It's the good old theory of relativity...

[Gnosis]

OK- this is an old-school example but I'm having problems
with it...

1. If you have a train moving at the speed of light and you
stand inside the train and then fire a beam of light from
the back of the train up to the locomotive. What wold happpen?
How fast would the beam travel inside the train?

2. If the beam is allowed to continue out of the front of the
train would the speed then be 2x lightspeed????

This problem is based around the the theory of relativity
and the concept of relative realities. I just can't get it
together. would the beam inside the train stop? Or
would it decrease its speed once it leaves the train or what?

 

[TuxDave]

Here's some twisted answers with little insight on why it is. I guess if I have time I can go into an intuitive way of 'seeing' it.

1. From inside the train, it'll look like it's moving down the train at the speed of light. From outside the train it'll look like it's moving at the speed of light and the train will look like it has a length of zero.

2. From outside the train, the beam will move at the same rate as the zero length train. It would never pull ahead of it.

 

[Gnosis]

If you have any good way of "seeing it" that you could explain - and
you feel that you have the time for it - please do!

To me it just seems like utter madness....

 

[gururu]

you can change the conditions to the following:

two cars moving the speed of light. one behind the other. can the car in the second position blast the first car with a laser beam?

the answer is no. light does not accelerate, its speed is constant; it cannot ever exceed what is defined as the speed of light. the car in the front will always be ahead of the car behind and any light projected from it because it passes every defined point in space before the light projected from the rear car.

this is how I understand it.

 

[CycloWizard]

Originally posted by: Gnosis
If you have any good way of "seeing it" that you could explain - and
you feel that you have the time for it - please do!

To me it just seems like utter madness....

If you want a simple answer, light has the same speed regardless of your point of observation. Other objects' speed/velocity depends on the point of observation. You're used to gauging velocity relative to some relative axes, but this is not really possible with light.

 

[f95toli]

Most modern physics seems like utter madness (if you think special relativity is strange try reading a book about quantum physics) at first, after a while you get used to it and almost seems "normal".

However, it IS important to understand(!) that no one really "understands" these things in the normal sense of the word, this is because our brains are used to the physics of everyday life where nothing moves at speeds close to c.
The theories look the way they do is simply because they work.

 

[Gnosis]

Yes I know. These theories exist not because they are correct but because
no one has proved them wrong....

Actually I find quantum physics somewhat easier to grasp since I'm prepared
for its "madness".

But just like you said - when you take the concepts of "the normal world" to
new extremes it just goes against common sense. And somewhere along the
way my brain starts to hurt because I want i to make sense.... *sob*....

 

[Matthias99]

Originally posted by: gururu
you can change the conditions to the following:

two cars moving the speed of light. one behind the other. can the car in the second position blast the first car with a laser beam?

the answer is no. light does not accelerate, its speed is constant; it cannot ever exceed what is defined as the speed of light. the car in the front will always be ahead of the car behind and any light projected from it because it passes every defined point in space before the light projected from the rear car.

this is how I understand it.

However, that's not what would happen. Light always travels at the speed of light relative to any observer.

Current science says you cannot ever accelerate to the speed of light; it would require an infinite amount of energy. However, you can get arbitrarily close to the speed of light. If you had two cars travelling at 99.99999% of the speed of light, and you were in the 'rear' car and fired a laser at the 'front' car, it would seem to you to travel towards the 'front' car at the speed of light, arriving in time (d/c), where d is the distance between the cars and c is the speed of light. Someone in the 'front' car would see the same thing.

However, an outside observer, would observe relativistic time dilation; to them, the time for the laser to reach the front car would seem much longer (and if you somehow *were* moving at the speed of light, they would see what you originally described; to them, the laser would *never* catch the 'front' car). Basically, time would slow down for the people in the cars. This seems extremely unintuitive, but if you say that light always travels at c no matter who observes it (which, as far as anyone can tell, appears to be true), it's the only result that logically works. You can't hold time, space, *and* the speed of light constant, and if the speed of light is held constant, time and space will change relative to your velocity.

 

[gururu]

Originally posted by: Matthias99

Originally posted by: gururu
you can change the conditions to the following:

two cars moving the speed of light. one behind the other. can the car in the second position blast the first car with a laser beam?

the answer is no. light does not accelerate, its speed is constant; it cannot ever exceed what is defined as the speed of light. the car in the front will always be ahead of the car behind and any light projected from it because it passes every defined point in space before the light projected from the rear car.

this is how I understand it.

However, that's not what would happen. Light always travels at the speed of light relative to any observer.

Current science says you cannot ever accelerate to the speed of light; it would require an infinite amount of energy. However, you can get arbitrarily close to the speed of light. If you had two cars travelling at 99.99999% of the speed of light, and you were in the 'rear' car and fired a laser at the 'front' car, it would seem to you to travel towards the 'front' car at the speed of light, arriving in time (d/c), where d is the distance between the cars and c is the speed of light. Someone in the 'front' car would see the same thing.

However, an outside observer, would observe relativistic time dilation; to them, the time for the laser to reach the front car would seem much longer (and if you somehow *were* moving at the speed of light, they would see what you originally described; to them, the laser would *never* catch the 'front' car). Basically, time would slow down for the people in the cars. This seems extremely unintuitive, but if you say that light always travels at c no matter who observes it (which, as far as anyone can tell, appears to be true), it's the only result that logically works. You can't hold time, space, *and* the speed of light constant, and if the speed of light is held constant, time and space will change relative to your velocity.

you pose a different scenario. I was talking hypothetical. obviously 1% of of the speed of light is going to 'seem' like the speed of light via our rudimentary perceptions. BUT, the question was IF we are indeed going the speed of light, which I think makes the question more interesting.

 

[unipidity]

Then the trains are made of massless particles?

 

[cquark]

Originally posted by: Gnosis
If you have any good way of "seeing it" that you could explain - and
you feel that you have the time for it - please do!

To me it just seems like utter madness....

You can find an index to special relativity visualization simulators and tutorials at
http://casa.colorado.edu/~ajsh/sr/srfs.html

 

[Matthias99]

Originally posted by: gururu
you pose a different scenario. I was talking hypothetical. obviously 1% of of the speed of light is going to 'seem' like the speed of light via our rudimentary perceptions. BUT, the question was IF we are indeed going the speed of light, which I think makes the question more interesting.

me:

...if you somehow *were* moving at the speed of light, they would see what you originally described; to them (an outside observer), the laser would *never* catch the 'front' car.

I addressed both situations. If you somehow were travelling at the speed of light (which is impossible according to physics as we know it), an infinite amount of time would pass to an outside observer before the laser caught the 'front' car. Time would stop for the people in the cars relative to the outside world, and the cars would appear to have a length of zero to an outside observer. To the people in the cars, everything in the cars would appear normal to them, but the outside world would appear to have stopped.

The degree of time dilation (as well as mass increase) is proportional to sqrt(1 - (v^2 / c^2)). As v->c, the relative amount of time that passes becomes infinite (or zero, depending on your perspective).

 

[Blackjack2000]

Originally posted by: Matthias99
I addressed both situations. If you somehow were travelling at the speed of light (which is impossible according to physics as we know it), an infinite amount of time would pass to an outside observer before the laser caught the 'front' car. Time would stop for the people in the cars relative to the outside world, and the cars would appear to have a length of zero to an outside observer. To the people in the cars, everything in the cars would appear normal to them, but the outside world would appear to have stopped.

The degree of time dilation (as well as mass increase) is proportional to sqrt(1 - (v^2 / c^2)). As v->c, the relative amount of time that passes becomes infinite (or zero, depending on your perspective).

I agree. Remember, as any object with mass approaches the speed of light, it's mass increases, and time slows down. That's why it's much easier to grasp relativity if you imagine a fractional speed of light. If an object with mass were actually travelling at the speed of light, time would stop (from its perspective) and it's mass would be infinate. That's why it's physically impossible for any object to reach that speed.

 

[bannanafish]

You could simply modify the initial scenario, e.g.:
Say there were two f1 cars in the year 5002. Somehow they managed to drive in opposite directions (don't ask me why). So Fred is driving from left to right (as you watch from the spectators stand). And Michael (Schumacher is STILL racing) is going from right to left.
i.e. <----Michael You(stationary) Fred---->
Since this is the pinnacle of motorsport, they are travelling at 0.6c (very possible, just not with current technology) WITH respect to you, the spectator.
Say they had rear lights (or plasma drive engines?).
So you will see the speed difference of Michael and Fred to be 1.2c. Which means, according to you (very important), neither Michael nor Fred will see each other's rear-light/plasma-engine in their respective rear-view mirrors.
NOW, according to Michael, he can safely assume he is not moving. Only the earth (carrying you) and Fred are moving with respect to the non-moving Michael. This is a perfectly valid frame of reference, as no inertial frame takes precedance, according to special relativity.
Michael will see Fred moving very fast (faster than 0.6c) yet not faster than the speed of light (not yet 1.2c which is the classical result). An explanation is that, Fred would have to be violating relativity by travelling faster than the speed of light, which is the same as Fred having more than infinite energy.
Fred's rear-light/plasma-engine radiates light out towards Michael at the speed of light (with respect to Michael, not with respect to Fred's moving car).
SO... Michael will be able to see Fred's rear-light/plasma-engine.

The results of such relatavistic scenarios, is that different observers will come to different conclusions/ see different phenomena. But this is fine, since they know they are in different frames of reference, and they could calculate/deduce what the other would see and get the 'correct' answer.

If the speed of light were not constant, with respect to ALL frames of reference, there would be some very interesting results and perhaps even more mind boggling consequences.
A person/object that is not accelerating (with respect to what is an interesting question in itself) has no way of intrinsiclly determining what velocity they are travelling at (zero or otherwise).
Hence only relative velocities are of any importance (e.g. you velocity with respect to the land, or the stars).
If the speed of light were not constant with respect to all frames of reference, then you would be able to figure out your velocity (with respect to the grand non-moving frame).
Then absolute velocty suddently has a meaning and becomes very important. Say you were holding an electronic device. Now the current in the device flows at the speed of light (now with respect to the grand non-moving frame). Hence your circuit would would differently depending on your speed and direction. (Optics would also become interesting/complicated).
Now, still keeping in mind this Gallelaean model, going backing to see the race. Now Micheal would 'see' Fred travelling at 1.2c and hence not see him.
This model would also let you travel at the speed of light (or faster, all with no space/time dilation) so in certain frames of references, certain directions of light would be stationary to you. i.e. you would see nothing in certain directions
But what would me more interesting, is what would happen if you saw light from something and then moved the the direction the light was travelling, faster than the speed of light and then turned your head for another look?
Would you see the same thing? Or would the photons be 'used' the first time and hence you wouldn't see them again. If they were 'used' then what if the first sighting was done by someone else? Would they still be 'used' when you look at them? Or would there be a one use poilicy for each person/object?

One way to explain why velocites aren't additive (as they are at non-relativistic speeds) is to ask why they should be?
Why SHOULD velocities simply add together (i.e. person moving at 0.2c with respect to the ship, ship moving 0.5c with respect to the ocean, therefore person moving 0.7c with respect to the ocean)?
If and apple plus and orange doesn't give a meaningful result, why should two velocities?
Although it is very convenient that velocites do (approxitely) add nicely at slow speeds, there is no natural reason that they should or have to, and as relativity suggets, they don't.

At the end of the day, relativity like-it-or-not in a way makes life EASIER. It keeps everyday activities simple, you don't need to keep in mind your velocity when making sence of observations etc.

.. the real question is, does Schumacher still cheat in 5002

 

[gururu]

Originally posted by: Matthias99

I addressed both situations. If you somehow were travelling at the speed of light (which is impossible according to physics as we know it), an infinite amount of time would pass to an outside observer before the laser caught the 'front' car. Time would stop for the people in the cars relative to the outside world, and the cars would appear to have a length of zero to an outside observer. To the people in the cars, everything in the cars would appear normal to them, but the outside world would appear to have stopped.

The degree of time dilation (as well as mass increase) is proportional to sqrt(1 - (v^2 / c^2)). As v->c, the relative amount of time that passes becomes infinite (or zero, depending on your perspective).

I agree with most of what this says, in regards to time dilation and length contraction. However, I do believe that if the two cars were moving at the speed of light in a plane devoid of light, and if the second car projected a light beam towards the first car, the observers in the second vehicle would not see the first vehicle. This would be EVEN if the two cars were almost touching. I think its even arguable that a light bulb would not illuminate a space within a vessel that is moving the speed of light. Only observers in the vessel behind the bulb would see the illuminated filament, but illumination would not be visible. And of course, this is all hypothetical, because we know mass cannot achieve the speed of light, but that is besides the point.