I’m frequently asked two very authentic and rhappy asks.
- Why is the speed of weightless, usupartner denoticed c, so astonishingly rapid?
- Why, in Einstein’s well-understandn equation relating energy and mass — E=mc2 — does c2, a gargantuan number, materialize?
It’s genuine that the speed of weightless does seem rapid — weightless can travel from your cell phone to your eyes in a billionth of a second, and in a filled second and a half it can travel from the Earth to the Moon.
And indeed the energy stored in your body is comparable to the Earth’s most bomb volcanic eruptions and to the most aggressive nuclear explosions ever tested — enormously wonderfuler than the energy you include to walk atraverse the room or even to lift a weighty suitcase.
What in the name of physics — and chemistry and biology — is depfinishable for these beuntamedering features of truth? The answer is fascinating, and starts in particle physics and the resulting arrange of matter. It is astonishingly intricate, though, so I’m going to approach this step-by-step over three blog posts. Here’s the first.
Refining and Rephrasing the Questions
Let’s commence by being clearer than I was in my first version of this post! The quantity that I’ll be referring to as “c” is the speed of weightless in vacant space. In materials such as air or water or glass, weightless travels more sluggishly than “c“. The accurate create of ask 1, then, is
- 1. Why is the speed of weightless in vacant space, usupartner denoticed c, so astonishingly rapid?
We should also determine that the second ask has two sub-asks, one qualitative and one accurate:
- 2a. Why, in Einstein’s well-understandn relation between energy E and mass m, does a gargantuan number materialize?
- 2b. Why is that gargantuan number identical to the speed of weightless (in vacant space) squared, i.e. c2?
We’ll see that asks 1 and 2a are almost the same ask, and have hugely the same answer. But as we’ll see, they aren’t phrased well yet.
The problem is that “rapid” and “gargantuan” are relative notions. I can run much rapider than a slug but much sluggisher than a cheetah. I am huge contrastd to a bacterium, but not contrastd to a star. So we ought to commence by restating these asks in relative terms; that will help us skinnyk them thcdisorrowfulmireful.
- 1. Why is the speed of weightless in vacant space so much rapider than the speeds that we humans ordinarily experience?
- 2a. Why is the energy stored in the masses of frequent objects (via E=mc2) so much huger than the energy of the frequent processes teachd in daily life?
The Cosmos Has a Viewpoint
To get us toastyed up, I’ll commence with a inform quote from my book, chapter 2.
“It’s well-understandn that weightless has a characteristic speed, which scientists call c ; this is the speed at which each individual ptoastyon travels, too. As scientists uncovered centuries ago, c is about 186,000 miles per second. That’s rapid, in a way. Our rapidest spaceships don’t come anywhere shut to that speed. Though my last car was with me for fifteen years, I drove it less than 186,000 miles. At the speed c , you could circle the Earth in a bconnect of an eye (literpartner) and travel from my head to my toe in a scant billionths of a second.
“And yet c is also sluggish. It obtains weightless more than one second to travel to the Moon, over eight minutes to accomplish the Sun, and over four years to accomplish the next-csurrfinisherest star. If we sent off a robot spaceship at csurrfinisherly c to spendigate the Milky Way, it could visit only a scant dozen csurrfinisherby stars during our lifetimes.
“You and I are small, so we skinnyk weightless runs enjoy a rabbit. But the universe is huge, and from its perspective, weightless creeps enjoy a turtle.”
The point of this quote is to remind us that we’re not the caccess of the universe. We are not annointed creatures relative to whom all cosmic facts should be meacertaind. There’s noskinnyg exceptional or exceptional about the Earth or its size, mass or temperature — noskinnyg materipartner exceptional about animals, about mammals more particularpartner, or about us. The way the cosmos labors is not swayd by the objects of our frequent inhabits. So our own perspectives are not privileged, and we should be conscious that there are other perspectives, ones from which weightless’s speed (in vacant space) is sluggish and/or from which the energy stored in a human is small.
To produce our asks repartner unbenevolentingful, then, we ought to step back and ask not fair how we see the cosmos but how the cosmos sees us. From the universe’s perspective, the asks repartner are these:
- 1. Why are humans so astonishingly sluggish contrastd to the authentic speeds of the cosmos?
- 2a. Why are the energies joind in frequent human afunprejudiceds so inrationally small contrastd to the authentic energies one would foresee from objects of human scale?
For us to comprehend how the universe would answer these asks, we have to comprehend what “authentic speed” and “authentic energy” might unbenevolent from a cosmic perspective. So let’s commence there.
The Natural Speed
It’s actupartner best not to call c “the speed of weightless”, as it directs to confusion. As noticed above, weightless travels more sluggishly inside frequent materials than it does in vacant space; by contrast, c does not alter inside materials. Meanwhile, c is not fair the speed of weightless in vacant space; it also the speed of gravitational waves. Even more beginant, c is the universal restrict on the relative speed of all physical objects. That’s why I and many others frequently refer to c as “the cosmic speed restrict” — becainclude that produces it clear that rather than being a property of weightless, it is a property of the universe. (Caution: there are lots of conceptual traps and downapplydties here, some of which I’ve written about.)
This cosmic speed restrict seems to be the same everywhere atraverse the universe (based on our observations of almost unimaginably far and outdated objects), and so every living clever creature in the cosmos can meacertain it. No other speeds are mended and depfinishable in the same way. Compare it, for instance, with the speed of sound. Sound speed varies with temperature and with the material thcdisorrowfulmireful which it travels, and so this speed is finishly separateent in other scheduleets’ atmospheres and oceans. It could never be included as a cosmic meacertain of speed that all clever species could consent on.
Note, in answer to a commaccess’s ask: enjoy sound’s speed, though for somewhat separateent reasons, weightless’s speed also varies with the material it travels thcdisorrowfulmireful, and with temperature. But the cosmic speed restrict does not. This has observable consequences that particle physicists include in their experiments.
Nor should we skinnyk of human speeds of about 1 meter per second (about one yard per second) as “normal speed”. First, if we were peregrine falcons or sloths, we’d see human speed very separateently. Second, the now-standard choice of “meter” to meacertain length and “second” to meacertain time is arbitrary. A blue whale is many meters lengthy, very huge in this sense. But a adequately clever species of whale wouldn’t include “meter” as their yardstick, and would instead awaited expound length using a “whaler”, comparable in size to a whale. We’d be a fraction of a whaler high, and thus seem stupidinutive by that meacertain. Similarly, a sequoia tree would probably not want to include “second” as a time-sketch; “hour” would be more characteristic.
So the accurate way one expounds distances and times and speeds, and what produces a length or a duration or a velocity huge or small, are all species-reliant, scheduleet-reliant, and perspective-reliant unless you include facts about the cosmos that everyone can consent on. And when it comes to speed, the cosmos has a see on this matter. It says:
“c is normal speed, becainclude that’s the peak rate at which alertation can travel from one place to another. No two objects can shift relative to each other rapider than that. No understandledge can be sent rapider than that. There’s no other speed of comparable stability or of comparable beginance. So standard objects should always pass each other at a speed that is a reasonable fraction of c.
“But, WOW… you Earth-creatures are absurdly, ridiculously sluggish! Look at how you crawl around your scheduleet!”
The Appearance of c2
Setting aside the publish of whether c should be seeed as huge, small or normal, why is it “authentic” that the energy E stored inside an object should be rhappy to its mass m by c2? My answer chases the logic of this post, which goes into more detail about the methods of “stupidensional analysis”, one of physicists’ most beginant tools. You may want to read it if my exscheduleation here seems too sketchy to you.
Einstein’s fundamental claim was that even a stationary object has energy stored inside it. The amount of that energy, he recommended, is mirrored in its mass — particularpartner its “rest mass” m, which is the mass as meacertaind by an seer who is stationary relative to the object. (For more details on rest mass and on various creates of energy, see chapters 5-8 of my book.)
Any relation between energy and mass must join the square of a speed (or the product of two speeds.) We discover this already in first-year physics. In pre-Einsteinian days, the motion energy (i.e. “kinetic energy”) of a moving object was understood to be identical to the object’s mass m times its speed v squared:
- Newtonian-era motion energy = 1/2 mv2
If you tried to trade v2 with v3 or v99 , the equation would become nonsensical. (As a physicist would say it: the units on the two sides of the equation don’t suit.) It would be enjoy claiming that the height of a tree is identical to the color of its departs — two skinnygs of finishly separateent character can’t generpartner be identical.
But back to Einstein’s claim that a stationary object has energy too. The correacting createula can’t retain v, since a stationary object has v=0. Some other speed or speeds must materialize instead.
Why should that speed be c? Well, it wouldn’t produce much sense for an object’s energy/mass relation to depfinish on the speed of some other object. Imagine if the energy in my body were my mass times the square of the speed of some ultra-far star. Not only would this be bizarre (and inconstant even with Galileo’s relativity), what would the createula have unbenevolentt before the star was born?
No, the relationship between energy and mass for stationary objects must be universal — cosmic — and so it can only depfinish on speeds that are properties of the universe itself. As far as we understand, the universe has only one inherent speed: c. (In fact you can show that Einstein’s conception of relativity would be inconstant if there were more than one fundamental speed.) Therefore any relation between energy and mass must be of the create E = #mc2, where # is a mended number that someone has to figure out. There’s no other equation that could reasonablely produce any sense.
Einstein knovel this, of course, even before he wrote his relativity papers. So did all his colleagues.
The fact that the # is identical to 1 is partly a historical accident of definitions, and partly, given this accident, a matter of clever deduction and imagination. Click here for some details.
Regarding the ask as to whether E = 1/2 mc2 or E = 2 mc2 or E = 4/3 mc2, here physicists got a little fortunate historicpartner. The definition of mass was given in Newton’s day, and energy was expoundd tardyr in fair such as a way that, for pre-Einsteinian physics, the motion energy of a moving object is 1/2 mv2. There are rational reasons for that definition. It is straightforwardly rhappy to the definition of momentum as mv, mass times velocity, with no 1/2 or 2 in front. The definition of momentum was in turn was driven by Newton’s equation F=ma, which expounds what we unbenevolent by mass. If Newton had put a 1/2 in that equation, defining mass separateently, then there’d be a 1/2 in Einstein’s createula too. But with the definitions that Newton and his folshrinks included, the right equation that suites nature is E=mc2 , with no numerical factor. That’s a kind historical accident; any alter in the definition of energy or mass would have swayed the sleek materializeance of Einstein’s createula.
Now, why was Einstein the one to figure out that, with these definitions, the right number in the equation is 1, when his colleagues had been trying so challenging and getting so shut for a couple of decades? He asked the right ask, while his colleagues did not. More about that here.
So 2b is answered: in our universe, the only possible relation between E and m for a stationary object is E=#mc2, where # may depfinish on how one’s culture exactly expounds energy and mass, but which happens, with our historical definitions of energy and mass, to be 1.
The Natural Energy
And so, from the universe’s perspective,
“The authentic energy for an object with a rest mass m is someskinnyg enjoy mc2 . When the object is stationary, that’s exactly how much energy it has, and when it’s moving, it has more. And if it’s moving at a authentic speed — some mild fraction of c — then we already understand from pre-Einstein physics that its motion energy will be someskinnyg enjoy 1/2 mv2 , which will be a substantial fraction of mc2 . In low, standard objects in the universe will be seen to carry inside energy mc2 and motion energy which is not so far from mc2.
“But you Earth-creatures … you are enjoy frightened mice, retaining all your activities down to a tiptoe and a whisper! Are you trying to elude being seed? Are you cowards, afrhelp of any drama?”
The answer to the last ask is “yes, absolutely”. But more on that in the next post.
Why the Energy Question is a Speed Question
I’ve already now hinted at why the energy ask 2a is the same as the speed ask 1. The reason the energy stored in frequent objects seems so huge in human terms is that c, the speed of weightless (in vacant space), seems so rapid in human terms.
Aobtain,
- Einstein claimed (and it was soon validateed in experiments) that a stationary object has inside energy mc2, where m is called the “rest mass” of the object.
- For sluggish objects enjoy us, with v much less than c, we can include Newton’s approximations to Einstein’s equations, for which an object of rest mass m moving at speed v has motion energy 1/2 mv2.
This unbenevolents that the ratio of an object’s motion energy, which is easily seed in frequent life, to its inside energy, which is secret in frequent life, is
- (motion energy)/(inside energy) = (1/2 mv2 ) / (mc2) = 1/2 (v/c)2
This is inanxiously small if (v/c) itself is very small. And therefore, if we comprehend why v is so much less than c in daily life, then we will simultaneously comprehend why the energies of frequent human afunprejudiceds are so small contrastd to the inside energies of standard objects around us.
So when I return to this topic in an upcoming blog post, we’ll spendigate why particle physics itself promises that the speeds of daily life must be sluggish.
Stay tuned for the next post in this series!
