May 12, 2005

Heavy as they hurtle

The Coca Cola logo, I read somewhere once, is the most widely recognized symbol in the world. (Considering I once found Coke in remote villages in Madagascar reachable only by a three day hike from the nearest town, I'm willing to believe that). Question: is there a scientific statement that might run Coke close, recognition-wise?

I don't know about "close", but one does come to mind, and I suspect it is at least known, if not understood, by hundreds of millions. I'm sure it came to your mind too: Albert Einstein's famous E = mc² .

In a time when every high school student is taught this as a routine part of a physics curriculum, it's hard to believe that when Einstein first propounded it, it was a revolution that turned the scientific world on its head. His theories shook those hoary pillars of physics, Newton's laws, mightily. Not that they were wrong, or at least, not wholly. But there were small, but troubling and significant, errors in how they explained certain phenomena. Only when Einstein came along were they satisfactorily explained.

Energy (E), Einstein tells us, equals mass (m) multiplied by the square of the speed of light (c). But what does that mean?

In essence, the equation says mass and energy are equivalent. If Celeste the elephant is moving, she has energy from that motion. That energy, being equivalent to mass, adds to Celeste's mass; that is, she becomes heavier. Not just that. Because she is heavier, it's harder to increase her speed -- it needs more energy to make her move even faster. Think of the effort you would put into pushing a SUV, and compare that to the gentle nudge a toy car needs to get moving (well, before my son gets at it). I'll take the toy, thank you.

Before you rush off to weigh yourself while running around at different speeds, hold on. A qualification is in order. The increase in mass is only noticeable at speeds close to the speed of light, a small matter of 300,000 km per second. Not even Carl Lewis runs that fast, so don't bother trying. This must remain a thought experiment.

Lumbering along at a tenth the speed of light, or 30,000 km/sec, Celeste becomes only 0.5 per cent heavier; if she weighed 1000 kg, she would now be up to 1005. But suppose she managed to ramp up to 90 per cent of the speed of light, to 270,000 km/sec? She'd be over twice her stationary mass.

That is, as Celeste nears the speed of light, her mass increases more and more rapidly. Which makes it more and more difficult for her to go faster -- she needs more and more energy to do so. And in turn, that adds ever more speedily to her mass. That's the energy-mass equivalence.

Will Celeste ever reach the speed of light? No, because getting there will need an infinite amount of energy, and there simply isn't quite that much around.

So Einstein's equation leads to this interesting conclusion: the only things that can zip around at the speed of light are those that have no mass to begin with. About the only such thing we know about is ... well, light. Einstein showed that other everyday objects -- your Carl Lewises, your suburban trains, your Celestes, your letters through the post -- are always restricted to speeds well below the speed of light.

And this is Einstein's central idea. The speed of light, said Einstein, is an absolute (about the only one around). Whoever you are, whatever you are doing, however fast you are moving, you will see light moving at the same speed. (And nothing can move faster).

A rather counter-intuitive idea, actually. Suppose you are in a car, rattling down the highway at 100 kmph. Going just slightly faster than you, let's say at 105 kmph, I overtake you in my car. As you wave frantically to me, it might strike you that I'm going rather slowly -- relative to you. At a mere 5 kmph, as a matter of fact.

But our mutual friend Shabnam, standing on the side of the road trying to thumb a lift, sees me going at a pretty fair clip. Relative to her, I'm doing that 105 kmph. Not the 5 kmph that you see. That is, you and Shabnam observe me travelling at different speeds.

However -- and this is the fun part -- if a massless Celeste trundled past at the speed of light, both you and Shabnam would see her moving at that speed. There would be no difference in her speed relative to Shabnam, and relative to you.

In other words, whoever measures the speed of light, however fast they themselves are moving, will produce the same figure. Now you know why Einstein called it the theory of relativity. Whether relative to a stationary Shabnam or relative to a speeding you, light moves at one speed.

Such a simple idea. But touched by genius, because of its revolutionary consequences. One of those is Einstein's energy-mass equivalence, as his equation spells out. There are others.

Einstein changed forever the way we look at gravity, at space, at time, even at our very place in the universe. Which is why, if there are other forms of life somewhere in the universe, it's a good bet they'd know about E = mc² before they know about Coke. So for now, Coke can rest on the laurels from remote Madagascar villages. When the aliens come calling, heavy as they hurtle through space, Coke might have to reconsider.


Postscript: I'm usually not inclined to take newspapers' internet polls too seriously. But yesterday's Times of India has the results for this poll they conducted: "Do you think planetary influences determine the outcome of people's lives?"

"Yes" beat "No", 61 per cent to 39.

Those numbers alarmed me. The occasional science column, like this one, is a small response to that alarm.


zap said...

Aah ! The science column starts to come at us more often. Goody.

As an aside, if Einstein had been a gym instuctor would e=mc2 have meant exercise=mass in motion?

I will let my theory on the TOI opinion polls rest easy, in case people decide to put mass in motion after being subjected to the torture.

Sunil said...

Yup....Coke will reconsider, ONLY when aliens land on earth.
I guess if they say "Take me to your leader", we'll have to lead them to Atlanta and the Coke CEO.

Anonymous said...

Recently one 'mass' moved faster than 'light'--but surprisingly with '0 energy'-- that is 'Sanjay Nirupam' from Shivsena to Congress

Kartik said...


Science is here, and the theory of relativity at that ... a good refresher / intro course to relativity Dilip!


Tagad_Tale said...

Some internet polls have pitifully low number of respondents. One easy way to check out whether the number is atleast 100 is by looking at the vote % before voting and after voting.

Try voting an option that is not usually chosen and check how the numbers change before and after the vote!!

Some polls do not even prevent multiple votes from the same person within a few seconds.


The Tobacconist said...

i did a course in pscyhology last semester and we had a section on human rationality. It turns out we aren't as rational as we credit ourselves as being (now do you really need a course to tell you that). In general many experiments have established that people don't even have a good notion of probability. In addition to this we work more generally using heuristics and our knowledge is usually far from scientific.

I would've been surprised myself had I not seen the evidence for the same. People tend to be irrational for a variety of reasons. One of the motivations is due to the bias of their beliefs. People would want planets to influence their lives because that way they'd have something else to blame their failures on. :)

Any how. Back to your science roots eh? Nice read.

***** said...

A comment on your Postscript:

A very good solution I believe would be to take a thick stick and beat the believers over their head and say "I bet the stars didn't see that coming"

There are a few problems to such a plan...I mean consider the number of sticks required if you had to do it. I would cause large spread deforestation. Suddenly the environmentalists would turn against you....99% of the people sympathetic to the environment live in the city so this would result in large scale bandhs and dharnas...causing medium and large BPOs and Software firms to take a beating...which in turn would affect the economy...I might even be out of a job. Too risky.

Pointless attempts at humor aside....good article on E=mc2. Liked it a lot. Also liked "Chutney..." quite a bit.

Anonymous said...

Well, I am here to nitpick. I think you missed the key thing about relativity that astounded scientists. It wasn't E=mc^2. If the speed of light is made absolute then time becomes partially ordered instead of totally ordered as one expects it. i.e. there exists two events e1 and e2 occuring at different places that happen neither before, together or after each other. There is no ordering between them. Certain people will see e1 happen before e2 and certain people will see e2 happen before e1, even after accounting for time taken by light to travel from e1 and e2. Also your 105 = 100 + 5 example is incorrect. Because velocities dont add up the way you expect them to thanks to relativity. So Shabnam never sees you travel at 105, but at 104.99... This is the crucial and most astounding aspect of relativity. Infact the equations for relativity were discovered much earlier twice by other scientists, one of them was Lorentz. But noone had the insight to see that bodies weren't shrinking as postulated by Lorentz but time itself was partially ordered.

Kartik said...


Everyone interested should pick up a copy of "E=mc2, A Biography of the World's Most Famous Equation" by David Bodanis ... amazing book!


Dilip D'Souza said...

Krishna, good point: I actually remember one poll where it was possible to tot up the number of respondents from looking at the voting percentages. And as I recall the total in that case was 17 whole votes.

Rahul, you are out of your job. I have informed your boss that you are on the net advocating mass assault with sticks.

Anonymous 345 am: you nitpick very correctly indeed. Good points. My challenge in these pieces is to explain some scientific idea in terms that everyone understands. That necessarily involves some simplifications and omissions.

Thanks for your thoughts, all! Perhaps I'll keep this science sideline going...

***** said...
This comment has been removed by a blog administrator.
***** said...

Now I doubt if I can be fired from my job...unless business takes a dive of course :)

Unknown said...

Bill Bryson's A Short History of Nearly Everything has this great explanation of Einstein's General and Special Theories. He uses the old ball and mattress form, so I guess it's just his style of writing that makes it great.