Is light breaking its own speed limit when cornering?

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• Dum Leme
When the wave encounters a gravitational field, some waves will be drawn inwards (close to the gravitational field), while others will be repelled away from the gravitational field.The waves that are drawn inwards will be shorter than the waves that are repelled away, and the waves that are drawn inwards will have a greater amplitude than the waves that are repelled away.This creates a curve in the light, which we call a light cone.When you see a “corner effect” on the “outside” you are actually seeing light from the “inside” that has reflected from the corner.A light cone does the same, and given that the outsidef

Dum Leme

Being a neophyte to physics, I try to visualize a light cone as it travels about.

I try to put myself in it and use my car to talk of it.

When I ride in my my car, I note that when I corner, one wheel will speed up as compared to the other side.

A light cone does the same, and given that the outside traveled further than the inside, this breaks the speed limit of light for a brief time.

What am I not seeing?

Regards
DL

It is not clear what you mean by light cone, but I’ll give it a try.
A beam of light does not act like a rigid body. It is a wave.
When you see a “corner effect” on the “outside” you are actually seeing light from the “inside” that has reflected from the corner.

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Dum Leme and sysprog
Being a neophyte to physics, I try to visualize a light cone as it travels about.

I try to put myself in it and use my car to talk of it.

When I ride in my my car, I note that when I corner, one wheel will speed up as compared to the other side.

A light cone does the same, and given that the outside traveled further than the inside, this breaks the speed limit of light for a brief time.

What am I not seeing?

Regards
DL
The first question is how you propose to cause light to move on a circular path.

Note that light is oscillating electromagnetic fields, so each light wave isn't like a car in the sense of a rigid body.

Dum Leme, vanhees71 and sysprog
The first question is how you propose to cause light to move on a circular path.
Fiber optics can be curved -- the outermore path is longer, so light that traverses it would take longer to reach the destination.

Dum Leme
As others have mentioned, light is a wave and not a rigid body, so it doesn't behave like your car at all. You've also asked a rather general question, and it's difficult to determine what you mean by "cornering", as light typically travels in straight lines unless it's traveling in a medium where its speed may well vary.

The only other case I can think of is gravitational lensing, and I'm not sure what does happen to the phase structure of light undergoing lensing. Shouldn't be too hard to figure out if that was what you were asking.

Dum Leme, vanhees71 and sysprog
It is not clear what you mean by light cone, but I’ll give it a try.
A beam of light does not act like a rigid body. It is a wave.
When you see a “corner effect” on the “outside” you are actually seeing light from the “inside” that has reflected from the corner.
Try light beam then, even as a cone is easier to visualize.

I agree with light being a wave.

That wave, when being bent by gravity is longer on one side that ends going faster than light speed.

Regards
DL

The first question is how you propose to cause light to move on a circular path.

Note that light is oscillating electromagnetic fields, so each light wave isn't like a car in the sense of a rigid body.
Put a magnet or gravity well near a light and it curves.

Put enough gravity wells, and you will get light to circle back.

Right?

Regards
DL

Fiber optics can be curved -- the outermore path is longer, so light that traverses it would take longer to reach the destination.
One side would be faster than the other though as it traveled further if we look at the outside curve. Right?

That faster or longer is what has light breaking it's own speed limit.

I think.

Regards
DL

As others have mentioned, light is a wave and not a rigid body, so it doesn't behave like your car at all. You've also asked a rather general question, and it's difficult to determine what you mean by "cornering", as light typically travels in straight lines unless it's traveling in a medium where its speed may well vary.

The only other case I can think of is gravitational lensing, and I'm not sure what does happen to the phase structure of light undergoing lensing. Shouldn't be too hard to figure out if that was what you were asking.
Light does travel in a straight line when not being acted upon by a gravity well.

When gravity pulls the bean off it'[s straight line and curves it, that creates your lensing.

The outside of the beam that is lensing is traveling further than the inside and breaks the speed limit of light while within a curved shape.

Regards
DL

That wave, when being bent by gravity is longer on one side that ends going faster than light speed.
An individual light wave does not have a physical width. The wave itself is oscillating EM fields. A beam of light of finite width is composed on many indidividual light waves that may get separated (e.g. in refraction, diffraction or by gravity).

Dum Leme
Light does travel in a straight line when not being acted upon by a gravity well.
There's no such thing as a straight line through space in curved spacetime. The path that light takes through space is essentially the nearest we can get to defining a straight line.

Or, to put it another way, it's space that is curved, and not the path of light.

The model you have in your mind of Euclidean space with light following a "curved" path is not correct. It's spacetime itself that is curved in the presence of a large mass. The curved spacetime is gravity.

The path of light through spacetime, whether you consider it curved or not, is determined by the local speed of light being ##c## along its path. And, again, an individual lightwave itself has no physical spatial width.

In this particular scenario, it might be ... illuminating ... to think of a light beam as loosely analogous to a spray of bullets from a machine gun.

No matter how the trajectories of any or all of the bullets are altered (be it gravity or richochet or what-have-you) it does not increase the speed of the individual bullets.

They're not "yoked together" like two oxen pulling a cart, or the wheels on the axle of your car.

sysprog
In this particular scenario, it might be ... illuminating ... to think of a light beam as loosely analogous to a spray of bullets from a machine gun.
The bullet has a finite radius, so as it falls the top travels a very slightly longer distance than the bottom, hence at a slightly greater speed.

That model, of light as a classical particle of finite size, cannot be right.

Dum Leme, sysprog and vanhees71
The bullet has a finite radius, so as it falls the top travels a very slightly longer distance than the bottom, hence at a slightly greater speed.

That model, of light as a classical particle of finite size, cannot be right.
I think you're taking the analogy too far.

Assume the bullets themselves are of zero size.
The light beam is represented by a spray of bullets.
The point is, the spray of bullets does not turn under influence of gravity, The top bullets don't go faster to keep up with the bottom bullets - the top bullets simply fall behind.

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I think you're taking the analogy too far.
I would suggest you're the one doing that!
Assume the bullets themselves are of zero size.
The light beam is represented by a spray of bullets.
The point is, the spray of bullets does not turn under influence of gravity, The top bullets don't go faster to keep up with the bottom bullets - the top bullets simply fall behind.
Bullets accelerate under gravity; light does not. I don't think "light as bullets" is valid.

Classically light is a propagating EM wave, which implies an EM field strength at various points in spacetime, but nothing with a physical spatial extent, as such.

vanhees71
Classically light is a propagating EM wave, which implies an EM field strength at various points in spacetime, but nothing with a spatiat extent, as such.
I grant that it is a very specious analogy, still...

Regardless of the how or why light behaves - the answer to the OP's equation is more universal than the nature of light - it happens to any emission of non-zero width. The far edge of a beam of anything doesn't "speed up" to keep up with its counterparts.

Others will give a more EM-specific explanation, but I hope the OP will intuit the general idea from my crude analogy, diagrammed in post 14.

The point is, the spray of bullets does not turn under influence of gravity, The top bullets don't go faster to keep up with the bottom bullets - the top bullets simply fall behind.
I'm not convinced that's an accurate representation of what happens to light in a gravitational field, though. If the "upper" parts of a ray fall behind then the wave front is tilted upwards, and that clearly isn't what happens in the case of gravitational lensing.
When gravity pulls the bean off it'[s straight line and curves it, that creates your lensing.
Not exactly. As PeroK has already mentioned, it's more accurate to think of light traveling in a straight line in a curved spacetime. You can project that line in spacetime onto "space" (there are some caveats...) and get a curve, but this is in many senses an artifact of you choosing to project a straight line onto a curved surface.

Futhermore, once you start discussing curved spacetime it isn't always obvious what you mean by "speed". In the sense that you end up meaning it when you talk about light paths around a star (technically called "coordinate speed") then yes, it does vary. Light speed is only an invariant in curved spacetime for local measurements. The actual generalisation of "light always travels at the same speed" to curved spacetime is that light always follows null trajectories, and these are always measured locally as traveling at ##c##.
The outside of the beam that is lensing is traveling further than the inside and breaks the speed limit of light while within a curved shape.
No - you're conflating the two meanings of "speed" here. You're mostly talking about coordinate speed (which can be anything at all, even for light), except when you talk about "the speed limit of light", where you're talking about the locally measured speed (which is always ##c## for light). You can (usually) get away with mixing these up in flat spacetime, but not in curved spacetime.
One side would be faster than the other though as it traveled further if we look at the outside curve. Right?
(This was in response to a comment about fiber optics.) In an optical fiber light is traveling in a medium at about 2/3 of its speed in vacuum, ##c##. Its speed (and note that we're back in flat spacetime here so we can casually talk about speed) can vary. Exactly how EM waves work in a waveguide is fairly complex. But suffice it to say that if you could get a short enough wavelength pulse into the fiber to be able to treat it as two separate bits, you'd probably find that the bits that are "outside" on the corner at one place are "inside" in another - light is not a rigid object like your car.

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Dum Leme, vanhees71 and PeroK
The outside of the beam that is lensing is traveling further than the inside and breaks the speed limit of light while within a curved shape.
The fixed coordinate lightspeed applies only in inertial coordinates. Like in the local free falling frame, in which the light beam is straight, not curved.

The coordinates where the beam is curved by gravity are not inertial, so you can have different coordinate lightspeeds at different locations.

Source: https://www.mathpages.com/rr/s8-09/8-09.htm

This is also related to gravitational time dilation: The reduction of the coordinate lightspeed (based on a clock at infinity) is exactly the reduction in local clock rate (compared to the clock at infinity). So the lightspeed based on a local clock is still c.

This is exactly backwards. Light propagates perpendicularly to the wavefront. So to have a curved beam (in some coordiantes), the coordiante speed of the outer wavefront must be greater than the coordiante speed of the inner part (like shown on the left).

Ibix
OK. Conceded. I've only succeeded in confusing the OP and polluting the thread.

Try light beam then, even as a cone is easier to visualize.
This "light cone" of which you speak. How are you planning to aim the thing so that one side goes faster than the other.

Light cones are invariant features of space-time. Every event has one. But they do not move. They are the outline of the portion of space-time that can be reached by signals from the event (future light-cone) or from which signals can be received at the event (past light-cone).

A "light cone" is not the outline of a poorly collimated flashlight beam.

OK. Conceded. I've only succeeded in confusing the OP and polluting the thread.

An individual light wave does not have a physical width. The wave itself is oscillating EM fields. A beam of light of finite width is composed on many indidividual light waves that may get separated (e.g. in refraction, diffraction or by gravity).
All light emanations have width, I think, and that makes one side break the speed of light when it is bent.

Regards
DL

There's no such thing as a straight line through space in curved spacetime. The path that light takes through space is essentially the nearest we can get to defining a straight line.

Or, to put it another way, it's space that is curved, and not the path of light.

The model you have in your mind of Euclidean space with light following a "curved" path is not correct. It's spacetime itself that is curved in the presence of a large mass. The curved spacetime is gravity.

The path of light through spacetime, whether you consider it curved or not, is determined by the local speed of light being ##c## along its path. And, again, an individual lightwave itself has no physical spatial width.

Light curves and when it does, it seems to break the speed limit of light.

Work with that instead of making statements that cannot be true,

How wide is your flashlight beam?

Regards
DL

In this particular scenario, it might be ... illuminating ... to think of a light beam as loosely analogous to a spray of bullets from a machine gun.

No matter how the trajectories of any or all of the bullets are altered (be it gravity or richochet or what-have-you) it does not increase the speed of the individual bullets.

They're not "yoked together" like two oxen pulling a cart, or the wheels on the axle of your car.
Your scenario is not useful when it is one beam of light and not a bunch of bullets.

The light cone is yoked together.

Regards
DL