# Could time illusion be used to send a spacecraft faster than the speed of light?

The Hubble measurement showed the jet was moving at an apparent velocity of seven times the speed of light. The radio observations show the jet later had decelerated to an apparent speed of four times faster than the speed of light.
In reality, nothing can exceed the speed of light, so this "superluminal" motion is an illusion. Because the jet is approaching Earth at nearly the speed of light, the light it emits at a later time has a shorter distance to go. In essence the jet is chasing its own light. In actuality more time has passed between the jet's emission of the light than the observer thinks. This causes the object's velocity to be overestimated – in this case seemingly exceeding the speed of light.

Could the time illusion be used to send a space slower than light but have it seem like it is travelling faster than light?

• "Could time illusion ...". Irrespective of the type of illusion, illusion is still illusion. The physics of the object in question do not alter just because of an illusion. Would you like to see me pull a rabbit out of a hat or to make the fat lady "disappear"? It would all be illusion.
– Fred
Oct 15, 2022 at 17:49

Could time illusion be used to send a spacecraft faster than the speed of light?

Absolutely not.

Could the time illusion be used to send a space [probe] slower than light but have it seem like it is traveling faster than light?

Yes, but it is of no use whatsoever. [**]

There's nothing special in the behavior of this particle jet that couldn't be done by a space probe. To make this happen we need to send a space probe to a point far out, turn it around and make it race towards us.

The effect described is nothing else than a variation of the well known Doppler effect. The sound of a vehicle speeding towards you sounds higher than the sound its horn can produce. In the same way, the image of the space probe seems to approach you faster than the speed the probe can reach:

Assume a probe is flying towards you. It travels for 100 years covering 99 ly at 99% the speed of light: Light emitted at the end of the journey reaches you "now". And light emitted 100 years earlier at the beginning needed 99 years to reach you, i.e. arrived 1 year ago. So, the image traveled 99 ly in 1 year, 99 times the speed of light. Also note that the effect strongly depends on the direction the probe is traveling in - an observer at the starting point of the journey sees the image moving away from them at only 0.5 times the speed of light. Light emitted at the end of the trip arrives at this observer 99 + 100 = 199 years after the start.

In conclusion, you can use this "time illusion" to make the image of a probe move faster than it actually does. But it all breaks down as soon as you take not only distance but also the time light needs to reach you into account properly.

[**] Apart from science fiction, where a war-faring, sub-luminous space civilization using long distance weapons would profit from it: The enemy wouldn't be able to detect their 99.9% c projectiles in time but only see them racing towards them at 1000x the speed of light in the very last moment.

• Can you explain why the apparent velocity was 7 times the speed of light ? I would think it could be 2 times at most, being the speed of light plus the at most speed of light of the object approaching toward the observer. Oct 14, 2022 at 12:53
• @Cornelis: If something travels for 100 years covering 99 ly at 99% the speed of light, towards you: Light emitted at the end of the journey reaches you "now". And light emitted 100 years ago at the beginning needed 99 years to reach you, i.e. arrived 1 year ago. So, the image traveled 99 ly in 1 year, 99 times the speed of light. Oct 14, 2022 at 14:41
• @asdfex comments don't always stick around (even though here on Space SE they really do seem to) so I think it would be good to work that explanation into your answer; I think most people that see the question will wonder what illusion could be going on, and your explanation is clear and concise. Oct 14, 2022 at 18:42
• @ErinAnne Done. Oct 15, 2022 at 8:26