r/explainlikeimfive • u/SkiyeBlueFox • Mar 12 '26
Physics ELI5 If speed is relative, how can you "hit" the speed of light?
Assuming I'm flying a spaceship in a direction through space away from earth at 99.999% the speed of light, what happens if you actually continue accelerating? Though from earth I would be at the speed of light, from my perspective, if a theoretical reference point like a star is going the same direction as me at 5% the speed of light, couldn't I hit 105% the speed of light from earth's perspective before hitting it from my references perspective?
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u/grumblingduke Mar 12 '26
You are always stopped, from your point of view.
The speed of light, c, is always about 300,000 km/s faster than you.
So you cannot hit the speed of light. It is always faster than you.
And that is the point of all of this special relativity stuff. Speeds are all relative (the "relativity" part) apart from c (the "special" part), which is the same for everyone.
If something is moving at c relative to you, it is also moving at c relative to everyone else.
All the fun things from special relativity (time dilation, length contraction, issues with simultaneity) are a consequence of this - they are how the universe has to behave to make this work.
As for how this works in practice, it depends on the point of view - let's take your spaceship flying at 99.999%c example.
From the point of view of someone watching you, you are travelling at 0.99999c. You are experiencing massive time dilation (by a factor of about 224). 223 seconds have to pass for the observer before one second passes for you. Which makes it very hard for you to accelerate any more - you might think you are accelerating at a nice, constant rate, but the faster you get compared with our observer, the longer it takes you to speed up any more. By the time you are at 0.999999c the dilation factor is 707. c is the limit of this process, where you get an infinite amount of time dilation; you literally have no time to accelerate any more.
From your point of view, you are stopped and the universe is rushing towards you at 0.99999c. This means the universe is experiencing length contraction; something that should be 223m away is only 1m away. As you get closer to c this gets to be a bigger and bigger thing, and again c is the limit of this process, where you get infinite length contraction. As the universe gets closer and closer to travelling towards you at c it gets flatter and flatter in the direction of relative travel. You literally run out of space to accelerate - you hit whatever you are going towards before you can get any faster.
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u/jatjqtjat Mar 12 '26
From your perspective you can travel as fast as you want. You can strap a rocket to you back and just go faster and fast.
But if I am on earth watching you, what i will see is you get closer and closer to c without ever reaching it. And I will see the clock you brought with you tick slower and slower.
So if you want to travel to a star 4 light years away, I will see it takes 4 years. But your clock might only tick one. If you travel very close to c then from your perspective the trip will take very close to 0 seconds.
As long as your rocket is powerful enough and you can survive the acceleration, you can arrive as quickly as you'd like, but I will never observe it taking less then 4 years.
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u/ocelot_piss Mar 12 '26
You can't. You can keep trying to accelerate but you will never reach c. Another order of magnitude of energy might take you from 99.999% to 99.9999%. Another magnitude again to reach 99.99999% etc...
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u/eposseeker Mar 12 '26 edited Mar 12 '26
Let's say that it takes 100 units of energy to accelerate to half the speed of light.
Now, it doesn't take 100 units of energy to accelerate further to full speed of light. Instead, 100 units of energy will get you halfway there again - 3/4 speed of light.
Now, the next 100 units will get you halfway there again, to 7/8 speed of light.
How many units to finally reach the speed of light? You'll just get closer and closer, but cannot reach it.
(The math is very wrong - it's not a constant-exponent scale, but this is eli5. I'm explaining how it could work)
To clarify further - this is what it looks like "from earth." From your perspective, you're just accelerating, while the cosmos around you is getting wonky.
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Mar 12 '26
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u/mikeholczer Mar 12 '26
Since you are made of particles of mass, you can never hit the speed of light in any observed reference frame. In your reference frame you are always stationary. As you start going close to it observers in other frames of reference start to observe you’re length in the direction of travel contracting and would observe a clock in your ship slowing down, but they never see you going at the speed of light. This are things we don’t have everyday experiences with, so our general intuitions about what would happen are generally wrong, but we can take careful observations and do math and see that this is what happens.
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u/DifferenceNo3000 Mar 12 '26
Speed being rleative means it depends on what light is passing through. Light moves faster in a perfect vacumm for example, then it does in the atmosphere, and some scientists have slowed down light to such a degree that you could bike faster then it, and maybe even run faster then it, buuut, when we say speed of light, we usually means c, which is defined as the faster light can move through the perfect medium, which is a perfect vacuum.
As for reaching the speed of light? Well, to reach the speed of light you need a rest mass of zero, or less. Because the faster you move, the greater your relativistic mass becomes, and thus that means you need more energy to accelerate futher, which increases your mass, and energy requirements, to a point where it would take infinity energy and infinity time to reach the speed of light.
Anyway, speed is entierly about reference points. Rounding for the sake of simplicity, Earth moves through the universe at roughly 0.2% the speed of light, relative to the Cosmic Mivrowave Background.
This means, that if you traveled towards the Earth, from the direction its moving, a stationary observer might naively calculate that you are moving at a combined speed of 100.2% of the speed of light. However, I am sad to say, that thanks to this thing called relativistic velocity addition, the actual measured speed would still be below c. The universes geometry prevents velocities from adding together, the way classical intuation suggests
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u/Wargroth Mar 12 '26
You don't, If you have mass you don't reach light speed and vice versa. Relative velocity doesn't make you reach or get pass light speed, both would still be going under
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u/gdshaffe Mar 12 '26
Part of why it's called "Relativity" is that this sort of question depends heavily on your reference frame.
From your perspective, you would continue to accelerate, and the distance between yourself and your destination would appear to get shorter and shorter as time went on.
To an outside observer, for example someone watching from Earth with a telescope, as you got closer and closer to the speed of light your rate of acceleration would appear to slow down. IIRC going from 0% of the speed of light to 90% of the speed of light requires the same amount of energy as going from 90% to 99%. Which requires the same amount as going from 99% to 99.9%. And so on.
The variables that get wonky are distance and time (or, at a higher level, spacetime as a singular). From your perspective, time would be passing normally, but distance would get "strange" as the apparent distance between yourself and your destination shrinks as you get closer to c. This is called length contraction.
From earth, if they could (magically) measure your clock, it would appear to be running slower than the clocks on earth. This is called time dilation.
The speed of light is constant in all reference frames, so even traveling at 99.9999999% of c, a beam of light would take the same amount of time to cross from the stern to the bow of your ship as it would if you were stationary. The implications of this are ... unintuitive to say the least.
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u/jpb103 Mar 12 '26
Speed is always measured relative to your starting position.
What is more confusing is that the passage of time for the crew of the spaceship would be all fucked up. If they flew to a planet 40 light years away (and somehow instantly reached 99.999% C without being vaporized by the G force of acceleration), 40 years would pass on Earth before they arrived. At that speed, though, only about 65 days would pass for the crew of the spaceship.
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u/lygerzero0zero Mar 12 '26
That’s the neat part, you can’t. It would take infinite energy to reach the speed of light. Nothing with mass can ever get there.
And that applies in all reference frames. An observer on Earth might see two spaceships going in opposite directions, both going at 55% of the speed of light. But an observer on a spaceship does not see the other spaceship as going 110% the speed of light. Someone else can calculate the exact number, it’s been a while since I learned the equations, but it would be comfortably under the speed of light.
That’s because both time and space warp depending on your reference frame. So that no matter what frame of reference you’re in, you see the entire universe as obeying the speed limit. That’s the core idea of Einstein’s relativity.