Understanding the Limitations of Faster-than-Light Travel in Physics

[fireman919]

In physics questions, objects are shown to travel at relativistic speeds, like 0.6c or 0.8c. This is all hypothetical, right? So how come an answer which generates a speed above the speed of light is wrong? Wouldn't one be traveling faster than the speed of the light if you were traveling in a spaceship at the speed of light, but running from one end to the other end? When I asked my teacher this, he said that its not possible, even taken hypothetically. Why is this?

 

[JesseM]

In physics questions, objects are shown to travel at relativistic speeds, like 0.6c or 0.8c. This is all hypothetical, right? So how come an answer which generates a speed above the speed of light is wrong? Wouldn't one be traveling faster than the speed of the light if you were traveling in a spaceship at the speed of light, but running from one end to the other end? When I asked my teacher this, he said that its not possible, even taken hypothetically. Why is this?

It would take an infinite amount of energy to accelerate an object with mass to the speed of light in a finite amount of time, so it's impossible (the energy of an object with rest mass m and velocity v is $$E = \frac{mc^2}{\sqrt{1 - v^2/c^2}}$$). A variation on your question would be, "if you were traveling in a spaceship at 0.9c relative to the Earth, and you ran from back to front at 0.2c relative to the ship, wouldn't you be traveling at 1.1c relative to the Earth"? In this case the answer would be no because velocity addition works differently in relativity, you'd only be traveling at (0.9c + 0.2c)/(1 + 0.9*0.2) = 1.1c/1.18 = 0.9322c relative to the Earth.

 

[jtbell]

This is all hypothetical, right?

At particle accelerators like Fermilab and CERN, physicists routinely produce particles traveling at large fractions of the speed of light. No matter how much energy they pump into the particles, they still have speeds below the speed of light, although very very very close to it.

 

[DaveC426913]

Wouldn't one be traveling faster than the speed of the light if you were traveling in a spaceship at the speed of light, but running from one end to the other end? When I asked my teacher this, he said that its not possible, even taken hypothetically. Why is this?

Inside your spaceship you would not experience any untoward effects. As far as you're concerned you're not moving at all, so you could run around as much as you wanted.

Outside your spaceship, from an external observer, you, and everything insde your spsceship would be greatly slowed down by time dilation, so you would appear to be almost frozen in your run. They would measure your combined speed at less than c.

 

[Bob S]

Look up Tachyon on the web. They were first proposed by A. Somerfeld. see
http://scienceworld.wolfram.com/physics/Tachyon.html

 

[DaveC426913]

Look up Tachyon on the web. They were first proposed by A. Somerfeld. see
http://scienceworld.wolfram.com/physics/Tachyon.html

Just note that - so much as it is impossible for anything below the speed of light to accelerate to or past the speed of light - so it is impossible for tachyons to deccelerate to or below the speed of light.

 

[Kruum]

I'm sorry if I'm doing something wrong here, but my question is close to this topic and I don't want to start a new one.

Anyways, I'm reading a book that says the following:

Let's start with two coherent electrons oscillating in unison. Next, let them go flying out in opposite directions.
...
Let's say the total spin of the system is zero, so thath if the spin of one electron is up, then you know automatically that the spin of the other electron is down. According to quantum theory, before you make a measurement, the electron is spinning neither up nor down, but exsists in a nether state where it is spinning both up and down simultaneously.
...
Even if the electrons are separated by many light-years, you instantly know the spin of the second as soon as you measure the spin of the first electron.
...
Did information really travel faster than light? Was Einstein wrong about the speed of light being the speed limit of the universe? Not really. Information did travel faster than the speed of light, but the information was random, and hence useless

Source: Michio Kaku, Physics of the Impossible, 1st edition, Anchor Books (2008).

I know the book has very little scientific value, but still the last quote interests me. How come the uselessness(?) of the information negates its speed? And how you determine "useless"? I mean if we have two bits (as in computers), the two bits independetly are usless, but once we tie them to a certain context it's very useful. I'm just beginning any heavier study on quantum mechanics and relativity, so I'm probably missing something here.

 

[JesseM]

I know the book has very little scientific value, but still the last quote interests me. How come the uselessness(?) of the information negates its speed? And how you determine "useless"? I mean if we have two bits (as in computers), the two bits independetly are usless, but once we tie them to a certain context it's very useful. I'm just beginning any heavier study on quantum mechanics and relativity, so I'm probably missing something here.

You can't actually verify that any causal effect was transmitted at great speed here, only that there's a correlation between distant measurements that can't be explained in terms of what are called "local hidden variables". And you can't affect the probabilities that your buddy at a distant location will get different results by choosing how you measure the particle over here, so it can't be used for communication. You might be interested in the analogy involving scratch lotto cards that I wrote up in post #3 of this thread in the QM forum.