Stompy

I'm trying to wrap my mind around this and make sense of it:

An observer chasing a beam of light will measure it moving away from him at the same speed as a stationary observer.

Ok, so if someone was throwing a ball at you 20 feet per second and you run away 8 feet per second, the ball is then coming at you 12 feet per second. Therefore, if you ran 20 feet per second, the ball would appear motionless to you (briefly).

Let's say a beam of light is shining in a straight line along and infinite path, and you are traveling the speed of light on a parallel path right next to it, that light will still appear to be going the speed of light... how is this possible?

Maybe I'm asking an incredibly difficult question, but is there any "layman's terms" for why this is so?

[edit]

Maybe I asked this wrong... in other words: if you chase after a beam of light and you're going light speed, why isn't the beam of light motionless, how is it still going light speed from YOUR perspective?

Isn't the speed of light a constant? If so, once you reach that constant and your speed is matched with the beam of light you're chasing, how can it still appear to go faster? Wouldn't that NOT be constant then?

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fckm

The speed of light is constant. No matter how fast you are moving, you will always measure the speed of light to be the same. ie. It's constant in all frames.

This is called a galilean transformation. In Newtonian mechanics, ie, what you are taught in high school, this is indeed the case. To find the relative speeds of two moving obects, simply subract their speeds.
However, it turns out that the Universe doesn't actually work this way. The Galilean transformation and the physics that you were taught in high school are simply an appoximation, albeit a very good appoximation. Once objects reach speeds of about 90% the speed of light, this approximation breaks down. If you want to find the relative speeds of two objects moving at near the speed of light, it is necessary to use a Lorentz transformation.
http://mathworld.wolfram.com/LorentzTransformation.html
http://en.wikipedia.org/wiki/Lorentz_transformation

The relationship between speeds is no longer simple. This goes against every intuition that you have. But remember, in the case that the speeds are much much slower than light, the Lorentz transformation simplifies to a Galilean transformation. Everything that you have every done, ever come across in your entire life occurs at speeds much much slower than light. Your intution is thus built on Galilean transformations, and do not carry across to relativistic (near light) speeds.

edit:spelling

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CSflim

Right so far.

How is this possible? It's not.
"and you are traveling the speed of light on a parallel path right next to it": you cannot travel the speed of light.


Trying to explain this very counter-intuitive theory in a single post on an internet forum would be largely pointless, so instead I will point you to an excellent book which you may be interested in; Six Not So Easy Pieces by Richard Feynman. It is easy to read and requires no prior knowledge. It is also quite short (maybe 150 pages).
Also it is the type of book which will give you a chance to actually understand the theory, rather than just telling you about it (I have found that many science popularisations are guilty of this).

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Stompy

Thank you very much for the replies - I'll definitely check that book out!

I've been searching all day on google for a better understanding of this, but have come up empty handed so far I figured as much though

I see the proofs as to WHY it is the way it is, but yeah... my math skills aren't *that* good.. yet

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ICER

Beats my answer. I was going to say that the ball was a solid object, therefore has mass which you can judge speed and distance. Light however has no mass. So you cannot properly judge its speed and distance.

Or is that being to literal?

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fckm

Feynman is awesome. He's very good at explaining physical concepts without using a lot of math. He's my hero.

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Pax131

fckm is right, most of the physics taught in high schools today is physics as the world knew it in the 1900s. We've come a long way since then, but many people are discomforted by the idea that reality can be so utterly different than what they've expierienced in the mild conditions on earth. I just took a very interesting physics course that touched on special relativity- the professor wrote his own text book which explained the reason why the speed of light is constant to all observers very well. Unfortunately I don't have that book with me right now and I would definately confuse and mix the ideas up if I tried to explain it from memory.

Also, Richard Feynman is the shit. Someone gave me Surely You're Joking Mr. Feynman! for christmas and I highly reccomend it. His stories about picking the safes in Los Alamos that contained the sum of American nuclear weapons knowledge as a way to relieve boredom during the cold war when everyone was freaked out about security are very intertaining and well worth the read.

Slavakion

Well, it's classical physics. Stuff like kinematics, energy, gravity. It all still applies, but now there are asterisks next to everything. Classical physics is a good base to start on before you start learning theoretical stuff.

Rangsk

Think about it this way:

You're sitting in a magic train with no windows so you can't see anything outside. This train is perfectly smooth and is moving at a constant 50 miles per hour (relative to the ground). You are inside the train. Note that the train is moving at a constant speed, so you cannot "feel" any motion whatsoever. Try to think of an experiment, any experiment, that you could do to tell you how fast you are moving.

You can't. Einstein showed us through relativity that nature's laws are constant no matter how fast you are moving, as long as you are moving at a constant velocity. Moving at a constant velocity is the SAME as being at "rest."

Now lets add a window to the train, and have another obsersver, let's call him Bob, standing on the train platform. Right as you shine the light in the train, he measures the speed at which the light is moving. You both measure the same speed, even though if you had, say, thrown a ball, you would have measured different speeds. This sums up the problem you are trying to grasp - how can this be?

Unfortunately, in order to understand why this is, you have to accept some things about the universe that are not observable in everyday life. In fact, the only reason we know about these things is that we can do similar experiments as shining the light in the train and have shown that it is true. From that, Einstein devoloped the thoery of special relativity (and then general relativity to describe a gravity that does not conflict with special relativity). Special relativity states that an object shrinks in its direction of motion. So, if you had a ruler that measured 1 foot lengthwise when it is moving the same speed as you, if you then put that ruler on a train and positioned it so that its two ends are facing the front and back of the train, then it would appear to be shorter than 1 foot (though by such a small amount at "normal" speeds that it's just not observable in everyday life). On top of that, if you have two clocks, one in your hand and the other on the train, the one on the train would tick slower than your clock.

Remember our magic train with no windows, though. We think we are at rest even though to someone on earth, we're moving at 50 miles per hour. Add a window. I could state truthfully that I am at rest when on the train, and everything else is moving at 50 miles per hour in the other direction. So, I am no different from Bob on the platform, so if I look at Bob holding up a ruler, it will look shorter. And if I look at Bob's watch, his watch also appears to be ticking slower than my watch.

So, to sum up: According to Bob, my ruler is shorter and my clock is slower. According to me, Bob's ruler is shorter and Bob's clock is slower. At this point, you're probably more confused than you were when you asked the question. You're probably wondering, "who's right, then? They can't BOTH be right, can they?" Well, the answer is yes, they are both right, as long as they both continue to move at their own constant speeds. However, if they ever want to meet up, one of them has to accelerate (either the train slows down, or Bob gets onto the train). The one who accelerates is admitting that he was the one moving, and thus his watch will appear to have been slow when they meet up.

So to make it more clear. I'm on the train and Bob is on the platform. If I stop the train and go onto the platform, my watch will read slower than Bob's. If Bob jumps into the train as it zooms past the platform, then Bob's watch will read slower than mine. Of course, once we're the same speed, they will both tick at the same pace, but my watch may show 5pm while his watch shows 4:59pm or 5:01pm depending on who met up with whom (I've exagerated the time difference to a great degree for the speeds we're talking about, but you get the idea).

I went off on a tangent there, but it's all interesting stuff that is a direct consquence of light always moving at the same speed, no matter the frame of reference.

Ok, so back to light. How is it always going the same speed, no matter what your speed is? Well, here's another problem to think about. You have two spaceships on Earth. One moves away from Earth at .9 times the speed of light (.9c from now on, c being the speed of light), and the other moves in the exact opposite direction at .9c. According to Newtonian physics, a guy on one spaceship would look at the other spaceship and see it going at 1.8c! But, relativity makes it very clear that you can't move faster than the speed of light. Remember something, though - speed is a measure of distance over a certain amount of time. In order to measure speed, you need to know a predetermined distance and have a clock measure the time it takes to cross that distance. Remember, though that distances shrink and time gets slower for objects moving at different speeds than you, so the speed you measure on one of the spaceships is in fact slower than the speed measured by someone on Earth! Thus, each spaceship sees the other spaceship flying away at a speed faster than .9c, but smaller than c (there are equations to calcualte this, but it's not important). So, what would you have to do to, say, shoot a bullet at the speed of light. Well, you'd have to accelerate it forever, since the faster it gets, the slower time gets for it.

I probably didn't help that much, but maybe I've given you a truer picture of relativity. If you want more reading material, I suggest reading "The Elegant Universe" by Brian Greene. It focuses on string theory, but it spends the first couple chapters explaining both relativity and quantum mechanics very, very well (much better than me). If you think relativity is out there and hard to grasp, you should read up on quantum mechanics.

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gar1976

It's my understanding that if you are traveling faster than the speed of light, you cannot slow down below the speed of light, and if you start out going slower than the speed of light, you cannot cross that threshold.

Hmmm...maybe I'll dig out the reference on that.

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If you liked that one, pick up its sequel What do YOU Care What Other People Think? It was also very good.

ICER

Well, Rangsk. I would have to disagree with your assessment. Although you explained it quite well. So allow me to recap and you can tell me why I should have studied all this before I replied

As I understand your post, the reason why we can't travel at the speed of light, is because we could not (cannot) measure the distance we are traveling. Hence the closer we get to that point, the farther we are from it (since the faster it gets, the slower time gets for it)

The reason why I disagree (if I understand the post correctly) the person inside the craft would not be able to tell if they had reached light speed because (to him) he is not going very fast at all. But to someone on the outside. They should be able to determine the proper speed. Because they would be able to tell the distance and the time it’s taking them to cover it.

Or is that to literal?

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Stompy

Awesome post, Rangsk. It actually does make sense, because if you think about it... even on earth we aren't truly at rest. Earth itself is rotating, spinning around the sun, and surely the galaxy itself is moving at a high speed. I never through of it that way before until I read the bit in your post about constant velocity being "at rest".

Yeah, I'm currently reading The Elegant Universe right now, but took a slight departure from the text right when it started talking about the constant speed of light. Maybe it touches up on it more later in the book, but I had that itch to know "why" then and there

I ordered those Feynman books too

Very fascinating stuff

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fckm

This is incorrect.
The reason why we cannot travel at the speed of light is because we have rest mass.
Any object which has rest mass cannot travel at the speed of light.
The faster you travel, the larger your apparent mass becomes. The larger your apparent mass, the more energy is required to increase your speed. At near the speed of light (say 99.9999%), your mass become so large, it requires more energy than exists in the entire universe to accelerate you.

What Rangsk is saying, is a rehash of the way that Lorentz transformations are derived. The idea being that since anything traveling at the speed of light must have the same velocity in all reference frames, the normal frame transformation (galilean transformation) must be incorrect. The correct transformation is one in which an object traveling at c has the same speed in all frames. The transformation that achieves this, is called the Lorentz transformation. This allows use to transform four-vector coordinates (3 space coordinates, and one time coordinate) from one frame to another frame.
Now that we can transform four-space coordinates, we can derive how to transform velocities. From velocities, we can transform momentums. Now we can calculate energiers. Anyways, we pretty much rederive our understanding of physics from the simple Lorentz transformations. One of things that we find out, is that objects with rest mass cannot travel at the speed of light. Light can travel at the speed of light because it has no rest mass. It can only travel at the speed of light. If it traveled at a speed lower than light, then it would have zero energy, and would cease to exist.

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KnifeMissile

I don't normally nit-pick but this is backwards. Special Relativity doesn't show us that nature's laws are constant. That is a postulate of the theory. In otherwords, it is an assumption that the theory of Special Relativity is based on. Why do we make this assumption? Because, experimentally, it seems to be true. However, you never know, it could be wrong and that's why we still call it a theory...

xandren

so if "Moving at a constant velocity is the SAME as being at 'rest.' ", does that mean that light is at rest?...I mean it has a constant velocity...
or maybe my brain is just fried from reading this thread...
props to Rangsk though...nice post...i feel somewhat smarter

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flstf

Sorry if this has been posted already, I didn't find anything when I searched TFP.

http://archives.cnn.com/2000/TECH/sp...d.of.light.ap/

Rangsk

I think you misunderstood what I was saying. We can measure distances, it's just that distances actually get shorter as we get faster. A consquence of this is that, for example, if you constantly accelerate at 10m/s for 1 year and then constantly decelerate at 10m/s for 1 year, you can go anywhere in the universe. However, don't try to go home, because if you do, millions or even billions of years would have passed on Earth, even though you only experienced 4 years. To Earth you were travelling slower than the speed of light, since to them you took millions of years to get to your destination. To you, you were travelling slower than the speed of light since the distance travelled seemed very short, even though to Earth it was a great distance.

This is an interesting thought problem. What does the universe look like to a light beam? Relativity says that at the speed of light, all distances are 0, and time is frozen. How do you define speed if all distances are 0? It's, however, slightly irrelevent since light has no mass, and we can never match its speed, so we will always see it going at a constant velocity. You can't really use light as a frame of reference.

I skimmed the article, and I think it's a bit misleading (those CNN reporters do love mangle science). I believe what is happening is they are shining light at a vapor, and then there is some kind of quantum mechanics phenomina is happening that causes the vapor to create light at the other end, but it takes less time than it would take light to travel that distance. Other things, such as quantum entanglement, have already shown that information can be *instantly* transmitted between two non-touching particals, though, so I don't see this as any kind of major breakthrough.

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fckm

No. You misunderstood the statement. It means that the laws of physics, and the mathematical methods that we use (calculus, vector math, etc) are the same in any inertial (constant velocity) reference frame.
In General Relativity, one works with reference frames that experience forces and acceleration. The result is that the laws of physics are no longer the same. Vectors don't add the way they used to. They are no longer othogonal. This is why we say that space-time becomes curved.
This is a generally held misconception. Objects with mass cannot travel at the speed of light (see above for explanation). Information cannot travel faster than the speed of light. Bcause of the way Lorentz transformations work, if I'm sitting somewhere and I see two events occuring some distance apart, I see that A happens then B happens. However, someone moving very fast with respect to me can see that B happens before A happens. But what if A caused B to happen? Well, if A caused B, then no matter how fast I move, I must always see A before I see B.
In order for this to be true (that A is always before B), the math tells us that for the given distance between A and B, the time between them must be larger than or equal to the time it takes light to tavel from A to B.
Philosophically, this means that something happens at A. A transmits some information (doesn't matter how) to where B is, causing B to occur. This transmition of information must take the same amount of time (or larger) as it would take light to travel the same distance. If not, then I can ways travel at some velocity where it looks like B occured before A. Thus, we say that Information cannot travel faster than the speed of light.

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Hain

Rangsk, I think you are right. I read up on that and what was happening was an effect of entanglement (I believe, and so does my AP Physics professor). If relativity is hard for anyone, QM gets really weird. People in my classes have "infinite improbability machine" written everywhere when it comes to entanglement.

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younggunz

"Light can travel at the speed of light because it has no rest mass. It can only travel at the speed of light. If it traveled at a speed lower than light, then it would have zero energy, and would cease to exist."

i have a question about this....does light travel at C (the speed of light) through any medium? If i shine a light through water, does the light travel through the water just as fast as through the air even though the water is more dense. i know that sometimes light exhibits wave property and sometimes particle property and sometimes both. I am curious about this though.

Does light only travel at the speed of light through a vaccuum?

fckm

The answer depends on if you're looking for a classical answer or a quantum answer. As far as a quantum answer goes, I haven't taken quantum optics yet, so I can't really give you a good answer. I can make up some BS about atoms absorbing a photon and reemiting the photon, thus causing it to take more time to travel the total distance, but I don't think this answer is right.
Classically, think about the atom as a positively charged ion attached to a negatively charged valence electron(s) with a spring. Light is an oscillating electric field. The electric field pulls on the electron and pushes on the positive core. (Or the other way around). Because the light-electric-field oscillates, this causes the electron-core system to also oscillate. Of couse, the oscillation of the electron-core system causes another oscillating electric field. This field interacts with the original light-field. The two effect each other to such a degree that they are pretty much indistinguishable from each other.
Looking at this problem mathematically, the presence of a material (the dipole created in the material) changes several constants, namely the permeativity and permeability, in the wave equation which describes how light travels. These constants are used to derive the "speed-of-light" and since they have changed from their freespace values, the speed of light in a material is different from its free-space value.
So long story short, the speed of light is usually slower going through a material than not. The speed is only incidentally related to the density of the material.

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