Special Relativity

[chris_uk_83]

Since Bootsiuv seems intent on persuing the issue of how time can possibly slow down with speed I've decided to start a thread about it. A place for everything and everything in its place.

BTW, I do remember hearing a good analogy for the correlation between speed and time.

A bullet and a runner.

You shoot a bullet. It flies at a constant speed.

A runner runs along side of the bullet, the faster he goes the closer he gets to the bullet, eventually, reaching the speed of the bullet, so the bullet would be like its standing still to him....If he could run faster than the bullet, the bullet would begin to go away from him....so does that mean that if we could figure out a way to faster than light, we could go back in time?

Right, it would help immensely if you read this article on special relativity first. I'm working on a slightly simpler explanation, but do the reading and I'll get back to you.

[Bootsiuv]

Thanks for your time, and help. It is greatly appreciated.

I'll begin reading the article now, and would greatly enjoy discussing this more with you and others in the future.

[chris_uk_83]

Right, as we all know, Albert Einstein came up with a wonderful theory in 1905. The upshot of which was the famous equation e = mc². This theory was called special relativity and some of its more mind boggling connotations are that you can actually experience time at different rates depending on your speed.

So, how does it work? Well first of all you need to know the two postulates of special relativity.
1. The laws of physics are the same in all inertial frames of reference.
2. The speed of light in a vacuum is constant.
Now on face value neither of these seem odd. I’ll explain a bit more about what they mean though.

A frame of reference is another way of saying ‘point of view’. For example if a train speeds past you while you stand on a platform, you see the train move past you at about 30mph. However, if you’re on the train you see the platform move backwards at 30mph. Your frame of reference is the place you’re stood. So, in this language: in the train’s frame of reference the platform moves backwards at 30mph, and in the platform’s frame of reference the train moves forward at 30mph.

Right, now onto inertial frames of reference. An inertial frame of reference is one that is neither accelerating nor decelerating (rotating counts as acceleration by a definition in physics that I’m not explaining here). Therefore if something is moving at a constant speed (including 0 m/s) it is an inertial frame of reference. We need to move into space for an example of this. Imagine there are two spaceships nowhere near any planets or stars, just hanging in the blackness of space. Ship 1 is moving toward ship 2. from ship 2’s point of view it is stationary and ship 1 is moving toward it. From ship 1’s point of view it is stationary and ship 2 is moving toward it. Who is right? Answer: both, it depends on your frame of reference. You can’t actually tell which is stationary and which is moving since no forces are acting on either, the both have inertial frames of reference.

Got that? Good, onto postulate 2. The speed of light in a vacuum is constant. Not too odd? Wrong! Imagine this scenario: you’re back on your train platform and your mate is stood on top of a train. You have a gun and fire a bullet in the same direction as the train just as it goes past. Your mate on the train measures the speed of the bullet and so do you. If the train is moving at 90mph, and you measure the bullet to be moving at 200mph (slow I know, but this is only an example) then your mate on the train will measure the bullet’s speed relative to him to be 200 – 90 = 110 mph. Follow?

On the same note, if he fired the bullet and you measured it, you’d measure the exit velocity of the bullet plus the speed of the train: 200 + 90 = 290 mph. So the speed of something necessarily depends on the frame of reference in which you take the measurement.

Now, the second postulate says that the speed of light is a constant. How is this? We’ve just shown that no speed can ever be constant, it depends on your frame of reference. However, Einstein showed, by maths, that it is true!

Time for another example. We need to imagine a really fast train here (don’t worry about whether it’s actually possible, it’s a thought experiment), one that can go at nearly the speed of light. Now take the bullet scenario and replace a gun with a laser (lasers ‘fire’ a beam of light that travels, surprisingly, at the speed of light). Now, imagine the train is moving at half the speed of light and you fire your laser from the platform. In the train’s reference frame you’d expect to measure the speed of the laser beam as half the speed of light (speed of light – half the speed of light = half the speed of light). You don’t. You actually measure it going at… the speed of light. What? How? Well that’s the beauty of this, it’s completely counter intuitive to our common sense, which isn’t used to travelling at light speeds.

Similarly if the laser is fired from the train (which is travelling at half the speed of light) the platform will measure the beam travelling at the speed of light (not the speed of light and a half as you might expect).

What does this mean then? Well, we know that distance = speed x time. What happens if we look at a laser beam from two different frames of reference? If you look at a bullet then speed will change from one frame to another (this should be obvious to you). But light doesn’t change speed. Therefore time and distance must change instead. What!? You can’t change time or distance! Actually you can, and you do. It’s been proven to happen already. An experiment was undertaken where two atomic clocks (that don’t lose or gain time) were synchronised, then one was put on a fast aeroplane. This plane flew round quickly for a while, then the clocks were brought back together. They were out of synch by the amount predicted by special relativity!

The next bit involves some maths. You can show, from these initial predictions and a lot of mathematical gymnastics that:

Where t’ is the time measured by a moving observer, t_o is the time measured by the stationary observer, v is the speed of the moving observer and c is the speed of light. γ is just a term used to express the whole square root bit but using less space.

From this equation you can see that as v gets closer to c, the square root term gets closer to zero. Divide something by a number smaller than 1 and you make it bigger. Therefore as v increases, t’ also increases. If you let v tend to c then t’ tends to infinity. So a moving observer has slower time than a stationary observer. This effect is only really apparent at close to light speeds. Try it for the speed you drive around at and see what kind of time dilation you experience. It won’t even be milliseconds.

The same can be said of length contraction. You just replace t in the formula with l. So fast things experience slower time (from the point of view of a slower moving observer) and they appear shrunk to a stationary observer. From their point of view of course everything is perfectly normal for them and it seems that time has sped up for the stationary observer.

I hope that brief introduction into the realms of special relativity has been helpful. There’s much more to learn about it but a grounding in maths is always useful. Any more questions? Just ask.

If that mammoth isn’t worth rep then I don’t know what is!

[Gary88]

where did you do your degree out of interest, you've clearly been taught well as my physics textbook wasnt always a concise as that. very good explanation.

[chris_uk_83]

I got it at Lancaster. Brilliant university, I loved it! It's also impossible to be concise about anything unless you understand it at least reasonably Textbooks try to be too complete and accurate. I'm not bothered about that too much, I just want to convery enough to make people understand

[Bootsiuv]

Wow, I actually understand that (although the equation is a little over my head).

Here's a question: Is there any theory in modern physics which allow energy to travel faster than the speed of light (my initial thought is no, as I've heard it's essentially an unbreakable barrier)?

I've also heard something about a time machine which has already been proposed using four lasers in a square, but only particles could be sent back, and these particles would only go back as far as when the machine was turned on. Sound familiar? I want to say Tyson is the name of the scientist who introduced this to me on a T.V. program, but can't remember exactly....I know he's often on the History Channel's "The Universe", and will be hosting this season's "Nova: Science" on PBS.

Well, thanks for your time.

[Sosobra]

Here's a question: Is there any theory in modern physics which allow energy to travel faster than the speed of light (my initial thought is no, as I've heard it's essentially an unbreakable barrier)?

My current theories anything with mass cannot exceed the speed of light because its mass increases exponentially as you approach the speed of light. Even energy has mass, as small as it is.

[Bootsiuv]

Yes, I've often heard that it would take an infinite amount of energy to make something go at the speed of light....and you can't have infinite energy, so it won't work. I was just curious if anyone has thought of any alternatives.

It appears as of right now, we may never travel to the stars a la Star Trek. Certainly there must be a way around this....besides having generations upon generations of people living on a spaceship to reach even the closest star, which is a paltry 4 light years away, if I'm not mistaken.

BTW, I'm working with a high school diploma here, and whatever I've been able to learn by reading during my own time, so, if my questions are ridiculous, I apologize for my ignorance.

[Shatterer]

Ah, special relativity...I did my Gr. 12 physics report on it this year. I also looked into time dilation and length contraction. I typed up a report on it. It's by no means professional (highschool level) but if you're interested, I can always send it to you.

Anyway, what I found quite helpful during my investigation on special relativity was this lecture video:
http://video.google.ca/videoplay?doc...arch&plindex=8

[chris_uk_83]

Even energy has mass, as small as it is.

Kind of, it's effective mass rather than real mass, and requires maths to describe.

Yes, I've often heard that it would take an infinite amount of energy to make something go at the speed of light....and you can't have infinite energy, so it won't work.

Correct. Although again, it takes maths a little more complicated than the previous time dilation equation to prove. There are a few ideas for faster than light travel, most involve wormholes. These are theoretically possible tears in space-time. They kind of bend space-time round and you jump between the ends, but they'd require an amazing amount of energy to hold open. We can't do this.

Incidentally you wouldn't need generations of people aboard a ship in order to get to far away places if it travelled fast enough, since time would slow down for those aboard, they wouldn't age much. People watching from Earth would though.

I've also heard something about a time machine which has already been proposed using four lasers in a square, but only particles could be sent back, and these particles would only go back as far as when the machine was turned on. Sound familiar?

I'm not familiar with this one, but there is a theory that you can open a wormhole and drag one end close to a black hole (strong gravity has the same effect as going fast, it slows time down) slowing down time for it. Take that end away from the black hole again and you have a tunnel that connects two times, since one end is 'older' than the other. And yes, you could only go back as far as when the machine was switched on in this case too.

BTW, I'm working with a high school diploma here, and whatever I've been able to learn by reading during my own time, so, if my questions are ridiculous, I apologize for my ignorance.

Don't worry about that, there's no such thing as a stupid question as long as you admit your ignorance. What is irritating is people who claim they know everything and actually know very little. They're usually around second year undergrads