Re: Simple question
- From: Ali <akousari@xxxxxxxxxx>
- Date: Wed, 31 Oct 2007 07:57:50 -0700
On Oct 29, 11:18 pm, PD <TheDraperFam...@xxxxxxxxx> wrote:
On Oct 29, 4:29 pm, Ali <akous...@xxxxxxxxxx> wrote:
It appears to me that the time for any other frame of reference can be
slowed down but not speeded up. That is true wether the other frame of
reference is moving relative to ours or is in a gravitational field. I
wonder if some one can kindly explain the following puzzle for me.
Suppose that you are traveling in a space craft looking at you twin
sister on earth. For both of you time for the other one is running
slower. You see your sister staying younger than you and she sees you
staying younger. Now, when you come back to the earth, slow down, and
stop (decelarating as if being in a gravitational field) still your
sister sees your time running slower ( as you see hers) and not
faster. But you should see her time run faster if she has to grow
older to catch up with you(of course the same is true otherway round).
Is there anyway that way that we can see the other clock run faster?
Thank you in advance for helping me in understanding this.
In most decent accounts of the twin paradox, where you ask "What does
the traveling twin see the Earth's twin's age to be when the traveling
twin turns around," the account is given that the traveling twin sees
the age of the Earth twin *leap forward* to be older than the
traveling twin during the turnaround. Thus, even when the traveling
twin is returning and sees the Earth twin's clock slow down again, the
NET effect is STILL that the Earth twin ages more than the the
traveling twin. The point is that you can't ignore the turnaround.
It's precisely what distinguishes one twin from the other.
Now, you could rightly ask, "But what if I make the traveling twin
turn only very, very gradually? In fact, what if I make it turn around
in a very big circle?" Here, interestingly, it is the case that the
traveling twin now sees the Earth twin's clock run *faster* throughout
the trip. This is in fact what's noted in GPS satellites.
And here is where the lesson is, because it's tempting to say that in
the circular trip, the Earth clock is still moving relative to the
traveling twin's clock, and doesn't relativity say that relatively
moving clocks always run slower, not faster? The answer is important:
NO. That is only true for clocks in *inertial* motion, and circular
motion is in no way inertial. Whether the traveling twin's
acceleration is smeared out over the whole trip or is concentrated all
in one short interval around the half-way point, there still remains
the fact that the traveling twin accelerates. And this is what breaks
the symmetry.
PD
Thank you very much for your answer. This might be the answer I was
looking for but I still need some clarification. Let me start from the
beginning and correct me where I am wrong:
1. First the traveling twin rides the rocket and accelerates into
space, acceleration is a gravitational field he sees Earth behind him
closer to the origin of gravitational filed so he sees his earthy twin
clock running slower, and his running twin agrees his traveling twin
clock is going faster at the same rate the traveling one calculated.
2. Acceleration phase ends soon and the clocks shows some time
difference (neglecting for time being the special relativity for this
period) that both brothers agree upon. Lets says the both agree that
brother on earth is 5 minutes behind (younger).
3. The traveling brother is moving at high speed for 30 minutes during
this time he sees (or measures) that his brother clock has gone
forward only 20 minutes so, according to traveling brother he is 35
minutes older while his brother is only 20 minutes older. To the
earthy brother though it seems that the traveling brother has only
aged 25 minutes while he him self has aged 30 minutes.
4. The traveling brother decelerates this time his clock is running
slower for 5 minutes than his brother due to gravity. Both brother
agree on this so now According to traveling brother he is 35 + 0 =35
and the other brother is 20 + 5 =25. According to the earthy brother
though traveling is 25 and he is 35.
5. the traveling brother starts accelerating toward earth. He is
closer to the center of gravity than his brother so both agree that
his clock ran slower for 5 minutes no now according to traveling
brother he is 35 while his earthy brother is 30 minutes older but
according to earthy brother the traveling one is 25 and he is 40
5. The traveling brother is moving at high speed for 30 minutes again.
During this time he sees (or measures) that his brother clock has gone
forward only 20 minutes so, according to traveling brother he is
30+35=65 minutes older while his brother is only 50 minutes older (20
+30). To the earthy brother though it seems that the traveling brother
has aged 25+20= 45 minutes while he him self has aged 40+30=70
minutes.
7.The traveling brother decelerates this time his clock is running
faster for 5 minutes (unlike line 4) than his brother due to gravity.
Both brother agree on this so now According to traveling brother he is
65 + 5 =70 and the other brother is 50 + 0 =50. According to the
earthy brother though traveling is 45+5 =50 and he is 70+0=70.
Now they are both on earth and meet each other, which one is right?
Thank you for your time and effort in helping me understand this.
Ali
.
- References:
- Simple question
- From: Ali
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- From: PD
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