My answer to If I’m on a plane traveling at the speed of light, can I walk to the front of the plane to go to the b…
Answer by Vishu Menon:
I am of the opinion that you should keep asking such questions to generate a debate among those who understand the relativity theory (mostly partially), and those who don’t. Unfortunately, Einstein is not among us and even if he were, this question would set him thinking. He was not a pretender to instant knowledge nor ever said his IQ was 160. He evolved his theories from the equations already developed by Newton, Maxwell, Lorentz and a host of many others and was not ashamed to make references to them, or even admit the “Greatest Mistake of My Life”. (A constant he invented to make some equations balance).
Theoretically, there is nothing wrong in assuming an airplane flying through space with the speed of light – at least as close to the speed of light as you would assume in a differential equation (dc). Einstein himself assumed many practically unattainable things to arrive at his Special and General Theories.
To arrive at most of his theories, he used an equation originally derived by Nobel Laureate Henric Lorentz and is known as Lorentz Transformation.
The expression on the left is simply a shortened version of the one on the right, v is the velocity of the moving body, and c, the most famous short for speed of light in vacuum. The expression on the right would seem innocuous when you fly in an airplane even at Mach2, but begins to turn terrible when your plane’s (or rocket’s) speed (v) begins to approach and then exceed some 90% of the speed of light(c). (Try sampling v/c= 99.99)
Now there are a few axioms on which the Relativity theory are based. (They are not mere assumptions; Einstein empirically as well as by mathematics).
- There is no absolute motion. Motion has to have a reference frame. (it can have many reference frames, including space as we know it. (Space with all the galaxies, stars and planet – before the big bang, there was no space and there was no time). Motion of a body has to be in reference to another body.
- Speed of light is the ceiling. Nothing can cross this ceiling.
- At speed of light, time stands still at zero.
- At speed of light, the mass of any body (other than one with no mass – a photon) becomes infinite.
- At speed of light, the length of a body shortens to nothing.
- By putting numbers closer and closer to the value of v (your plane’s velocity) to c, you will find that not much of these happens till you get too close.
With these in mind, we will assume a speed very close to the speed of light c (as they do in calculus – without goint in to the mathematics of it – try to analyse your situation
- The plane traveling very very close to the speed of light is your reference frame since you are moving along with it. So your own speed is zero. If you ever sat in the closed cabin of a smoothly but fast flying airplane with the windows closed, you would know what I mean. You hear the hum of the engines, but do not move.
- The plane will shorten to a foil (front to back-wise) of virtually zero thickness. I doubt if this will also happen to you since your relative speed is zero, However, since all your reference surroundings have flattened, you might flatten too and might not even be aware of the happening. Or you might get crushed to a film of no thickness. (You might then piddle a thin trickle without having to go to the toilet).
- The plane will assume a near-infinite mass. (near-infinite, assuming its speed is 0.0000000000001 Kms/S short of the speed of light. You might also assume the same mass, I guess. So a pico-meter thin person in a nano-meter thin plane, assuming a number 10 raised to several hundred zeros might not know the difference. I am not sure of this, though. Perhaps since your own velocity of motion is zero, you may not grow heavy, nor thin, and might burst or get crushed by the mass and by the thinness of the plane. ( Einstein did not think of a situation like this, that’s what his look says in this photo when I asked him – just kidding.)
4. However these things might turn out, and no matter how far your target star or planet, you will reach there in (virtual) zero time. Hence unless you lacked the common sense to start a journey after a visit to the toilet, you will not need to go to bathroom. In the plane, you’ll have no time. (For a friend or your spouse watching from the earth, it would appear to be a few years, depending on the distance to your target. When you return with the same uniform speed close to that of light, you’d still be of nearly the same age as you started, but your spouse, poor thing, would have gone old, toothless and senile. Figure that out.) Assuming your speed only approximates very closely to the speed of light (say 299,999.999999999 Kms/S), you will reach there in a fraction of a pico (10^-12) second. No time to piddle; not even to sneeze.
I am still a bit dizzy figuring this out myself and fearing that I could have got it all wrong. But when you find and get an offer of a lift in that plane, give me a call. If they took the risk of taking a physically helpless physicist of the caliber of Stephen Hawking in a Vomit Comet that rose sharply and plunged to zero-gravity up in the air, I can risk the humble me traveling in that crushing craft through unknown space.
Note : The terrific image of Einstein in a contemplative pose is from Madame Tussaud’s Wax Museum in Sydney.