Why you can't travel faster than the speed of light

[lw24]

Hi all,

I've always wondered why you can't travel faster than the speed of light, and I suspect many of you do too. I always thought it was just a barrier in the universe, set by the laws of physics (which it is to some extent), however I never really knew the full understanding of it.

I found an article which explains it brilliantly, and I have cut out the best bits so that you can have a read. Enjoy

All credit goes to W.Daniel Hillis for writing this essay.

Einstein realized, to everyone one's surprise, was that energy and mass are also just two different ways of measuring the same thing. It turns out that just a little bit of mass is equal to a whole lot of energy, so in the equation, the conversion constant is very large. For example, if we measure mass in kilograms and energy in joules, the equation can be written like this: e = 90,000,000,000,000,000 m. This means, for example, that a charged-up battery (which contains about one million joules of energy) weighs about 0.0000000001 grams more than a battery that has been discharged.

It doesn't matter whether the energy is electrical energy, chemical energy, or even atomic energy. It all weighs the same amount per unit of energy. In fact, the equation even works with something physicists called "kinetic" energy, that is, the energy something has when it is moving. For example, when I throw a baseball, I put energy into the baseball by pushing it with my arm. According to Einstein's equation, the baseball actually gets heavier when I throw it. (A physicist might get picky here and distinguish between something getting heavier and something gaining mass, but I'm not going to try. The point is that the ball becomes harder to throw.) The faster I throw the baseball, the heavier it gets. Using Einstein's equation, e = mc2, I calculate that if I could throw a baseball one hundred miles an hour (which I can't, but a good pitcher can), then the baseball actually gets heavier by 0.000000000002 grams — which is not much. Now, let's go back to your starship. Let's assume that your engines are powered by tapping into some external energy source, so you don't have to worry about carrying fuel. As you get going faster and faster in your starship, you are putting more and more energy into the ship by speeding it up, so the ship keeps getting heavier. (Again, I should really be saying "massier" not "heavier" since there is no gravity in space.) By the time you reach 90 percent of the speed of light, the ship has so much energy in it that it actually has about twice the mass as the ship has at rest. It gets harder and harder to propel with the engines, because it's so heavy. As you get closer to the speed of light, you begin to get diminishing returns — the more energy the ship has, the heavier it gets, so the more energy that must be put into it to speed it up just a little bit, the heavier it gets, and so on.

The effect is even worse than you might think because of what is going on inside the ship. After all, everything inside the ship, including you, is speeding up, getting more and more energy, and getting heavier and heavier. In fact, you and all the machines on the ship are getting pretty sluggish. Your watch, for instance, which used to weigh about half an ounce, now weighs about forty tons. And the spring inside your watch really hasn't gotten any stronger, so the watch has slowed way down so that it only ticks once an hour. Not only has your watch slowed down, but the biological clock inside your head has also slowed down. You don't notice this because your neurons are getting heavier, and your thoughts are slowed down by exactly the same amount as the watch. As far as you are concerned, your watch is just ticking along at the same rate as before. (Physicists call this "relativistic time contraction.") The other thing that is slowed down is all of the machinery that is powering your engines (the dilithium crystals are getting heavier and slower, too). So your ship is getting heavier, your engines are getting sluggish, and the closer you get to the speed of light, the worse it gets. It just gets harder and harder and harder, and no matter how hard you try, you just can't quite get over the light barrier. And that's why you can't go faster than the speed of light.

Hope you learnt something, I certainly did!

Cheers

[chemtom24]

can i be a picky ****** and say that the speed of light is the speed limit of the universe, so light travels at this speed by default since it has no mass.

and time differences - ive only seen spacetime diagrams i think theyre called which say that you have a maximum quota to move along the space or time axis, so if you move alot along the space axis, ie move very fast, then you have little left for your time axis, therefore you experience slow time relative to a stationary object.

the particles having more mass and therefore moving slower in your body is an interesting view tho, makes you think about it differently.

was in no way trying to contradict anything or be picky, just trying to get a thread going on a subject i find interesting

cloudy nights.. (to unjinx everyones bad blumming luck lately!)

tom

[Earl]

from what i have read it would take an infinite amount of energy to accelerate a mass to the speed of light, hence impossible.

[Superewza]

from what i have read it would take an infinite amount of energy to accelerate a mass to the speed of light, hence impossible.

And yet if you had an infinite amount of energy then that mass would get infinitely large as it reached the speed of light...

[chemtom24]

brian cox either wrote or co wrote a book called why e=mc^2 (and why we shoudl care). read it recently, is well worth a read for anyone interested

[Earl]

humm

so if you can convert a mass into energy, beam it at the speed of light and reassemble the mass....

[chemtom24]

humm

so if you can convert a mass into energy, beam it at the speed of light and reassemble the mass....

can sense feynman diagrams cropping up..

[malc-c]

OK gonna show my ignorance here.. but lets just say I (or you or we for that matter) were in a craft traveling at the speed of light... If I turned on a torch would I see the beam of light out in front of me? If so then wouldn't that mean that the photons would of accelerated faster than light speed ?

[chemtom24]

OK gonna show my ignorance here.. but lets just say I (or you or we for that matter) were in a craft traveling at the speed of light... If I turned on a torch would I see the beam of light out in front of me? If so then wouldn't that mean that the photons would of accelerated faster than light speed ?

that question was dealt with in the above book i mentioned, tho i cant for the life of me remember what it said!! sadly i dnt have the book to hand.

either way, i think i remember somehtign along the lines of .. the light beam will always be a certain distance away from you no matter what speed you are going. think maybe because its a constant of the universe rather than 'how fast light can travel', im not totally sure on that tho. but this doesnt mean the light beam breaks the speed limit.

another thing to think about is that anythign like this is ALWAYS relative to an outside observer just as much as an inside observer. so what would an outside observer see? an outside stationary observer would see a beam of light

[Jack123456]

Reading this has made lots of rediculous and strange thoughts run through my head....

I am struggling with one condition.

If i am in a spacecraft traveling near the speed of light, that has no windows in it (so i have no reference to outside the spacecraft). would i be affected by it traveling near the speed of light? I would only be moving relative to the spacecraft.

Sorry if i haven't explained my question very well.

[adamsp123]

This is worth a read, explaining the concepts in a easily understood manner the results of the special theory of relativity and the question regarding this threads topic.

Mr Tompkins in Paperback: Containing 'Mr Tompkins in Wonderland' and 'Mr Tompkins Explores the Atom': Amazon.co.uk: George Gamow, John Hookham: Books

[chemtom24]

thanks adam, just got a copy for 7 quid posted. amazon is a dangerous place for me, could buy book after book after book after book after book

[rabbithutch]

Cox and Forshaw's book, why does E=mc² (and why should we care?) rests beside me as I type this. For the life of me, I can't get my brain around the concepts well enough to explain them; although reading what they write seems reasonable at the time of reading.

What has always puzzled me is that I somehow have the notion that light IS energy. Am I misinformed? If so, the equation seems a bit perplexing: A thing "E" is the same thing as its velocity squared multiplied by its mass? Does that mean that all energy has inherent velocity (I won't go into whether or not it is moving as we perceive it. I suppose we could posit that all mass is moving through space (or as I'm still trying to understand it, spacetime) and therefore has velocity. I'm still struggling with a thing becoming of greater mass as it travels at greater velocity. The descriptions of physicists - and their mathematical proofs - I cannot refute; but I cannot grasp it well enough to find an example to relate to. After all, we were all buzzing along happy as beans before Pythagoras or any maths. What if there are other fundamental properties not yet imagined and for which mathematical proofs can be found? I can accept, for now, that we cannot make mass travel faster than 299,792,458 meters/second; but suppose we measured velocity in terms of something other than time and distance (meters/second)?

I'm an old man and all this is much of a muchness to me.

[chemtom24]

yes light is energy and its energy can be determined from the formula E=hv where h is plancks constant and v (actually its the greek letter mu but dont know who to spell it lol) is the frequency.

a higher frequency means higher energy. this is why a blue flame is hotter than a red flame, and why x rays are harmful but radiowaves are not

[Big Jim Slade]

@rabbithutch: I think you've gone down a blind alley there. You're trying to apply an equation that deals with the relationship between mass and energy, to something that has no mass (a photon). E=mc2 by definition can only be applied to things with mass (I think; IMNAPhysicist etc.)

[toml42]

In response to the spacecraft traveling near light speed shining a light question:

As one travels closer to the speed of light, their subjective time is dilated - clocks will run slower for you than for a stationary observer. You won't notice anything different, of course, but if you look outside the window, everything appears to be happening in fast-forward.

light always travels at 299,792,458 m/s, no matter what speed the emitter is.

let's round this up to 300,000,000, for convenience, and say you are traveling at 299,999,999 m/s.

a stationary observer will say that the light beam moves away from you at 1 m/s, so far so good.

you however, in your reference frame - experiencing time dilation - have a subjective second 300,000,000 times slower than your stationary friend: so you still measure light as traveling at 300,000,000 m/s!

(This is not entirely physically accurate, as there is also length contraction to take into account, but it serves to demonstrate the general idea)

[adamsp123]

The E=mc^2 as I understood, relates to the amount of energy released if matter is destroyed, hence the awesome energy of an atomic bomb - a relative small amount of mass is destroyed releasing a huge energy blast.

Light travels a the speed of light regardless of the observers speed, Michelson Morley in an experiment 1887 proved this to be true. What happens is the frequency shifts - red/blue shift but the velocity of light in a vacuum is always c

The mathematics of special relativity shows that as matter travels faster its mass increases such that at the speed of light its mass would be infinate and hence require infinate energy, thus impossible, to accelerate it to c.

There are also significant time effects if one could travel near the speed of light, time itself run slower at these relatavistic velocities - see twin paradox.

Newtonian laws do not work at these extreme speeds, ok for normal life calculations eg moon shots/satellites etc but it is no good at relativistic velocities.

[Big Jim Slade]

I should have added: another great book about Einstein's equation is "E=mc2, The Biography of an Equation' by David Bodanis. It explains the physics very well, but is also a brilliant whistlestop history of the science that led to Einstein's annus mirabilis, touching on Faraday, Voltaire, Lavoisier, Curie, Planck, Meitner et al.

[adamsp123]

Then of course we have the duality of light when it behaves as a particle and not a wave just to make life "easier".

[Superewza]

@rabbithutch: I think you've gone down a blind alley there. You're trying to apply an equation that deals with the relationship between mass and energy, to something that has no mass (a photon). E=mc2 by definition can only be applied to things with mass (I think; IMNAPhysicist etc.)

Why do electrons have mass?

[jaquesnoir]

thanks adam, just got a copy for 7 quid posted. amazon is a dangerous place for me, could buy book after book after book after book after book

Does the total mass of the books you own affect how fast you read?

[toml42]

Regarding E=mc^2:

This equation is only valid for stationary objects! The true equation is rarely seen because it doesn't so neatly fit on a t-shirt or coffee mug

E^2 = (mc^2)^2 + (pc)^2

Where p is momentum.

I wonder if this helps with the conceptual difficulty you were having Rabbithutch? if we now apply this to light, which has m=0:

E^2 = 0 + (pc)^2

E = pc

This is a well known result from quantum mechanics.

If you're wondering how something with m=0 can have momentum, p can also be defined as planks constant (written as h) divided by the wavelength of the wave.

this gives us the relation between the energy of a photon and its wavelength

E = hc / wavelength

from this we can see that increasing the wavelength decreases the energy of the photon, so red light has less energy than blue.

[TFC]

Albert was certainly a smart fellow, but I can't get past the fact that it is only the THEORY of relativity.

The universe is larger than any of us can even begin to imagine and there's a whole lot we don't know, can't know or even begin to know.

Albert theorised we can't travel faster than the speed of light and so far, nobody has been able to dispute that theory, but it doesn't mean it's not possible - not so long ago it was thought the speed of sound couldn't be exceeded...........

I choose to believe anything is possible.

[Superewza]

E^2 = (mc^2)^2 + (pc)^2

Why would it be written like that? Surely:

E^2=mc^4+pc^2

Would make more sense?

[toml42]

that'd be E^2 = m^2c^4 + p^2c^2

It is sometimes written like that, but i find it neater to write it with the brackets because it allows you to easily think in terms of components, by analogy to Pythagoras:

a^2 = b^2 + c^2

you've got your rest mass term and your momentum term on the right, which you can think of as the vertical and horizontal sides of the triangle

then the energy term on the left is the hypotenuse - it feels more intuitive to me to think of it like that