# What is the mechanism that restricts a body from accelerating past the speed of light? [duplicate]

Let's say initially from an observer's point of view, a spaceship in perfect vacuum is at rest. From the observer's point of view, once the ship starts accelerating what is causing the ship from accelerating past the speed of light? What is physically causing this resistance to acceleration as the ships velocity and therefore its relativistic mass (as opposed to its actual physical mass) increases? On earth terminal velocity exists solely because we have an atmosphere. What is physically responsible for the terminal velocity of vacuum?

I understand that this question has been asked here many times and I have read quite of few of them. All the answers I found were mathematically driven and answers the question quite satisfactorily but from my understanding, none tackled the actual physical mechanism behind this phenomenon.

• I guess at a really low level, it gets "heavier" (bends the spacetime around more) as it gets more energy. This requires more force to accelerate it.,which then increases its energy more which then makes it harder to, etc etc. Jan 20, 2017 at 7:18
• @RobJeffries Top answer in that post explains the mathematics behind the phenomenon which I am quite familiar with myself, but fails to explain the physical cause of the phenomenon. So I asked this question. Jan 20, 2017 at 7:44
• Jan 20, 2017 at 8:28
• @RobJeffries That particular thread doesn't apply as well because the op is simply trying to prove that special relativity is false. That is not what I am here for. I am making the assumption that special relativity is true. What I want to know is what is causing it. For example we know that gravity is real and we have mathematical models that describes the effects of gravity, but the physical cause of it is still a matter of debate, is it gravitons, is it mass bending space-time, etc. Jan 20, 2017 at 14:30
• @RobJeffries: Could you look at edit (infinite mass) to my answer to this question and let me know if it needs to be removed, and why.
– kpv
Jan 20, 2017 at 16:02

A body can always accelerate, so there is no mechanism preventing acceleration to do its thing.

Why you cannot accelerate past the speed of light is just because velocity composition is not linear.

Rapidity composition is linear (in one dimension). Acceleration allows you to reach any rapidity, but of course infinite rapidity is forever out of reach. Since the speed of ligth is the asymptotic velocity at infinite rapidity, it can never be reached.

This is somewhat similar to wondering why a boat can never move across the horizon: it can always move, but the horizon is a relative, moving target so it will never be reached.

• But you see rapidity is a mathematical concept that is assuming special relativity to be true from a mathematical standpoint. So is it not circular logic? Now I am not arguing that special relativity is false, as we have countless examples were effects of special relativity has been observed. What I am still failing to understand is what physical thing in this universe the speed of light to be asymptotic? Is it the interaction of matter with space-time? Is it something else? Jan 20, 2017 at 13:35
• It is the nature of spacetime, the way space and time are articulated, that is responsible for the fact that accelerating a body will never lead to the speed of light. I guess the physical thing you are looking for is spacetime itself. I would say that in Special Relativity velocity is not a secondary notion (in Newtonian physics it is a plain ratio of independant quantities); rather, it is a fundamental one. See this other answer of mine. Jan 20, 2017 at 15:03

If an object accelerates towards the speed of light many known rules of physics don't apply or at least have to be adapted to fit.

An easy "key" to the problem is that the speed of light is not relative. It is always constant regardless of the speed/location of the observer.

Let's say someone shoots a laser beam on the moon and watches the reflected signal from earth. He sees light, that travels to and from the moon. It travels twice the distance from earth to moon.

Someone in a really fast spaceship sees the moon and the light flying by. Thus, the light from earth to moon and the light from moon to earth are not on the same line but are tilted. A person in the spaceship sees some kind of V-shape for the way the light travels. Assuming that the speed of light is constant for everyone that leaves only one choice:

The light observed from the spaceship travels a longer distance. Therefore, the time has to go slower in the spaceship than on earth. This phenomenon is known as time dilation. Similar things happen to distances.

The factor by which lengths/time are changed is called Lorentz Factor. It is calculated this way:

$\gamma = \frac{1}{\sqrt{1-\frac{v^2}{c^2}}}$

This factor also applies to mass. The mass of not moving object is multiplied with this factor. If the value of v increases towards the speed of light c, the term under the square root will become smaller and eventually 0 for $v = c$. The whole term $\gamma$ increases with increasing speed. The relative mass of a moving object with the mass $m_0$ is $m = \gamma \cdot m_0$.

Because of the increasing mass, more and more energy is needed to accelerate towards the speed of light and eventually you need an infinite amount to reach the speed of light. Therefore it is not possible to reach the speed of light through standard acceleration.

There's a theoretical approach for realizing speeds higher than the speed of light: The Alcubierre Drive. It basically deforms the space the traveller is in, so it doesn't move faster than the speed of light inside its space but seen from the outside it is faster.

• I am very familiar with the mathematics of special relativity as I finished my bachelors in physics recently. What I failed to understand during my course was, what was physically responsible for the speed limit. Is it the interaction between matter and fabric of space-time, is it something else? Jan 20, 2017 at 7:52
• In that case the reason: "It is as it is" describes it best. you can always dig deeper. But at some point you get to phenomena that you have to accept as they are.
– GNA
Jan 20, 2017 at 11:22
• Ah, the satisfying answer to scientists everywhere "It is as it is". I believe it is something to do with energy required to travel through space-time varies with a gamma factor. I'm not 100% so I'll do some more digging to try to formulate that into an answer. As I'm sure your degree taught you, maths is at the root of all solutions but as a physicist you want the phenomena behind the maths. Jan 20, 2017 at 11:37
• @LioElbammalf The gamma factor is the mathematical concept that was born out of necessity from special relativity. Unfortunately, the gamma factor is true because special relativity is true and not the other way around. And as you said I wish to know the phenomena behind the maths. Jan 20, 2017 at 14:18
• @Icarus Just as the $\frac{1}{r^{2}}$ is a mathematical concept used to describe many forces when considering movement spatially. I believe the gamma factor is similarly necessary when considering events in space-time. However I hadn't meant that as my answer and I agree it still isn't satisfactory just as saying gravity varies with an inverse $r^{2}$ factor wouldn't sufficiently describe the phenomena. I'm still trying to get enough of a handle on it myself to describe it. No point in me writing a badly researched answer :) Jan 20, 2017 at 17:13

All the answers I found were mathematically driven and answers the question quite satisfactorily but from my understanding, none tackled the actual physical mechanism behind this phenomenon.

# Physical mechanisms vs Mathematics

I think you may have a mistaken view of what Physics is. The nitty gritty of Physics is mathematical models. There are no "physical mechanisms behind" the most fundamental phenomena.

See Richard Feynman - Why : video and transcript

" I really can't do a good job, any job, of explaining magnetic force in terms of something else you're more familiar with, because I don't understand it in terms of anything else that you're more familiar with."

You should watch or read the whole interview though, its short (7 mins, 1300 words = 2-3 pages) and, as you should expect of Feynman, both enlightening and entertaining.

• In my 4 years of study of physics, I have come to the realisation that physics is the study of the physical universe and the language used for this study is mathematics. For example we understand the effects of gravity quite well. We can easily predict the trajectory of a multi-body system (given, a good enough computer is employable). Einstein will argue that an body with mass curve the fabric of space-time and this is what causes gravity. Ask some other physicists and they might argue that it this elusive particle, graviton, that maybe responsible. Jan 20, 2017 at 13:46
• Similarly, we are very familiar with the effects special relativity, we have beautiful mathematical models describing these effects. What I wish to know is what is physically responsible for this. Jan 20, 2017 at 13:48
• @Icarus: suppose there is nothing "physically responsible" for the relationship between momentum and velocity. Jan 20, 2017 at 14:27
• First of all momentum and velocity is the same concept described in two different fashion. But sure let us assume that. In that case, can I also assume that the moon is orbiting the earth because why not, instead of the curvature of space-time or gravitons being responsible? I hope you understand that physics is a way of explaining the reality in terms of mathematics and not the other way around. Mathematics is a human construct after all and the reality isn't. Jan 20, 2017 at 14:39
• @Icarus no, momentum and velocity are not the same thing, momentum is conserved and velocity is not.
– user126422
Jan 20, 2017 at 16:25

The Universe has fundamental symmetries. Rules of physics should be invariant by translation trough time and space, or by arbitrary rotation for instance.

Say you know the coordinates $(x,y,z,t)$ of a particle in a given frame, and you try to express it in another one $(x',y',z',t')$. In the most generic case, using the symmetries mentioned above, you are one relation short to solve the linear system. Actually, two reasonable choices can be made

• either $t'=t$, ie time is invariant, and the transformation corresponds to Galilean relativity
• or $v=c \Rightarrow v'=c$, ie the speed of light is invariant, and the transformation corresponds to special relativity, resulting in all you know

So I would answer your question saying : the mechanism limiting speed below c is the invariance of c by frame change (note that c does not have to be the speed of light here, but is defined as a limit speed). There is no "reason" why c is invariant by frame change, just like there is no reason for the Universe to be invariant under translation.

Well, the mathematics does not tackle physical mechanism generally. It only gives quantitative analysis.

There is no physical mechanism that prevents accelerating faster than light.

What limits the acceleration within speed of light, is speed with which of the accelerating force itself acts. Whenever we accelerate something, we (in most cases) accelerate by applying electromagnetic force (repulsion). When you push a car with your hand, the electrons in your hand repel the electrons of the car at the point of contact.

Now considering the electromagnetic repulsion as cause of acceleration, the acceleration will be limited to the speed with which the force propagates. The force propagates at speed of light. So, it can not accelerate anything faster than it itself can act.

Imagine a car passes by you at 300 miles/hour. Do you think you can accelerate it further by pusing with your hands. Most likely not. Because human beings can not move their hands faster than 300 miles/hour, not even close.

The electromagnetic repulsion propagates through space to act on anything. That propagation speed is c. Something already moving at c, the force does nothing in that direction.

Therefore, as a body approached c, any force you apply on it, becomes ineffective and so, it does not accelerate further in that direction.

However, the force is effective if you want to slow it down because, then it has to act in opposite direction and it is able to.

Other type of forces also act at c. So in general it is not possible for the forces to accelerate anything faster than c.

The natural next question is why the forces propagate at c. Well that is a property, not a limit. It is property because the forces propagate exacly at c, no faster, no slower. It would have been a limit if the forces propagated at various speeds up to c. But they do not.

Edit: Infinite mass argument - Lot of people are giving argument that the mass approaches infinity as speed approaches c.

I am sure this also fits into mathematics, otherwise people would not be making this argument.

I may be wrong, and please feel free to correct me if you think so. But I do not think that is the case - i.e. mass does not approach infinite.

My simple argument is - if the mass of a moving particle approaches infinite and that infinite mass moving at speeds close to c, then it would be almost impossible to stop that particle.

We all know that though it is not possible to accelerate the particle further, it is no big deal to slow it down. Slowing down an infinite mass would not be that easy. Infinite mass reasoning must apply both ways - in speeding up as well as in slowing down. Which it does not seem to.

Therefore, I can argue that mass does not approach infinite, it is the forces that are rendered ineffective at such speeds.

This may be an example where it makes mathematical sense, but no real sense. Please correct if I am missing something, instead of blank down voting.

If a charged particle like electron is accelerated. it seems that mass is increased because mass cannot travel the speed of massless particles. This is called Relativistic momentum. Measuring why that happeneds requires the charged particle to be accelerated to light speed, which requires infinite energy. It could be because of an interaction with space time and that's why a hyperdrive/Alcubierre drive is theorically possible.