Why Do Events Freeze For Me at the Speed of Light?

[RobbyQ]

TL;DR

Why Events Freeze For Me

Is my thinking correct ?
Assuming I can see you throughout my journey... If I accelerate away from Earth towards the speed of light and you are waving to me, I start to see your waving slow down and eventually at speed to light your waving stops like a photographic image. Almost like the last image I took of your photons relative to my speed. There is now no new information reaching me. i.e that last image is stuck with me forever ?

 

[jbriggs444]

TL;DR Summary: Why Events Freeze For Me

Is my thinking correct ?
Assuming I can see you throughout my journey... If I accelerate away from Earth towards the speed of light and you are waving to me, I start to see your waving slow down and eventually at speed to light your waving stops like a photographic image. Almost like the last image I took of your photons relative to my speed. There is now no new information reaching me. i.e that last image is stuck with me forever ?

Yes, there is a last instant of your home world's future that you will ever see.

However, this last instant is not seen when you reach the speed of light. It can't be. Because you never reach the speed of light. Instead, there is an instant (on Earth) when it passes beyond your Rindler horizon. Ideally, the light speed information from Earth never stops arriving. Though as a practical matter you'll see the Earth fade into red-shifted darkness long before that.

 

[PeroK]

What you see in a scenario like this depends on the travel time of light from an event on Earth to your spaceship. This sort of effect is not in itself relevant to the theory of relativity.

Indeed, in classical mechanics, you could in principle exceed the speed of light and you would see all sorts of weird effects in such a scenario.

Although the special theory of relativity can describe accelerating reference frames, it's more usual to present the basic theory in terms of inertial frames of reference.

 

[pervect]

TL;DR: Why Events Freeze For Me

Is my thinking correct ?
Assuming I can see you throughout my journey... If I accelerate away from Earth towards the speed of light and you are waving to me, I start to see your waving slow down and eventually at speed to light your waving stops like a photographic image. Almost like the last image I took of your photons relative to my speed. There is now no new information reaching me. i.e that last image is stuck with me forever ?

You can't move at the speed of light, but it turns out you that relativity depicts what you describe.

There's another way of saying this - given a head start, a rocket with a constant acceleration can outrun a light beam. In the case of a rocket accelerating at approximately 1g (the exact number i am using is actually 9.5 m/s^2, which is equal to one light year/year^2), a rocket with a headstart of one year will outrun a light beam as long as it continues to accelerate.

The equations for the motion of the rocket are detailed in the wiki article https://en.wikipedia.org/wiki/
Hyperbolic_motion_(relativity)

The rocket can continue to outrun the light beam only as long as it keeps accelerating, though. So, an observer on the rocket will never see a photon emitted one year after they leave their point of origin (presumed to be the Earth) unless they stop accelerating. If they stop accelerating, the photon will eventually catch up to them.

Because the accelerating rocket is always further away from the Earth than the light beam, they will never see the light beam. In order to see the light beam, it would need to catch up to the rocket so it was in the same place as the rocket, and it never does, the rocket is always ahead of it. The rocket never reaches the speed of light, but because of it's head start and the details of the motion, it's always further away from the earth than the light beam.

On a space-time diagram, the path of a rocket is a hyperbola (this is why it's called hyperbolic motion), and in the example I described, the light beam emitted one year after the rocket takes off is the asymptote of the hyperbola. And the hyperbola never reaches it's asymptote.

 

[PeterDonis]

The OP is unable to respond any longer, so this thread is closed. Thanks to all who posted for the good responses.