# If it is impossible to travel at the speed of light, then what is the theoretical max speed a spaceship could go? [closed]

I'm just pondering this so I can ask another question intelligently. Thank you

• This question needs some content and clarification or else it will likely get downvoted and/or flagged. Please add some more to the question. Dec 4 '19 at 21:38
• Why do people keep asking this question? It has been asked and answered many times in many different physics forums, and the answer never changes! Nothing with mass can travel faster than $c$! Dec 4 '19 at 22:03
• and nothing with mass can reach speed $c$. Dec 4 '19 at 22:10
• Also, a possible duplicate of this question from 2010! physics.stackexchange.com/questions/1557/… Dec 4 '19 at 22:11

Your desk is already moving at 99% of the speed of light, in an appropriately chosen frame of reference. Your desk is already moving at 99.9999999% of the speed of light, in an appropriately chosen frame of reference. That sentence remains true if you put in any number less than 100.

In theory, a spaceship could travel infinitely close to the speed of light without reaching it. This would require a near infinite force, however. As you come closer to the speed of light, you become more massive. A greater force is necessary to push a greater mass. As you go infinitely close, you require an almost infinite force. At the speed of light, and object’s mass becomes infinite and this requires an infinite force. The exception is massless particles, which don’t have mass to become infinite. So, again, a spaceship could go infinitely close to the speed of light without reaching it.

There is a maximum speed, but you haven't given enough information to calculate it.

If you go fast enough, then the relativistically beamed and boosted cosmic microwave background could become a significant source of radiation pressure (that opposes any accelerating thrust) and heating, which you either have to reflect or deal with in some way.

Secondly, there will be some maximum speed with respect to the interstellar medium. This will come when individual dust particles have sufficient kinetic energy to cause your ship's hull to ablate.

There is no maximum speed. You can approach $$c$$ arbitrarily closely, but since you cannot reach it it is an asymptotic limit rather than a maximum.

There is a famous (but wrong) explanation, why you can never go from $$A_0$$ to $$B$$. It goes as follows:

• In order to reach $$B$$ you first have to reach the mid-point between $$A_0$$ and $$B$$. Let's call this mid-point $$A_1$$ and let's assume, that you need the time $$T_1$$ to reach this mid-point.
• Next, let's assume, that you have reached the mid-point $$A_1$$. Again, before you reach the point $$B$$ you will have to reach the mid-point between $$A_1$$ and $$B$$. Let's call this mid-point $$A_2$$ and let's assume that you need the time $$T_2$$ to reach this point.
• As this series goes on forever, "we see" that the total time is a sum of infinitely many times, $$T_{total} = \sum_{i=1}^\infty T_i$$. Therefore, the time to reach $$B$$ must be infinite.

This argument is flawed, as not all infinite sums diverge. However, in the case of your question, we merely have to swap "travelled distance" with "current velocity" and "time" with "needed energy".

While the time in my example does not diverge, the amount of energy needed to obtain the speed of light does. Nevertheless, in principle, the space ship can get as close to the speed of light as you wish. To put this phenomena into an example: It's not allowed to divide one by zero, $$1/0$$. However, in principles you can take any other number (but zero) and put it into the denominator. Thus, it's not really meaningful to ask, what is the closest number to zero, which I am allowed to put into the denominator.