Accelerating over speed of light?

Question

I study physics and I know that speed of light can't be reached by anything other than electromagnetic waves/photons.

But what I don't understand is, if you have a constant acceleration in space and experience no friction, would you not reach the speed of light in the end and even go beyond that?

I mean, if you constantly accelerate in space and finally reach the speed of light and accelerate even more, would you travel faster than the speed of light?
Would this situation be possible?

Answer 1

No, not in the way an observer would measure your speed, however if you measure the time it takes you to travel to a star system which is 4 light years away, if you accelerate quickly and have the energy to decelerate once you arrive fast enough, you can accomplish the trip in a much less time than the 4 light years you could have measured back on Earth.by the watch you took with you on the trip. So in that way it would appear you traveled the distance faster than the speed allocated within your proper perspective, relative to that of the speed of light you used to measure the Earth's distance to that star system.

Answer 2

>> ...if you have a constant acceleration in space

The point is, you can't have a constant acceleration like that. As you go faster and faster, it takes more and more energy to gain the next increment of speed. Eventually you reach a point where it would it take all the energy in the universe plus more, just to get to half-way from your current speed to light speed.

Answer 3

"Accelerating over speed of light?"



Not enough energy in the Universe.



"I study physics and I know that speed of light can't be reached by anything other than electromagnetic waves/photons."



"But what I don't understand is, if you have a constant acceleration in space and experience no friction, would you not reach the speed of light in the end and even go beyond that?"



No. The math is here:

http://www.physics.adelaide.edu.au/~dkoks/Faq/Relativity/SR/Rocket/rocket.html

... no finite acceleration, yields a speed of c. You just get closer and closer, and time dilation makes you feel like you are getting a lot... but only in your frame.



"I mean, if you constantly accelerate in space and finally reach the speed of light"



But you don't. Ever.



"and accelerate even more, would you travel faster than the speed of light?"



"Would this situation be possible?"



Nope.

Answer 4

As far as being on the ship goes, you can continue to accelerate beyond light speed in an absolute sense----but then TIME slows down for you---a light year trip might seemingly take a week. To an outside observer you do not go beyond light speed and the trip take a year to him.



This happens because movement between two observers is relative and is a function of a constant light speed, inherent "motion" in the direction of the fourth dimension. relative 3D motion is a function of the 4D angle between the observers. If the angle is the same, then there is no apparent motion (like cars matching speed side by side on the highway) a slight angle results in a slight relative motion (as when one car veers away) The greater the 4D angle, the greater the relative speed.----But since the 4D speed is always light speed, one observer will drop behind the other as the angle/speed gets greater---from the other guys POV.---Just like the car on the highway, veering away, it will drop back if it does not increase speed to make up for the horizontal component.

Since the 4D speed is constant , and drops back--it drops back in TIME relative to the observers in the 3D world.



That's why time slows down with relative speed in a 3D POV. ---You gotta think about it for it to make sense.

Answer 5

You cannot (if you measure it against the speed of light) in your inertial/timeframe ever reach the slightest fraction of the speed of light - not even by 1mm a second closer. C is ALWAYS c faster than you. This is a relative observational viewpoint under special relativity when people talk about time dilation. You cannot perceive this in your frame of reference - a second will always take a second to pass for you.



Under General Relativity and the Metric Expansion of the Universe it is (or was) possible to exceed light speed.

Answer 6

As you get faster your kinetic energy (K) increases.



We know E=mc². So there is additional mass, Δm, associated with your kinetic energy:

Δm = K/c²



Your total mass (often called relativistic mass) is rest mass ('intrinsic' mass, m₀) plus Δm.

Total mass = m₀ + K/c²



It turns out from the maths in Special Relativity that:

m₀ + K/c² = m₀ / √(1 - v²/c²)



Look at the right hand side. It means the total mass gets bigger and bigger as v get nearer to c. If v=c, total mass = m₀/0 = infinity.



To maintain a constant acceleration would need an ever-increasing force (since F=ma and m is increasing). The force would need to be infinite to reach the speed of light.

Answer 7

All conventional physics relates to simple particles / objects acted on by external forces.



Under those conditions, "Mass dilation" [Mass-speed dependence, as someone else refers to it] occurs as energy (and equivalent mass) are added by the external acceleration.





With a self-propelled object or craft that has continuous thrust (eg. a hypothetical ion engine), there is no mass dilation - it's effective mass can never be higher than it's initial rest mass; for it to be so would violate the basic principle of "conservation of energy".



Likewise, there is no such thing as "Escape velocity" for a continuous-thrust craft; escape velocity only applies to ballistic objects.



eg. as long as the thrust exceeds gravity wherever it is, it can keep climbing / accelerating.

Answer 8

When all energy needed available, your train will go faster and faster ... approaching light speed ... equal to light speed and your train become a light. Once become a light your train will go in light speed, not more.

Answer 9

Constant-thrust and constant-acceleration trajectories involve the spacecraft firing its engine in a prolonged constant burn. In the limiting case where the vehicle acceleration is high compared to the local gravitational acceleration, the orbit approaches a straight line.

Answer 10

It's about the geometry of spacetime.

(The what?)



In special relativity (SR), "boosting" to a frame of reference with a different velocity, mixes space and time coordinates, (x,t), in a similar (but not identical) way that rotating a geometrical figure in the xy-plane does with those two space coordinates.



When you start with an x-line-segment, and rotate it through an angle θ₁, you can see that it gets a slope of

s₁ = tanθ₁

If you rotate it further, by an angle θ₂, so that a second x-line-segment, acquires a slope of

s₂ = tanθ₂

the original segment doesn't get a slope of

s₁ + s₂

instead, it now slopes at an **angle** of

θ₁ + θ₂



In other words, we all realize that in successive rotations, slopes don't add; angles do.



In SR, when "boosting," there is a quantity that acts like the angle in a rotation; call it the "velocity parameter," α.



Now the analogy here is that velocity for boost transformations, is like slope for rotations.

So that when successive boosts are done, it isn't the velocities that add; it's the velocity parameters.



And the value of a velocity parameter is unbounded; it keeps growing, linearly, as you constantly accelerate. Only now, instead of the

"slope = tangent of angle" . . . . s = tanθ

rule for rotations, there is a

"β = velocity/c = hyperbolic tangent of velocity parameter" . . . . β = v/c = tanhα

rule for boosts.



From this, you can derive the "velocity-addition formula" for SR, from the formula for tanh of a sum of angles:

tanh(A+B) = (tanhA + tanhB)/(1 + tanhA tanhB):

β = (β₁ + β₂)/(1 + β₁β₂)



This is the analog of the tan of a sum of angles:

tan(A+B) = (tanA + tanB)/(1 - tanA tanB)

which can be used to find the slope of that original x-segment after two rotations:

s = (s₁ + s₂)/(1 - s₁s₂)



You can also see that, as α→∞, v→c⁻, not ∞, because of the behavior of tanh, as its argument grows arbitrarily large.

And that, for non-relativistic boosts, for which the α values are very small (|α|<<1), v ≈ α, and velocities *do* add (in the sense that the fractional error goes to 0 in the limit), for this Newtonian approximation.

Just as, for rotations by very small angles, slopes *do* add (fractional error again going to 0 in the limit).

Answer 11

You want to look into special relativity - approaching the speed of light affects distances, mass, and the passing of time itself.

Answer 12

Ohh ok, but how does the mass increase?

If you drive a car of mass 2000 kg and accelerate, isn't the mass of the car still 2000 kg?

Answer 13

Nope, as you approach light speed your mass increases and the power required to move you increases too. It would take infinity energy to get you past light speed.

Answer 14

Yep, just keep pelting a "sail" with photons from earth

Answer 15

you need to study some more