Stephen Sekula – Page 32 – Going Up Alleys

October 1, 2011October 1, 2011

The Physics of a Dangerous Commute

Or, “How simple physics can keep you from killing somebody.”

The Problem

Lane jumping on the Dallas HOV system is deadly, and the laws of physics tell me so.

You are sitting in stand-still traffic in the fast lane of a commuter highway. You are impatient. You have an inflated sense of your own self-importance to the human race. Your job is so important to the fate of our species that if you don’t get to work on time the world might end. You make a decision. You are going to jump from the stand-still fast lane to your left, across a line of plastic barricades and into the currently empty high-occupancy vehicle (HOV) lane. You check your left mirror and see no cars in the lane within your field of view.

Not only are you breaking the rules of HOV lane usage (it is a violation to cross the barricade to enter or leave the HOV lane), you are dangerously ignorant of basic physics to the point where you are potentially about to kill or maim an individual.

The Physics – Stopping Distance

A car moving in the HOV lane at the maximum allowed speed (60 mph) requires a minimum distance to come to a complete stop. Let’s explore this problem with physics.

Let us begin with the kinetic energy (KE) of the car. This is given simply by the following equation:

KE = (1/2)mv²

where m is the mass of the car (in kilograms) and v is the speed (in meters per second). We need to convert the speed in miles per hour (mph) to meters per second:

60 mph = (60 mph) x (1/3600 h/s) x (1594.2 meters/mile) = 26.57 m/s

The mass of a 2-ton car, in kilograms, is 1814.36 kg. Thus a 2-ton car moving at 60 mph has the following kinetic energy, in Joules:

6.404×10⁵ J

This is the amount of energy that needs to be taken out of the car in order to stop it (bring its speed to zero meters per second). When you hit the brakes on a car, you are applying a friction force to the wheels to slow them. The wheels are still in motion, so they are working against kinetic friction from the brakes. Friction is a contact force, so depending on the contact area the force will be lesser or greater.

Let’s look at one specific case where the braking distance is made as short as possible. This is when the driver who must stop hits the brakes and locks them so that the wheels stop turning. The static friction that normally holds a point of contact between the wheels and the road now turns into kinetic friction as the wheels skid on the road. We need to know the coefficient of kinetic friction between rubber tires and a highway surface. In Dallas, this is concrete. Let’s assume dry conditions. The number is μ_k=1.0 [1]. The force due to kinetic friction between the car and roadway is given by:

F_k = μ_k(mg)

where m is the mass of the car and g is the acceleration due to gravity at the surface of the Earth (9.8 m/s²). The force due to friction, in Newtons, is then 1.778×10⁴ N.

How do we determine the stopping distance? A force like friction does WORK – that is, exerts itself in a direction opposite the motion along a certain distance – until all the kinetic energy of the car is gone and there is no more movement. All of the energy of the car is then expended overcoming the opposing force of friction. The equation that relates the two is:

(1/2)mv² = μ_k(mg) D

where D is the stopping distance (the distance over which friction acts against the motion of the car). So, what is D for a 2-ton car moving originally at 60 mph with rubber tires sliding on a dry concrete roadway?

D = 36.02m = 118.18 feet.

From this we conclude that if you, the driver who wants to jump into the HOV lane (which is already breaking a law), see a car in the HOV lane that is within 120 feet of your vehicle, then jumping into the HOV lane anyway is an intentional act of manslaughter, suicide, or both. If you are a terrible judge of distance, which you will be because those side mirrors distort distances (we’ll get to that in a bit), you should just stay where you are.

Please note! The above calculation assumed a dry day. If there is anything wet or slick on the road (water, oil, etc), this reduces the coefficient of friction. On a wet day, μ_k=0.3, which makes the stopping distance D under those conditions 3 TIMES LONGER. So instead of 118 feet, the car requires 354 feet to come to a complete stop. That’s almost a twentieth of a mile . . . !

Also, note that the mass of the car plays no role in the stopping distance – it cancels from both sides of the equation. So a Chevy Equinox, which weighs about 63% more than my Honda Civic, has the same 118 foot stopping distance.

Speed plays a huge role in the stopping distance. If a car is speeding in the HOV lane – going 70 mph, for instance, which is 17% faster – then since the stopping distance goes as the SQUARE of the speed the distance increases not by 17% but by 36% over the car at 60 mph. So the stopping distance at 70 mph is 161 feet!

OK, but let’s say you’ve looked in that left-side rearview mirror and see no cars in the HOV lane. Are you safe?

Human Reaction Time and the Speed of the Other Vehicle

Human reaction time is about 0.2 seconds. That means from the moment you decide to take an action to the time you physically initiate the action is about 0.2 seconds. So once you commit to illegally jumping into the HOV lane, it will be about 0.2 seconds before your foot presses on the gas and your hands turn the wheel to cut into the lane. What can happen in 0.2 seconds?

That depends on the speed of the vehicle you didn’t notice before you decided to make your move. How far can a car travel when at a speed of 60 mph?

That one’s easy. The relationship between distance, time, and speed is:

D = vt

so if the car in the HOV lane is going 60 mph (26.57 m/s) then in 0.2s it can travel 5.3 meters, or about 17 feet.

That doesn’t sound so bad, but what if the HOV lane in your mirror only sees back as far as the crest of a hill? By the time you start making your move, the car in the HOV lane will have moved 17 feet, which could easily bring it over the crest of the hill and into view. But now you, the driver jumping into the HOV lane, are not looking for a car anymore; you’re too busy spinning your steering wheel and hitting the gas to pull into the HOV lane.

You will accelerate into the HOV lane. How long will it take for you to cross the distance from the fast lane to the HOV lane? That’s a distance of about 1 car length, which for a full-size car is 5 meters. If you floor the accelerator on a typical car, how long will it take to travel the 5 meters into the HOV lane? Remember, we’re adding this to your reaction time, which was the time between when you decided to jump and when you physically began the steps needed to jump. So whatever we find here, we add 0.2 seconds (17 feet traveled by the car you didn’t see in the HOV lane).

A typical car has a maximum rate of acceleration of about 0.5g, or one-half the acceleration due to gravity at the surface of the Earth [2]. The relationship between time, acceleration, and distance is:

D=(1/2)at²

if one assumes that the acceleration begins from rest (v=0 at t=0). So how much time does it take to go the 5 meters into the HOV lane?

Solving for time, we find t = 1.4 seconds! Add to that your reaction time – 0.2s – and the whole maneuver (from deciding to go to making it into the lane) takes 1.6 seconds! And that is a best case scenario for a standard car – I assumed the upper range of acceleration for a full-size car.

So you’ve jumped into the lane. It took 1.6 seconds for the whole move. How far does a car traveling 60 mph in the HOV travel in that time? The answer is 136 feet. Holy crap! That’s more than the braking distance required for that same car. In the time it took you to execute a bad and illegal decision, any car already in the HOV lane might not stand a chance since it will travel further than braking distance in the time it takes you to execute your move.

So if you are going to be a dumbass . . .

Let’s review. A car moving at 60 mph in the HOV lane under dry conditions required 118 feet to come to a complete stop while skidding on the concrete roadway. So if you’re going to make an illegal jump into the HOV lane, you had better be a good judge of distance and know that the car already in the HOV lane is at least 118 feet behind you. But it’s worse than that, because it will take 1.6 seconds from the moment you decide to jump to the moment when your acceleration puts you in the HOV lane. In that time, a car in the HOV lane will go 136 feet. If you are then expecting that car to slam on its brakes and avoid hitting you, you have to plan even further ahead. Since the car in the HOV lane will travel 136 feet and then requires 118 feet to come to a complete stop, the minimum distance away that car should be when you decide to jump is 254 feet. Are you a good judge of distance to at least 254 feet? I’ll bet you’re not.

Oh, and guess what: the driver in the HOV lane is human, too. They also have a reaction time of at least 0.2 seconds, from the time they see you lane-jumping to the time they apply the brakes and go into a skid (unless they are anti-lock brakes, in which case the stopping distance will be elongated!). So that means you need to have judgement to a distance corresponding to 1.8 seconds (at least), which is 271 feet (your reaction time, plus their reaction time, plus the time it takes you to accelerate into the HOV lane, plus the time it takes for them to come to a complete stop by skidding on a dry concrete roadway).

Judging distance – objects in the rearview mirror . . .

Next time you check your mirror on the driver side, look for the message written on the mirror that reads, “Objects in the mirror may appear further away than they actually are.” That message tells you you’re really screwed, because the convex surface of the mirror causes a distortion of distance. This distortion allows you to see more than you otherwise would for a planar mirror, but it comes at a cost to your ability to judge distance.

Conclusions

Basic physics – energy conservation and forces – can teach us a lot about the quality of our decisions. From a legal perspective, it’s already a punishable action to jump into the HOV lane anywhere but at an entrance. From a physics perspective, you have to be able to be absolutely sure that any car behind you in the HOV lane is at least 271 feet away (and that’s the BARE MINIMUM to be safe – you probably want to be sure the car is more like 400-500 feet away to account for longer reaction times, lower acceleration of your vehicle, and the fact that the vehicle in the HOV lane is probably speeding (going faster than 60 mph). Are you a good judge of distance to 500 feet? Does the curving of the highway, combined with long lines of traffic behind you, even allow that kind of visibility?

People often argue that science cannot provide us with any kind of morality. I disagree. Jumping into the HOV lane, independent of human law, is a sign of complete immorality. By doing it, you are disregarding energy conservation and the effects this has on the lives of individuals in your car and in the cars in the HOV lane. Because energy must be conserved, and if it can’t all be put into working against friction, it will instead be put into compressing the structures of the cars involved in the subsequent collision.

For an independent view of this issue, see Ref. 3.

[1] http://en.wikipedia.org/wiki/Sliding_friction

[2] http://physics.info/acceleration/

[3] http://transportationblog.dallasnews.com/archives/2009/07/should-hovers-turn-in-cheaters.html

September 24, 2011September 24, 2011

Head Start

[This post was inspired by a comment in an article on PhysOrg, http://www.physorg.com/news/2011-09-cern-faster-than-light-particle.html. Thanks to Randy Scalise for bringing it to my attention.]

Supernova 1987a seen in visible and x-ray light — The expanding supernova remnant around Supernova 1987A and its interaction with its surroundings, seen in X-ray and visible light.

In 1987, a distant star exploded. Here on Earth, it was named “SN1987a” – Supernova 1987a. Here are some basic facts about SN1987a: it occurred (51.4 +/- 1.2) kiloparsecs from Earth, corresponding to a distance in meters of (1.586 +/- 0.037)x10²¹m, and we saw the visible light from the event beginning on Feb. 23, 1987.[1] [2]

Light travels at a finite speed. In the vacuum – completely empty space – that speed is 299,792,458 m/s (meters per second). The uncertainty on that speed is in the last digit, which represents a precision far greater than our knowledge of the distance to SN1987a. Therefore, in all future calculations the uncertainty on this speed will be ignored and numbers will be assumed to have uncertainties dominated by the distance measurement.

Once the light from the supernova collapse and subsequent explosion escapes the star, the time required to travel from SN1987a to Earth is (5.290 +/- 0.0736)x10¹²s. There are about 3.153×10⁷ seconds per year (fast fact: you can very closely approximate the number of seconds in a year by multiplying the number π, 3.14159…, times 10⁷s. That gives you 3.14×10⁷s, which we see is extremely close to the correct number). If we convert to years, the light from SN1987a required (167,800 +/- 3900) years to travel to Earth.

A recent preliminary, un-reviewed, unpublished, and unconfirmed result from the OPERA Collaboration suggests that neutrinos travel faster than light [3]. Specifically, within the framework of their measurement they find that the speed that muon neutrinos travel through the Earth from CERN to their experiment is (299,799,893 +/- 1,230) m/s.

Supernova collapse is known to lead to the production of neutrinos; in fact, neutrinos from SN1987a were detected by multiple neutrino experiments that were operating in the late 1980s. Based on the difference in speed between light and muon neutrinos, where muon neutrinos are measured by OPERA to travel at a speed EXCEEDING that of light in vacuum, let’s see when we would have expected the supernova-produced neutrinos to arrive at Earth.

Before we proceed, let’s note that we have a potential problem with this calculation – the uncertainty on the distance to SN1987a is HUGE. Our uncertainty on how long light took to travel from SN1987a to Earth has an uncertainty of 3900 years – that covers the entire period of human development back to ancient civilizations such as China and Egypt. Instead, let’s calculate the RATIO of travel times of light and neutrinos. We can then apply this ratio to any time period and evaluate the relative arrival times of neutrinos and light.

The OPERA paper actually provides this number. The ratio of travel times between neutrinos and light is:

(v-c)/v = (2.48 +/- 0.41)x10^-5

which means that the neutrinos arrive 0.00248% faster than light. What does that mean for SN1987a?

If we take the light travel time to be 167,800 years (exactly), then in that same time neutrinos take 167,796 years to reach Earth. That’s 4 years earlier than the light. What if, instead, the travel time was 3900 years less (one standard deviation DOWN). Then the travel time of light is 163,900 years and for neutrinos it is 163,896 years – again, 4 years earlier.

So the time difference, regardless of the ACTUAL time it took light to travel, is about 4 years. One would not expect neutrinos to accompany the light when the light reached Earth in 1987.

What was observed?

Here is the summary from the Wikipedia article on SN1987a:

Approximately three hours before the visible light from SN 1987A reached the Earth, a burst of neutrinos was observed at three separate neutrino observatories. This is likely due to neutrino emission (which occurs simultaneously with core collapse) preceding the emission of visible light (which occurs only after the shock wave reaches the stellar surface). At 7:35 a.m. Universal time, Kamiokande II detected 11 antineutrinos, IMB 8 antineutrinos and Baksan 5 antineutrinos, in a burst lasting less than 13 seconds. Approximately three hours earlier, the Mont Blanc liquid scintillator detected a five-neutrino burst, but this is generally not believed to be associated with SN 1987A. [4]

Neutrino interactions in the detectors were observed to increase in rate just before the light reached the Earth. This was consistent with the physics noted above; neutrinos are essentially free to leave the star once it collapses since the material density in the star is not sufficient to completely prevent neutrinos from leaving. Light, however, is trapped in the collapse until the blast wave reaches the surface of the star; this is at a later time than the nuclear reactions that produced neutrinos. So even though light travels slightly faster than neutrinos (due to the neutrinos’ small but non-zero masses), the light didn’t catch up before reaching Earth and the neutrinos arrived about 3 hours before the light.

So the time difference was just 3 hours, not 4 years. Of course, nobody was looking for neutrinos from SN1987a 4 years before it happened, but the fact that a burst of neutrinos was observed just hours before the light is evidence that the neutrinos were not too far ahead of the light. Calculations of the neutrino and light arrival times within the framework of core-collapse supernova modeling suggest that this time difference (neutrinos leading light) is not a surprise, given that neutrinos escape before light escapes the supernova.

Some criticisms of this calculation

This calculation assumed that the neutrinos produced by supernova are the same as those studied by OPERA. OPERA studies muon neutrinos. The neutrino experiments which detected neutrinos from SN1987a were sensitive to electron neutrinos. So all we can really say is that electron neutrinos arrived just hours before light. Muon neutrinos may have also been produced directly by SN1987a, or produced by neutrino mixing between the explosion and the time the neutrinos reached Earth. One could argue, therefore, that perhaps the undetected muon neutrinos arrived much earlier.
Nobody was looking for muon neutrinos from space/supernovas in 1983. That’s a hole in the argument, given that the calculation suggests the muon neutrinos would arrive 4 years before the light.

A comment on item #1: there is no evidence that electron neutrinos are so different from muon neutrinos. One would have to gather such evidence. In the meantime, one would have to postulate a mysterious and VAST difference in the speeds of electron and muon neutrinos.

Another comment: neutrino mixing is easily explained if neutrinos have mass. Mass prevents a particle from traveling at the speed of light in vacuum. If the OPERA result is correct, very little makes sense anymore regarding the Theory of Relativity, which has withstood precision tests for about a half-century. Certainly, it only takes one confirmed and reproducible measurement to bring a scientific theory into question. The OPERA result is neither confirmed nor even reproduced at this point. It’s not even published.

Conclusions

The neutrino is a mysterious particle. But so far, it hasn’t been so mysterious as OPERA would suggest. Data from SN1987a suggests that electron-type neutrinos arrived just hours before light, consistent with the different interactions neutrinos and light would suffer in the environment of a core-collapse supernova. This contradicts the expectation from OPERA, albeit that measurement applies to muon-type neutrinos.

Personally, I’m not holding my breath for this result. I’ll bet anybody $10 it’s wrong. And if instead I am wrong, I will pay up with a smile on my face and joy in my heart.

[1] http://heritage.stsci.edu/1999/04/fast_facts.html

[2] Panangia, N. “Distance to SN 1987 A and the LMC.” New Views of the Magellanic Clouds, IAU Symposium #190, Edited by Y.-H. Chu, N. Suntzeff, J. Hesser, & D. Bohlender. http://adsabs.harvard.edu/full/1999IAUS..190..549P

[3] http://arxiv.org/abs/1109.4897

[4] http://en.wikipedia.org/wiki/SN_1987A

September 5, 2011

Physics in Collision 2011

This is a brief report of what I learned from Physics in Collision 2011, held in Vancouver, British Columbia, Canada from August 28-September 1. I cannot cover everything here; I mention topics of interest to me and a few that are of general interest.

The Search for the Standard Model Higgs Boson

The Higgs Boson is the physical state that remains after breaking the electroweak symmetry in the Standard Model. This act of symmetry breaking is the key mechanism for introducing mass into the Standard Model. The Higgs, therefore, is a central prediction of the SM which has yet to be verified. Finding the Higgs is a key goal of particle collider programs at Fermilab (the Tevatron and the experiments CDF and D0) and CERN (the Large Hadron Collider and the experiments ATLAS and CMS).

The was no new information released at PIC2011, so what we know we learned in Mumbai at Lepton-Photon 2011 a couple of weeks ago. The Tevatron and LHC experiments have seen no convincing evidence of the existence of the Standard Model Higgs Boson, though people use words like “hints” to refer to regions of Higgs masses where the data measurement doesn’t agree perfectly with the “null hypothesis” – a treatment of the data where the analysts assume there is no Higgs at all. The Tevatron and LHC have delivered very large data sets which allow the experiments to reach or come close to the production rates predicted by the Standard Model. For the Tevatron, the results are based on samples up to about 3/4 the total expected data sample (~12/fb to be delivered by the Tevatron by its shutoff in October). For the LHC, the results are based on 1-2/fb, representing most of the data collected this year but only about ~1/3 the data expected by summer 2012.

The plots below were taken from talks by Jocobo Konigsberg (University of Florida, on behalf of CDF and D0 Collaborations) and Paolo Meridiani (INFN Rome, on behalf of the ATLAS and CMS Collaborations). They show in yellow the 95% upper limit on the production rate of Higgs bosons in the data sets. All experiments are punching through the SM predicted rate in wide ranges of Higgs mass, and based on the current data from all experiments it seems that most of the masses above about 140 GeV and below 115 GeV are excluded at 95% confidence level. There are regions in the high mass which are not excluded, but what seems clear is that all experiments are going to have sensitivity to these uncovered patched in the next year. That statement seems to also go for the region between 115-140 GeV, which is quickly turning into the most eagerly watched mass range for results since this seems to be the region where the “hints” I mentioned above are residing.

[nggallery id=1]

The Top Quark

Discovered in 1994 at the Tevatron, the Top Quark is rapidly become the new tool of the LHC. Its production rate, both in pairs and as single quarks (thus probing strong production mechanisms, like gluon fusion, and weak production methods, like W exchange, in more detail at 7 TeV collision energy). All experiments presented their latest results on top quarks through talks by Dave Mietlicki (University of Michigan), Dr. Francesco Spano (University of London), Yvonne Peters (University of Manchester), and Jenny Lyn Holzbauer (Michigan State University).

Understanding the proton in collision

Representation of a proton collision event

A fundamental ingredient in interpreting all new physics results at the high energies of the LHC is understanding how the proton looks when it collides with another proton at these energies. There were talks on QCD, jet production, and understanding the “underlying event” in proton-proton collisions. My favorite graphic (left) resulted from one of these talks: a cartoon of what the proton collisions “actually” look like when represented by Feynman-diagram-like images (from the talk by Richard Teuscher (University of Toronto)).

Searches at colliders for physics beyond the Standard Model

In short: nothing yet. If we had all been optimistic that new physics would rain from the LHC once it was turned on, reality has been a harsh truth. That isn’t to say that new physics isn’t there to be discovered. It is, however, fair to say that all the “low-hanging fruit” we expected to pick early and fast – the minimal Supersymmetric Standard Model (MSSM), or new heavy long-lived particles, or extra spatial dimensions, or quantum black holes – are not easy picking. It may be that new physics just won’t follow the conventions that have been expecting for the last 3 decades. Whatever the reason, the road ahead to discovering what lies beyond the Standard Model may prove a tricky one.

Searches for Dark Matter

Colliding galaxy clusters separate into their collisionless and interactive components, revealing dark matter.

There were a few talks on the status of searches for dark matter. These covered astrophysical measurements (Hendrik Hildebrandt, University of British Columbia), collider searches for dark gauge bosons (Matt Graham, SLAC National Accelerator Laboratory), and direct searches for dark matter scattering off atomic nuclei (Emilija Pantic, UCLA). My favorite talk was definitely by Dr. Hildebrandt, who gave a sweeping and well-written overview of gravitational lensing and the astrophysical evidence for dark matter as a form of matter. He showed the bullet cluster and other galaxy cluster collisions, evidence that galaxies contain collisionless components (stars plus dark matter) that contain most of the mass and highly interacting components (the hot gas that emits x-rays) which are separated visibly by the collisions of the galaxy clusters.

Dr. Pantic spent a lot of time explaining how recent results from CoGENT and DAMA/LIBRA have been interpreted – often in what seems like a strained way – to mean there is a low-mass dark matter constituent. Many other experiments, often with similar or better sensitivity in the same interpretive framework, have seen no such thing. Clearly, a lot more work is needed to understand what is going on. My favorite bit of news was that a new experiment, DarkIce, will run at the South Pole and look for the same physical effect as has been observed by DAMA/LIBRA, albeit with an independent collaboration and detector.

Neutrino Physics

T2K's electron neutrino appearance measurement.

The one place where revelatory discoveries have been made in the last 20 years – neutrino physics – was very much on display at PIC2011. There were talks discussing the measured properties of neutrino interactions (Ronald Ransome, Rutgers University) as well as the status of current neutrino experiments. Of interest to many in the audience was the T2K Collaboration’s recent publication: Phys. Rev. Lett.107:041801,2011, “Indication of Electron Neutrino Appearance from an Accelerator-produced Off-axis Muon Neutrino Beam,” http://arxiv.org/abs/arXiv:1106.2822. T2K is reporting an inconsistency in their data with the null hypothesis for the neutrino mixing angle, θ₁₃, which suggests that this mixing angle may be accessible to precision measurement by current beam and reactor-based neutrino experiments. I am VERY excited by this. It suggests, it it holds up under the strain of more data, that the reactor experiments will nail down this angle and the beam experiments can begin to probe CP violation in the lepton sector while further nailing down the angle.

Sensitivities of current reactor-based neutrino experiments.