moving toward the source at x m/sec, from your point
of view it is moving toward you at x m/sec.

Where does the
additional energy the light has come from? Is it a relativistic
effect?

The idea that kinetic energy of an object is relative is part
of classical physics. If two spaceships A and B are in
relative motion in space (with no other reference points
nearby), I can describe them from a point of view where A
is stationary, one where B is stationary, or one where both
are in motion. If I accelerate so that the speeds of
A and B relative to me change, I haven't added or subtracted
any energy from them. I've merely changed points of view.

- Randy

I understand that when we talk about classical mechanics, we are
talking about Newton's laws. But the Doppler effect for light, which
is different from that for sound or water waves, has nothing to do
with Newton. No?

Depends. Just as with sound waves, you can deduce two different
expressions for Doppler effect with purely classical assumptions
and old-fashioned Newtonian physics. In that classical version,
you could have either a source moving relative to the medium,
or you could have the receiver moving relative to the medium.

The reasoning is exactly the same as for sound. If the source
is moving in the medium, then the waves travel at c, but the
wave peaks are closer together in the forward direction than
the wavelength if the source were at rest (see picture here
for instance:http://archive.ncsa.uiuc.edu/Cyberia/Bima/doppler.html

In SR, this phenomenon still happens, but there is also a
slight correction due to the time-dilation effect.

When the source is at rest and the receiver is moving, in
classical doppler the apparent propagation velocity of
the waves relative to the observer is c - v. This causes
the frequency at which the receiver encounters them to
change.

In SR, we don't have that version. No matter what source
and receiver are doing, the propagation speed of the
radiation between them is c.

Well, mainly to yank people's chains, I point out that even in
relativity we still have a perfectly good object which might be called
"mbcv", for "maneuvering board closing velocity" (after the naval
chart on which relative behavior of ships surrounding own ship is
plotted).

To illustrate this simple concept in the case you cite above, we could
say that the light crests are moving at c, while the receiver (sink)
is moving at u, at therefore the crests are closing the receiver at
(mbcv) c-u. This is perfectly correct, analyzing the situation in a
frame in which the light (as it always does) is traveling at c, and
the sink at u. No, that's _not_ the closing velocity at measured in
the rest frame of the sink, but who says it was!? Not I.

As you imply above, the correction to this in calculating observed
frequency at the sink takes into account relativistic time dilation
(in our frame of analysis) of the sink.

To illustrate another simple use of this concept, suppose we were in a
space ship and we actually _were_ plotting trajectories of surrounding
vessels on a (presumably 3-D) maneuvering board -- a "maneuvering
sphere", maybe. No matter how damn relativistic those other vessels
were relative to us or each other, if two of them happened to be on a
collision course we could, correctly and simply, calculate time to
collision in our frame via u-v -- their dumb as bricks "uncorrected"
closing velocity in our frame. (Meanwhile our less insightful second
officer would laboriously calculate the time to collision in the rest
frame of one of the ships, using the "correct relativistic expression
for relative velocity", and then convert the time back to our rest
frame -- wonder how we got the answer 10 minutes ago, and went to the
galley to get a cup of coffee).

(I may point out in this example that an intergalactic computer virus
has disabled all the ships computers, forcing to fall back on our star
fleet training with pencil and paper).

This is no big deal, except that I had to recover this simple Bell-
esque idea myself over strenuous opposition of pundits who fixate on
the idea that "relativistic closing velocity" must be taken as the
velocity calculated in the rest frame of one of the bodies involved,
and that the closing velocity in all other frames is "wrong" (whatever
that means) or nonsense or meaningless or what have you -- they are so
primed to pounce on the imagined oolie-violation that they lose sight
of common sense understanding. (That sounds cranky, and is cranky,
with the exception that "cranks" are wrong, and I, in this instance,
happen to be right :-).

So yes, Randy, in SR we do have that version, and it makes good
sense. In fact the analysis is precisely the same as the case of a
moving source, corrected, as you mention, by time dilation for the
object taken to be in motion. We can even forget the verbal
workaround "mbcv", a sop to convention, and simply agree that closing
velocity is not a frame invariant (as we know), but that the closing
velocity in any frame of reference does exactly what we expect it to,
for that frame of reference.

(Ed continues to jump up and down on the straw dog even after must of
the stuffing has been knocked out, and all that's left is an empty
burlap sack).
.

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