From: Dan Fabulich (daniel.fabulich@yale.edu)
Date: Sat Apr 11 1998 - 18:09:01 MDT
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Reilly Jones wrote:
>This time difference is a function of the measuring mechanism itself. You
>are not saying that the Planck moment has changed during the flight, are
>you? Is the Planck moment constant or is it not?
While I can't answer the point about the Plank moment, I can answer your
point about the time difference being "a function of the measuring
mechanism itself." While this may actually be the case, this is NOT what
is happening if you presume that light in a vacuum travels at the same
speed in all reference frames. Here's why.
Suppose you have two observers, Alice and Bob. Alice is on a train, moving
horizontally relative to Bob, at a speed v. Now suppose Alice has a simple
mirror attached to the ceiling of the train and a lightbulb on the floor,
which she uses to measure the time it takes light to travel from the floor
to the ceiling and back. If we define the distance D to be the distance
between the ceiling and the floor, she should measure that
t_a = 2D/c. (1)
where c is the speed of light in a vacuum. (See Figure 1.)
Figure 1 Figure 2
--- ---
^| /|\
|| D / | \
|| / D| \L
|v / | \
-*- * ------> *
v*t_b
However, Bob will see something VERY different. He will also see the light
leave the lightbulb, hit the mirror and strike the lightbulb again, but in
his reference frame the lightbulb has moved a distance v*t_b (where v,
again, is the speed at which Alice is moving relative to Bob, and t_b is
the time the light travels in Bob's reference frame). So he sees the light
travelling twice the length of the hypotenuse of the right triangle formed
by v*t_b/2 and D, whose length is given by the Pythagorean Theorem to be:
L^2 = D^2 + (v*t_b/2)^2. (2)
(See Figure 2.)
It is worth now pointing out that if it were simply a ball bouncing up and
down in this train, Bob would observe t_b=t_a, since Alice and Bob are not
moving vertically to one another. Thus he would observe the speed of the
ball to be c_b=L/t_a, and Alice would observe c_a=D/t_a. This is the form
of relativity we're used to; just as one runner appears motionless to the
runner next to him travelling at the same velocity, or how trees appear to
be moving relative to you when you drive past them in a car. We naturally
observe different speeds as our speeds change.
However, when we presume the speed of light to be constant, something
entirely different happens. In this case, Bob must observe
t_b = 2L/c (3)
where c is *the same c observed by Alice*. Solving for D in equation (1),
we get
D = c*t_a/2 (4)
which we can substitute in equation (2):
L^2 = (c*t_a/2)^2 + (v*t_b/2)^2. (5)
Now if we solve equation (3) for L^2
L^2 = (c*t_b/2)^2 (6)
and eliminate L^2, we get
(c*t_b/2)^2 = (c*t_a/2)^2 + (v*t_b/2)^2 (7).
To solve this equation for t_b, we can multiply both sides by 4 = (1/2)^2
(c*t_b)^2 = (c*t_a)^2 + (v*t_b)^2 (8),
subract (v*t_b)^2 from both sides and factor t_b from the left,
(c*t_b)^2 - (v*t_b)^2 = (c*t_a)^2 = t_b^2*(c^2 - v^2)
then divide both sides by (c^2 - v^2) and divide the numerator and
denominator by c^2
t_b^2 = (c*t_a)^2/(c^2 - v^2) = t_a^2/(1-v^2/c^2)
and finally take the square root of both sides:
t_b = t_a/(1-v^2/c^2)^0.5
What does all this mean? Well, suppose v = 0.6c, or 60% the speed of
light, and t_a = 10 seconds. Plugging into the equation above, we get t_b
= 12.5 seconds, where we SHOULD have gotten t_b = 10 seconds if c_a != c_b.
At this point, you should be saying to yourself "OK, nice math. But does
it actually apply to reality? That is, IS c the same in all reference
frames?"
Which is, of course, the job of scientists to determine. And fortunately
for us incoherent relativists [ ;) ], they have given us plenty of evidence
that this theory is precisely correct. For example, according to this
theory, the speed of an object approaches c as the kinetic energy
approaches infinity, contrary to what Newton's laws would have told you.
And sure enough, in 1964, W. Bertozzi accelerated electrons to various
measured speeds and measured their kinetic energy using a different method.
As we all had expected, their kinetic energy did increase, but their speed
did not.
Not conclusive enough for you? Well, it has also been observed that muons,
which have an average lifetime of 2.200 microseconds, have an average
lifetime of 63.5 microseconds when moving at 0.9994c relating to the
laboratory; precisely the value predicted by special relativity.
Still not conclusive enough? Physicists at the University of Maryland
performed an experiment which involved taking a high-precision clock and
flying it around Chesapeake Bay at extremely high velocities; they verified
the time dilation predicted by this experiment to better than 1%.
I must admit that at first, while I was immediately convinced that IF we
presume that the speed of light is constant in all reference frames, time
must dilate in the manner prescribed here. However, it took a great deal
of experimental evidence before I was convinced that this was actually the
case. Check it out for yourself. I got most of the information here from
_Fundamentals of Physics, 5th Edition_ by Halliday, Resnick and Walker.
(Further reference upon request.)
>I agree that the speed of light being the same for any observer is
>absolute, an absolute metaphysical assumption. Verification continues...
Verification is complete. It is not metaphysical, it is repeatable and
observable to within 1%.
>This is science, not mysticism. I have not rejected QM, I have simply
>noted that QM and Relativity are not reconciled, and they are not
>reconciled for a reason that science has not discovered yet.
Perhaps not, but the reason we accept both is because both theories predict
the behavior of the world around us to as close as we can measure. One day
we may find the true model, but until then we accept these models because
they work.
>They have not
>discovered it yet because something is wrong with some of the metaphysical
>assumptions underlying the current Kuhnian paradigm and it is very hard to
>buck dogmatism when you are trying to suck in grant money.
However, I take offense at charges of dogmatism. People only confuse
science and religion until they actually start taking a look at the very
real repeatable experiments which have been performed throughout this
century. Mysticism and dogmatism can never provide such evidence.
>I also can't believe that individuals who proclaim themselves to be
>scientists, promote the Big Bang as science. Creation ex nihilo was
>formulated as a pious scientific doctrine at the Fourth Lateran Council in
>1215. All the kooky machinations undergone since then to undergird this
>doctrine resemble Ptolemy's increasingly convoluted epicycles more than
>anything else.
Uhm... Kooky, huh? Care to explain that in a fashion which doesn't
contradict experimental evidence?
>There is a lot of kookiness in science I don't go for. Time travel, for
>one. Utterly senseless.
Good for you! I don't believe much of that garbage either. There hasn't
been any conclusive repeatable evidence, after all. :)
>Basement or attic universes for another, unless
>the Planck moment for each is different from ours and different from each
>other, then I'd be willing to entertain the idea.
That's fine. Many accomplished scientists, who agree with special/general
relativity and accept QM reject the idea of basement universes.
>Singularities inside
>black holes for another. Black holes are just like glaciers, if you want
>to free up the matter in them, just raise the background temperature around
>them.
This, however, is not true. Remember that absolute speed of light
constant, presumed above? Well, as Bertozzi showed, increasing the kinetic
energy STILL doesn't increase the speed faster than c; and since it
doesn't, you STILL can't extract matter from a black hole, no matter how
hot it gets.
>The idea of a space-time continuum for another, I'd go for a
>space-time conjunction or a space continuum, though.
Depends on what you mean by continuum, and what effects you claim this has
on physical objects. As empirically observed above, velocity DOES affect
the way time flows, but a lot of people use the space-time continuum to
explain all kinds of kooky things.
>The Planck moment is
>not a variable, not involved in any continuum, at least not locally anyway.
This is an interesting one which I haven't heard talked about much. Does
the Plank moment dilate along with the rest of time? Does anybody here
know much about this?
>I don't just pick on junk physics either, biology makes no sense when it
>takes randomness (as in mutations) to be some ontological aspect, rather
>than an epistemological aspect. If there was one ounce of ontological
>randomness in the universe, the universe would be entirely unintelligible.
Now you've gone and challenged all of QM, which has more experimental
evidence behind it than I can shake a stick at. What's with that?
>Lastly, I can't think of any greater credibility problem that to take
>information as an ontological primitive.
This sentance doesn't make any sense to me, even after I looked up the noun
"primitive" for double meanings.
>Information has no existence without a knower and a known.
Statistical thermodynamics, too? What's up, guy?
Information is a signal which reduces uncertainty.
Pop quiz: Is there information in a closed book?
>It is a common fallacy to say that DNA
>transmits information, without referencing the knower who can translate the
>information.
It is a similarly common fallacy to say that there can be information in a
book which has not been read. Oh, wait, THAT's not a fallacy...
>DNA replication, the thing-in-itself, is not transmitting
>information, it is simply molecules bumping around and lining up in
>preferred developmental branches.
Indeed, and all those letters are just little splotches of ink.
>The "everything is digital" worldview I
>always held to be harmless idiocy until I was shown that it leads to a
>mandate to guillotine half my state. I will take it seriously now.
And as to your thoughts on abortion, I have this to say:
Your position is not empirical until you prove that the fetus is living
organism which can be killed. (The finger, for example, cannot be
"killed," even though the cells in the finger can die.) Most, if not all
people who support abortion do NOT think that the fetus can be killed.
I concede that you do have a concrete definition of what's living and
what's not, and within this context, you are 100% correct. However, this
is not a sufficient proof. I could just as easily say that a person cannot
be killed until they are born.
So here's a quick course on logic for you:
You cannot prove an assertion by defining your assertion to be true. To
provide a logical argument, use COMMON definitions. If two parties do not
use definitions, you must use other common definitions to show why the
other definitions are wrong. But anyway you run it, we have to use
premises upon which everyone agrees in order to have a logical discussion.
I challenge you to prove, using definitions and premises upon which we both
agree, that abortion is immoral; if you can't or won't, then don't try to
have a logical argument with me.
Have fun!
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