# Faster than the speed-of-light

1. Nov 10, 2009

### Elvin12

Einstein claims that is impossible for any object (with a mass) to reach the speed of light, however I have many questions that I would appreciate if were answered.
To start with, the Largest Hadron Collider can accelerate an electron to a speed equivalent to 99.9999991% of the speed of light and the weight of that electron would be equal to the weight of a train moving at 80 km/h, which is huge (considering the initial weight of the electron), yet not infinitely huge. And it was only a tiny city on the border between Switzerland and France that was able to do it.
Moreover, I once read that it would physically impossible for a space ship moving at the speed of light to reach the end of the universe, because universe is expanding at the speed higher than the speed of light. The only way something could move at the speed of light is if it had an infinite amount of energy, but then that doesn't make sense. For the universe to have an infinite amount of energy, the space it must be contained in must be infinite also, but since the universe is expanding, it can't be infinitely large, because otherwise it wouldn't have a value to its size.
I also read somewhere else that in first second (up to 1^-37 seconds) after big-bang the laws of physics were different, in fact the 4 forces (electromagnetic, gravitational, weak and strong) didn't exist but there was only one force (Unified Force, where gravitational force was as strong as other forces) which later split into two different forces which after split again to become the 4 that we know now. So I thought that maybe in those first second, there was no limit to the speed, and it was that initial push that set us off on the speed faster than the speed of light, and then following the Newton's law of motion, the universe kept increasing at that speed because there were no external forces (assuming that there is nothing outside the universe) that would slow it down.
And also wouldn't the particles during the "inflation" expand at a faster-than-the-speed-of-light velocity?
Any opinion or answer will be appreciated,
Thanks

2. Nov 10, 2009

### mgb_phys

The universe can and does expand faster than light.
Relativity prevents information (which in this case also means mass) going faster than light. There is nothing to stop two points moving apart faster than light - they just can't send information from one to the other.

3. Nov 10, 2009

### Quinzio

Well, if I'm not wrong in understanding the expanding universe, it's not really that two galaxy at the opposite ends of the universe are moving apart at a pace faster than light.
Rather, there is a creation of space in which the galaxy and all the universe is immersed.
Just like if on a ballon I draw two point, then I inflate the ballon. The point are not exactly moving, it's the baloon surface that is expanding.
Please so. correct me if I'm wrong.

4. Nov 10, 2009

### Quinzio

If I may add something about travelling faster than light, let's say I make a trip 1 light year long.
I begin the trip, I accelerate fast to 3/5 of c, travel 4/5 of a year, the I stop.
My average speed has been v= s/t where space is 1 light year and time is 4/5 years.
Can't I say I travelled at (5/4)c ?
(Even if relative speed respect my original frame never exceeded c)

5. Nov 10, 2009

### JesseM

Are you talking about inertial coordinate systems in SR, or non-inertial coordinate systems in GR? If the former, then it's impossible for two objects with mass to have a relative velocity faster than c, so "there is nothing to stop two points moving apart faster than light" would be wrong (unless you're talking about the 'closing speed' between two objects as seen in the inertial rest frame of a third object, rather than the velocity of one of two object in the other's rest frame, which is how 'relative velocity' is normally defined in SR). If you're talking about non-inertial GR coordinate systems, the speed-of-light limit only applies in inertial frames, so it is quite possible for things (including photons) to move faster than c in a non-inertial coordinate systems and to pass information to each other. As mentioned on p. 4 of http://www.scientificamerican.com/article.cfm?id=misconceptions-about-the-2005-03 [Broken], we actually can observe galaxies that are receding from us "faster than light" in the standard cosmological coordinate system, so clearly we are getting information from these galaxies:

Last edited by a moderator: May 4, 2017
6. Nov 10, 2009

### JesseM

But no matter how close you get, you can never actually get a particle with mass to reach the speed of light; that last 0.0000009% would increase the particle's weight by infinity (or to put it another way, it would take an infinite amount of energy to increase the particle's velocity from 99.9999991% to 100%).
It would be physically impossible for a space ship to travel at the speed of light "locally", period. To understand what I mean by "locally" here, I'll quote something I wrote on another thread:
A lot less than the first second--do you understand that 10^-37 seconds is a tiny fraction of a second? Also, gravity would only have been united with the other forces for about 10^-44 seconds, i.e. Planck time, after that it'd be separate, then after about 10^-36 seconds the strong force would become separate from the electroweak force, and finally the electromagnetic and weak force would become separate after about 10^-12 seconds (see the timeline here).
I think all the mainstream theories of the grand unification era, when strong, weak and electromagnetic were united into one, would still be relativistic (Lorentz-symmetric) theories where c would be the top speed. As for the TOE era when gravity is united with the other three forces, there aren't really any complete theories to deal with this, but the attempts I know of like string theory are relativistic too.
Not in the "local" sense I discussed above.

Last edited by a moderator: May 4, 2017
7. Nov 11, 2009

### Elvin12

So if the universe expands faster than the speed of light and it is not through inflation, what else would expand the space in the universe? and since vacuum in the universe is not absolute vacuum, would a random generation of space defy one of the laws of physics? Matter can not be created nor destroyed?

8. Nov 11, 2009

### JesseM

Do you understand that nothing moves faster than light if you pick a local inertial coordinate system to analyze it? And do you also understand that when physicists say that nothing can move faster than light they are only talking about what is true in inertial coordinate systems, that there is no restriction in the laws of physics that says things can't move faster than c in a non-inertial coordinate system? This need not have anything to do with the "expansion of space", even in a flat SR spacetime you can pick a non-inertial coordinate system where things move faster than c, even though if the same objects were analyzed from the perspective of an inertial coordinate system we would find that none of them were moving faster than c. For example, I could define a coordinate system in my room in which my head was moving away from my computer monitor at 1000c...
I don't understand what you mean by "a random generation of space". The expansion of space in general relativity is not random, it follows in a deterministic way from the motion and distribution of matter in the universe.

9. Nov 11, 2009

### Naty1

10. Nov 11, 2009

### TMFKAN64

I don't know... let's say you make a trip 100 miles long. You accelerate to 60mph, travel for an hour, and stop. Your average speed has been v=s/t where the distance is 100 miles and time is 1 hour. Can't you say you travelled at 100 mph?

11. Nov 11, 2009

### Elvin12

if by v you mean velocity, then shouldn't it be v=d/t (velocity = distance/time) as opposed to v=s/t (velocity = speed/time) as velocity is an s (speed) but with direction.

12. Nov 11, 2009

### TMFKAN64

I just copied what Quinzo used in #4 above. That post refered to "space" which is why s was used for distance.

I suppose instead of just trying to make a joke, I should have pointed out the importance of making all of the measurements in the same frame of reference when you calculate velocity, but...

13. Nov 11, 2009

### pervect

Staff Emeritus
What you are describing is not a velocity - but it's a useful concept, it just needs another name. Some authors, see for instance http://arxiv.org/abs/physics/0608040 , call it a celerity.

I'll take the liberty of quoting from the paper, since I suspect people won't read it otherwise. (the numbers are footnotes which are references in the original paper).

14. Nov 11, 2009

### cfrogue

Please show me the math for this.

Thank you.

15. Nov 11, 2009

### Al68

A simple example is the reference in which I am currently at rest (earth's surface). The star Sirius is 8.6 light years away, and therefore moving at almost 20,000 times c relative to earth's surface.

(2)(3.14)(8.6 ly)(365 rev/yr) = ~20,000 c = coordinate velocity of Sirius relative to earth's surface.

16. Nov 11, 2009

### Mentallic

wait... what?
I'm not understanding your logic in multiplying by the amount of days Earth has in a year. Firstly you have the circumference of the circle $2\pi r$ and then...?

17. Nov 11, 2009

### cfrogue

Use SR's multiple velocity equation.

No,

I want to see this in non-inertial frames.

18. Nov 11, 2009

### cfrogue

19. Nov 11, 2009

### Al68

Just to make the units work out. Alternatively, we could say that Sirius is (8.6)(365) light-days away. Either way, Sirius' velocity would be about 20,000 light-years/year or 20,000 light-days/day, or 20,000 c.

20. Nov 11, 2009

### Al68

Earth's surface is non-inertial. I was just giving a simple example of an object's coordinate velocity exceeding c in a non-inertial frame.

21. Nov 11, 2009

### JesseM

Only applies in inertial frames.
A rotating frame in which the surface of the Earth is at rest is a non-inertial one. Since points on the surface of the Earth aren't moving inertially, there is no inertial frame where they are permanently at rest.

Anyway, if you want something more mathematical, let x,t be the coordinates in some inertial frame. Then define the following coordinate transformation to get a non-inertial frame:

x' = x + t*100c
t' = t

If an object is at rest in the inertial frame, then it is moving at 100c in this non-inertial frame. For example, suppose one point on the object's worldline has coordinates x=0 light-seconds, t=0 seconds in the inertial frame, and another point has coordinates x=0 l.s,t=10 s in the inertial frame. Then in the non-inertial frame, the first point has coordinates x'=0 l.s.,t'=0 s and the second has coordinates x'=1000 l.s., t'=10 s. So, in this non-inertial system, in 10 seconds the object has moved 1000 light-seconds, a speed of 100c.

Last edited: Nov 11, 2009
22. Nov 12, 2009

### yuiop

Let us say we have a distant galaxy that appears to be moving away from us at 5c. We can send information to that galaxy and obviously the galaxy can send information to us, or we would not be able to see it. I suspect mgb meant to say "they just can't send information from one to the other" faster than the speed of light.

The statement "There is nothing to stop two points moving apart faster than light" also needs clarification. mgb was careful to use the word "points" rather than particles so I assume he is referring to two locations in space moving away from each other. Now the trouble is that it is difficult to visualise how to measure the velocity of one piece of vacuum relative to another piece of vacuum, so it might be helpful in these discussions to think of the vacuum as a fluid with special properties, the presence of which can be inferred from those properties. It is a bit like air. We may not be able to directly see air, but few of us have any doubts about the existence of air, as we can readily see the effects of movement of air in our every day lives.

Now let us say we observe a particle (A) going to the left at 0.9c and another particle (B) going to the right at 0.9c then in a naive sense we might say they are going apart from each other at 1.8c. However, if we use the equation for relativistic addition of velocities, the result is less than c. This means that from the point of view of each of the particles, the other particle is receding at less than c and this is always the case locally. So why is that when A and B are many light years apart, they can measure each other to be moving at velocities greater than c? The answer is that SR can not account for this because it assumes a flat spacetime everywhere. In Cosmology over vast distances the spacetime is like an expanding fluid and objects are restricted to moving at less than c relative to that spacetime fluid. The result is that the velocity of the particle combined with the velocity of the fluid can add up to a value greater than c. On the other hand, two nearby objects that are moving in the same direction, are moving in the same local patch of fluid and because they are constrained to moving at less than c relative to the local fluid, then they are constrained to moving at less than c relative to each other locally. You could for example imagine the objects as little powered boats that have a maximum velocity of cb relative to calm water. In a river two such boats could have a relative velocity greater than cb is one is slow water and the other is in fast flowing water. Now if we had a rapid whirlpool, a small un-powered boat on the perimeter of the whirlpool could have a tangential velocity much great than the cb relative to a non rotating island in the centre but the important thing is that the boat always has a velocity of less than cb relative to the water local to it. This is some ways similar to the case of Sirius star appearing to have a tangential velocity relative to the Earth of 2000c. The important thing is that the star always has a velocity less than c relative to the spacetime fluid that is swirling around the Earth (in the frame where the Earth is regarded as non rotating.) So in some ways, spacetime can be visualised as a dynamic fluid that can expand, contract, curve, warp, rotate or flow and all motion is less than c relative to the spacetime fluid in the immediate vicinity of the particle, giving a informal "picture" of the meaning of local.

23. Nov 12, 2009

### Ich

There is no "spacetime fluid" relative to which things are moving or not. You know, "The idea of motion may not be applied to it." (A.E.)
Further, spacetime curvature is not necessary for this kind of superluminal speed. Superluminal speeds easily occur when you measure distance vs. proper time, as it is done in cosmology.

24. Nov 12, 2009

### JesseM

I think he was taking the fact that Sirius travels (2)(3.14)(8.6 ly) per day in this rotating coordinate system (since in this system Earth is fixed while the stars rotate around it), and then dividing it by c=(1/365 ly/day), in order to figure out the factor by which Sirius' velocity exceeds c in this coordinate system. Analogously, if I know an object travels 150,000 km per second, I can divide by c=300,000 km/s to conclude the object is traveling at 0.5c.

25. Nov 12, 2009

### Elvin12

I spent the last three days trying to figure this out, and at last i get it, thanks so much kev.
But one thing that still puzzles me is the theory of inflation. The speed at which our universe was increasing during that miserable time (the period of inflation) was thousands times the speed of light on a non-inertial (in my understanding) coordinate plate?