If a car travels at the speed of light and turns headlights on what happens?

Visage said:
OK. lets clear this up.

For ANY observer, light will always travel at c. No ifs, no buts, no maybes.

Always.

Apparent paradoxes like 'What ahppens if you turn the lights on while travelling at c' are a result of applying galilean transformations to objects in relative motion - simply put, saying 'If object A travels away from me at 10 mph in a given direction, and object b travels away from object a at 20mph in the same direction, then object b is travelling away from me at 30mph'.

That doesnt work when the magnitude of velocities involved approach c. The basic reason for this is that velocity of an object in a given frame is defined as the rate of change of distance with respect to time of that object, in that frame.

The simple derivations of SR between inertial frames shows that, in frames moving with respect to an observer, time is observed to flow at a different rate than the frame in which the observer is situated.

It is the notion that conversion between frames is galilean that creates the apparent paradox. Once you use lorentzian transforms the figures resolve themselves and all is well.

(The apparent contradiction between high speed - lorentzian and low speed - galilean is reconciled by the fact that the lorentzian transform reduce to their gallilean counterparts for small values of v).
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Didn't i try to explain something like this, but without the funny words? (any word with a Z just aint right!)

Might have been a bit simplified but i think it sort off had the gist.

What i'm now interested in is for massive objects momentum is m(u)*u

what values does the m and u represent?
 
callmeBadger said:
Didn't i try to explain something like this, but without the funny words? (any word with a Z just aint right!)

Might have been a bit simplified but i think it sort off had the gist.

What i'm now interested in is for massive objects momentum is m(u)*u

what values does the m and u represent?
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Its a shorthand way of saying that m (mass) is now a function of u (velocity)

Specifically,

m = m0 * (1 - (v/c)^2)^(-1/2).

Where m0 is the mass at rest.

So if v = 0.5c, m will increase by about 15% (if my frazzled friday afternoon maths is correct).

This in turn is why attaining c is impossible for anything with mass - as v approaches c, m tends to infinity.
 
The biggest problem with people understanding this question is that they don't take into account that the flow of time will be different for the person in the car compared to someone watching from the outside who is stationary*.

Since the car can't go at the speed of light (bit of a flaw in the question) let's assume it's going a tiny fraction slower than the speed of light.

Now we can compare the observations of the two people:

In the car: He's happily driving along and turns his headlights on. He sees the light go out in front of him at the speed of light just as you would if you were driving at 30mph, it's no different from his POV at all.

Observer: He sees the car woosh past at very nearly the speed of light. The light from the headlights is going ever so slightly faster than this, 299 792 458 m / s to be precise, the speed of light.

Suppose there's a clock on the dashboard. The person in the car sees it tick over every second just like a clock should. The outside observer (who apparently has super fast reaction times and amazing eyesight) sees this clock tick over maybe something like once every 10000 years (Apparently the observer also has a very healthy lifestyle to live so long).

I'm sure there's no extra information in this post but hopefully it'll help a few people understand.

*technically there's no such thing as stationary but we can compare all velocities relative to this person.

edit- one more point, the observer will also see an incredibly thin car because that's another effect of travelling near c.
 
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Amleto said:
and a rotated car, and a different colour car.... :p ;)
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The colour would change so much it wouldn't even be visible anymore :p
Rotation? That's a new one to me. Rotated in what way?
 
Amleto said:
If a bystander is watching a car travelling at c, the bystander will not know when the car's lights turn on, since the light (from the headlights) cannot go any faster (and therefore never appears to leave the headlight) relative to that bystander.

On the other hand, the driver will know exactly when the lights operate, as he will see the light extend from the front of the car.
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I'm sure you're right but I can't get my head around that second part. Is a light "particle" (photon?) travelling at the SOL different from an object with mass travelling at the SOL? Say he pulled out a gun inside the car, aimed directly forward and fired a bullet at the SOL. Is this bullet also going to extend/travel out on to the road or will it just float next to him in the cab? I'm thinking of the headlight as firing out photon bullets. :D
 
the car would explode IMO. you'r traveling at the speed of light. You turn your lights on. The packets of energy (eg light) are going to get stuck in your headligh and just keep building up untill it melts or burns a hole all the way though your car..
 
Visage said:
now my BRANE HURTS.
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Tee hee. Was that deliberate?

Anyway, what happens is that you end up dividing by zero and everything blows up in your face. Cause the gamma factor, g, is

g = 1/Sqrt(1-v^2/c^2) ,

and if you whack v=c in there you get into a world of pain. FACT.
 
wush said:
I'm sure you're right but I can't get my head around that second part. Is a light "particle" (photon?) travelling at the SOL different from an object with mass travelling at the SOL? Say he pulled out a gun inside the car, aimed directly forward and fired a bullet at the SOL. Is this bullet also going to extend/travel out on to the road or will it just float next to him in the cab? I'm thinking of the headlight as firing out photon bullets. :D
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Light particle = photon. FACT :D

Think of your gun as an electron that you excite (fire) - when it 'un excites' it emits a photon (bullet) :)

If you're in the car and fire the gun, your photon will shoot off at SoL (mixed mataphors :D ) relative to you.

If you watch some guy, in a car travelling at (a smidge under) c, fireing a gun, it's a different story - the photon will be travelling at c relative to you.

Most people might think that that would immediatley lead to a contradiction, but they are not taking into account that each other's perception of time is not necessarily coincident.

HTH :)
 
wush said:
I'm sure you're right but I can't get my head around that second part. Is a light "particle" (photon?) travelling at the SOL different from an object with mass travelling at the SOL? Say he pulled out a gun inside the car, aimed directly forward and fired a bullet at the SOL. Is this bullet also going to extend/travel out on to the road or will it just float next to him in the cab? I'm thinking of the headlight as firing out photon bullets. :D
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The difference is in the perception of time. One thing you have to remember is that whatever speed you are going, everything will seem normal.

Because time is flowing slower for the person in the car (compared to the bystander) BOTH people see the light travelling at 299 792 458 m / s.

For example this is how the bystander will see time flow if you compare a clock on the dashboard to a stopwatch he is holding:
1 second on the dashboard clock = 10000 years on stopwatch.

Of course these numbers are just plucked out of thin air but the theory is there.

I think that Einstein figured out all these crazy effects like time slowing down, distances contracting, colours changing, etc. from the simple fact that light appears to travel at the same speed (relative to your own speed) whatever speed you are travelling at.
 
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Thanks for the insight, guys. I didn't consider time.

I guess I'm too used to thinking of things in a simplified virtual/programming world, where every object is going to have an absolute speed in a common "world space" and share the same "time domain" :)

Also, anyone who gets in the way of the car is going to be SOL too - **** outta luck! :D
 
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Psyk said:
I think that Einstein figured out all these crazy effects like time slowing down, distances contracting, colours changing, etc. from the simple fact that light appears to travel at the same speed (relative to your own speed) whatever speed you are travelling at.
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Yup.

The crazy thing is that, once you say: All onservers measure the speed of light to be the same, regardless of their state of motion, the derivation of Special relativity is easy - you could write it down on 1/2 a side of A4 and anyone with a decent grade in GCSE maths could understand it. But its that one posutulate that everyone missed.....
 
Visage said:
Yup.

The crazy thing is that, once you say: All onservers measure the speed of light to be the same, regardless of their state of motion, the derivation of Special relativity is easy - you could write it down on 1/2 a side of A4 and anyone with a decent grade in GCSE maths could understand it. But its that one posutulate that everyone missed.....
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Ok go on then :p
 
Psyk said:
Ok go on then :p
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Thought you'd never ask ;)

OK, imagine a train passing through a station. On a table in the train is a device that sends a photon up to the ceiling of the train, where there is a detector. A timing device measures the time taken.

Meanwhile, on the platform are two accurate clocks, one as either end (the length of the platform has been arranged so that a photon fired as the traoin passes the first clok will hit the detctor at the time the train passes the second.

All measurements will have a 1suffix for the train measurement, and a 2 for the platform. The train is travelling at v m/s and the distance between the emittor and the mirror is h.

SO, for the person on the train

c1 = distance/time = h/t1. (distance travelled, divided by time taken *on the train*) EQUATION 1

For the person on the platform the light leaves a point at one end of the platform, and hits the detctor when the train reaches the end of the detector

Now, the total horizontal distance travelled by the train is v*t2. Both observers agree on the relative speed of the train, so there is no need for s suffix on the v.

the height, again is h.

So, for the person on the platform, the light beam travels along a path of length, given by Pythagoras' theorem, as sqrt (h^2 +(vt2)^2)

so, for the stationary observer:

c2 = sqrt (h^2 +(vt2)^2)/t2 EQUATION 2

BUT: c2 = c1, as postulated, so, equation equation 1 and 2, and squaring both sides to get rid of the nasty square root,

h^2/t1^2 = h^2/t2^2 +v^2 = c^2

Divide both sides by c^2, and let a = (v/c)^2:

h^2/(t2^2 * c^2) + a = 1 EQUATION 3

But, from EQN 1, h^2/c^2 = t1^2, so substituting this into EQN3 gives:

(t1/t2)^2 = 1-a

And so, finally, we get the time dilation equation:

t2/t1 = (1-a)^(-1/2) where a = (v/c)^2:

As i say - its simply algebra, Phythagoras' equation, and the postulate that both observers agree on c.

I need a beer.
 
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I prefer to use the notation v/c = b, rather than a, lest people confuse it with acceleration.

Ok thread done now :)
Move along - nothing to see here! :p
 
Pickers said:
I prefer to use the notation v/c = b, rather than a, lest people confuse it with acceleration.

Ok thread done now :)
Move along - nothing to see here! :p
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Well if i was writing it down i'd use alpha, as is traditionally used for ratios...i guess a seemd the obvious choice.....
 
Psyk said:
The colour would change so much it wouldn't even be visible anymore :p
Rotation? That's a new one to me. Rotated in what way?
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Code: 
                         [1..........................2]
                         [............................]
                     <---[........moving body.........]                                                                                           
                         [3..........................4]

.........0(Bystander)


If the body is moving fast enough, the light reflected from 1 gets blocked out by the corner at three, and the corner 4 moves out of the way fast enough that the light from corner 2 can be seen by the bystander. Obviously this is very schematic, but you get the idea :)
 
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