Thursday, August 27, 2015

The twin paradox

You may be familiar with the twin paradox of special relativity.

One twin stays on earth, while the other twin flies off to a nearby star at nearly the speed of light.  On reaching that star, she turns round and comes back to earth.  For all the time travelling at nearly the speed of light, each twin sees the other twin's clock running slowly (according to special relativity, which is correct).   Yet when the traveller returns to earth, they really are younger than their stay-at-home twin.

There are various explanation of this, which are almost certainly correct (because some very smart people thought about this), but I don't like them.  They are unsatisfying.  They rely on the lack of symmetry - one twin sits still, the other has to turn around, and it is the turnaround that leads to the asymmetry.  So I figure there must be a symmetric version of the twin paradox.

This time our intrepid twins are both travelling at nearly the speed of light, parallel to each other, when without changing speed they take circular paths of the same radius that diverge.  At some point they will converge again, having each done a full circle, and can compare clocks, or look for visible signs of aging, or whatever.  The situation is symmetric, so when they compare clocks, both clocks must show the same time.  But at various points in their trip, they are moving very fast relative to each other, and so must both see each others clocks running slow.  So how, when they meet again, can their clocks show exactly the same time?  And now there is no asymmetry to hang your hat on.

Oh well, I'll have to ask some of the very smart people I work with...


Wednesday, August 26, 2015

Capitalism

The goal of any business is to sell lots of stuff and reduce their costs.  The biggest cost is often labour, so it is only natural that companies try and use less labour.  After all, who wants farmers to plough by hand?  Who wants armies of government clerks filing paper copies of everything?

The only problem with this is that when you are replaced by a machine or a computer, you aren't earning money any more, and that makes life kind of difficult.

Anyway, it seems to me that over time less and less labour will be used, and that means less and less people having money from working.  And maybe more and more people having money from investing.  And herein lies a problem.  Most of us can imagine earning a living by selling our labour.  There is probably something we are good at.  But you can't make a living from investing unless you have money.

Now governments can actually take money and redistribute it.  And they do this.  But there is a movement that, while not actually stating they don't agree with redistribution, are advocating less tax.   I guess if you want, you can pretend that you can collect less tax and still do the necessary redistribution.  But it is just pretending.

Of course in the long term, new industries will spring up to employ those displaced by technology.  Just look at the number of coffee shops that have sprung up.  Personal trainers did not exist 30 years ago.  A great number of various types of therapist have exploded in number in recent years.

So the amount of redistribution needed is not fixed, and not necessarily ever growing, but right now the pace of change is great, so more redistribution is needed.  The other path leads to revolution and destruction.

Tuesday, August 18, 2015

Westboro Baptist Church

So I watched a Louis Theroux documentary about the Westboro Baptist Church.

Its kind of mean doing a documentary about crazy people.

The members of this church are, one presumes, Christians.  Yet they seem to show not the slightest understanding of His teachings.  They seem instead to be a bizarre sect of trolls.  Not internet trolls, but trolls in the real world.  An internet troll will lash out at people online, trying to hurt their feelings.  These guys are totally weird, and do the same thing in real life, during things like funerals.  They really enjoy inflicting pain on others, and are really tempting others to hit them.

And I guess that is it.  They feel deeply unloved, and hurt, and in hurting others, they seek to get some hurt back in return.  And they do this in the name of a religion that preaches love.

If Jesus did return, he would, no doubt, love them.  But I'm not sure they'd enjoy it.  And I'm certain they would have no idea who He was.

Saturday, August 15, 2015

Melde's Experiment part II

OK, the idea is to create an extended, explorational type experiment for PHYS1002 students.

I have a long fascination with Melde's experiment.

In theory, it is a nice simple experiment used to verify that the speed of propagation of a wave is equal to its frequency times its wavelength (v = f lambda).  You set up standing waves in a length of string using a pulley and weights to maintain the tension in the string, and you measure the node-to-node distance.  The frequency is known (50 Hz), and the velocity should be given by sqrt(T/mu), where T is the tension in the string and mu is the linear density of the string.

In practice, the v = f lambda relationship doesn't seem to hold very well.  It seems quite possible to establish standing waves which don't have the "right" wavelength.

Anyway, I did the experiment in (what I thought was) a new and interesting way.  I established the resonance in the length of string hanging down from the pulley to the weight providing the tension.  I used a bulldog clip to grip the string, allowing easy small changes to the length of the string.  And I observe some weird things.  At long lengths, no standing wave forms.  As you get shorter, you get a standing wave.  The polarisation is such that the string vibrates at roughly right angles to the pulley.  As the string gets shorter, the size of the vibrations increases a bit, and then seems to decrease a little, and then, rather surprisingly to me, the plane of polarisation of the vibrations shifts by 90 degrees.

Then as you keep shortening the string, the vibrations increase a bit again, and then, quite suddenly, they are gone.  At the point where they are only just "gone", if you "twang" the string, you can make them come back.  A bit shorter again, and there is no standing wave, and you can't make it come back by "twanging" the string.

So the things that interest me.  At what length to the vibrations vanish?  At what length does the polarisation change?  These things could be measured for a range of values of tension.

Lastly, and completely puzzlingly, yesterday I tried this using an alligator clip rather than a bulldog clip.  And I could engender no standing wave in the vertical length of string, no matter how I tried.  I gave up, went and got the bulldog clip, and standing waves appeared.  Why these two methods of terminating the string at a given length produce different results, I have no idea.

Saturday, August 8, 2015

Melde's Experiment

We do a variation of Melde's Experiment at uni.  What we do is have a metal strip that has its length adjusted so that it will naturally vibrate at around 50 Hz.  We attach a string to this, and then pass the string over a light pulley.  The end of the string is attached to a weight to keep tension in the string.

The metal strip is then induced by mains power to be an electromagnet with its polarity switching 50 times per second.  A permanent magnet is placed near the strip, inducing the strip to vibrate.  Adjustment of the length and/or tension in the string results in standing waves in the string.  We know the frequency of the waves (50 Hz), and we can measure their wavelength (twice the distance between successive nodes - points of no vibration - in the string), so we now know the velocity of waves in the string.  Theory says it is sqrt[T/mu], where T is the tension in the string in Newtons, and mu is the linear density in kg/m.  And sometimes when you do the experiment you get pretty close to that, and sometimes you don't.  The metal strip vibrates horizontally, producing horizontal standing waves in the string, but sometimes you get vertical standing waves as well, and when you do, they have different wavelengths to the horizontal ones, which is weird.

Actually, the different wavelengths for vertical and horizontal standing waves is not so weird.  In the vertical direction, the point of attachment of the string to the metal strip *must* be a node - a place of minimal displacement - because the strip is only free to vibrate horizontally.  But for horizontal standing waves, the point of attachment of the string can be a node or an anti-node (place of maximum displacement), or anything in between.  Where the string goes over the pulley is always a node.  So the different wavelengths arise from these different constraints.

But, and its a big but, the speed of propagation of waves in the string, together with the frequency of vibrations, is supposed to fully determine the wavelength.  And it is not supposed to be different for horizontal and vertical vibrations.  But it is.

Standing waves occur when the wave transmitted down the string by the vibrating strip is reflected at the pulley, and travels back down the string.  Mathematically, two waves of equal amplitude and frequency travelling in opposite directions will cause a standing wave pattern.  And nodes in that standing wave are a half wavelength apart.  If the length of the string is adjusted correctly, the returning wave will be in phase with the vibrations of the metal strip, causing an increase in the amplitude of the vibrations.  This is termed resonance.

Anyway, one time I noticed a standing wave in the section of string hanging vertically down from the pulley to the weight.  And it occurred to me that this was different.  Each end of the string was definitely a node.  The weights hanging from the string form a pendulum with a natural frequency so far from 50 Hz that they are effectively fixed in position.  At the other end, the pulley is no doubt vibrating, but its motion is not detectable by the naked eye.  So I expected that for certain lengths of vertical string between the pulley and the weight, resonance would occur, and standing waves would form.   If the length is not quite the right length (an integer multiple of half a wavelength), then imperfect resonance should occur, and I expected the resulting standing wave to have a smaller amplitude.  But it was not quite like this.  Rather, if there was a standing wave present, it seemed to have a pretty fixed amplitude.  And if the length strayed too far from the ideal length, there was no standing wave at all.

And the vanishing of the standing wave was a rather sudden thing.  Adding 1 mm of string seemed to be enough for the standing wave to switch from "on" to "off".   And there was still more subtlety.  If the length of string was adjusted so that it was at the maximum length for which the standing wave was present, and the standing wave was stopped (by touching the string, for example), it did not necessarily restart on its own.  But if you "twanged the string", it could be made to restart.

Anyway, I'm interested in getting the precise minimum and maximum lengths that do result in standing waves, and see if the midrange of these corresponds to half a wavelength, based on the frequency and speed of the waves.

Having said this, I also tried to do this set up with thin wire instead of string.  The wire had about the same linear density (1 g/m).  But unlike the string, it is not "stretchy".  As a result when you got resonance going in the wire, the weight attached to the end vibrated up and down noticeably, which seems wrong, because then the tension in the wire is maybe not constant.  The wire also has a feature that it shouldn't have - a natural resistance to bending.  The theory is for something that has no natural resistance to bending, so that only its tension tends to pull it straight.  The string has no resistance to bending, but the string is stretchy.  The theory is for an inelastic string.  So in both cases, the actual material is not the theoretically ideal material.

This makes me question using a weight to provide the tension in the string/wire.  The problem with a weight is that when a standing wave is present, if the string is inelastic (as it should be), it will jiggle the weight up and down.  But such jiggling means the weight is accelerating up and down, so it is no longer providing the constant tension in the string that it is supposed to.

Maybe a spring would work better.   An ideal, massless spring, that had to be stretched a long way to provide the necessary tension - so that the tiny extra movements would barely change the tension.   Sounds nice, but how do you do it?

Actually, what having the string attached to an elastic band that is attached to the weight?  The elastic band acts like a shock absorber.  Again, it sounds nice, but I'm not sure.  The nice thing about having a weight attached directly to the string is that it ensures that point is a node.  Add elastic or a spring, and that point will no longer be a node, and the elastic or spring will become part of the vibrating system, corrupting it.

Anyway, for now, I'll just explore the max/min lengths and see what that shows.

Tuesday, August 4, 2015

Penalty rates

There is a move afoot to start cutting penalty rates in Australia.  What are penalty rates?  If you work nights, or Saturday, Sunday or public holidays, you are paid extra.  Its to compensate you for the inconvenience of working when others are sleeping or playing.

Anyway, the first step in this bold initiative is to cut Sunday penalty rates from 100% to 50%.  But not for everyone - essential workers like police, emergency workers and nurses will be exempt.  It will hit non-essential workers, like those in hospitality, retail etc.  The argument for the cuts is that society has changed, and Sunday is no longer the sacrosanct family day it once was, so the amount of extra compensation you need for working Sundays is less, or even none at all.

Now, those of you who know my lefty tendencies will expect me to be outraged by these proposals.  But you'd be wrong.  I don't think they go far enough.  You see, there are occupations that don't explicitly have penalty rates, but those penalty rates are built in.

An example is politicians.  Being a pollie has always been a 7-day a week job.  And we can assume that this was acknowledged a long time ago in setting the pollies pay.  That would have included the standard 100% penalty rate for Sunday.  Perhaps you can see where I'm going?  If we are going to cut penalty rates for shop assistants and baristas, we will have to cut the wages of pollies too.  How much?  Well, assuming a 7 day week with normal pay for Monday to Friday and a 50% penalty on Saturday and a 100% penalty on Sunday, we'll be cutting just 50% on Sunday, which makes a pay cut of about 6%.

Now some could argue that pollies are essential workers like nurses and police.  But if you don't enjoy people laughing at you, don't try and make that argument.

And of course its not just pollies.  Take CEOs.  They work 7-day weeks, so clearly they should take the 6% cut too.  If any of them are unhappy about this, I'll be very happy to fill in for them, and I'm sure that many others will join the queue to help embattled CEOs out.

I do, however, have an out for the pollies.  What you could do for shop assistants etc is  change the Sunday penalty rate, but at the same time, give them a 6% pay increase.  That way it would be fair, and not seen as a naked grab for cash by big business.

Sunday, August 2, 2015

Oooh! Oooh! I want that job!

Bronwyn Bishop, the ex-speaker of the House of Representatives has stood down.  She's quit because she couldn't figure out on her own that spending $5000 of taxpayers money so that she could make a spectacular entrance at a Liberal Party fundraiser was wrong.  Or that attending fellow MP's weddings was not government business.

But I don't want her job.  I want the job that decides if politicians expenses will be paid by the taxpayer, or not.  I figure its not a hard job.  So maybe pay me $70,000 per year (that is 14 helicopter flights to Geelong) and I'll do it.  Trust me, I have experience.  When I ran a small business (look, it was just me, so that probably makes it a micro-business), I used to claim mileage when driving down to Perth from the hills, because I would stop in at the Post Office and clear the PO box, and sometimes do the banking.  While this stuff had to be done, the real reason for my trip was usually to meet a friend, go cycling on the flats, or just go to the beach or a favourite coffee shop.  I mean, I did have to clear the PO box.

Even worse, when I lived in Wembley, I'd take the train to Freo and do the banking there, and claim the train ticket.  Well, I did have to do the banking, and it was too far to walk to the bank in Subi, so I reckon it was ok.  But when I got to Freo, I'd have a coffee and do the puzzles in the paper (as well as the banking).

So I know how murky issues of "necessary expenditure" can be.  I can truly appreciate how a politician can get personal and parliamentary business mixed up.

Give me the job.  Pollies would submit claims for payment, and those that I wasn't sure about, I'd put on social media.  After a week or so, the verdict would be in, and I could inform the polly of the public's decision.  It is their money, after all.  Too easy.