# What is the formula for relativistic acceleration?

$$BACKGROUND:$$

I was recently watching a youtube video about Unruh radiation:https://youtu.be/7cj6oiFDEXc

In this video, the host said that we need to accelerate at $$10^{20}m/s^2$$ to raise the temperature by $$1 kelvin$$.

This got me thinking about relativistic acceleration because if you accelerate at $$10^{20}m/s^2$$, you will pass the speed barrier in less than a second if we apply the math of Newtonian mechanics in which if you are travelling at v and you start accelerating at a then after time t your velocity will be $$v+at$$ which cannot be true so I want to know the relativistic formula for acceleration.

(If you are thinking that how on earth can someone talk about Unruh radiation but don't know the formula for relativistic acceleration, then let me point out that I am not a physicist, I am just a high school student who tries to learn as many things as possible from the internet. Sometimes that information can be incomplete but slowly I manage to gain the full information.)

• This explains it rather well; en.wikipedia.org/wiki/Unruh_effect#Temperature_equation Commented Jan 2, 2021 at 7:18
• The Unruh effect is a prediction, observations are in debate, and there is some doubt about the existence of Unruh radiation. Commented Jan 2, 2021 at 7:25
• @Adrian howard, I think you should read her question again. She used Unruh effect as an example for her question about relativistic acceleration. Commented Jan 2, 2021 at 8:44
• In SR you can accelerate forever and never go faster than light. See this article. Commented Jan 2, 2021 at 18:08
• @Jhuma Sarkar. You may find it better to find a suitable book on SR and learn from that. It will be more work than watching video, but that's what it takes to understand a subject. Also, you may find that even reading the first chapter will give you most of the info you want to know. Finally, books, the good ones, tend to be wrong less often than videos (@G. Smith already gave a good reference, so my reply is just rambling :-))
– Cryo
Commented Jan 2, 2021 at 22:19