# If two objects fly in opposite directions can they both reach the speed of light relative to the starting point?

Asked by Zyx (4142) July 13th, 2012

I’m just wondering how stuff works and my mind is melting, I fear for my life. Seriously though. If stuff is “relative” why can’t infinite speed be achieved?

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Well the speed of light isn’t infinite, but it’s simple. You can’t acheive infinity because it has no value, if you were accelerating you infinite speed you would just go faster and faster for infinity, and the vessel you were in would contiue accelerating for eternity, unless it collided with something.

You can’t divide by 0, same as you can’t divide by infinity, its not possible.

XOIIO (18054)

No, if it’s an object, that implies that the object has mass. And nothing that has mass can reach the speed of light. It takes extremely high amounts of energy to accelerate something approaching the speed of light. That’s why they had to build a cyclotron with a circumference of 27 kilometers to have enough magnets to accelerate a proton (which isn’t heavy compared to spaceships) to close to the speed of light.

Rarebear (23419)

Not really the point guys. I just realised light travels in all directions so the speed of light can be achieved in opposite directions… obiously. But then how is the speed of light determined? Is it the difference between massive and massless particles? Higgs field stuff?

Zyx (4142)

1) How is the speed of light determined? It’s not determined by anything. The speed of light is a constant of physics, just like any other physics constant. Note, though, that the speed of light will change depending on the medium that light is moving through.

2) Is it the difference between massive and massless particle? Is what the difference? Particles without mass (photons, and presumably gravitons) can travel at the speed of light because they have no mass. Particles with mass cannot because it would necessitate a divide by zero in the Lorentz Contraction, and you can’t divide by zero. In order to accelerate a particle with mass to the speed of light it would require infinite energy and its relativistic mass would go to infinity. It would also shrink to zero length in the direction of travel.

3) Higgs field stuff? No, I don’t think so. Higgs field is what gives mass to particles. Since photons have no mass, they do not interact with the Higgs field.

Rarebear (23419)

Two photons (or other zero-mass particles) traveling in opposite directions have a relative speed that is twice the speed of light. No violation there. Objects with mass can travel in opposite directions at nearly the speed of light (say, at 0.99c) so that an observer at rest between them observes a relative speed of 1.98c. From the vantage point of each object, however, the other is moving away at less than c.

Ever since Einstein we accept as a law of physics that the speed of light is constant and always the same to all observers in all frames of reference. We actually measure c in the usual way we measure speed: Divide distance traveled by time elapsed.

The reason why it’s so counter-intuitive is because we humans spend our life developing notions of time, space, and speed based on non-relativistic systems. When applied to objects traveling very fast, however, our intuition is simply wrong.

gasman (11261)

To answer @zyx ‘s question directly: yes that happens all the time – photons depart from stars in opposite directions, and travel at the speed of light.

Perhaps you were conflicted because the relative speed between the two photons is 2c, but we all know that 1c (1x speed of light) is max? In actuality, the 1c limit applies to a single object relative to the space-time continuum. The 1c limit does not apply to the relative speed between 2 moving objects.

RocketGuy (8432)

@RocketGuy But let’s say you’re riding a spaceship at .99c going one direction looking at a spaceship going .99c in the other direction. The other spaceship wouldn’t be receding from you at .99X2c, but at something like .999c.

Rarebear (23419)

Oh wow, so space and time aren’t actually seperate? Or is what I just said ridiculous?

I’m still curious if this means stuff can travel faster than light and we just haven’t figured out how yet…

Zyx (4142)

@rarebear – that would blow anyone’s mind, and would actually happen too!

@zyx – you should read Stephen Hawking’s “A Brief History of Time”. All human observations indicate that nothing has gone faster than c.

RocketGuy (8432)

@Zyx space and time arenâ€™t actually separate? Right, that’s what relativity taught us. There’s one four-dimensional structure we call space-time in which all events are embedded. Relativistic travel is something like a rotation in space-time, in the following sense:

Imagine observing a horizontal yardstick at some distance, extending from left to right but not front to back, so every point is roughly the same distance from you. Now rotate it so one end moves closer to you while the other end moves farther. It appears to be “shrinking” left to right, as it lengthens front to back. You’re trading off one dimension for another. In reality the stick hasn’t changed length (it is invariant) even though it appears to shorten.

Something similar happens with relativistic travel. A spaceship moving close to the speed of light appears to shorten in the direction of travel while time gets stretched making clocks appear to tick more slowly. It’s like a rotation in space-time, trading off space for time. In reality the ship hasn’t changed length even though it appears to shorten according to observers at rest. Once again things remain invariant – the ship doesn’t really shorten, nor do the local clocks aboard the ship actually slow down. Einstein disliked calling his theory “Relativity” and said he would have preferred “Theory of Invariance.”

gasman (11261)

Right. That’s why it’s called “spacetime”.

Rarebear (23419)

I am not going to pretend to understand any of this, but there is a theory that faster than light travel is possible, not by traveling through space, but by surfing a bubble in space. See here and here

@LostInParadise Makes perfect sense, sort of what I was thinking of, fascinating and thank you.

Zyx (4142)

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