I've known about the effects of near light-speed travel, but no one ever mentioned this fascinating phenomenon to me
Relativity is weird.
I knew about time dilation: the closer you are to the speed of light, the slower you go in time, from an outside observer's perspective (who is not going at this speed). But your perception of time (who is moving close to the speed of light) stays the same.
Furthermore, your mass increases, the faster you go.
I also knew how you would perceive the world around you at this speed. The lights become more blueshifted, intense and concentrated in front of you (the direction where you're going) and redshifted, dimmer and more spread out behind you.
And I could go on about some of the other effects.
But there's another effect I didn't hear about until now, which no space channel, documentary and article have ever mentioned for some reason and I'm quite fascinated by it.
It's called the Lorentz factor.
This is the explanation for it:
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"In simple terms, the Lorentz factor is a number that shows how much time slows down, lengths contract, and mass increases as an object moves faster and faster. The faster the object moves, the larger this number/factor becomes.
Mathematically, the Lorentz factor (gamma) is given by:
gamma = 1 / square root(1 - (v² / c²))
where: - v is the speed of the object. - c is the speed of light in a vacuum (about 299,792 kilometers per second or 186,282 miles per second).
How it works: - When an object is at rest (v = 0), the Lorentz factor is 1, so there’s no change. - As the object's speed approaches the speed of light, the denominator: square root(1 - (v² / c²)) gets very small, making gamma very large.
Effects: 1. Time Dilation: Clocks on the moving object run slower compared to those at rest. 2. Length Contraction: The length of the moving object is shorter in the direction of motion compared to when it’s at rest. 3. Relativistic Mass Increase: The object's mass increases as it moves faster."
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Now on the surface, this seems like the effects I mentioned and have known about. But what this gamma means or in other words, what the combination of these effects does for someone traveling close to the speed of light, is what matters.
Let me explain. Ever heard someone say it would take 4.24 years to get to Proxima Centauri at the speed of light, because it's 4.24 light years away? (it's the closest star to our solar sytem). Well it's partly true. It does take that much time from OUR perspective on Earth for light to get there, but if YOU were traveling at, let's say 99% of the speed of light onboard a spaceship, in your perspective, it actually takes less time to get there (less time pass for you than 4.24 years), because of the Lorentz factor.
And it's all caused by relativity...
In this case (99% of the speed of light) the Lorentz factor is 7.0888, which means it takes 7.2 months for you to get to Proxima Centuri (I mention the formula later), which is way less than 4.24 years.
For people on Earth, you get there in 4.24 light years and for you, in 7.2 months, even though you're not even going at the speed of light (which by the way is theoretically impossible).
Honestly, it's still hard to believe that this is a real phenomenon, if you were on a spaceship or something else, that was going at this speed. I'm surprised no source has ever mentioned this to me before, but it's part of near light-speed travel. They tell you it would take, this or that many years for you to get to somewhere, at or near the speed of light and they don't really mention the relativity part of it, so the information is not really correct.
I've put together the following chart, which shows how much you'd actually travel near light-speed. The time to travel a certain distance exponentionally decreases, the closer and closer you are to light-speed. Note that some of the numbers might seem off and it's just because of relativity.
Of course these speeds aren't possible with our current technology, but it doesn't break the laws of physics.
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"Formulas:
- Travel time from the traveler's perspective:
t_traveler = d / (v × gamma)
Where: - d is the distance to the destination in light-years. - v is the velocity as a fraction of the speed of light. - gamma is the Lorentz factor.
- Distance traveled in one year from the traveler’s perspective:
Distance_traveler = v × gamma × 1 year
This formula gives the distance contracted as seen from the traveler’s perspective."
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In the Traveler's Perpective:
Speed: 50% of the Speed of Light (0.5c)
- Lorentz Factor (γ): 1.1547
- Time to Proxima Centauri (4.24 light-years): 7.34 years
- Time to Cross the Milky Way (100,000 light-years): 173,205 years
Distance Traveled in 1 Year: 0.577 light-years
Speed: 75% of the Speed of Light (0.75c)
Lorentz Factor (γ): 1.5119
Time to Proxima Centauri (4.24 light-years): 3.74 years
Time to Cross the Milky Way (100,000 light-years): 88,170 years
Distance Traveled in 1 Year: 1.134 light-years
Speed: 99% of the Speed of Light (0.99c)
Lorentz Factor (γ): 7.0888
Time to Proxima Centauri (4.24 light-years): 7.2 months
Time to Cross the Milky Way (100,000 light-years): 14,260 years
Distance Traveled in 1 Year: 7.017 light-years
Speed: 99.999% of the Speed of Light (0.99999c)
Lorentz Factor (γ): 223.61
Time to Proxima Centauri (4.24 light-years): 6.9 days
Time to Cross the Milky Way (100,000 light-years): 447 years
Distance Traveled in 1 Year: 223.6 light-years
Speed: 99.999999% of the Speed of Light (0.99999999c)
Lorentz Factor (γ): 7,071.07
Time to Proxima Centauri (4.24 light-years): 5.21 hours
Time to Cross the Milky Way (100,000 light-years): 14.14 years
Distance Traveled in 1 Year: 7,071 light-years
Speed: 99.99999999999999999999% of the Speed of Light (0.999999999999999999999c or 22 nines)
Lorentz Factor (γ): 223,607,000,000
Time to Proxima Centauri (4.24 light-years): Virtually instantaneous, but 0.6 milliseconds
Time to Cross the Milky Way (100,000 light-years): 14 seconds (yes, you would actually see the Milky Way zoom by, because of the extreme time dilation and length contraction, considering the doppler effect isn't unbearable. Also in those 14 seconds 100000 years pass for people on Earth, which is just insane)
Distance Traveled in 1 Year: ~223.6 billion light-years
Thank you for reading this post!
Edit: I see how you guys say I should have known this, if I understood the effects of relativity, but I didn't think that it actually makes the time to get to somewhere shorter than even light in our perspective to get there...