## Traveling Faster Than The Speed Of Light.

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The-Rabid-Monkey
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### Traveling Faster Than The Speed Of Light.

Why is it said that we can not travel faster than the speed of light?
I really don't understand why, it's only a speed, sure it's light speed, but surely you can still go faster. Hell I don't see why you couldn't move at 9.9999x1099 ms-1.
Is it proven that particles begin to break down at light speed because the electrostatic forces holding the particles together get left behind? Even then, surely if you applied enough energy to something, you could make it move faster than the speed of light, and keep moving it infinitely faster, I suppose until you start to rip the universe apart due to the fact that you're sucking up all the energy by moving at that speed or something.
This is also a thing that strikes to me as weird when people say that when you hit the speed of light, time begins to slow. WHAT THE HECK!? Time and Speed are both human inventions. No matter how quickly you move from one place to another, you still take time. Even if you go at a billion billion times light speed, you're still taking time to get from one place to another, no matter how small.
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Archena
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### Re: Traveling Faster Than The Speed Of Light.

As I understand, the energy required to accelerate an object toward the speed of light does not grow linearly with the velocity and it works out that in order to actually hit the speed of light you would need an infinite amount of energy.

What I don't understand is why the limit has the value it does. Presumably it is a property of space and "just is", but I wonder if the universe could have plausibly been configured with a different speed. Hopefully someone can shed more light on that... (no pun intended).

The time slowing thing is to do with time dilation. The rate at which an observer experiences time may differ from that of another observer, depending on their velocities. The rate should slow as you approach light speed.
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telcontar42
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### Re: Traveling Faster Than The Speed Of Light.

Relativistic kinetic energy is
$KE=\frac{mc^{2}}{\sqrt{1-(v/c)^{2}}}-mc^{2}$
As you can see, the energy goes approaches infinity as v approaches c. In other words as you approach the speed of light it takes more and more energy to increase the velocity.

Also, time begins to slow whenever you move, not just when you hit the speed of light. Time will appear to slow down as speed increases relative to the observer. These are all consequences of special relativity, and it is a bit complicated so you may want to read up on it for a better explanation but I'll see what I can explain. The basic concept is that the speed of light is the same for all inertial reference frames.

Picture a box with a photon bouncing between the top and bottom of the box. If an observer is a t rest with respect to the box it sees the photon moving vertically up and down across a distance equal to the height of the box. The time between the photon leaving the top of the box and hitting the bottom of the box is (height of the box)/c. However, from the perspective of an observer moving relative to the box, the photon is moving in diagonal paths as it bounces up and down and moves horizontally with the box. From this reference frame, the photon is moving across a distance equal to the (height of the box^2 + the horizontal distance traveled^2)^(1/5). However, the photon is still moving at speed c. Therefore the time between the photon leaving the top of the box and hitting the bottom of the box is ((height of the box^2 + the horizontal distance traveled^2)^(1/5))/c. Note that (height of the box)/c < ((height of the box^2 + the horizontal distance traveled^2)^(1/5))/c. The observer at rest with respect to the box sees one time interval between the photon leaving the top and hitting the bottom and the observer moving relative to the box seems a longer time interval between the same two events. In other words the observer moving relative to the box sees time pass slower for things that are moving relative to his reference frame. The actual relation ship is
$t'=\frac{t}{\sqrt{1-(v/c)^{2}}}$
As v goes to c, t' goes to infinity. As something approaches the speed of light relative to an observer, the observer will see time pass more slowly for the object approaching time stopping as the speed approached c.

I hope that is somewhat understandable, but you really should just read up on special relativity.

Edit:
As for the reason for c having the value that it does, it comes out of Maxwell's equations describing the propagation of an electromagnetic wave (light is a electromagnetic wave). It is given by $\frac{1}{\sqrt{\mu_o\epsilon_o}}$where mu and epsilon are the permeability and permittivity, respectively, of free space.

yy2bggggs
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### Re: Traveling Faster Than The Speed Of Light.

I could have sworn there was a thread on this already. Did you use the search function? (Not counting the obvious current FTL thread, which is really about something else...)

Regardless, to run this through the intuition pump on a lay level--light per se isn't particularly special--rather, there's a special speed.

We know from Newton that F=ma, so, naturally, a=F/m. Given this, imagine what would happen if you have a particle that is massless and you apply a tiny force to it. The results, using this equation, are division by 0; it would be as if you had infinite acceleration.

Light consists of photons, which are massless, so they behave like this. However, light in a vacuum travels at c, not at infinite speeds. What's more, if you shine light to the east, it's the same speed as when you shine light to the west. This in itself shouldn't be true in normal "Newtonian" physics, since we're on a giant ball that spins and circles the sun, but it is true.

From this you can gather that there's a maximum possible speed, and that this speed doesn't depend on how fast you are going (alternate phrasing--there's no preferred reference frame; i.e., there's no absolute "still"). Photons, which are massless, only travel at the fastest speed possible. This has a bunch of strange implications in itself--the simplest of which is relativity. Relativity incorporates how light can travel at c to someone on the ground, and to you, at the same time, when you're on a train traveling a good half c with respect to the guy on the ground; this requires some odd tricks to be played on how you and the person on the ground perceive space and time.

That's theory, and then there's practice. Oddly enough, the practice seems to match the theory on this one.

Klotz
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### Re: Traveling Faster Than The Speed Of Light.

You can't travel faster than light because even if you're going close to the speed of light, if someone turns on a flashlight it'll still look like it's going at the speed of light.

danpilon54
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### Re: Traveling Faster Than The Speed Of Light.

What they said, and as to the why question, there really is no answer to that. It's like asking why the big bang? Science strives to model nature, but can never explain nature's purpose. So we observe that no matter how fast you are moving relative to another object, light for both you and the object appears to be going at the speed c. This does not make sense with the normal formulation of speed, and in order to correct for this you get relativity. Consequences of relativity include the speed of light being a speed limit, time dilation, and spacial contraction. We can say space contracts relative to an object if you are moving relative to that object because the speed of light is the same in all inertial reference frames, but we can't say why the speed of light is the same in all inertial reference frames.

Unless of course I don't know something that others do.
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thoughtfully
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### Re: Traveling Faster Than The Speed Of Light.

Another way to visualize the speed limit is this:

There is no limit, there is one speed: everything travels at the speed of light, in four dimensional spacetime. How you divide up the space and time components is up to you, but the total is invariant.

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Woofsie
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### Re: Traveling Faster Than The Speed Of Light.

Telcontar, in the first two equations you've shown, the problem seems to be that you end up dividing by zero. How does division by zero translate to infinity? I've always heard that division by zero is "undefined", or alternatively that it makes the universe asplode.

doogly
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### Re: Traveling Faster Than The Speed Of Light.

Division by zero isn't tricky, it's infinite when you have a nonzero number on top. If you want to be more precise, take the limit instead of just plugging in c. Don't worry, the universe is not going to asplode. Remain calm, all is well.
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Xanthir
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### Re: Traveling Faster Than The Speed Of Light.

doogly wrote:Division by zero isn't tricky, it's infinite when you have a nonzero number on top.

No, it's still undefined. However:
If you want to be more precise, take the limit instead of just plugging in c.

This is correct. The limit as v approaches c is infinity.
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telcontar42
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### Re: Traveling Faster Than The Speed Of Light.

Yeah, you never start with something traveling at speed c. You can try to accelerate something to c, but as you get close, the denominator of those equations will approach 0 and the limit as the speed goes to c is infinity. It's true that at c, you get values that are undefined, but you'll never actually have something (other than light) traveling at speed c.

An interesting side note: There are theoretical particles that travel faster than c, such as tachyons. In a similar manner, they would be unable to travel any slower than c because as their speed approached c, the equations above would blow up. These are very theoretical, however, any even if they did exist I don't think there would be any way to detect them.

Also, doogly, I'm pretty sure I had you as a TA for an astro class I took a couple of years ago. Unless its just a coincidence that someone else studying theoretical physics in Somerville used doogly in their email address, but I'm guessing not.

Woofsie
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### Re: Traveling Faster Than The Speed Of Light.

Ah, that clears it up nicely. Thanks a bunch.

gmalivuk
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### Re: Traveling Faster Than The Speed Of Light.

yy2bggggs wrote:I could have sworn there was a thread on this already.

Yeah, pretty sure you're right.
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