# Simultaneity at Speed of Light: Twin Paradox Explained

• Guybrush
In summary, the conversation discusses a question about the concept of simultaneity in special relativity when traveling at the speed of light. It is concluded that this premise is impossible and does not make sense, and instead calculations can be done for speeds close to the speed of light to understand the concept better.

#### Guybrush

Hi,

I have been pondering a special relativity question about the concept of simultaneity when moving at speed of light.

Say for instance I took a round trip to Alpha Centauri 4 light years away, traveling at the speed of light both out and home (using negligible time to turn around). Then no time would have passed for me, while 8 years have gone by on Earth, but does that imply that everything that happened on Earth in the meantime happened simultaneously as seen from my perspective?

From what I know the answer to the question above is 'no' because time like events can never appear to be simultaneous to any observer. Yet, it still seems to me that if 8 years passed on Earth, and no time passed for me, then everything that passed in-between should be simultaneous.

I realize that this is just an example of the twin paradox, and I feel I can make sense of it when the round trip is made below the speed of light, but not when traveling at the speed of light.

Your problem is that you have based everything on an impossible premise. There is no such thing as traveling at the speed of light (for things, like you, with mass), and there IS no frame of reference for light itself, so it's no good asking "how would light see it?" because that is a meaningless question.

It's impossible for a massive body such as yourself (no offence) to travel at the speed of light. That is a feature of special relativity that protects us from having to resolve the various divide-by-zero errors that you get if you try to define a frame co-moving with light.

In other words, I'm afraid that the question you're asking doesn't really make sense.

You cannot travel at c; light can do that, but it always travels at c wrt all inertial reference systems. And light is not an observer.

Instead you can actually calculate everything for the case v=0.8c (the numbers work out nice). Then work it again with v=.99c, and so on to get your limit.

## 1. What is the Twin Paradox?

The Twin Paradox is a thought experiment that explores the concept of simultaneity at the speed of light. It involves two twins, one of whom stays on Earth while the other travels through space at a speed close to the speed of light. When the traveling twin returns, they have aged significantly less than the twin who stayed on Earth, even though they experienced the same amount of time.

## 2. How does the Twin Paradox relate to simultaneity at the speed of light?

The Twin Paradox highlights the fact that simultaneity is relative in the special theory of relativity. This means that two events that appear simultaneous to one observer may not be simultaneous to another observer who is moving at a different speed. This is due to the fact that the speed of light is constant and the faster an object moves, the slower time passes for that object.