The really clever ones will say that their total velocity is the vector sum of the velocity of the cab plus the velocity of the earth as it spins around its axis plus the velocity of the earth as it revolves around the sun plus the velocity of the solar system as it revolves around the galactic center plus the velocity of the Milky Way galaxy as it travels outward from the singularity that expanded into our Universe. This would be a very large number and a very clever answer, but it still wouldn't be close. [**]
One of the more startling conclusions of the theory of special relativity is that we are each of us individually and at all times, moving at the speed of light.
We know that each of us moves freely in three dimensions and forward-linearly in a fourth. The four dimensions are x, y, z and time.
It is easy to think about motion in terms of three dimensions. Newtonian mechanics does exactly this. Then Einstein came along and introduced the idea of space-time as a single fabric. The theory of Special Relativity states that each of us is, individually and at all times, moving at the speed of light. This is the only idea that explains time dilation.
This seems astonishing, but here's one way to visualize this.
Note: What follows below is not meant to be an intuitive proof, and certainly not a mathematical one. Also, it uses sex to get your attention.
Let's say that you are strolling in a park and this being your lucky day, you see this cute thang in a thong in the distance. You readily and randily figure out that she's about 100 yards away from you. You start running towards her at the speed of 1 yard per second to take a closer look at her
Now imagine a slightly different scenario. Same girl, same park, same distance, same loser...you. But this time, you are prepared. You are brandishing a shiny new toy that you picked up at the Radioshack: a LOX Jetpack. Humor me.
Wanting to impress the Fraulein, you fire up your jetpack and take off at a 45 degree slope from the ground. After traveling at the same speed of 1 yard per second and for the same 100 seconds, you stop and hover over the park. Anybody with basic spatial sense will know that if you now dropped a perpendicular from your position in the sky to the ground, you will find that you are still some distance away from the Fraulein.
You travel the same 100 yards in both instances. But you cover less ground in the second case. In the first case, all of your motion was in the x dimension--you traveled straight to the girl. In the second case, however, your motion was shared by both the x and z dimensions, i.e. you traveled both forward and up. To reach the girl within the same time in both cases, you would have to increase your speed in the second case.
You travel the same 100 yards in both instances. But you cover less ground in the second case. In the first case, all of your motion was in the x dimension--you traveled straight to the girl. In the second case, however, your motion was shared by both the x and z dimensions, i.e. you traveled both forward and up. To reach the girl within the same time in both cases, you would have to increase your speed in the second case.
The key idea here is that motion can be shared among dimensions.
We are each of us moving relentlessly in all four dimensions at the speed of light. But this motion is shared by all four dimensions. We inhabit a low-velocity world and therefore move quite slowly in the three spatial dimensions. Most of our velocity is in the temporal dimension. We are moving at nearly the speed of light through time.
Since the speed of light is the theoretical maximum speed at which any particle/wave can move, it follows that if we increase our motion in one dimension, there should be a corresponding decrease in our motion in another dimension. In the case of the girl in the park, we increased our motion in the z direction with the jetpack. This decreased our motion in the x direction and we failed to reach the girl.
Similarly, if we were to hop on board a really fast spaceship that was traveling at close to the speed of light in space, our increase in motion through space will decrease our motion through time. In other words, time slows down as we approach the speed of light. Time dilation occurs.
Time dilation has been observed experimentally [cf Hafele-Keating Experiment]. Time dilation occurs perceptibly for objects moving at near-light speeds. If you are a passenger on a spacecraft that is moving at a significant fraction of the speed of light, time will noticably slow down for you. Clocks on this spaceship will move slower relative to clocks not on the spaceship. Physical processes will slow down relative to other frames of reference.
In theory, it is possible for you or I to accelerate to near the speed of light. If we did that and since we are now moving faster and faster in space, we will have to "borrow" this motion from somewhere. And we'll have to borrow it from--you guessed it--the temporal dimension. This is why time slows down as we approach the speed of light. When our speed through space reaches the speed of light, our speed through time is zero.
A particularly interesting limiting case is that of a photon--a particle of light. A photon is always traveling at, well, the speed of light. Since all its motion is in space and at the theoretical maximum, it has no motion left in time. Time does not exist for a photon. It is, in a literal sense, immortal.
We are each of us moving relentlessly in all four dimensions at the speed of light. But this motion is shared by all four dimensions. We inhabit a low-velocity world and therefore move quite slowly in the three spatial dimensions. Most of our velocity is in the temporal dimension. We are moving at nearly the speed of light through time.
Since the speed of light is the theoretical maximum speed at which any particle/wave can move, it follows that if we increase our motion in one dimension, there should be a corresponding decrease in our motion in another dimension. In the case of the girl in the park, we increased our motion in the z direction with the jetpack. This decreased our motion in the x direction and we failed to reach the girl.
Similarly, if we were to hop on board a really fast spaceship that was traveling at close to the speed of light in space, our increase in motion through space will decrease our motion through time. In other words, time slows down as we approach the speed of light. Time dilation occurs.
Time dilation has been observed experimentally [cf Hafele-Keating Experiment]. Time dilation occurs perceptibly for objects moving at near-light speeds. If you are a passenger on a spacecraft that is moving at a significant fraction of the speed of light, time will noticably slow down for you. Clocks on this spaceship will move slower relative to clocks not on the spaceship. Physical processes will slow down relative to other frames of reference.
In theory, it is possible for you or I to accelerate to near the speed of light. If we did that and since we are now moving faster and faster in space, we will have to "borrow" this motion from somewhere. And we'll have to borrow it from--you guessed it--the temporal dimension. This is why time slows down as we approach the speed of light. When our speed through space reaches the speed of light, our speed through time is zero.
A particularly interesting limiting case is that of a photon--a particle of light. A photon is always traveling at, well, the speed of light. Since all its motion is in space and at the theoretical maximum, it has no motion left in time. Time does not exist for a photon. It is, in a literal sense, immortal.
I am taking a bit of liberty here. I think photon decay is a thing, but the physics of that is beyond my tiny brain. At any rate, even with photon decay, photons have incredibly long lifetimes. A billion billion years or sumsuch. That is way more time than the Universe itself has been around.
Each of us is moving at the speed of light. All the time. So the next time a police officer pulls you up for speeding and asks you if you know how fast you were going, you know what to say. Remember to say it with a straight face. You'll probably make his day.
[**] The Milky Way is moving at about 600 km/s towards the constellation Hydra. Compare that to the speed of light, which is almost 300,000 km/s.
[Ref: The Elegant Universe, Brian Greene]
Each of us is moving at the speed of light. All the time. So the next time a police officer pulls you up for speeding and asks you if you know how fast you were going, you know what to say. Remember to say it with a straight face. You'll probably make his day.
[**] The Milky Way is moving at about 600 km/s towards the constellation Hydra. Compare that to the speed of light, which is almost 300,000 km/s.
[Ref: The Elegant Universe, Brian Greene]
13 comments:
That is a lucid and great post. I have been studying Astronomy at school for the last 2 semesters and painfully trying to grasp these concepts! It is fun though, I love the subject - except when it comes to the exams!
Jyoti
Wonder if this also explains how fast we move in our careers.. :)
Are you saying if my job involves a lot of travel, I'll age slower?
:-))
Only if you are a very, very fast mover.
I was fascinated with astronomy from an early age. When I first learned about stuff like time dilation, my young mind went, "Cooool! Now if I can only figure out a way to travel at near-light speed, I can live longer."
As I grew older, I learned two things:
(1) A long life is not necessarily a blessing.
(2) Traveling at near-light speeds will not make me live longer. Not really. It's no accident that it's called the theory of relativity. It's all relative. I will age slower or live longer only compared to someone who is NOT moving at near-light speed. Within my own frame of reference, which is to say within my own spaceship, nothing will change for me. Time will not appear to be any slower. I will not get more done in less time. Within the same frame of reference, Newtonian physics applies with iron force. For all intents and purposes, I will live my regular life, which will be no "longer" than if I had inhabited any other frame of reference.
It is only when I descend to Earth and step out of my spaceship, I will not find any people I know because they will be long dead, having lived out their own equally "long" lives in a different and slower frame of reference. I gain nothing. Nature is not in the business of handing out free lunches.
we can safely rule out the possibility of traveling at the speed of light. At the speed of light, our mass becomes infinite and that is a natural barrier. We can either travel slower than the speed of light or faster, but not equal to. Heard of Tachyons?
Quantum Mechanics has pretty much changed the way we think about time and motion. I have often fantasized about time travel and other sci-fi aspects of QM when I was much younger, and even contemplated majoring in Particle Physics, Cosmology and QED. These are topics that are very close to my heart.
I dig tachyons.
So why didn't you take up Particle Physics?
Had to come to the US for that and it was not an option for me at the time.
Too bad. "Dr. Balajee" would have sounded waaay cool.
You would reconcile General Relativity with Quantum Mechanics. You would tame the tachyon. You would photograph the photon. You would boss around the boson. You would kick the quark in the ass. Three consecutive Nobel Prizes in Physics. At least. One for Peace thrown in just for being an all-around nice guy.
People would chant your name. I would drop your name.
Yes, I can see the banners now. Untold wealth, fame, and screaming teen groupies would have been your lot. Ok, maybe not the last.
Not to mention that fluttering thrill you'd feel every time someone came up to you and said, "So, are you like, a real doctor?"
My First Pome
Sitting at home with the flu
I have nothing to do
The meds are making me goofy
Can you tell me what besides "poo" rhymes with "do"?
Sougata "Soggy" Tennyson, Esq.
I don't know about all that, but those exact thoughts did cross my mind.. :)
How about taking a shot at writing a short story Issac Asimov style.. maybe you can write a sequel on that entropy story..
Visiting these parts after a long time. As I typed the URL, I wondered about the 777. Does that have anything to do with being one-up on the Devil?
On topic: The only quark I know is suffixed by an express :)
Thanks for stopping by. I am rather fond of the number 7 too. Three significant events in my life fall on 7th.
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