One of the most useful, general tools in physics is symmetry. To a scientist, a symmetry is any change we can make to reality that is undetectable. For example, if I moved the entire universe five metres to my right, how would anyone know? All we can measure are the relative positions of objects, e.g. the Earth relative to the Sun. If I move the everything the same amount, then relative locations are unchanged. This is then a symmetry of nature. Hopefully, it is clear that there is nothing special about the distance and direction I chose; all such shifts are unobservable.
Why is this helpful? The key lies in Noether's Theorem, named after the German mathematician Emmy Noether. This states that whenever we have a symmetry in nature, there is a conserved quantity associated with it. Conserved quantities make our lives easier, since they simplify calculations. Amount in equals amount out is a pretty easy expression, after all. (Not all physics demands advanced mathematics!) For example, the symmetry I mentioned in the previous paragraph leads to conservation of momentum, while the fact that physics is constant in time means energy is conserved.
Friday, 25 May 2012
Sunday, 20 May 2012
Statistics
I'm planning another post on a recent research paper, but in preparation I want to talk about statistics. Specifically, I want to talk about Frequentist versus Bayesian perspectives for the interpretation of experiments. I won't get technical, or go into the actual details about how calculations are done, but rather talk about philosophy.
My casual impression, based on reading papers to stay abreast of the field, is that most experiments use Frequentist methods in analysing their data. In this approach, discovery of new phenomena is based on disproving the null hypothesis, the assumption that there is nothing to discover. In this sense, Frequentist methods are very Popperian. Frequentists will argue that this ensures their methods are objective, which is more or less true.1
The problem with Frequentism is that it has a tendency to be misinterpreted. For example, let's say in a particular experiment we can exclude the null hypothesis at 95% confidence level. What does that mean? It is tempting to interpret it as saying that there is a 95% probability that the null hypothesis is false. However, this is wrong. The strictly correct statement is: if the null hypothesis is true, the probability of getting this experimental result is 5% or less.
My casual impression, based on reading papers to stay abreast of the field, is that most experiments use Frequentist methods in analysing their data. In this approach, discovery of new phenomena is based on disproving the null hypothesis, the assumption that there is nothing to discover. In this sense, Frequentist methods are very Popperian. Frequentists will argue that this ensures their methods are objective, which is more or less true.1
The problem with Frequentism is that it has a tendency to be misinterpreted. For example, let's say in a particular experiment we can exclude the null hypothesis at 95% confidence level. What does that mean? It is tempting to interpret it as saying that there is a 95% probability that the null hypothesis is false. However, this is wrong. The strictly correct statement is: if the null hypothesis is true, the probability of getting this experimental result is 5% or less.
The Trouble With Travel
This little corner of the internet of mine has gone quite quiet for the last couple of weeks. The reason is simple; I've been travelling, and between the travel time itself, the jet lag and the things I've been up to at the places I've visited (conferences, meeting old friends) I've been unable to find the time to write anything worth publishing.
I'm currently in a relatively calm period, where I'm spending two weeks in the same place (visiting family). So I hope to get back into a somewhat regular publishing schedule for the next week. After that, I'm off to Warsaw for another conference, followed in turn by conferences in Vancouver and Calgary. So I likely will be posting rarely during those three weeks.
I'm currently in a relatively calm period, where I'm spending two weeks in the same place (visiting family). So I hope to get back into a somewhat regular publishing schedule for the next week. After that, I'm off to Warsaw for another conference, followed in turn by conferences in Vancouver and Calgary. So I likely will be posting rarely during those three weeks.
Monday, 7 May 2012
Hollande wins French Presidency
I haven't said anything about the French presidential elections, not least because I know little about French politics. However, the election of a socialist president for the first time in 24 years will be interesting. According to the BBC, Hollande describes himself as a moderate and was praised by former conservative president Jacques Chirac. Of course, this is France; Hollande has proposed a 75% upper income tax bracket (to apply to incomes above one million Euros).
I don't describe myself as a socialist, but I do tend to broadly align with socialist economic opinions. So I'm tentatively welcoming of this result. In particular, I hope it will encourage a reconsideration of the politics of austerity that have hit Europe in recent years. Times of economic recession are exactly the times that governments would be expected to run deficits. High poverty and unemployment mean that welfare spending should increase, while low tax returns cut government income. To be sure, too much government spending can lead to excessive inflation and make things worse. But I think things have swung too far against this.
Of course, ignoring Hanlon's Razor it's easy to believe that this is deliberate. The push for austerity and tax cuts by the IMF and other organisations seems tailor-made to benefit powerful corporations and wealthy individuals, at the expense of the poor.
I don't describe myself as a socialist, but I do tend to broadly align with socialist economic opinions. So I'm tentatively welcoming of this result. In particular, I hope it will encourage a reconsideration of the politics of austerity that have hit Europe in recent years. Times of economic recession are exactly the times that governments would be expected to run deficits. High poverty and unemployment mean that welfare spending should increase, while low tax returns cut government income. To be sure, too much government spending can lead to excessive inflation and make things worse. But I think things have swung too far against this.
Of course, ignoring Hanlon's Razor it's easy to believe that this is deliberate. The push for austerity and tax cuts by the IMF and other organisations seems tailor-made to benefit powerful corporations and wealthy individuals, at the expense of the poor.
Sunday, 6 May 2012
Dark Matter Found (or not)
So earlier this week I offered a brief overview of the Dark Matter problem. (See also the Font of All Knowledge for more.) Today I want to talk about a paper from two weeks ago relating to a possible discovery (or more accurately, hint of a signal).
Now, this is far from the first time such a hint has been found. The DAMA experiment is perhaps the longest-standing claim of discovery; that question, and why it's not widely accepted, is a whole blog post in itself. I want to start with this one because it is recent, and also most closely related to the work I have done in dark matter detection.
Now, this is far from the first time such a hint has been found. The DAMA experiment is perhaps the longest-standing claim of discovery; that question, and why it's not widely accepted, is a whole blog post in itself. I want to start with this one because it is recent, and also most closely related to the work I have done in dark matter detection.
The Heartland Institute Climate Denial Ads
Yesterday, the Heartland Institute put up some billboards comparing Global Warming to mass murder:
Thankfully they've already taken them down in the face of a torrent of criticism. But I couldn't comment on this yesterday, I was too angry and needed to calm down.
Thankfully they've already taken them down in the face of a torrent of criticism. But I couldn't comment on this yesterday, I was too angry and needed to calm down.
Wednesday, 2 May 2012
The Dark Matter Problem
One big and as-yet unanswered problem in modern physics is the dark matter problem. The problem is astrophysical: a number of observations, from galactic to universal scales, show a difference between the mass distributions observed directly (in visible stars, galaxies etc) and indirectly (through its gravitational effects). As the name of the problem suggests, it looks as though there is a lot of extra matter that we can't see (because it's dark).
The canonical example of such an observation is also the first one made (by the brilliant but prickly Zwicky), that of galactic rotation curves. In particular, let us focus on objects (stars, globular clusters) orbiting a galaxy but not really part of it. We are in the limit of weak gravitational fields and small speeds, so Newtonian mechanics is adequate. The gravitational force due to the galaxy drops off with the standard inverse-squared law:
$F = \frac{G M m}{R^2}$
Here, G is Newton's constant; M and m are the masses of the galaxy and the object orbiting it, respectively; R is the distance between them and F the force. Using Newton's second law of motion gives us the acceleration:
$a = \frac{G M}{R^2}$
Lastly, we use the relation between acceleration and velocity for objects moving in a circle:
$a = \frac{V^2}{R} ; \therefore V = \sqrt{\frac{G M}{R}}$
The main point is that we expect the speeds of objects orbiting a galaxy to decrease as they get further away from it. We can extend this for objects within the galaxy itself, but then we need to take the finite size of the galaxy into account. The result is that we expect the orbital speed to increase with distance within the galaxy, then decrease with distance outside it.
What we see looks like this:
The canonical example of such an observation is also the first one made (by the brilliant but prickly Zwicky), that of galactic rotation curves. In particular, let us focus on objects (stars, globular clusters) orbiting a galaxy but not really part of it. We are in the limit of weak gravitational fields and small speeds, so Newtonian mechanics is adequate. The gravitational force due to the galaxy drops off with the standard inverse-squared law:
$F = \frac{G M m}{R^2}$
Here, G is Newton's constant; M and m are the masses of the galaxy and the object orbiting it, respectively; R is the distance between them and F the force. Using Newton's second law of motion gives us the acceleration:
$a = \frac{G M}{R^2}$
Lastly, we use the relation between acceleration and velocity for objects moving in a circle:
$a = \frac{V^2}{R} ; \therefore V = \sqrt{\frac{G M}{R}}$
The main point is that we expect the speeds of objects orbiting a galaxy to decrease as they get further away from it. We can extend this for objects within the galaxy itself, but then we need to take the finite size of the galaxy into account. The result is that we expect the orbital speed to increase with distance within the galaxy, then decrease with distance outside it.
What we see looks like this:
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