special relativity - Does the increase of (relativistic) mass, while flying near speed of light, has any impact on astronauts?

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Would travelling at relativistic speeds have any impact on human biology?

I am asking myself this question for a few days. What is the correct answer on: Does the increase of (relativistic) mass, while flying near speed of light, has any impact on astronauts?

I mean let's pretend a spaceship will be able to travel in space with nearly the speed of light. Does the astronaut on this ship, while its (relativistic) mass increases, feel any difference on gravity or anything else? Or is the increase simultaneous to his own?

Answer

No.

Your mass doesn't increase when you move at relativistic speeds. Nothing changes at all. You feel exactly the same. Although the world around you will appear distorted, nothing endogenous to your spaceship feels any difference. This is in fact the fundamental idea of relativity. See this Wikipedia article for more detail. Also check out Galileo's original description.

Sometimes, when people are trying to explain relativity, they say that your mass increases when you go faster. Einstein said this, and you can find it in books as late as the Feynman lectures, perhaps later. Unfortunately, while it is possible to use this idea responsibly, it is subtle and not especially helpful, so that by now most physicists do not use it any longer. First, it is easily misunderstood by thinking that the changing mass is happening to the astronaut. Not so. It is just an artifact of different observers in different frames of reference. It is a bit like velocity - different people on different planets might look at the spaceship and claim that it has different velocities. They could even say "the velocity of that spaceship increases when it is moving near the speed of light", which sounds silly but is essentially the same thing as saying the mass increases. Of course, from the astronaut's point of view, he's just sitting around in his spaceship unmoving. Similarly, from his own point of view his mass is just the normal mass.

Additionally, if we say that the mass increases, it leads to separate ideas for mass in the direction of motion and mass perpendicular to the motion. This is confusing and unnecessary, so the idea of increasing mass is best left alone.

When you read a physics paper and it refers to a particle's mass, it means the "rest mass", the mass it has in its own reference frame. The old idea of changing relativistic mass is really just energy. People took the equation $E = mc^2$, noticed that the energy of the astronaut increases as they move faster, and said that means the mass increases as well. A better way to do it is to write the new equation $E = \gamma m_0 c^2$ and say that as the astronaut moves faster and faster, the mass $m_0$ is constant, but it is multiplied by a Lorentz factor called $\gamma$ equal to $\frac{1}{\sqrt{1-v^2/c^2}}$.

When you learn a little more about relativity, you can come back to this idea after reading about four-vectors. Energy and momentum are parts of an object's energy-momentum four-vector. Mass squared is the norm of this four-vector, so mass is the same in every reference frame. You can read more about this here, but it is somewhat more advanced than the other articles I linked.

Finally, there is this article on mass in special relativity.