Physics question about the speed of light

Poststructural Pub
1

I have a couple of related questions that I’ve played with in my head for years and never yet have answered to my own satisfaction.

Here’s the scenario:

You are on a spaceship going half the speed of light.

The spaceship has forward-facing headlights. You turn them on.

Relative to you, the light leaving the headlights is going…well…the speed of light, right?

You and the ship together are already moving at half the speed of light relative to an observer standing at the ship’s launch pad.

From that observer’s perspective, is the light from the ship’s headlights going forward at the speed of light or at 1.5 times the speed of light? and if the latter, how can it–doesn’t that break the “universal speed limit?”

Ok, let’s make it a little more complicated. In the first example, we’re just talking photons, subatomic wave particles.

Now lets say the ship has a railgun that can fire a projectile at three-fourths the speed of light. (We’ll assume it is detachable so that the recoil doesn’t destroy the spaceship and everyone on it dies.)

Ok, first lets start with the spaceship just hanging in space, with no forward velocity relative to its starting point.

Fire the railgun, and you’ve not done anything that breaks the laws of physics. (You may well have broken interstellar law, but that’s an entirely different subject.) The projectile hurtles forward at a devastating .75c .

Ok, now load your railgun again, and hook it up to the ship, and take the ship up to its cruising speed of half light-speed.

Now disengate the railgun and fire it. Relative to your perspective, is the projectile going at 3/4 c?

How can it be, because relative to the perspective of someone standing at the ship’s launch pad, wouldn’t the projectile be hurtling forward at an impossible 1.75 times the speed of light, and thus going backwards in time as a result? (Tachyons always move faster than light and move backwards through time as a result, or so at least our current understanding of physics seems to indicate.)

Finally, to really complicate the issue, of course, it’s almost impossible for the ship to ever stay still relative to the exact point in space from which it launched. Why? Planets move around their stars. The stars themselves move within their galaxies. The galaxies themselves hurtle away from each other at massive speeds.

Help! This boggles my poor brain and I’m confused!!! :astonished: :boggle: :stuck_out_tongue:

–James.tar.gz

2

Okay, I’ll tackle the easy one first. The speed of light is constant, and it doesn’t matter that the beam comes from a moving object. Remember that the person launching that beam is also travelling through time far more slowly than the ‘stationary’ person. So the stationary person (stationary to the ship moving at 1/2 C and the light beam moving at C) has a different measuring stick compared to the person on the ship.

This also takes care of the issue of the rail gun issue. Time and mass are affected by the increased speed.

I don’t know about tachyons. Sorry!

The concept of stationary is relative, yes, but consider it to be anything other than the light beam and you’re pretty set for armchair physics.

Sincerely,
Tyg

3

The trick is that the speed of light is constant, and time will slow down or speed up for different observers. If an astronaut goes on a long trip in a spaceship that goes above C/2 time will significantly slow down on that spaceship. When the astronaut returns home, he/she will only have aged a little bit, while his contemporaries at home will experience time at the normal rate.

Einstein did many thought experiments similar to the original post. They helped him a great deal when formulating his theories. There are probably some PBS specials explaining his theories to a lay person.

4

Good question James, and good answers. It’s easy to forget the piece about time being relative to the observer.

5

If my explanation did not make it clear here is another one:

From
http://www.unmuseum.org/einstein.htm
What the experiment showed was that light is unique in that it always moves at the same speed (approximately 186,000 miles per second, sometimes referred to as the constant “c”) no matter how fast the observer is moving.

This seemed to create a strange contradiction. If a rocket pilot was traveling near the speed of light - “c” - a motionless observer would see him almost keeping up with a light beam traveling in the same direction. Einstein said that if you asked the rocket pilot about the beam of light, however, he would say that no matter how fast he accelerated the beam was still traveling at speed “c” faster away from him.

Einstein realized that the only way this could happen was if time slowed down for the rocket pilot as he accelerated to near the speed of light. Since his clock would be running slower, when he measured the light beam traveling next to him it would seem to be still moving at “c.” This idea that time did not have to be the same for all observers in all places but is “relative” differs radically from Newton’s thinking and is the heart of the Special Theory.

Experiments have proven that Einstein was right about time dilation of accelerated objects. Today the GPS satellites that provide position information to receivers on Earth must correct their onboard clocks by a tiny amount to account for their speed as they orbit the planet. Time moves just slightly faster for the satellites than it does down here on Earth.

Not only does time change as the result of acceleration, but physical objects get distorted too. Yardsticks under Newton’s laws were the same anywhere in the universe under all conditions, but according to Einstein they actually get shorter in the direction of travel as they are accelerated. This isn’t noticeable to the traveler, as everything around him, including he and his spaceship, grows shorter also.

6

Actually, people give Einstein too much credit for general relativity; Lorentz developed the equations on which mass increase and time dilation are based.

There’s an interesting problem, posibly one of those Bill cited Einstein mulling over. It’s called the Butcher and the Worm. A butcher is cutting up chops with a couple of cleavers. A worm comes through going 0.85 c. The worm is 12" long, and the butchers cleavers are 8" apart. But from the butcher’s frame, the worm is only 6" long. So the butcher chops both cleavers simultaneously, but the worm fits between them comfortably. In the worm’s frame, he’s 12" long, but the cleavers are 6" apart. But we know he makes it through, right? What happens?

In the worm’s frame, the two cleavers don’t come down at the same time. The first one he encounters comes down later than the second one he encounters. (The difference is a few hundred picoseconds, I think.)

7

That problem fascinates me because it not only baffles–it’s also really, really gross.

8

I think worms are cute. :slight_smile:

But butchers (more specifically, butcherings) make me sick, so I agree with that much.

I find this whole thread to be terribly fascinating.

9

When you turn on the light on the spaceship (or fire the gun thingy), doesn’t that also push back against the spaceship’s inertia, slowing it down a bit as well?

I still have trouble with this one, where, if a spaceship on the launch pad fires its rockets, the rockets push against the launch pad, but if the spaceship fires its rockets in space, what does it push against? The textbook answer is that in space, the spaceship pushes against its own inertia, but I have trouble conceptualizing this.

But back to the beam of light question, doesn’t the spaceship, even in movement, have some bit of inertia, and doesn’t the beam of light push against this, slowing the spaceship down a tad?

djm

10

I still have trouble with this one, where, if a spaceship on the launch pad fires its rockets, the rockets push against the launch pad, but if the spaceship fires its rockets in space, what does it push against? The textbook answer is that in space, the spaceship pushes against its own inertia, but I have trouble conceptualizing this.

I don’t know if you’ve ever fired a handgun, but if you have, you know that the firearm will “kick” back against your hand, even though the firearm is much heavier than the bullet that is getting pushed out of the barrel.

That is the same “kick” that drives the rocket forward in space.

When you accelerate exhaust out of the nozzle of the rocket engine, the compression of the combusting fuel not only pushes the exhaust out of the nozzle, it pushes the combustion chamber forward.

Just as when you fire a firearm, the burning powder accelerates exhaust out of the barrel, which coincidentally propels the bullet out of the barrel; however, that’s not all that happens. The burning powder also propels the combustion chamber (which is held firmly in the firearm and can’t move independently) back against your hand.

So, yes, a firearm would fire in space even with no air, and the resulting kick would not only drive the bullet forward, it would push you backward unless you were firmly anchored against something with much more mass than either you or the bullet.

So what’s the practical difference between a firearm and a solid-fuel rocket engine? Very little, actually. The main difference is the size and composition of its exhaust.

–James

11

Yes, but when I am wearing my tachyon bracelet, I feel much better about the whole question at hand.

12

Answer to question two, Yes, with the tad being very small.

Answer to question A (same as James’s, which I didn’t read first, but phrased differently): It’s conservation of momentum, same as what propels a jet. If you’re on a good pair of rollerblades on a good level surface and you throw a basketball, it will set you moving backward. It’s the same idea; the spaceship is propelling fuel backward, thus propelling itself forward.

You’re not the only one confused by this. The New York Times ran an editorial in the 1950’s saying that “anyone with the most basic knowledge of physics” knew that a spaceship couldn’t accelerate in space, where there’s no air to push against. I’m not quite sure where they learned their physics.

13

This may well be completely wrong, but it is the way I think of it.

The speed of light is a limiting condition of the universe as we perceive it.
If you manage to approach the speed of light you will also approach large massiveness and you will also approach ubiquity - being in more than one place at once. Assuming you can pass this barrier, you and your spaceship will cease to perceive the universe as previously percieved, and percieve a “meta-universe” or a different perception of the same universe. One in which you will be moving much more slowly, or perhaps stationary.

The other possibility is that as you become infinitely massive, you gravitational force will become critical, attracting all other physical objects in the universe towards you, until you and the universe beome one big (small?) implosion and the whole damn thing starts all over again. :smiling_imp:

14

Just remember folks, drive fast, take chances. 186,000 miles per second is not just a good idea, it’s the law. :smiley:

15

I think you would reach critical mass before anything else happened, and you would die in a rather spectacular nuclear explosion where you were the fissionable material, leaving an impressively-long rainbow-colored “grease spot” for anyone not immediately slain in the explosion to observe with suitable awe.

That’s just my understanding–I may be mistaken on this.

–James

16

Only if you were radioactive to begin with. Are you? :stuck_out_tongue:

17

Only when moving at speeds approaching c.

This usually only happens after eating hibachi. :sunglasses: :laughing: :smiling_imp:

–James

18

Darn nice thread James. It brings memories of a sci-fi book I read ages ago, about some people who wanted to go through some black hole in space, where time started to get distorted and all.

19

I liked the answers I got in the thread, but I wanted more of the “why.”

So I read wikipedia’s article on relativity, and it referenced an online article called “Albert Einstein’s Theory of Relativity in Words of Four Letters or Less.”

Here it is: http://www.muppetlabs.com/~breadbox/txt/al.html

This is an outstanding article…and it actually answered other questions I didn’t even know I had. The bit about why the earth goes in a circle around the sun in particular is nice: it doesn’t. It goes in a line. The sun’s mass bends space and time around itself, so that the line looks like a circle when seen from one perspective.

It is a lasting regret that I never took physics.

Folks, thanks for some fascinating answers to my questions.

:slight_smile:

–James

20

Don’t have too many regrets. College level physics requires a solid understanding of college level calculus. Even with that, I remember some of my physics classes. The median on tests often fell at 20% to 25% with 100% possible. This means the average student absorbed about 20% of the material. The lower level students probably less than 5%! And this was non-relativity physics, mechanics or electricity and magnetism.

I guess my point is that studying physics is considered hard, and even if a person studies it, only maybe the top 5% of students absorb much of it. If a person has trouble with thought experiments, through in a bunch of equations, plus complex mathematics and see how it mixes.

The holy grail of a grand unified theory is still out there. The current theories only explain a part of the observable universe.