Bass Coast Sojourn
2 Mar 2021 1:13:12 UTC
Topic 224953
(moderation:
A wonderful opportunity arose to take a break from work and have a week off. I am in a beachfront house watching some strong winds and rain rake the coast, and beyond which are waters of the infamous Bass Strait. My thoughts, as is usual with my beach holidays, turns to the topic of tides.
One can't think of tides without a mention of Isaac Newton who was the first to work it out properly. He discovered his famous inverse square law of gravitation that gives the force of attraction between them. So for two bodies of mass m1 and m2 separated by a distance r between them : well, you know the formula, which also involves a universal constant G. The key point is the greater the distance the less the force. At the time Isaac knew the acceleration of bodies falling near the Earth's surface. He had an estimate for the distance to the Moon, as determined by astronomers, and could work out what it's acceleration toward the Earth should be. But wait, he knew that another way! The Moon takes one month to circle the Earth entirely and that gives an acceleration number too. He found that the two estimates of the Moon's acceleration agreed pretty much and hence was very happy that his force law was justified so.
He recognised that it is our orbiting around Moon* that generates the tides. The Earth is solid, the water is liquid and thus the water sloshes around the globe. But the water on the side of the Earth opposite the Moon is further away from the Moon and thus attracted less than the underlying Earth. The water on the nearside closer to the Moon is more attracted that the underlying Earth. Hence two bumps appear in the distribution water around the Earth, one on the side furthest from the Moon and one on the side closest to the Moon. Now add in the fact that the Earth rotates beneath it's liquid oceans and you have two tide cycles per today. In about 24 hours at a given Earth coastline the water goes in an out twice, where the Moon has moved a little bit in it's orbit during that period. Other commentators in Newton's day only predicted one tide cycle per day so his theory got that dead right.
But wait, there's more ! The Sun has an effect also and while quite a distance away it is very massive and thus would produce Earth tides even if there was no Moon. Combined they both affect the oceans and the basic Earth-Moon tides are thus modulated by this aspect depending on the relative orientation of the Moon and Sun. By extension you could blame other planets for their direct tidal effects on Earth's water bodies too, but the effect is much less so. I don't know if anyone calculates or measures that. This was also part of Newton's law of gravity : it is universal.
Did you know that the substance of the Earth also undergoes tides ? It doesn't deform much, but it does. Indeed the interferometers at LIGO and elsewhere must account for this small deformation. Jupiter's moon Io undergoes much deformation of it's substance from it's proximity to Jupiter, and this heats the interior. Which is why it is so violent and volcanic on it's surface.
Earth water tides act like brake shoes on the rotation rate of the Earth and thus have and will continue to cause a slowing of the rate and a lengthening of the day.
So the old saying goes : time and tide wait for no man. Sailors when close to shore knew the imperative to know whence the tides would turn. When it is safe to go in and when it is safe to go out. Down here at the Bass Coast where I am the water recedes by around one hundred meters when the tide is out. Then six hours later it is back in again. So the water is quite shallow and doesn't deepen until well offshore. That's great if you surf, where the wind also is at play. I saw a windsurfer yesterday, some ultra fit guy just be tearing along on a board with a sail. The Moon is pretty full at night and so it is the time of 'Spring' tides when the effects of the Moon and the Sun are additive.
You could perhaps predict the tides with fair regularity, a straight forward formula to be applied for some time. But alas no, because the Moon is inconstant in it's orbit due to the other planets. Sometimes it goes faster than usual, sometimes slower. It never quite turns up at an expected place and time due to these effects. So in a way Jupiter, for instance, by affecting the Moon's orbit changes the tidal pattern here on Earth.
You could ask : how do tides on Earth affect the Moon ? They do, and while that is rather more complicated to explain, it has the effect of gradually increasing - over the aeons - the length of the month and 'pushing' the Moon further out in it's orbit. The Moon's substance is also affected by tidal effects from the Earth and that in turn - over aeons again - causes the period of rotation of the Moon about it's own axis to ( nearly ) equal it's orbital period around Earth. This is called tidal locking which is why we always see the same side of the Moon as viewed here on Earth. So a full 'day' on the moon lasts one month.
{ BTW there is no 'dark side' of the Moon, there is just the far side that we can't see from Earth. }
Now go skywards and imagine two stars orbiting one another. The same principles as above apply. They each deform the other. In fact one can say that tides are gravity, you can't - or at least I can't - have one without the other.
* The Moon-Earth system can described from the centre of mass viewpoint, but that only unnecessarily complicates the story.
Cheers, Mike
I have made this letter longer than usual because I lack the time to make it shorter ...
... and my other CPU is a Ryzen 5950X :-) Blaise Pascal
So I walk on the beach when
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So I walk on the beach when it is windy, when the wind direction is along the line of the shore and blowing at a good fresh pace, say 20km/h. Walking downwind the task is easy as I have the wind on my back and it helps me along. To come back I reverse course and walk upwind with the wind now in my face, and that's a little harder. So with a constant level of effort I will go faster downwind than upwind. Does that remind me of anything ? It surely does :
In the late 1800s there was much afoot in physics. Alot of stuff was being discovered eg. the equations of electromagnetism of James Clerk Maxwell. These beautifully and concisely summarise many phenomena heretofore discovered. There are four equations. These equations predict that electromagnetic waves are possible and the speed of those waves is then determined theoretically. It is the speed of light, usually denoted as c in the mathematics. Much to celebrate. Now the physicists figure that it must be waves in some medium or material. Like water is for water waves or the air for sound waves. Seems a natural conclusion and a reasonable extension of what they already knew. But for light what is the medium ? What are the properties of the medium ? Can we detect any other effects of the presence of the medium ? All good questions. They call the medium the aether.
So Albert Michelson and Edward Morley get their heads together to determine the following question : what is the velocity of the Earth with respect to this new medium ? Now it was known that if a source of, say, sound waves was moving in still air then the motion of the source would affect the propagation of any wave. Surely then by studying this new aether idea one could find out how fast the Earth was going through it. They called it the aether wind by analogy. How then to set up an experiment to detect this ? They came up with the following idea : to measure the speed of light in one direction and compare it with the speed in a perpendicular direction.
The Michelson-Morley Experiment : Set up the apparatus as follows. Have a beam of light from a source be split into two mutually perpendicular paths. For each path place a mirror at the end to reflect the beam back the way it had come. One beam would go upwind and downwind ( like me walking on the beach ) and the other beam would go crosswind and back. Make the up/downwind leg the same length as the crosswind one. If the aether had an effect it would be to delay the passage of one beam through the aether with respect to the other. The light would come back from the two paths at different times. See which gets back first. However they couldn't measure the speed of light in a direct way with this setup and the instruments of the time. Plus they couldn't be sure the paths were exactly of equal length. In addition they couldn't be sure that the beams were precisely perpendicular. So they used another effect known at the time : the interference of light waves.
Light has a frequency and a wavelength. Now it had been shown that an interferometer constructed as above would produce a pattern of bright and dark bands to be observed at the finishing line. Because the beam paths weren't identical and perpendicular the maxima of one wave would coincide with the minima of the other causing what was called a dark fringe, and the maxima of one could coincide with the maxima of the other causing what was called a bright fringe. For a given fixed arrangement there would be light and dark bands to be seen by the optics used at the output of the device, especially if those optics were slightly rotated when viewing the interference pattern.
This was not enough however. One couldn't be sure of the direction of the aether wind at any given moment, after all they hadn't detected it yet ! So one couldn't align the interferometer to be sure that the different beams were actually up or downwind or crosswind. Also the Earth's rotation was rotating the interferometer whether you liked it or not. But you if could rotate the device during some short observation period then maybe, just maybe, one could notice a difference in the fringe pattern as the light beams within the apparatus became suitably aligned with respect to the aether wind. This was called a fringe shift. To magnify the effect they also had each separate light path 'folded' by mirrors several times so that a beam would travel up/downwind ( or crosswind and back ) many times. This saved them building a really long interferometer. After all if the two beams were going at different speeds then a longer 'race' between the two would make it easier to sense any time difference at the finish.
So each day for several months, and several times each day, they would carefully rotate the interferometer and look for a fringe shift. They hoped to catch the interferometer in the right orientation with regard to the aether wind and see the fringe shift. There were other effects of a local nature that they had to account for, and the optics of the time had their limitations etc, but they kept such errors below the expected fringe shift.
You know the answer of course. There wasn't any significant shift. The aether wind, if there was one, must have been blowing very quietly. Various explanations for this famous negative result were proposed but none held sway. That is, until the then unknown Swiss patent clerk made his now famous explanation. So the speed of light can't be used to measure some absolute reference frame : the one in which the aether is motionless. The aether idea was unnecessary and so ought be discarded. There is no ultimate reference frame which light prefers.
Now no one can give a deeper reason why the speed of light is always a constant, independent of the motion of the source. It just is. It may be difficult to accept as it seems counter-intuitive to everyday life. But the rigor of physical theory and measurement demands that be true.
Cheers, Mike.
I have made this letter longer than usual because I lack the time to make it shorter ...
... and my other CPU is a Ryzen 5950X :-) Blaise Pascal
Mike Hewson wrote:So Albert
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If you have access to Amazon Prime video Down Under, I think you will find this explanation quite fascinating. I had never seen the background or the operation of the experiment really well-explained before.
Start at 35:35, or do the entire history of the Allegheny Observatory, if you can put up with the commercials.
https://www.amazon.com/Undaunted-Forgotten-Giants-Allegheny-Observatory/dp/B01LBTUEEA/ref=sr_1_1
Jim1348 wrote:Mike Hewson
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Darn, I haven't subscribed to Amazon Prime. But I just might, if this program is available. Thanks for mentioning it ! :-)
One can't live in the past but one can always learn from it. Take the Lorentz contraction for instance. He turned out to be right but for the wrong reasons. Einstein showed the formula comes from careful reasoning but pretty simple maths : though provided one is not scared of a little algebra and square roots etc. It comes from applying Pythagorus' Theorem to the 'crosswind' paths taken. A few people nearly got relativity eg. Poincare, but didn't go the final leap. Albert Einstein had no reputation to risk then, and what an advantage that was .....
I almost forgot to mention that the current interferometers are superficially similar to the Michelson-Morley type. We still send beams - from high precision lasers now - there and back along orthogonal paths and seek to detect and respond to the tiniest of fringe shifts. There is so much cutting edge technology in the devices. I think the black hole detections are a real mind boggle.
May E@H's turn come soon. I can't wait for a rhythmic beat from the heavens.
Cheers, Mike.
( edit ) Then there is good old serendipity, right place and time with a good idea. Take the polymerase chain reaction for instance. One can effectively use this biotech ability to amplify DNA/RNA without the least idea of how it came to be so. There was a guy with a problem to solve and he arranged existing technology - invented by other people - in just the right fashion with a feedback loop. Hey presto ! One can look into the microcosm. Brilliant stuff but he made his own luck by careful thinking too. I order PCR tests routinely and it can cut through a muddle of possibilities so quickly. The up-the-nose COVID test is one of those.
( edit ) Darn! I can get Amazon Prime but the 'video is not available in your location' alas. :-(
I have made this letter longer than usual because I lack the time to make it shorter ...
... and my other CPU is a Ryzen 5950X :-) Blaise Pascal
Mike Hewson wrote:The
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If you haven't come across it previously, here is a reasonably concise presentation of this topic, that is on the PBS Spacetime youtube channel. The main reason for drawing your attention to it is that the presenter is a Melburnian - so it must be worthwhile and right up your alley, eh? :-).
There are lots of high level Physics vids on the channel, and in particular, this one released just over a week ago is entitled, "Gravitational Wave Background Discovered?". If you've got nothing better to do, you might like to dive right into the weeds on that one :-).
Cheers,
Gary.
Thanks for the links Gary,
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Thanks for the links Gary, most informative. :-)
He got the date of the Michelson-Morley experiment forward by a decade ( it's eighteen years prior to Einstein's Special Relativity in 1887, not eight in 1897 ) but I'll forgive him 'cos he comes from Melbourne. Also I think that the Einstein Equivalence Principle is best stated as the limiting case for spacetime : it approaches a flat/Minkowskian metric only with sufficiently small intervals. Gravity is technically stronger at your feet than your head - when you stand upright! But this all raises the question of how tightly curved can spacetime get in the limit of the ultra-ultra-tiny scale. Which it must at the centre of a black hole. Does it go smooth as General Relativity requires or does it gnarl up into knots? For me I don't think it is a coincidence that subatomic particles are primarily characterised by their mass, angular momentum and electric charge, just like black holes. I get the feeling that we are missing something, probably simple, in our assumptions. Anyway that implies that gravity is well off the inverse square law at that scale. A key problem is how to elucidate new phenomena to test any new theory ( you can't see into black holes ). You have to be able to disambiguate candidate ideas. So if you can't test it then why include it in a theoretical edifice, apart from maybe ease of understanding or computation or likewise convenience ?
Now pulsar timing arrays are a fascinating application of technology. That could uncover some pretty funky stuff, like the mega black holes mentioned. But there is much more to look on this PBS channel.
Cheers, Mike.
I have made this letter longer than usual because I lack the time to make it shorter ...
... and my other CPU is a Ryzen 5950X :-) Blaise Pascal
Here is the most relevant
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Here is the most relevant portion about the MM experiment from that video.
https://www.youtube.com/watch?v=7qJoRNseyLQ&ab_channel=FutureScienceMedia
However, it appears to leave out the very interesting part about how the precision optics came to be made at the Allegheny Observatory. I hope that might be available elsewhere.
Jim1348 wrote: Mike Hewson
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I took a class at the AO almost 20 years ago. Sadly at the time the 30" refactor was still being used for research (proper motion studies using 100+ year old plates as a baseline, and looking for planets around red dwarfs) and the 30" RC in the other big dome was down with mechanical problems. Which meant I only got to use the 13" Fitz-Clark refractor, which was an 1860's 2 elemment lens and had a lot of chromatic aberration in the blue; and a 10" Meade that lived in the shadow of the broken RC.
I kinda wonder what they're doing now. ESA's Gaia project would've killed the proper motion study; and Pittsburgh hasn't exactly gotten any darker over the years with the observatory stuck in the middle of the city.
DanNeely wrote:I kinda wonder
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It looks more like a museum to me. I want to stop in the next time I am over there (at the other end of the state). But back in its heyday, I think it was out in the country, or at least the far suburbs. It is fortunate that the big money guys in P-burgh took an interest in science. They wouldn't have been funded otherwise.
I'm back at work, alas. But
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I'm back at work, alas. But I've just seen some really big numbers from the recent publication of E@H work to cheer me up :
"The total number of templates that we searched with Einstein@Home is 7.9 × 1017. The search is split into work units (WUs) sized to keep the average Einstein@Home volunteer computer busy for about 8 CPU hours. A total of 8 million WUs are necessary to cover the entire parameter space, representing of order 10,000 CPU years of computing.
Each WU searches 9.8 × 1010 templates, and covers 50 mHz, the entire spin-down range and a portion of the sky. Out of the detection statistic values computed for the 9.8 × 1010 templates, the WU-search returns to the Einstein@Home server only the information of the highest 7500
results."
What a boggle ! But all the more so when one considers the entire multidimensional parameter space. How great is that ? It's been fifteen years and I'm just as passionate about the project as when I started, more so really ..... :-))
Cheers, Mike.
I have made this letter longer than usual because I lack the time to make it shorter ...
... and my other CPU is a Ryzen 5950X :-) Blaise Pascal
Our results exclude neutron
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Our results exclude neutron stars rotating faster than 5 ms with equatorial ellipticities larger than 10−7 closer than 100 pc. These are deformations that neutron star crusts could easily support, according to some models.
https://iopscience.iop.org/article/10.3847/1538-4357/abc7c9#apjabc7c9s4
Are we done with this batch? Does that mean we have more work to do on it (as we await the next one)?