There are two space ships. One of them is standing still on earth, and the other is in space, thrusting with constant force and therefore accelerating exactly at 9.807 m/s2, which happens to be exactly the same as the gravity constant on earth. A person is standing in both of the rockets, but they were brought to the ship in a way that they do now know which ship it is. Assuming the passenger cabins are completely isolated from the environment (no windows, sound protected), would there be any means for the passenger to find out somehow which ship it is?
Let's try some classic Newton physics. Jumping around or throwihg around objects will feel exactly the same on both ships. No help there.
If classical physics does not help, what about relational physics then? Let's try to measure speed of light for instance. Maybe the moving ship will capture rays of light differently than the ship that stays still? Unfortunately not. Speed of light is constant and does not depend on the speed of the observer. Besides earth is also moving, very fast. Our galaxy is not staying still.
Butwhat happens when the accelerating ship starts to reach the speed of light? The Lorenz formula below can be used to calculate moving objects' relational mass.
Assume that after a while of thrusting, the velocity is 95% of light speed. The ship mass has become over 3 times its original mass. Maybe all the passenger needs to do is to weight some known object (like himself) regularly and if the weight increases, he will know that the ship is moving very fast. But no, even in the moving ship, the weight will measure the same. The inertial mass has no meaning for the moving object itself - it is a relational mass. It only has meaning for objects that observe its speed. But if the ship would crash into another ship with its full speed, it would feel its increased mass...
Only the fuel reserve set the limits how long the ship could accelerate. There is no other limit. And no matter how close to the speed of light the ship reaches, still, there is no way for the passenger to notice any difference.
Now, if you made it this far, here's something different to think. In the first ship, which force creates the push towards the floor? Yes, gravity. Generated by the planet. There is a field, or little particles if you will, that penetrate even the ship's thick walls that causes all atoms to draw themselves towards eachother. This appears as gravity.
What about the other case? What causes the push towards the floor in the other ship? There are no gravitational sources (at least none significant so we can ignore that) We know that the ship is accelerating, but how do the objects inside the ship know that? What is the coordinate system tied into? it could as well be tied into the ship, in which case the objects in the ship would be floating in zero gravity. But it is not. It seems like the coordinate system system was tied into a point outside of the ship - in the universe itself. So what is the zero point of the coordinate system? What creates this coordinate system, and what creates the force?
Answer to this is the Higgs field. The coordinate system is tied to the average center point of the universe, and the Higgs field itself causes all objects to resist sudden movements. This is what we experience as "mass".
Best wishes for LHC folks at CERN. Hope you catch the Higgs Boson soon! :-)
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