Arrow of Time in Wigton churchyard

 

For the first time ever I went into the secret garden behind the church. It turns out that there are some memorials on the outside of the church down there with musings about the nature of time. I assume that the quiver full of arrows represents the "arrow of time". This is a good bit of physics. Unlike any other concept in physics like for example forces, which can act equally well forwards or backwards, time only goes forwards. This is now usually explained as a consequence of entropy. We are headed from order to disorder, when averaged out across the universe.

An interesting wordsearch

 

This was in the Daily Express. I was very pleased. I'd never heard of Svedbergs. It is a non-metric way of measuring the size of particles based on their sedimentation rate.

Less evidence of desert sands in Wigton

 After finding lots of evidence of desert-blown sands in stone of a similar age in Ardrossan, I had a look at the sandstone blocks in Wigton. Most of them are structureless like the one below.

But I did find this one which has horizontal layers on top of slanted layers that might come from small dune fronts.

This amazing sundial is in the gardens at RHS Rosemoor. The curved lines are to cope with the different height of the sun in the sky at different times of year. There is a line for every 15 minutes. I was there at 12.15 BST.

Notice that there is a scale above it.

The top scale is consulted between winter solstice and summer solstice. The lower scale is for the second half of the year. Not sure why that is. Notice also that the other side of the stone is for the afternoon.

 

How long does it take for the disc of the Sun to disappear?

 

I was stood on the beach at Croyde hoping to see the Green Flash at sunset. It occurred to me to time how long it took from the bottom of the disc touching the water to the top of the disc finally disappearing. The Sun subtends an angle of 0.5 degrees at the eye. 360 degrees of rotation in 24 hours means 15 degrees per hour or 1 degree of movement every 4 minutes. (The true answer needs to take into account that the Earth is moving around the Sun as well as spinning on its axis. I have simplified it down) Anyway, that meant the Sun should disappear in 2 minutes. I timed 3 min 30 seconds. That couldn't be explained by the reason given above. Looking it up online, it says that the time depends on how far away from the Equator you are and what time of year. It seems to be that 2 minutes would be fine on the Equator at a time when the Sun is going down perpendicular to the horizon. But that isn't the case in the UK so the Sun must be moving diagonally across. I need to think about how that makes the angular movement different for a circular object.

New style of electricity pylon

 

We spotted the new-style electricity pylons from the M5 near Bridgwater. It turns out that the change has been made to make them less of an eyesore - they are much shorter than previous pylons. Read about it here.

Partial eclipse

 I set up my telescope in Wigton to project the partial eclipse at about 10.15am. It was even more impressive in Penrith an hour later. Obviously not visible to the naked eye but it was hard to tell if the noticeable dimming was due to the moon or the high cloud - or both!

Thinking Physics in the hot tub

 

I was doing all right with a temperature of about 35 degrees until the bubbles were turned on. This created a greater surface area for evaporation and the extra warm water vapour round my head nearly caused me to faint!

Evidence of desert sand in the walls of Ardrossan

 

The sandstone in the Ardrossan area was deposited in the Permian period when Britain was in a desert region above the Equator - the zone currently occupied by the Sahara Desert. It's the same in the Wigton area. I have seen these slanted lines in deposits near Appleby. They represent the outlines of dunes. It is interesting that there seem to be natural horizontal lines through as well. Maybe earlier deposits were weathered flat and new deposits formed on top.

Quantum guitar

 

I've been reading Jim Al-Khalili and Johnjoe McFadden's book on Quantum Biology. They use the idea of stringed instruments to highlight the difference between the classical and quantum understandings. I'm a guitarist - it's easy to hit the right note because there are frets. I can be a centimetre out with my finger and it doesn't matter. With a violin, slightly out means a slightly different note. There is continuous variation through the frequencies. This isn't true with the guitar. Only certain frequencies associated with the frets are allowed. That means the guitar is quantum and the violin is classical. That's appropriate, perhaps!

Ketchup

Another thing that Helen Czerski produces a very clear explanation for is why ketchup only moves when you bash it. Apparently there are cross-links between the molecules that give it some of the properties of a solid. When bashed, the forces are enough to break the cross-links and allow the molecules to flow over each other as in a liquid.

Colours on the fidget spinner

 

I was handed this fidget spinner and found that it was more fun to spin the middle - the bit you hold with your fingers. When spun fast, this is what you see

The colours almost mix to make white. The spiral design is interesting because it should mean that every radius has the same mix of colours.

As it slows down, the colour spiral re-emerges but this time as continuous colours, not as the discrete blobs you see when it is stationary. This must be due to the persistence of vision phenomenon - the time delay for rod and cone cells to refresh.

Why is it brighter under a rainbow? Part 4

 Doing the maths on the two simultaneous equations produces a curve like this. The deviation angle cannot be bigger than 180 degrees but has a definite minimum. Notice that there is a range of other angles of incidence close to the minimum which will have almost exactly the same deviation - they will come out along the same path.

Here's an attempt to show it. There are 3 rays that come out close together but notice that the outliers A and B both end up ABOVE those 3 rays. That's a consequence of it being a minimum.

This grouping of those 3 rays together coming out along the same path is apparently called the RAINBOW RAY - a reinforcement. Now the rainbow ray is wavelength specific - it is different for each colour because each wavelength has a different refractive index and thus is bent by a different amount. 

The final bit that it took me some time to comprehend is the idea that raindrops fall. If my eye is lined up with the direction of the rainbow ray, I see a colour. The drop has to be in a particular place. If it is above that point, notice that no light comes out of the drop below the rainbow ray so I won't see it - it looks dark.

However, a drop below the rainbow ray will send light to my eye. It will be the rays I've labelled A and B. You get these rays whatever the wavelength, so there is a mixing and it appears white. That's why it looks brighter underneath a rainbow. I got there in the end thank to https://plus.maths.org/content/rainbows

Why is it brighter under a rainbow? part 3

 

To complete the deviation analysis we need to eliminate one of a or b by coming up with another equation linking the two. This is the Snell's Law equation. I have given it here in the version that makes most sense to me. Medium 1 is air so refractive index n1 = 1. My source also makes explicit something that was bugging me when I was thinking about thin film interference: yes, different frequencies do have different refractive indices in the same medium, otherwise there would be no spreading of the spectrum.

Why is it brighter under a rainbow? part 2

 

The next bit to consider is called the deviation of the ray. One red ray is going into the water droplet top left heading down and right. It emerges after refracting twice and reflecting off the back of the droplet to head down and left. It has been turned but by how many degrees has it been rotated? This is the deviation. The red dotted line at the top shows the original direction. The ray is pulled out of line by (a-b) at this point. It is then bent back on itself. The internal angle is 2b but the rotation is 180 degrees less 2b. Finally there is a bending by another (a-b) coming out. This adds up to a total deviation D of (a-b) + (180-2b) + (a-b). The derivation of this is critical to the analysis I'm following from this site and was one of the bits I didn't really understand. 

Why is it brighter under a rainbow? part 1

 

You can see from the picture above that the sky is clearly much brighter underneath a rainbow. I started trying to find out why about 5 years ago but found the optical geometry hard and then other stuff got in the way... So I found my way back to my source and have been forcing myself to work through the examples so that I understand what is going on. I started with what is happening inside a water droplet

The black circle is my water droplet. The black radial lines are there because they are normal lines used in the geometrical optics. A ray of light hits the drop at X. Water is optically more dense than air so on entering the drop, the light slows down and bends towards the normal line. Angle alpha > angle beta. There is a reflection at the back of the drop at Y so angle of incidence = angle of reflection. Then exiting the drop on the left at Z is symmetrical to what happened at X.

Where is a relection?

 

A text book will tell you that the reflection is the same distance behind the mirror as the image is in front of the mirror. This can be proven using ray diagrams. I always used to like to use a set up like the one above to use the partial reflection in a pane of glass. I used a safety screen so it was easy to measure in front and then push a ruler behind the reflection. Not so easy to do from the carriage at Bassenthwaite Lake Station!

Vector field at Spout Force, Whinlatter

 

They have felled trees at Spout Force. It reminded me of a vector field like the drawing of arrows to show compass directions for a magnetic field. The trees could be said to show magnitude by their length and also direction. Thus the field would be uniform on the right but on the left the directions vary. Perhaps it is a grad field, showing the magntitude and direction of the slope.

How wide has the contrail become?

I noticed this plane flying close to an earlier contrail that has expanded and been blown. If the plane were 50m long, then the contrail would be maybe 600 to 700m wide. I think it fair to assume the contrail and the plane might be at the same height. I wonder how long it takes to get this wide.

Bourdon Gauge at Bassenthwaite Lake Station

 The central gauge on the train at Bassenthwaite Lake Station bears the name "Bourdon".

The train is a replica built for Kenneth Brannagh's Murder on the Orient Express film. I am familiar with Bourdon gauges for pressure but I had never stopped to consider who Bourdon was. The principle is that the gas is in a flexible metal tube. When the pressure increases, the metal flexes more and that is geared to a needle which goes round a scale which can then be calibrated. Putting the name Bourdon onto the gauge is a nice touch.

Scattering on the Arran Ferry

 

The salt on the window made the scene seem misty. The particles scatter the light meaning that it looks more like white light is coming from all directions. It's a version of what goes on inside a cloud.

Another corona around the Moon

 

The Moon was shining through high cloud producing a clear corona. To my eye, there was a clear red outer edge to it but viewing the photos, you'd take some convincing. I re-read this article about the phenomenon. I'm not sure I'd noticed before that this diffraction pattern is an Airy Disc. I know the Airy Disc as the bright central view through a circular aperture such as a telescope. Unlike with the refraction halos, there is not set angular width here apparently, as it depends on the droplet size. Given that the Moon subtends 0.5 degrees at the eye, I'd say here the corona subtends 1.5 degrees.

Counterweights on a tractor

 

These iron blocks are 5cm wide and 50cm long. I'm estimating about 25cm deep. That means a volume of 6250 cubic centimetres. The density of iron is 7.9 grams per cubic centimetre. The mass of one block is therefore 49375 grams to too many sig figs. Since I'm extimating, best to say 50kg. There are 8 of them. That means 400kg. Not quite half a tonne!

What would be the mass of ATP needed to run the Basal Metabolic Rate?

 

The book is way too advanced for me but I have really enjoyed the scientific justification for the training programmes. There's a claim in the book that if we didn't recycle ATP, we'd need 60 - 70kg a day just to run the resting metabolism. ATP is C10H13N5O13P3. That means 1 mole has a mass of 504 grams. So 70kg would be 140 moles. I looked up the energy release for ATP to ADP. The two commonly quoted figures are 7300 calories per mole and 12000 calories per mole. Sources seem to say that the latter figure is for inside the body. So 140 moles x 12000 = 1680000 calories. Now the problem with calories is that when people talk about calories in food, they mean kilocalories. So that's 1680 kcal which is close to the figure of 2000 kcal that I was taught a human really needs each day. There. It works.

Rolling thunder

 

Once again, Helen Czerski's book Storm in a Teacup has got me thinking about simple ideas that I'd never considered. She tackles the idea of why thunder is often a prolonged rolling sound. The answer is to do with the distance away. The sound is made from all points on the tall discharge but because sound travels so much slower than light and the distances are big enough to make a difference, the sound from the top of the discharge arrives later than the sound from the bottom. In the example above, if sound travels at 330m/s, it will take 6.1 seconds for the sound to arrive. From the top it would take 6.8 seconds. That is a noticeable difference. However, I think that the further away you get the less the difference will be. Perhaps I'm not understanding this correctly.

Gaia at Greenbelt - why is it a blue planet?

The Gaia installation was at the Greenbelt Festival and was especially effective when illuminated at night.

They call us the blue planet. I have been very interested in Helen Czerski's brilliantly clear explanation of why water that comes out of a tap colourless actually looks blue when in the sea. It's in her book Storm in a Teacup. She explains that light entering the water is bounced around, heading mainly downwards but that eventually some is reflected back up out of the water and that is what we see. She explains that water molecules are able to absorb the other colours if the water is deep enough but not blue, so that is what we see. My next thing is to try to find out why water prefers to absorb red and not blue.

 

Looking for a parallel road above Mitchellslacks

 

Parallel roads are the old shorelines of glacial lakes, relics of the Ice Ages. I've never been to Glen Roy so I was excited to read in Ronald Turnbull's Cicerone guide to the Southern Uplands that one was visible from the route up Queensberry. It does have a rough road along it - the vehicles of a shoot are just visible - but it is a natural feature. He points out that there are more streams coming down the hillside to that line than there are continuing down the hillside below the line - a sign of an ancient boundary.

Looking for an anti-reflective coating

 Researching about thin film interference brought up the idea of anti-reflective coatings for glasses. This page says that they can produce colours at oblique angles. I noticed these reflections.

The concave side shown above produces multiple images. I think that is because it has a wider field of view but I'll need to draw a ray diagram to prove it to myself.

The convex side is shown above. I'm not sure I'd describe the angle as particularly oblique but the white lights do come out as green. You get double images which must be reflections from top and bottom surface. The lens on the left is thicker which probably explains the bigger distance between the pair of images.

Imaging: working out what's inside (with a knife!)

 

Mrs B pointed out that if you slice an apple across the equator, you get a star. I didn't know that. She then pointed out that this is like imaging for medical purposes or for finding out what's inside an atom. What you see depends on which way you slice it - a pole to pole slice of the apple doesn't give a star cavity. Good imaging needs lots of slices in different orientations stitched together.

How to work the poles on the ends of a solenoid

 We think this is supposed to be a bike rack but it looks like a solenoid:

If the current flows into the solenoid at this end, it goes anit-clockwise. Drawing arrows onto a curvy stylised N points anticlockwise so this is the North pole.

The current must be coming out at the other end meaning current flows clockwise. Adding arrows to an S points clockwise. This end is a South pole.