Can human body be accelerated to 99% of the speed of light?

Question

I wrote a comment at Hacker News to say that human body could not be accelerated to close to the speed of light. There were several comments saying that this was possible. Can you please help?

1. Can the human body be accelerated to 99% of the speed of light? I'm not asking as a thought experiment, I'm asking in practice.
2. If humans could be accelerated to the 99% of the speed of light without bodily damage, how long would that take? I understand that to increase our speed to 99% of the speed of light we need to do it with gentle accelerations. Assume that we are astronauts in a space ship and we have enough fuel to reach 99% of the speed of light. How long would it take for us to reach 99% of the speed of light?
3. Since only massless particles can go with the speed of light how do we make the human body massless?

Edit: As my comment to @The Photon, the third question should be read as: Only massless particles will and must travel with the speed of light. Human body is not a massless particle. The logical question to ask is how can human body can reach the speed of light if it is not a massless particle?

I apologize if these are too elementary questions. Thanks

Answer 1

I know we cannot reach the speed of light, let's say 99% of speed of light.

You're already doing it! There exists a reference frame where you are moving at 99% of the speed of light right now.

If you mean relative to an "initial" rest frame, then you can easily calculate how much energy you need to do this for $v=0.99c$

$$K=(\gamma-1)mc^2\approx 6mc^2$$

This is a lot of energy, but you can take this with whatever method you're thinking of to also see how long it would take, resources needed, etc.

Answer 2

Can the human body be accelerated to the speed of light?

No. It can be accelerated very, very close to the speed of light, but not actually to the speed of light.

You're thinking of these two cases as equivalent, but to physicists there's a very important distinction between "the speed of light" and "something really close to the speed of light".

I'm not asking as a thought experiment, I'm asking in practice.

In practice, it depends on having enough energy available to do it, and to also accelerate a living environment to keep the human alive while they travel in space, and also on being able initially to accelerate the fuel that you're going to use for further acceleration later.

With our current technology, it's not practically possible, but that does not mean it couldn't be done in principle.

how long would that take?

Someone in this Reddit thread calculated, for a 1g acceleration,

Your rapidity would increase linearly. 0.99 c corresponds to a rapidity of artanh(0.99)=2.65. You have to accelerate for a time where you would reach 2.65 times the speed of light in Newtonian mechanics, or 920 days.

As pointed out in the Reddit thread, this is in the traveller's frame. In the initial reference frame (i.e. the Earth's frame) it's about 2484 days (hat tip to @PM2Ring in comments).

Since only massless particles can go with the speed of light how do we make the human body massless?

We can't. If we did, it wouldn't make sense to call the result a "human body" any more.

Answer 3

1. Can the human body be accelerated to 99% of the speed of light?

Yes.

2. If humans could be accelerated to the 99% of the speed of light without bodily damage, how long would that take?

From the equations of the relativistic rocket it is fairly easy to derive that the time to accelerate to v/c = 0.99 with constant acceleration of 1g is:

$$t = \frac {v}{g\sqrt{1-v^2/c^2} }\approx 2483 \ \text{days}$$

of coordinate time. (Wolfram Alpha calculation here) Similarly we can derive:

$$T = \frac{c}{g} \ \tanh^{-1} \left(\frac vc\right) \approx 936 \ \text{days}$$

of proper or in other words how much the traveller ages.
(Wolfram Alpha calculation here)

3. Since only massless particles can go with the speed of light how do we make the human body massless?

It is not possible to make the human body massless, unless you somehow changed all the mass of the body into light and it would no longer be a human.

The logical question to ask is how can human body can reach the speed of light if it is not a massless particle?

The logical answer is that it is not possible for the human body to reach the speed of light.