Does Light Have Zero Length and What Does That Mean for Velocity?

[Char. Limit]

My physics teacher told me that any object traveling at the speed of light would have its length compressed to zero, as well as the mass extended to infinity.

Does light have zero length, and how can something without length have a velocity? Is light zero-dimensional?

 

[mgb_phys]

Does light have zero length, and how can something without length have a velocity?

Same way something with zero mass can have a velocity!

Is light zero-dimensional?

Thats a reasonable way of thinking about it.

 

[Char. Limit]

Well, I'm not sure why massless objects have velocity either, but I didn't want to sound like a fool. I try to save that for the politics forum.

Seriously, think about it. In order to push light, it must have a mass (F=ma). Also, if objects traveling at lightspeed have infinite mass, and light has zero mass...

I need to put my head into some frozen crystalline combinations of hydrogen and oxygen.

 

[cepheid]

Seriously, think about it. In order to push light, it must have a mass (F=ma). Also, if objects traveling at lightspeed have infinite mass, and light has zero mass...

Well, infinity is not a number. What your physics teacher should have said is that the mass of an object approaches infinity as its speed approaches the speed of light. What that means is that there is no upper bound (limit) on the mass as its velocity increases. The higher the mass, the greater the force that is needed in order to maintain even just a constant acceleration. What that means is that massive particles (where the word "massive" here just means "having a non-zero mass") CANNOT reach the speed of light. It is a sort of universal speed limit. This is a basic consequence of Einstein's Special Theory of Relativity.

However, Special Relativity also affords a 'loophole' of sorts in the equations. If a particle were to have zero mass, and if it were to be traveling exactly at c, then that would be okay. But it would have to always travel at c, no matter what. So photons always travel at the speed of light. There is no need to 'push' on them in order to accelerate them, because they always travel at c, period.

So you have two possibilities: a particle can have non-zero mass and travel at any velocity strictly less than c, or it can have zero mass and travel exactly at c. Does that resolve your difficulty?

 

[Char. Limit]

Yes, except for one question: how, then, is light bent by a gravitational force? Light has no mass, so I would think nothing could affect it. But, light IS bent, bent often, and bent by everything with mass.

Is a photon the only massless particle? What is mass, anyway? Apparently mass isn't needed to exist...

 

[Nabeshin]

To [properly] explain the bending of light, one needs to defer to the full theory of general relativity, rather than a simplified Newtonian understanding of gravity. In GR, mass bends spacetime and all objects with no force (in GR gravity is not a force) applied to them merely follow geodesics (paths of shortest distance between points in spacetime). Light is not exempt from this requirement to follow geodesics, so it responds to curves in spacetime similarly (not identically) to how normal matter does.

 

[Born2bwire]

Yes, except for one question: how, then, is light bent by a gravitational force? Light has no mass, so I would think nothing could affect it. But, light IS bent, bent often, and bent by everything with mass.

Is a photon the only massless particle? What is mass, anyway? Apparently mass isn't needed to exist...

Relativity concerns itself with the Minkowski space, a four-dimension system of position and time. Light moves along a geodesic in space-time, that is, it moves along the shortest path between two points in space-time. Space-time is not a flat "surface" and general relativity discusses the idea of gravity being distortions in space-time. So while light always travels in a geodesic in space-time, since gravity distorts space-time, we observe this "straight line" in space-time as a curved line in space.

 

[Char. Limit]

Ah, if only I could visualize \mathbb{R}^4.

Thanks for the info. It sounds confusing, a curve being the shortest point, but I imagine it's probably like a banking on a racetrack, but in 4-d... And bigger.

So, are there other massless particles?

 

[Nabeshin]

The only currently known massless particles are the photon (which mediates electromagnetism) and the gluon (which mediates the strong force). It has been proposed that gravitons, the particle mediator of the gravitational force, would also be massless, but that's for a different thread.

 

[Born2bwire]

Ah, if only I could visualize \mathbb{R}^4.

Thanks for the info. It sounds confusing, a curve being the shortest point, but I imagine it's probably like a banking on a racetrack, but in 4-d... And bigger.

...
...
Billions and billions... It's so much fun to say.

EDIT: Banking on a racetrack... eh kind of... It depends on what you are talking about. For example, let's say you live in flatland that is mapped onto the surface of a sphere. You are in a two-dimensional world but your world exists in three-dimensions, just like how you walk around on the Earth's surface. But if you want to go from Chicago to Rockford, you walk in a straight line hoping to avoid the occasional collision with automobiles and other large immobile objects. To you, it's travel that follows a flat straight line, but in the three-dimensional space, you traversed an arc, a curved line in space.

EDIT EDIT: Sagan's talk and demo of the shadows of the cube in projecting it down a dimension is a great lecture. The flatland lecture is a popular one but I haven't seen anyone else do the shadow portion.

 

[A.T.]

My physics teacher told me that any object traveling at the speed of light would have its length compressed to zero,

An object with finite proper length, yes. But for a light pulse you cannot define a proper length, because you cannot define a rest frame for light in which you would measure that proper length.

Does light have zero length,

No, you could even say (but not to loud ;-)) that a light pulse has an infinite proper length which in our frame is infinitely contracted to yield a finite length. Sounds weird and is not 100% clean math, because you can only work with the limit -> c.

and how can something without length have a velocity?

The size of something doesn't limit it's velocity.

as well as the mass extended to infinity.

Similar thing here. An object with non zero rest mass, yes.

 

[mudderrunner]

However, Special Relativity also affords a 'loophole' of sorts in the equations. If a particle were to have zero mass, and if it were to be traveling exactly at c, then that would be okay. But it would have to always travel at c, no matter what. So photons always travel at the speed of light. There is no need to 'push' on them in order to accelerate them, because they always travel at c, period.

So you have two possibilities: a particle can have non-zero mass and travel at any velocity strictly less than c, or it can have zero mass and travel exactly at c. Does that resolve your difficulty?

I thought it was possible to slow light down.

 

[FoxCommander]

yes you can slow light down, but this is because 'c' changes due to what medium you are in, light travels slower in glass than in air, that is what causes diffration. If I am not mistaken someone has actually stopped light. which is sweet.


FoxCommander

 

[Char. Limit]

Stopped... light?

What sort of medium, other than a black hole, can do that?

To Born2bwire, I'll see the YouTube video once I'm out of school. Blocking systems and all that.

 

[mgb_phys]

Stopped... light?

Sort of.
Light slows down in a material with a refractive index, so in glass it slows to 1/1.5 the speed of ligth and in diamond to 1/2.4

If you make a very high refractive index material you can slow it a lot more, the record is something like 10m/s.

BUT the speed of light doesn't change. The easiest way to think of it is that between the atoms the ligth moves at the speed of light (c) but when it hits an atom it is absorbed and a short time later the atom re-emits the ligth again going at c. The time it takes for each atom to do this slows down the average speed of light through the material.

 

[gmax137]

BUT the speed of light doesn't change. The easiest way to think of it is that between the atoms the ligth moves at the speed of light (c) but when it hits an atom it is absorbed and a short time later the atom re-emits the ligth again going at c. The time it takes for each atom to do this slows down the average speed of light through the material.

Is this right? I never really thought about it before. Is there enough space between molecules in a material like glass for the light rays to pass through without scattering off any? (apparently not, since glass slows down the transmission). What about air - is air transparent because of the space between molecules?

 

[Bob S]

The photon from the Mossbauer source iron-57 has a 14.7-KeV metastable state with a lifetime of 10^-7 seconds:
http://hyperphysics.phy-astr.gsu.edu/Hbase/Nuclear/mossfe.html
The corresponding energy uncertainty is given by ΔE ≈ h-bar/2Δt.
The emitted photon "remembers" its energy uncertainty when it reaches a Mossbauer absorber, as in the Pound Rebka experiment. See
http://en.wikipedia.org/wiki/Pound–Rebka_experiment
So this 14.7-KeV photon has a "length" 10^-7 seconds·c ≈ 30 meters.
Bob S

 

[mgb_phys]

Is there enough space between molecules in a material like glass for the light rays to pass through without scattering off any?

No - pretty much any solid material isn't going to let light striaght through.

What about air - is air transparent because of the space between molecules?

Largely, it's also because most of the molcules in air don't have any properties that can absorb photons with the energy in visible light.

How and why a material is transparent is quite complicated.
Conductors ,like metals, are usually opaque because the free electrons on the surface can absorb light and re-emit it back toward so you have a shiny surface. But even a very thin layer of metal can block the transmitted light.

Insulators are more transparent but the light that is absorbed is still re-emitted in random directions so you can't see through them but they aren't reflective.

With crystals (or glass) the regular arrangment means that light is absorbed but then emitted in the same direction that it was going - so it is passed-along through the crystal and out the other side pretty much unchanged. It can also be emitted at other fixed angles (depending on the crytal arrangement) which is why you get reflections in gemstones.

If there are atoms in the crystal that absorb a particular energy then that color isn't transmitted and the white light comes out colored.

 

[Char. Limit]

Light is 30 meters long?

Doesn't transparency usually involve light going through the item? If the light was reflected because the absorption area was infrared or violet... Wouldn't it be white?

I believe that with certain compounds, cutting them extremely fine (nanoparticles, really) will cause a change in color. It's in my AP Chemistry textbook.