# I Light pulse path, length and shape, when bouncing between two mirrors

#### fog37

So.... is it correct to think that every law of physics has an associated equation?

#### Sagittarius A-Star

Question: is the path followed by the light pulse straight or zig-zag? Which one is physically true? Both, even if they are different in length and shape?
Both are true. That is not specific for SR, but also true in classical mechanics from Newton/Galilei:

Please assume for a moment, that the laws of classical mechanics from Newton/Galilei were true, and that a ball gets elastically reflected forth and back by the mirrors.
• In the reference system of an observer at rest relative to the mirror system, the path of the ball is straight.
• In the reference system of an observer, moving relative to the mirror system, the path of the ball is zig-zag.
The difference between classical mechanics (Newton) and SR (Einstein) is:
• Newton: The speed of the ball in the "zig-zag" case is increased by the same factor as the path length.
• Einstein: The speed of light in the "zig-zag" case is invariant c.

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#### pervect

Staff Emeritus
So.... is it correct to think that every law of physics has an associated equation?
A philosopher might say "No", but most useful expressions of laws involve numbers and equations that I can imagine.

The most useful tool for making laws of physics covariant is tensors. Any law of physics written in tensor form is covariant, and it's independent of things like the choice of coordinates.

There are some common, and very useful, physical laws that are not usually taught in tensor form, however. An example of this would be Ohm's law, voltage = current * resistance, or E=I*R. In fact, all of circuit theory can be put in this category.

None of these quantities are by themselves tensors, the law is not in a tensor form.

Laws like these make some hidden, but not necessarily discussed, assumptions in order to actually work in a useful manner that agrees with experiment. But they are useful, and common, though they lack in generality. They just might not be applicable to extreme or unusual circumstances, like analyzing the current flow in a relativistically moving medium. Difficulties arise when the lack of generality of these "laws" isn't appreciated.

Tensors are quite an advanced tool, but they're very useful in minimizing and perhaps even eliminating common sorts of "hidden assumptions", due to their general nature.

#### fog37

Thank you.
• So "most" laws of physics have an equation associated to them. The form of this equation does not change. If it changes from different reference frames, it means that the equation is not representing a true law.
• In special relativity, the 2nd postulate is sometimes expressed to say that an experiment performed in a frame at rest is identical, does not change if the same experiment is performed in a uniform motion reference frame is the same (inertial): the laws of physics don't change so the way the phenomenon evolves is the same. What if the same experiment is performed in a noninertial frame? In the general theory of relativity, the laws of physics are valid in ALL reference frames (inertial and not), I think.
• Velocity of light: it is constant in all inertial frames but its direction can change. See the headlight effect:L if a light source approaches an observer, the perceived light is stronger for two reasons: because the source is getting closer and also because the light rays change direction and bend toward the direction of motion, correct?

#### jbriggs444

Homework Helper
if a light source approaches an observer, the perceived light is stronger for two reasons: because the source is getting closer and also because the light rays change direction and bend toward the direction of motion, correct?
The light rays do not bend. In special relativity, every "ray of light" (by which I assume that you mean "trajectory of a light pulse") is straight in every inertial frame. It is not clear what verb should be used to speak of the difference between the coordinate-velocity of the same ray of light in two different frames, but "bend" is not it.

Light rays are also straight in general relativity. It's just that we use the term "geodesic" to denote a "straight" trajectory.

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#### weirdoguy

Velocity of light
Speed. Velocity (a vector) is not constant, it can have different directions in different frames.

#### Mister T

Gold Member
Summary: The path of a light pulse moving bouncing between two mirrors (top and bottom) from two different inertial frames.

Question: is the path followed by the light pulse straight or zig-zag? Which one is physically true? Both, even if they are different in length and shape?
Note that you don't have to look at special relativity to address this issue. Imagine you are in a commercial airliner cruising at a steady speed of, say, 600 mi/h. As you sit in your seat you toss a ball upward, and it comes back down to land in your hand. The ball's path is straight.

Now suppose I am on top of a mountain with a telescope watching you. I will see the ball travel in a parabola.

Which is the true path of the ball, a straight line or a parabola?

#### fog37

Thank you everyone.

#### Xforce

I’m confused by the basis of relativity, why everything, including the spacetime and everything in this universe does not have an absolute velocity, but have a relative velocity to others. Everything around us is actually constantly moving, depending on the perspective. What makes photons so special, they have a fixed, absolute value of velocity? No matter the perspective, even you are just going one Planck distance (or the diameter of singularity)/second slower than c?

#### PeterDonis

Mentor
What makes photons so special, they have a fixed, absolute value of velocity?
The fact that they are massless--they have zero invariant mass. Anything with zero invariant mass must move at the same invariant velocity in all reference frames. That's one of the basic facts of relativity.

"Light pulse path, length and shape, when bouncing between two mirrors"

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