Intuitive Special Relativity - Why You Can't Go Faster Than The Speed of Light
A consequence of Special Relativity is that you cannot go faster than the speed of light.
Even more, particles with a non-zero rest mass can approach the speed of light but they cannot equal it.
Many websites try to explain this, usually with math and they often fail to make it clear why it is so in an intuitive manner.
In this post, I will try to explain in a simple way the reasoning behind this phenomenon.
A Playground Carousel
Imagine a manual playground carousel. You are standing beside it and with a push of your hand you start it spinning.
Then you push it again and get it spinning even faster. Then you push it again and get it spinning even faster.
Eventually if you do this enough times you will not be able to swing your arm fast enough to get that carousel to spin any faster. The bars of the carousel are whipping by so fast that you just can't exceed their speed.
So there is a natural upper limit to how fast you can make it go.
This is a big clue as to why you cannot go faster than the speed of light.
A Light Sail Space Ship
Now imagine a space ship with a large light sail that is driven by the light of a very powerful laser. You are the person operating the laser and for argument's sake the colour of the light is blue (wavelength = 450 nm, frequency = 667 THz).
The light reflects off of the mirrored sail and because light has momentum it gives a kick of momentum to that space ship.
That space ship keeps accelerating and eventually it reaches a significant fraction of the speed of light.
We know from physics that the energy of a photon is proportional to the frequency of the light according to the following equation:
Where E is energy, h is Planck's constant and f is the frequency of the light.
When the space ship is stationary it will see that the laser is emitting blue light and have a high frequency of about 667 THz.
As the ship goes faster and faster the light will redshift because it is receding from the stationary laser.
Eventually the light will appear to be red in colour to the people on the ship. Red light has a wavelength of around 700 nm and a frequency of around 430 THz.
Looking at the equation above, this means that the red light has a lower energy than the blue light it saw when it was just starting out and this light which now appears to be red will give a smaller kick to the solar sail space ship. The spaceship will thus accelerate more slowly.
Eventually the ship will accelerate so much that the light will appear to be infrared and have even lower energy and the ship will accelerate even more slowly.
This keeps going and eventually as the speed of the ship gets very close to the speed of light the energy of the laser light, as seen by the ship, will drop of to a value very close to zero.
Basically the acceleration essentially stops and there is nothing that can be done to get around this.
Closing Words
This is an intuitive and practical way to understand how you cannot go faster than the speed of light. Due to redshift and other relativistic effects, the energy of any accelerating mechanism will always drop off to zero as you get closer to the speed of light.
Equations created using CodeCogs' online LaTex Equation editor.
Thank you for reading my post.
Being A SteemStem Member
Thx Mr. Bot for the support.
As long as the SBD prices are above $1, you should NOT be 100% powering up if you want to maximize profits. You're losing a lot of money this way (since every $1 of SBD is currently multiplied by 4).
Of course, powering up does help the steem economy, but hey.
Thx for the tip. I will consider it.
Hi @procrastilearner,
I am interested in physics too much. This explanation is really interesting. However, I do not understand why people in the ship see the colorshifting. I think source is coming from outside (it should be like that because of conservation of energy.) and when the ship goes faster, how they see red color? They need to see same color. There is nothing to see different color. Also I understood that the light energy does not convert to anything such as there is absorption.
I think the case is like this. When the light collides the sail, it gives a push according to its energy. When the ship starts to accelerate then the momentum needs to be protected so it will collide the sail with a lower energy. This ower energy not due to frequency shifting. The reason is that after acceleration there are two moving particle and the collision energy will change according to light.
If I misunderstood can you explain? This explanation is really interesting...
Check this out
The ship is moving away from the stationary light source which in the example is blue.
It is essentially 'running away' from the light and will see the peaks and troughs of the light at a slower rate.
This is equivalent to reducing its frequency.
The faster you away from the source go the lower the frequency. It will go to green, then yellow, then orange, then red, then infrared and so on and so forth.
Also look up Doppler Shift.
Hope this helps.