Re: Using a pulsar to measure time dilation

[Tom Roberts]

On 8/12/21 4:02 PM, Ed Lake wrote:
> [description of situation omitted]
> We both used the SAME clock,

Right. So why do you expect "time dilation" to apply? The clock you are
using is that pulsar, and IT is not moving at 99.4988339567% of the
speed of light.

Tom Roberts

[Maciej Wozniak]

Learn what the word mean, poor halfbrain.
https://www.google.pl/search?source=univ&tbm=isch&q=clock+picture&sa=X&ved=2ahUKEwimrYvS0LLyAhXOjqQKHfz9BvEQjJkEegQIExAC&biw=1920&bih=969
https://en.wikipedia.org/wiki/Pulsar

[Sylvia Else]

On 13-Aug-21 7:02 am, Ed Lake wrote:
> Imagine that there is a pulsar 4,000 light years away that rotates once per second. It can be viewed this way:
>
> |-----------------------------------------------------------------------------------------------0
>
> The pulsar is the circle on the right. The HORIZONTAL dotted
> line is the beam of photons that stream out of the pulsar like a
> light beam from a lighthouse. The beam rotates and hits that
> VERTICAL line on the left TEN TIMES PER SECOND.
>
> The vertical line has the earth at the bottom and a planet (Planet X)
> orbiting around Alpha Centauri at the top.
>
> BOTH Earth AND Planet X count one pulse every TEN seconds.
>
> Now assume that I get in a rocket ship and travel to Planet X at
> 99.4988339567% of the speed of light. At that speed, due to
> Time Dilation, one second for me will be 10 seconds back on
> earth (and on Planet X).
>
> I will count 1 pulse from the pulsar every second because my
> seconds are ten times longer than seconds on the two planets.
>
> If the round trip to Planet X takes 1 year for me, it will be 10 years
> as measured on Earth and on Planet X.
>
> During that time, I will count the SAME number of pulses as they
> counted on Earth and on Planet X, BUT I counted those pulses in ONE
> YEAR of spaceship time, while on Earth and on Planet X it took them
> 10 years to count the pulses between my departure and my return.
>
> What this thought experiment does is eliminate all arguments that
> people on earth will see my clock running slow while I will see the
> clocks on earth as running slow. We both used the SAME clock,
> and that clock ticked 10 times faster for me than for people on the
> "stationary" planets.
>
> Discussion?
>
>
>
>

What's the point of posting this repeatedly. Do you imagine you get
different response?

Sylvia.

[Ed Lake]

Because when we both use the same PULSAR clock, time dilation
shows up as a difference in how many pulses from the clock are
observed PER SECOND by the "stationary" and the moving observer.

Ed

[Ed Lake]

Tom Roberts started this thread, I didn't.

But threads over 100 messages in length can be tedious.

Ed

[Michael Moroney]

No, he did not. YOU did, in Message-ID:
<49a76373-7cba-4cd4...@googlegroups.com>. Tom only
responded to your post. Sylvia even quoted your post. Do you deny
writing that?

[Tom Roberts]

So instead of "the SAME clock", you are using three clocks.
Here "three" != "SAME", so it's no wonder you are confused.

Tom Roberts

[Ed Lake]

It's not that complicated, Tom.

I have a clock on my space ship. People back on earth also have clocks.
AND we all can see a pulsar that can ALSO be used as a clock.

That means I can compare tick rates between my clocks on my ship and
the pulsar clock.

The people on earth can compare their clocks to the pulsar clock.

This means that when I start accelerating, I will see the pulses from
the pulsar speed up. Instead of one pulse every ten seconds, the
pulses will come once every nine seconds, then every eight seconds,
then every seven seconds, etc. etc., until I reach 99.9488339567%
of the speed of light, when I will see the pulsar pulse once per second.

Why? Because my motion slows down time for me (and the clocks
on my space ship) but doesn't affect the pulsar or clocks back on
Earth.

It's called "Velocity Time Dilation."

Ed

[Arthur Adler]

On Tuesday, August 17, 2021 at 7:24:08 AM UTC-7, det...@newsguy.com wrote:
> ... until I reach 99.9488339567% of the speed of light, when I will see the

> pulsar pulse once per second.

Yes.

> Why? Because my motion slows down time for me (and the clocks
> on my space ship) but doesn't affect the pulsar or clocks back on
> Earth.

That's the description in terms of the reference system in which the Earth is stationary and the ship is moving at 0.994988c perpendicular to the incoming rays. The ships clock runs slow in terms of that system. However, the situation can equally well be described in terms of the inertial reference system in which the ship is stationary and the Earth and Alpha Centauri are moving at speed 0.994988c almost directly away from the incoming rays, only 5.7 degrees off (due to relativistic aberration). The Earth's clocks run slow in terms of this system, but the pulses still arrive less frequently on Earth than on the ship because of the large Doppler effect since the Earth is moving away from the rays. This is all explained in Einstein's 1905 paper. This illustrates the reciprocity of time dilation during the coasting phases of the scenario.

[Maciej Wozniak]

On Tuesday, 17 August 2021 at 16:58:25 UTC+2, Arthur Adler wrote:
> That's the description in terms of the reference system in which the Earth is stationary and the ship is moving at 0.994988c perpendicular to the incoming rays. The ships clock runs slow in terms of that system.

In some delusions of some brainwashed halfbrains, sure. Not
in the real GPS.

[Ed Lake]

On Tuesday, August 17, 2021 at 9:58:25 AM UTC-5, Arthur Adler wrote:

For the final time: NONSENSE! You can create a mathematical model where
the spaceship is stationary, and the earth is moving, but it would have NOTHING
to do with reality.

Furthermore, the pulses from the pulsar result from the pulsar rotating once
every ten seconds. Those pulses hit the earth once every ten seconds. When
the spaceship travels at a right angle to those pulses, any "Doppler Effect"
is IRRELEVANT. The Doppler Effect is about the frequency of light WAVES
or the frequency of the oscillating electric and magnetic fields of a photon.
While there might be some Doppler Effect when the spaceship hits the
photons in the rotating light beam, that effect will NOT IN ANY WAY change
how FREQUENTLY the ship OR EARTH will hit those rotating BEAMS.

The earth is NOT moving away from the pulsar. Nor is it moving away from
the photons coming from the pulsar.

The spaceship is also NOT moving away from the pulsar. Yes, because of
the ship's high speed, it will hit many of the moving photons from the side,
instead of the photons mainly hitting the top of the ship, but that is
IRRELEVANT. The pulses will still hit the ship once per ship second when
the ship is traveling at 99.9488339567% of the speed of light.

Your screwball BELIEFS do not change anything, and ALL TIME DILATION
EXPERIMENTS show you are WRONG. To quote Richard Feynman,
" It doesn't matter how beautiful your theory is, it doesn't matter how smart
you are. If it doesn't agree with experiment, it's wrong."

Bye bye.

Ed

[Michael Moroney]

On 8/17/2021 1:25 PM, Ed Lake wrote:

Back so soon?

> On Tuesday, August 17, 2021 at 9:58:25 AM UTC-5, Arthur Adler wrote:
>> On Tuesday, August 17, 2021 at 7:24:08 AM UTC-7, wrote:
>>> ... until I reach 99.9488339567% of the speed of light, when I will see the
>>> pulsar pulse once per second.
>> Yes.
>>> Why? Because my motion slows down time for me (and the clocks
>>> on my space ship) but doesn't affect the pulsar or clocks back on
>>> Earth.
>> That's the description in terms of the reference system in which the Earth is stationary and the ship is moving at 0.994988c perpendicular to the incoming rays. The ships clock runs slow in terms of that system. However, the situation can equally well be described in terms of the inertial reference system in which the ship is stationary and the Earth and Alpha Centauri are moving at speed 0.994988c almost directly away from the incoming rays, only 5.7 degrees off (due to relativistic aberration). The Earth's clocks run slow in terms of this system, but the pulses still arrive less frequently on Earth than on the ship because of the large Doppler effect since the Earth is moving away from the rays. This is all explained in Einstein's 1905 paper. This illustrates the reciprocity of time dilation during the coasting phases of the scenario.
>
> For the final time: NONSENSE! You can create a mathematical model where
> the spaceship is stationary, and the earth is moving, but it would have NOTHING
> to do with reality.

Tell that to Galileo.

Tell that to Newton.

Tell that to all the scientists who built current classical physics.

Tell that to Einstein.

Tell that to all who did further development on SR and GR since Einstein.

It's you vs. many of the greats of physics. Why do you think you are
correct, all by yourself and all physicists, including some of the
greatest, are wrong?

>
> Furthermore, the pulses from the pulsar result from the pulsar rotating once
> every ten seconds. Those pulses hit the earth once every ten seconds. When
> the spaceship travels at a right angle to those pulses, any "Doppler Effect"
> is IRRELEVANT. The Doppler Effect is about the frequency of light WAVES
> or the frequency of the oscillating electric and magnetic fields of a photon.
> While there might be some Doppler Effect when the spaceship hits the
> photons in the rotating light beam, that effect will NOT IN ANY WAY change
> how FREQUENTLY the ship OR EARTH will hit those rotating BEAMS.
>
> The earth is NOT moving away from the pulsar. Nor is it moving away from
> the photons coming from the pulsar.

In the frame of the earth (and pulsar, assuming the pulsar is stationary
wrt to the earth), true.

>
> The spaceship is also NOT moving away from the pulsar. Yes, because of
> the ship's high speed, it will hit many of the moving photons from the side,
> instead of the photons mainly hitting the top of the ship, but that is
> IRRELEVANT.

In the frame of the ship, because of aberration, it is moving TOWARD the
pulsar. Doppler blueshift causes the pulses to speed up as far as it's
concerned.

> The pulses will still hit the ship once per ship second when
> the ship is traveling at 99.9488339567% of the speed of light.

Because of Doppler blueshift, according to the spaceship observers.

>
> Your screwball BELIEFS do not change anything,

That is modern standard physics.

> and ALL TIME DILATION
> EXPERIMENTS show you are WRONG.

Nope. Time dilation experiments are all consistent with this.

> To quote Richard Feynman,
> " It doesn't matter how beautiful your theory is, it doesn't matter how smart
> you are. If it doesn't agree with experiment, it's wrong."

Yes. You need to look at your "beautiful" beliefs which disagree with
experiment and ask yourself, why are your "beautiful" beliefs wrong.

[Arthur Adler]

On Tuesday, August 17, 2021 at 10:25:52 AM UTC-7, det...@newsguy.com wrote:
> You can create a mathematical model where the spaceship is stationary,
> and the earth is moving, but it would have NOTHING to do with reality.

That's untrue, because both of the reference systems provide equally valid descriptions of the actual physical phenomena. To dispute this, you would need to explain why the description in terms of one reference system has to do with reality while the equally valid description in terms of the other reference system does not.

> The pulses from the pulsar result from the pulsar rotating once every ten seconds.

Well, your scenario stipulates that the pulses hit the earth once per 10 seconds in the direction perpendicular to the line from Earth to Alpha Centauri, and this is really all we need to know. If you want to relate this to the description in terms of the pulsar's reference system, you can do that, but it doesn't change the relevant aspects of the scenario. There are infinitely many different combinations of conditions of the pulsar (rotation rate and relative speed and direction of motion) that would yield the stipulated conditions, all irrelevant to the discussion.

> Those pulses hit the earth once every ten seconds.

Right, this is what you are stipulating, so there's no need to discuss the description in terms of the pulsar's reference system.

> When the spaceship travels at a right angle to those pulses, any "Doppler Effect"
> is IRRELEVANT.

Well, in the transverse condition this is merely a matter of semantics, since the relativistic Doppler formula includes the effect of time dilation, which is why there is a Doppler shift even for purely transverse motion. If you prefer to call that "time dilation" rather than "Doppler", that's fine, but just be aware that the common terminology refers to it as transverse Doppler. And, no, it is not irrelevant at all. The Doppler effect is significant in the descriptions for both reference systems.

> The Doppler Effect is about the frequency of light WAVES ...

The generic Doppler effect doesn't just apply to things like electromagnetic waves, it applies to every kind of propagating frequency. For example, if the machine gun on an jet fighter shoots 3 bullets per second, and the plane is approaching you at 500 mph, the bullets will hit you at a higher frequency as given by the Doppler formula. It applies to the frequency of any propagating sequential entities, not just wave crests or oscillations of electromagnetic fields.

> While there might be some Doppler Effect when the spaceship hits the
> photons in the rotating light beam, that effect will NOT IN ANY WAY change
> how FREQUENTLY the ship OR EARTH will hit those rotating BEAMS.

You're mixing up two different frequencies: (1) the frequency with which the beams hit something, and (2) the frequency of the electromagnetic oscillations comprising the beams. Those are totally different frequencies, and the relevant frequency for your scenario is the frequency with which the beams hit the objects. The Doppler effect and the motions of the objects determine those frequencies. You need to stipulate the conditions of your scenario if you want to relate the frequencies in the pulsar's reference system to the frequencies in the earth's or the ship's reference system, or you can just stipulate that the pulses strike the earth once per 10 seconds, and then you don't need to worry about the pulsar's reference system.

In any case, once you've stipulated that the pulses strike the earth once per 10 seconds, that is the frequency with which the pulses strike the earth, and it applies regardless of which reference system we use to describe the events. Likewise we have established that the pulses hit the ship at a frequency of once per 1 second, and this too applies regardless of which reference system we use. So, you can calm down and stop shouting that we can't change the frequency the beams hitting the earth or the ship. Those frequencies have their stipulated values in terms of both reference systems. So neither reference system is better or more accurate than the other.

> The earth is NOT moving away from the pulsar.

Again, you can stipulate how the earth and the ship are moving (or not moving) relative to the pulsar, however you like, but the bottom line is that you are saying the pulses strike the earth once per 10 seconds, and the rays are perpendicular to the line from Earth to AC in terms of the earth's reference system. That is all we need to know.

> The pulses will still hit the ship once per ship second when the ship is traveling
> at 99.9488339567% of the speed of light.

I think you have a typo in that number (transposed 9 and 4), but yes, as explained repeatedly, the pulses hit the ship once per ship second, and this is true regardless of whether we describe the events in terms of the earth's reference system or the ship's reference system (or any other reference system). Nevertheless, as explained previously, we have reciprocal time dilation.

> Your screwball BELIEFS do not change anything

I wish I could take credit for them, but they are not uniquely "my" beliefs, they are elementary Relativity 101. Anyone who has even a rudimentary understanding of relativity will instantly give you the same explanation.

> and ALL TIME DILATION EXPERIMENTS show you are WRONG.

No, as you may recall, we invalidated all your purported counter-examples, because they all refer to either difference in gravitational potential or accelerated clocks. Reciprocal time dilation applies to the reciprocal slowness of each clock in terms of the *inertial* coordinates in which the other clock is at rest. This has been abundantly verified experimentally, and there are no counter-examples.

In summary, your pulsar scenario is a good illustration of reciprocal time dilation.

[Wally Oldham]

Ed Lake wrote:

> This means that when I start accelerating, I will see the pulses from
> the pulsar speed up. Instead of one pulse every ten seconds, the pulses
> will come once every nine seconds, then every eight seconds, then every
> seven seconds, etc. etc., until I reach 99.9488339567%
> of the speed of light, when I will see the pulsar pulse once per second.

idiot, speed of light see no time nor space. Piss off, you are too stupid
to talk with us.

[Ed Lake]

On Tuesday, August 17, 2021 at 2:21:29 PM UTC-5, Arthur Adler wrote:

> On Tuesday, August 17, 2021 at 10:25:52 AM UTC-7, wrote:
> > and ALL TIME DILATION EXPERIMENTS show you are WRONG.
> No, as you may recall, we invalidated all your purported counter-examples, because they all refer to either difference in gravitational potential or accelerated clocks. Reciprocal time dilation applies to the reciprocal slowness of each clock in terms of the *inertial* coordinates in which the other clock is at rest. This has been abundantly verified experimentally, and there are no counter-examples.

Okay, you are saying all KNOWN time dilation experiments do NOT
support your BELIEFS because they involve gravity and acceleration.

Yet you appear to CLAIM there are some experiments which support
your BELIEFS. Why are you unable to name them and discuss them?

Ed

[Arthur Adler]

On Wednesday, August 18, 2021 at 8:13:17 AM UTC-7, det...@newsguy.com wrote:
> Okay, you are saying all KNOWN time dilation experiments do NOT
> support your BELIEFS because they involve gravity and acceleration.
> Yet you appear to CLAIM there are some experiments which support
> your BELIEFS. Why are you unable to name them and discuss them?

I have discussed them. It is *you* who refused to discuss them. Remember? You shouted at me (all caps and exclamation point) to cite experiments that establish reciprocal time dilation, and I carefully explained the experiments of Kaufmann, et al, and your (rather disgraceful) response was to dismiss all these experiments by saying "In other words, IF I believe the nonsense you believe, then these "experiments" support that belief, otherwise they do not." You did not explain why you put the word "experiments" in quotes, as if they were not real experiments, but I assure you they were real experiments, and they conclusively corroborate Lorentz invariance, which entails time dilation, length contraction, and the skew of inertial simultaneity. You also didn't explain which of the aspects of those experiments you regard as nonsensical, so basically you just covered your ears and declined to address the experimental results. Now, just a couple days later, you scold me for being unable to name or discuss any experiments! Your behavior is sort of bewildering.

Admittedly, when you dismissed all the experimental results, there's a sense in which what you said was true: In order for any experimental result to be intelligible (let alone convincing) to an individual, he must have at least the bare minimum of the conceptual foundations in terms of which we (normal rational adults) conceive of the world of our external experience. For someone who rejects many of the most basic aspects of the shared human conception of the world, it's more or less pointless to talk about high-level physics experiments, because he lacks any rational context in which to comprehend them.

That's why I can cite for you the experiments of Kaufmann, et al, but I fully realize that these mean nothing to you, because your conception of physics deviates from that of normal people at a far more fundamental level. It would take a long time and a lot of study for you to reach the level of understanding necessary to understand experimental tests of Lorentz invariance. For example, you would need to learn what Lorentz invariance means, and in order to understand that, you would need to understand how the descriptions of the attributes of phenomena are quantified, which means you would need to understand coordinate systems, and so on. I'm not exactly sure how far down we would have to go to find the fork in the road where your thinking diverged from the thinking of most people.

Let me just give one example of the very rudimentary discussion that would be needed to even begin on the road toward understanding Lorentz invariance: A careful archeologist may stake out a grid of strings at his dig site, dividing the region into small areas so he can assign coordinates to the locations of each object at the site. This is a coordinate system. At this point you amy say "That has nothing to do with reality! I will not discuss anything with the archeologist if he insists on talking about such nonsense as coordinate systems!!!" Even worse, the archeologist may go home for the season, taking down his grid, and another team may show up later and make their own grid on the same site. Now, these grids will not generally be identical, but by noting the positions of a couple of specific items in terms of each grid, we can translate the coordinates of every object from one system to the other. At this point you may say "No! no! no! That is nonsense, and has nothing to do with reality! Why can't you understand this!?!" Or you may say "The first grid is reality, but the second grid has nothing to do with reality!!! Why can't you understand this!?!?"

Obviously, it isn't the archeologists who lack understanding. There is nothing wrong with coordinate systems, and indeed they can be highly useful in facilitating the descriptions of scientific findings, and communicating scientific facts. Moreover, in the field of physics, coordinate systems take on even greater significance, because they serve not merely as labels but as a means of quantifying kinematic and dynamic variables. For example, a grid of rulers and clocks enables us to assign numerical positions (x) and times (t) to every event, and the speed of an object (in terms of that coordinate system) is then equal to the change in x for a given change in t. Of course, there any many different coordinate systems that can be defined for the same region (like the two string grids of the archeologists), and the speed of objects will be different in different coordinate systems, but we can translate from one to the other, and there is a special class of space-time coordinate systems in terms of which the patterns followed by all phenomena take a very simple homogeneous and isotropic form, and reciprocal time dilation refers to the mappings between the events on relatively moving objects given by the temporal foliations of those physically distinguished systems.

So, in this very slow and laborious way, we would gradually work our way up to understanding Lorentz invariance (time dilation, length contraction, skew of simultaneity, inertia of energy, etc.) and the experimental demonstrations of these things. But until we go through all this, you really can't understand the experiments at all, let alone decide whether they are convincing.

[Odd Bodkin]

Ed Lake <det...@newsguy.com> wrote:
> On Tuesday, August 17, 2021 at 2:21:29 PM UTC-5, Arthur Adler wrote:
>> On Tuesday, August 17, 2021 at 10:25:52 AM UTC-7, wrote:
>>> and ALL TIME DILATION EXPERIMENTS show you are WRONG.
>> No, as you may recall, we invalidated all your purported
>> counter-examples, because they all refer to either difference in
>> gravitational potential or accelerated clocks. Reciprocal time dilation
>> applies to the reciprocal slowness of each clock in terms of the
>> *inertial* coordinates in which the other clock is at rest. This has
>> been abundantly verified experimentally, and there are no counter-examples.
>
> Okay, you are saying all KNOWN time dilation experiments do NOT
> support your BELIEFS because they involve gravity and acceleration.

I’m pretty sure you are not aware of most of the experiments exhibiting
time dilation. The couple you’re aware of involve gravity or noninertial
motion. What about the dozens of others?

>
> Yet you appear to CLAIM there are some experiments which support
> your BELIEFS. Why are you unable to name them and discuss them?
>
> Ed
>

--
Odd Bodkin -- maker of fine toys, tools, tables

[Paul B. Andersen]

Den 12.08.2021 23:02, skrev Ed Lake:
> Imagine that there is a pulsar 4,000 light years away that rotates once per second. It can be viewed this way:
>
> |-----------------------------------------------------------------------------------------------0
>
> The pulsar is the circle on the right. The HORIZONTAL dotted
> line is the beam of photons that stream out of the pulsar like a
> light beam from a lighthouse. The beam rotates and hits that
> VERTICAL line on the left TEN TIMES PER SECOND.
>
> The vertical line has the earth at the bottom and a planet (Planet X)
> orbiting around Alpha Centauri at the top.

We will assume that the Earth, planet X and the pulsar are
stationary relative to each other.
The distance Earth - planet X is L = 4.7 light year.

>
> BOTH Earth AND Planet X count one pulse every TEN seconds.

Typo! 10 counts per second.

f₀ = 10 Hz

>
> Now assume that I get in a rocket ship and travel to Planet X at
> 99.4988339567% of the speed of light. At that speed, due to
> Time Dilation, one second for me will be 10 seconds back on
> earth (and on Planet X).

v = 0.994988339567 γ = 10.00

>
> I will count 1 pulse from the pulsar every second because my
> seconds are ten times longer than seconds on the two planets.

When your velocity is perpendicular to the wave vector from
the pulsar, you will observe the signal from the pulsar
to be blue shifted. (Transverse Doppler shift).
So you will observe the frequency:

f = f₀⋅γ = 100 Hz, 100 pulses per second on your wristwatch.

>
> If the round trip to Planet X takes 1 year for me, it will be 10 years
> as measured on Earth and on Planet X.

The round trip to planet X takes:
Measured in Earth's rest frame: t = 2⋅L/v = 9.447346 years
Measured on your wristwatch : τ = t/γ = 0.9447346 years

>
> During that time, I will count the SAME number of pulses as they
> counted on Earth and on Planet X, BUT I counted those pulses in ONE
> YEAR of spaceship time, while on Earth and on Planet X it took them
> 10 years to count the pulses between my departure and my return.

Number of pulses that hit the Earth:
N_Earth = t⋅f₀ = 9.447346⋅31536000⋅10 = 2979315034 pulses

Number of pulses that hit you:
N_you = τ⋅f = 0.9447346⋅31536000⋅100 = 2979315034 pulses

>
> What this thought experiment does is eliminate all arguments that
> people on earth will see my clock running slow while I will see the
> clocks on earth as running slow. We both used the SAME clock,
> and that clock ticked 10 times faster for me than for people on the
> "stationary" planets.

What does it mean that people on Earth see your clock running slow?

If an observer on Earth see your clock through a telescope
(or receives a video signal of your clock), he will see
your clock run slow by the factor 0.05012 on your way out,
and he will see your clock run fast by the factor 19.95
on your way back.

>
> Discussion?

Nothing to discuss.
But you can learn something by reading the following:

https://paulba.no/pdf/TwinsByDoppler.pdf
https://paulba.no/pdf/TwinsByMetric.pdf

https://paulba.no/twins.html

--
Paul

https://paulba.no/

[Arthur Adler]

On Wednesday, August 18, 2021 at 2:09:53 PM UTC-7, Paul B. Andersen wrote:
> Den 12.08.2021 23:02, skrev Ed Lake:
> > light beam from a lighthouse. The beam rotates and hits that
> > VERTICAL line on the left TEN TIMES PER SECOND.

That's a garbled quote. Ed's original message had a typo in the first line, but in all subsequent places he consistently said the beam sweeps past the Earth once every ten seconds (of earth time). Here's the actual line from his original post:

> light beam from a lighthouse. The beam rotates and hits that

> VERTICAL line on the left once every TEN seconds.

Since the pulses hit Earth once per ten earth-seconds, and the ship is moving (in terms of the earth's frame, x,t) transversely at speed such that dtau/dt = 1/10, the ship is receiving pulses once every ship-second. Ed thought this means the time dilation between earth and the coasting ship is not reciprocal, because (he reasoned) if the earth's clock was running slow compared with the ship's clock, the earth should be receiving pulses at ten times the rate as they are received on the ship. The explanation was given in the other thread, namely, he neglected the relativistic aberration, which shows that in terms of the coasting ship's frame the earth is moving almost directly away from the pulsar (at 5.7 degrees), so even though the Earth clocks runs slow by 1/10 in terms of the ship's inertial frame, it still receives pulses only 1/10 the frequency as they are received on the ship, because of the large longitudinal Doppler effect in terms of the ship's frame.

> > BOTH Earth AND Planet X count one pulse every TEN seconds.
> Typo! 10 counts per second.

No, the first sentence was a typo, but this sentence was consistent with all the others, and he has re-affirmed that this is what he meant, i.e., the earth receives one pulse every 10 earth-seconds.

> So [the ship] will observe the frequency:

> 100 pulses per second on your wristwatch.

Given that the earth receives one per 10 earth-second (per above), the ship receives 1 per ship-second.

> The round trip to planet X takes:

Ed's paradox is not related to the round trip, it is focused on either of the coasting legs of the trip, during which the ship has constant speed. He's trying to say this scenario disproves reciprocal time dilation for two inertially moving clocks. The resolution of the paradox is as noted above (the relativistic aberration and longitudinal Doppler for the earth in the ship's frame). See the other thread for details (and for Ed's original scenario, since someone apparently mangled it when posting it to this splinter thread).

[RichD]

On August 17, Arthur Adler wrote:
>> ... until I reach 99.9488339567% of the speed of light, when I will see the
>> pulsar pulse once per second.
>
> Yes.
>

>> Because my motion slows down time for me (and the clocks
>> on my space ship) but doesn't affect the pulsar or clocks back on
>> Earth.
>
> That's the description in terms of the reference system in which the Earth
> is stationary and the ship is moving at 0.994988c perpendicular to the incoming
> rays. The ships clock runs slow in terms of that system.

I was thinking of the football QB analogy. He leads the receiver,
aiming at the point where the receiver will be.

Now, modify Ed Lake's scenario, such that the pulsar 'aims' the light
(the normal to the wavefronts) at the spaceship's projected point of
reception, along its path to Alpha Centauri. And continuously modulates
this vector, as necessary.

How would you model that?
How does it affect the paradox parameters?

--
Rich