## Approaching light speed.

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My understanding is when an object approaches the speed of light from the point of view of an outside viewer the object contracts in the direction of the path?

If an object could actually reach the speed of light would the object become 2 dimensional from everyone else's perspective?

Is there any hypothetical way an object can travel in all directions at the same time? If that were so would it not be expanding? And if it were doing that at the speed of light would it not also be becoming 0 dimensional?
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Is there any hypothetical way an object can travel in all directions at the same time?

Big Bang?
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If an object could actually reach the speed of light would the object become 2 dimensional from everyone else's perspective?

There is a belief that we travel through time at the speed of light.
Sabine Hossenfelder: Do we travel through time at the speed of light?
If this is the case, objects travel through time at the speed of light yet remain spatially three-dimensional from everyone else's perspective.
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ITS ALL RELATIVE!

The Earth is rotating on its axis at about 1,674.4 km/h (1,040.4 mph)
The orbital speed of the Earth around the Sun is 108,000 km/h.
The orbital speed of our solar system around the centre of the milkyway is about 700,000 kilometers per hour.
If you/I were (as Einstein tried to imagine himself) sitting on a photon, as it travelled at light speed. Then just like me, sitting typing this, I would experience no sensation of movement at all and from my reference frame, I would age and time would pass, at the exact same rate it does now.
It appears to us that a photon does not age and an object travelling away from us at light speed will look redshifted. Carl Sagan gives a good example, in his COSMOS series, in the 4.5 min clip below:
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My understanding is when an object approaches the speed of light from the point of view of an outside viewer the object contracts in the direction of the path?

If an object could actually reach the speed of light would the object become 2 dimensional from everyone else's perspective?

Is there any hypothetical way an object can travel in all directions at the same time? If that were so would it not be expanding? And if it were doing that at the speed of light would it not also be becoming 0 dimensional?

You're right in that at the speed of light spatial dimension (distance) contracts infinitely. At the same time let's not forget that time dilates infinitely (the inverse). This is relativity proposed by Einstein.

So that in conclusion, at the speed of light, all distances and all times are simultaneous. A singularity. Therefore matter cannot exist. Only pure "potential" energy.

This is reinforced by physics understanding that photons (which travel at c - the speed of light) do not have matter.

Thus energy, time and space are negligible as energy (at c) is "the ability to do work", or in other words the ability to cause change.

But change can only occur in a temporal and spatial dimension. Ie. One not travelling at the speed of light.
Hence why energy travelling at the speed of light is only potential as potential requires no dimensions.

The effects of change/ability to do work (potential) can only be measured from the realm of matter - energy that is not travelling at the maximum speed and thus is subject to time and space and manifests as material substance. (e=mc2)

This means essentially that everything that is matter, is under the duress of spacetime and energy. When it is only potential energy, not "acted energy", these things do not exist. "Action requires the time to act and the space in which to act."

So one can imagine it as a spectrum. Between rates of reaction (time/distance).
When time and distance are negligible, rate is 0 (pure potential), when time passes and space exists as distance, rate is not negligible. Ie >0
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Say your friend is traveling to Alpha Centauri, about 4 light-years away.
As his spaceship approaches the speed of light, it flattens in the direction of travel as seen by you, the stationary observer. From your friend's perspective, you, the earth, and the distance to Alpha Centauri flattens as well.
He would arrive quickly (depending on how close to "c" he's traveling) because of this shortening of the distance, which also translates into the time shortening effect experienced by your friend in the fast moving rocket. From your perspective however, your friend is moving at almost "c", so it takes him 4 years to arrive at A.C.
Since the rocket has mass, theoretically it could get close to the speed of light but never reach it, since it takes an infinite amount of energy to accelerate any mass to "c"

For a photon, which has no mass and always travels at the speed of light, distance and time only exist from the perspective of the observer: to a photon there is no such thing as distance and time, once it's emitted, it reaches its destination instantly in zero time.

The other question about an object traveling in all directions at the same time: by definition, velocity is a vector, which can only have one direction.
Instead of saying an object, you could speak about an expanding gas, but that is really not an object but a collection of very small objects (atoms).
You could also say our expanding universe, the accepted theory is that space is growing at a rate of about 50 miles a second for every megaparsec (3.3 million light years), which means the farthest parts of the observable universe are receding away faster than light, but space, being different than an object, does not follow the rules of relativity the same way matter does, and there is no flattening.

Hope this helps.
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For a photon, which has no mass and always travels at the speed of light, distance and time only exist from the perspective of the observer: to a photon there is no such thing as distance and time, once it's emitted, it reaches its destination instantly in zero time.

For the photon without distance and time how can there be speed of any kind? Is the photon everywhere at once?
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From the perspective of any observer in any frame of reference, all photons travel at the speed of light, it is a universal constant. If you accelerated to nearly the speed of light to catch up with photons emitted from your flashlight, you will find that no matter how close to the speed of light you get, those photons will still be traveling at exactly the speed of light regardless of your velocity.

But from the perspective of the photon, there is no distance and no time. If unobstructed, it will reach the "edge of the universe" (if there was such a thing) in zero time. It's not something you can think of intuitively because we exist in a realm where relativistic effects are not part of our experience, but the Lorentz factor that is applied to distance, time, and mass calculations, is a well proven part of the theory of relativity.
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Perhaps, but who would be there to see it. It's just interesting to think of something expanding into all space and into no space at the same time.
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Perhaps if an object expanding in all directions at the speed of light being made of many atoms at what point is a bunch of atoms an object and when is it just atoms traveling in exactly one direction each?
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My understanding is when an object approaches the speed of light from the point of view of an outside viewer the object contracts in the direction of the path?
Speed is a relative thing, so a more correct way to say this is that anything (Earth say) contracts in the direction of motion relative to any reference frame in which Earth moves quickly.
No rockets or other acceleration is necessary for it.

If an object could actually reach the speed of light would the object become 2 dimensional from everyone else's perspective?
This is meaningless. Light does not define a valid reference frame.
So better to say that as the reference frame approaches the speed of light relative to the object being measured, the object does indeed approach negligible thickness relative to that frame.

My apologies for rewording everything, but the wordings in the OP imply a sort of absolute velocity, which is meaningless in relativity theory.

Is there any hypothetical way an object can travel in all directions at the same time?
Linear velocity is a vector relative to some arbitrary reference. That vector can only point in one direction, so no, at least not relative to any specific reference.
Still, I can be moving west relative to the center of Earth and East relative to the sun, so given different references, one's velocity can be anything you want, all at once.
Angular velocity is also a vector (an absolute one this time), so say a spinning two-dimensional ring can contract in all directions as its absolute rate of rotation increases.

And if it were doing that at the speed of light would it not also be becoming 0 dimensional?
Speed of light is a constant scalar, not a dimensional thing at all.

Say your friend is traveling to Alpha Centauri, about 4 light-years away.
...
From your friend's perspective, you, the earth, and the distance to Alpha Centauri flattens as well.
He would arrive quickly (depending on how close to "c" he's traveling) because of this shortening of the distance, which also translates into the time shortening effect experienced by your friend in the fast moving rocket.
Not disagreeing with any of this, but from the friend's perspective, he's not travelling at all and it is simply Alpha Centauri traveling to him in presumable some short time possibly less than 4 years.

But from the perspective of the photon, there is no distance and no time. If unobstructed, it will reach the "edge of the universe" (if there was such a thing) in zero time
This cannot work. For one thing, as stated above, there is no valid 'perspective of the photon'. Secondly, if unobstructed, no photon reaches an edge of the universe. For instance, light currently emitted from a star 16 billion light years away will never reach here period after any amount of time as measured by anything. This of course cannot be true in Minkowskian flat spacetime, but spacetime isn't flat in reality.
Relative to a cosmological coordinate system (a coordinate system in which the size of the universe is not bounded), light fades to zero energy (proper distance method) or coasts to a halt (comoving distance method). Both of those are the same coordinate system with different methods of specifying distance between objects.

Perhaps if an object expanding in all directions at the speed of light being made of many atoms at what point is a bunch of atoms an object and when is it just atoms traveling in exactly one direction each?
OK, I'll buy that. You inflate a balloon, and each part of the balloon moves at a different velocity relative to the center. But this isn't the velocity of the balloon, it is a bunch of separate velocities of a set of parts, each with different motion.
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He would arrive quickly (depending on how close to "c" he's traveling) because of this shortening of the distance,

Well, that's a twist I was not aware of. :chin:
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This cannot work. For one thing, as stated above, there is no valid 'perspective of the photon'. Secondly, if unobstructed, no photon reaches an edge of the universe. For instance, light currently emitted from a star 16 billion light years away will never reach here period after any amount of time as measured by anything. This of course cannot be true in Minkowskian flat spacetime, but spacetime isn't flat in reality.
Relative to a cosmological coordinate system (a coordinate system in which the size of the universe is not bounded), light fades to zero energy (proper distance method) or coasts to a halt (comoving distance method). Both of those are the same coordinate system with different methods of specifying distance between objects.

Clearly a photon does not have a perspective, just trying to get the point across that to a photon there is no such thing as time. From a Minkowskian perspective it is easy to graph an object traveling at the speed of light and realizing that as a light-like object, it will experience no time and arrive at its destination, whatever it is, instantly. Of course, the real universe is expanding so the locality simplifications of minkowskian space do not apply in reality. In an expanding universe, an unobstructed photon would become redshifted until its wavelength approaches infinity and its energy approaches zero, dimming out to nothing. However this is besides the point... the point is that although to any observer, that photon would be traveling at the speed of light and take up and ungodly amount of time to fade into nothingness, to the photon this happens instantly and in zero time.
By the way, no photon will ever "coast to a halt". Any photon, regardless of energy or frame of reference will always travel exactly at the speed of light.
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Well, there seems to be a consensus among the posters regarding what happens to time at lightspeed and perhaps beyond via simple extrapolation. There are attempts to describe this state but I feel we could improve upon them if only those who have the relevant info tried ... a little harder.
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So that in conclusion, at the speed of light, all distances and all times are simultaneous. A singularity. Therefore matter cannot exist. Only pure "potential" energy.

For a photon, which has no mass and always travels at the speed of light, distance and time only exist from the perspective of the observer: to a photon there is no such thing as distance and time, once it's emitted, it reaches its destination instantly in zero time.

...and which can explain the hypothesis of the big bang and the universe as we know it being a "bubble" in a pure energy field. Like, if infinite and there are infinite quantum possibilities that can occur in that infinite energy, it would eventually lead to the possibility of a bubble where energy fades out and then deflates back into pure energy. Since that pure energy "locally" fades and that energy is between singularities within its "bubble" (like black holes), it appears as matter, like gas crystalizing in the air.
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Well, there seems to be a consensus among the posters regarding what happens to time at lightspeed and perhaps beyond via simple extrapolation. There are attempts to describe this state but I feel we could improve upon them if only those who have the relevant info tried ... a little harder.

I could tell you there is a vein of gold 1 mile under your feet, but if you want to see that gold with your own eyes, you've got to dig.
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I could tell you there is a vein of gold 1 mile under your feet, but if you want to see that gold with your own eyes, you've got to dig.

On point! Good logic!
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Clearly a photon does not have a perspective, just trying to get the point across that to a photon there is no such thing as time.

In QFT, the universe contains 'interacting' fields. Every field permeates the entire universe, yes?
So does a 'photon'/field excitation really 'travel' at all?
Like a water wave or a mexican wave in a crowd of people. Each person just undulates in sequence order. Each person just stands up and sits down at the correct time. This gives the appearance of a moving wave. If a photon can appear at any point in space or time then perhaps it does not have to travel as it is already there and has been there since the big bang singularity. The speed of light would then be an observed constant of propagation through a universal field, but the 'photon' can arrive at any point in the universe instantly as a 'photon' has always existed at every point in the universe.
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In QFT, the universe contains 'interacting' fields. Every field permeates the entire universe, yes?
So does a 'photon'/field excitation really 'travel' at all?
Like a water wave or a mexican wave in a crowd of people. Each person just undulates in sequence order. Each person just stands up and sits down at the correct time. This gives the appearance of a moving wave. If a photon can appear at any point in space or time then perhaps it does not have to travel as it is already there and has been there since the big bang singularity. The speed of light would then be an observed constant of propagation through a universal field, but the 'photon' can arrive at any point in the universe instantly as a 'photon' has always existed at every point in the universe

I like this analogy a lot. Seems very intuitively logical and reasonable. My mind is chewing on it. Food for thought.
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...and which can explain the hypothesis of the big bang and the universe as we know it being a "bubble" in a pure energy field. Like, if infinite and there are infinite quantum possibilities that can occur in that infinite energy, it would eventually lead to the possibility of a bubble where energy fades out and then deflates back into pure energy. Since that pure energy "locally" fades and that energy is between singularities within its "bubble" (like black holes), it appears as matter, like gas crystalizing in the air.

Yes. That's a good explanation I enjoyed picturing it mentally. It runs in tandem with the underlying notion I have considered through several variations/ analogies of my own. It seems we are in some form of fundamental agreement here about the contraction and expansion of the universe and that interplay (material precipitation) between energy and time as it does.
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I like this analogy a lot. Seems very intuitively logical and reasonable. My mind is chewing on it. Food for thought.

:up: Quantum entanglement seems to be a way for information to appear at more than one place at the same instant in time, regardless of the distance between the two points. This does not mean we can therefore find a way to 'send' or 'transmit' information instantly. It suggests to me, that certain information was always there, and certain events allow certain forms of information to appear.
All electrons are identical. Wheeler and Feynman even introduced the idea of a single electron universe with a positron simply being that single electron moving backwards in time. It was discarded mainly because there seems to be many more electrons than positrons, but superposition may be two separated but connected, identical excitations with identical information, that appear to be/are the same object.
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In QFT, the universe contains 'interacting' fields. Every field permeates the entire universe, yes?
So does a 'photon'/field excitation really 'travel' at all?
Like a water wave or a mexican wave in a crowd of people. Each person just undulates in sequence order. Each person just stands up and sits down at the correct time. This gives the appearance of a moving wave. If a photon can appear at any point in space or time then perhaps it does not have to travel as it is already there and has been there since the big bang singularity. The speed of light would then be an observed constant of propagation through a universal field, but the 'photon' can arrive at any point in the universe instantly as a 'photon' has always existed at every point in the universe.

As you know, QFT, as QM and QP, are mere mathematical abstractions that predict with extreme accuracy how a quantum system behaves, but offer very, very little in creating a picture of what is actually happening. I usually try to keep clear from the "shut up and calculate" mentality when trying to form a picture of reality.

The phenomenon I was describing has very little to do with quantum theory and almost everything with Special Relativity, which describes how time and distance measurements in different inertial frames of reference (aka objects moving at a different speed from the observer) change and relate to each other. At the velocities we are used to, these changes negligible, but as an object approaches the speed of light, the changes become dramatic. On the other hand, SR offers very little on the nature or reality of the photon.

..and which can explain the hypothesis of the big bang and the universe as we know it being a "bubble" in a pure energy field. Like, if infinite and there are infinite quantum possibilities that can occur in that infinite energy, it would eventually lead to the possibility of a bubble where energy fades out and then deflates back into pure energy. Since that pure energy "locally" fades and that energy is between singularities within its "bubble" (like black holes), it appears as matter, like gas crystalizing in the air.

That sounds very poetic and has a nice ring to it. The issue arises when mixing poetry with jargon, so within the context of your interpretation, I'm unsure of what to make of it.
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My understanding is when an object approaches the speed of light from the point of view of an outside viewer the object contracts in the direction of the path?

If an object could actually reach the speed of light would the object become 2 dimensional from everyone else's perspective?

Is there any hypothetical way an object can travel in all directions at the same time? If that were so would it not be expanding? And if it were doing that at the speed of light would it not also be becoming 0 dimensional?

I put your question to OpenAI's ChatGPT. I've also included some of my own questions (based on the above exchange between @staticphoton and @noAxioms). To the best of my knowledge, the responses are correct.

According to the theory of relativity, as an object approaches the speed of light, it will appear to contract in the direction of its motion. This is known as length contraction. However, the object itself does not actually shrink; it is only its appearance that changes from the perspective of an outside observer.

If an object were to reach the speed of light, it would not become two-dimensional from the perspective of outside observers. This is because the speed of light is a limiting speed; it is impossible for any object to actually reach the speed of light, so the question of what would happen if an object did is purely hypothetical.

It is also not possible for an object to travel in all directions at the same time, since this would violate the laws of physics. In order for an object to move, it must have a definite direction and speed. An object that is expanding, such as the universe, is not moving in any particular direction, but rather is increasing in size in all directions simultaneously.

As for the question of an object becoming zero-dimensional, this is also not possible according to the laws of physics. An object must have a non-zero size in order to exist, so it is not possible for it to become zero-dimensional.
— ChatGPT

Isn't a photon an object?

A photon is not an object in the traditional sense of the word. A photon is a type of elementary particle, which is a fundamental building block of matter. Unlike objects, which have a definite size and shape, photons do not have any physical form or structure. They are characterized by their energy and momentum, and they can travel through space at the speed of light. Because of their unique properties, photons are sometimes described as "particles of light." — ChatGPT

Can a photon travel to the edge of the universe?

It is impossible for a photon, or any other form of matter or energy, to reach the edge of the universe. This is because the universe is expanding, and the space between galaxies is getting larger all the time. As a result, the distance to the edge of the universe is constantly increasing, so it is not possible for anything to reach it. Additionally, the concept of the "edge" of the universe is not well-defined, since the universe is thought to be infinite in size. — ChatGPT

How about in the reference frame of the photon?

In the reference frame of a photon, time does not pass, so the concept of the photon reaching the edge of the universe is not well-defined. In the reference frame of a photon, the universe appears to be a sphere with a radius of zero, and the photon is always at the center of the sphere. This is because the speed of light is constant in all reference frames, so from the perspective of the photon, it is always at the same point in space, no matter how far it has traveled. — ChatGPT
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By the way, no photon will ever "coast to a halt". Any photon, regardless of energy or frame of reference will always travel exactly at the speed of light.
This is true only of an inertial frame of reference, and only in flat Minkowskian spacetime (with no gravity anywhere). It isn't true of any other kind of coordinate system.
My apology to Paris for being the Guinea pig of this example.
Relative to Paris, it takes light less time to go to the moon and back than the distance involved. It's really close, but light travels faster than c relative to Paris, at least along this path. This is due to spacetime not being Minkowskian between here and the moon, and not so much due to the how Paris moves during that experiment.
In the frame of Paris (the coordinate system in which Paris stays stationary), eastbound light goes slower than westbound light, so signals sent via say 20 mirrors around the world will get back to Paris quicker in one direction than the other. This is the well known Sagnac effect.
In the frame of Paris, a light pulse in just the right place somewhere around the orbit of Neptune will coast to a halt, then reverse and go back the way it came.

Oh yea: In cosmological coordinates with distance measured as comoving distance, light speed (comoving distance per second) in a vacuum slows over time, approaching but never reaching a halt. But there's a distance (about 16 BLY from where it gets emitted today) beyond which it will never reach even in infinite time, so if it doesn't slow to a halt, it will surpass this limit. That's the current comoving distance to the event horizon, and if light emitted now from there can never reach us, then light from here can't reach them either.
I have a graph of such coordinates if you don't know what I'm talking about.

Light also comes to a halt in an accelerated coordinate system such as Rindler coordinates.

I put your question to OpenAI's ChatGPT. To the best of my knowledge, the responses are correct.
I agree with the answers, but I still have commentary.

According to the theory of relativity, as an object approaches the speed of light, it will appear to contract in the direction of its motion. This is known as length contraction. However, the object itself does not actually shrink; it is only its appearance that changes from the perspective of an outside observer. — ChatGPT
This can be interpreted in different ways, so to clarify, relative to some inertial frame in which some object is moving, that object will be measured to be contracted.
Usage of the word 'appearance' is deceptive. For instance, relative to that frame, the fast clock slows down (time dilation). But the dilated clock is moving towards above referenced obverser, the appearance of that clock will be of it running faster than normal, not slower. This is due to Doppler effect, which is a stronger effect than is dilation for objects changing distance with the observer.

As for the question of an object becoming zero-dimensional, this is also not possible according to the laws of physics. An object must have a non-zero size in order to exist, so it is not possible for it to become zero-dimensional. — ChatGPT
Isn't a photon an object?
Good question. All fundamental particles lack a meaningful size. Size is a classic concept and only applies to classic things. Size in this context means distance between different components of an object, and photons, electrons, etc do not have components, and thus have no meaningful size and cannot meaningfully contract relative to some frame.
I'm not disagreeing with ChatGPT's answer here, just spouting how I would have put it.

Can a photon travel to the edge of the universe?
It is impossible for a photon, or any other form of matter or energy, to reach the edge of the universe. This is because the universe is expanding, and the space between galaxies is getting larger all the time. As a result, the distance to the edge of the universe is constantly increasing, so it is not possible for anything to reach it. Additionally, the concept of the "edge" of the universe is not well-defined, since the universe is thought to be infinite in size. — ChatGPT
OK, this answer implies that there is a meaningful edge to the universe, which is not part of any accepted theory I've seen. No information emitted now can get beyond the current event horizon, per the top of this post. That distance is a lot closer than the nonexistent "edge of the universe". We can see stuff beyond that horizon, but only via light that was emitted back when the objects we see were much closer and the event horizon was further away ('further' depending heavily on how such distances are measured).

So does a 'photon'/field excitation really 'travel' at all?
The field doesn't, but the excitation does. A field is something that is by definition 'everywhere' and so it isn't meaningful to speak of it travelling, which implies it gets to a location where it wasn't before.
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Relative to Paris, it takes light less time to go to the moon and back than the distance involved. It's really close, but light travels faster than c relative to Paris, at least along this path. This is due to spacetime not being Minkowskian between here and the moon, and not so much due to the how Paris moves during that experiment.
In the frame of Paris (the coordinate system in which Paris stays stationary), eastbound light goes slower than westbound light, so signals sent via say 20 mirrors around the world will get back to Paris quicker in one direction than the other. This is the well known Sagnac effect.

This is due to the rotary motion of the moon around the earth and has nothing to do with the speed of light changing. The Sagnac effect was conceptualized before the theory of General Relativity was created.

In the frame of Paris, a light pulse in just the right place somewhere around the orbit of Neptune will coast to a halt, then reverse and go back the way it came

Again, this has nothing to do with light moving at any other velocity than c.
The two examples are within local space where Minkowskian space coordinates and cosmological coordinates are undifferentiable.

Oh yea: In cosmological coordinates with distance measured as comoving distance, light speed (comoving distance per second) in a vacuum slows over time, approaching but never reaching a halt. But there's a distance (about 16 BLY from where it gets emitted today) beyond which it will never reach even in infinite time, so if it doesn't slow to a halt, it will surpass this limit. That's the current comoving distance to the event horizon, and if light emitted now from there can never reach us, then light from here can't reach them either.
I have a graph of such coordinates if you don't know what I'm talking about.

It is obvious that in a large enough expanding universe, to any observer there is a horizon beyond which the expansion happens faster than the speed of light, and that a photon emitted from his flashlight will never reach this horizon. But to use jargon such as "commoving distances" in the context of this thread to imply light slows down as it approaches this horizon is misleading. A photon can only, and will always, travel at the speed of light.
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OK, this answer implies that there is a meaningful edge to the universe, which is not part of any accepted theory I've seen.

True, though neither is it ruled out. As physicists' Sabine Hossenfelder and Max Tegmark note:

Whenever you try to measure something infinite, the best you can do in practice is to say it’s larger than something finite that you have measured. But to show that it was really infinite you would have to show the result was larger than anything you could possibly have measured. And there’s no experiment that can show that. So, infinity is not real in the scientific sense.

Nevertheless, physicists use infinity all the time. Take for example the size of the universe. In most contemporary models, the universe is infinitely large. But this is a statement about a mathematical property of these models. The part of the universe that we can actually observe only has a finite size.
...
But maybe using infinity and zero in physics brings in mistakes because these assumptions are not only not scientifically justified, they are not scientifically justifiable. And this may play a role in our understanding of the cosmos or quantum mechanics. This is why some physicists, like George Ellis, Tim Palmer, and Nicolas Gisin have argued that we should be formulating physics without using infinities or infinitely precise numbers.

Let’s face it: Despite their seductive allure, we have no direct observational evidence for either the infinitely big or the infinitely small.
...
Our challenge as physicists is to discover this elegant way and the infinity-free equations describing it—the true laws of physics. To start this search in earnest, we need to question infinity. I’m betting that we also need to let go of it.
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OK, this answer implies that there is a meaningful edge to the universe, which is not part of any accepted theory I've seen.
— noAxioms
True, though neither is it ruled out. As physicists' Sabine Hossenfelder and Max Tegmark note:
The selected quotes from the above physicists concern infinity, which I did not mention in my comment. I did reference infinite time.
My comment concerned chatGPT's response to a reference to an 'edge', which implies a spatial boundary with matter, light, and stars on one side and nothing on the other. He does say that such a thing isn't well defined. Again, I don't disagree with any of his responses.
There are models of finite size universes, but most/all(??) of them curve in on themselves, much like Earth having finite surface area without anywhere having an edge. It was the reference to that edge at which I balked.

Concerning my illustrations of light moving at coordinate speeds other than c, I need to label my 4 examples described in my prior posts.
M) Light to moon and back
S) Sagnac
N) Light coming to halt near Neptune (Sagnac being driven more to extremes)
C) Comoving coordinates

This is due to the rotary motion of the moon around the earth and has nothing to do with the speed of light changing. The Sagnac effect was conceptualized before the theory of General Relativity was created.
You quoted two examples in that comment (M and S). Only S has to do with rotation, and if you read my comment carefully, I said S has nothing to do with the motion of anything, but rather with a rotating frame of reference. Motion, after all, is entirely frame dependent. In an inertial frame, light moves east and west at the same speed and the only reason one takes longer than the other is because the path taken is longer one way than the other.
Relative to the rotating coordinates, both paths are identical in length and since light takes different times to make the trip, light speed is not constant. My point (of all four examples) was that this was a coordinate effect.

Light goes faster (relative to our Paris observer) than c to the moon and back even if both moon and Paris are held stationary, so that example isn't about motion, it is about higher gravitational potential along the entire route taken by light. This has been demonstrated experimentally, but light admittedly goes slower than c while going through the atmosphere, a small segment of the round trip.

It is obvious that in a large enough expanding universe, to any observer there is a horizon beyond which the expansion happens faster than the speed of light, and that a photon emitted from his flashlight will never reach this horizon.
Careful about the use of the word 'obvious' since it almost always means one is relying on intuition instead of what the mathematics says, which is anything but intuitive.

First of all, expansion rates are not a speed. For instance the universe is currently expanding at 70 km/sec/mpc which is different than any speed which is measured in units of km/sec or some such.

Yes, to any observer, there is a distance at which comoving objects increase their proper distance from that observer at a rate of c. This is known as the Hubble radius, and it about 14 BLY away. The event horizon is beyond that at about 16 BLY.

If what you say is true, then a galaxy beyond the Hubble radius (purple line below) can only emit light on our side and would be invisible on the other since it is outrunning its own light. Of course that's not the case, and so light emitted away from us recedes from us at well over c. And that's using proper distance coordinates which wasn't even one of my examples.
To illustrate the difference between the two ways of measuring distance in cosmological (expanding) coordinates, you can compare these two spacetime diagrams which depict all the same things, but with different distance measuring methods.

The upper one shows proper distance. My example galaxy might be GN-z11, a long-time holder of most-distant galaxy record until JWST found all sorts of more distant things. The worldlines of galaxies are those dotted lines. GN-z11 meets the blue 'now' line in both graphs at a distance of about 31 Glyr. In proper distance terms (the upper graph), the thing is receding at around 2.3c, and yet we see it because its worldline crosses our past light cone (in red).

The lower graph shows all the same thing but with distance measured in comoving distance. Under this coordinate system, most objects (pretty much any galaxy) is essentially stationary and has vertical worldlines. GN-z11 is still there, but a vertical dotted line now at 31 Glyr. Our light will never reach it in any amount of time, so light has to slow down to not make it there ever.

The red light-cone line is most interesting since it illustrates my points in both cases. The red line shows everything that we can see. If it's not on that line, we can't see it. So you can see your mug because that red line crosses the worldline of your mug.
In the upper illustration, light that got emitted straight towards Earth early on (say the CMB light) actually gets further away at first, coasts to a halt about 9 billion years ago, and then starts making its way to where we are now, to be detected today. The chart shows light not moving at all relative to us when that red line is perfectly vertical.
In the lower illustration the same red line changes slope the whole way as well, but it was moving faster than c up until now. It will continue to slow and light emitted from here today will never reach what is today's event horizon, which is about 16 Glyr away today (the orange line in both diagrams).
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He would arrive quickly (depending on how close to "c" he's traveling) because of this shortening of the distance, — staticphoton

Well, that's a twist I was not aware of. :chin:

I'm still curious about this. If we measure interstellar distances in km and not light years, and our clock is ticking a bit slower as we advance to our destination explain how that actual distance may diminish from our perspective beyond that calculated by D=RT, thus having us arrive early? Is my question even valid in the context of relativity?
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If we measure interstellar distances in km and not light years, and our clock is ticking a bit slower as we advance to our destination explain how that actual distance may diminish from our perspective beyond that calculated by D=RT, thus having us arrive early?
"A high speed traveler is never late. Nor is he early. He arrives precisely when he means to."

That reference out of the way, km is no different than light years. There's just 13 orders of magnitude more of them but they're still measuring the same thing.
From your own perspective, your own clock never ticks slower since it is stationary relative to itself. So from your perspective, it is the destination that is coming to you quickly, and the distance to it is what contracts. I don't know what R is in D=RT. It looks like distance = velocity•time, but R doesn't look much like velocity, so maybe you mean something else.
So say you want to get to the far side of the galaxy before you die. 10 years we'll give it, and it's 7e17 km away (70000 light years). Can do. Accelerate quickly up to about 0.99999999c. In your frame, the far side of the galaxy is now about 10 light years away and will be here in 10 years as measured on your stationary clock. Clocks at the fast moving far side of the galaxy will tick 7000x slower of course, at least while moving at that speed.
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$\frac{m_t}{s_t}$ = d

mt = moving time
st = stationary time
d = time dilation factor (how slowly is time passing for the moving observer).
v == velocity
c = speed of light
Tm/s [relative time, moving observer (m) relative to stationary observer (s)] = mt $\times\space d$

d $\propto$ $\frac{1}{v}$

As v $\to$ c, d $\to 0$ and Tm/s $\to 0$
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I'm still curious about this. If we measure interstellar distances in km and not light years, and our clock is ticking a bit slower as we advance to our destination explain how that actual distance may diminish from our perspective beyond that calculated by D=RT, thus having us arrive early? Is my question even valid in the context of relativity?

The concept of the traveler arriving early assumes a universal clock and a universal metric. In first order, ditch the universal clock: To an observer, any moving object will run on a slower clock and measure a shorter length in the direction of motion than if the object was at rest in relation to the observer. At slow speeds the effect is negligible, but as the object approaches the speed of light the effect becomes dramatic.

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