Relativity rotations rockets Doppler shift

Lecture for chapter 3 section 3 of
http://www.modernrelativitysite.com

Category:

Education

Tags:

• relativity
• rocket
• Doppler
• rotation

[SuperFinGuy]

Also as it is well known objects traveling at the same speed have zero kinetic energy to each other, so for the engine the rocket is relatively stationary and weight the same as at rest. I don't see how the relativistic KE would not allow light speed.

[WaiteDavidMSPhysics]

@SuperFinGuy The *weight* you refer to is called the proper acceleration. For example if you burn the rocket at constant proper acceleration so that the crew always feels like their weight never changes then the velocity is

v = ctanh(gt'/c)

It doesn't matter how long you run it, that tanh function asymtotes to 1 limiting the speed to less than c. Thats just the way it is.

[WaiteDavidMSPhysics]

@SuperFinGuy No absolutely not. v is not the proper velocity, it is the coordinate velocity dx/dt. 

[WaiteDavidMSPhysics]

@SuperFinGuy That is not a proof. That is a statement which is wrong in terms of your equation for the kinetic energy. The correct kinetic energy for something with nonzero mass is

KE = (gamma - 1)mc^2

You can't just assert an equation and assume that its representative of special relativistic physics, and even if the equation were correct YOUR own wrong equation for kinetic energy would still also not allow it to reach the speed of light.

[SuperFinGuy]

@WaiteDavidMSPhysics I have to disagree, here's the proof that the energy is the energy of motion of the mass or its kinetic energy. Where x = sqrt (1-(v/c)^2) is the relativistic fraction, kinetic E = m*v^2/x is equal to the energy of a mass in special relativity or m*c^2/sqrt (1-(v/c)^2). As expected when v = c the energy reaches infinity.

I think the twist here is because the Lorentz factor is a reciprocal of x, 1/x = c/sqrt(c^2-v^2). The relativistic fraction that is the real number.

[WaiteDavidMSPhysics]

@SuperFinGuy NO. The energy calculated for a speed v IS the energy required to reach that speed. And actually it has been shown to be impossible for a mass to reach c in special relativistic physics, in fact that IS what my derivation shows. You're just plain wrong. Deal with it.

[SuperFinGuy]

@WaiteDavidMSPhysics In Einstein's special relativity as in his 1905 paper, the energy calculated when v = c is the energy of motion at that speed. It is not the energy that the mass needs to reach c, it is the energy it has at c. It is never shown it's impossible for a mass to reach c. You have included g, but in special relativity the mass remains constant, what changes with speed is the momentum/energy.

[WaiteDavidMSPhysics]

@WaiteDavidMSPhysics The derivation is at the link in the description bar. The factor is on the fuel.

[WaiteDavidMSPhysics]

@SuperFinGuy Its limited *because* that factor blows up. That factor is a factor in how much energy something with mass would need, according to a frame for which its speed is v, in order to travel at that speed v. In special relativistic physics because that factor diverges as v goes to c it would take an infinite amount of energy in order to get a cockpit with mass up to the speed of light, even if you consider the factor on the relativistic energy of the fuel itself. Look at the derivation.

[SuperFinGuy]

Relativistic geometry shows this, objects separated by a light ray have zero separation in s/t. Take for example that the time dilation factor blows up to infinity when v is the fraction c/1. If v = c/1 than the factor is

1/sqrt (1-(299792458/299792458)^2) or infinity (division by zero).

v can be equal to c and it seems that our s/t dimensions that are limited not v. How can v be limited?