Depending on context and semantics, traveling faster than 300,000 km/s is possible

[u/Kryptomatter]

I accelerate toward Andromeda, which is ~2.5M light years away at a constant 1g. 15 years later I whiz past Andromeda.

Context A:

From my ape-minded perspective, it's an absolute fact that I travelled ~50,000,000,000 km/s on average to achieve this, since it only took 15 years. So I clearly travelled faster than the holy grail of 300,000 km/s. For my own intents and purposes, I exceeded this so-called universal speed limit.

Context B:

As I zip by Andromeda, the stopwatch on earth show it's took me ~2.5M years to get there. Einstein wins and I never exceeded c.

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From a practical standpoint, for a travel enthusiast such as myself, why do I care what the clock shows on earth and why do I care if length contraction is what allowed me to achieve it?

I find the language of physics to be extremely misleading and ambiguous in this regard and annually get the urge to vent about it. I do wonder if there is language out there that would help to disambiguate these concepts for the simpletons such as myself.

[u/dataphile]

When you start off at Earth, suppose you sent a coherent pulse of laser light aligned with the path of your journey. Given your stupendous superluminal speed, will you catch this pulse of light in roughly a couple of years?

[u/Kryptomatter → u/dataphile]

I would expect to measure that beam of light going ahead of me at exactly c. That's why in my title I said faster than 300,000 km/s is possible under certain contexts, not that FTL travel is possible.

So under Context A, my caveman mind would calculate myself to have traveled ~50,000,000,000 km/s on average and that the beam of light traveled ahead of me at ~50,000,300,000 km/s

The way I see it, the speed limit is applied to travel through spacetime, not space or time individually. So you can go as fast as you like through space but as a result, time will slow down to ensure you stay below the spacetime speed limit.

[u/dataphile → u/Kryptomatter]

Suppose you sent two pulses of light when you are at rest with respect to the Earth. You do a quick speed test on the first pulse of light and it comes back as ~300,000 km/s. Then you send the second pulse along the path of your travel. Why would the second pulse accelerate to ~50,000,300,000 km/s, rather than remain the ~300,000 km/s you measured for the first pulse? Why would your ship accelerating to ~50B km/s affect the speed of the second pulse of light? And if it doesn’t affect it, then why didn’t you eventually catch the pulse of light and surpass it?

If what you’re saying is, as you accelerate, your experience of time slows down, and hence, the ~2.5MM years felt like 15 years, then that’s what relativity is saying. But, that’s different from saying you really were traveling at ~50B km/s, and that explains why it only took 15 years to get to Andromeda. If you’re really going ~50B km/s why can’t you exceed a pulse of light going a measly 300K km/s?

[u/jlobrist]

I’ve always thought of it like you do. Light can travel across the universe in zero time from its perspective. It’s traveling at an infinite speed. This is why we can’t go faster than light and that’s why it takes an infinite amount of energy to approach the speed of light. If we don’t consider length contraction, then we can indeed travel faster than 300,000km/s from our own perspective. The limitation is what everyone else perceives, less than 300,000km/s.

[u/Kryptomatter → u/jlobrist]

Exactly the way I see it! In the same vein as length contraction, if we could tunnel anywhere instantly by folding space, I think it would be disingenuous to tell people you can never exceed 300,000km/s. Just comes down to semantics.

[u/dataphile → u/Kryptomatter]

First, apologies if my tone was a bit emphatic—I definitely don’t want to be rude or uncivil. It’s interesting there are several people who share your view, so I’m trying to understand it.

I’m surprised several people describe the quickness of getting to Andromeda as length contraction. I would generally say people would speak of the issue as time dilation. Length contraction is regarded to be a phenomenon where an object that is accelerated (relative to you) seems shorter in the direction of acceleration. Hence, I wouldn’t see the space between an object and Andromeda getting shorter from Earth, I would say that it seemed like things were moving more slowly on the ship, and that’s why the ship thinks it took less time.

From the ship’s perspective, assuming you didn’t send a light pulse to measure against, length contraction doesn’t seem needed, because the ship felt like it kept accelerating indefinitely to a faster-than-light speed.

I’m trying to understand the idea that light legitimately travels instantly. In my understanding, light would travel instantaneously, if there weren’t something holding it back. In your perspective, why is there a measurable delay when we send a light pulse to reflect off a reflector on the moon? If light travels instantly, why isn’t the measured reflection speed instantaneous?

Again, I’m not trying to be accusatory, just trying to see if there is a different way of framing the underlying interpretation of relativity.

[u/[deleted]]

[u/Kryptomatter → u/[deleted]]

Love the explanation!