Go to Alpha Centauri, 4.25 light years away, at 99.9 percent the speed of light, the journey as observed by an observer on Earth would take a bit more than 4.25 years.  On the ship, however, the travel time would be a little more than 60 days. 

The equivalence between time dilation and Lorentz contraction (linear, in the direction you are traveling) seems to throw people off.

On the ship, one could easily imagine one had got to Centauri much faster than light, based on the subjective shipboard time and one's belief that the star is over 4 LY away.  But really one has just contracted the intervening space wrt the ship.  

Edited April 21, 20232 yr by TheVat
decimal off on ship transit time, hope fixed it

1 hour ago, Genady said:

I don't think you need an equation for this. If you convert the entire mass to something massless, like e.g., light, then that something moves with the speed of light. Regardless of the initial mass.

Well ,the last massive particle that remained before all the fuel supplies were exhausted  would be travelling at a finite speed (below c)

And if the size of the initial  system was increased without  limit would there be an equation that  would  come out to  c in the limit?

(Hope my limits are not self contradictory)

42 minutes ago, geordief said:

Well ,the last massive particle that remained before all the fuel supplies were exhausted  would be travelling at a finite speed (below c)

And if the size of the initial  system was increased without  limit would there be an equation that  would  come out to  c in the limit?

(Hope my limits are not self contradictory)

Yes.

v² = 1 - m²/M²

M - initial mass

m - final mass

v - final speed, in units of c.

On 4/8/2023 at 6:01 PM, Moontanman said:

Now I see one of my most respected scientific sources seemingly asserting that all I've been taught was solid as a rock is in fact on shaky ground at best, Sabine Hossenfelder has blown my mind by suggesting all I know might not be as solid as I was led to believe. Is anyone willing to watch this video and assure me that Sabine has slipped a cog so I can let go of the nearest pine tree and return to the idea of solid ground being solid ground? 

Yes Sabine kind of slipped a cog. I watched her video (I am subscribed) and I see that she became more interested in gaining views than in being logical. With that title, and the ambiguity, she definitely gained a lot of views ...

What she missed?

1. She based her arguments on a theory (GR) she considered (in the end of the video) in order to be replaced with a new one, quantum gravity, making her arguments more or less irrelevant.

2. She missed the fact that the speed of interaction is also c, so if you move faster than c, you would normally brake apart.