# Relativity And Light

1. Sep 28, 2006

### Line

Why is it that relativity doesn't work with light? I'm trying to understand
if light is moving at you at the speed of light, and you are moving towards it at the speed of light why would your equipment measure it at the speed of light. Shouldn't it read twice the speed of light?

2. Sep 28, 2006

### Staff: Mentor

(I'm going to use 0.9c for your velocity because massive objects can't travel at c.) In relativity, the "velocity addition" formula is different from what you're probably accustomed to. Instead of u' = u + v = c + 0.9c = 1.9c you have to use

$$\frac{u + v}{1 + uv/c^2} = \frac{0.9c + c}{1 + (0.9c)(c)/c^2} = c$$

3. Sep 28, 2006

### Line

Ok but it doesn't explain it.

4. Sep 28, 2006

### MeJennifer

Well think about it, how do you know you are moving towards it with a certain speed?
It is always relative to something else, and how do you know that it is you who is moving.
When someone states that something is going at x% of the speed of light it is always relative to something else. Everything with mass is always going at 0% of the speed of light in an absolute sense.

Only a change in movement, e.g. acceleration is absolute, but even there you can have the situation that some frames think you decelerate while others think you accelerate.

Last edited: Sep 28, 2006
5. Sep 28, 2006

### pervect

Staff Emeritus
You can't move at the speed of light.

As other posters have mentioned, for any velocity lower than 'c', if you move towards the light source (or if the light source is moving towards you) you will still measure the speed of light as 'c'.

The later case has been measued in the laboratory - the speed of gamma rays emitted from VERY fast moving particles has been measured, and been found to be equal to 'c', regardless of the motion of the source.

6. Sep 29, 2006

### Emanresu

The speed of light is constant no matter how you are moving or how the light source is moving. This is fact and has been well proven.

To answer your question then something has to give. It turns out that the things we expect to be always constant - time and distance - are not.

You have to get over this fact before you can start dealing with all the apparent paradoxes in relativity.

E.

7. Sep 29, 2006

### AnssiH

I believe Line is trying to ask, what is it that justified the idea that the speed of light is isotropic in the first place.

After Einstein had considered simple emission theory (where speed of light is measured as C + V of the emitter), he couldn't really make it work and started to consider other options. Usually when we think about motion, we think about ordinary newtonian velocity addition (C+V), but Einstein started to ponder on the possibility, that different "inertial frames" are symmetrical also by the speed of light they measure.

It is not immediately obvious how one could make that work. Like he put it himself, the "principle of relativity" (newtonian) and the "principle of the constancy of the velocity of light" are two "apparently incompatible" principles. But there was a way out if that mess.

The key to relativity theory (and this is how relativity should be taught to mainstream), is to understand, that it is an arbitrary assumption about reality, that two events that happen in two different places "simultaneously", are really simultaneous in an absolute sense. When we receive information about event A and event B that happened in opposite directions, we cannot really say which one had happened first. So to replace newtonian addition of velocities, Einstein could attach a different notion of "simultaneity" to each inertial frame, in such way that when a beam of light does hit an observer, we can figure out just when the light started its journey by claiming it moved at the speed C. And the way to make this work as a coherent whole, is to perform Lorentz-transformation on spacetime between inertial frames. (hence the idea that reality is a spacetime)

Note how the relativity is simultaneity is NOT about the order in which you observe events, but it is an assumption made about the real "now-moment" being relative, so to replace newtonian velocity addition.

And when you consider motion this way, it just follows that by accelerating towards another object, your notion of simultaneity is also changing in such manner that you can never reach relative speeds more than C between each others. And what also follows is time dilation, and length contraction; The geometry of an object is defined by where each of its element is in space simultaneously, but as notion of simultaneity changes, the back and the front (to the direction of motion) of the object are found to exist closer to each others "simultaneously".

Well, by invoking the idea of length contraction may be saying too much. Because after all is said and done, you should be pretty careful with the ontological idea that there really is a spacetime instead of motion.

Here is a good longer read about how Einstein got to relativity:
http://www.aip.org/history/einstein/essay-einstein-relativity.htm

8. Sep 29, 2006

### AnssiH

To measure the speed of any thing, you must register its position at one moment, and then again at another moment.

If you allow for adjusting these "moments", you can always get to isotropic C for light (as long as its the absolutely fastest thing in the universe, for anything faster would be moving backwards in time in some inertial frames, and so it would break the whole logic of static spacetime).

Well, you are talking about a model that is completely different from SR. I personally think it is very much possible, if not even likely, that the speed of light is not constant, but the path it takes is a result of the complex "web of matter" that is present in the situation. But that is completely different matter, what is important here is that SR is logically valid model as far as current observations and useful predictions go. Emission theories are not completely unproblematic either, albeit somewhat possible.

Nevertheless, just saying "it is so" doesn't get us anywhere if we cannot show that it really is so.

9. Sep 29, 2006

### Staff: Mentor

Relativity does work for light - it is about light! That's the whole point (the reason it was developed) - to explain/deal with the observed behavior of light.

What you are really asking is why does light not work the way particles work and the answer is (redundantly): because it is light! It has no (rest) mass so it travels at C.

If, then, you are meaning to ask why light behaves like light -- well, why is anything the way it is? It just is. And that's not a question for science.

AnssiH - neophysique deleted the post you responded to and it would probably be best if you deleted your response to avoid confusion...

Last edited: Sep 29, 2006
10. Sep 29, 2006

### Line

And why is it that light can't rest?

11. Sep 29, 2006

### Line

No something goign X% of C is relative to the speed of light.And what's this that any mass is always movign at 0% of C. In that case they're not moving. WHat about cosmic rays, they move at near the speed of light.

12. Sep 29, 2006

### JesseM

No, MeJennifer is correct, you can only talk about about the speed of an object relative to another, or relative to a particular reference frame. When people use a phrase like "0.8c", what they mean is that in the reference frame they're using, the velocity of the object is 0.8 that of light in that particular reference frame, but in other reference frames it'd be a different fraction. Light travels at c in all reference frames, and relative to all observers--so if you are travelling at 0.8c in my reference frame, that doesn't mean you will only measure the light beam to be moving away from you at 0.2c, you will still measure the light beam to be moving away from you at exactly 1 c in your own reference frame.

13. Sep 29, 2006

### Line

Can someone give me a down to Earth explanation why this works?

14. Sep 30, 2006

### Aether

Newton's laws are valued for their simplicity, and they are reasonably accurate when relative speeds are low. An "inertial frame" is a coordinate system in which Newton's laws hold (e.g., we assume that Newton's laws are accurate, and we build a set of coordinate systems that make this so).

Newton's laws become less and less accurate as relative speeds increase, and they become completely wrong as speeds approach c. This is because we measure time with clocks and distance with "rulers" (theodolites), and these measuring devices are physically affected by speed changes.

Special relativity is a tool for describing mathematically how two or more inertial frames relate to one another. It is a mixture of mathematical and physical concepts.

15. Sep 30, 2006

### Sojourner01

'Light' is a manifestation of disturbances in the electromagnetic field. Disturbances in the electromagnetic field propogate at a constantly-measured speed because they do. There isn't an explanation, that's just how fields behave. It's kind of like a first cause.

16. Sep 30, 2006

### Aether

We can measure round-trip speeds in a coordinate-system independent way, and the round-trip speed of light is isotropic. We can not measure any one-way speed in a coordinate-system independent way (at least not so far).

17. Sep 30, 2006

### Sojourner01

I'm not sure whether you're disagreeing with me or not, there. Am I being quoted because I said something inaccurate?

18. Sep 30, 2006

### Aether

Your statement may be accurate if you are only talking about round-trip EM field propagation, but it is not accurate if you are also talking about one-way propagation. The difference is that we can actually "measure" round-trip speeds (isotropy) in a coordinate-system independent way, but not one-way speeds; at least not so far.

19. Sep 30, 2006

### Farsight

It's difficult to get a handle on all this if you're lumbered with light travels at the speed of light. It's rather like talking about bullets travelling at the speed of bullets. In a weird kind of way light doesn't move at any speed. What relativity is all about is how we perceive things like time and speed via comparison of electromagnetic propagation within our atoms, bodies, and clocks, against electromagnetic propagation over some perceived distance. All this can get very deep very quickly, so to keep it simple for now: instead of thinking light travels at the speed of light, think light travels at the speed of time.

20. Sep 30, 2006

### Staff: Mentor

Give us a break!

Much better would be to accept that fact that--per relativity--there is a "speed limit" built into the very structure of space-time itself. This speed limit, which happens to equal the speed of light in vacuum, affects the kinematic behavior of everything: light, bullets, you name it.

The implication for light itself is that, as has been mentioned several times in this thread, light must travel at speed c as measured by any inertial observer.

To really understand what this means you'll have to break down and learn some relativity. (I recommend N. David Mermin's latest pedagogical effort, "It's About Time".)

21. Sep 30, 2006

### rbj

first, Line, do you understand that "light" is the propagation of electromagnetic (E&M) fields or "waves" and the physics that describes that propagation (called "Maxwell's Equations"). are you at that level? if not, i don't know quite where to begin with a down to Earth explanation.

i would not call the constancy of c (for all frames of reference) an axiom for which there is no idea why such principle exists (and we just notice it experimentally). it's because we can detect no intrinsic difference between different inertial frames of reference (two observers moving at constant velocities relative to each other both have equal claim to being "stationary", there is no good reason to say that one is absolutely stationary and the other is the one that is moving) and that the laws of physics, namely Maxwell's equations, apply to both frames of reference equally. if two different observers, neither accelerated and moving relatively to each other, are examing the very same beam of light (an electromagnetic wave), for both observers, when they apply and solve Maxwell's equations for the propagation of the EM wave, they both get the same speed of c out of solving Maxwell's eqs.

so we do have a good idea for why the speed of propagation of E&M is the same for all inertial observers that may or may not be moving relative to each other. it's because, we cannot tell the difference between a "moving" vacuum and "stationary" vacuum, that there is no difference between a moving and stationary vacuum and then there is not apparent reason for the observed speed of light to be different.

this is different than for sound. the physics of Maxwell's Equations make no reference to a medium that conducts the electromagnetic field (and, indeed, the Michaelson-Morley experiement failed to show that such a hypothetical medium, called "aether" exists - if it does exist, it seems to be moving around in the same frame of reference as the Earth going around the sun because no matter what time of day or season of the year, no one could detect with the M-M apparatus any motion through this aether). but for sound, the physics describe it as compressions and rarefractions of the air (or whatever other matter medium). there is no such thing as sound in a vacuum (but there is light). so if you feel the wind moving past your face from left to right (say at a speed of 20 m/s), you will also measure the speed of sound from a source on your left to be 20 m/s faster than sound from a source in front of you and 40 m/s faster than a sound that is at your right. now you can repeat that setup and get an identical result if there is no wind but you are moving (toward your left) through the air at a speed of 20 m/s. so the observer that is stationary (relative to the air) will look at a sound wave and measure it at something like 334 m/s, but you, moving through the air toward the source at 20 m/s will measure the speed of that very same sound wave to be 354 m/s.

now think of the same thing, but instead you two observers are out in some vacuum of space somewhere and are looking at the same beam of light. the other observer is holding the flashlight and measuring the speed of light to be 299792458 m/s. you are moving toward that observer at a speed of, say, 1000 m/s and looking at the very same beam of light that the other observer is. you are thinking that you would measure it at a speed of 299793458 m/s, right? but why should it be any different for you? you have equal claim to being stationary (and it's the guy with the flashlight is moving toward you at 1000 m/s). you cannot feel the vacuum moving past you at a speed of 1000 m/s, in fact there is no physical meaning to the vacuum moving past your face at 1000 m/s like it's a wind. you cannot tell the difference between you moving and the other guy as stationary or if the roles were reversed and there is no meaning to any notion of who is stationary absolutely and who is moving.

so then, if there is no meaningful difference, if both of you have equal claim to being stationary (and it's the other guy that is moving), then the laws of physics (particularly Maxwell's Equations) have to be exactly the same for both of you, both in a qualitative sense, and in a quantitative sense. both of you have the same permittivity of free space ($\epsilon_0$) and permealbility of free space ($\mu_0$). so when you apply Maxwell's equations to this E&M wave (of this flashlight beam), you will see that this changing E field is causing a changing B field which, in turn, is causing a changing E field which is causing a changing B field, etc. now for both of you, the laws (Maxwell's Eqs. and the parameters $\epsilon_0$ and $\mu_0$) are the same. now, it turns out, when we solved Maxwell's Equations for this case, we get a propagating wave and the wave speed is

[tex] c = \sqrt{\frac{1}{\epsilon_0 \mu_0}} [/itex]

but that's the same for both you and the other observer!! (even though you are both moving relative to the other.) there is no reason that the other guy should solve the Maxwell's equations and get a different $c$ than you get (because you have the same $\epsilon_0$ and $\mu_0$)! even if you two are looking at the very same beam of light. this is as far down to Earth as i can put it. does it do it for you, Line?

22. Sep 30, 2006

### MeJennifer

Wow, great explanation rbj!

23. Sep 30, 2006

### AnssiH

Farsight is not far off the mark, it is much clearer to look at light as it exists in static sense in spacetime if you really want to understand relativity.

It is not like relativity is based on the idea that "nothing moves faster than light". This speed limit is just what naturally follows from the two postulates. It is rather topsy-turvy way to explain relativity to someone as if it is the assumption about the speed limit that causes relativistic effects.

Like I said, it is imperative to understand how relativity of simultaneity can replace newtonian velocity addition. This is the key to grasping the idea, and everything else (like the speed limit) will follow. This is the unintuitive part of the theory, and this is exactly what makes it tick. It is rather abhorrent to reply to Line's question with "Because the formula to calculate motion is this and that". Having any arbitrary formula doesn't change reality. It is the formula that follows from the assumption about relativity of simultaneity!

So, Line, let's try a simple thought experiment for a fit.

I assume you are very much familiar with newtonian relativity of motion.

Let's consider a lab frame where you are standing 10 light seconds away from a pole (You and the pole are at rest in lab frame).

Let's say the speed of light is mere 1 m/s. (the pole is 10 meters away from you)

Whenever you receive a light pulse from the pole, we assume the light started its journey 10 seconds ago. And indeed, we can verify this by placing a clock at the pole to register the moment the light departs. If the clock by the pole shows "0 seconds" when the light departs, an identical synchronized clock by your position shows "10 seconds" when the light is received.

So far all fine and well, but what if we suppose there is another observer (B), only he is moving towards the pole at 5 m/s. Let's consider a light pulse that you both receive at the very moment you pass each others. How could it be that the light was approaching him also at 10 m/s instead of 15 m/s? How to "lower" the speed of light from 15 m/s to 10 m/s?

Well, looking at the situation from B's inertial frame, the moment the light departed is not known. We get to the intuitive 15 m/s only by assuming the light departed at such and such moment. If we can assume the light departed much earlier, we can lower the "required" speed to 10 m/s. (Note how in B's frame the light moves much longer distance than 10 meters; after all, it is the pole that is moving towards B, and the light must have started its journey much earlier than when the distance between was reduced to 10 meters)

If there are clocks at rest in B's inertial frame that are registering where the light pulse was at different moments, the clocks would show - according to relativity - that the pulse was on its way much longer than 10 seconds.

This assumption about relativity of simultaneity (=notion of simultaneity is different in each inertial frame) also means that at the moment you two are passing each others, the clock at the pole has different reading in Bs inertial frame from that of yours. In your "now-moment" the clock reads 10 seconds (albeit you cannot see this yet), and in his "now-moment" it reads more than 10 seconds (obviously he cannot see it either).

It also immediately follows, that if you consider there to really exist any "now-moment", then you must also accept that if the observer now stops, the clock in his own "reality" snaps backwards in time to 10 seconds (beyond his observations of course). Hence the idea about static spacetime.

And finally, when you assume this sort of reality, from the point of view of that light pulse, time did not move at all during its "journey". When it departed, sure, the clock at the pole showed 0 seconds, but the clock in your wrist was already showing exactly 10 seconds and observer B was also already next to you. So in a very real sense, relativity says that the light did not move at all (hence what Farsight said). Its whole path merely "exists" in different inertial frame from yours, and in its own frame its whole motion exists "simultaneously". Only in our frame we find it in one place at one instant and in a new place at another instant.

Well, I hope this helps little bit. It may take a moment to really wrestle the idea in. If you have access to any 3D-modeling software, it may help to build spacetime diagrams which you can then simply scale to perform Lorentz-transformation (to get from one inertial frame to another properly). I'll explain you how if you want to.

-Anssi

24. Sep 30, 2006

### AnssiH

I must add, that even if there was ordinary velocity addition to the speed of light, you couldn't tell which observer is moving. You could merely tell if you are moving relative to a given light source. (After all, Line's ordinary question was why there is no velocity addition)

Einstein's motivation, or at least part of it, to disgard velocity addition was that with relativity of simultaneity you can keep light from "mixing up" rather trivially (This all of course with rather naive idea about just what is "space" or "vacuum", but nevertheless). Of course with aether you could also keep light from mixing up, but that idea is even more naive.

And let it also be said that the constancy of speed of light is not a requirement for symmetry between different inertial frames. The constancy is a separate postulate on top of "ordinary" symmetry. Even if C was not isotropic, the laws of nature would be symmetrical (Maxwell's equations would need to be adjusted in some cases, but they would hold "within" any observer), or another way to put it, isotropic C does not make the measurements of light symmetrical between inertial frames (each measure different frequency in any case)

25. Sep 30, 2006

### Thrice

Light is a strange thing. It has 0 mass and yet it carries momentum. In order to know where it is, you have to give up information about how fast it's travelling. And vice versa. It exhibits both wave-like and particle-like properties. How is that possible? And that's just the beginning

It has a well defined velocity, but no rest frame. Meaning you can't look at things from the photon's perspective. As you've probably heard, you hit a singularity when you try reach the photon's frame. This singularity suggests that thinking of light as an entity in itself moving through space might be a little misleading. Think of it as interaction between two massive bodies along a null spacetime interval. The two events - emitting light and absorbing it are simultaneous. That's why c is the maximum speed of interaction.

So think about it that way. You can move at any speed you want. Given enough fuel, you can get to anywhere in the universe in 5 min. The question of what time their clocks read when you get there is a little more complicated. Point here is however fast you're going, you cannot get past that singularity. You still take time to get where you're going.

Last edited: Sep 30, 2006