# The speed of light. What's the story, really?

• Homesick345
In summary: Anything with mass, no matter how small, will never reach the speed of light because the energy needed to get there is infinite. This includes photons, the particles that make up light.
Homesick345
Why can't we go any faster? If the speed of light is measured, why can't we go 1 mph faster? What's the theoretical barrier that makes it so unbreakable? why all this respect for this speed limit? Who's giving the tickets?

C is a very special number. C is the speed of all massless particles in a vacuum, so anything with 0 mass travels at C.

Anything with mass does not and cannot travel at C. As anything with mass accelerates towards C it takes more and more energy to get closer to C, to actually reach the speed of light would take more energy than is in the entire universe.

General Relativity forbids anything reaching C as it is mathematically impossible for mass to go at that speed.

That is a simplified explanation but holds true.

Light speed isn't a "wall" that we can't get past like the sound barrier was thought to be. When you accelerate a jet up to near the speed of sound, you can easily accelerate another 1 mph or 10 or whatever. This isn't so when the velocity approaches c. Once you reach about 10%-20% of c you have to start accounting for the increasing effect of time dilation, length contraction, and differing frames of reference. The simple explanation is that once your speed is a significant fraction of c your acceleration isn't the same as it was your speed was slower. This means that accelerating at 1g for 1 minute when you reach 50% c doesn't increase your speed as much as it did when you were only going 10% c. Commonly you will read or hear that this is because the "mass" increases as your speed increases. This isn't really true, and is based on an old misuse of the term "mass". My understanding is that time dilation is the reason, but I'm not certain.

Honestly the whole subject is rather complicated and requires a basic understanding of Special and General Relativity. I advise you to purchase a book on Relativity from a local bookstore or online.

Hi,

The reason we can not go faster than the speed of light is simple. As you accelerate, your energy gets higher and higher. And from E=mc2, we know that this also increases your mass. The higher your mass, the harder it is to increase your speed(just think about how much easier it is to move a basketball rather than a car.). Therefore, as you go faster, it gets harder and harder to continue to accelerate. To accelerate to the speed of light, you would need to exert an infinite amount of energy. So, even if you had a particle collider with a ridiculous amount of energy you could only make a particle going 99.9% of the SoL continue to approach the SoL but never reach it (i.e. 99.9999999...% of the SoL)

The reason light can reach this speed is that it is massless, unlike matter.

Mark M said:
Hi,

The reason we can not go faster than the speed of light is simple. As you accelerate, your energy gets higher and higher. And from E=mc2, we know that this also increases your mass. The higher your mass, the harder it is to increase your speed(just think about how much easier it is to move a basketball rather than a car.). Therefore, as you go faster, it gets harder and harder to continue to accelerate. To accelerate to the speed of light, you would need to exert an infinite amount of energy. So, even if you had a particle collider with a ridiculous amount of energy you could only make a particle going 99.9% of the SoL continue to approach the SoL but never reach it (i.e. 99.9999999...% of the SoL)

The reason light can reach this speed is that it is massless, unlike matter.

As I said in my above post, this is not true. The mass of an object does not change. If it did, then at a certain speed anything would be transformed into a black hole, which does not happen.

Drakkith said:
As I said in my above post, this is not true. The mass of an object does not change. If it did, then at a certain speed anything would be transformed into a black hole, which does not happen.

You are referring to he invariant mass, m0 , which you are correct, doesn't change in different speeds. Rather, it is inertial mass(or relativistic mass), the object's resistance to acceleration that increases with acceleration, so that:

ER = γmc2

where ER is the relativistic energy.

So the same conclusion still holds: as you approach c, you require an infinite amount of energy to reach c itself.

I tried to simplify it for the person asking the question by just using the term "mass", mistake on my part.

EDIT: Oh, I forgot to say: You're right about time dilation preventing you from going faster than c, there are several other factors. Obviously, the Universe is pretty strict on maintaining it's speed limit.

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The speed of light is not technically an impossible goal for a massive object as it could theoretically be possible that infinite application of energy could be had over an endless time interval. But I digress, this is really semantical.

For all practical purposes, it's safe to assume that it would require an unfathomable amount of energy to accelerate a massive object to the speed of light. And it's also safe to assume that any object of significant mass will never be able to approach a significant proportion of light speed. For instance, we're not talking about it being extremely difficult to make a chunk of matter reach 99.999999% the speed of light. More realistically we're talking about reaching maybe a few percent of light speed. You can pretty much end there.

This is not necessarily related to the limitations of light speed. As I'm not sure you're talking about approaching but instead exceeding.

Also, all of this must be referenced within the perspective of a continuous piece of one dimension of space. The speed of light between two points goes to hell if you include the possibility of hyper-spacial travel. This is likely how pair-bonded particles can react instantaneously over any distance.

If it was required that communication be only through one dimension, then light speed is an actual limit. As exceeding it would break the causal chain.

In other words, let's take an explosion. When an explosion happens, photons are released and travel in all different directions. Let's start a clock right when the photons are emitted and stop that clock when a photon hits a distant object. If this were ideally in a vacuum, the amount of time that passed from the point of emission to the point of impact divided by the distance from emission to impact should equal c.

What happens if it takes longer? This is okay and could be explained, for instance, if the light traveled through some medium.

What if it takes a shorter period of time? This is a serious problem. Why? It can be looked at like this. Let's say that, under normal conditions, it takes light 1 second to travel from the point of emission to the point of impact. We would observe the explosion 1 second after it occurred. What if we somehow measured time and distance and found that time was shorter than expected; taking only .7 seconds? This would mean that the part of time that is missing would be pushed backwards into the 4th dimension past the point at which the explosion occurred. The emission would have to result before the explosion.

This is called breaking causality.

Normally...

(explosion)-------------------------------(impact)
(time at explosion/time of emission)--->--------------->----------(time at impact)
[-----------fixed to c-----------]

shortened observed time

(time of emission)--->-----(time at explosion)-------->-----------(time at impact)
[----------] [--------------------]

This is not necessarily a problem until we make clear that the emission is caused by the explosion. At that point, it would be impossible for the emission to occur before the explosion. Making the above diagram nonsensical.

Thanks all. Wow, I'm a bit more "enlightened". I heard one theoretical physicist on TB asserting the following: "the speed of light is not 300,000km/s, the speed of light is infinite". This was more than 20 years ago, by some famoust french physicist. It stuck with me. Is this bull?

I meant on french TV

Homesick345 said:
Is this bull?

Yes, if that is in fact what he said. Perhaps a translation error? Perhaps you misunderstood him? Perhaps he's an idiot? (one of the first two is more likely).

phinds said:
Yes, if that is in fact what he said. Perhaps a translation error? Perhaps you misunderstood him? Perhaps he's an idiot? (one of the first two is more likely).

Hi - I'm sure this is what he said. I will maybe remember his name. He's kind of famous (in France at least) - he wrote many books "for the public" - (no, not Hubert Reeves, who is Candian I think). French is almost a mother tongue for me - so there is no mistake - or translation, I'm 100% sure this is exactly what he said. This was around 1980 on a famous french TV "litterary" talk show, hosted by the famous Bernard Pivot. But well, I guess it's not really important

Homesick345 said:
Hi - I'm sure this is what he said. I will maybe remember his name. He's kind of famous (in France at least) - he wrote many books "for the public" - (no, not Hubert Reeves, who is Candian I think). French is almost a mother tongue for me - so there is no mistake - or translation, I'm 100% sure this is exactly what he said. This was around 1980 on a famous french TV "litterary" talk show, hosted by the famous Bernard Pivot. But well, I guess it's not really important

Well, perhaps he meant it in a "literary" way ... the speed of light can't be reached by normal matter so it might as well be infinite ... that kind of thing. Still, I dislike it when supposedly reputable physicists get caught up in popularization and making money and start saying things that are either blatantly wrong (check out "Through the Wormhole" with Morgan Freeman) or at the very least, misleading (watch anything on TV with Michio Kaku)

EDIT: Morgan Freeman is not a physicist, so can be forgiven for reading nonsense, but the show's writers should be shot.

Drakkith said:
As I said in my above post, this is not true. The mass of an object does not change. If it did, then at a certain speed anything would be transformed into a black hole, which does not happen.

It's not the mass that causes gravitation, but all energy. However, kinetic energy enters into the equations of GR differently from other (for example thermal or mass-like) energies, as the Einstein equation relates metric to the 4d energy-momentum tensor. I have not done the explicit calculations but I'm sure you are right in that fast moving things don't collapse into black holes. :-)

clamtrox said:
It's not the mass that causes gravitation, but all energy. However, kinetic energy enters into the equations of GR differently from other (for example thermal or mass-like) energies, as the Einstein equation relates metric to the 4d energy-momentum tensor. I have not done the explicit calculations but I'm sure you are right in that fast moving things don't collapse into black holes. :-)

Maybe they would. =D

I'm pretty sure the mass of an object at any particular value of v is determined by the lorentz factor for that v. Anything traveling at 99.9%c would therefore be 22 times more massive than in its rest frame. So maybe our sun traveling at 99.9%c would collapse into a black hole, but a tiny little spaceship wouldn't. But that's just an assumption. I couldn't tell you if some unusual counter-effects would apply, or if it even works that literally.

salvestrom said:
Maybe they would. =D

I'm pretty sure the mass of an object at any particular value of v is determined by the lorentz factor for that v. Anything traveling at 99.9%c would therefore be 22 times more massive than in its rest frame. So maybe our sun traveling at 99.9%c would collapse into a black hole, but a tiny little spaceship wouldn't. But that's just an assumption. I couldn't tell you if some unusual counter-effects would apply, or if it even works that literally.

As clamtrox said in the previous post, mass enters into Relativity differently than in Newtonian classical mechanics. When people say "mass", they are almost always referring to the standard type of mass, "rest mass" or "invariant mass". In relativity, relativistic mass is used, which is how much mass an object appears to have to an observer in relative motion.

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Say you have three adjacent observers, all at rest relative to each , A,B,C.

A stays at rest with respect to itself, B and C each accelerate to .5 c in opposite directions with respect to A.

From A's perspective, would it not be the case that B, and C, are moving away from each other at the speed of light? What is the trick, that allows A to see B moving away in one direction at .5 c, and C the other at .5 c, without seeing C, and B moving away from each other at C.

How about C, and B what would they observe? What would be the difference between the speed A would observe between C, and B, and the speed B, and C would observe between each other and A?

It doesn't take any energy at all to travel at any speed you desire short of c. All you have to do is transform the Frame of Reference in which you are at rest into some other Frame of Reference moving at v with respect to your rest Frame of Reference and you will be traveling at v. The reason why you cannot travel at c or exceed c is because the transformation process results in an undefined or imaginary result due to the fact that you have to multiply by gamma which is 1/√(1-v2/c2). It is easy to see that when v = c, you need to divide by zero which is undefined and when v > c, you need to take the square root of a negative number which is imaginary.

It was for purely mathematical reasons involving gamma that Einstein stated in his 1905 paper introducing Special Relativity, that velocities at or above c are meaningless. He also stated that for this reason, "the velocity of light in our theory plays the part, physically, of an infinitely great velocity" (section 4), which is probably what the French physicist was alluding to. This doesn't mean that the speed of light is infinite, it just means that no matter how much you have accelerated and no matter how much you have increased your speed, you are no closer to the speed of light than when you started.

salvestrom said:
Maybe they would. =D

I'm pretty sure the mass of an object at any particular value of v is determined by the lorentz factor for that v. Anything traveling at 99.9%c would therefore be 22 times more massive than in its rest frame. So maybe our sun traveling at 99.9%c would collapse into a black hole, but a tiny little spaceship wouldn't. But that's just an assumption. I couldn't tell you if some unusual counter-effects would apply, or if it even works that literally.

No, this is a misconception. Mass refers to the invariant mass, the "rest" mass, named invariant because everyone in all frames would agree on it. Since any object is stationary in it's own frame, the mass of an object does not change no matter how fast it goes and it will never collapse into a black hole. Think about this, to a neutrino flying towards us at 99%+ c, the Sun should collapse into a black hole if mass changed with velocity.

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jreelawg said:

Say you have three adjacent observers, all at rest relative to each , A,B,C.

A stays at rest with respect to itself, B and C each accelerate to .5 c in opposite directions with respect to A.

From A's perspective, would it not be the case that B, and C, are moving away from each other at the speed of light? What is the trick, that allows A to see B moving away in one direction at .5 c, and C the other at .5 c, without seeing C, and B moving away from each other at C.

How about C, and B what would they observe? What would be the difference between the speed A would observe between C, and B, and the speed B, and C would observe between each other and A?
If you look up velocity addition in wikipedia, you will get the answer that 0.5c + 0.5c = 0.8c.

ghwellsjr said:
If you look up velocity addition in wikipedia, you will get the answer that 0.5c + 0.5c = 0.8c.

Does that follow that the sum of the distances traveled away from the object would also be 80% of what you would expect?

Because the observer can say definitively, that each other observer separately has traveled a certain distance based on their speed .5 C, and you would think that two certain distances should ad up without relativistic effects. I'm confused.

ghwellsjr said:
If you look up velocity addition in wikipedia, you will get the answer that 0.5c + 0.5c = 0.8c.

jreelawg said:
Does that follow that the sum of the distances traveled away from the object would also be 80% of what you would expect?

Because the observer can say definitively, that each other observer separately has traveled a certain distance based on their speed .5 C, and you would think that two certain distances should ad up without relativistic effects. I'm confused.

To observer A, both B and C are traveling at 0.5c away. So the distance between them is increasing at 1.0 c which is perfectly ok, because to observer B, observer c is only moving 0.8 c, and observer C see's B receding at 0.8c also. So between any two observers there is no one traveling faster than c. To the moving observers they would experience time dilation and length contraction, so the distance to an object would appear shorter than to observer A.

Drakkith said:
To observer A, both B and C are traveling at 0.5c away. So the distance between them is increasing at 1.0 c which is perfectly ok, because to observer B, observer c is only moving 0.8 c, and observer C see's B receding at 0.8c also. So between any two observers there is no one traveling faster than c. To the moving observers they would experience time dilation and length contraction, so the distance to an object would appear shorter than to observer A.

But who is to say which object is moving after B, and C reach .5 c and stop accelerating?
According to B, A could be moving at .5 C, and then A would be experiencing the relativistic effects.

It seams like in order to work, you would have to consider that for every two objects increasing or decreasing in distance from one another, both are moving relativistically at an equal rate. Otherwise, you could say that one or the other is moving any arbitrary speed so long as the sum of the two is less than C. But which speed you assign to which objects makes a difference in which object is experiencing which effects, and thus if and when they meet again, which one will be older than the other.

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jreelawg said:
But who is to say which object is moving after B, and C reach .5 c and stop accelerating?

According to B, A could be moving at .5 C, and then A would be experiencing the relativistic effects.

For one thing, A never experienced an acceleration. This is noticeable in all 3 frames. A, B, and C would all agree on that. Once B and C stop accelerating then it is equally valid to say that any of them are moving. We could say that all 3 observers accelerated to 0.9 c from starting point D before B and C moved away from A.

jreelawg said:
But who is to say which object is moving after B, and C reach .5 c and stop accelerating?
According to B, A could be moving at .5 C, and then A would be experiencing the relativistic effects.

It seams like in order to work, you would have to consider that for every two objects increasing or decreasing in distance from one another, both are moving relativistically at an equal rate. Otherwise, you could say that one or the other is moving any arbitrary speed so long as the sum of the two is less than C. But which speed you assign to which objects makes a difference in which object is experiencing which effects, and thus if and when they meet again, which one will be older than the other.

You are correct in saying that A would say B and C were undergoing relativistic effects, but B would say A and C were undergoing said effects. I'll illustrate where the error comes in your thinking:

Let's first take the role of observer B. We are moving at a constant velocity, so we claim A and C are moving away from us, and hence we claim that they are undergoing time dilation. Observer A makes a similar claim: he is at rest, but we are in motion, so B is experiencing time dilation. As observer B, we wish to demonstrate to A that his clock is slower than ours by flying over to him. And this is where the problem comes in - by changing our frame of reference we relinquish our ability to claim we are at rest, so once we get back to A, B and A agree that B's clock ran slower. Even if we send a signal, this must also travel at finite speed, so the same thing applies.

jreelawg said:
Does that follow that the sum of the distances traveled away from the object would also be 80% of what you would expect?
No, there is length contraction involved as well as time dilation.

So let's assume that one second has gone by for A. In A's frame, B and C are located 0.5 light-seconds away from him on either side.

In B's frame, his clock is running slow by a factor 0.866 so for him only 0.866 seconds has gone by. Since A is moving away from him at 0.5c, A will be 0.433 light-seconds away but since C is moving away at 0.8c he will be 0.693 light-seconds away.
jreelawg said:
Because the observer can say definitively, that each other observer separately has traveled a certain distance based on their speed .5 C, and you would think that two certain distances should ad up without relativistic effects. I'm confused.
Like I said, there's length contraction but there's also relativity of simultaneity, so the events of B and C arriving 0.5 light-seconds away from A simultaneously does not correspond with A arriving at 0.433 ls at the same time as C arriving at 0.693 ls.

Drakkith said:
For one thing, A never experienced an acceleration. This is noticeable in all 3 frames. A, B, and C would all agree on that. Once B and C stop accelerating then it is equally valid to say that any of them are moving. We could say that all 3 observers accelerated to 0.9 c from starting point D before B and C moved away from A.

So if two observers start in about the same frame at rest with each other, and they move apart at some fraction of C, and eventually meet again;

Will it be the case that the only factor effecting an actual difference what their clocks will read once back in the same frame, will be the acceleration and gravitational effects, and their relativistic speeds will not have had any effect on their clocks, other than in the changes in appearance while they were moving apart, or towards each other?

jreelawg said:
But who is to say which object is moving after B, and C reach .5 c and stop accelerating?
According to B, A could be moving at .5 C, and then A would be experiencing the relativistic effects.
You get to say who is moving which you did back in post #16 when you said A remained at rest while B and C moved away. Then you wanted to see what things looked like from B and C's frame of reference which means that they were at rest in a second (and third) frame of reference with A now moving and C or B also moving.
jreelawg said:
It seams like in order to work, you would have to consider that for every two objects increasing or decreasing in distance from one another, both are moving relativistically at an equal rate. Otherwise, you could say that one or the other is moving any arbitrary speed so long as the sum of the two is less than C. But which speed you assign to which objects makes a difference in which object is experiencing which effects, and thus if and when they meet again, which one will be older than the other.
Yes, you are correct, if A is at rest and B is moving at some speed, then when B is at rest, A is moving at the negative of that speed. The same is true between A and C and between B and C. It's just that you can't add the speeds that A sees B and C moving away from him to get the speed that B and C will see each other moving away from each other.

jreelawg said:
So if two observers start in about the same frame at rest with each other, and they move apart at some fraction of C, and eventually meet again;

Will it be the case that the only factor effecting an actual difference what their clocks will read once back in the same frame, will be the acceleration and gravitational effects, and their relativistic speeds will not have had any effect on their clocks, other than in the changes in appearance while they were moving apart, or towards each other?

If both observers experience the same acceleration for the same amount of time, both away and back, then their clocks will read the same. Note that you are creating a scenario in which two observers leave a location at the same speeds for the same amount of time and then return to that same location. If we say the location contains observer E then both ships show the exact same relative effects to E.

Drakkith said:
If both observers experience the same acceleration for the same amount of time, both away and back, then their clocks will read the same. Note that you are creating a scenario in which two observers leave a location at the same speeds for the same amount of time and then return to that same location. If we say the location contains observer E then both ships show the exact same relative effects to E.

But what if two objects move apart from the third observer at rest, and each experience the same amount of acceleration, and the same gravitational field strengths,

but one just happens to have gone further before turning around. So even though it experienced the exact same amount of acceleration, it was moving at .5 C relative to the third observer for a longer period of time.

When they all meet eventually, will their clocks all read the same?

jreelawg said:
But what if two objects move apart from the third observer at rest, and each experience the same amount of acceleration, and the same gravitational field strengths,

but one just happens to have gone further before turning around. So even though it experienced the exact same amount of acceleration, it was moving at .5 C relative to the third observer for a longer period of time.

When they all meet eventually, will their clocks all read the same?

They will agree that some have slower clocks and some had clocks that were ahead: but they wouldn't see each having aged less, like in the twin paradox.. See my previous post:

Mark M said:
You are correct in saying that A would say B and C were undergoing relativistic effects, but B would say A and C were undergoing said effects. I'll illustrate where the error comes in your thinking:

Let's first take the role of observer B. We are moving at a constant velocity, so we claim A and C are moving away from us, and hence we claim that they are undergoing time dilation. Observer A makes a similar claim: he is at rest, but we are in motion, so B is experiencing time dilation. As observer B, we wish to demonstrate to A that his clock is slower than ours by flying over to him. And this is where the problem comes in - by changing our frame of reference we relinquish our ability to claim we are at rest, so once we get back to A, B and A agree that B's clock ran slower. Even if we send a signal, this must also travel at finite speed, so the same thing applies.

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jreelawg said:
But what if two objects move apart from the third observer at rest, and each experience the same amount of acceleration, and the same gravitational field strengths,

but one just happens to have gone further before turning around. So even though it experienced the exact same amount of acceleration, it was moving at .5 C relative to the third observer for a longer period of time.

When they all meet eventually, will their clocks all read the same?

No, their clocks will not read the same. If A moves away from C at 0.5c for 1 hour before returning, and B moves away from C at 0.5c for 2 hours before returning, and both accelerate the same amount, then B will have had less time pass than A.

Drakkith said:
No, their clocks will not read the same. If A moves away from C at 0.5c for 1 hour before returning, and B moves away from C at 0.5c for 2 hours before returning, and both accelerate the same amount, then B will have had less time pass than A.
And both A and B will have less time pass than C.

(Don't get confused--in this scenario, C is the stationary one. In jreelawg's scenario, A is the one that remains at rest.)

I came to this thread late in it's evolution. Everything seems well sewn up except the subjective experience of the intrepid pilot.

His on-board clocks continue to show subjective elapsed time. He calculates his speed from his known rate of acceleration. After 3 years at at just under 1 g he calculates a velocity of c. Subjectively he is correct. He is one and a half a light years from his departure point.

Meanwhile observers at the pilot's departure point (they have his flight plan) calculate after (their) three years that his vessel is traveling at about .8 c. (That's from memory, I may be wrong as to the exact figure.) He is only 1.2 light years distant.

It looks like a free ride to the pilot. If he keeps accelerating at that rate he'll have traveled 4.5 light years after 6 subjective years, and after 9 he'll have AVERAGED 1 light year per subjective year. But things are not all beer and skittles for him. Unless he has extraordinary shielding he'll soon die from radiation sickness as photons originating from ahead have (subjectively) blue shifted radically. What he thought would be visible light is now hard xrays. Xrays have become gamma rays etc. etc..

So the universe does not impose speed limits on travellers unless they choose to catch up with friends. Our captain now reverses thrust but he'll have been away for 36 years subjective before he returns home. I leave it to the mathematicians to say how long 'home' thinks he's been away.

Cosmo Novice said:
C is a very special number. C is the speed of all massless particles in a vacuum, so anything with 0 mass travels at C.

Anything with mass does not and cannot travel at C. As anything with mass accelerates towards C it takes more and more energy to get closer to C, to actually reach the speed of light would take more energy than is in the entire universe.

General Relativity forbids anything reaching C as it is mathematically impossible for mass to go at that speed.

That is a simplified explanation but holds true.

I'm sorry if this makes no sense, but do massless particles have energy then? If so, would there be any difference in the speed of some massless particle that has more energy than another? I have a minimal understanding of SR but I just wanted to ask.

pawprint said:
I came to this thread late in it's evolution. Everything seems well sewn up except the subjective experience of the intrepid pilot.

His on-board clocks continue to show subjective elapsed time. He calculates his speed from his known rate of acceleration. After 3 years at at just under 1 g he calculates a velocity of c. Subjectively he is correct. He is one and a half a light years from his departure point.

Meanwhile observers at the pilot's departure point (they have his flight plan) calculate after (their) three years that his vessel is traveling at about .8 c. (That's from memory, I may be wrong as to the exact figure.) He is only 1.2 light years distant.

It looks like a free ride to the pilot. If he keeps accelerating at that rate he'll have traveled 4.5 light years after 6 subjective years, and after 9 he'll have AVERAGED 1 light year per subjective year. But things are not all beer and skittles for him. Unless he has extraordinary shielding he'll soon die from radiation sickness as photons originating from ahead have (subjectively) blue shifted radically. What he thought would be visible light is now hard xrays. Xrays have become gamma rays etc. etc..

So the universe does not impose speed limits on travellers unless they choose to catch up with friends. Our captain now reverses thrust but he'll have been away for 36 years subjective before he returns home. I leave it to the mathematicians to say how long 'home' thinks he's been away.
Why do you keep saying subjective?

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